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https://blog.octo.com/en/introduction-to-grid-computing-for-value-at-risk-calculatio/
[ "Risk management is today a strategic objective for financial institutions such as, but not limited to, investment banking and insurance companies. Such risk evaluation uses advanced mathematical theory and requires a lot of data computing. In this article, we will introduce basic concepts of Value At Risk estimation in order to show which kind of calculation is required. We will introduce grid computing in order to show how such architecture can help financial companies producing quickly these very important VAR figures. In later articles, we will describe in detail implementations of that algorithm on several grid middlewares.\n\n### Value at Risk\n\nThe Value at Risk is one of the major risk indicators for financial portfolio or product. It was introduced in the late 1980’s by American banks (first Banker’s Trust then J.P. Morgan). It gives a measure of the maximal potential loss, during a defined period, under a given probability for a financial product or portfolio. If the “1 day VAR at 90% for your portfolio” is -5%, it means you got less than 10% chance of loosing more than 5% of the value tomorrow.", null, "More mathematically, the value of a financial product or portfolio can be represented by a probability distribution. The graph above shows a hypothetic probability curve for the value of a product or portfolio for the next business day. The average closing price is 100€ and the vertical axis shows the probability to occur. The red area represents a cumulated probability of 10%. So a price inferior to 75€ in the red area has less than 10% of chance to occur. In conclusion the 1 day Value at Risk at 90% is 25€=-25%. For a sample of data, it is related to the percentile at 10%.\n\nFor listed products like stocks and bonds, we have enough historical data to evaluate the percentile based on that history. For more exotic products, like structure products, built on demand, prices are not available. In that case, prices are simulated and the same formula is then used like for historical values.\n\n### Monte-Carlo simulation\n\nThe method used is a computational algorithm based on random sampling. This technique is known as the Monte-Carlo method, by reference of the gambling games to the famous casinos in Monte-Carlo.\nTo quickly describe how such method can lead to precise result with random values; let’s see how to compute the", null, "number. Take a square with an edge length of 1.0 and a quarter of circle with radius length of 1.0 as in the schema thereafter.", null, "If you generate two independent random numbers x and y uniformly distributed between 0 and 1.0, it’s like putting random dots on your square. With infinity of dots, the whole area is uniformly covered. The ratio between the number of dots in the circle (", null, ") and the total number of dots equals the ratio between the areas of the quarter of the circle and the square.\nSo", null, ".\nThe algorithm consists in generating random couples and counting the proportion of ranks in the circle. Multiplying it by 4 gives an approximation of the", null, "number.\n\nFor financial purpose, we will replace random dots by random simulations of market parameters (such as underlying price, interest rate) and the circle area by a predictable model allowing computing the portfolio value with these parameters.\n\n### A simple example: portfolio with one call\n\nFor the purpose of this article, I chose a very simple portfolio with only one product: a long position on a call (i.e. the owner has bought a call). A call is an option of buying, a financial contract giving the right but not the obligation to the buyer to buy a certain quantity of a financial instrument (the underlying) at a given date (the maturity date) at a given price (the strike). The seller sells this contract for a given fee (the premium).\n\nWe can then build a first model of the payoff of this call according to the price that the underlying will have at maturity date (lets say in a year).", null, "We now want to be able to build a model for the price of a call with a maturity in one year. But today we ignore the price of the underlying that might be in a year. I won’t go deeper into details and will just say that a more complicated model exists. It is based on probability theory: the Black and Scholes model. It can determine the price of the call by knowing only:\n\n• characteristics of the call : maturity date and strike price\n• the price of the underlying as of today (and not anymore in the future)\n• the risk free interest rate\n• a parameter of the derivative market known as implied volatility.\n\nThe risk free interest rate can be estimated on Libor today’s value (close to 5%). The underlying volatility can be deducted from listed options or from specific index like VIX and VAEX (see sample market values). In the example, we will take a value of 20.\nThe Black and Scholes model for a single call can be expressed as a quite complex but closed formula (i.e. is predictable and can be easily computed). It is an arithmetic expression involving exp, sqrt and N(.) (cumulative distribution of normal distribution functions named NORMSDIST in Excel). See this Wikipedia article for more details and pay close attention to the available graphic which shows how the price of the option is modified when the price of the underlying is modified.\n\n### Estimation of the required computing power\n\nBy mixing these two methods, we can estimate the VAR for our sample portfolio. Required steps involved :\n\n• Generating sample data for the three parameters that we have chosen: the underlying stock price, the interest rate and the underlying volatility. To keep it simple, we assume that these three parameters follow independent normal distributions.\n• Calculating for each set of generated parameters, the corresponding option price according to the Black and Sholes expression\n• Calculating the percentile at 1% for the distribution of option prices\n\nSuch individual computing is quite short but a large number of samples are required to get a correct precision of the end result. To give an order of magnitude, about 100,000 samples are required in our case. Using Excel 2007, on my laptop (a Dell Latitude with a core i7 with 2 multi-threaded cores and 4 GB RAM) 100,000 samples took approximately 2 s. for one option and one sample parameter simulated (underlying price). On the same laptop a mono-threaded Java program (using only one core) took about 160 ms. It seems to be quick but in real life, each exotic product in a portfolio is a combination of multiple options. A portfolio probably contains tens or hundreds of exotic products. Moreover, more complicated modeling is today used instead of Black and Scholes model requiring more complex calculation or more samples. So, the required computing power can easily get really huge.\n\n### The grid computing architecture", null, "In order to deal with so much computing power at the best cost, the grid computing architecture is the best solution. A grid is a computing architecture which allows coordinating a big number of distributed resources toward a common objective. In our case these resources are computers whose processors are used to do that calculation. These resources can be distributed, i.e. physically distant and linked by a computer network.", null, "Each of these N nodes (i.e. computers) will do a small part of the calculation on its processors, allowing in giving out the result (in an ideal world) N times faster than with one single computer. We will now describe how to write the algorithm for that grid.\n\n### How to compute the VAR\n\nIn order to be able to split, to distribute the VAR calculation, the algorithm should be adapted.\nThe easiest way to get an approximation of the VAR of a portfolio could be by summing up the VAR of each product. The VAR of each product can be computed independently on each node. The algorithm can in that case remain unmodified. In the above schema, Compute part x corresponds to the calculation of an individual VAR. However, it will not allow speeding up the VAR calculation of our single call portfolio. And in a real life example, it would not allow us scaling up the number of samples so the precision.\n\nDespite these flaws, lets see how we would implement it. We can use the map/reduce pattern. This pattern comes from functional programming where map m() list function applies the function m() to each element of the list, and reduce r() b list aggregates b parameter and all values of list into one single value.\nLets take a practical example.\n\n• The map (\\x -> 2*x) [1,2,3] returns [1*2,2*2,3*2]=[2,4,6].\n• The reduce (\\x y -> x+y) 0 [2,4,6] returns 0+2+4+6=12.\n\nWith such a pattern, the list can be split in N sub lists, sent to the N nodes of the grid. In that example, 1 is sent to the first node, 2 to the second, etc. The \\x -> 2*x function code, sent with the values, is executed by each node: 2*1 by the first, 2*2 by the second, etc. You need to imagine that \\x->2*x is replaced by a computer intensive function. Executing it in parallel will therefore divide the total required computing time. All results 2, 4, etc. are sent back to the sender node. The results are concatenated in the list [2,4,6] and the reduce (\\x y -> x+y) is applied. The map function is split across nodes but not the reduce function which is executed by the sender node.\n\nIn our case, each sample generation will represent an element of the list. The map() function will, on each node, generate the sample data, compute the corresponding call price and return it. Then all call prices are sent to the reduce node. The reduce() function computes the percentile at 1% of the resulting data. Consequently it will give us the VAR at 99% of our portfolio.", null, "This first version works, but can still be a bit improved.\n\n• First, the reduce() function is not distributed, so it is better to minimize the amount of data it has to process.\n• Next, moving 100,000 prices over the network is resource consuming. In reality, network bandwidth is a scarce resource in a grid\n\nAlso we might notice that computing the percentile at 1% comes to sorting the data, and taking the highest value of the smallest 1% values. I presume that for the particular business case of this example the intermediate results can be discarded. In that case, this elimination algorithm can be distributed too.\nThe idea is that the 10 smallest values of a set are included in the 10 smallest values of each of its subsets. Lets imagine that I’m looking up the 4 highest value cards of a poker deck. The deck has been split by suit into 4 sets. I can look in each set for the 4 highest cards. I will get an ace, a king, a queen and a jack for each suit. Then, I can merge these 4*4=16 cards and look again up the 4 highest ones. I will get the 4 aces. That can be generalized for any subsets.\n\nSo now, lets say we are computing 100,000 samples on two nodes. The percentile at 1% corresponds to the highest value of the 1,000 lowest values. On each node 50,000 values have been computed. On each node, we can take the 1,000 lowest values and send them as results instead of the 50,000. Then the reduce() function will only merge the two lists of the 1,000 lowest values, take the 1,000 lowest ones and identify the highest value. Indeed in the worst case where generated prices are totally sorted across nodes, the node with all the lowest values will give us the 1,000 lowest ones, guaranteeing that the percentile is still transmitted. Such optimization allows dividing by 50 the data that are transmitted thru the network. The benefit goes down when the number of nodes increases. In the worst case scenario, with 100 nodes there is no more benefit: each node has computed 1% of the data. But in practice, distributing small list of samples is counter-productive as distribution overhead is higher than the parallel computing gain. As you can see, these kind of business specific optimization ca really help minimizing the required resources.\n\nThe final algorithm is summarized in the following schema:", null, "### Conclusion\n\nFrom a business point of view, risk estimation is becoming more and more important for financial institutions to prevent financial losses on fluctuant markets. Moreover, new regulation rules such as Basel III and Solvency II take into account the VAR in their requirements. Computing efficiently such figures is a key requirement for Information System of financial institutions. Through a very simple example, this article has shown that such calculation consists in generating sample data, doing some mathematical processing to compute a value for the portfolio for each sample data. The amount of sample data and sometimes the complexity of the processing require specific architectures to finish such calculations in a reasonable time. Grid computing is the most up-to-date architecture to solve these problems. Using map reduce pattern is one of the easiest way to write an algorithm that benefitiates of grid computing parallel capabilities. Also, business requirements understanding is a key point in optimizing the code. In this example, dropping the intermediate results allows to speed up the calculation. In another article, I will describe an implementation of that example using a grid computing middleware and will give some performance figures.\n\n## 4 commentaires sur “Introduction to Grid Computing for Value At Risk calculation”\n\n•", null, "Great article, if you could also cover financial library such as JQuantlib, it would be great. Nicolas\n•", null, "I'm currently working on articles about implementation of VaR calculation, but later JQantlib could be an interesting subject.\n•", null, "I have a problem with your methodology of computing the VaR independently for each portfolio product. The VaR should reflect the value distribution of the entire portfolio, including correlations between different assets. When you add up individual VaRs you ignore the correlations and end up with an estimate that can be significantly different than the real VaR, especially when you have a mixed portfolio with different types of assets, like stocks, bonds and options.\n•", null, "I totally agree with you. Due to the subadditivity of the VaR, individual VaRs of different products should not be added. That's why I have described a very simple example -a \"portfolio\" with only one call- in order to avoid this subadditivity problem. All my samples are for one product: a call. It is not a realistic example from a financial point of view but my goal was rather to introduce grid computing engineering (see my later articles). So introducing a realistic financial example with several products and correlated variables to simulate would have been too complex for the size of this article." ]
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https://open.metu.edu.tr/handle/11511/95570
[ "1985-06-15\nÇalıkoğlu, Doğan\n\n# Suggestions\n\n Thermal rectification behaviour of some small quantum systems Zervent, Selahittin Atılay; Turgut, Sadi; Department of Physics (2021-9-10) Thermal rectification behaviors for some small quantum systems are studied by using the Lindblad master equation. From the underlying Hamiltonian dynamics of the composite quantum systems consisting of small quantum systems and reservoirs, Lindblad master equations are obtained by using certain approximations. Optimum operation parameters are determined for a single two-level and two two-level quantum systems. It is shown that there is no thermal rectification behavior when the contact between two reservoir...\n Developing a computer program for evaluating uncertainty of some typical dimensional measuring and gauging devices Çelebioğlu, Hasan Emrah; Akkök, Metin; Department of Mechanical Engineering (2005) In dimensional measurements, it is required to specify uncertainty in the measurement as the range of possible deviation for the measurement result. In this thesis, a computer program is developed for evaluating uncertainty inmeasurement of commonly used dimensional measuring devices like vernier callipers, micrometers, comparators, and gauge blocks. In evaluation of the uncertainty in measurement, some uncertainty sourceslike temperature difference between the measured part and the instrument, uncertainty ...\n The Influence of some embedding properties of subgroups on the structure of a finite group Kızmaz, Muhammet Yasir; Ercan, Gülin; Department of Mathematics (2018) In a finite group \\$G\\$, a subgroup \\$H\\$ is called a \\$TI\\$-subgroup if \\$H\\$ intersects trivially with distinct conjugates of itself. Suppose that \\$H\\$ is a Hall \\$pi\\$-subgroup of \\$G\\$ which is also a \\$TI\\$-subgroup. A famous theorem of Frobenius states that \\$G\\$ has a normal \\$pi\\$-complement whenever \\$H\\$ is self normalizing. In this case, \\$H\\$ is called a Frobenius complement and \\$G\\$ is said to be a Frobenius group. A first main result in this thesis is the following generalization of Frobenius' Theorem. textbf{Theorem...\n Super symmetric quantum mechanics applications on some diatomic potentials Kaya, Murat; Sever, Ramazan; Department of Physics (2015) One dimensional molecular potentials are studied by solving the Schrödinger Equation for some well known potentials, such as the deformed Morse, Eckart and the Hua potentials. Parametric generalization of Hamiltonian Hierarchy is introduced. Nikiforov-Uvarov method and SUSYQM with Hamiltonian Hierarchy method is used in the calculations to get energy eigenvalues and the corresponding wave functions exactly.\n Optical and electrical transport properties of some quaternary thallium dichalcogenides Güler, İpek; Hasanlı, Nızamı; Department of Physics (2011) In this thesis, in order to study the structural, optical and electrical transport properties of Tl2In2S3Se, TlInSeS and Tl2In2SSe3 crystals, X-ray diffraction (XRD), energy dispersive spectroscopic analysis (EDSA), transmission, reflection, photoluminescence (PL), thermally stimulated current (TSC) and photoconductivity decay (PC) measurements were carried out. Lattice parameters and atomic composition of these crystals were determined from XRD and EDSA experiments, respectively. By the help of transmissio...\nCitation Formats\nD. Çalıkoğlu, “Bazı tür hücresel yapılar (Hücresel hareketliler) için bir simülatör,” 1985. Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/95570.", null, "" ]
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https://bookdown.org/ekothe/navarro26/hypothesistesting.html
[ "# Chapter 11 Hypothesis testing\n\nThe process of induction is the process of assuming the simplest law that can be made to harmonize with our experience. This process, however, has no logical foundation but only a psychological one. It is clear that there are no grounds for believing that the simplest course of events will really happen. It is an hypothesis that the sun will rise tomorrow: and this means that we do not know whether it will rise.\n\n– Ludwig Wittgenstein156\n\nIn the last chapter, I discussed the ideas behind estimation, which is one of the two “big ideas” in inferential statistics. It’s now time to turn out attention to the other big idea, which is hypothesis testing. In its most abstract form, hypothesis testing really a very simple idea: the researcher has some theory about the world, and wants to determine whether or not the data actually support that theory. However, the details are messy, and most people find the theory of hypothesis testing to be the most frustrating part of statistics. The structure of the chapter is as follows. Firstly, I’ll describe how hypothesis testing works, in a fair amount of detail, using a simple running example to show you how a hypothesis test is “built”. I’ll try to avoid being too dogmatic while doing so, and focus instead on the underlying logic of the testing procedure.157 Afterwards, I’ll spend a bit of time talking about the various dogmas, rules and heresies that surround the theory of hypothesis testing.\n\n## 11.1 A menagerie of hypotheses\n\nEventually we all succumb to madness. For me, that day will arrive once I’m finally promoted to full professor. Safely ensconced in my ivory tower, happily protected by tenure, I will finally be able to take leave of my senses (so to speak), and indulge in that most thoroughly unproductive line of psychological research: the search for extrasensory perception (ESP).158\n\nLet’s suppose that this glorious day has come. My first study is a simple one, in which I seek to test whether clairvoyance exists. Each participant sits down at a table, and is shown a card by an experimenter. The card is black on one side and white on the other. The experimenter takes the card away, and places it on a table in an adjacent room. The card is placed black side up or white side up completely at random, with the randomisation occurring only after the experimenter has left the room with the participant. A second experimenter comes in and asks the participant which side of the card is now facing upwards. It’s purely a one-shot experiment. Each person sees only one card, and gives only one answer; and at no stage is the participant actually in contact with someone who knows the right answer. My data set, therefore, is very simple. I have asked the question of $$N$$ people, and some number $$X$$ of these people have given the correct response. To make things concrete, let’s suppose that I have tested $$N = 100$$ people, and $$X = 62$$ of these got the answer right… a surprisingly large number, sure, but is it large enough for me to feel safe in claiming I’ve found evidence for ESP? This is the situation where hypothesis testing comes in useful. However, before we talk about how to test hypotheses, we need to be clear about what we mean by hypotheses.\n\n### 11.1.1 Research hypotheses versus statistical hypotheses\n\nThe first distinction that you need to keep clear in your mind is between research hypotheses and statistical hypotheses. In my ESP study, my overall scientific goal is to demonstrate that clairvoyance exists. In this situation, I have a clear research goal: I am hoping to discover evidence for ESP. In other situations I might actually be a lot more neutral than that, so I might say that my research goal is to determine whether or not clairvoyance exists. Regardless of how I want to portray myself, the basic point that I’m trying to convey here is that a research hypothesis involves making a substantive, testable scientific claim… if you are a psychologist, then your research hypotheses are fundamentally about psychological constructs. Any of the following would count as research hypotheses:\n\n• Listening to music reduces your ability to pay attention to other things. This is a claim about the causal relationship between two psychologically meaningful concepts (listening to music and paying attention to things), so it’s a perfectly reasonable research hypothesis.\n• Intelligence is related to personality. Like the last one, this is a relational claim about two psychological constructs (intelligence and personality), but the claim is weaker: correlational not causal.\n• Intelligence is* speed of information processing. This hypothesis has a quite different character: it’s not actually a relational claim at all. It’s an ontological claim about the fundamental character of intelligence (and I’m pretty sure it’s wrong). It’s worth expanding on this one actually: It’s usually easier to think about how to construct experiments to test research hypotheses of the form “does X affect Y?” than it is to address claims like “what is X?” And in practice, what usually happens is that you find ways of testing relational claims that follow from your ontological ones. For instance, if I believe that intelligence is* speed of information processing in the brain, my experiments will often involve looking for relationships between measures of intelligence and measures of speed. As a consequence, most everyday research questions do tend to be relational in nature, but they’re almost always motivated by deeper ontological questions about the state of nature.\n\nNotice that in practice, my research hypotheses could overlap a lot. My ultimate goal in the ESP experiment might be to test an ontological claim like “ESP exists”, but I might operationally restrict myself to a narrower hypothesis like “Some people can see’ objects in a clairvoyant fashion”. That said, there are some things that really don’t count as proper research hypotheses in any meaningful sense:\n\n• Love is a battlefield. This is too vague to be testable. While it’s okay for a research hypothesis to have a degree of vagueness to it, it has to be possible to operationalise your theoretical ideas. Maybe I’m just not creative enough to see it, but I can’t see how this can be converted into any concrete research design. If that’s true, then this isn’t a scientific research hypothesis, it’s a pop song. That doesn’t mean it’s not interesting – a lot of deep questions that humans have fall into this category. Maybe one day science will be able to construct testable theories of love, or to test to see if God exists, and so on; but right now we can’t, and I wouldn’t bet on ever seeing a satisfying scientific approach to either.\n• The first rule of tautology club is the first rule of tautology club. This is not a substantive claim of any kind. It’s true by definition. No conceivable state of nature could possibly be inconsistent with this claim. As such, we say that this is an unfalsifiable hypothesis, and as such it is outside the domain of science. Whatever else you do in science, your claims must have the possibility of being wrong.\n• More people in my experiment will say “yes” than “no”. This one fails as a research hypothesis because it’s a claim about the data set, not about the psychology (unless of course your actual research question is whether people have some kind of “yes” bias!). As we’ll see shortly, this hypothesis is starting to sound more like a statistical hypothesis than a research hypothesis.\n\nAs you can see, research hypotheses can be somewhat messy at times; and ultimately they are scientific claims. Statistical hypotheses are neither of these two things. Statistical hypotheses must be mathematically precise, and they must correspond to specific claims about the characteristics of the data generating mechanism (i.e., the “population”). Even so, the intent is that statistical hypotheses bear a clear relationship to the substantive research hypotheses that you care about! For instance, in my ESP study my research hypothesis is that some people are able to see through walls or whatever. What I want to do is to “map” this onto a statement about how the data were generated. So let’s think about what that statement would be. The quantity that I’m interested in within the experiment is $$P(\\mbox{\"correct\"})$$, the true-but-unknown probability with which the participants in my experiment answer the question correctly. Let’s use the Greek letter $$\\theta$$ (theta) to refer to this probability. Here are four different statistical hypotheses:\n\n• If ESP doesn’t exist and if my experiment is well designed, then my participants are just guessing. So I should expect them to get it right half of the time and so my statistical hypothesis is that the true probability of choosing correctly is $$\\theta = 0.5$$.\n• Alternatively, suppose ESP does exist and participants can see the card. If that’s true, people will perform better than chance. The statistical hypotheis would be that $$\\theta > 0.5$$.\n• A third possibility is that ESP does exist, but the colours are all reversed and people don’t realise it (okay, that’s wacky, but you never know…). If that’s how it works then you’d expect people’s performance to be below chance. This would correspond to a statistical hypothesis that $$\\theta < 0.5$$.\n• Finally, suppose ESP exists, but I have no idea whether people are seeing the right colour or the wrong one. In that case, the only claim I could make about the data would be that the probability of making the correct answer is not equal to 50. This corresponds to the statistical hypothesis that $$\\theta \\neq 0.5$$.\n\nAll of these are legitimate examples of a statistical hypothesis because they are statements about a population parameter and are meaningfully related to my experiment.\n\nWhat this discussion makes clear, I hope, is that when attempting to construct a statistical hypothesis test the researcher actually has two quite distinct hypotheses to consider. First, he or she has a research hypothesis (a claim about psychology), and this corresponds to a statistical hypothesis (a claim about the data generating population). In my ESP example, these might be\n\nDan.s.research.hypothesis Dan.s.statistical.hypothesis\nESP.exists $$\\theta \\neq 0.5$$\n\nAnd the key thing to recognise is this: a statistical hypothesis test is a test of the statistical hypothesis, not the research hypothesis. If your study is badly designed, then the link between your research hypothesis and your statistical hypothesis is broken. To give a silly example, suppose that my ESP study was conducted in a situation where the participant can actually see the card reflected in a window; if that happens, I would be able to find very strong evidence that $$\\theta \\neq 0.5$$, but this would tell us nothing about whether “ESP exists”.\n\n### 11.1.2 Null hypotheses and alternative hypotheses\n\nSo far, so good. I have a research hypothesis that corresponds to what I want to believe about the world, and I can map it onto a statistical hypothesis that corresponds to what I want to believe about how the data were generated. It’s at this point that things get somewhat counterintuitive for a lot of people. Because what I’m about to do is invent a new statistical hypothesis (the “null” hypothesis, $$H_0$$) that corresponds to the exact opposite of what I want to believe, and then focus exclusively on that, almost to the neglect of the thing I’m actually interested in (which is now called the “alternative” hypothesis, $$H_1$$). In our ESP example, the null hypothesis is that $$\\theta = 0.5$$, since that’s what we’d expect if ESP didn’t exist. My hope, of course, is that ESP is totally real, and so the alternative to this null hypothesis is $$\\theta \\neq 0.5$$. In essence, what we’re doing here is dividing up the possible values of $$\\theta$$ into two groups: those values that I really hope aren’t true (the null), and those values that I’d be happy with if they turn out to be right (the alternative). Having done so, the important thing to recognise is that the goal of a hypothesis test is not to show that the alternative hypothesis is (probably) true; the goal is to show that the null hypothesis is (probably) false. Most people find this pretty weird.\n\nThe best way to think about it, in my experience, is to imagine that a hypothesis test is a criminal trial159the trial of the null hypothesis. The null hypothesis is the defendant, the researcher is the prosecutor, and the statistical test itself is the judge. Just like a criminal trial, there is a presumption of innocence: the null hypothesis is deemed to be true unless you, the researcher, can prove beyond a reasonable doubt that it is false. You are free to design your experiment however you like (within reason, obviously!), and your goal when doing so is to maximise the chance that the data will yield a conviction… for the crime of being false. The catch is that the statistical test sets the rules of the trial, and those rules are designed to protect the null hypothesis – specifically to ensure that if the null hypothesis is actually true, the chances of a false conviction are guaranteed to be low. This is pretty important: after all, the null hypothesis doesn’t get a lawyer. And given that the researcher is trying desperately to prove it to be false, someone has to protect it.\n\n## 11.2 Two types of errors\n\nBefore going into details about how a statistical test is constructed, it’s useful to understand the philosophy behind it. I hinted at it when pointing out the similarity between a null hypothesis test and a criminal trial, but I should now be explicit. Ideally, we would like to construct our test so that we never make any errors. Unfortunately, since the world is messy, this is never possible. Sometimes you’re just really unlucky: for instance, suppose you flip a coin 10 times in a row and it comes up heads all 10 times. That feels like very strong evidence that the coin is biased (and it is!), but of course there’s a 1 in 1024 chance that this would happen even if the coin was totally fair. In other words, in real life we always have to accept that there’s a chance that we did the wrong thing. As a consequence, the goal behind statistical hypothesis testing is not to eliminate errors, but to minimise them.\n\nAt this point, we need to be a bit more precise about what we mean by “errors”. Firstly, let’s state the obvious: it is either the case that the null hypothesis is true, or it is false; and our test will either reject the null hypothesis or retain it.160 So, as the table below illustrates, after we run the test and make our choice, one of four things might have happened:\n\nretain $$H_0$$ retain $$H_0$$\n$$H_0$$ is true correct decision error (type I)\n$$H_0$$ is false error (type II) correct decision\n\nAs a consequence there are actually two different types of error here. If we reject a null hypothesis that is actually true, then we have made a type I error. On the other hand, if we retain the null hypothesis when it is in fact false, then we have made a type II error.\n\nRemember how I said that statistical testing was kind of like a criminal trial? Well, I meant it. A criminal trial requires that you establish “beyond a reasonable doubt” that the defendant did it. All of the evidentiary rules are (in theory, at least) designed to ensure that there’s (almost) no chance of wrongfully convicting an innocent defendant. The trial is designed to protect the rights of a defendant: as the English jurist William Blackstone famously said, it is “better that ten guilty persons escape than that one innocent suffer.” In other words, a criminal trial doesn’t treat the two types of error in the same way~… punishing the innocent is deemed to be much worse than letting the guilty go free. A statistical test is pretty much the same: the single most important design principle of the test is to control the probability of a type I error, to keep it below some fixed probability. This probability, which is denoted $$\\alpha$$, is called the significance level of the test (or sometimes, the size of the test). And I’ll say it again, because it is so central to the whole set-up~… a hypothesis test is said to have significance level $$\\alpha$$ if the type I error rate is no larger than $$\\alpha$$.\n\nSo, what about the type II error rate? Well, we’d also like to keep those under control too, and we denote this probability by $$\\beta$$. However, it’s much more common to refer to the power of the test, which is the probability with which we reject a null hypothesis when it really is false, which is $$1-\\beta$$. To help keep this straight, here’s the same table again, but with the relevant numbers added:\n\nretain $$H_0$$ reject $$H_0$$\n$$H_0$$ is true $$1-\\alpha$$ (probability of correct retention) $$\\alpha$$ (type I error rate)\n$$H_0$$ is false $$\\beta$$ (type II error rate) $$1-\\beta$$ (power of the test)\n\nA “powerful” hypothesis test is one that has a small value of $$\\beta$$, while still keeping $$\\alpha$$ fixed at some (small) desired level. By convention, scientists make use of three different $$\\alpha$$ levels: $$.05$$, $$.01$$ and $$.001$$. Notice the asymmetry here~… the tests are designed to ensure that the $$\\alpha$$ level is kept small, but there’s no corresponding guarantee regarding $$\\beta$$. We’d certainly like the type II error rate to be small, and we try to design tests that keep it small, but this is very much secondary to the overwhelming need to control the type I error rate. As Blackstone might have said if he were a statistician, it is “better to retain 10 false null hypotheses than to reject a single true one”. To be honest, I don’t know that I agree with this philosophy – there are situations where I think it makes sense, and situations where I think it doesn’t – but that’s neither here nor there. It’s how the tests are built.\n\n## 11.3 Test statistics and sampling distributions\n\nAt this point we need to start talking specifics about how a hypothesis test is constructed. To that end, let’s return to the ESP example. Let’s ignore the actual data that we obtained, for the moment, and think about the structure of the experiment. Regardless of what the actual numbers are, the form of the data is that $$X$$ out of $$N$$ people correctly identified the colour of the hidden card. Moreover, let’s suppose for the moment that the null hypothesis really is true: ESP doesn’t exist, and the true probability that anyone picks the correct colour is exactly $$\\theta = 0.5$$. What would we expect the data to look like? Well, obviously, we’d expect the proportion of people who make the correct response to be pretty close to 50%. Or, to phrase this in more mathematical terms, we’d say that $$X/N$$ is approximately $$0.5$$. Of course, we wouldn’t expect this fraction to be exactly 0.5: if, for example we tested $$N=100$$ people, and $$X = 53$$ of them got the question right, we’d probably be forced to concede that the data are quite consistent with the null hypothesis. On the other hand, if $$X = 99$$ of our participants got the question right, then we’d feel pretty confident that the null hypothesis is wrong. Similarly, if only $$X=3$$ people got the answer right, we’d be similarly confident that the null was wrong. Let’s be a little more technical about this: we have a quantity $$X$$ that we can calculate by looking at our data; after looking at the value of $$X$$, we make a decision about whether to believe that the null hypothesis is correct, or to reject the null hypothesis in favour of the alternative. The name for this thing that we calculate to guide our choices is a test statistic.\n\nHaving chosen a test statistic, the next step is to state precisely which values of the test statistic would cause is to reject the null hypothesis, and which values would cause us to keep it. In order to do so, we need to determine what the sampling distribution of the test statistic would be if the null hypothesis were actually true (we talked about sampling distributions earlier in Section 10.3.1). Why do we need this? Because this distribution tells us exactly what values of $$X$$ our null hypothesis would lead us to expect. And therefore, we can use this distribution as a tool for assessing how closely the null hypothesis agrees with our data.", null, "Figure 11.1: The sampling distribution for our test statistic $$X$$ when the null hypothesis is true. For our ESP scenario, this is a binomial distribution. Not surprisingly, since the null hypothesis says that the probability of a correct response is $$\\theta = .5$$, the sampling distribution says that the most likely value is 50 (our of 100) correct responses. Most of the probability mass lies between 40 and 60.\n\nHow do we actually determine the sampling distribution of the test statistic? For a lot of hypothesis tests this step is actually quite complicated, and later on in the book you’ll see me being slightly evasive about it for some of the tests (some of them I don’t even understand myself). However, sometimes it’s very easy. And, fortunately for us, our ESP example provides us with one of the easiest cases. Our population parameter $$\\theta$$ is just the overall probability that people respond correctly when asked the question, and our test statistic $$X$$ is the count of the number of people who did so, out of a sample size of $$N$$. We’ve seen a distribution like this before, in Section 9.4: that’s exactly what the binomial distribution describes! So, to use the notation and terminology that I introduced in that section, we would say that the null hypothesis predicts that $$X$$ is binomially distributed, which is written $X \\sim \\mbox{Binomial}(\\theta,N)$ Since the null hypothesis states that $$\\theta = 0.5$$ and our experiment has $$N=100$$ people, we have the sampling distribution we need. This sampling distribution is plotted in Figure 11.1. No surprises really: the null hypothesis says that $$X=50$$ is the most likely outcome, and it says that we’re almost certain to see somewhere between 40 and 60 correct responses.\n\n## 11.4 Making decisions\n\nOkay, we’re very close to being finished. We’ve constructed a test statistic ($$X$$), and we chose this test statistic in such a way that we’re pretty confident that if $$X$$ is close to $$N/2$$ then we should retain the null, and if not we should reject it. The question that remains is this: exactly which values of the test statistic should we associate with the null hypothesis, and which exactly values go with the alternative hypothesis? In my ESP study, for example, I’ve observed a value of $$X=62$$. What decision should I make? Should I choose to believe the null hypothesis, or the alternative hypothesis?\n\n### 11.4.1 Critical regions and critical values\n\nTo answer this question, we need to introduce the concept of a critical region for the test statistic $$X$$. The critical region of the test corresponds to those values of $$X$$ that would lead us to reject null hypothesis (which is why the critical region is also sometimes called the rejection region). How do we find this critical region? Well, let’s consider what we know:\n\n• $$X$$ should be very big or very small in order to reject the null hypothesis.\n• If the null hypothesis is true, the sampling distribution of $$X$$ is Binomial$$(0.5, N)$$.\n• If $$\\alpha =.05$$, the critical region must cover 5% of this sampling distribution.\n\nIt’s important to make sure you understand this last point: the critical region corresponds to those values of $$X$$ for which we would reject the null hypothesis, and the sampling distribution in question describes the probability that we would obtain a particular value of $$X$$ if the null hypothesis were actually true. Now, let’s suppose that we chose a critical region that covers 20% of the sampling distribution, and suppose that the null hypothesis is actually true. What would be the probability of incorrectly rejecting the null? The answer is of course 20%. And therefore, we would have built a test that had an $$\\alpha$$ level of $$0.2$$. If we want $$\\alpha = .05$$, the critical region is only allowed to cover 5% of the sampling distribution of our test statistic.", null, "Figure 11.2: The critical region associated with the hypothesis test for the ESP study, for a hypothesis test with a significance level of $$\\alpha = .05$$. The plot itself shows the sampling distribution of $$X$$ under the null hypothesis: the grey bars correspond to those values of $$X$$ for which we would retain the null hypothesis. The black bars show the critical region: those values of $$X$$ for which we would reject the null. Because the alternative hypothesis is two sided (i.e., allows both $$\\theta <.5$$ and $$\\theta >.5$$), the critical region covers both tails of the distribution. To ensure an $$\\alpha$$ level of $$.05$$, we need to ensure that each of the two regions encompasses 2.5% of the sampling distribution.\n\nAs it turns out, those three things uniquely solve the problem: our critical region consists of the most extreme values, known as the tails of the distribution. This is illustrated in Figure 11.2. As it turns out, if we want $$\\alpha = .05$$, then our critical regions correspond to $$X \\leq 40$$ and $$X \\geq 60$$.161 That is, if the number of people saying “true” is between 41 and 59, then we should retain the null hypothesis. If the number is between 0 to 40 or between 60 to 100, then we should reject the null hypothesis. The numbers 40 and 60 are often referred to as the critical values, since they define the edges of the critical region.\n\nAt this point, our hypothesis test is essentially complete: (1) we choose an $$\\alpha$$ level (e.g., $$\\alpha = .05$$, (2) come up with some test statistic (e.g., $$X$$) that does a good job (in some meaningful sense) of comparing $$H_0$$ to $$H_1$$, (3) figure out the sampling distribution of the test statistic on the assumption that the null hypothesis is true (in this case, binomial) and then (4) calculate the critical region that produces an appropriate $$\\alpha$$ level (0-40 and 60-100). All that we have to do now is calculate the value of the test statistic for the real data (e.g., $$X = 62$$) and then compare it to the critical values to make our decision. Since 62 is greater than the critical value of 60, we would reject the null hypothesis. Or, to phrase it slightly differently, we say that the test has produced a significant result.\n\n### 11.4.2 A note on statistical “significance”\n\nLike other occult techniques of divination, the statistical method has a private jargon deliberately contrived to obscure its methods from non-practitioners.\n\n– Attributed to G. O. Ashley162\n\nA very brief digression is in order at this point, regarding the word “significant”. The concept of statistical significance is actually a very simple one, but has a very unfortunate name. If the data allow us to reject the null hypothesis, we say that “the result is statistically significant”, which is often shortened to “the result is significant”. This terminology is rather old, and dates back to a time when “significant” just meant something like “indicated”, rather than its modern meaning, which is much closer to “important”. As a result, a lot of modern readers get very confused when they start learning statistics, because they think that a “significant result” must be an important one. It doesn’t mean that at all. All that “statistically significant” means is that the data allowed us to reject a null hypothesis. Whether or not the result is actually important in the real world is a very different question, and depends on all sorts of other things.\n\n### 11.4.3 The difference between one sided and two sided tests\n\nThere’s one more thing I want to point out about the hypothesis test that I’ve just constructed. If we take a moment to think about the statistical hypotheses I’ve been using, $\\begin{array}{cc} H_0 : & \\theta = .5 \\\\ H_1 : & \\theta \\neq .5 \\end{array}$ we notice that the alternative hypothesis covers both the possibility that $$\\theta < .5$$ and the possibility that $$\\theta > .5$$. This makes sense if I really think that ESP could produce better-than-chance performance or worse-than-chance performance (and there are some people who think that). In statistical language, this is an example of a two-sided test. It’s called this because the alternative hypothesis covers the area on both “sides” of the null hypothesis, and as a consequence the critical region of the test covers both tails of the sampling distribution (2.5% on either side if $$\\alpha =.05$$), as illustrated earlier in Figure 11.2.\n\nHowever, that’s not the only possibility. It might be the case, for example, that I’m only willing to believe in ESP if it produces better than chance performance. If so, then my alternative hypothesis would only covers the possibility that $$\\theta > .5$$, and as a consequence the null hypothesis now becomes $$\\theta \\leq .5$$: $\\begin{array}{cc} H_0 : & \\theta \\leq .5 \\\\ H_1 : & \\theta > .5 \\end{array}$ When this happens, we have what’s called a one-sided test, and when this happens the critical region only covers one tail of the sampling distribution. This is illustrated in Figure 11.3.", null, "Figure 11.3: The critical region for a one sided test. In this case, the alternative hypothesis is that $$\\theta > .05$$, so we would only reject the null hypothesis for large values of $$X$$. As a consequence, the critical region only covers the upper tail of the sampling distribution; specifically the upper 5% of the distribution. Contrast this to the two-sided version earlier)\n\n## 11.5 The $$p$$ value of a test\n\nIn one sense, our hypothesis test is complete; we’ve constructed a test statistic, figured out its sampling distribution if the null hypothesis is true, and then constructed the critical region for the test. Nevertheless, I’ve actually omitted the most important number of all: the $$p$$ value. It is to this topic that we now turn. There are two somewhat different ways of interpreting a $$p$$ value, one proposed by Sir Ronald Fisher and the other by Jerzy Neyman. Both versions are legitimate, though they reflect very different ways of thinking about hypothesis tests. Most introductory textbooks tend to give Fisher’s version only, but I think that’s a bit of a shame. To my mind, Neyman’s version is cleaner, and actually better reflects the logic of the null hypothesis test. You might disagree though, so I’ve included both. I’ll start with Neyman’s version…\n\n### 11.5.1 A softer view of decision making\n\nOne problem with the hypothesis testing procedure that I’ve described is that it makes no distinction at all between a result this “barely significant” and those that are “highly significant”. For instance, in my ESP study the data I obtained only just fell inside the critical region - so I did get a significant effect, but was a pretty near thing. In contrast, suppose that I’d run a study in which $$X=97$$ out of my $$N=100$$ participants got the answer right. This would obviously be significant too, but my a much larger margin; there’s really no ambiguity about this at all. The procedure that I described makes no distinction between the two. If I adopt the standard convention of allowing $$\\alpha = .05$$ as my acceptable Type I error rate, then both of these are significant results.\n\nThis is where the $$p$$ value comes in handy. To understand how it works, let’s suppose that we ran lots of hypothesis tests on the same data set: but with a different value of $$\\alpha$$ in each case. When we do that for my original ESP data, what we’d get is something like this\n\nValue of $$\\alpha$$ Reject the null?\n0.05 Yes\n0.04 Yes\n0.03 Yes\n0.02 No\n0.01 No\n\nWhen we test ESP data ($$X=62$$ successes out of $$N=100$$ observations) using $$\\alpha$$ levels of .03 and above, we’d always find ourselves rejecting the null hypothesis. For $$\\alpha$$ levels of .02 and below, we always end up retaining the null hypothesis. Therefore, somewhere between .02 and .03 there must be a smallest value of $$\\alpha$$ that would allow us to reject the null hypothesis for this data. This is the $$p$$ value; as it turns out the ESP data has $$p = .021$$. In short:\n\n$$p$$ is defined to be the smallest Type I error rate ($$\\alpha$$) that you have to be willing to tolerate if you want to reject the null hypothesis.\n\nIf it turns out that $$p$$ describes an error rate that you find intolerable, then you must retain the null. If you’re comfortable with an error rate equal to $$p$$, then it’s okay to reject the null hypothesis in favour of your preferred alternative.\n\nIn effect, $$p$$ is a summary of all the possible hypothesis tests that you could have run, taken across all possible $$\\alpha$$ values. And as a consequence it has the effect of “softening” our decision process. For those tests in which $$p \\leq \\alpha$$ you would have rejected the null hypothesis, whereas for those tests in which $$p > \\alpha$$ you would have retained the null. In my ESP study I obtained $$X=62$$, and as a consequence I’ve ended up with $$p = .021$$. So the error rate I have to tolerate is 2.1%. In contrast, suppose my experiment had yielded $$X=97$$. What happens to my $$p$$ value now? This time it’s shrunk to $$p = 1.36 \\times 10^{-25}$$, which is a tiny, tiny163 Type I error rate. For this second case I would be able to reject the null hypothesis with a lot more confidence, because I only have to be “willing” to tolerate a type I error rate of about 1 in 10 trillion trillion in order to justify my decision to reject.\n\n### 11.5.2 The probability of extreme data\n\nThe second definition of the $$p$$-value comes from Sir Ronald Fisher, and it’s actually this one that you tend to see in most introductory statistics textbooks. Notice how, when I constructed the critical region, it corresponded to the tails (i.e., extreme values) of the sampling distribution? That’s not a coincidence: almost all “good” tests have this characteristic (good in the sense of minimising our type II error rate, $$\\beta$$). The reason for that is that a good critical region almost always corresponds to those values of the test statistic that are least likely to be observed if the null hypothesis is true. If this rule is true, then we can define the $$p$$-value as the probability that we would have observed a test statistic that is at least as extreme as the one we actually did get. In other words, if the data are extremely implausible according to the null hypothesis, then the null hypothesis is probably wrong.\n\n### 11.5.3 A common mistake\n\nOkay, so you can see that there are two rather different but legitimate ways to interpret the $$p$$ value, one based on Neyman’s approach to hypothesis testing and the other based on Fisher’s. Unfortunately, there is a third explanation that people sometimes give, especially when they’re first learning statistics, and it is absolutely and completely wrong. This mistaken approach is to refer to the $$p$$ value as “the probability that the null hypothesis is true”. It’s an intuitively appealing way to think, but it’s wrong in two key respects: (1) null hypothesis testing is a frequentist tool, and the frequentist approach to probability does not allow you to assign probabilities to the null hypothesis… according to this view of probability, the null hypothesis is either true or it is not; it cannot have a “5% chance” of being true. (2) even within the Bayesian approach, which does let you assign probabilities to hypotheses, the $$p$$ value would not correspond to the probability that the null is true; this interpretation is entirely inconsistent with the mathematics of how the $$p$$ value is calculated. Put bluntly, despite the intuitive appeal of thinking this way, there is no justification for interpreting a $$p$$ value this way. Never do it.\n\n## 11.6 Reporting the results of a hypothesis test\n\nWhen writing up the results of a hypothesis test, there’s usually several pieces of information that you need to report, but it varies a fair bit from test to test. Throughout the rest of the book I’ll spend a little time talking about how to report the results of different tests (see Section 12.1.9 for a particularly detailed example), so that you can get a feel for how it’s usually done. However, regardless of what test you’re doing, the one thing that you always have to do is say something about the $$p$$ value, and whether or not the outcome was significant.\n\nThe fact that you have to do this is unsurprising; it’s the whole point of doing the test. What might be surprising is the fact that there is some contention over exactly how you’re supposed to do it. Leaving aside those people who completely disagree with the entire framework underpinning null hypothesis testing, there’s a certain amount of tension that exists regarding whether or not to report the exact $$p$$ value that you obtained, or if you should state only that $$p < \\alpha$$ for a significance level that you chose in advance (e.g., $$p<.05$$).\n\n### 11.6.1 The issue\n\nTo see why this is an issue, the key thing to recognise is that $$p$$ values are terribly convenient. In practice, the fact that we can compute a $$p$$ value means that we don’t actually have to specify any $$\\alpha$$ level at all in order to run the test. Instead, what you can do is calculate your $$p$$ value and interpret it directly: if you get $$p = .062$$, then it means that you’d have to be willing to tolerate a Type I error rate of 6.2% to justify rejecting the null. If you personally find 6.2% intolerable, then you retain the null. Therefore, the argument goes, why don’t we just report the actual $$p$$ value and let the reader make up their own minds about what an acceptable Type I error rate is? This approach has the big advantage of “softening” the decision making process – in fact, if you accept the Neyman definition of the $$p$$ value, that’s the whole point of the $$p$$ value. We no longer have a fixed significance level of $$\\alpha = .05$$ as a bright line separating “accept” from “reject” decisions; and this removes the rather pathological problem of being forced to treat $$p = .051$$ in a fundamentally different way to $$p = .049$$.\n\nThis flexibility is both the advantage and the disadvantage to the $$p$$ value. The reason why a lot of people don’t like the idea of reporting an exact $$p$$ value is that it gives the researcher a bit too much freedom. In particular, it lets you change your mind about what error tolerance you’re willing to put up with after you look at the data. For instance, consider my ESP experiment. Suppose I ran my test, and ended up with a $$p$$ value of .09. Should I accept or reject? Now, to be honest, I haven’t yet bothered to think about what level of Type I error I’m “really” willing to accept. I don’t have an opinion on that topic. But I do have an opinion about whether or not ESP exists, and I definitely have an opinion about whether my research should be published in a reputable scientific journal. And amazingly, now that I’ve looked at the data I’m starting to think that a 9% error rate isn’t so bad, especially when compared to how annoying it would be to have to admit to the world that my experiment has failed. So, to avoid looking like I just made it up after the fact, I now say that my $$\\alpha$$ is .1: a 10% type I error rate isn’t too bad, and at that level my test is significant! I win.\n\nIn other words, the worry here is that I might have the best of intentions, and be the most honest of people, but the temptation to just “shade” things a little bit here and there is really, really strong. As anyone who has ever run an experiment can attest, it’s a long and difficult process, and you often get very attached to your hypotheses. It’s hard to let go and admit the experiment didn’t find what you wanted it to find. And that’s the danger here. If we use the “raw” $$p$$-value, people will start interpreting the data in terms of what they want to believe, not what the data are actually saying… and if we allow that, well, why are we bothering to do science at all? Why not let everyone believe whatever they like about anything, regardless of what the facts are? Okay, that’s a bit extreme, but that’s where the worry comes from. According to this view, you really must specify your $$\\alpha$$ value in advance, and then only report whether the test was significant or not. It’s the only way to keep ourselves honest.\n\n### 11.6.2 Two proposed solutions\n\nIn practice, it’s pretty rare for a researcher to specify a single $$\\alpha$$ level ahead of time. Instead, the convention is that scientists rely on three standard significance levels: .05, .01 and .001. When reporting your results, you indicate which (if any) of these significance levels allow you to reject the null hypothesis. This is summarised in Table 11.1. This allows us to soften the decision rule a little bit, since $$p<.01$$ implies that the data meet a stronger evidentiary standard than $$p<.05$$ would. Nevertheless, since these levels are fixed in advance by convention, it does prevent people choosing their $$\\alpha$$ level after looking at the data.\n\nTable 11.1: A commonly adopted convention for reporting $$p$$ values: in many places it is conventional to report one of four different things (e.g., $$p<.05$$) as shown below. I’ve included the “significance stars” notation (i.e., a * indicates $$p<.05$$) because you sometimes see this notation produced by statistical software. It’s also worth noting that some people will write n.s. (not significant) rather than $$p>.05$$.\nUsual notation Signif. stars Signif. stars The null is…\n$$p>.05$$ NA The test wasn’t significant Retained\n$$p<.05$$ * The test was significant at $= .05 but not at $$\\alpha =.01$$ or $$\\alpha = .001$$.$ Rejected\n$$p<.01$$ ** The test was significant at $$\\alpha = .05$$ and $$\\alpha = .01$$ but not at \\$= .001 Rejected\n$$p<.001$$ *** The test was significant at all levels Rejected\n\nNevertheless, quite a lot of people still prefer to report exact $$p$$ values. To many people, the advantage of allowing the reader to make up their own mind about how to interpret $$p = .06$$ outweighs any disadvantages. In practice, however, even among those researchers who prefer exact $$p$$ values it is quite common to just write $$p<.001$$ instead of reporting an exact value for small $$p$$. This is in part because a lot of software doesn’t actually print out the $$p$$ value when it’s that small (e.g., SPSS just writes $$p = .000$$ whenever $$p<.001$$), and in part because a very small $$p$$ value can be kind of misleading. The human mind sees a number like .0000000001 and it’s hard to suppress the gut feeling that the evidence in favour of the alternative hypothesis is a near certainty. In practice however, this is usually wrong. Life is a big, messy, complicated thing: and every statistical test ever invented relies on simplifications, approximations and assumptions. As a consequence, it’s probably not reasonable to walk away from any statistical analysis with a feeling of confidence stronger than $$p<.001$$ implies. In other words, $$p<.001$$ is really code for “as far as this test is concerned, the evidence is overwhelming.”\n\nIn light of all this, you might be wondering exactly what you should do. There’s a fair bit of contradictory advice on the topic, with some people arguing that you should report the exact $$p$$ value, and other people arguing that you should use the tiered approach illustrated in Table 11.1. As a result, the best advice I can give is to suggest that you look at papers/reports written in your field and see what the convention seems to be. If there doesn’t seem to be any consistent pattern, then use whichever method you prefer.\n\n## 11.7 Running the hypothesis test in practice\n\nAt this point some of you might be wondering if this is a “real” hypothesis test, or just a toy example that I made up. It’s real. In the previous discussion I built the test from first principles, thinking that it was the simplest possible problem that you might ever encounter in real life. However, this test already exists: it’s called the binomial test, and it’s implemented by an R function called binom.test(). To test the null hypothesis that the response probability is one-half p = .5,164 using data in which x = 62 of n = 100 people made the correct response, here’s how to do it in R:\n\nbinom.test( x=62, n=100, p=.5 )\n##\n## Exact binomial test\n##\n## data: 62 and 100\n## number of successes = 62, number of trials = 100, p-value =\n## 0.02098\n## alternative hypothesis: true probability of success is not equal to 0.5\n## 95 percent confidence interval:\n## 0.5174607 0.7152325\n## sample estimates:\n## probability of success\n## 0.62\n\nRight now, this output looks pretty unfamiliar to you, but you can see that it’s telling you more or less the right things. Specifically, the $$p$$-value of 0.02 is less than the usual choice of $$\\alpha = .05$$, so you can reject the null. We’ll talk a lot more about how to read this sort of output as we go along; and after a while you’ll hopefully find it quite easy to read and understand. For now, however, I just wanted to make the point that R contains a whole lot of functions corresponding to different kinds of hypothesis test. And while I’ll usually spend quite a lot of time explaining the logic behind how the tests are built, every time I discuss a hypothesis test the discussion will end with me showing you a fairly simple R command that you can use to run the test in practice.\n\n## 11.8 Effect size, sample size and power\n\nIn previous sections I’ve emphasised the fact that the major design principle behind statistical hypothesis testing is that we try to control our Type I error rate. When we fix $$\\alpha = .05$$ we are attempting to ensure that only 5% of true null hypotheses are incorrectly rejected. However, this doesn’t mean that we don’t care about Type II errors. In fact, from the researcher’s perspective, the error of failing to reject the null when it is actually false is an extremely annoying one. With that in mind, a secondary goal of hypothesis testing is to try to minimise $$\\beta$$, the Type II error rate, although we don’t usually talk in terms of minimising Type II errors. Instead, we talk about maximising the power of the test. Since power is defined as $$1-\\beta$$, this is the same thing.\n\n### 11.8.1 The power function", null, "Figure 11.4: Sampling distribution under the alternative hypothesis, for a population parameter value of $$\\theta = 0.55$$. A reasonable proportion of the distribution lies in the rejection region.\n\nLet’s take a moment to think about what a Type II error actually is. A Type II error occurs when the alternative hypothesis is true, but we are nevertheless unable to reject the null hypothesis. Ideally, we’d be able to calculate a single number $$\\beta$$ that tells us the Type II error rate, in the same way that we can set $$\\alpha = .05$$ for the Type I error rate. Unfortunately, this is a lot trickier to do. To see this, notice that in my ESP study the alternative hypothesis actually corresponds to lots of possible values of $$\\theta$$. In fact, the alternative hypothesis corresponds to every value of $$\\theta$$ except 0.5. Let’s suppose that the true probability of someone choosing the correct response is 55% (i.e., $$\\theta = .55$$). If so, then the true sampling distribution for $$X$$ is not the same one that the null hypothesis predicts: the most likely value for $$X$$ is now 55 out of 100. Not only that, the whole sampling distribution has now shifted, as shown in Figure 11.4. The critical regions, of course, do not change: by definition, the critical regions are based on what the null hypothesis predicts. What we’re seeing in this figure is the fact that when the null hypothesis is wrong, a much larger proportion of the sampling distribution distribution falls in the critical region. And of course that’s what should happen: the probability of rejecting the null hypothesis is larger when the null hypothesis is actually false! However $$\\theta = .55$$ is not the only possibility consistent with the alternative hypothesis. Let’s instead suppose that the true value of $$\\theta$$ is actually 0.7. What happens to the sampling distribution when this occurs? The answer, shown in Figure 11.5, is that almost the entirety of the sampling distribution has now moved into the critical region. Therefore, if $$\\theta = 0.7$$ the probability of us correctly rejecting the null hypothesis (i.e., the power of the test) is much larger than if $$\\theta = 0.55$$. In short, while $$\\theta = .55$$ and $$\\theta = .70$$ are both part of the alternative hypothesis, the Type II error rate is different.", null, "Figure 11.5: Sampling distribution under the alternative hypothesis, for a population parameter value of $$\\theta = 0.70$$. Almost all of the distribution lies in the rejection region.", null, "Figure 11.6: The probability that we will reject the null hypothesis, plotted as a function of the true value of $$\\theta$$. Obviously, the test is more powerful (greater chance of correct rejection) if the true value of $$\\theta$$ is very different from the value that the null hypothesis specifies (i.e., $$\\theta=.5$$). Notice that when $$\\theta$$ actually is equal to .5 (plotted as a black dot), the null hypothesis is in fact true: rejecting the null hypothesis in this instance would be a Type I error.\n\nWhat all this means is that the power of a test (i.e., $$1-\\beta$$) depends on the true value of $$\\theta$$. To illustrate this, I’ve calculated the expected probability of rejecting the null hypothesis for all values of $$\\theta$$, and plotted it in Figure 11.6. This plot describes what is usually called the power function of the test. It’s a nice summary of how good the test is, because it actually tells you the power ($$1-\\beta$$) for all possible values of $$\\theta$$. As you can see, when the true value of $$\\theta$$ is very close to 0.5, the power of the test drops very sharply, but when it is further away, the power is large.\n\n### 11.8.2 Effect size\n\nSince all models are wrong the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned with mice when there are tigers abroad\n\n– George Box 1976\n\nThe plot shown in Figure 11.6 captures a fairly basic point about hypothesis testing. If the true state of the world is very different from what the null hypothesis predicts, then your power will be very high; but if the true state of the world is similar to the null (but not identical) then the power of the test is going to be very low. Therefore, it’s useful to be able to have some way of quantifying how “similar” the true state of the world is to the null hypothesis. A statistic that does this is called a measure of effect size (e.g. Cohen 1988; Ellis 2010). Effect size is defined slightly differently in different contexts,165 (and so this section just talks in general terms) but the qualitative idea that it tries to capture is always the same: how big is the difference between the true population parameters, and the parameter values that are assumed by the null hypothesis? In our ESP example, if we let $$\\theta_0 = 0.5$$ denote the value assumed by the null hypothesis, and let $$\\theta$$ denote the true value, then a simple measure of effect size could be something like the difference between the true value and null (i.e., $$\\theta - \\theta_0$$), or possibly just the magnitude of this difference, $$\\mbox{abs}(\\theta - \\theta_0)$$.\n\nbig effect size small effect size\nsignificant result difference is real, and of practical importance difference is real, but might not be interesting\nnon-significant result no effect observed no effect observed\n\nWhy calculate effect size? Let’s assume that you’ve run your experiment, collected the data, and gotten a significant effect when you ran your hypothesis test. Isn’t it enough just to say that you’ve gotten a significant effect? Surely that’s the point of hypothesis testing? Well, sort of. Yes, the point of doing a hypothesis test is to try to demonstrate that the null hypothesis is wrong, but that’s hardly the only thing we’re interested in. If the null hypothesis claimed that $$\\theta = .5$$, and we show that it’s wrong, we’ve only really told half of the story. Rejecting the null hypothesis implies that we believe that $$\\theta \\neq .5$$, but there’s a big difference between $$\\theta = .51$$ and $$\\theta = .8$$. If we find that $$\\theta = .8$$, then not only have we found that the null hypothesis is wrong, it appears to be very wrong. On the other hand, suppose we’ve successfully rejected the null hypothesis, but it looks like the true value of $$\\theta$$ is only .51 (this would only be possible with a large study). Sure, the null hypothesis is wrong, but it’s not at all clear that we actually care, because the effect size is so small. In the context of my ESP study we might still care, since any demonstration of real psychic powers would actually be pretty cool166, but in other contexts a 1% difference isn’t very interesting, even if it is a real difference. For instance, suppose we’re looking at differences in high school exam scores between males and females, and it turns out that the female scores are 1% higher on average than the males. If I’ve got data from thousands of students, then this difference will almost certainly be statistically significant, but regardless of how small the $$p$$ value is it’s just not very interesting. You’d hardly want to go around proclaiming a crisis in boys education on the basis of such a tiny difference would you? It’s for this reason that it is becoming more standard (slowly, but surely) to report some kind of standard measure of effect size along with the the results of the hypothesis test. The hypothesis test itself tells you whether you should believe that the effect you have observed is real (i.e., not just due to chance); the effect size tells you whether or not you should care.\n\n### 11.8.3 Increasing the power of your study\n\nNot surprisingly, scientists are fairly obsessed with maximising the power of their experiments. We want our experiments to work, and so we want to maximise the chance of rejecting the null hypothesis if it is false (and of course we usually want to believe that it is false!) As we’ve seen, one factor that influences power is the effect size. So the first thing you can do to increase your power is to increase the effect size. In practice, what this means is that you want to design your study in such a way that the effect size gets magnified. For instance, in my ESP study I might believe that psychic powers work best in a quiet, darkened room; with fewer distractions to cloud the mind. Therefore I would try to conduct my experiments in just such an environment: if I can strengthen people’s ESP abilities somehow, then the true value of $$\\theta$$ will go up167 and therefore my effect size will be larger. In short, clever experimental design is one way to boost power; because it can alter the effect size.\n\nUnfortunately, it’s often the case that even with the best of experimental designs you may have only a small effect. Perhaps, for example, ESP really does exist, but even under the best of conditions it’s very very weak. Under those circumstances, your best bet for increasing power is to increase the sample size. In general, the more observations that you have available, the more likely it is that you can discriminate between two hypotheses. If I ran my ESP experiment with 10 participants, and 7 of them correctly guessed the colour of the hidden card, you wouldn’t be terribly impressed. But if I ran it with 10,000 participants and 7,000 of them got the answer right, you would be much more likely to think I had discovered something. In other words, power increases with the sample size. This is illustrated in Figure 11.7, which shows the power of the test for a true parameter of $$\\theta = 0.7$$, for all sample sizes $$N$$ from 1 to 100, where I’m assuming that the null hypothesis predicts that $$\\theta_0 = 0.5$$.\n\n## 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.11837800\n## 0.08257300 0.05771362 0.19643626 0.14945203 0.11303734 0.25302172\n## 0.20255096 0.16086106 0.29695959 0.24588947 0.38879291 0.33269435\n## 0.28223844 0.41641377 0.36272868 0.31341925 0.43996501 0.38859619\n## 0.51186665 0.46049782 0.41129777 0.52752694 0.47870819 0.58881596\n## 0.54162450 0.49507894 0.59933871 0.55446069 0.65155826 0.60907715\n## 0.69828554 0.65867614 0.61815357 0.70325017 0.66542910 0.74296156\n## 0.70807163 0.77808343 0.74621569 0.71275488 0.78009449 0.74946571\n## 0.81000236 0.78219322 0.83626633 0.81119597 0.78435605 0.83676444\n## 0.81250680 0.85920268 0.83741123 0.87881491 0.85934395 0.83818214\n## 0.87858194 0.85962510 0.89539581 0.87849413 0.91004390 0.89503851\n## 0.92276845 0.90949768 0.89480727 0.92209753 0.90907263 0.93304809\n## 0.92153987 0.94254237 0.93240638 0.92108426 0.94185449 0.93185881\n## 0.95005094 0.94125189 0.95714694 0.94942195 0.96327866 0.95651332\n## 0.94886329 0.96265653 0.95594208 0.96796884 0.96208909 0.97255504\n## 0.96741721 0.97650832 0.97202770 0.97991117 0.97601093 0.97153910\n## 0.97944717 0.97554675 0.98240749 0.97901142", null, "Figure 11.7: The power of our test, plotted as a function of the sample size $$N$$. In this case, the true value of $$\\theta$$ is 0.7, but the null hypothesis is that $$\\theta = 0.5$$. Overall, larger $$N$$ means greater power. (The small zig-zags in this function occur because of some odd interactions between $$\\theta$$, $$\\alpha$$ and the fact that the binomial distribution is discrete; it doesn’t matter for any serious purpose)\n\n## 11.9 Some issues to consider\n\nWhat I’ve described to you in this chapter is the orthodox framework for null hypothesis significance testing (NHST). Understanding how NHST works is an absolute necessity, since it has been the dominant approach to inferential statistics ever since it came to prominence in the early 20th century. It’s what the vast majority of working scientists rely on for their data analysis, so even if you hate it you need to know it. However, the approach is not without problems. There are a number of quirks in the framework, historical oddities in how it came to be, theoretical disputes over whether or not the framework is right, and a lot of practical traps for the unwary. I’m not going to go into a lot of detail on this topic, but I think it’s worth briefly discussing a few of these issues.\n\n### 11.9.1 Neyman versus Fisher\n\nThe first thing you should be aware of is that orthodox NHST is actually a mash-up of two rather different approaches to hypothesis testing, one proposed by Sir Ronald Fisher and the other proposed by Jerzy Neyman (for a historical summary see Lehmann 2011). The history is messy because Fisher and Neyman were real people whose opinions changed over time, and at no point did either of them offer “the definitive statement” of how we should interpret their work many decades later. That said, here’s a quick summary of what I take these two approaches to be.\n\nFirst, let’s talk about Fisher’s approach. As far as I can tell, Fisher assumed that you only had the one hypothesis (the null), and what you want to do is find out if the null hypothesis is inconsistent with the data. From his perspective, what you should do is check to see if the data are “sufficiently unlikely” according to the null. In fact, if you remember back to our earlier discussion, that’s how Fisher defines the $$p$$-value. According to Fisher, if the null hypothesis provided a very poor account of the data, you could safely reject it. But, since you don’t have any other hypotheses to compare it to, there’s no way of “accepting the alternative” because you don’t necessarily have an explicitly stated alternative. That’s more or less all that there was to it.\n\nIn contrast, Neyman thought that the point of hypothesis testing was as a guide to action, and his approach was somewhat more formal than Fisher’s. His view was that there are multiple things that you could do (accept the null or accept the alternative) and the point of the test was to tell you which one the data support. From this perspective, it is critical to specify your alternative hypothesis properly. If you don’t know what the alternative hypothesis is, then you don’t know how powerful the test is, or even which action makes sense. His framework genuinely requires a competition between different hypotheses. For Neyman, the $$p$$ value didn’t directly measure the probability of the data (or data more extreme) under the null, it was more of an abstract description about which “possible tests” were telling you to accept the null, and which “possible tests” were telling you to accept the alternative.\n\nAs you can see, what we have today is an odd mishmash of the two. We talk about having both a null hypothesis and an alternative (Neyman), but usually168 define the $$p$$ value in terms of exreme data (Fisher), but we still have $$\\alpha$$ values (Neyman). Some of the statistical tests have explicitly specified alternatives (Neyman) but others are quite vague about it (Fisher). And, according to some people at least, we’re not allowed to talk about accepting the alternative (Fisher). It’s a mess: but I hope this at least explains why it’s a mess.\n\n### 11.9.2 Bayesians versus frequentists\n\nEarlier on in this chapter I was quite emphatic about the fact that you cannot interpret the $$p$$ value as the probability that the null hypothesis is true. NHST is fundamentally a frequentist tool (see Chapter 9) and as such it does not allow you to assign probabilities to hypotheses: the null hypothesis is either true or it is not. The Bayesian approach to statistics interprets probability as a degree of belief, so it’s totally okay to say that there is a 10% chance that the null hypothesis is true: that’s just a reflection of the degree of confidence that you have in this hypothesis. You aren’t allowed to do this within the frequentist approach. Remember, if you’re a frequentist, a probability can only be defined in terms of what happens after a large number of independent replications (i.e., a long run frequency). If this is your interpretation of probability, talking about the “probability” that the null hypothesis is true is complete gibberish: a null hypothesis is either true or it is false. There’s no way you can talk about a long run frequency for this statement. To talk about “the probability of the null hypothesis” is as meaningless as “the colour of freedom”. It doesn’t have one!\n\nMost importantly, this isn’t a purely ideological matter. If you decide that you are a Bayesian and that you’re okay with making probability statements about hypotheses, you have to follow the Bayesian rules for calculating those probabilities. I’ll talk more about this in Chapter 17, but for now what I want to point out to you is the $$p$$ value is a terrible approximation to the probability that $$H_0$$ is true. If what you want to know is the probability of the null, then the $$p$$ value is not what you’re looking for!\n\n### 11.9.3 Traps\n\nAs you can see, the theory behind hypothesis testing is a mess, and even now there are arguments in statistics about how it “should” work. However, disagreements among statisticians are not our real concern here. Our real concern is practical data analysis. And while the “orthodox” approach to null hypothesis significance testing has many drawbacks, even an unrepentant Bayesian like myself would agree that they can be useful if used responsibly. Most of the time they give sensible answers, and you can use them to learn interesting things. Setting aside the various ideologies and historical confusions that we’ve discussed, the fact remains that the biggest danger in all of statistics is thoughtlessness. I don’t mean stupidity, here: I literally mean thoughtlessness. The rush to interpret a result without spending time thinking through what each test actually says about the data, and checking whether that’s consistent with how you’ve interpreted it. That’s where the biggest trap lies.\n\nTo give an example of this, consider the following example (see Gelman and Stern 2006). Suppose I’m running my ESP study, and I’ve decided to analyse the data separately for the male participants and the female participants. Of the male participants, 33 out of 50 guessed the colour of the card correctly. This is a significant effect ($$p = .03$$). Of the female participants, 29 out of 50 guessed correctly. This is not a significant effect ($$p = .32$$). Upon observing this, it is extremely tempting for people to start wondering why there is a difference between males and females in terms of their psychic abilities. However, this is wrong. If you think about it, we haven’t actually run a test that explicitly compares males to females. All we have done is compare males to chance (binomial test was significant) and compared females to chance (binomial test was non significant). If we want to argue that there is a real difference between the males and the females, we should probably run a test of the null hypothesis that there is no difference! We can do that using a different hypothesis test,169 but when we do that it turns out that we have no evidence that males and females are significantly different ($$p = .54$$). Now do you think that there’s anything fundamentally different between the two groups? Of course not. What’s happened here is that the data from both groups (male and female) are pretty borderline: by pure chance, one of them happened to end up on the magic side of the $$p = .05$$ line, and the other one didn’t. That doesn’t actually imply that males and females are different. This mistake is so common that you should always be wary of it: the difference between significant and not-significant is not evidence of a real difference – if you want to say that there’s a difference between two groups, then you have to test for that difference!\n\nThe example above is just that: an example. I’ve singled it out because it’s such a common one, but the bigger picture is that data analysis can be tricky to get right. Think about what it is you want to test, why you want to test it, and whether or not the answers that your test gives could possibly make any sense in the real world.\n\n## 11.10 Summary\n\nNull hypothesis testing is one of the most ubiquitous elements to statistical theory. The vast majority of scientific papers report the results of some hypothesis test or another. As a consequence it is almost impossible to get by in science without having at least a cursory understanding of what a $$p$$-value means, making this one of the most important chapters in the book. As usual, I’ll end the chapter with a quick recap of the key ideas that we’ve talked about:\n\n• Research hypotheses and statistical hypotheses. Null and alternative hypotheses. (Section 11.1).\n• Type 1 and Type 2 errors (Section 11.2)\n• Test statistics and sampling distributions (Section 11.3)\n• Hypothesis testing as a decision making process (Section 11.4)\n• $$p$$-values as “soft” decisions (Section 11.5)\n• Writing up the results of a hypothesis test (Section 11.6)\n• Effect size and power (Section 11.8)\n• A few issues to consider regarding hypothesis testing (Section 11.9)\n\nLater in the book, in Chapter 17, I’ll revisit the theory of null hypothesis tests from a Bayesian perspective, and introduce a number of new tools that you can use if you aren’t particularly fond of the orthodox approach. But for now, though, we’re done with the abstract statistical theory, and we can start discussing specific data analysis tools.\n\n### References\n\nCohen, J. 1988. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Lawrence Erlbaum.\n\nEllis, P. D. 2010. The Essential Guide to Effect Sizes: Statistical Power, Meta-Analysis, and the Interpretation of Research Results. Cambridge, UK: Cambridge University Press.\n\nLehmann, Erich L. 2011. Fisher, Neyman, and the Creation of Classical Statistics. Springer.\n\nGelman, A., and H. Stern. 2006. “The Difference Between ‘Significant’ and ‘Not Significant’ Is Not Itself Statistically Significant.” The American Statistician 60: 328–31.\n\n1. The quote comes from Wittgenstein’s (1922) text, Tractatus Logico-Philosphicus.\n\n2. A technical note. The description below differs subtly from the standard description given in a lot of introductory texts. The orthodox theory of null hypothesis testing emerged from the work of Sir Ronald Fisher and Jerzy Neyman in the early 20th century; but Fisher and Neyman actually had very different views about how it should work. The standard treatment of hypothesis testing that most texts use is a hybrid of the two approaches. The treatment here is a little more Neyman-style than the orthodox view, especially as regards the meaning of the $$p$$ value.\n\n3. My apologies to anyone who actually believes in this stuff, but on my reading of the literature on ESP, it’s just not reasonable to think this is real. To be fair, though, some of the studies are rigorously designed; so it’s actually an interesting area for thinking about psychological research design. And of course it’s a free country, so you can spend your own time and effort proving me wrong if you like, but I wouldn’t think that’s a terribly practical use of your intellect.\n\n4. This analogy only works if you’re from an adversarial legal system like UK/US/Australia. As I understand these things, the French inquisitorial system is quite different.\n\n5. An aside regarding the language you use to talk about hypothesis testing. Firstly, one thing you really want to avoid is the word “prove”: a statistical test really doesn’t prove that a hypothesis is true or false. Proof implies certainty, and as the saying goes, statistics means never having to say you’re certain. On that point almost everyone would agree. However, beyond that there’s a fair amount of confusion. Some people argue that you’re only allowed to make statements like “rejected the null”, “failed to reject the null”, or possibly “retained the null”. According to this line of thinking, you can’t say things like “accept the alternative” or “accept the null”. Personally I think this is too strong: in my opinion, this conflates null hypothesis testing with Karl Popper’s falsificationist view of the scientific process. While there are similarities between falsificationism and null hypothesis testing, they aren’t equivalent. However, while I personally think it’s fine to talk about accepting a hypothesis (on the proviso that “acceptance” doesn’t actually mean that it’s necessarily true, especially in the case of the null hypothesis), many people will disagree. And more to the point, you should be aware that this particular weirdness exists, so that you’re not caught unawares by it when writing up your own results.\n\n6. Strictly speaking, the test I just constructed has $$\\alpha = .057$$, which is a bit too generous. However, if I’d chosen 39 and 61 to be the boundaries for the critical region, then the critical region only covers 3.5% of the distribution. I figured that it makes more sense to use 40 and 60 as my critical values, and be willing to tolerate a 5.7% type I error rate, since that’s as close as I can get to a value of $$\\alpha = .05$$.\n\n7. The internet seems fairly convinced that Ashley said this, though I can’t for the life of me find anyone willing to give a source for the claim.\n\n8. That’s $$p = .000000000000000000000000136$$ for folks that don’t like scientific notation!\n\n9. Note that the p here has nothing to do with a $$p$$ value. The p argument in the binom.test() function corresponds to the probability of making a correct response, according to the null hypothesis. In other words, it’s the $$\\theta$$ value.\n\n10. There’s an R package called compute.es that can be used for calculating a very broad range of effect size measures; but for the purposes of the current book we won’t need it: all of the effect size measures that I’ll talk about here have functions in the lsr package\n\n11. Although in practice a very small effect size is worrying, because even very minor methodological flaws might be responsible for the effect; and in practice no experiment is perfect, so there are always methodological issues to worry about.\n\n12. Notice that the true population parameter $$\\theta$$ doesn’t necessarily correspond to an immutable fact of nature. In this context $$\\theta$$ is just the true probability that people would correctly guess the colour of the card in the other room. As such the population parameter can be influenced by all sorts of things. Of course, this is all on the assumption that ESP actually exists!\n\n13. Although this book describes both Neyman’s and Fisher’s definition of the $$p$$ value, most don’t. Most introductory textbooks will only give you the Fisher version.\n\n14. In this case, the Pearson chi-square test of independence (Chapter 12; chisq.test() in R) is what we use; see also the prop.test()` function." ]
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[ " Effects of Hydromagnetic and Thermophoresis of Unsteady Forced Convection Boundary Layer Flow over Flat Plates\n\nJournal of Applied Mathematics and Physics\nVol.04 No.09(2016), Article ID:70899,21 pages\n10.4236/jamp.2016.49182\n\nEffects of Hydromagnetic and Thermophoresis of Unsteady Forced Convection Boundary Layer Flow over Flat Plates\n\nMd. Jashim Uddin1,2, Md. Yeakub Ali1*\n\n1Department of Mathematics, Chittagong University of Engineering & Technology, Chittagong-4349, Bangladesh\n\n2Department of Electrical & Electronic Engineering, International Islamic University Chittagong, Chittagong-4318, Bangladesh", null, "", null, "", null, "", null, "Received: August 2, 2016; Accepted: September 24, 2016; Published: September 27, 2016\n\nABSTRACT\n\nIn this paper, we analyze unsteady two dimensional hydromagnetic forced convection boundary layer flow of a viscous incompressible fluid along flat plates with thermophoresis. The potential flow velocity has been taken as a function of the distance x and time t. The governing partial differential equations are transformed to ordinary differential equation by applying local similarity transformation. The resulting similarity equations are then solved numerically for unsteady case, applying Nachtsheim-Swigert shooting iteration technique with six order Runge-Kutta method. The variations in fluid velocity, fluid temperature and species concentration are displayed graphically and discussed for different material parameters entering into the analysis. The effects of the pertinent parameters on the skin-friction coefficient, wall heat transfer coefficient and wall deposition flux rate are also displayed in tabulated form and discussed them from the physical point of view. An analysis of the obtained results shows that the flow field is influenced appreciably by the magnetic field parameter and the thermophoresis particle deposition.\n\nKeywords:\n\nForced Convection, Hydromagnetic Field, Similarity Solution, Unsteady, Thermophoresis", null, "1. Introduction\n\nIn recent years, the problems of forced convective boundary layer flow over flat plates with thermophoresis under the influence of a magnetic field have been attracted the attention of a number of researchers because of their possible applications in many branches of science and technology, such as its applications in transportation cooling of re-entry vehicles and rocket boosters, cross-hatching on ablative surfaces and film vaporization in combustion chambers. Forced convective boundary layer flows have a great interest from both theoretical and practical point of views because of its vast and significant applications in cosmic fluid dynamics, solar physics, geophysics, electronics, paper production, wire and fiver coating, composite processing and storage system of agricultural product etc.\n\nThe objective of the present paper is to obtain a local similarity solution of an unsteady two dimensional hydromagnetic forced convective boundary layer flow of a viscous incompressible fluid over flat plates with thermophoresis and be attempted to investigate the effects of several involved parameters on the velocity, temperature, concentration and other flow parameters like the skin-friction coefficient, local Nusselt number (wall heat transfer coefficient) and local Stanton number (wall deposition flux) across the boundary layer.\n\n2. Mathematical Analysis and Governing Equations of the Problem\n\nIn this work, we considered the unsteady, laminar, hydromagnetic combined heat and mass transfer by forced convection flow along a flat plate. With x-axis measured along the plate, a uniform magnetic field", null, "is applied in the y direction which is normal to the flow direction. A heat source is placed within the flow to allow for possible heat generation effects. The fluid is assumed to be Newtonian, electrically conducting and heat generating. The governing continuity, momentum, energy and diffusion equations can be written as:", null, "(1)", null, "(2)", null, "(3)", null, "(4)\n\nwhere", null, "are the velocity components in the x and y directions respectively, v is the kinematic viscosity, g is the acceleration due to gravity,", null, "is the density of the fluid,", null, "is the volumetric coefficient of thermal expansion.", null, "are the temperature of the fluid inside the thermal boundary layer, the plate temperature and the fluid temperature in the free stream, respectively, while", null, "are the corresponding concentrations,", null, "is the electrical conductivity,", null, "is the uniform magnetic field, U is the free stream velocity ,", null, "is the thermal conductivity of fluid,", null, "is the specific heat at constant pressure,", null, "is the heat generation coefficient, D is the molecular diffusivity of the species concentration and", null, "is the thermophoretic velocity. The\n\nthermophoretic velocity", null, "can be written as:", null, "(5)\n\nwhere k is the thermophoretic coefficient and Tref is the reference temperature.\n\nThe appropriate boundary conditions for the above model are as follows:\n\n(6)\n\nand (7)\n\nThe continuity Equation (1) is satisfied by introducing the stream function\n\nsuch that (8)\n\nThe momentum, energy and diffusion Equations (2)-(4) can be transformed to the corresponding ordinary differential equations by introducing the following similarity transformations:\n\n(9)\n\nThe momentum, energy and diffusion Equations (2)-(4) after some simplifications, reduce to the following forms:\n\n(10)\n\n(11)\n\n(12)\n\nwhere, Pr (Prandtl number) = (13)\n\nM (Modified Local Magnetic field Parameter) = (14)\n\nQ (Modified local heat generation Parameter) = (15)\n\nSc (Schmidt number) = (16)\n\nTa (Thermophoretic Parameter) = (17)\n\nThe corresponding boundary conditions are:\n\n(18)\n\nand (19)\n\nwhere the prime ( ) denotes differentiation with respect to.\n\nThe Prandtl number (Pr) or Prandtl group is a dimensionless number and is defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number contains no such length scale in its definition and is dependent only on the fluid and the fluid state. As such, the Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity. For most gases over a wide range of temperature and pressure, Pr is approximately constant. Therefore, it can be used to determine the thermal conductivity of gases at high temperatures, where it is difficult to measure experimentally due to the formation of convection currents. Small values of the Prandtl number, , means the thermal diffusivity dominates. Whereas with large values, , the momentum diffusivity dominates the behavior. In heat transfer problems, the Prandtl number controls the relative thickness of the momentum and thermal boundary layers. When Pr is small, it means that the heat diffuses quickly compared to the velocity (momentum). This means that for liquid metals the thickness of the thermal boundary layer is much bigger than the velocity boundary layer. The mass transfer analog of the Prandtl number is the Schmidt number.\n\nSchmidt number (Sc) is a dimensionless number with important applications to transport phenomena and is defined as the ratio of momentum diffusivity (viscosity) and mass diffusivity and is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer.\n\nThermophoretic parameter is a phenomenon observed in mixtures of mobile par- ticles where the different particle types exhibit different responses to the force of a temperature gradient. Thermophoretic force has been used in commercial precipitators for applications similar to electrostatic precipitators. It is exploited in the manu-fac- turing of optical fiber in vacuum deposition processes. It can be important as a transport mechanism in fouling.\n\nMagnetic field Parameter is a dimensionless number used in magneto fluid dynamics, equal to the product of the square of the magnetic permeability, the square of the magnetic field strength, the electrical conductivity and a characteristic length, divided by the product of the mass density and the fluid velocity. Magnetic fields can be produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property. Magnetic field lines would start or end on magnetic monopoles, so if they exist, they would give exceptions to the rule that magnetic field lines neither start nor end.\n\nA heat generation site is a structure where heat is generated for distribution to other structures and its parameter is known as heat generation parameter. The power consumption and the heat generation in metal cutting processes are dependent on a combination of the physical and chemical properties of the work piece material and cutting tool material, cutting conditions and the cutting tool geometry.\n\nImportant Physical Parameters\n\nThe skin-friction coefficient, local Nusselt number (wall heat transfer coefficient), and local Stanton number (wall deposition flux):\n\nThe parameters of engineering interest for the present problem are the skin-friction coefficient, local Nusselt number and the local Stanton number which indicate physically wall shear stress, rate of heat transfer and wall deposition flux respectively. These can be obtained from the following expressions:\n\nA dimensionless skin-friction coefficient expressing the proportionality between the frictional force per unit area, or the shearing stress exerted by the wind at the earth's surface, and the square of the surface wind speed. Skin friction coefficient is a component of parasitic drag that occurs differently depending on the type of flow over the lifting body (laminar or turbulent). Just like any other form of drag, the coefficient of skin friction drag is calculated with various equations and measurements depending on the flow and then added to coefficients of other forms of drag to calculate total drag.\n\nThe skin-friction coefficient is given by\n\n(20)\n\nIn heat transfer at a boundary (surface) within a fluid, the local Nusselt number is the ratio of convective to conductive heat transfer across (normal division by its area then takes care of the local factor and the normalization). The local Nusselt number analog has on occasion been used to actually.\n\nThe local Nusselt number may be written as\n\n(21)\n\nThe local Stanton number is a dimensionless number that measures the ratio of heat transferred into a fluid to the thermal capacity of fluid. This number arises in the consideration of the geometric similarity of the momentum boundary layer and the thermal boundary layer, where it can be used to express a relationship between the shear force at the wall (due to viscous drag) and the total heat transfer at the wall (due to thermal diffusivity).\n\nThe Stanton number can be written as\n\n(22)\n\nwhere, is the wall shear stress on the surface, be the rate of heat transfer and be the rate of transfer of species concentration.\n\n3. Numerical Solution\n\nThe set of ordinary differential Equations (10) to (12) with boundary conditions (18) and (19) are nonlinear and coupled. A standard initial value solver i.e., the shooting method is used to solve these equations numerically. For this purpose we applied the Nacthsheim-Swigert iteration technique (Nachtsheim and Swigert, 1965) . In the process of iteration the velocity, temperature and concentration profile, the skin-fric- tion coefficient, , local Nusselt number (wall heat transfer coefficient), and local Stanton number (wall deposition flux), are evaluated. The numerical results obtained for several selected values of the established parameters are displayed in graphs and tables below. These graphs and tables show that velocity, temperature, concentration, wall heat transfer coefficient, wall deposition flux and the skin-friction coefficient are affected significantly with the variations of the considered controlling parameters.\n\n4. Results and Discussion\n\nIn order to investigate the physical representation of the problem, the numerical values of velocity field (), temperature field () and concentration () have been computed for resultant for various physical parameters like local heat generation parameter, Schmidt parameter, local magnetic field parameter and thermophoretic parameter. The parameters are chosen arbitrarily where Pr = 0.71 corresponds physically to air at 20˚C, Pr = 1.10 corresponds to electrolyte solution such as salt water and Pr = 7.0 corresponds to water, and Sc = 0.30 for helium and Sc = 0.60 water vapor at approximate 25˚C and 1 atmosphere. In order to get clear insight into the physics of the problem, a representative set of numerical results are shown graphically in Figures 1-15.\n\n4.1. Velocity Profiles\n\nThe dimensionless velocity profiles for the influence of various physical parameters are\n\nFigure 1. Effect of dimensionless velocity profiles across the boundary layer for different values of M and for Pr = 0.71, Q = 2.50, Sc = 0.60, Ta = 0.50.\n\nFigure 2. Effect of dimensionless velocity profiles across the boundary layer for different values of Pr and for M = 1.50, Q = 2.50, Sc = 0.60, Ta = 0.50.\n\npresented in Figures 1-15.\n\nFigure 1 presents typical profiles for the velocity for various values of the local magnetic field parameter, M. The presence of a magnetic field normal to the flow in an electrically conducting fluid introduces a Lorentz force which acts against the flow. This\n\nFigure 3. Effect of dimensionless velocity profiles across the boundary layer for different values of Q and for M = 1.50, Pr = 0.71, Sc = 0.60, Ta = 0.50.\n\nFigure 4. Effect of dimensionless velocity profiles across the boundary layer for different values of Sc and for M = 1.50, Pr = 0.71, Q = 2.50, Ta = 0.50.\n\nresistive force tends to slow down the flow and hence the fluid velocity decreases with the increase of the local magnetic field parameter as observed in Figure 1. Higher the Lorentz force lesser is the velocity. This is true for steady and unsteady cases. This result qualitatively agrees with the expectations, since the magnetic field exerts a retarding\n\nFigure 5. Effect of dimensionless velocity profiles across the boundary layer for different values of Ta and for M = 1.50, Pr = 0.71, Q = 2.50, Sc = 0.60.\n\nFigure 6. Effect of dimensionless temperature profiles across the boundary layer for different values of M and for Pr = 0.71, Q = 2.50, Sc = 0.60, Ta = 0.50.\n\nforce on the forced convection flow.\n\nDue to forced convection flow, the Prandtl number Pr affects the velocity distribution. Figure 2 represents the dimensionless velocity profiles for several values of the\n\nFigure 7. Effect of dimensionless temperature profiles across the boundary layer for different values of Pr and for M = 1.50, Q = 2.50, Sc = 0.60, Ta = 0.50.\n\nFigure 8. Effect of dimensionless temperature profiles across the boundary layer for different values of Q and for M = 1.50, Pr = 0.71, Sc = 0.60, Ta = 0.50.\n\nPrandtl number Pr, the velocity along the plate decreases with increase in Pr. It is evident from the decrease in the velocity profiles along x-direction and y-direction respectively as Pr increases that, the fluid’s velocity components decrease at every point above\n\nFigure 9. Effect of dimensionless temperature profiles across the boundary layer for different values of Sc and for M = 1.50, Pr = 0.71, Q = 2.50, Ta = 0.50.\n\nFigure 10. Effect of dimensionless temperature profiles across the boundary layer for different values of Ta and for M = 1.50, Pr = 0.71, Q = 2.50, Sc = 0.60.\n\nthe surface.\n\nFigure 3 displays the effects of the heat generation parameter Q on the velocity component. This is represented in the increases the fluid velocity as the heat generation parameter Q increases, as seen from Figure 3. This is expected since heat generation (Q >\n\nFigure 11. Effect of dimensionless concentration profiles across the boundary layer for different values of M and for Pr = 0.71, Q = 2.50, Sc = 0.60, Ta = 0.50.\n\nFigure 12. Effect of dimensionless concentration profiles across the boundary layer for different values of Pr and for M = 1.5, Q = 2.50, Sc = 0.60, Ta = 0.50.\n\n0) causes the thermal boundary layer to become thicker and the fluid become warmer.\n\nThe influences of the Schmidt number, Sc on the velocity profiles are plotted in Figure 4. The Schmidt number embodies the ratio of the momentum to the mass diffusivity.\n\nFigure 13. Effect of dimensionless concentration profiles across the boundary layer for different values of Q and for M = 1.5, Pr = 0.71, Sc = 0.60, Ta = 0.50.\n\nFigure 14. Effect of dimensionless concentration profiles across the boundary layer for different values of Sc and for M = 1.5, Pr = 0.71, Q = 2.50, Ta = 0.50.\n\nThe Schmidt number therefore quantifies the relative effectiveness of momentum and mass transport by diffusion in the hydrodynamic (velocity). As the Schmidt number\n\nFigure 15. Effect of dimensionless concentration profiles across the boundary layer for different values of Ta and for M = 1.5, Pr = 0.71, Q = 2.50, Sc = 0.60.\n\nincreases the velocity increases.\n\nFigure 5 exhibits the behavior of dimensionless velocity profiles for some the values of the thermophoretic parameter Ta. From this figure it is clear that the fluid velocity increases rapidly with the increase of the thermophoretic parameter Ta.\n\n4.2. Temperature Profiles\n\nThe dimensionless temperature profiles are presented in Figures 6-10.\n\nFor different values of the magnetic field parameter M on the temperature profiles are plotted in Figure 6. It is observed that the temperature profile slightly decrease with the increase of magnetic field parameter. Therefore, an applied magnetic field can be used to control the flow, rotation of micro-constituents and heat transfer characteristics.\n\nFigure 7 illustrates the temperature profiles for different values of the Prandtl number Pr.\n\nPrandtl number defines the relative effectiveness of the momentum transport by diffusion in the hydrodynamic boundary layer to the energy transported by thermal diffusion in the thermal boundary layer. According to the definition of Prandtl number high Pr fluids possess lower thermal conductivities which reduce the conduction heat transfer and increases temperature variations at the wall. The Prandtl number defines the ratio of momentum diffusivity to thermal diffusivity. This figure reveals that an increase in Prandtl number Pr results in a decrease in the temperature distribution, because, thermal boundary layer thickness decreases with an increase in Prandtl number, Pr.\n\nFrom Figure 8, we observe that when the value of the heat generation parameter, Q increases, the temperature distribution also increases significantly which implies that owing to the presence of a heat source, the thermal state of the fluid increases causing the thermal boundary layer to increase.\n\nThe influence of the Schmidt number on the temperature is presented in Figure 9. From this fig. we see that the temperature monotonically decreases with an increase of Schmidt number, Sc.\n\nThe dimensionless temperature profiles along x-direction for different values of Ta are presented in the Figure 10 and also showing the effects of the thermophoretic parameter, Ta. It is observed that the temperature profiles decrease with the increase of the thermophoretic parameter, Ta.\n\n4.3. Concentration Profiles\n\nIn order to gain physical insight of the problem, the numerical results for the dimensionless concentration profiles have been presented graphically in Figures 11-15.\n\nThe effect of the local magnetic field parameter (M) on concentration fields have shown in Figure 11. In Figure 11, the effect of an applied magnetic field is found to decrease the concentration profiles, and hence increase the concentration boundary layer with the increasing of magnetic field parameter (M).\n\nFrom Figure 12, we can ascertain that the isotherms are almost linear and distributed inside the cavity for Pr = 0.71, which is due to the combined effect of conduction and forced convection. From this Figure 12, we observe that the temperature profiles increase swiftly with the increase of the Prandtl number (Pr).\n\nIn Figure 13, we have plotted the variation of the dimensionless concentration distribution for different values of Q and also showing the effects of the local heat generation parameter Q. It is seen from Figure 13 that when the heat is generated, the buoyancy force increase, which induces the flow rate to increase giving, rises to the increase in the concentration profiles. On the other hand, we see that the concentration profiles increase rapidly while the concentration boundary layer decreases as the heat generation parameter Q increases.\n\nFigure 14 displays the variation of dimensionless concentration profiles for several value of Schmidt number, Sc. The Schmidt number embodies the ratio of the momentum to the mass diffusivity. The Schmidt number therefore quantifies the relative effectiveness of momentum and mass transport by diffusion in the concentration (species) boundary layers. As the Schmidt number increases the concentration also increases. This causes the concentration buoyancy effects to increase yielding a reduction in the fluid velocity.\n\nThe effect of the thermophoretic parameter (Ta) on concentration field is presented in the Figure 15. From Figure 15, it is noticed that the effect of increasing the thermophoretic parameter (Ta) increasing slightly the wall slope of the concentration profiles.\n\nThe skin-friction coefficient, , local Nusselt number (wall heat transfer coefficient), and local Stanton number (wall deposition flux), are important physical parameters .These tables are given below.\n\nThe numerical results are illustrated in Tables 1-5 for the effect of various parameters on the Skin-friction coefficient, local Nusselt number, and local Stanton number. From Table 1, it is clear that the Skin-friction coefficient and the local Nusselt number increases while the local Nusselt number decreases with the increases of the local Magnetic field parameter (M). From Table 2 and Table 5, it is clear that the Skin-friction\n\nTable 1. Skin-friction coefficient, , local Nusselt number (wall heat transfer coefficient), and local Stanton number (wall deposition flux), for different values of M.\n\nTable 2. Skin-friction coefficient, , local Nusselt number (wall heat transfer coefficient), and local Stanton number (wall deposition flux), for different values of Pr.\n\nTable 3. Skin-friction coefficient, , local Nusselt number (wall heat transfercoefficient), and local Stanton number (wall deposition flux), for different values of Q.\n\nTable 4. Skin-friction coefficient, , local Nusselt number (wall heat transfer coefficient), and local Stanton number (wall deposition flux), for different values of Sc.\n\nTable 5. Skin-friction coefficient, , local Nusselt number (wall heat transfer coefficient), and local Stanton number (wall deposition flux), for different values of Ta.\n\ncoefficient and the local Nusselt number decrease while the local Nusselt number increases with the increase of the Prandtl number (Pr) and the Thermophoretic parameter (Ta) respectively. For the the increases of local heat generation parameter (Q), the Skin-friction coefficient and the local Stanton number decrease while the local Nusselt number inccreases in Table 3. In Table 4 revels that the Skin-friction coefficient and the local Stanton number increase while the local Nusselt number decrease with the increase of Schmidt number (Sc).\n\nIn the presence of a magnetic field, the fluid velocity is found to be decreased, associated with a reduction in the velocity gradient at the wall, and thus the local skin-fric- tion coefficient decreases. Also, the applied magnetic field tends to decrease the wall temperature gradient and concentration gradient, which yield a decrease the local Nusselt number and the local Stanton number. The local skin friction coefficient as well as rate of heat transfer in the micropolar fluid is lower compared to that of the Newtonian fluid. The above table is highly significant influences of on skin friction, the rate of heat transfer and wall deposition flux have been found which can be physically realizable.\n\n5. Conclusions\n\nIn this paper, we have discussed the effects of thermophoresis on an unsteady two dimensional forced convective heat and mass transfer boundary layer flow over flat plates. The results are analyzed for various physical parameters such as local magnetic field parameter, Prandtl number, Schmidt number, local heat generation parameter, magnetic parameter, thermophoretic parameter, heat and mass transfer characteristics. The numerical results have been presented in the form of graphs and tables. The particular conclusions drawn from this study can be listed as follows:\n\n・ Thermophoretic particle deposition velocity decreases with the increasing values of the thermophoretic coefficient and concentration ratio where as it increases with the increasing values of the thermophoresis parameter.\n\n・ The plate couple stress increases with the increase values of the magnetic field parameter.\n\n・ Magnetic field significantly controls the flow, rotation of micro-constituents and heat transfer characteristics of a micropolar fluid.\n\n・ Magnetic field retards the motion of the fluid.\n\n・ Thermophoresis is an important mechanism of micro-particles transport due to a temperature gradient in the surrounding medium and has found numerous applications, especially in the field of aerosol technology and industrial air pollution.\n\n・ The Prandtl number as well as the Schmidt number varies significantly within the boundary layer when the thermal conductivity is temperature dependent.\n\n・ In forced convection regime, the surface mass flux increases with the increase of the thermophoretic parameter.\n\n・ The local skin friction coefficient, Nusselt number and Sherwood number are higher for the fluids of constant electric conductivity than those of the variable electric conductivity.\n\n・ The velocity profiles increase whereas temperature profiles decrease with an increase of the forced convection current.\n\n・ Concentration within the boundary-layer decreases with the increasing values of the thermophoretic parameter whereas it increases as increases the thermophoretic coefficient as well as the concentration ratio.\n\nCite this paper\n\nUddin, M.J. and Ali, M.Y. (2016) Effects of Hydromagnetic and Thermophoresis of Unsteady Forced Convection Boundary Layer Flow over Flat Plates. Journal of Applied Mathematics and Physics, 4, 1756-1776. http://dx.doi.org/10.4236/jamp.2016.49182\n\nReferences\n\n1. 1. Duwairi, H.M. and Damesh, R.A. (2008) Effects of Thermophoresis Particle Deposition on Mixed Convection from Vertical Surfaces Embedded in Saturated Porous Medium. International Journal of Numerical Methods for Heat & Fluid Flow, 18, 202-216.\nhttp://dx.doi.org/10.1108/09615530810846347\n\n2. 2. Postelnicu, A. (2012) Thermophersis Partical Deposition in Natural Convection over Inclined Surfaces in Porus Media. International Journal of Heat and Mass Transfer, 55, 2087-2094. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.12.011\n\n3. 3. Goren, S.L. (1977) Thermophoresis of Aerosol Particles in the Laminar Boundary Layer on a Flat Surface. 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ARPN Journal of Engineering and Applied Science, 7, 731-739.\n\n8. 8. Seth, G.S. and Ansari, M.S. (2010) MHD Natural Convection Flow Past an Impulsively Moving Vertical Plate with Ramped Wall Temperature in the Presence of Thermal Diffusion with Heat Absorption. International Journal of Applied Mechanics and Engineering, 15, 199-215.\n\n9. 9. Nandkeolyar, R. and Das, M. (2013) Unsteady MHD Free Convection Flow of a Heat Absorbing Dusty Fluid Past a Flat Plate with Ramped Wall Temperature. Afrika Matematika, 25, 779-798.\nhttp://dx.doi.org/10.1007/s13370-013-0151-9\n\n10. 10. Kim, Y.J. (2000) Unsteady MHD Con-vective Heat Transfer past a Semi-Infinite Vertical Porous Moving Plate with Variable Suction. International Journal of Engineering Science, 38, 833-845.\nhttp://dx.doi.org/10.1016/S0020-7225(99)00063-4\n\n11. 11. Ishak, A., Nazar, R. and Pop, I. (2008) MHD Boundary Layer Flow of a Micropolar Fluid Past a Wedge with Variable Wall Temperature. Acta Mechanica, 196, 75-86.\nhttp://dx.doi.org/10.1007/s00707-007-0499-8\n\n12. 12. Elbashbeshy, E.M.A., Bazid, M.A. and Aldawody, D.A. (2011) Effect of Magnetic Field on Boundary Layer Flow over an Unsteady Stretching Surface in a Micropolar Fluid. International Journal of Heat and Technology, 29, 69-74.\n\n13. 13. Alam, M.S. and Chapal Hossain, S.M. (2013) A New Similarity Approach for an Unsteady Two Dimensional Forced Convective Flow of a Micropolar Fluid along a Wedge. International Journal of Applied Mathematics and Mechanics, 9, 75-89.\n\n14. 14. Jia, G., Cipolla, J.W. and Yener, Y. (1992) Thermophoresis of a Radiating Aerosol in Laminar Boundary Layer Flow. Journal of Thermophysics and Heat Transfer, 6, 476-482.\nhttp://dx.doi.org/10.2514/3.385\n\n15. 15. Chiou, M.C. and Cleaver, J.W. (1996) Effect of Thermophoresis on Submicron Particle Deposition from a Laminar Forced Convection Boundary Layer Flow on to an Isothermal Cylinder. Journal of Aerosol Science, 27, 1155-1167.\nhttp://dx.doi.org/10.1016/0021-8502(96)00045-6\n\n16. 16. Selim, A., Hossain, M.A. and Rees, D.A.S. (2003) The Effect of Surface Mass Transfer on Mixed Convection Flow Past a Heated Vertical Flat Permeable Plate with Thermophoresis. International Journal of Thermal Sciences, 42, 973-982.\nhttp://dx.doi.org/10.1016/S1290-0729(03)00075-9\n\n17. 17. Seth, G.S. and Sarker, S. (2015) Hydromagnetic Natural Convection Flow with Induced Magnetic Field and nth Order Chemical Reaction of a Heat Absorbing Fluid Past an Impulsively Moving Vertical Plate with Ramped Temperature. Bulgarian Chemical Communications, 47, 66-79.\n\n18. 18. Parvin, S., Nasrin, R., Alim, M.A. and Hossain, N.F. (2013) Effect of Prandtl Number on Forced Convection in a Two Sided Open Enclosure Using Nanofluid. Journal of Scientific Research, 5, 67-75.\n\n19. 19. Chamkha, A.J. (2004) Unsteady MHD Convective Heat and Mass Transfer past a Semi-Infinite Vertical Permeable Moving Plate with Heat Absorption. International Journal of Engineering Science, 42, 217-230.\nhttp://dx.doi.org/10.1016/S0020-7225(03)00285-4\n\n20. 20. Jhankal, A.K. and Kumar, M. (2013) MHD Boundary Layer Flow Past a Stretching Plate With Heat Transfer. International Journal of Engineering Science, 2, 9-13.\n\n21. 21. Bhattacharyya, K. (2012) Mass Transfer on a Continuous Flat Plate Moving in Parallel or Reversely to a Free Stream in the Presence of a Chemical Reaction. International Journal of Heat and Mass Transfer, 55, 3482-3487.\nhttp://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.03.005\n\n22. 22. Kuiry, D.R. and Bahadur, S. (2015) Steady MHD Flow of Viscous Fluid between Two Parallel Porous Plates with Heat Transfer in an Inclined Magnetic Field. Journal of Scientific Research, 7, 21-31.\nhttp://dx.doi.org/10.3329/jsr.v7i3.22574\n\n23. 23. Khan, M.S., Alam, M.M. and Ferdows, M. (2013) Effects of Magnetic Field on Radiative Flow of a Nanofluid Past a Stretching Sheet. Procedia Engineering, 56, 316-322.\nhttp://dx.doi.org/10.1016/j.proeng.2013.03.125\n\n24. 24. Noor, N.F.M., Abbasbandy, S. and Hashim, I. (2012) Heat and Mass Transfer of Thermophoretic MHD Flow over an Inclined Radiate Isothermal Permeable Surface in the Presence of Heat Source/Sink. International Journal of Heat and Mass Transfer, 55, 2122-2128.\nhttp://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.12.015\n\n25. 25. Haddad, Z., Nada, A., Oztop, F. and Mataoui, A. (2012) International Journal of Thermal Sciences, 57, 152-162.\nhttp://dx.doi.org/10.1016/j.ijthermalsci.2012.01.016\n\n26. 26. Khaleque, S.T. and Samad, M.A. (2010) Effects of Radiation, Heat Generation and Viscous Dissipation on MHD Free Convection Flow along a Stretching Sheet. Research Journal of Applied Sciences, Engineering and Technology, 2, 368-377." ]
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https://arxiv.org/abs/1605.08094
[ "# Title:$\\mathcal{N}=2$ Super-Teichmüller Theory\n\nAbstract: Based on earlier work of the latter two named authors on the higher super-Teichmueller space with $\\mathcal{N}=1$, a component of the flat $OSp(1|2)$ connections on a punctured surface, here we extend to the case $\\mathcal{N}=2$ of flat $OSp(2|2)$ connections. Indeed, we construct here coordinates on the higher super-Teichmueller space of a surface $F$ with at least one puncture associated to the supergroup $OSp(2|2)$, which in particular specializes to give another treatment for $\\mathcal{N}=1$ simpler than the earlier work. The Minkowski space in the current case, where the corresponding super Fuchsian groups act, is replaced by the superspace $\\mathbb{R}^{2,2|4}$, and the familiar lambda lengths are extended by odd invariants of triples of special isotropic vectors in $\\mathbb{R}^{2,2|4}$ as well as extra bosonic parameters, which we call ratios, defining a flat $\\mathbb{R}_{+}$-connection on $F$. As in the pure bosonic or $\\mathcal{N}=1$ cases, we derive the analogue of Ptolemy transformations for all these new variables.\n Comments: v2: 41 pages, published version Subjects: Geometric Topology (math.GT); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Differential Geometry (math.DG) Journal reference: Advances in Mathematics 336 (2018) 409-454 DOI: 10.1016/j.aim.2018.08.001 Cite as: arXiv:1605.08094 [math.GT] (or arXiv:1605.08094v2 [math.GT] for this version)\n\n## Submission history\n\nFrom: Anton Zeitlin [view email]\n[v1] Wed, 25 May 2016 22:22:48 UTC (32 KB)\n[v2] Sun, 25 Nov 2018 03:34:45 UTC (35 KB)" ]
[ null ]
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https://open.library.ubc.ca/cIRcle/collections/ubctheses/24/items/1.0066987
[ "# Open Collections\n\n## UBC Theses and Dissertations", null, "## UBC Theses and Dissertations\n\n### Optimal design of over-the-counter derivatives in a principal-agent framework : an existence result and… Moreno-Bromberg, Santiago 2008\n\nMedia\n24-ubc_2008_fall_moreno-bromberg_santiago.pdf [ 1.9MB ]\nJSON: 24-1.0066987.json\nJSON-LD: 24-1.0066987-ld.json\nRDF/XML (Pretty): 24-1.0066987-rdf.xml\nRDF/JSON: 24-1.0066987-rdf.json\nTurtle: 24-1.0066987-turtle.txt\nN-Triples: 24-1.0066987-rdf-ntriples.txt\nOriginal Record: 24-1.0066987-source.json\nFull Text\n24-1.0066987-fulltext.txt\nCitation\n24-1.0066987.ris\n\n#### Full Text\n\n`Optimal Design of Over-the-counter Derivatives in a Principal-Agent Framework An Existence Result and Numerical Implementations by Santiago Moreno-Bromberg B.Sc., National University of Mexico, 2000 M.Sc., CINVESTAV del IPN, 2004 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in The Faculty of Graduate Studies (Mathematics) The University Of British Columbia (Vancouver) August, 2008 © Santiago Moreno-Bromberg 2008 Abstract This work lies in the intersection of Mathematical Finance, Mathematical Economics and Convex Analysis. In terms of the latter, a new result (to the author’s knowledge) on a Lipschitz property of the derivatives of a convex function is presented in the first chapter. An important result on its own, it might also provide a stepping stone to an extension to Hubert spaces of Alexandrov’s theorem on the second derivatives of convex functions. The second chapter considers the problem of Adverse Selection and op timal derivative design within a Principal-Agent framework. The principal’s income is exposed to non-hedgeable risk factors arising, for instance, from weather or climate phenomena. She evaluates her risk using a coherent and law invariant risk measure and tries to minimize her exposure by selling derivative securities on her income to individual agents. The agents have mean-variance preferences with heterogeneous risk aversion coefficients. An agent’s degree of risk aversion is private information and the principal only knows their overall distribution. It is shown that the principal’s risk mini mization problem has a solution and, in terms of the pricing schedule, the latter is unique. Finding a solution to the principal’s problem requires solving a varia tional problem with global convexity constraints. In general, this cannot be done in closed form. To this end an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions is presented in the fourth chapter of this work. Several examples are provided. 11 Table of Contents Abstract Table of Contents ii II’ List of Tables vi List of Figures . vu Acknowledgements Dedication 1 Introduction yin ix 1 8 8 20 21 22 the Revelation and Tax- 3 Optimal Derivative Design 3.1 The microeconornic setup 3.2 Solving the principal’s problem 3.2.1 Minimizing the risk for a given function v 22 24 27 Convex Analysis 2 Preliminaries . 2.1 Some results in 2.2 U-Convexity 2.3 Some Contract Theory 2.3.1 Mechanism Design 2.3.2 Principal-Agent models and ation Principles 2.3.3 A standard screening model 2.4 Risk measures in L2 31 31 34 39 ill Table of Contents 3.2.2 Minimizing the overall risk 43 3.3 A characterization of optimal contracts 49 3.3.1 The Lagrangian and the characterization 50 3.3.2 An application to entropic risk measures 52 3.4 Example: A single benchmark claim 53 3.4.1 Description of the constrained claims 54 3.4.2 The optimization problem 54 3.4.3 A solution to the principal’s problem 55 4 An Algorithm to Solve Variational Problems with Convexity Constraints 59 4.1 Setup 60 4.2 Description of the algorithm 61 4.3 Convergence of the algorithm 62 4.4 Examples 68 4.4.1 The Mussa-Rosen problem in a square 68 4.4.2 The Mussa-Rosen problem with a non-uniform density of types 69 4.4.3 An example with non-quadratic cost 71 4.4.4 Minimizing risk 72 4.5 A catalogue of put options 76 4.5.1 An existence result 77 4.5.2 An algorithm for approximating the optimal solution 78 5 Conclusions 83 Bibliography 85 Appendices A Matlab and Maple Codes 90 A.1 MatLab code for the example in Section 4.4.1 90 A.2 MatLab code for the example in Section 4.4.2 93 A.3 MatLab code for the example in Section 4.4.3 94 iv Table of Contents A.4 MatLab code for the example in Section 4.4.4 98 A.5 Maple code for the example in Section 4.5.2 102 V List of Tables 4.1 The optimal function v and the strikes. Entropic case . . 76 4.2 The optimal function v and the strikes. Case 1 80 4.3 The optimal function V and the strikes. Case 2 81 vi List of Figures 4.1 Optimal solution for uniformly distributed agent types . 70 4.2 Optimal solution for normally distributed agent types 71 4.3 The optimal function Y 72 4.4 Optimal solution for underwriting call options. Entropic case 75 4.5 Optimal solution for underwriting put options, Case 1 80 4.6 Optimal solution for underwriting put options. Case 2 82 vii Acknowledgements I would like to thank Professor Ivar Ekeland for having given me the oppor tunity to come to UBC, for all that he has taught me, for the guidance he has given me and for being such a magnanimous person. I would also like to acknowledge the support Professor Ulrich Horst has given me, as well as the time he dedicated to many fruitful discussions we have had. Professor Guillaume Carlier has always been generous in sharing his knowledge and deep insight on many topics, which I sincerely appreciate. Professors Pierre André Chiappori, Ulrich Haussman, Yves Lucet and Michael Peters have been great role models for me. I thank them for their kindness, patience and thoroughness when answering my questions. I would like to acknowl edge the help and support I have received from the faculty and staff in the Mathematics Department at UBC, the Pacific Institute for the Mathemat ical Sciences and the Mathematics Department at CINVESTAV, especially Professors Alejandro Adem, Isidoro Gitler and Onésimo I-Iernández-Lerma. I can not leave my office mates unmentioned: Au, Amir, Bruno, Enrique, German, Gilles, José, Michele and Ramón. I have discussed Math with them, shared good and not-so-good times together, and learned about the World in the process. Finally, I would like to express my gratitude to the Mexican Council for Science and Technology for its financial support. vi” Dedication A aquellos que con su cariño y apoyo han hecho posible este trabajo. Es innecesario nombrarlos, ustedes saben quienes son. ix Chapter 1 Introduction The origins of the theory of asset pricing can be traced back to the early work of F. Black, M. Scholes and R. Merton. Their work led to the arbitrage paradigm for pricing financial derivatives. Two essential assumptions of this theory are market completeness and the fact that the underlying assets are liquidly traded in the financial market. To a certain extent, products written on companies’ equity can be priced in a satisfactory manner using arbitrage arguments. The latter transform the problem of pricing a certain derivative into replicating the products’ payoffs using the underlying assets. When such replication is not possible, either due to incompleteness of the market or the unavailablity of the assets required to form a hedging portfolio, then alternative pricing mechanisms must be used. An example of such a scenario is the pricing of weather derivatives. The history of financial derivatives whose underlying is the weather dates back to 1996 with the famous contract between Aquila Energy and Consol idated Edison Co. From that point on, trading on these kinds of contract started to gain momentum, first with Enron’s EnronOnline Unit and then with their introduction in the Chicago Mercantile Exchange in 1999. Other financial products based on non-tradeable risk include Collateralized Mort gage Obligations (first issued by Fannie Mae in 1985), Asset Backed Securi ties and Risk bonds. All these STRUCTURED PRODUCTS are the end-result of a process known as SECURITIZATION, which transfers risk into the financial markets. The idea of pooling and underwriting risk that cannot be hedged through investments in the capital markets alone has long become a key factor driving the convergence of insurance and financial markets. As these products became more popular, and given that they fall outside the scope of the traditional pricing-by-replication arguments, the need for an adequate 1 Chapter 1. Introduction pricing theory became evident. Structured products are often written on non-tradable underlyings, tai lored to the issuers specific needs and traded “over the counter”. Insurance companies, for instance, routinely sell weather derivatives or risk bonds to customers that cannot go to the capital markets directly and/or seek finan cial securities with low correlation with stock indices as additions to diversi fied portfolios. The market for such claims is generally incomplete and illiq uid. In such a market framework, preference-based valuation principles that take into account characteristics and endowment of trading partners may be more appropriate for designing, pricing and hedging contingent claims. These valuation principles have become a major topic of current research in economics and financial mathematics. They include rules of Pareto opti mal risk allocation (, ), market completion and dynamic equilibrium pricing (, ) and, in particular, utility indifference arguments (, , , , , ...). The latter assumes a high degree of market symmetry. For indifference valuation to be a pricing rather than valuation principle, the de rnand for a financial security must come from identical agents with known preferences and negligible market impact while the supply must come from a single principal. When the demand comes from heterogeneous individuals with hidden characteristics, indifference arguments do not always yield an appropriate pricing scheme. This work deviates from the assumption of investor homogeneity and al lows for heterogeneous agents. The model considers a single principal with a random endowment whose goal is to lay off some of her risk with hetero geneous agents by designing and selling derivative securities on her income. The agents have mean variance preferences. An agent’s degree of risk aver sion is private information, i.e. hidden from the principal. However, the principal does know the distribution of the risk aversion coefficients. This setting puts the principal at an informational disadvantage. If all the agents were homogeneous, the principal, when offering a structured product to a single agent, could extract the indifference (maximum) price from each trad ing partner. In the presence of agent heterogeneity this is no longer possible, either because the agents would hide their characteristics from the princi 2 Chapter 1. Introduction pal or prefer another asset offered by the principal but designed and priced for another customer. The latter would render the principal’s knowledge of the distribution of the agents’ types useless. The principal therefore needs to design a catalogue of derivatives and price them as to achieve the sec ond best solution. Although the problem of optimal mechanism design in principal-agent games is a standard problem of economic theory, it has only recently been applied to structured products. The problem of optimal derivative design in a Principal-Agent framework with informed agents and an uninformed principal has first been addressed in a recent paper by Carlier, Ekeland and Touzi . With the agents being the informed party, theirs is a screening model. The literature on screen ing within the Adverse Selection framework can be traced back to Mussa and Rosen , where both the principal’s allocation rule and the agents’ types are one-dimensional. Armstrong relaxes the hypothesis of agents being characterized by a single parameter. He shows that, unlike the one- dimensional case, “bunching” of the first type is robust when the types of the agents are multi-dimensional. In their seminal paper, Rochet and Choné further extend this analysis. They provide a characterization of the con tracts, determined by the (non-linear) pricing schedule, that maximize the principal’s utility under the constraints imposed by the asymmetry of infor mation in the models. Building on their work, Carlier, Ekeland and Touzi study a Principal-Agent model of optimal derivative design where the agents’ preferences are of mean-variance type and their multi-dimensional types characterize their risk aversions and initial endowments. They assume that there is a direct cost to the principal when she designs a contract for an agent, and that the principal’s aim is to maximize profits. This work starts from a similar set-up, but the idea that providing prod ucts carries a cost is substituted for the idea that traded contracts expose the principal to additional risk, as measured by a convex risk measure, in exchange for a known revenue. This may be viewed as a partial extension of the work by Barrieu and El Karoui (, ) to an incomplete information framework. The principal’s aim is to minimize her risk exposure by trading with the 3 Chapter 1. Introduction agents subject to the standard incentive compatibility and individual ratio nality conditions on the agents’ choices. In order to prove that the principal’s risk minimization problem has a solution incentive compatible catalogues are characterized in terms of U-convex functions. When the impact of a single trade on the principal’s revenues is linear as in Carlier, Ekeland and Touzi , the link between incentive compatibility and U-convexity is key to es tablish the existence of an optimal solution. In the model presented here, the impact is non-linear as a single trade has a non-linear impact on the principal’s risk assessment. This non-linearity is reflected in a non-standard variational problem where the objective cannot be written as the integral of a given Lagrangian. Instead, this problem can be decomposed into a standard variational part representing the aggregate income of the principal, plus the minimization of the principal’s risk evaluation, which depends on the ag gregate of the derivatives traded. This non-standard formulation not with standing, the principal’s problem can be considered within the framework of variational problems subject to global convexity constraints. Sufficient conditions that guarantee that the principal’s optimization problem has a (unique) solution are given, as well as a partial (implicit) characterization of the optimal contracts. Since the principal’s problem can only be solved in closed form in very particular cases, this work also includes an algorithm to tackle variational problems with convexity constraints. Arguably, Newton’s problem of the body of minimal resistance is the original problem of this kind. It con sists of finding the shape of a solid that encounters the least resistance when moving through a fluid. This is equivalent to finding a convex func tion from a convex domain (originally a disk) in ]R2 to JR that minimizes a certain functional (see Section 4). Newton’s original “solution” assumed radial symmetry. This turned out to be false, as shown by Brock, Ferone and Kawohl in , which sparked, new interest to the study of variational problems with convexity constraints. One can also find these kinds of prob lems in finance and economics. Starting in 1978 with the seminal paper of Mussa and Rosen [39j, the study of non-linear pricing as a means of mar ket screening under Adverse-Selection has produced a considerable stream 4 Chapter 1. Introduction of contributions (, , ,...). In models where goods are described by a single quality and the set of agents is differentiated by a single parameter, it is in general possible to find closed form solutions for the pricing schedule. This is, however, not the case when multidimensional consumption bundles and agent types are considered. Although Rochet and Choné provided conditions for the existence of an optimal pricing rule and fully characterized the ways in which markets differentiate in a multidimensional setting, they also pointed out that it is only in very special cases that one can expect to find closed form solutions. The same holds true for models where the set of goods lies in an infinite-dimensional space, even when agent types are one-dimensional. Given that a great variety of problems, such as product lines design, op timal taxation, structured derivatives design, etc. can be studied within the scope of these models, there is a clear need for robust and efficient numer ical methods that approximate their optimal pricing schedules. Note that this also provides an approximation of the optimal “products”. Most of the papers mentioned above eventually face solving a variational problem under convex constraints. This family of problems has lately been studied under different perspectives. Carlier and Lachand-Robert have studied the C’ regularity of minimizers when the functional is elliptic and the admissible functions satisfy a Dirichiet-type boundary condition. Lachand-Robert and Pelletier characterize the extreme points of a functional depending only on Vf over a set of convex functions with uniform convex bounds. The algorithm presented in this work is based on the idea of approximat ing a convex function by an affine envelope, to solve variational problems under convexity constraints. This deviates from previous work by Choné and Hervé and Carlier, Lachand-Robert and Maury , where the au thors use finite element methods. In the former case, a conformal (interior) method is used and a non-convergence result is given. As a consequence, the latter uses an exterior approximation method, which is indeed found to be convergent in the classical projection problem in H. Lachand-Robert and Oudet present in an algorithm for minimizing functionals within convex bodies that shares some similarities to the one presented here. For a 5 Chapter 1. Introduction particular problem, they start with an admissible polytope and iteratively modify the normals to the facets in order to find an approximate minimizer. In the process of gathering and generating the theory on convex functions required for the proof of convergence of the algorithm, several interesting results were found. The one that stands out is that the Fréchet derivatives of a convex function mapping a Hubert space into the Real numbers are locally Lipschitz on a dense subset. This builds on the celebrated result by Ekeland and Lebourg that states that convex functions defined on Banach spaces that accept a differentiable norm (off the origin) are Fréchet differentiable on a dense G3 set. In this work, the minimizers for several problems with known, closed form solutions are studied as a means of comparing the output of the algo rithm to the true solutions. These are taken from and . Then two risk minimization models are explored. The first one reduces to a non-linear program and falls within the scope of the algorithm. The second one re quires de computation of a minimax point and therefore requires a modified approach, which nevertheless still follows the philosophy of approximating a convex function by the envelope of a family of affine functions. It should be noted that the results contained in this thesis stem from work in progress by Ivar Ekeland and the author (Chapter 2) and the papers of the author and Ulrich Horst , which will appear in Mathematics and Financial Economics (Chapter 3), and Ivar Ekeland , which has been submitted to Numerische Mathematik (Chapter 4). The remainder of this work is organized as follows: Chapter 2 is divided into four sections. First a presentation of properties of convex functions to be used in the following two chapters is given. This section starts with well know facts and ends with the new (to the author’s knowledge) result that the derivatives of a convex function from a Hubert space into the Real num bers are densely Lipschitz. The latter is given as Corollary 2.1.19. Second is some standard theory on U-convex functions. Third a brief crash course in Mechanism Design. Finally a description of Convex Risk measures and some of their more useful (for this work’s purposes) properties. Chapter 3 presents a pricing method for over-the-counter financial derivatives to be 6 Chapter 1. Introduction traded between a single seller (the Principal) and a continuum of buyers (the Agents). The Principal evaluates the performance of her pricing sched ule via a convex risk measure. The main result in this chapter, Theorem 3.1.3, is one of existence and (partial) uniqueness of a pricing rule. Chapter 4 presents an algorithm to estimate the solutions of variational problems subject to convexity constraints. These include, but are not limited to, problems found in the previous chapter. A proof of convergence, Theorem 4.3.7, and various examples are provided. Finally, all the computer code is given in the Appendix. 7 Chapter 2 Preliminaries This work lies in the intersection of the Theory of Contracts and Convex Analysis. The purpose of this chapter is to provide the reader with the sufficient theory from these fields. It must be noted that some of the results contained in the section devoted to Convex Analysis are not used in the following chapters. However, they have been included to provide a broader view of some powerful (and beautiful) properties of convex functions. Special attention is called to Corollary 2.1.19, which states that the derivatives of a convex function defined on a Hubert space are densely locally Lipschitz. Although the theory of Convex Risk Measures can be set within that of Convex Analysis, this topic is treated in a separate section. 2.1 Some results in Convex Analysis This Section contains the theory on convex functions used throughout this work. In this case, the domains considered are subsets of Hubert spaces. The results on existence of optimal derivatives are set in L2 of a particular probability space, whereas the work on numerical methods is set in R’. In what follows H denotes a separable Hilbert space. Definition 2.1.1 A convex function f : H —* JR is said to be PROPER if f> —oc and f is not identically +oo. Definition 2.1.2 Given a convex function f : H —+ IR, the set Dom(f) := {x e H 1 If(x)I <oo} is called the EFFECTIVE DOMAIN off. The following characterization of proper, lower sernicontinuous convex functions plays a central role: 8 Chapter 2. Preliminaries Proposition 2.1.3 Let f : H —p R be a proper, lower semi-continuous con vex function. Then there is another convex, lower semi-continuous function f* such that f(x) = sup {(x,y) — f*(y)} (2.1) yEH f is then called the CONVEX CONJUGATE of f* (and viceversa). Any proper, lower semicontinuous convex function f satisfies f = (f*)*. The set Of(x) := {y E H I f(x) = (x,y) — f*(y)} is called the SUBDIFFERENTIAL of f at x. In what follows and unless noted otherwise, f : H —* R will be a proper, lower semi-continuous convex func tion. Notice that the set epi(f) := {(x,r) xe H, r f(x)}, which is called the EPIGRAPH of f is a closed and convex set. Since H is reflexive then epi(f) is weakly closed. Proposition 2.1.4 f remains lower semicontinuous with respect to weak (u(H, H*)) convergence. Proposition 2.1.4 can be used to prove the following useful result that will appear in Chapters 3 and 4. Proposition 2.1.5 Assume C C H is a closed and bounded convex set. Then the minimization problem inf f(x) has at least one solution. PROOF. Let {x} beaminimizing sequence offonCand let a = infecf(x). Since C is closed, bounded and convex there is a subsequence {x,-k} and e C such that Xk converges weakly to It follows from Proposition 2.1.4 9 Chapter 2. Preliminaries that f() liminf f(xflk) = a flk—OO so is a minimizer. D Proposition 2.1.6 Let 7(f) be the interior of Dom(f). Then (i) Of (x) # 0 for any x E 7(f), (ii) f is continuous on 7(f). In fact, it is locally Lipschitz. The following proposition shows that the supremum in equation (2.1) can actually be taken over a bounded set for points in 7(f). Proposition 2.1.7 Define for anya 0 B(x,a) := {y e H I lix—yll <a}. Let x e 7(f), then there exists e > 0 such that the set {y*EH I f(y)=(y,y*)_f*(y*)} is bounded for all y E B(x, e). PROOF. Note that if x belongs to 7(f), then f is continuous at x and Of(x) 0. Let 6 > 0 be such that B(x, 6) C 7(f). It follows from the convexity of f and the fact that Of(y) 0 for all y E B(x, 6) that for all h such that lihil 6/2, and all y in B(x, 6/2), and all y E Of(y) (h, f(y + h) — f(y) (2.2) Taking the supremum over all {h I lihil 6/2} on both sides of expression (2.2) yields IIy*II sup 21f(y)I := K < oo.6 yEB(x,5) Setting e = (6K) /2 concludes the proof. i:i 10 Chapter 2. Preliminaries The following is a well known property of convex functions. It is fre quently used in the current literature (see Carlier ), but it probably dates back to Mosco or Joly (see for example ). Lemma 2.1.8 Let A c W be a convex, open set. Assume the sequence of convex functions {fk : A —* R} converges uniformly to f, then Vfk —* Vf almost everywhere on A. PROOF. Denote by Df the derivative of f in the direction of e. The convexity of fk and f implies the existence of a set B C A, with /1(A\\B) = 0 such that the partial derivatives of fk and f exist and are continuous in B. Let x e B. To prove that Djfk(x) —* Df(x), consider i > 0 such that x + 77ej E A. Since fk is convex fk(x + hej) — fk(x) > Djfk(x)> fk(x — he) — fk(x) for all 0 < h < i. Hence fk(x + hej) - fk(x) -Dj(x) Df(x) -DJ(x) fk(x - hej) - fk(x) -Dj(x). The left-hand side of the first inequality is equal to fk(x + he) — J(x+ he) J(x) — fk(x) J(x + he) — J(x) - h + h + h — For c> 0 let 0 < 6 ij be such that J(x-i-he)—J(x) —D1J(x) <e for hi <6. Let N e N be such that —e6 f(x)—f(x) <eJ for all n> N. Hence, taking h = 6 and ii N f(x+he)—7(x+he) <e and 7(x)—f(x) <• h — h — 11 Chapter 2. Preliminaries Thus 3c Df(x) — D2f(x) for all x E B. The same argument shows that —3e Df,() — D2f(x) for all n N and all x e B, which concludes the proof. D Proposition 2.1.9 Let U C R’2 be a convex, compact set and let g : U —* R be a convex function such that for all x E U, the subdifferentials ög(x) are contained in Q for some compact set Q. Then there exists {gj : U —* R} such that g, E C1 (U) and gj —* g uniformly on U. PROOF. Fix S > 0 and define Uö := {(i + 5)x I x E U}. Extend g to be defined on U by setting g(x) := maxyEQ {(x, s,,) for all x e Jô Notice that in this way the convexity of g and the bounds on Og(x) are preserved. Let K6 be a family of mollifiers (see, for instance ), then the functions h6 g * K6 are convex, smooth and they converge uniformly to g on U as long as e is small enough so that V€:={xEU d(x,0U6)>c} is contained in U. Let n e N be such that V1,, C U, then the sequence {g3 := h113} has the required properties. E:I A set G c H is called RESIDUAL or dense G6 if it is the denumerable in tersection of open, dense sets. By the Baire category theorem, a residual set is dense. An Apslund space is a Banach space in which every convex, lower semicontinuous function is Fréchet differentiable on a dense C5 subset. The 12 Chapter 2. Preliminaries following theorem proved one half of a long standing conjecture that a space is Apsiund if and only if it accepts an equivalent norm that is differentiable off the origin. In what follows f’(x) denotes the Fréchet-derivative of f at x. Theorem 2.1.10 (Ekeland, Lebourg /21]) Let X be a Banach space that supports a Frechet-differentiable function ‘P : X —* 1 such that ‘I’(O) > 0, ‘P(x) 0 for some ball B(0, cr), ‘P = 0 on the complement of B(0, os). Let Y be an abstract set and f : X x Y —* IR a Frechet-differeritiable function such that for all x e X, inf f(x,y) =: F(x) > —00 yEY Assume that for every x E X there exist 0> 0 and > 0 so that {f(z,y) I liz —xli i, f(z,y) F(x)+0} is a bounded set in X*, and {z—*f(z,y) I f(x,y)F(x)+0} is equicontinuous at x in X. Then there is a residual set G C X where F is Fréchet differentiable. Remark 2.1.11 A space X supports a function ‘P if it accepts an equivalent norm that is differentiable off the origin. Lemma 2.1.12 Let H be a Hubert space and F: H —* R a proper, lower semicontinuous convex function. Then there is a residual set G C H such that F is CONTINUOUSLY Frechét-differentiable on G. PROOF. To see that H supports a function ‘P as described in the statement of Theorem 2.1.10 notice that lix Ii = is Fréchet-differentiable off the origin. Let f(x, y) = F*(y) — (x, y) and define G(x) := infeH f(x, y). It follows from Proposition 2.1.7 that if G > —oo then for all x e H, there exist 13 Chapter 2. Preliminaries , 0 > 0 such that the set {f(z, y) I lix — li 17, f(z, y) G(x) + 0} is bounded, since it coincides with the set {—y E H I lix — zil i,f(z,y) G(x) +8}. Moreover, the set of functions {z-f(z,y) I f(x,y)F(x)+0} is clearly equicontinuous at each x E H, since f(z, y) = y. Hence the hypothesis of Theorem 2.1.10 are satisfied. It is shown in , page 466, that the sets G such that for any €> 0 there exist , 0 0 such that llzi—xli m f(yi,x) G(x)+8 iif(y1,z1)-f(y2,z2)li (2.3)IIz2il 7], f(y2,x) G(x)+8 j are open and dense. In particular, given > 0 we can find ö, 0> 0 such that G(x)+0 f(x,y2) G(x)+8 } iIf(x,yi) -f(z,y2)ii (2.4) Therefore IIG’(x) — G’(z)lI IIG’(x) — f(x,yi)ii+ IIf(z,y2) — G’(z)Ii + IIf(x,yi) — f(z,y2)i (2.5) Since f(y,x) —* F(x) = f(y,x) —* F’(x) (See (61) and (62) in ), then yi and y2 can be chosen such that IIG’(x) — f(x,yi)II and IIf(zy2) — G’(z)II (2.6) Inserting (2.6) and (2.4) into (2.5) concludes the proof. ci 14 Chapter 2. Preliminaries In the case of finite dimensional spaces, the set G is in fact of full measure. The next corollary is used in the proof of convergence of the numerical algorithm in Chapter 4. Corollary 2.1.13 Let g : JRTh —* JR be a convex function, then the mapping x — Vg(x) is well defined and continuous almost everywhere. Corollary 2.1.13 can be thought of as the first half of Alexandrov’s The orem, which states that a convex function f : R’ —+ JR is twice differentiable (actually C2) almost everywhere in the following sense: Definition 2.1.14 A convex function f : JRTh —* R is said to be twice A- DIFFERENTIABLE at a point xo e R’ if Vf(xo) exists and if there is a symmetric, positive definite matrixD2f(xo), such that for any e> 0 there is 6 > 0 such that if lix — xoIi < 6, then sup iIx* — Vf(xo) —D2f(xo)(x — xo)Il cllx — xoII (2.7) x eOf(x) It turns out that in the case of Hubert spaces, the mapping x — g’(x) (the Fréchet-derivative of g at x) is locally Lipschitz on a dense set. In order to prove the latter, the following definitions are necessary: Definition 2.1.15 A function g : H —* JR is said to be locally upper sup ported (l.u.s.) by h : H —* JR at x e H if: (i) g(x) = (ii) g(y) h(y) for all y in a neighborhood of x. The following theorem is a “smooth version” of the Ekeland variational principle. It will be used to characterize the local upper support functions of a convex function. 15 Chapter 2. Preliminaries Theorem 2.1.16 (Borwein, Preiss ) Suppose g : H —p R is lower semi- continuous and bounded from below. Let e, ). > 0. Assume that xo satisfies g(xo) <infg + c Then there exists w e H and e H such that for all x e H g(x) + — g() + II — while I—xoII<A and g)<ifg+c Proposition 2.1.17 Let f : H —* R be a proper, lower semicontinuous convex function. Then f is l.u.s. by quadratic functions on a dense subset of its effective domain. PROOF. Let x be in the interior of the effective domain of f. Since f is lower semicontinuous there is a > 0 and M 0 such that (f(y) <M for all y in B(x, 2a). Thus, f is continuous on B(x, a) (the closed ball centered in x of radius a). Define () f —f(y),if yEB(x,a); +00, otherwise. The function g is lower semicontinuous and bounded below by —M. Consider e > 0 and xo e B(x,a) such that g(xo) < infHg + e. Given that g is continuous on B(x, a), we can assume xo E B(x, a), since its closure is the only region where g is finite. Let A > 0 be such that B(xo, A) is contained in B(x, a). It follows from Theorem 2.1.16 that there exists and w in H such that g(x) + IIx — w112 g() + — w112 while Ilxo—II<A and g()<ifg+e. 16 Chapter 2. Preliminaries The left hand side inequality above implies that belongs to B(x, a). Since —g = f as long as x e B(x, a), the function Q(x) := f() + IIx w112 — C — w112 is a local upper support function of f at . 0 Theorem 2.1.18 (Ekeland, Moreno) Let f : H — R be a proper, lower semicontinuous convex function. 1ff is l.u.s. by a quadratic function at , then f’ is locally Lipschitz at PROOF. Let Q : H —* R be a quadratic function as in Proposition 2.1.17 such that f isl.u.s. by Q at on B := B(,J) for some 5>0. Let 3 = for notational convenience. It follows from Proposition 2.1.7 that it can be assumed without loss of generality that sup IIf’(x)II <00. Q(y) = f() + IIx — w112 — — w112 Notice that f’() = Q’(E) and Q’(y) /3(y — w) therefore w = — This in turn allows Q to be expressed as Q(y) f() + IIx — + /T’f’()II2— IIfI()II2 (2.8) It follows from the fact that Q(y) f(y) for all y E 13 that Q(y) — (y—,f’()) — f() f(y) — (y—,f’()) — f() Define q5(y) := f(y) — (y — , f’()) — f(E). Notice that ‘() = 0 and 17 Chapter 2. Preliminaries Q(y) - (y - , f’()) - f() = - + 3’f’(), y - + /31f’()) _IIfI() 112 — — fI()) = (y-,y-) +/3(y-,/3’f’()) — f’()) /3 - - = Thus, for y E B (Y) By convexity, for all x, y q(y) (x) + (y — x, ‘(x)), (2.9) Letting z’ = x and x = in equation (2.9) yields ) + (x-’()) + (y-x,’(x)). Writing x — + y — y for x — in the second summand of the right hand side of expression above and noting ‘() = 0 gives (y-x,’(x)-’()). Let j() = be such that y + (‘(x) — q’()) belongs to B, for all x e B. This number exists due to the boundedness of f’ on B. Then -‘()), ‘(x)-’())) (-x+’(x) -‘()), ‘(x)-’()). 18 Chapter 2. Preliminaries Hence ll’(x) _!()ll2 (-x,’(x) -‘()) +‘(x) _()li2. The expression above can be written as (x - , ‘(x) - ‘())> ( - ii’(x) - 1()ii2. Using the Cauchy-Schwartz inequality yields lix - ilii’() - ‘(x)li (ii ) lI’() - (x)II2. (2.10) Note that = 0 and q’(x) = f’(x) — f’() so expression (2.10) becomes llf’() - f’(x)ll - is - ill. Since ( — > 0 the proof is complete. As a direct implication of Proposition 2.1.17 and Theorem 2.1.18 one obtains the following Corollary 2.1.19 Let f : H — R be a proper, lower semicontinuous convex function. Then the assignment x—*f’(x) is locally Lipschitz on a dense subset of H. 19 Chapter 2. Preliminaries 2.2 U-Convexity The analysis of optimality in Chapter 3 is based on the notion of U-convex functions. These can be thought of as a generalization of convex functions, and can be found throughout the literature of optimization within Principal- Agent models (see, for example and ). Definition 2.2.1 Let two spaces A and B and a function U : A x B —k JR be given. (i) The function f : A —* JR is called U-convex if there exists a function p: B —* JR such that f(a) = sup {U(a, b) — p(b)}. bEB (ii) For a given function p: B — R the U-conjugate pU(a) of p is defined by pU(a) = sup {U(a, b) — p(b)}. beB (iii) The U-subdifferential of p at b is given by the set 9up(b) := {a E A I pU(a) = U(a,b) —p(b)}. (iv) If a e e9p(b), then a is called a U-subgradient of p(b). The following proposition is analogous to the characterization of proper, lower semicontinuous, convex functions as those that coincide with their twice convex conjugate. It shows that a function is U-convex if and only if it equals the U-conjugate of its U-conjugate. Proposition 2.2.2 A function f A —* JR is U-convex if and only if (fU)U = f. PROOF. 20 Chapter 2. Preliminaries (i) Let us first assume that (fU) U = • Then f(a) = sup{U(a, b) — bEB and hence it is U-Convex. (ii) Conversely, if f is U-convex, then there is a function p: B —* R such that f(a) = supbEB{U(a, b) — p(b)}. Since fU(b) = sup{U(a,b) — sup {U(a,b’) —p(b’)}} aEA b’EB sup{U(a,b) — (U(a,b) —p(b))} =p(b) aEA we see that (fU)U (a) = sup {U(a, b) - fU(b)} beB sup {U(a,b) _pU(b)} = f(a). beB On the other hand fU(b) U(a, b) — f(a) for all a e A. Thus (fU)U (a) = sup {U(a, b) — fU(b)} bEB sup {U(a,b) — U(a,b) + f(a)} = f(a). bEB This concludes the proof. El 2.3 Some Contract Theory Contract Theory is a branch of Economics that studies the ways in which contractual agreements between economic actors are made. This is mainly studied under the assumption of ASYMMETRIC INFORMATION; that is, a 21 Chapter 2. Preliminaries scenario in which one of the parties involved is better informed. In most cases the models contemplate a firm who is dealing with a group of agents. 2.3.1 Mechanism Design The general model in the theory of mechanism design contemplates two par ties. The first one consisting of the AGENCIES who want to trade ACTIONS with a second party: the AGENTS. Actions can represent labor to be hired, public policies to be implemented, products to be sold, etc. The agents, whose behavior is assumed to be rational, evaluate the welfare they obtain from interacting with the agencies via utility functions. These take into con sideration the EFFORTS associated with dealing with the agencies, as well as the TRANSFERS from the agencies to the agents for given actions. De pending on the model, the efforts may represent actual physical output from performing a duty, prices to be paid, etc. The caveat from the point of view of the agencies is that the agents’ efforts are not directly observable. The agents may choose to alter the signals sent to the agencies (Moral Hazard), or they may have preferences that are private information (Adverse Selec tion). The objective of the agencies is to extract as much welfare from the agents given this asymmetry of information. The disutility to the agencies stemming from this asymmetry is usually called the INFORMATION RENT. The agents must be given appropriate incentives to share private informa tion or to reveal unobservable efforts. These are called COMMUNICATION MECHANISMS. 2.3.2 Principal-Agent models and the Revelation and Taxation Principles The particular case where there is a single agency, which is then called the PRINCIPAL, is referred to as a Principal-Agent model. This work is set within such framework under Adverse-Selection. Perhaps the main appeal of this kind of hidden information model is the possibility of reducing all feasible communication mechanisms that satisfy the incentive constraints of the agents to DIRECT-REVELATION mechanisms. 22 Chapter 2. Preliminaries Denote by A the set of all possible actions and by T the set of possible transfers. Let the types 0 of the agents belong to some set 0. The (type dependent) utility functions for the agents will be denoted by u(x,0,t) : Axe x T—*R. A mechanism is defined as follows: Definition 2.3.1 A MECHANISM is a message space M and a mapping G: M -+ A x T which writes as G(m) (q(m),t(m)) for all m eM. It is through elements of M that the agents “inform” the principal of their action of choice. The set M can be quite complex, and dealing directly with a mechanism as defined above can prove hard (or impossible) to track. On the other hand, if the message space could be reduced to the type space, the analysis would be considerably simplified. This is in general possible, as shown by the Revelation and Taxation Principles given below. Definition 2.3.2 A DIRECT-REVELATION MECHANISM is a mapping g 0 —* A x T which writes as g(0)=(q(0),t(0)) forall 0cC. If a direct-revelation mechanism is such that u(q(0),0,t(O)) u(q(),0,t()) for all 0, e 0 then it is called INCENTIVE-COMPATIBLE or TRUTHFUL. Notice that in a truthful, direct-revelation mechanism it is optimal for each agent report her type or level of effort. The following theorem is the crux of the theory of mechanism design in Principal-Agent models. Theorem 2.3.3 (Revelation Principle ) To any optimal (from the point of view of the principal), incentive compatible mechanism of a Principal 23 Chapter 2. Preliminaries Agent game of incomplete information, there corresponds an associated incen tive- compatible direct-revelation (IC-DR) mechanism. If the preferences of the agents are given by quasi-linear utility functions u(q, 0, t) = U(0, q) — t the following theorem provides the necessary setting to allow for a mathe matical analysis of these models. Theorem 2.3.4 (Taxation Principle ) An allocation rule X : 0 —+ A can be associated with an IC-DR mechanism if and only if there is a function ir : A —* R such that for all 0 e 0 sup {U(O, q) — ir(q)} qeA is attained by x = X(0). 2.3.3 A standard screening model The model described below can be found throughout the literature of Prin cipal-Agent models under Adverse Selection. It is used, for example, in the Rochet-Model for which numerical solutions are computed in Chapter 4. Consider an economy with a single principal and a continuum of agents. The latter’s preferences are characterized by n-dimensional vectors. These are called the agents’ TYPES. The set of all types will be denoted by 0 c R’. The individual types 0 are private information, but the principal knows their statistical distribution, which has a density f(0). The model takes a HEDONIC approach to product differentiation: goods are characterized by (n-dimensional) vectors describing their utility-bearing attributes. The set of TECHNOLOGICALLY FEASIBLE goods that the princi pal can deliver is denoted by Q C 1R, which is assumed to be compact and convex. The cost to the principal of producing one unit of product p is de noted by C(p), which is assumed to be measurable in the sense of Lebesgue. 24 Chapter 2. Preliminaries Products are offered on a take-it-or-leave-it basis, each agent can buy one or zero units of a single product p and it is assumed there is no second-hand market. The (type.-dependent) preferences of the agents are represented by the (measurable) function U:OxQ—*R. The (non-linear) price schedule for the technologically feasible goods is rep resented by When purchasing good q at a price ir(q) an agent of type 0 has net utility U(8,q) — ir(q) Each agent solves the problem max{U(0,q) — ir(q)}. qEQ By analyzing the choice of each agent type under a given price schedule ir, the principal screens the market. Let the INDIRECT UTILITY of an agent of type 6 be v(0) := U(0, q(0)) — ir(q(0)), (2.11) where q(0) belongs to argmaxqQ {U(0, q) — ir(q)}. Note the use of the Tax ation Principle here. The following holds for all q in Q we have v(0) U(0, q) — ir(q) (2.12) Recall from Section 2.2 that the subset of Q where (2.12) is an equality is the U-SUBDIFFERENTIAL of v at 0 and v is the U-CONJUGATE of it, i.e. v(6) 25 Chapter 2. Preliminaries and Ouv(O) : {q e Q U(o) + ir(q) = U(8, q)} To simplify notation let ir(q(9)) ‘ir(O). A mechanism is called INDIVID UALLY RATIONAL if v(O) vo(O) for all 9 E e, where vo(9) is type 9’s reservation utility. It is standard to normalize the reservation utility of all agents to zero, and assume there is always an OUTSIDE OPTION qo that denotes non-participation. This simplified model then only considers fünc tions v > 0. The Principal’s aim is to devise a (non-linear) pricing function Q —* R as to maximize her aggregate surplus f (r(9) — C(q(O))) f(O)d9 (2.13) Inserting (2.11) into (2.13) yields the alternate representation f (U(6, q(8)) - v(9) - C(q(9))) f(O)dO. (2.14) Expression (2.14) is to be maximized over all pairs (v, q) such that v is U-convex and non-negative and q(9) E Duv(9). Characterizing Ouv(9) in a way that makes the problem tractable can be quite challenging. In the case where U(O, q(O)) = 9 . q(O), as in , for a given price schedule i- : Q —* R, the indirect utility of an agent of type 0 is v(0) :=max{0.q—r(q)} (2.15) qeQ Since v is defined as the supremum of its affine minorants, it is a convex function of the types. It follows from the Envelope Theorem that the max imum in equation (2.15) is attained if q(0) = Vv(0) almost everywhere, hence v(0) = 0 Vv(0) — r(Vv(0)). (2.16) The principal’s aggregate surplus is given by fe (ir(q(0)) - C(q(0))) f(0)dO. (2.17) 26 Chapter 2. Preliminaries Inserting (2.16) into (2.17) transforms the principal’s objective into maxi mizing I[v] := f(0. Vv(O) - C(Vv(0)) - v(O)) f(0)dO (2.18) over the set C := {v :0 —* R vconvex, v 0, Vv(0) eQ a.e.}. 2.4 Risk measures in L2 This section contains some properties and representation results for risk measures on L2 spaces. These can be found in and . A classical reference for the theory of risk measures on L°° is . All random variables are defined on some standard non-atomic probability space (, F, IP). Definition 2.4.1 (i) A monetary risk measure on L2 is a function p L2 —* R U {oo} such that for all X, Y e L2 the following conditions are satisfied: • Monotonicity: if X Y then p(X) p(Y). • Cash Invariance: if m e R then p(X + m) = p(X) — m. (ii) A risk measure is called coherent if it is convex and homogeneous of degree 1, i.e., if the following two conditions hold: • Convexity: for all c e [0, 1] and all positions X, Y e L2: p(oX + (1 — o)Y) op(X) + (1 — a)p(Y) • Positive Homogeneity: For all A 0 p(AX) = Ap(X). 27 Chapter 2. Preliminaries (iii) The risk measure is called law invariant, if, p(X) = p(Y) for any two random variables X and Y which have the same law. (iv) The risk measure p on L2 has the Fatou property if for any sequence of random variables X1,X2,... that converges in L2 to a random variable X we have p(X) liminfp(X). Given A E (0, 1], the Average Value at Risk of level A of a position Y is defined as 1 p; AV©RA(Y) := —— J qy(t)dt,A0 where qy(t) := sup{x I IP[Y <x] t} is called the upper t-quantile of Y. If Y E L°°, then AV©RA admits the following characterization AV©RA(Y) = sup —EQ[YJ QeQ,. where and Q << P means that Q is absolutely continuous with respect to P. Proposition 2.4.2 For a given financial position Y E L2 the mapping A ‘—* AV©R,(Y) is decreasing in A. PROOF. Differentiate AV©RA(Y) with respect to A to get AV©RA(Y) (—AV©RA(Y) — qy(A)) (2.19) 28 Chapter 2. Preliminaries Notice that qy (A) is increasing in A, so A qy(A) J qy(t)dt.0 This in turn makes the right hand side of equation (2.19) negative. 0 It turns out the Average Value of Risk can be viewed as a basis for the space of all law-invariant, coherent risk measures with the Fatou property. More precisely: Theorem 2.4.3 The risk measure p : L2 —* R is law-invariant, coherent and has the Fatou Property if and only if p admits a representation of the following form: ( j1 p(Y) = sup / AV©RA(Y)(dA) ,tEM (JO where M is a set of probability measures on [0, 1]. Proposition 2.4.2 and Theorem 2.4.3, together with the fact that AV©R1(Y) = E[—Y] yield the following Corollary: Corollary 2.4.4 If p : —* R is a law-invariant, coherent risk measure with the Fatou Property then p(Y) —IE[Y]. Corollary 2.4.4 will be essential to establish certain bounds in Chapter 3 that are necessary for the existence of optimal derivatives catalogues. An important class of risk measures are comonotone risk measures. Comonotone risk measures are characterized by the fact that the risk as sociated with two position whose payoff “moves in the same direction” is additive. 29 Chapter 2. Preliminaries Definition 2.4.5 A risk measure p is said to be comonotone if p(X + Y) = p(X) + p(Y) whenever X and Y are comonotone, i.e., whenever (X(w) — X(w’))(Y(w) — Y(w’)) > 0 IP-a.s. Comonotone, law invariant and coherent risk measures with the Fatou property admit a representation of the form F’ p(Y) = J AV©RA(Y)u(dA)0 for some probability measure on [0, 1]. 30 Chapter 3 Optimal Derivative Design This chapter studies the problem faced by a monopolist, whose income is exposed to non-hedgeable risk, when she trades over-the-counter derivatives with a set of heterogenous buyers. The monopolist’s aim is to minimize her risk exposure, which she evaluates via a coherent risk measure. The main result in this chapter is Theorem 3.1.3, which states that, when facing agents whose preferences are of the Mean-Variance type, the monopolist’s problem has a solution. Moreover, if the risk measure in use is strictly convex, then the resulting price schedule is unique. The proof of existence and uniqueness is contained in Section 3.2. The optimal contracts can be further characterized. Section 3.3 is devoted to this purpose. Finally, an example that can be solved in closed form is presented in Section 3.4. 3.1 The microeconomic setup The model considers an economy with a single principal whose income W is exposed to non-hedgeable risk factors rising from, e.g., climate or weather phenomena. The random variable W is defined on a standard, non-atomic, probability space (, .F, IP) and it is square integrable: WEL2(1,..’F,IP). The principal’s goal is to lay off parts of her risk with individual agents. The agents have heterogenous mean-variance preferences and their types are represented by their coefficients of risk aversion 0 e a Given a contingent 31 Chapter 3. Optimal Derivative Design claim Y e L2(,F, P) an agent of type 0 enjoys the utility U(0,Y) = E[Y] — 0Var[Y]. (3.1) Types are private information; however, the principal does know their dis tribution . It is assumed that the agents are risk averse and that the risk aversion coefficients are bounded away from zero. More precisely, 0 = [a, 1] for some a> 0. The principal offers a derivative security X(0) written on her random income for every type 0. The set of all such securities is denoted by X := {X = {X(O)}OE9 I X e L2(2 x 9, P® IL), X is a(W) x 13(0) measurable}, where 13(0) denotes the Borel a-algebra on 9. A list of securities {X(0)} is called a contract. A catalogue is a contract along with prices 7r(0) for every available derivative X (0). For a given catalogue (X, ir) the indirect utility of the agent of type 0 is given by v(0) = sup {U(O,X(O’)) — r(0’)}. (3.2) OEO Remark 3.1.1 No assumption is made on the sign of ir(0); the model con siders both the case where the principal takes additional risk in exchange of financial compensation and the one where she pays the agents to take part of her risk. A catalogue (X, 7r) is called incentive compatible (IC) if the agents’ in terests are best served by revealing their types. This means that the indirect utility of an agent of type 0 is achieved by the security X (0): U(0, X(O)) — ir(0) U(0, X(0’)) — 7r(O’) for all 0, 0’ E 0. (3.3) it is assumed that each agent has an “outside option” (no participation) that yields a utility of zero. A catalogue is called individually rational (IR) 32 Chapter 3. Optimal Derivative Design if it yields at least the reservation utility for all agents, i.e., if U(O, X(O)) — 7r(O) 0 for all 0 E 0. (3.4) Remark 3.1.2 By offering only incentive compatible contracts, the princi pal induces the agents to reveal their types. Offering contracts where the IR constraint is binding allows the principal to exclude undesirable agents from participating in the market. It can be shown that under certain conditions, the interests of the principal are better served by keeping agents of “lower types” to their reservation utility; Rochet and Choné have shown that in higher dimensions this is always the case. If the principal issues the catalogue (X, 7r), she receives a cash amount of ir (0) d,u(0) and is subject to the additional liability fe X(0)ii(dO). She evaluates the risk associated with her overall position w + f((o) - X(0))d(0) via a coherent and law-invariant risk measure p : L2(,F, IP) —* IR U {oo} that has the Fatou property. It can be shown that such risk measures can be represented as robust mixtures of Average Value at Risk (Theorem 2.4.3). The principal’s risk associated with the catalogue (X, ir) is given by p (w + f(ir(0) - X(0))dIL(0)). (3.5) Her goal is to devise a catalogue (X, ir) that minimizes (3.5) subject to the incentive compatibility and individual rationality restrictions: inf { (w + f(ir(0) — X(0))dIL(0)) I X e X, (X, ir) is IC and IR}. (3.6) The main result in this chapter is the following: Theorem 3.1.3 If p is a coherent and law invariant risk measure on L2(IP) and if p has the Fatou property, then the principal’s optimization problem 33 Chapter 3. Optimal Derivative Design has a solution. Moreover, if the risk measure is strictly convex, then there exists a unique pricing schedule ir that minimizes the overall risk. For notational convenience all results will be developed for the special case di(O) = dO. The general case follows from straightforward modifica tions. The proof of Theorem 3.1.3 requires rephrasing the principal’s prob lem as an optimal control problem, as well as several intermediate steps. These are contained in the following section. 3.2 Solving the principal’s problem Let (X, ir) be a catalogue. It is convenient to assume that the principal offers any square integrable contingent claim and to view the agents’ optimization problems as optimization problems over the set L2 (IP). This can be achieved by identifying the price list {ir(O) } with the pricing scheme iT: L2(IP) —* R that assigns the value ir(O) to an available claim X(O) and the value E{Y] to any other claim Y E L2. Note this reduces the principal’s problem to offering products indexed on 0, and it is an application of the Taxation Principle (, ) in the particular case of Mean-Variance preferences. In terms of this pricing scheme the value function v defined in (3.2) satisfies, for any incentive compatible catalogue, v(0) = sup {U(O, Y) — ir(Y)}. (3.7) YEL2(P) The value function is U-convex in the sense of Definition 2.2.1. In fact, it turns out to be convex and non-increasing. The goal is therefore to identify the class of IC and IR catalogues with a class of convex and non-increasing functions on the type space. To this end, recall the link between incentive compatible contracts and U-convex functions from Carlier, Ekeland and Touzi : 34 Chapter 3. Optimal Derivative Design Proposition 3.2.1 If a catalogue (X, ir) is incentive compatible, then the function v defined by (3.2) is proper (i.e., never —oo and not identically +oo) and U-convex and X(O) E Ouv(O). Conversely, any proper, U-sub- differentiable and U-convex function induces an. incentive compatible cata logue. PROOF. Incentive compatibility of a catalogue (X, ir) means that U(O, X(9)) — 7r(O) U(O, X(O’)) — ir(O’) for all 0, 0’ e 0, so v(O) = U(O, X(O)) — ir(O) is U-convex and X(O) e Ouv(O). Conversely, for a proper, U-convex function v and X(O) e 9uv(O) let r(O) := U(9,X(O)) —v(O). By the definition of the U-subdifferential, the catalogue (X, ir) is incentive compatible. D The following is a fundamental lemma. It shows that the U-convex func tion v is convex and non-increasing and that any convex and non-increasing function is U-convex, i.e., it allows a representation of the form (3.7). This allows for the principal’s problem to be restated as an optimization problem over a set of convex functions. Lemma 3.2.2 (i) Suppose that the value function v as defined by (3.7) is proper. Then v is convex and non-increasing. Any optimal claim X*(O) is a U-subgradient of v(O) and almost surely _Var[X*(O)] = v’(O). (ii) If Y 0 — IR+ is proper, convex and non-increasing, then ii is U convex, i.e., there exists a map : L2(IP) —* R such that (O) = sup {U(O, Y) — YEL2(F) 35 Chapter 3. Optimal Derivative Design Furthermore, any optimal claim .(O), that is any claim for which the sup above is attained, belongs to the U-subdifferential of 3(O) and satisfies —Var[X(O)] = v3’(O). PROOF. (i) Let v be a proper, U-convex function. Its U-conjugate is: v1’(Y) = sup {E{Y]—OVar{Yj---v(O)} OEO E[Y] + sup {O(—Var[Y]) — v(9)} oee = E[Y] + v*(_Var{Y]), where v” denotes the convex conjugate of v. By Proposition 2.2.2, the map v is characterized by the fact that v = (vU)U. Thus v(O) = (vU)U(9) = sup {U(O,Y)_IE[Yj_v*(_Var[Y])} YEL2(,P) = sup {IE[Y] — OVar[Y] — IE[Y] — v*(_Var[Yj)} Y€L2(,P) = sup{O.y_v*(y)} vo where the last equality uses the fact that the agents’ consumption set contains claims of any variance. It follows from the preceding representation that v is non-increasing. Furthermore v = (v*)* so v is convex. Ouv(O) is characterized as follows: 9uv(O) = {Y EL2 I v(O) = U(O,X) _vU(Y)} {Y E L2 I v(O) = E[Y] — OVar[Y] — v’(Y)} = {Y E L2 I v(O) = )E[YJ — OVar[Y] — IE{Yj — v*(_Var[Y])} = {Y E L2 I v(8) = O(—Var[Y]) — v*(_Var[Y])} = {Y E L2 —Var[Y] E Ov(8)} 36 Chapter 3. Optimal Derivative Design By Corollary 2.. 1.13, the convexity of v implies it is a.e. differentiable, thus öuv(0) {Y E L2 v’(O) = —Var{Y1}. (ii) Consider a proper, non-negative, convex and non-increasing function 9 —* JR. There exists a map f : JR —‘ JR (see Proposition 2.1.3) such that (9) =sup{9.y—f(y)}. yo Since 3 is non-increasing there exists a random variable Y(O) e L2 such that —Var[Y(O)] E (O) and the definition of the subgradient yields 3(9) = sup {O(—Var[Y]) — f(—Var[Y])}. Y€L2 With the pricing scheme on L2(IP) defined by (Y) := —E[Y] — f(—Var[Y]) this yields v(8) = sup {U(O, Y) — r(Y)}. Y€L2 The characterization of the subdifferential follows by analogy to part (i). U The preceding lemma along with Proposition 3.2.1 shows that any con vex, non-negative and non-increasing function v on 9 induces an incentive compatible catalogue (X, 7r) via X(O) e 9uv(O) and ?r(6) = U(O, X(O)) — v(O). Inserting this representation of the pricing function into equation (3.5) and using the cash invariance of the risk measure, the principal’s aggregate risk 37 Chapter 3. Optimal Derivative Design can be expressed as p (w + f (E[X(O)j - X(O))dO) - f (Ov’(O) - v(O)) dO. (3.8) Therefore, it can be assumed with no loss of generality that IE[X(O)] = 0. In terms of the principal’s choice of v her income is given by 1(v) =10 (Ov’(O) - v(O)) Since v 0 is non-increasing and non-negative the principal needs only to consider functions that satisfy the normalization constraint v(1) = 0. The class of all convex, non-increasing and non-negative real-valued func tions on 0 that satisfy the preceding condition is denoted by C: C = {v : 0 —* R v is convex, non-increasing, non-negative and v(l) = O.} Conversely, any IC and IR catalogue (X, ir) can be associated to a non negative U-convex function of the form (3.7) where the contract satisfies the variance constraint —Var [X (0)] = v’ (0). In view of the preceding lemma this function is convex and non-increasing so after normalization it can be assumed that v belongs to the class C. This yields the following Theorem 3.2.3 The principal’s optimization problem allows the following alternative formulation: inf { (w fo X(O)dO) — 1(v) v E C, IE[X(O)] 0, —Var{X(O)] = v’(O)} The next preliminary result states that a principal with no initial en dowment will not issue any contracts. Lemma 3.2.4 If the principal has no initial random income, i.e., if W = 0, 38 Chapter 3. Optimal Derivative Design then (v, X) = (0,0) solves her optimization problem. PROOF. Since p is a coherent, law invariant risk measure on L2(IP) that has the Fatou property, it follows from Corollary 2.4.4 that p(Y) —IE[Y] for all Y E L2(IP). (3.9) For a given function v e C the normalization constraint E[X(O)J 0 there fore yields p (- f X(8)dO) - 1(v) E [f X(O)dO] - 1(v) = -1(v). Since v is non-negative and non-increasing —1(v) 0. Taking the infimum in the preceding inequality shows that v 0 and hence X(O) 0 is an optimal solution. D 3.2.1 Minimizing the risk for a given function v In the general case the principal’s problem is approached in two steps. At first a function v from the class C is chosen and the associated risk p (W_fX(O)dO) subject to the moment conditions E[X(O)j = 0 and —Var[X(6)J = v’(O) is minimized. To this end, a relaxed optimization problem, where the variance constraint is replaced by the weaker condition Var[X(O)] —v’(O) is shown to have a solution given by optimal contracts Xi,. In a subsequent step it is shown that based on X,,, the principal can transfer risk exposures among the agents in such a way that the aggregate risk remains unaltered, but the variance constraint becomes binding. Since v is a convex function, it is continuous in the interior of its effective domain. It will be assumed that v does not have a jump at 0 = a. 39 Chapter 3. Optimal Derivative Design The relaxed optimization problem Let v e C and consider the convex set of derivative securities : {X e X I E[X(O)j = 0, Var[X(O)] —v’(O) a.e.} (3.10) The function v is called acceptable for the principal if there exists some contract X e X,, such that the implementation of (X, v) does not increase the principal’s original risk. Lemma 3.2.5 (i) All functions v E C that are acceptable for the principal are uniformly bounded. (ii) Under the conditions of (i) the set X,, is closed andL2-bounded. More precisely, IIXIIv(a) forall XEX. PROOF. (i) If v is acceptable for the principal, then there exists some X e X, that satisfies p (w -19 X(O)dO) - 1(v) p(W). It follows from (3.9) and that fact that IE[X(O)] = 0 that -E{W] - 1(v) p (w -1 X(O)dO) - 1(v) p(W) so —1(v) E[W] + p(W) =: K. Integrating by parts and using that v is non-increasing and v(1) = 0 we see that 1 K> —1(v) = av(a) + 2f v()dO av(a). This proves the assertion because a > 0. 40 Chapter 3. Optimal Derivative Design (ii) For X e X we deduce from the normalization constraint v(1) = 0 that iixii = f fx2(o,w)clIPde - J v’(O)dO = v(a) so the assertion follows from part (i). D Remark 3.2.6 From this point on, it will be assumed with no loss of gen erality that the set C contains only acceptable functions. This follows from the fact that any choice by the principal of a function v (an hence a pricing schedule) which does not lie within the set of acceptable functions will result in an increment of her initial risk assessment. Since p is a 1.s.c. convex risk measure on L2(IP) and because the set X of contingent claims is convex, closed and bounded in L2(IP) the following result follows from proposition 2.1.5. Proposition 3.2.7 If the function v is acceptable for the principal, then there exists a contract X, such that p (w — fe x(o)de) = p (w — Jo x(o)do). The contract X, along with the pricing scheme associated with v does not yield an incentive compatible catalogue unless the variance constraints happen to be binding. However, it will be shown below that based on X, the principal can find a redistribution of risk among the agents such that the resulting contract satisfies the IC condition. Redistributing risk exposures among agents Let 8X, = {X E X,, E[X(O)j = 0, Var{X(O)] = —v’(O) a.e.} 41 Chapter 3. Optimal Derivative Design be the set of all contracts from the class X where the variance constraint is binding. Clearly, p (w — fe X(O)dO) p (w — fe X(O)dO). Define := {e E 0 I Var[X(O)] < —v’(8)}, the subset of types for which the variance constraint is not binding. If = 0, then X, yields an incentive compatible contract. Otherwise, let e X,,, fix some type 0 and define Y:= . (3.11) Var[Y()] The purpose of introducing Y is to offer a set of structured products Z, based on X,, such that Z, together with the pricing scheme associated with v yields an incentive compatible catalogue. Choose constants á(O) for 0 E such that Var[X(0) + &(0)Yj —v’(9). This equation holds for c(8) = —Cov[X(0),Y] ± /Cov2[Xv(0),Y] — v’(O) — Var[X(0)]. For a type 0 € O the variance constraint is not binding. Hence —v’(O) — Var[X(0)] > 0 so that a(0) > 0 and c(0) <0. Notice that Var[X(0)j is a measurable and integrable function by Fubini’s theorem. This, together with Cauchy’s inequality, implies Cov{X(0), Y] is measurable and integrable as well. Jensen’s inequality implies f Cov[X(0),Y] —v’(8) —Var[X(0)]d0 f(Cov[xv(o)Y1 —v’(O))dO— The expression above, together with Lemma 3.2.5 and the fact that IIXvII2 42 Chapter 3. Optimal Derivative Design is bounded shows that & are j-integrable functions. Therefore, there is a threshold type 0* E G such that I &(O)d0 + I &(0)dO = 0.Jevn(a,o*l JOVn(0,1] In terms of 0*, define the function f a(0), if 00*c(0) := c c(0), if 0>0* and the contract Z, :=X+oYEOX. (3J2) Since f cd0 0 the aggregate risks associated with X, and Z,, are equal. As a result, the contract Z1, solves the risk minimization problem inf p (w — f X(0)1(d0). (3.13)XEc3X . e ./ 3.2.2 Minimizing the overall risk The final step in the proof of the existence part of Theorem 3.1.3 is to show that the minimization problem inf { (w — I Zv(o)IL(do)) — I(v)} has a solution and the infimum is attained. Proposition 3.2.8 The set C is closed with respect to uniform convergence on compact subsets. PROOF. The functions in C are locally Lipschitz continuous because they are convex. In fact they are uniformly locally Lipschitz: by Lemma 3.2.5 (i) the functions v e C are uniformly bounded and non-increasing so all the elements of Ov(0) are uniformly bounded on compact subsets of types. As a result, 43 Chapter 3. Optimal Derivative Design any sequence {v} C C is a sequence of uniformly bounded and uniformly equicontinuous functions when restricted to compact (strict) subsets of 0. Thus, the Arzela-Ascoli theorem guarantees the existence of a function 15 E C such that, passing to a subsequence if necessary, urn v = IS uniformly on compact subsets. n—*oo Remark 3.2.9 If the sequence {v} —> V uniformly on compact subsets, then it follows from Proposition . 1.8 that lim v = 15’ almost surely. n—*oo Proposition 3.2.10 Let Z,, E OX,, be such that p (w1 Zv(O)iL(dO)) = p (w + f X(O)IL(dO)). Then the mapping p (w +10 z(O)(dO)) is convex on C. PROOF. Let c E [0, 1] and u, v E C and consider corresponding Z E OX and Z,, E OX,,. It follows from the convexity of the risk measure that p (w+ J(zu +(1 _a)Zv)(dO)) ap(W+f0Zt dO)) +(1 — o)p (W + feZv1u(dO)). The convexity of the variance operator X —* Var[X] implies Var[oZ + (1 — o)Z,,] aVar[Z] + (1 — o)Var[Z,,], 44 Chapter 3. Optimal Derivative Design Hence cZ + (1 — a)Zu belongs to the set and by definition p (w +1 ZU+(l_)L(dO)) p (w +1 (Z + (1 )Z) I1(dO)) Therefore p (w +1 Zau+(l_)v(dO)) <ap (W + fe Z(dO)) — a)p (w + fe Zi(d6)) which concludes the proof. Lemma 3.2.11 Let Z, be as in Proposition 3.2.10, then the mapping v —* p (w + I Z(O)L(dO)) — I[v] is lower semi-continuous on C. PROOF. Consider {v} c C. by Proposition 3.2.8 it can be assumed without loss of generality that there exist ‘Y e C such that urn v = J uniformly on compact subsets. n—+oo Since —6v(6) + v(O) 0 it follows from Fatou’s lemma that —I(v) 1iminf. —I(v) so liminf {p (w — f z(0)(do)) — I(v)} liminfP(W_f0Zv(O)IL(d9)) +1iminf—I(v) liminf p (w z(o)/L(de)) — IQu) 45 Chapter 3. Optimal Derivative Design and it remains to analyze the associated risk process. For this, observe that for e OX Fubini’s theorem yields IIzvnhI = ffzc1IPdo = _f v(O)dO = v(a). (3.14) Since all the functions in C are uniformly bounded, the contracts are contained in an L2 bounded, convex set. It follows from the reflexiveness of L2 and the Banach-Alaoglu theorem that there is a square integrable random variable Z such that, after passing to a subsequence if necessary, Z—Z weaklyin L2(P®), (3.15) which implies the convergence of aggregate risks: Jo Z(O,w)dO —* f Z(O,)dO weakly in L2(IP). It follows from Proposition 2.1.4 and the Fatou property of the risk measure p that liminfp (w — I Z(O)/L(dO)) p (w — f Z(O)It(dO)). Let Z13 e X be an optimal claim associated with the limiting function 3 as constructed above. If the weak limit Z belongs to X, then (Z, i3) satisfies the principal’s problem because p (w - I Z(O)L(dO)) p (w - I Z(O)[(dO)). (3.16) If such were not the case, given that Xy is closed, the Hahn-Banach theorem would guarantee the existence of and I E L2(IP 0 i) and c E IR such that (l,Z) > c and (I,Y) <c for all Ye X, (3.17) 46 Chapter 3. Optimal Derivative Design Since v —* t3’ almost everywhere, Egoroff’s theorem guarantees that for each k N there is a set ek c e such that v - ‘5’ uniformly on ek and (€ \\ Ok) < Note that since the probability space is atomless, there is a k such that 0k satisfies lZdlPdp> c (3.18) and trivially 10k f lYd1Pd < c for all Y E X (3.19) By the uniform convergence of z% —* 3’, there is a sequence {€ : [1, oo) } that converges uniformly to one and such that for almost all 0 e 0k Var{Y(0)] < —v/(0)c(0) for all Y, e Then X C Xy and X C X (3.20) Given Y E X there is a unique Y E Xy such that II — = mm lW — YII2 (3.21) WEX, This is simply the projection of Y onto X, since the latter is convex. Consider Y E OX, then e öX and Y — —Y II”II2 1— KS (3.22) where K is the uniform bound for v(a) and 6, —* 0. Any W e XE either belongs to X3, in which case the minimum in equation (3.21) is zero, or it belongs to Xe \\ X. In such case its distance to X, is smaller than the distance between its projection onto X13 and the latter’s distance to OXye, 47 Chapter 3. Optimal Derivative Design which has been bounded in expression (3.22). Therefore II<nII2 Kö This implies, together with the first inequality in (3.20) that for n large enough 10k f lYdIPdp < c for all Y E Xc,, (3.23) Define l*(w,O) := f l(,O), 0 e 0, otherwise. Expression (3.23) implies that 1* separates the sequence {X } from its weak limit Z, which is a contradiction. Therefore Z e X, and p (w — I Z(0)/.L(d0)) p (w — I Z(0)u(d0)). Thus liminfp (w - I z(0)(d0)) p (w -10 Z(0)IL(d0)) Lemma 3.2.12 There exists a catalogue (Zfl, ‘5) that solves the Principal’s problem inf { (w — I z(9)1(d0) — I(v)} PROOF. By Lemma 3.2.5 and Proposition 3.2.8 and the set C is closed and bounded. Moreover, Proposition 3.2.10 and Lemma 3.2.11 imply that the mapping F(v) = p (w - f Z(O)1(d0) - 1(v) is convex and lower semi-continuous. It follows from Proposition 2.1.5 that F attains its minimum in C. 48 Chapter 3. Optimal Derivative Design Note that the solution to the principal’s problem is characterized in terms of a convex function v and a contract Z,. Associated with Z, there is a random variable X,, that solves the relaxed optimization problem. The variable is unique if p is strictly convex. However, there are many ways of “pushing X to the boundary”, i.e., of defining Z,.,. As a result, there is no reason to assume that the solution to principal’s problem is unique. However, in terms of the pricing schedule induced by v, the following Lemma follows from Proposition 3.2.10 Lemma 3.2.13 If the risk measure p is strictly convex, then there exists a unique function 13 that minimizes the overall risk. In particular, the prin cipal’s optimization problem has is unique solution up to the definition of zij. Lemma 3.2.12 together with Lemma 3.2.13 are precisely Theorem 3.1.3. 3.3 A characterization of optimal contracts Typically, the solution to the principal’s problem cannot be given in closed form. However, its structure can be further characterized. More specifically, the following holds. Proposition 3.3.1 If {Y(O)} is an optimal contract, then all the random variables Y(O) are co-linear. More precisely, there exists a random variable Z e L2(IP) and a function a: 0 —* R such that almost surely Y(O,) = a(O)Z(w). To prove Proposition 3.3.1, it is enough to fix a function v e C and charac terize the infimum among all the random variables X e X of the operator R(X) := p (w -Jo X(e)dO) 49 Chapter 3. Optimal Derivative Design subject to the moment conditions Ep[X(O)]=O, and Var[X(O)]+v’(O)=O. In order to deal with the constraints consider the operators V, U : X —* L2() defined by U(X)(O) := f X(O,w)dJP and V(X)(O) := fX2(O,w)d1P+v(O), respectively, so that the minimization problem can be rewritten as inf R(X) s.t. U(X) = 0 and V(X) = 0. (3.24) XEX 3.3.1 The Lagrangian and the characterization In order to study the Lagrangian associated with the constrained optimiza tion problem notice that the Frechét-differentials of V and U at X in the direction h e X are given by, respectively, V’(X)h = f 2X(O, w)h(9, w)dlP and U’(X)h = f h(O, w)dIP. The Frechét differential of R at X in the direction h E X is given by R’(X) = p’ (w —19 X(O)dO) (f h(O, w)dO). The derivative is well defined because pE(L2(1P))* and _fh(O,L)d8eL2(P). Since, for all H E L2(IP), the map K —* p’(H)K is linear the Riesz repre sentation theorem yields a random variable Z E L2(IP) such that p’ (w —19 X(O)de) (_ f h(O, L)dO) = f Zx() (—19 h(O, w)dO) 50 Chapter 3. Optimal Derivative Design As a result, the operator R has an extremum at Y under the moment con straints, if there exist Lagrange multipliers A, e L2(ji) such that ff0—Zy(w)h(O, w)dOdlP +10 i(O) (f h(O, w)dlP) 210 A(O) (f h(O, L,J)Y(O)dlP) dO = 0 for all h e X. This equation can be written as f 10 h(9, w) (—Zy(w) + i(O) + 2A(O)Y(O,))dOdlP = 0. for all h E X. Since (0, w) —* —Zy(w) + ,(0) + 2A(0)Y(0, c) is an integrable function this implies —Zy() + i(O) + 2A(O)Y(O,w) = 0 (3.25) due to the DuBois-Reymond lemma. Integrating both sides of this equation with respect to IP, and noting that Ep[Y(O)] 0, yields Ejp [—Zy] + (O) 0. In particular, does not depend on 0. Thus, with Z := Zy — ij and a(O) := (2A(0))’ and Y(0,c’) = a(O)(w). The function a is well-defined due to the fact that the variance constraint Var[Y(0)] = —v’(O) is binding for all types so A(0) 0 almost surely. As suming without loss of generality that = 1 the variance constraint implies that a(0) = This proves the following result which also establishes the characterization of optimal contracts. Proposition 3.3.2 Let Z, be an optimal solution of the problem (3.24). 51 Chapter 3. Optimal Derivative Design Then Z takes the form Z(9,w) = 3.3.2 An application to entropic risk measures The preceding considerations show that the optimization problem (3.24) can be reduced to finding inf p (w - zf /ZO)d9) where P := {Z E X E[Z] = 0, IZII = 1}. This characterization of the optimal contracts given a price schedule induced by v E C can be taken further in the particular case of the entropic risk measure 1 p(X) = inlEp [exp(—3X)j which is strictly convex. Assuming for simplicity /3 = 1, the Frechét differential of R is given by R’(X)h= where 8(X) = E[exp(R(X))]. Equation (3.3.2) can be rewritten as R’(X)h = f f S(X)’exp (_w +10 x(O)dO) h(O, w)dOdlP Hence R’(X) e PC’ can be identified with exp (_w + f X(6)dO), 52 Chapter 3. Optimal Derivative Design and problem (3.24) is reduced to finding inf ln (1 —w+Zfe ../—v’(O)dO ZEF \\jç In terms of a(v) = fe \\/—v’(O)dO the objective is to find a stationary point of the Lagrangian L(Z, r, ,) = ln (f e_W+Za(dP) + rf ZdIP + J Z2dIP where r = r(v) and , = ic(v) belong to R. These are the Lagrange Multipli ers associated with the mean and variance constraint, respectively. Equat ing the Frechét-derivative to the zero operator in L2(P) yields the following equation: e_W+2(v) fçe_’)d1P + r + 2,cZ = 0. (3.26) The values of the multipliers are obtained from the moment constraints. In particular, this yields an implicit expression for the solution of (3.26): e_+Za(v) — E fe_B+Z(v) Var (eW+Za(’)) This equation must hold almost everywhere. It is straightforward to see that it has a unique solution for each realization z of Z and w of W, since the line of negative slope 1(z) E [e 7+Za(v)] — Var (e_W+Za(v))z intersects the exponential function f(z) = only once. 3.4 Example: A single benchmark claim This section considers an example where the principal’s choice of contracts is restricted to a certain class of securities. Namely, a situation where the 53 Chapter 3. Optimal Derivative Design principal offers type-dependent multiples of some benchmark claim. This case is motivated by characterization result of Section 3.3 which states that all the optimal contracts are co-linear. In this case the principal’s problem can be reduced to a constrained variational problem that can be solved in closed form. It is worth mentioning that in terms of “real life” products, simpler contracts like the one described below and those studied numerically in Chapter 4 stand a better chance of being accepted by traders. 3.4.1 Description of the constrained claims The model contemplates a principal who sells a type-dependent multiple of a benchmark claim f(W) 0 to the agents. More precisely, the principal offers contracts of the form X(O) = a(O)f(W). (3.27) In order to simplify the notation, the T-bond’s variance will be assumed to be normalized: Var{f(W)] = 1. 3.4.2 The optimization problem Let (X, ir) be a catalogue where the contract X is of the form (3.27). By anal ogy to the general case it will be convenient to view the agents’ optimization problem as an optimization problem of the set of claims {7f(W) I y E R} so the function a: e —+ R solves sup {U(O,7f(W)) — ir(O)}. yER In view of the variance constraint on the agents’ claims, the principal’s problem can be written as inf p {(W - a(v)f(W)) - I(v)} where a(v) =10 -v’(O)dO. (3.28) Note that E[f(W)] > 0, so the term E[f(W)]—v’(O) must be included 54 Chapter 3. Optimal Derivative Design in the income. Before proceeding with the general case, consider a situation where in addition to being coherent and law invariant, the risk measure p is also comonotone. In this case each security the principal sells to some agent increases her risk by the amount p (_(f(w) — + (v(O) — Ov’(O)) > 0. This suggests that it is optimal for the principal not to sell a bond whose payoff moves into the same direction as her initial risk exposure. Proposition 3.4.1 Suppose that p is comonotone additive. If f(W) and W are comonotone, then v = 0 is a solution to the principal’s problem. PROOF. If W and f(W) are comonotone, then the risk measure in equation (3.28) is additive and the principal needs to solve p (W) + inf f (v(o) + p (f(W) - E[f(W)]) -v’(O) - Ov’(O)) dO.vEC e Since p (f(W) — E{f(W)]) 0 and —Ov’(O) > 0 then f (v(o) + p (F(W)) /-v’(O) - Ov’(O)) dO 0 and hence v 0 is a minimizer. 0 In view of the preceding proposition the principal needs to design the payoff function f in such a way that W and f(W) are not comonotone. An optimal payoff function is constructed in the following subsection. 3.4.3 A solution to the principal’s problem Considering the fact that p(.) is a decreasing function, the principal’s goal must be to make the quantity a(v) as small as possible while keeping the income as large as possible. In a first step she solves, for any constant A e R 55 Chapter 3. Optimal Derivative Design the optimization problem sup a(v) subject to f (E[f(w)]/_v’(o) - v(O) + ov’(o)) dO = A. (3.29) The constrained variational problem (3.29) captures the problem of risk minimizing subject to an income constraint. It can be solved in closed form. The associated Euler-Lagrange equation is given by A = (_Ao + ____ (3.30) where A is the Lagrange multiplier. The income constraint and boundary conditions are: v’(a) = and v(l) = 0 where = (AE[f] — 1). Integrating ‘both sides of equation (3.30) and taking into account the nor malization condition v(1) = 0 yields v(O) = 1 ()2 [2o a 2 a] (3.3) Inserting this equation into the constraint yields A = E[fJ/()f 20- a - ()2 ía’ { [2e a - + (20 - a)2 } dO. In terms of 11111 1 1 1 1 6 ‘I 1’ dO M:__jtL2o]+()2IdO and N:=J29 the problem is reduced to finding the roots of the quadratic equation 56 Chapter 3. Optimal Derivative Design which are _____ A — NE[f] — /(NE[f])2— 4AM (3 322M The root with negative sign is used, as it is required that the problem reduces to p(W) for A 0. Remark 3.4.2 Notice that the constrained variational problem (3.9) is independent of the risk measure employed by the principal. This is because the risk has been minimized pointwise subject to a constraint on aggregate revenues. In view of the preceding considerations the principal’s problem reduces to a one-dimensional minimization problems over the Reals: p (w — f(W)N2+ f(W)y(NE[f])2 — 4AM) — A. Once the optimal value A* has been determined, the principal offers the securities \\4OA—2Aa) “ at a price AE[f] — 1 (3EA(20 — a) — a + — 1 1 2 (40A — 2Aa) A2 2 — a Example 3.4.3 Assume that the principal measures her risk exposure us ing Average Value at Risk at level 0.05. Let W be a normally distributed random variable with mean 1/2 and variance 1/20. W can be thought to represent temperature. Suppose that the principal’s initial income is exposed to temperature risk and it is given by W = 0.1(W — 1.1) with associated risk p(W) = 0.0612. Suppose furthermore that the principal sells units of a put option on W with strike 0.5, i.e., f(W) = (W — 0.5) 57 Chapter 3. Optimal Derivative Design By proceeding as above principal’s new risk exposure is approximately —0.6731 and she offers the security X(9) = 459f(W) to the agent of type 0 for a price — 1.1921 — (1.1921)0 — (0.22)(20 — a) “18(2—a) /(2O_a)2 58 Chapter 4 An Algorithm to Solve Variational Problems with Convexity Constraints This chapter presents a numerical algorithm to approximate the solutions of some variational problems subject to global convexity constraints. The initial motivation for such algorithm was solving optimal derivative design problems as in Chapter 3 where the class of derivatives available to the principal is constrained. However, besides tackling those problems, the al gorithm can be used to approximate solutions of various variational problems under convexity constraints. A classical example of the latter is Newton’s problem of the body of minimal resistance, which, given e a smooth, convex subset of R2, consists of minimizing I dOI[v] = ie 1 + vvI2’ over the set of convex functions {f 9 — R}. The types of problems that the algorithm is designed to solve are de scribed in Section 4.1. The description of the algorithm is given in Section 4.2. The main result in this Chapter is Theorem 4.3.7. The proof of the latter makes up Section 4.3, and most of the examples are given in Section 4.4. Finally, Section 4.5 contains an example that is solved using similar methodology. However, its structure fails outside the scope of the problems described in Section 4.1. Namely, it requires solving a continuous minimax problem. The latter is done using a quasi-Newton descent method. 59 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints 4.1 Setup The following notation is used throughout this chapter: • e, Q C R’ are convex and compact sets, • denotes the Lebesgue Measure on 1R, • f is a (probability) density on 0, • L(O, z,p) = z — 0 . p + C(p), where C is strictly convex and C’. • C:={v:0—*IR IvOisconvex, and VveQa.e}, • I[f] := L(0,v(0),Vv(0))f(0)dO. The objective is to (numerically) estimate the solution to P:=infl[fj (4.1) It is assumed that C is such that (4.1) has a unique solution (see, for exam ple, ). The properties of L and C yield the following Proposition 4.1.1 Assume Y solves 1’, then there is 0 in 0 such that = 0. PROOF. Let 7o = minOEO Y(0) (recall 0 is compact). If o > 0, define ii(0) :=Y(0)—Yo, then = f((O) — . Vi(0) + C(Vi(0)))f(0)d0 I[u] — This contradicts the hypothesis of Y being a minimizer of I over C. D It follows from proposition 4.1.1 that C can be redefined to include only functions that have a root in 0. This, together with the compactness of Q and 0 implies the following proposition, which is used frequently: Proposition 4.1.2 There exists 0 < K < co such that v K for all v in C. 60 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints It follows from Proposition 4.1.2 and the restriction on the gradients that for each choice of function C, problem P has a unique solution, since the functional I will be strictly convex, lower semi continuous and the admissible set is bounded. Remark 4.1.3 The algorithm will still work with more general L’s as long as one can prove that the family of feasible minimizers is uniformly bounded. 4.2 Description of the algorithm From this point on, the use of superscripts refers to vectors. For example V’ (Vt, . . . , V,). On the other hand a subscript indicates a function to be evaluated over some closed, convex subset of of non-empty interior, ie, {Vk} is a sequence of functions Vk : X —* Jl for some X contained in R. Assumption 4.2.1 It will be assumed that e = [a, b]’. The algorithm to find an approximate solution to? works as follows: 1. The domain e is discretized in the following way: Partition e into k, which consists of k’ equal cubes of volume 1u(k) := ()fl. The elements of the lattice k will be denoted by 4, 1 j k’. Now define ek as the set of centers of the 4’s. The elements of ek will be denoted by O. The choice of a uniform partition is done for computational simplicity. 2. Denote f = f f (0) dO and associate such weight with O. 3. Associate to each element 0 of ek a non-negative number v and an n-dimensional vector D. The former represents the value of v(O) and the latter Vv(O). 4. Solve the (non-linear) program flf t(E,) > L (of, v, D) fjc (4.2) 61 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints over the set of all vectors of the form v = (vi,.. . , vj) and all matrices of the form D = (D1,. . . , Dn) such that: (a) v 0 (non-negativity), (b) D e Q for i 1,.. . k” (feasibility), (c) vj_vj+Dj.(Oj_Oj)0fori,jé{1,...,kn,ij (convexity). If the problem in hand includes Dirichiet boundary conditions these can be included here as linear constraints that the Di’s corresponding to points on the “boundary” of ek must satisfy. _kk . —5. Let (v , D ) be the solution to Pk• Define vk(9) := maxp2(O), where —k —kp(O)=v +D •(O—O,). 6. Vk yields an approximation to the minimizer of P. Remark 4.2.2 The constraints of the non-linear program determine a con vex set. Remark 4.2.3,4 (c) guarantees that p is a supporting hyperplane of the convex hull of the points {(O, vl),. . . , (O, vkn)}. Note that Tik is a piecewise affine convex function. 4.3 Convergence of the algorithm In this section convergence of the algorithm is proved. Define, for notational convenience Jk(Vk, Dk) := (v - . D + C(D)) (Ek)f Proposition 4.3.1 Under the assumptions made on L, the problem Pk has a unique solution. 62 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints PROOF. The mapping (v’,D’) — Jk(v,Dc) is strictly convex. It follows from proposition 4.1.2 that any feasible vector- matrix pair (vc, D’) must lie in [0, K]k x Qk, which together with Remark 4.2.2 implies Pk consists of minimizing a strictly convex function over a compact and convex set. The result then follows Proposition 2.1.5. 0 Proposition 4.3.2 There exists Y E C such that: 1. The sequence {Yk} generated by the Pk ‘s has a subsequence {13k}that converges uniformly to . 2. limkI[vk] I[J]. PROOF. The bounded (Proposition 4.1.2) family {Uj} is uniformly equicon tinuous, as it consists of convex functions with uniformly bounded subgradi ents. The Arzela-Ascoli theorem implies that, upon passing to a subsequence if necessary (which for simplicity will still be denoted by {J, }), there is a non-negative and convex function 7 such that Vk —* 7 uniformly on By convexity VYk —p Vi almost everywhere (lemma 2.1.8); since VJk(O) belongs to the bounded set Q, the integrands are dominated. By Lebesgue Dominated Convergence lim I [] = I[].k—400 C Let ii be the minimizer of I[.] within C. The aim is to show that {ik } is a minimizing sequence of problem P, in other words that lim I [ii,j = I [u].k—*oo 63 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints To this end, the following auxiliary definition is necessary Definition 4.3.3 Let i be such that infUEc I[u} = I[Tz}. Given ek, define fori=1,...,k: 1. 2. G Vu(O), 3. qj(O) :=+G.(6—O) and 4. uj(8) :—maxq(O). Notice that 11k (0) is constructed as the convex envelope of a family of affine functions. The inequalities jk(Uk,Gk) Jk(Vk,D) (43) ‘[Uk] I[i] (4.4) follow from the definitions of jk (Uk k) Uk and 1k, as does the following Proposition 4.3.4 Let i and Uk be as above, then Uk —* U uniformly as k —* 00. The following lemma is key to establishing the convergence result at hand. Lemma 4.3.5 Consider q(0,z,p) E C1 (€ x R x Q — IR), wheree = [a,b] and Q is a compact convex subset of R. Let {fk : 0 — R} be a family of convex functions such that Ofk(O) C Q for all 0 E 0, and whose uniform limit is 7. Let Ek be the uniform partition of 0 consisting of k cubes of volume p(Ek) := ()‘. Denote by u, 1 j kTh, the elements of and let I1(Ek) q5(0, fk(O), Vfk(9)) 64 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints be the corresponding Riemann sum approximating Se q5(x, fk(O), Vfk(O))dO, where O e 4 and 4 E Ek. Then for any e> 0 there is K e N such that fe fk(O), Vfk(O))dO - k) q5(O,4,fk(O), Vfk(O)) e (4.5) for any k K. PROOF. By lemma 2.1.9, for each fk there exists a sequence of continuously differentiable convex functions {g } such that g — fk uniformly. Let hk be the first element in {g} such that IIhk — fkII and IIVhk(O) — Vfk(O)II for all 0 e e where Vfk is continuous. Then hk —f f uniformly, and by Lemma 2.1.8 we have that Vhk(O) —÷ VJ(9) a.e. It follows from Egoroff’s theorem that for every n e N there exists a set A C 0 such that: (0 \\ Ar,,) <1/n and Vhk —f V7 uniformly on A. Let X (.) be the 1-0-valued indicator function of 4 and define gk(0) := (0, hk(9),Vkk(0)) - Fix n, consider 0 e A and let {0 } be a sequence of 0 ‘s converging to 0o as the partition is refined. By uniform convergence, Vf is continuous on A, hence lim hk(0) 7(0°) and lim Vhk(0) = V7(00) (4.6) k—*oo k—+oo It follows from (4.6) and the continuity of that Yk — 0 almost everywhere on A,.. The following inequalities follow from the Mean Value Theorem, the 65 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints compactness of (9 and Q and the definition of hk II(6,fk(O),Vfk(O))IIK1, forall Oee andsome K1>O. and gk() - fk(O),Vfk(O)) - Xk(O)(9, fk(O)Vfk(O))) for some K2 > 0 and all 0 e (9 where Vfk is continuous. Therefore fe cb(0, fk(0), Vfk(0))dO - f(O), Vfk(0)) < K2(9 I k + JYk(0)d8 Since g — 0 aimost everywhere on A, by Lebesgue Dominated Conver gence urn / gk(0)d00,k—ooJA moreover, the definition of A and the fact that IIc’(O, fk(O), Vfk(0))II K implie 2K1f gk(0)dO Given e> 0 take n e N such that ‘ and K such that K2H(9II + f gK(e)dO Then equation (4.5) holds for all k K. Proposition 4.3.6 For each k there exist ci(k) andc2(k) such that jk(vk,D)_I[vkj ei(k) (4.7) 66 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints Jk(Uk,Gk)_1[UkJ E2(k) (4.8) andei(k),c2(k)—*0 ask —* 00. PROOF. It will be shown that (4.7) holds, the proof for (4.8) is analogous. Define the simple function Wk(O) := L(O, i4, D), 0 e hence Jk(Vk,D) = fet0d0 (4.9) The left-hand side of (4.7) can be written as fWk(0)dO — I[ik1 (4.10) It follows from Lemma 4.3.5 that = satisfies ei(k)—*0 k—+oo. ci The main theorem in this chapter can now be proved, namely: Theorem 4.3.7 The sequence {Yk} is minimizing for problem P. PROOF. It follows from Proposition 4.3.6 and equations (4.3) and (4.4) that I[Zkj +c2(k) +ci(k) I[] I[j (4.11) Letting k —* cc in (4.11) and using Proposition 4.3.2 yields the desired result. ci 67 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints Remark 4.3.8 Notice that given the kthstep approximation vk(O), an ini tial state for problem Pk+1 can be generated by evaluating Vk and VVk at the elements of9k+1• This allows for an iterative approach to solving larger problems, which may speed up running times considerably. 4.4 Examples This section contains some results from implementing the algorithm. The first two examples to reduce quadratic programs, whereas the third and fourth ones are more general non-linear optimization programs. All the computer coding has been written in MatLab. However, in both cases sup plemental Optimization Toolboxes were used. In the first two examples we used the Mosek 4.0 Optimization Toolbox, whereas in the last two we used Tomlab 6.0. These four examples share the common microeconomic motivation provided in Section 2.3.3. 4.4.1 The Mussa-Rosen problem in a square The following structures are shared in the first two examples, where n = 2 • x = (vk, Dk), this structure will determine any possible candidate for a minimizer to Jk(•,•) in the following way: vk is a vector of length k2 that will contain the approximate values of the optimal function evaluated on the points of the lattice. The vector D’ has length 2* k2 and it contains what will be the partial derivatives of at the same points • h is a vector of length 3*k2. The product hx provides the discretization of the integral fe(° Vv — v(O))f(O)dO. • B is the matrix of constraints. The inequality Bx 0 imposes the non-negativity of v and D’ and the convexity of the resulting Jk• Remark 4.4.1 The density f(O) is “built into” vector h and the cost func tion C. 68 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints Let 0 = [1, 2]2, C(q) = IIqll, and assume the types are uniformly distributed. This is a benchmark problem, since the solution to the princi pal’s problem can be found explicitly . This case reduces to solving the quadratic program sup hx — xtHx subject to Bx<O H is a (3 * k2) x (3 * k2) matrix whose first k2 columns are zero, since v does not enter the cost function; the four k2 x k2 blocks towards its lower right corner form a (2* k2) x (2 * k2) identity matrix. Therefore xtHx is a discretization off0 IIVv(O)IIdO. Figure 4.1(a) was produced using a 17 x 17- points lattice and a uniform density, whereas Figure 4.1(b) shows the traded qualities. 4.4.2 The Mussa-Rosen problem with a non-uniform density of types In this section the cost function from the previous example is kept, but it is now assumed that the types are distributed according to a bivariate normal distribution with mean (1.9, 1) and variance-covariance matrix .3 .2 .2 .3 As noted before, the weight assigned to each to each agent type is built into h and H, so the vector x remains unchanged. The execution of the algorithm yields the figure 4.2(a). Remark 4.4.2 It is interesting to see that in this case bunching of the sec ond kind, as described by Roche and Choné in /44], appears to be eliminated as a consequence of the skewed distribution of the agents. This can be seen in the non-linear level curves of the optimizing function v. This is also quite evident in the plot of the qualities traded, which is shown below. 69 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints —0.5 0 0.5 1 1.5 2 2.5 (b) The qualities traded. Figure 4.1: Optimal solution for uniformly distributed agent types. The MatLab programs for the two previous examples were run on Mat- Lab 7.0.1.24704 (R14) in a Sun Fire V480 (4x1.2 HGz Ultra III, 16 GB RAM) computer running Solaris 2.10 OS. In the first example 57.7085 sec onds of processing time were required. The running time in the second example was 81.7280 seconds. (a) The optimal function v. 2.5 2 1.5 0.5 0 —0.5 70 —0.5 0 0.5 ‘.5 2.5 4.4.3 An example with non-quadratic cost This example approximates a solution to the problem of a principal who is selling over-the-counter financial derivatives to a set of heterogeneous agents. This model is presented by Carlier, Ekeland and Touzi in . They start with a standard probability space (cl, F, F), and the types of the agents are given by their risk aversion coefficients under the assumption of mean- variance utilities; namely, the set of agent types is 0 = [0, 1], and the utility Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints (a) The optimal function v. 2.5 1.5 (b) The qualities traded. Figure 4.2: Optimal solution for normally distributed agent types. 71 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints of an agent of type 0 when facing product X is U(0, X) = E[X] — OVar[X] Under the assumptions of a zero risk-free rate and that the principal has access to a complete market, her cost of delivering product X (0) is given by —i/—v’(0); where is the variance of the Radon-Nikodym derivative of the (unique) martingale measure, and Var[X(0)j = —v’(O). The principal’s problem can be written as sup J (Ov’(O) + —v’(0) — v(0)) dOVEC 0 (4.12) whereC := {v :0 —*IR v convex, v O,v’ 0 and Var [X(0)] = —v’(O)}. Figure 4.4.3 shows an approximation of the maximizing using 25 agent types. Figure 4.3: The optimal function . 4.4.4 Minimizing risk This example falls within the framework of the risk minimization problem studied in Chapter 3. In this case, the principal underwrites a catalogue of 0.2 0.4 72 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints call options on her income and their corresponding prices. Notice that the contracts will be characterized by the different strikes. An analysis of the agents’ problem as done in Chapter 3 yields derivatives of the form: X(O) = (IWI — K(O)) with 0 < K(O) < IIWII. The principal evaluates the risk associated with her overall position W + f(ir(O) - X(O))dO via the “entropic measure” of her position, i.e. p (w + f(x(o) - Tr(O))dO) where p(X) = logE[exp{—/3X}] for some /3> 0. The principal’s problem is to devise a catalogue as to minimize her risk exposure. We assume the set of states of the World is finite with cardinality m. Each possible state wj can occur with probability Pj• The realizations of the principal’s wealth are denoted by W = (Wi,. . . ,Wm). Note that p and W are treated as known data. The objective function of the non-linear program is F(v, v’, K) = log (ex {_ wipi + (T(K — IWI)) pii=1 i=1 j=1 — (LTKi_1wi1DPi}) + where K = (K1, . . . , K) denotes the vector of type dependent strikes. We denote by ng the total number of constraints. The principal’s problem is to find 73 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints mm F(v,v’,K) subject to G(v,v’,K) 0(v,v,.K) where G : — determines the constraints that keep (v, v’, K) within the set of feasible contracts. Let (1/6, 2/6,.. ., 1) be the uniformly dis tributed agent types, and • W=4*(—2,—1.7,1.4,—.7,—.5,0), • P = (1/10, 1.5/10, 2.5/10, 2.5/10, 1.5/10, 1/10). The principal’s initial evaluation of her risk is 1.52. The plots for the approx imating U and the strikes are given in Figure 4.4. Note that for illustration purposes the scale for the agent types in the second plot has been changed. The interpolates of the approximation to the optimal function U and the strikes are given in the table following the plots. 74 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints (b) The type-dependent strikes Figure 4.4: Optimal solution for underwriting call options. Entropic case. The Principal’s valuation of her risk after the exchanges with the agents decreases from 1.52 to —3.56. Remark 4.4.3 Notice the “bunching” at the bottom. (a) The optimal function v. 75 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints _________ K1 1.078869 __ K2 0.785079 K3 0.733530 K4 0.713309 K5 0.713309 K6 0.713309 Table 4.1: The optimal function v and the strikes. Entropic case 4.5 A catalogue of put options This section discusses the case where the principal restricts the type of contracts offered to put options underwritten on her income. In other words, the elements of the catalogues that are offered by the principal are of the form ((K— WIY,ir(K)) Notice that the different contracts are determined by the choice of K. As studied in Chapter 3, given a price schedule it, an agent of type 0 computes sup{U((K— IWI),0) —ir(K)} K It will be assumed that W 0 is a bounded random variable. Then the principal considers contracts of the form X(0) = (K(0) — WI) with 0 K(0) 11W1100. The boundedness assumption on the strikes is made with no loss of generality as each equilibrium pricing scheme is necessarily non-negative. Note that in this case the risk measure can be defined on L°° (IP), so only convergence in probability is required to use the Fatou property. Both the agents’ net utilities and the variance of their positions are bounded from above by some constants K1 and K2, respectively. Thus, the principal chooses a function v and contract X from the set {(X,v) I v e C, v K1, —Var[(K(0)—WI)j = v’(O), Iv’I K2, 0 K(O) 11W1I00}. 4.196344 3.234565 2.321529 1.523532 0.745045 0.010025 76 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints The variance constraint v’(O) = —Var[(K(O) — IWI)] implies the strikes can be expressed in terms of a continuous function of v’, i.e., K(O) = F(v’(O)). The risk measure considered is AV©RA, and therefore the numerical pro cedure deviates from the algorithm presented above. This is caused by the fact that solving the “risky” part of the principal’s problem involves finding a minimax point. However, the philosophy of approximating a convex func tion via an envelope of affine functions still applies. The Principal’s problem can be written as inf { (w - f {(F(v’(O)) - IWI) - E{(F(v’(O)) - IWI)j} do) - I(v)} where the infimum is taken over the set of all functions v E C that satisfy v <K1 and Iv’I K2. Remark 4.5.1 Within the current framework the contracts are expressed in terms of the derivative of the principal’s choice of v. This reflects the fact that the principal restricts herself to type-dependent put options. This is not always true in the general case. 4.5.1 An existence result Let {v} be a minimizing sequence for the principal’s optimization problem. The functions v are uniformly bounded and uniformly equicontinuous so we may with no loss of generality assume that v —f Y uniformly. Recall this also implies a.s. convergence of the derivatives. Lebesgue Dominated Convergence and the continuity of F, along with the fact that W is bounded yield f(F(v(O)) - IWI)dO —* fe0 - WIidO P-a.s. 77 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints and mofe — IWIY’dO = fe’° — IWI)dO This shows that the principal’s positions converge almost surely and hence in probability. Since p is lower-semi-continuous with respect to convergence in probability then solves the principal’s problem. 4.5.2 An algorithm for approximating the optimal solution In the following numerical implementation it is assumed that the set of states of the World is finite with cardinality m. Each possible state Wj can occur with probability pj. The realizations of the principal’s wealth are denoted by W = (Wi,. . . , Wm). Note that p and W are treated as known data. The principal evaluates risk via the risk measure p(X) = — sup qEQ j=1 where QA:={qeIR I p.q1,qj<A4}. It is also assumed that the set of agent types is finite with cardinal ity n, i.e. 0 = (Oi’.. . ,0,). The density of the types is given by M := (Mi,.. . , M,). In order to avoid singular points in the principal’s objective function, the option’s payoff function f(x) = (K — x) is approximated by the differentiable function ( 0, if xK—e, T(x, K) = S(x, K), if K — e < x <K + e, ( x—K, if xK+E. where X2 c—K K2—2Kc+cS(x,K)=—+4€ 2€ 4€ The algorithm uses a penalized Quasi-Newton method, based on Zakovic 78 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints and Pantelides , to approximate a minimax point of F(v, K, q) = — Wpq + — IWI)) piqi — i=1 1=1 j=1 (T(K_w))P+ i=1 j=1 1 / Vj — V”\\ 1 / Vn — . lViOi J +— jVj n=1 \\ °i+10iJ fl where v = (vi,. . . , v,) stands for the values of a convex, non-increasing function, v’ = (vi,.. . , v) are the corresponding values for the derivative and K = (K1, . . . , K,) denotes the vector of type dependent strikes. The need for a penalty method arises from having to face the equality constraints v’(O) = —Var{(K(O)—IWI)j and p•q = 1. In order to implement a descent method, these constraints are relaxed and a penalty term is added. Let ng be the total number of constraints. The principal’s problem is to find mm max F(v, K, q) subject to G(v, K, q) 0 (v,K) qEQA where G : jR2n+m RT1J determines the constraints that keep (v, K) within the set of feasible contracts and q e QA. Example 4.5.2 The effects of risk transfer on the principal’s position are illustrated in two models with five agent types and two states of the world. In both cases W = (—1,--2), 0 (1/2, 5/8,3/4,7/8, 1) and A = 1.1 The starting values vo, qo and K0 we set are (4,3,2, 1,0), (1, 1) and (1,1, 1, 1, 1) respectively. i) Let p = (0.5,0.5) and the types be uniformly distributed. The princi pal’s initial evaluation of her risk is 1.52. The optimal function v and strikes are: 79 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints V1 0.1055 K1 1.44 V2 0.0761 r 1.37 V3 0.0501 K3 1.07 V4 0.0342 K4 1.05 V5 0.0195 K5 1.05 Table 4.2: The optimal function v and the strikes. Case 1. The Principal’s valuation of her risk agents decreases to 0.2279. after the exchanges with the 1.45 I.15 45 5 (a) The type-dependent strikes. (b) The optimal function v. Figure 4.5: Optimal solution for underwriting put options, Case 1. 80 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints ii) In this instance p (0.25,0.75) and M = (1/15,2/15,3/15,4/15,5/15). The principal’s initial evaluation of her risk is 1.825. The values for the discretized v and the type-dependent strikes are: V1 0.0073 K 1.2!J V2 0.0045 IR 1.16 V3 0.0029 K3 1.34 V4 0.0026 K4 0.11 V5 0.0025 K5 0.12 Table 4.3: The optimal function V and the strikes. Case 2 The Principal’s valuation of her risk after the exchanges with the agents is 0.0922. 81 Chapter 4. An Algorithm to Solve Variational Problems with Convexity Constraints C 1:5 2 2.5 3 3.5 4 4.5 5 (a) The type-dependent strikes. 7510 2.53455 (b) The optimal function v. Figure 4.6: Optimal solution for underwriting put options. Case 2. 82 Chapter 5 Conclusions This work borrows tools from several fields; namely, Mathematical Fiance (Convex Risk measures), Mathematical Economics (Contract Theory) and Convex Analysis. Chapter 2 includes a new (to the author’s knowledge) re sult stating that a convex function defined on a Hubert space, which accepts an equivalent norm that is differentiable off the origin, is not only densely Fréchet differentiable (this is a well known result); but these derivatives are actually locally Lipschitz on a dense subset. Chapter 3 analyzes a screening problem where the principal’s choice space is infinite dimensional. The main motivation was to present a nonlin ear pricing scheme for over-the-counter financial products, which she trades with a set of heterogeneous agents with the aim of minimizing the exposure of her income to some non-hedgeable risk. U-convex analysis has been used in order to characterize incentive compatible and individually rational cata logues. To keep the problem tractable the agents have been assumed to have mean-variance utilities, but this is not necessary for the characterization of the problem. Considering more general utility functions is an obvious exten sion to this work. The main result is a proof of existence of a solution to the principal’s risk minimization problem in a general setting. The structure of optimal contracts has also been characterized and as it has been shown that the optimal solution is, in some sense, unique. In Chapter 4 a numerical algorithm to estimate the minimizers of vari ational problems with convexity constraints has been developed. The main motivation for the study of such algorithm stems from the fact that in most situations finding closed-form solutions to the principal’s problem described in Chapter 3 is not possible. This an INTERNAL method, i.e., at each preci sion level the approximate minimizer lies within the acceptable set of func 83 Chapter 5. Conclusions tions. The examples are developed over one or two dimensional sets for illustration reasons, but the algorithm can be implemented in higher dimen sions. 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A.1 MatLab code for the example in Section 4.4.1 The main bodies of the codes for examples in Sections 4.4.1 and 4.4.2 use the following function, which generates the envelope of affine functions as described in Section 4.2. function val= V(x, y, ii) global S X Y u=zeros(1, ii); val = sizexy = size(x); for i = 1:sizexy(1), forj = 1:sizexy(2), xval = x(i,j); yval = y(i,j); for k=1:n u(k)=S(k) +S(k+n) *(xval X(k))+S(k+ *n) *lyval Y(k)); end val(i,j) = max(u); 90 Appendix A. Matlab and Maple Codes end end The following is the main body of the code: % The Mussa.-Rosen Problem in a Square global S X Y n=8; % The matrix H corresponds to the one in section 4.4.1. Hi =zeros(n2, H.2=/zeros(n, n&) eye(n2,nzeros(n2,n)J; H3=/zeros(n,n)zeros(n,n eye(ri,n)]; H=[Hi; H; H3]; H=sparse (H); XN=zeros (n, n); for i=i:n XN(i, :)=(i + ((i-i)/(n-i))) *ones(i, n); end % The vectors X and Y make up the lattice of types. X—tzeros(i, 0); for i=i:n X=/X XN(i, :)J; end YN=zeros(n, n); for i=i:n YN(:, i)=(i +((i-i)/(n- 1))) *ones(’n, i); end Y=zeros(i, 0); for i=i:n 91 Appendix A. Matlab and Maple Codes Y=/Y YN(i,:)]; end % f holds the linear part of the quadratic objective. f_—/ones(1,n2)-x -Y]; % Bi and B3 will set the positivity constraints on v and its partial deriva tives. Bi =[ eye(n2,n2) zeros(n2,n)zeros(n2,n)]; B3=/ zeros(n,n)eye(n,n eye(n2,n2)]; % B2 sets the convexity constraints. B=zeros(n4,9*(n2)); for j=1:n2 for i=1:n2 if (i-i == 0) B2(i+(j-1) *n2,:)=zeros(1, g*n2); else B2(i+(j-1)*(n2),j)z1; B2(i+(j-1)*(n),i)z_1; B2(i+ (j-i) *(n2),j+(’n)=X(1 , i)-X(1,j); B(i+ (j-i)*(n),j+*(n2))r Y(1, i)- Y(1,j); end end end B=[B1; B3;-B2]; B=sparse(B); % There is no a priori bound on the function v. buc=/J; 92 Appendix A. Matlab and Maple Codes % This a corresponds to the one mentioned in Section 4.4.1 in the constraints of the quadratic program. a=zeros(2*(n)+n4,1); % This instruction records running times. t—clock; % The following is the call to the quadratic solver. Q—tmskqpopt(H, f, B, a, buc); S=Q. sol. itr. xx; % The outputs: Elapsed time and plot. etime(clock, t) xvec = (1:.O1:); yvec = (1:.O1:2); [Xmesh, Ymesh] = meshgrid(xvec,yvec); xv = (1:.1:2); yv = (1:.1:2); [Xm,Ym] = meshgrid(xv,yv); Vmesh = V(Xmesh, Ymesh, n2); contour3(Xrnesh, Ymesh, Vmesh, 35) hold on; surface (Xmesh, Ymesh, Vmesh, ‘EdgeColor’,[.8 .8 .8], ‘FaceColor’, ‘none’) grid off view(-15,25) colormap cool A.2 MatLab code for the example in Section 4.4.2 This example differs from the one presented above in the non-uniform dis tribution of types. % This part of the code includes the density into the cost-function matrix 93 Appendix A. Matlab and Maple Codes H. mu = [1.9 1]; Sigma = [.3 .2; .2 .3]; xl = 1+1/17:1/17:2; x2 = 1+1/17:1/17:2; [X1,X2] = meshgrid(xl,x2); D = mvnpdf([Xi (:) X2(:)], mu, Sigma)’; Hi =zeros(n2,3*(rj2)); H22=zeros(n n2); H33=zeros(n,n); for i=1:n2 H22(i, i)=D(1, i); H33(i, i)=D(1, i); end H2=[zeros(n,n2) H22 zeros(n,rt2)]; H3=[zeros(n n2) zeros(m2,n2) H33]; H=[H1; H2; H3]; % The density has to be included in the linear part of the objective function. f=[D - (X. *D) - (Y. *D)]; A.3 MatLab code for the example in Section 4.4.3 This non-linear example requires the objective function to be build outside the main body of the optimization routine. Both this code and the one in section A.4 employ the following function: 94 Appendix A. Matlab and Maple Codes % The one-dimensional version of the function that generates the convex envelope of a family of affine functions. function val=Vonediin(x,y, X) sizex = size(x); sizeX = size(X); n=sizeX(2); u=zeros(1, n); val = forj = 1:sizex() xval = x(1,j); for k=1:n u(k)=y(1,k)+y(1,k+n)*(’xvalX(l,k)); end val(1,j) = max(u); end The following is the objective function in the principal’s non-linear program. function val=CEkTomlab(x) sizeof=size (x); n=(1/) *sizeof(2); X=zeros(n, 1); for i=1:n X(i, n,)=i/n; end f=zeros (n, 1); F=zeros(n, 1); G=zeros(n, 1); for i=1:n f(i, 1)=x(i, 1); F(i, 1)=x(n+i, 1); G(i, 1)=(-F(i, 1))(1/2); end 95 Appendix A. Matlab and Maple Codes g—-(F. *x); val==sum(f-i-g- C); The following is the main body of the routine. n=20; X=zeros(1, n); xo=zeros(1,n); fo =zeros (1, n); % The partition of the interval and the initial values for the variables vector. for i=1:n X(1,i)=i/n; xo (1,i)=n-i; fo (1,i)=t-1-(n_i); end % The starting point X0 = [xof0]; % The matrix A contains the convexity constraints. A=zeros(n2,2*n); for j=1:n for i—tl:n if (i-i == 0) A(i+(j1)*n,:)=zeros(1, 2*n); else A (i+(j-1) *n,j)1; A(i+(j1)*n,i)=1; A (i+(j-1) *n,i+n)zzx(1,i)_x(1,j); 96 Appendix A. Matlab and Maple Codes end end end % The bounds for the constraints (b and b1), for the variables (xl and x). Name= ‘CEkT’; = zeros(1,n2); b1 =11; xi=[zeros(1,n) 1000O*ones(1,n)]; U =110000 *ones (1, n) zeros(1, n)]; flowBnd=- 100000; % This is the call to the nonlinear solver. Prob=conAssign(’CEkTomlab’, U I1 U xj, x, Name, X0, , flowBnd, A, b1, ba); Prob.NumDiff=1; Prob. ConsDiff=5; Prob.Solver.Alg=0; Result=tomRun(’conSolve’, Prob, ); % The output. Z=(Result.xk — [Result .xk(n) * ones(n, 1); zeros(n, 1)])’; xvec = (0:.01:1); Vmesh = Vonedim( xvec, Z, X); hold on; plot (xvec, Vmesh); 97 Appendix A. Matlab and Maple Codes A.4 MatLab code for the example in Section 4.4.4 The code for this example is separated into several subroutines which are then integrated in the main body. % This is the payoff of a call option. function val=Call(W,K) if (W>=K) val=W-K; else val=O; end The non linear constraints are built separate from the main body. %The non-linear (variance) constraints function val=NL CHMTomlab2(x) % The number of types n and states of the world s. n—JO; s=10; % The principal’s risky initial endowment W and the corresponding proba bilities. W=4*[2; -1.7; 1.4;-.7; -.5; 0]; P=/1/1 0; 1.5/10; 2.5/10; 2.5/10; 1.5/10; 1/10]; % The initial values of the function and the strikes. V=zeros(n, 1); K=zeros (n, 1); for j=1:n V(j,1)=x(j+n,1); K(j, 1)=x(ji2*n, 1); 98 Appendix A. Matlab and Maple Codes end M=zeros(s,n); for i=1:s for j=i:n M(i,j)=Call(abs(W(i, 1)),K(’j, 1)); end end * P).2+V; The following is the objective function in the principal’s non-linear program. function val=HMTomlab2(x) n—6; s=6; T=zeros(n, 1); W=4*[2; -1.7; 1.4;-.7; -.5; 0]; P=[1/1 0; 1.5/10; 2.5/10; 2.5/10; 1.5/10; 1/10]; Beta—. 5; % Separating the variables vector into its three components. v=zeros (n, 1); V=zeros (n, 1); K=zeros(n, 1); for j=1:n v(j, 1)=x(j, 1); V(j, 1)=x(j+n, 1); K(j, 1)=x(j+2*n, 1); 99 Appendix A. Matlab and Maple Codes end % Computing the Risky Part of the Principal’s Problem. M—zeros(s, n); for i=1:s for j=i:n M(i,j)=Call(abs(W(i, 1)),K(j, 1)); end end Y=M*ones(n, 1); B=exp (-Beta *( W+ Y)); R__P*B; % Computing the Income of the Principal’s Problem. D=P *M I=sum(-D-(T. *V) ‘+v’); % The value of the objective function. val=R +1; The following is the main body of the optimization routine for the principal’s problem in Section 4.4.4. % The TomLab routine for the one-dimensional HM Problem. n=6; X=zeros(’l,n); vo =zeros (1 , Vo =zeros (1, n); Ko=zeros(1,n); m=6; % The partition of the interval and the initial values for the variables vector. 100 Appendix A. Matlab and Maple Codes for i—1:n X(1,i)_—(i/n); vo (1,i)=n-i; Vo (1,i)=-.l-(n-i); K0 (1,i)=1; end %The starting point. X0 = [v0VK]; % The matrix A contains the convexity constraints. A=zeros(m2,3*n); for j=1:ri for i=1:ri if (i-i == 0) A (i+ (j-1) *, :)=zeros(1, 3*n); else A (i+(j-1) *n,j)1; A (i+(j-1) *n,i)1; A (i+(j-1) *n,j+n)=x(1,ifx(1,j); end end end % The bounds for the constraints (b and b1), for the variables (xj and xv). Name= ‘HM’; b=zeros(1,n2); b1 =11; Xi =[zeros (1 , n) -10000 *ones (1, n) zeros (1, n)]; Xu/10000*OneS(1,n) zeros(1,n) 10000*ones(1,n)]; CL =-ones(n, 1); cu=ones(n, 1); flowBnd=-1 00000; % This is the call to the nonlinear solver. Prob_-conAssign(’HMTomlab2’, U [1, L1 x, x, Name, Xo, U flowBnd, A, b1, ba,’ NLCHMTom1ab2’, [1, [1, U, CU); Prob.NumDiff=1; Prob. ConsDiff=5; 101 Appendix A. Matlab and Maple Codes Prob.Solver.A lg=O; Result=tomRun(’conSolve Prob, 2); Z = (Result.xk)’; W=Z(1, 1:n); % The output. xvec = (O:.O1:1); Vmesh = Vonedim( xvec, Z, X); hold on; plot (xvec, Vmesh); A.5 Maple code for the example in Section 4.5.2 with(LinearAlgebra) n := 5: m := 2: ng := 2*m+4*n+1: This section constructs the objective function f and its gradient. x := Vector(2*n, symbol = xs): q := Vector(m, symbol = qs): f := add(—G[j] *p[j] * q[j],j = 1..m)+ add(add(T(x[i + n], W(j]) * M[ij * p[jj * q[j], i = 1..n),j add(add(T(x[i+n],W[j]) *M[ij *p[jl,i 1..n),j = 1..m)+ add((x[i] — t[i] * (x[i + 1] — x[i])/(t[i + 11 — t[iJ)) * M[i}, i = 1..n — x[n] — t[nl * (x[nj — x[n — 1]) * M[nj/(t[n] — t[n — 1]) TT := (x, K)-L 1/4*x/eps+1/2*(eps_K)*x/eps+1/4*(K_2*K*eps+eps)/eps: T := (x, K) - piecewise(x K-eps, 0, x K+eps, TT(x, K), K+eps x, x-K): gradfx := 0: gradfq := 0: for i from 1 to 2*n do gradfx[i} := diff(f, xlii) 102 Appendix A. Matlab and Maple Codes end do: for i from 1 to m do gradfq[iJ := diff(f, q[i]) end do: This section constructs the constraint function g and its gradient. g := Vector(ng, symbol tt): for j from 1 to n do g[j] := -xU] end do: for j from 1 to n-i do g[j+n] := x[j+1]-x[j] end do: for i from 1 to n-i do g[i+2*n_i] := add(T(x[i+n], W])*p[jj, j = 1 .. m)-add(T(x[i+n], W[j])*p[j], j = 1 .. m)+(x[i+1]-x[i])/(t[i+1]-t[i])-eps2 end do: g[3*n_1} := add(T(x[2*nJ, W[j])*p[j], j = 1 .. m)_add(T(x[2*n], W])*p[j, j = 1 m)+(x[n]-x[n-1] )/(t [nJ-t[n-1] )-eps2: for i from 1 to n-i do g[i+3*ni] := -add(T(x[i+n], Wj])*p[j}, j = 1 .. m)+add(T(x[i+n], W[j])*p[j], j = 1 .. m)-(x[i+i]-x[i])/(t[i+1]-t[i})-eps2 end do: g[4*n4} := _add(T(x[2*n], W[j])*p[j], j = 1 .. m)+add(T(x[2*n], W[j])*p[j], j = 1 m)-(x[n]-x[n-i])/(t[n]-t[n-i])-eps2: g[4*n] := add(pfi]*q[i], i = 1 .. m)-i+eps3: g14*n+il := _add(p[i]*q[iJ, i = 1 .. m)-i-eps3: for i from 1 to m do g[i+4*n+1] := -q[i] end do: for i to m do g[i+m+4*n+i] := q[i]-lambda end do: gradgx := 0: gradgq := 0: for i from 1 to ng do for j from 1 to 2*n 103 Appendix A. Matlab and Maple Codes do gradgx[i, j] := diff(g[i], x[j]) end do: end do: for i from 1 to ng do for j from 1 to m do gradgq[i, j] : diff(g[i], qU]) end do: end do: This section constructs the slackness structures. e := Vector(ng, 1): s := Vector(ng, symbol si): z := Vector(ng, symbol = zi): S :=DiagonalMatrix(s): Z := DiagonalMatrix(z): This section initializes the variable and parameter vectors. x := Vector(2*n, symbol xs): q := Vector(m, symbol = qs): p :=Vector(m, symbol = ps): W := Vector(m, symbol = ws): G := Vector(m,symbol = gs): t := Vector(n, symbol = ts): M := Vector(n, symbol = ms): chi := convert([x, q, s, z], Vector): This section constructs the Lagrangian and its Hessian matrix. F :=convert ( [gradfx+(VectorCalculus[DotProduct]) (Transpose(gradgx), z), gradfq-(VectorCalculus[DotProduct] ) (Transpose(gradgq), z), (VectorCalculuslDotProduct]) ((VectorCalculus[DotProduct]) (Z, S), e)_mu*e, g+s], Vector): DF =0: for i from 1 to 2*n+m+2*ng 104 Appendix A. Matlab and Maple Codes do for j from 1 to 2*n+m+2*ng do DF[i, j] :=diff(F[i], chiLj]) end do: end do: This section inputs the initial values of the variables and the values of the param eters. xinit := (4,3, 2, 1, 0, 1, 1, 1, 1, 1): qinit := (1, 1): sinit : (.1 1, .1, .1): zinit := (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1): tinit := (1/2, 5/8, 3/4, 7/8,1): pinit := (.5, .5): ginit := (-1, -2): minit := (1,1, 1, 1, 1): winit := (1, 2): tau := .1; mu := .1; rho := .5: lambda := 1.1: eps := .1: eps2 := .1: eps3 := .2: xo := xinit; qo :=qinit; so := sinit; zo := zinit; p0 := pinit; go := ginit; mo := minit; wo : winit; xs := xinit; qs := qinit; Si := sinit; zi := zinit; ps := pinit; gs := ginit; ms := minit; ws := winit; ts := tinit: The following section contains the executable code. i := 0; j := 0 normF:=Norm(F,2): while (normF > mu and j <40) do printf(” Inner loop: #Iteration %g /n” ,j); printf(” - Solve Linear System (11) ...“); d := LinearSolve(DF, -Transpose(F)): printf(” doneN”); 105 Appendix A. Matlab and Maple Codes printf(” - Update Params ...“); alphaS:=min(seq(select(type,-s[k] /d[2*n+m+k] ,positive), k = 1 .. Dimension(s))); alphaZ:=min(seq(select(type,-z[k]/d[2*n+m+ng+k] ,positive), k = 1.. Dimension(z))); alphamax:=min(alphaS,alphaZ): alphamax:=min(tau*alphamax,1); printf(” done/n”); chiold := chi; chinew := chio1dja1phamax*d; xs := chinew[1 .. 2*n]: ys := chinew[2*n+1 .. 2*n+mJ: si := chinew[2*n+m+1.. 2*n+m+ng]: zi := chinew[2*n+m+ng+1.. 2*n+m+2*ng]: normF:=Norm(F,2); printf(” doneN”); j:=j+1; end do: 106`\n\n#### Cite\n\nCitation Scheme:\n\nCitations by CSL (citeproc-js)\n\n#### Embed\n\nCustomize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.\n``` ```\n<div id=\"ubcOpenCollectionsWidgetDisplay\">\n<script id=\"ubcOpenCollectionsWidget\"\nsrc=\"{[{embed.src}]}\"\ndata-item=\"{[{embed.item}]}\"\ndata-collection=\"{[{embed.collection}]}\"", null, "Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:\n`https://iiif.library.ubc.ca/presentation/dsp.24.1-0066987/manifest`" ]
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https://mirangu.com/kings-chamber/
[ "Categories\n\n# The King’s chamber\n\nA pyramid with a square base and sides that are equilateral triangles contains a cube. If the cube is taking maximum space as shown, what is the fraction of its volume to the pyramid’s volume?\n\nScroll down for a solution to this problem.\n\n## Solution\n\nThe volume fraction is 30-21√2, which is approximately 0,30.\n\nSetting the cube side to 1 for convenience, we have to find the pyramid side a and height h. We can extract this from the cross section shown above. From the Pythagorean theorem in the left side, we derive h=a/√2.\n\nNow going to the right triangle in the lower right corner, which is similar to half the cross section, we can determine its base as 1/√2. This fixes a=1+√2 and h=1+1/√2.\n\nFinally, the cube’s volume is 1 and the pyramid’s is a2h/3, leading to the desired result.\n\n#", null, "Don’t miss these puzzles!\n\nSubscribe to the weekly geometry puzzle e-mail." ]
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https://goiit.com/t/doubt-from-probability/46135
[ "", null, "Doubt from Probability\n\n#1\n\nAman, six of his friends, and a monkey are standing at different vertices of a big cube. Aman has a banana and is a neighbour to the monkey. On each turn, whoever has the banana throws it at random to one of his three neighbours. If the monkey gets the banana he eats it. What is the probability that Aman is the one who feeds the monkey?\n\nSubmit detailed solution.\nThanks\n\n#2\n\n3/7\n\n2 Likes\n#3\n\nAgreed Sir!\nWe get a GP with common ratio as \\frac{2}{9} and first term \\frac{1}{3}\nBasically we need to first see how this works by taking a few cases... We then see that the banana will reach Aman in even no. of steps and for each added step we have two more possibilities... Indeed a nice problem involving logic\n\n1 Like\n#4\n\nAnswer is 7\\12 @Sourav_Dey @Mayank_2019_1 sir\n\n#5\n\nOkay, I understood my mistake, I did not consider the fact that if monkey gets the banana then the process will stop... Basically 2 of his friends will have only two other places to pass the banana if Aman has to give the banana to the monkey.\nNow, that 1/9 term is okay but for the multiplication by 2 there will be more cases\nWait will have to see the question\n\n1 Like\n#6\n1 Like\n#7\n\nThe Cube is shown above, where A is aman and M is the monkey. Let p be the probability that Aman feeds the monkey given that he is holding the banana. For each non-monkey neighbor of aman, let q be the probability that aman feeds the monkey\ngiven that the neighbor is holding the banana. (By symmetry, it is the same probability for each neighbor.) For each non-aman neighbor of the monkey, let r be the probability that aman feeds the monkey given that the neighbor is holding the banana. (Again, by symmetry, it is the same probability for each of the monkey's\nother neighbors.) Finally, let s be the probability that aman feeds the monkey given that the person opposite from aman is holding the banana. Note also that if the person who is opposite the monkey has the banana, then the probability that aman feeds the monkey is 1 \\over 3 , by symmetry, since each of the monkey's three neighbors is then equally likely to be the feeder. These probabilities are labeled on the diagram above. When aman has the banana, he has probability 1 \\over 3 of immediately feeding the monkey, and probability 2 \\over 3 of passing it to a neighbor. Therefore,\np = 1\\over 3 + 2 \\over 3 q\nWhen one of aman's non-monkey neighbors has the banana, she has probabilty 1\\over 3 of throwing\nthe banana back to aman, probability 1 \\over 3 of throwing the banana to one of the monkey's other neighbors, and probability 1 \\over 3 of throwing the banana to the person opposite the monkey. Therefore,\nq= 1 \\over 3 p + 1 \\over 3 r + 1 \\over 9\nWhen one the monkey's other neighbors has the banana, he has probability 1 \\over 3 of feeding the monkey (in which case aman does not feed the monkey), probability 1 \\over 3 of throwing the banana to one of aman’s neighbors, and probability 1 \\over 3 of throwing the banana to the person\nopposite aman. Therefore,\nr = 1 \\over 3 q + 1 \\over 3 s.\nFinally, when the person opposite aman has the banana, she has probability 2 \\over 3\nof throwing it to one of the monkey’s non-aman neighbors, and probability 1 \\over 3\nof throwing it to the person opposite to the monkey. Therefore,\ns = 2 \\over 3 r + 1 \\over 9\nThus, we have the system of equation\np= 1 \\over 3 + 2 \\over 3 q\nq= 1\\over 3 p + 1 \\over 3 r + 1 \\over 9\nr= 1 \\over 3 q + 1 \\over 3 s\ns= 2 \\over 3 r + 1 \\over 9\nSolving this system of equation gives p= 7 \\over 12 and q= 3 \\over 8 . So the probability that aman feeds the monkey is 7 \\over 12\n\nThanks.\n\n1 Like" ]
[ null, "https://gt-uploads0002.s3.dualstack.ap-south-1.amazonaws.com/original/2X/e/efa0a2c2784bb5a857e38dbe792cabf37ba70384.png", null ]
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https://interhit.org/different-initialization-methods-in-neural-networks-towards-ai-the-best-of-tech-science-and-engineering/
[ "# Different Initialization methods in Neural Networks – Towards AI — The Best of Tech, Science, and Engineering\n\n#### Author(s): Mayank Choudhary", null, "### Different Initialization Methods in Neural Networks\n\nThis is one of the assignments of the hyperparameters tuning specialization from Andrew Ng. It is very important that you regularize your model properly because it could dramatically improve your results.\n\nBy completing this assignment we will:\n\n– Understand that different initialization method and their impact on your model performance\n\n– Implement zero initialization and see it fails to “break symmetry”,\n\n– Recognize that random initialization “breaks symmetry” and yields more efficient models,\n\n-Understand that you could use both random initialization and scaling to get even better training performance on your model.\n\n### Initialization\n\n“Improving Deep Neural Networks”.\n\nTraining your neural network requires specifying an initial value of the weights. A well-chosen initialization method will help learning.\n\nIf you completed the previous course of this specialization, you probably followed our instructions for weight initialization, and it has worked out so far. But how do you choose the initialization for a new neural network? In this notebook, you will see how different initializations lead to different results.\n\nA well-chosen initialization can:\n\nSpeed up the convergence of gradient descent\nIncrease the odds of gradient descent converging to a lower training (and generalization) error\n\nTo get started, run the following cell to load the packages and the planar dataset you will try to classify.\n\nIn :\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport sklearn\nimport sklearn.datasets\nfrom init_utils import sigmoid, relu, compute_loss, forward_propagation, backward_propagation\nfrom init_utils import update_parameters, predict, load_dataset, plot_decision_boundary, predict_dec\n%matplotlib inline\nplt.rcParams[‘figure.figsize’] = (7.0, 4.0) # set default size of plots\nplt.rcParams[‘image.interpolation’] = ‘nearest’\nplt.rcParams[‘image.cmap’] = ‘gray’\n# load image dataset: blue/red dots in circles\ntrain_X, train_Y, test_X, test_Y = load_dataset()", null, "You would like a classifier to separate the blue dots from the red dots.\n\n### 1 — Neural Network model\n\nYou will use a 3-layer neural network (already implemented for you). Here are the initialization methods you will experiment with:\n\nZeros initialization — setting initialization = “zeros” in the input argument.\nRandom initialization — setting initialization = “random” in the input argument. This initializes the weights to large random values.\nHe initialization — setting initialization = “he” in the input argument. This initializes the weights to random values scaled according to a paper by He et al., 2015.\n\nInstructions: Please quickly read over the code below, and run it. In the next part you will implement the three initialization methods that this model() calls.\n\nIn :\n\ndef model(X, Y, learning_rate = 0.01, num_iterations = 15000, print_cost = True, initialization = “he”):\n“””\nImplements a three-layer neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SIGMOID.\nArguments:\nX — input data, of shape (2, number of examples)\nY — true “label” vector (containing 0 for red dots; 1 for blue dots), of shape (1, number of examples)\nlearning_rate — learning rate for gradient descent\nnum_iterations — number of iterations to run gradient descent\nprint_cost — if True, print the cost every 1000 iterations\ninitialization — flag to choose which initialization to use (“zeros”,”random” or “he”)\nReturns:\nparameters — parameters learnt by the model\n“””\ngrads = {}\ncosts = [] # to keep track of the loss\nm = X.shape # number of examples\nlayers_dims = [X.shape, 10, 5, 1]\n# Initialize parameters dictionary.\nif initialization == “zeros”:\nparameters = initialize_parameters_zeros(layers_dims)\nelif initialization == “random”:\nparameters = initialize_parameters_random(layers_dims)\nelif initialization == “he”:\nparameters = initialize_parameters_he(layers_dims)\n# Loop (gradient descent)\nfor i in range(0, num_iterations):\n# Forward propagation: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.\na3, cache = forward_propagation(X, parameters)\n# Loss\ncost = compute_loss(a3, Y)\n# Backward propagation.\ngrads = backward_propagation(X, Y, cache)\n# Update parameters.\nparameters = update_parameters(parameters, grads, learning_rate)\n# Print the loss every 1000 iterations\nif print_cost and i % 1000 == 0:\nprint(“Cost after iteration {}: {}”.format(i, cost))\ncosts.append(cost)\n# plot the loss\nplt.plot(costs)\nplt.ylabel(‘cost’)\nplt.xlabel(‘iterations (per hundreds)’)\nplt.title(“Learning rate =” + str(learning_rate))\nplt.show()\nreturn parameters\n\n### 2 — Zero initialization\n\nThere are two types of parameters to initialize in a neural network:\n\nthe weight matrices (W,W,W,…,W[L−1],W[L])(W,W,W,…,W[L−1],W[L])\nthe bias vectors (b,b,b,…,b[L−1],b[L])(b,b,b,…,b[L−1],b[L])\n\nExercise: Implement the following function to initialize all parameters to zeros. You’ll see later that this does not work well since it fails to “break symmetry”, but lets try it anyway and see what happens. Use np.zeros((..,..)) with the correct shapes.\n\nIn :\n\n# GRADED FUNCTION: initialize_parameters_zeros\ndef initialize_parameters_zeros(layers_dims):\n\n“””\n\nArguments:\n\nlayer_dims — python array (list) containing the size of each layer.\n\nReturns:\n\nparameters — python dictionary containing your parameters “W1”, “b1”, …, “WL”, “bL”:\n\nW1 — weight matrix of shape (layers_dims, layers_dims)\n\nb1 — bias vector of shape (layers_dims, 1)\n\nWL — weight matrix of shape (layers_dims[L], layers_dims[L-1])\n\nbL — bias vector of shape (layers_dims[L], 1)\n\n“””\n\nparameters = {}\nL = len(layers_dims) # number of layers in the network\nfor l in range(1, L):\nparameters[‘W’ + str(l)] = np.zeros((layers_dims[l], layers_dims[l-1]))\nparameters[‘b’ + str(l)] = np.zeros((layers_dims[l], 1))\nreturn parameters\n\nIn :\n\nparameters = initialize_parameters_zeros([3,2,1])\nprint(“W1 = ” + str(parameters[“W1”]))\nprint(“b1 = ” + str(parameters[“b1”]))\nprint(“W2 = ” + str(parameters[“W2”]))\nprint(“b2 = ” + str(parameters[“b2”]))\nW1 = [[ 0. 0. 0.]\n[ 0. 0. 0.]]\nb1 = [[ 0.]\n[ 0.]]\nW2 = [[ 0. 0.]]\nb2 = [[ 0.]]\n\nExpected Output:\n\nW1[[ 0. 0. 0.] [ 0. 0. 0.]]b1[[ 0.] [ 0.]]W2[[ 0. 0.]]b2[[ 0.]]\n\nRun the following code to train your model on 15,000 iterations using zeros initialization.\n\nIn :\n\nparameters = model(train_X, train_Y, initialization = “zeros”)\nprint (“On the train set:”)\npredictions_train = predict(train_X, train_Y, parameters)\nprint (“On the test set:”)\npredictions_test = predict(test_X, test_Y, parameters)\nCost after iteration 0: 0.6931471805599453\nCost after iteration 1000: 0.6931471805599453\nCost after iteration 2000: 0.6931471805599453\nCost after iteration 3000: 0.6931471805599453\nCost after iteration 4000: 0.6931471805599453\nCost after iteration 5000: 0.6931471805599453\nCost after iteration 6000: 0.6931471805599453\nCost after iteration 7000: 0.6931471805599453\nCost after iteration 8000: 0.6931471805599453\nCost after iteration 9000: 0.6931471805599453\nCost after iteration 10000: 0.6931471805599455\nCost after iteration 11000: 0.6931471805599453\nCost after iteration 12000: 0.6931471805599453\nCost after iteration 13000: 0.6931471805599453\nCost after iteration 14000: 0.6931471805599453", null, "On the train set:\nAccuracy: 0.5\nOn the test set:\nAccuracy: 0.5\n\nThe performance is really bad, and the cost does not really decrease, and the algorithm performs no better than random guessing. Why? Let’s look at the details of the predictions and the decision boundary:\n\nIn :\n\nprint (“predictions_train = ” + str(predictions_train))\nprint (“predictions_test = ” + str(predictions_test))\npredictions_train = [[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0]]\npredictions_test = [[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]\n\nIn :\n\nplt.title(“Model with Zeros initialization”)\naxes = plt.gca()\naxes.set_xlim([-1.5,1.5])\naxes.set_ylim([-1.5,1.5])\nplot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)", null, "The model is predicting 0 for every example.\n\nIn general, initializing all the weights to zero results in the network failing to break the symmetry. This means that every neuron in each layer will learn the same thing, and you might as well be training a neural network with n[l]=1n[l]=1 for every layer, and the network is no more powerful than a linear classifier such as logistic regression.\n\nWhat you should remember:\n\nThe weights W[l]W[l] should be initialized randomly to break symmetry.\nIt is however okay to initialize the biases b[l]b[l] to zeros. Symmetry is still broken so long as W[l]W[l] is initialized randomly.\n\n### 3 — Random initialization\n\nTo break symmetry let’s initialize the weights randomly. Following random initialization, each neuron can then proceed to learn a different function of its inputs. In this exercise, you will see what happens if the weights are initialized randomly, but to very large values.\n\nExercise: Implement the following function to initialize your weights to large random values (scaled by *10) and your biases to zeros. Use np.random.randn(..,..) * 10 for weights and np.zeros((.., ..)) for biases. We are using a fixed np.random.seed(..) to make sure your “random” weights match ours, so don’t worry if running several times your code gives you always the same initial values for the parameters.\n\nIn :\n\n# GRADED FUNCTION: initialize_parameters_random\ndef initialize_parameters_random(layers_dims):\n\n“””\n\nArguments:\n\nlayer_dims — python array (list) containing the size of each layer.\n\nReturns:\n\nparameters — python dictionary containing your parameters “W1”, “b1”, …, “WL”, “bL”:\n\nW1 — weight matrix of shape (layers_dims, layers_dims)\n\nb1 — bias vector of shape (layers_dims, 1)\n\nWL — weight matrix of shape (layers_dims[L], layers_dims[L-1])\n\nbL — bias vector of shape (layers_dims[L], 1)\n\n“””\n\nnp.random.seed(3) # This seed makes sure your “random” numbers will be the as ours\nparameters = {}\nL = len(layers_dims) # integer representing the number of layers\nfor l in range(1, L):\nparameters[‘W’ + str(l)] = np.random.randn(layers_dims[l], layers_dims[l-1])* 10\nparameters[‘b’ + str(l)] = np.zeros((layers_dims[l], 1))\nreturn parameters\n\nIn :\n\nparameters = initialize_parameters_random([3, 2, 1])\nprint(“W1 = ” + str(parameters[“W1”]))\nprint(“b1 = ” + str(parameters[“b1”]))\nprint(“W2 = ” + str(parameters[“W2”]))\nprint(“b2 = ” + str(parameters[“b2”]))\nW1 = [[ 17.88628473 4.36509851 0.96497468]\n[-18.63492703 -2.77388203 -3.54758979]]\nb1 = [[ 0.]\n[ 0.]]\nW2 = [[-0.82741481 -6.27000677]]\nb2 = [[ 0.]]\n\nExpected Output:\n\nW1[[ 17.88628473 4.36509851 0.96497468] [-18.63492703 -2.77388203 -3.54758979]]b1[[ 0.] [ 0.]]W2[[-0.82741481 -6.27000677]]b2[[ 0.]]\n\nRun the following code to train your model on 15,000 iterations using random initialization.\n\nIn :\n\nparameters = model(train_X, train_Y, initialization = “random”)\nprint (“On the train set:”)\npredictions_train = predict(train_X, train_Y, parameters)\nprint (“On the test set:”)\npredictions_test = predict(test_X, test_Y, parameters)\n\n/home/jovyan/work/week5/Initialization/init_utils.py:145: RuntimeWarning: divide by zero encountered in log\nlogprobs = np.multiply(-np.log(a3),Y) + np.multiply(-np.log(1 – a3), 1 – Y)\n/home/jovyan/work/week5/Initialization/init_utils.py:145: RuntimeWarning: invalid value encountered in multiply\nlogprobs = np.multiply(-np.log(a3),Y) + np.multiply(-np.log(1 – a3), 1 – Y)\n\nCost after iteration 0: inf\nCost after iteration 1000: 0.6242434241539614\nCost after iteration 2000: 0.5978811277755388\nCost after iteration 3000: 0.5636242569764779\nCost after iteration 4000: 0.5500958254523324\nCost after iteration 5000: 0.544339206192789\nCost after iteration 6000: 0.5373584514307651\nCost after iteration 7000: 0.469574666760224\nCost after iteration 8000: 0.39766324943219844\nCost after iteration 9000: 0.3934423376823982\nCost after iteration 10000: 0.3920158992175907\nCost after iteration 11000: 0.38913979237487845\nCost after iteration 12000: 0.3861261344766218\nCost after iteration 13000: 0.3849694511273874\nCost after iteration 14000: 0.3827489017191917", null, "On the train set:\nAccuracy: 0.83\nOn the test set:\nAccuracy: 0.86\n\nIf you see “inf” as the cost after the iteration 0, this is because of numerical roundoff; a more numerically sophisticated implementation would fix this. But this isn’t worth worrying about for our purposes.\n\nAnyway, it looks like you have broken symmetry, and this gives better results. than before. The model is no longer outputting all 0s.\n\nIn :\n\nprint (predictions_train)\nprint (predictions_test)\n[[1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1\n1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0\n0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1\n1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0\n1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1\n0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1\n0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1\n1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1\n1 1 1 0]]\n[[1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0\n1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1\n1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0]]\n\nIn :\n\nplt.title(“Model with large random initialization”)\naxes = plt.gca()\naxes.set_xlim([-1.5,1.5])\naxes.set_ylim([-1.5,1.5])\nplot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)", null, "Observations:\n\nThe cost starts very high. This is because with large random-valued weights, the last activation (sigmoid) outputs results that are very close to 0 or 1 for some examples, and when it gets that example wrong it incurs a very high loss for that example. Indeed, when log(a)=log(0)log⁡(a)=log⁡(0), the loss goes to infinity.\nPoor initialization can lead to vanishing/exploding gradients, which also slows down the optimization algorithm.\nIf you train this network longer you will see better results, but initializing with overly large random numbers slows down the optimization.\n\nIn summary:\n\nInitializing weights to very large random values does not work well.\nHopefully intializing with small random values does better. The important question is: how small should be these random values be? Lets find out in the next part!\n\n### 4 — He initialization\n\nFinally, try “He Initialization”; this is named for the first author of He et al., 2015. (If you have heard of “Xavier initialization”, this is similar except Xavier initialization uses a scaling factor for the weights W[l]W[l] of sqrt(1./layers_dims[l-1]) where He initialization would use sqrt(2./layers_dims[l-1]).)\n\nExercise: Implement the following function to initialize your parameters with He initialization.\n\nHint: This function is similar to the previous initialize_parameters_random(…). The only difference is that instead of multiplying np.random.randn(..,..) by 10, you will multiply it by 2dimension of the previous layer⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2dimension of the previous layer, which is what He initialization recommends for layers with a ReLU activation.\n\nIn :\n\n# GRADED FUNCTION: initialize_parameters_he\ndef initialize_parameters_he(layers_dims):\n\n“””\n\nArguments:\n\nlayer_dims — python array (list) containing the size of each layer.\n\nReturns:\n\nparameters — python dictionary containing your parameters “W1”, “b1”, …, “WL”, “bL”:\n\nW1 — weight matrix of shape (layers_dims, layers_dims)\n\nb1 — bias vector of shape (layers_dims, 1)\n\nWL — weight matrix of shape (layers_dims[L], layers_dims[L-1])\n\nbL — bias vector of shape (layers_dims[L], 1)\n\n“””\n\nnp.random.seed(3)\nparameters = {}\nL = len(layers_dims) – 1 # integer representing the number of layers\nfor l in range(1, L + 1):\nparameters[‘W’ + str(l)] = np.random.randn(layers_dims[l], layers_dims[l-1]) * np.sqrt(2./layers_dims[l-1])\nparameters[‘b’ + str(l)] = np.zeros((layers_dims[l],1))\nreturn parameters\n\nIn :\n\nparameters = initialize_parameters_he([2, 4, 1])\nprint(“W1 = ” + str(parameters[“W1”]))\nprint(“b1 = ” + str(parameters[“b1”]))\nprint(“W2 = ” + str(parameters[“W2”]))\nprint(“b2 = ” + str(parameters[“b2”]))\nW1 = [[ 1.78862847 0.43650985]\n[ 0.09649747 -1.8634927 ]\n[-0.2773882 -0.35475898]\n[-0.08274148 -0.62700068]]\nb1 = [[ 0.]\n[ 0.]\n[ 0.]\n[ 0.]]\nW2 = [[-0.03098412 -0.33744411 -0.92904268 0.62552248]]\nb2 = [[ 0.]]\n\nExpected Output:\n\nW1[[ 1.78862847 0.43650985] [ 0.09649747 -1.8634927 ] [-0.2773882 -0.35475898] [-0.08274148 -0.62700068]]b1[[ 0.] [ 0.] [ 0.] [ 0.]]W2[[-0.03098412 -0.33744411 -0.92904268 0.62552248]]b2[[ 0.]]\n\nRun the following code to train your model on 15,000 iterations using He initialization.\n\nIn :\n\nparameters = model(train_X, train_Y, initialization = “he”)\nprint (“On the train set:”)\npredictions_train = predict(train_X, train_Y, parameters)\nprint (“On the test set:”)\npredictions_test = predict(test_X, test_Y, parameters)\nCost after iteration 0: 0.8830537463419761\nCost after iteration 1000: 0.6879825919728063\nCost after iteration 2000: 0.6751286264523371\nCost after iteration 3000: 0.6526117768893807\nCost after iteration 4000: 0.6082958970572938\nCost after iteration 5000: 0.5304944491717495\nCost after iteration 6000: 0.4138645817071794\nCost after iteration 7000: 0.3117803464844441\nCost after iteration 8000: 0.23696215330322562\nCost after iteration 9000: 0.18597287209206834\nCost after iteration 10000: 0.15015556280371806\nCost after iteration 11000: 0.12325079292273546\nCost after iteration 12000: 0.09917746546525934\nCost after iteration 13000: 0.08457055954024278\nCost after iteration 14000: 0.07357895962677369", null, "On the train set:\nAccuracy: 0.993333333333\nOn the test set:\nAccuracy: 0.96\n\nIn :\n\nplt.title(“Model with He initialization”)\naxes = plt.gca()\naxes.set_xlim([-1.5,1.5])\naxes.set_ylim([-1.5,1.5])\nplot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)", null, "Observations:\n\nThe model with He initialization separates the blue and the red dots very well in a small number of iterations.\n\n### 5 — Conclusions\n\nYou have seen three different types of initializations. For the same number of iterations and same hyperparameters the comparison is:\n\nModel ===========Train accuracy — — — — — —-—-—>Problem\n\n3-layer NN with zeros initialization =====50% — — — —> fails to break symmetry\n\n3-layer NN with large random initialization ===== 83% — — — >too large weights\n\n3-layer NN with He initialization=====99% — — — ——> recommended method\n\nWhat you should remember from this notebook:\n\nDifferent initializations lead to different results\nRandom initialization is used to break symmetry and make sure different hidden units can learn different things\nDon’t initialize to values that are too large\nHe initialization works well for networks with ReLU activations.\n\nCoursera | Online Courses & Credentials From Top Educators. Join for Free | Coursera\n\nTaught by: Andrew Ng, Instructor\n\nFounder, DeepLearning.AI & Co-founder, Coursera", null, "Different Initialization methods in Neural Networks was originally published in Towards AI on Medium, where people are continuing the conversation by highlighting and responding to this story.\n\nPublished via Towards AI" ]
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{"ft_lang_label":"__label__en","ft_lang_prob":0.668576,"math_prob":0.9815143,"size":20025,"snap":"2021-04-2021-17","text_gpt3_token_len":6765,"char_repetition_ratio":0.24918835,"word_repetition_ratio":0.38272727,"special_character_ratio":0.3898627,"punctuation_ratio":0.1501938,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9761027,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-13T10:15:24Z\",\"WARC-Record-ID\":\"<urn:uuid:89a99892-a675-4a80-95aa-ae97972d01bc>\",\"Content-Length\":\"61922\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:af8ef451-599d-411d-883d-596d165acac7>\",\"WARC-Concurrent-To\":\"<urn:uuid:5cfaa561-f360-4951-bdfe-b05a45e30db6>\",\"WARC-IP-Address\":\"52.8.103.111\",\"WARC-Target-URI\":\"https://interhit.org/different-initialization-methods-in-neural-networks-towards-ai-the-best-of-tech-science-and-engineering/\",\"WARC-Payload-Digest\":\"sha1:4W47YWFB67WQOTWS5P7BSDVFZNOWHQS7\",\"WARC-Block-Digest\":\"sha1:IRNRJEIFJCCX7RREAAVCDML67FJ5F6LK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038072180.33_warc_CC-MAIN-20210413092418-20210413122418-00181.warc.gz\"}"}
https://www.colorhexa.com/97a6a4
[ "# #97a6a4 Color Information\n\nIn a RGB color space, hex #97a6a4 is composed of 59.2% red, 65.1% green and 64.3% blue. Whereas in a CMYK color space, it is composed of 9% cyan, 0% magenta, 1.2% yellow and 34.9% black. It has a hue angle of 172 degrees, a saturation of 7.8% and a lightness of 62.2%. #97a6a4 color hex could be obtained by blending #ffffff with #2f4d49. Closest websafe color is: #999999.\n\n• R 59\n• G 65\n• B 64\nRGB color chart\n• C 9\n• M 0\n• Y 1\n• K 35\nCMYK color chart\n\n#97a6a4 color description : Dark grayish cyan.\n\n# #97a6a4 Color Conversion\n\nThe hexadecimal color #97a6a4 has RGB values of R:151, G:166, B:164 and CMYK values of C:0.09, M:0, Y:0.01, K:0.35. Its decimal value is 9938596.\n\nHex triplet RGB Decimal 97a6a4 `#97a6a4` 151, 166, 164 `rgb(151,166,164)` 59.2, 65.1, 64.3 `rgb(59.2%,65.1%,64.3%)` 9, 0, 1, 35 172°, 7.8, 62.2 `hsl(172,7.8%,62.2%)` 172°, 9, 65.1 999999 `#999999`\nCIE-LAB 66.924, -5.662, -0.775 33.098, 36.532, 40.427 0.301, 0.332, 36.532 66.924, 5.715, 187.798 66.924, -8.128, -0.19 60.441, -8.025, 2.652 10010111, 10100110, 10100100\n\n# Color Schemes with #97a6a4\n\n• #97a6a4\n``#97a6a4` `rgb(151,166,164)``\n• #a69799\n``#a69799` `rgb(166,151,153)``\nComplementary Color\n• #97a69d\n``#97a69d` `rgb(151,166,157)``\n• #97a6a4\n``#97a6a4` `rgb(151,166,164)``\n• #97a1a6\n``#97a1a6` `rgb(151,161,166)``\nAnalogous Color\n• #a69d97\n``#a69d97` `rgb(166,157,151)``\n• #97a6a4\n``#97a6a4` `rgb(151,166,164)``\n• #a697a1\n``#a697a1` `rgb(166,151,161)``\nSplit Complementary Color\n• #a6a497\n``#a6a497` `rgb(166,164,151)``\n• #97a6a4\n``#97a6a4` `rgb(151,166,164)``\n• #a497a6\n``#a497a6` `rgb(164,151,166)``\n• #99a697\n``#99a697` `rgb(153,166,151)``\n• #97a6a4\n``#97a6a4` `rgb(151,166,164)``\n• #a497a6\n``#a497a6` `rgb(164,151,166)``\n• #a69799\n``#a69799` `rgb(166,151,153)``\n• #6f827f\n``#6f827f` `rgb(111,130,127)``\n• #7c8e8c\n``#7c8e8c` `rgb(124,142,140)``\n• #899a98\n``#899a98` `rgb(137,154,152)``\n• #97a6a4\n``#97a6a4` `rgb(151,166,164)``\n• #a5b2b0\n``#a5b2b0` `rgb(165,178,176)``\n• #b2bebc\n``#b2bebc` `rgb(178,190,188)``\n• #c0c9c8\n``#c0c9c8` `rgb(192,201,200)``\nMonochromatic Color\n\n# Alternatives to #97a6a4\n\nBelow, you can see some colors close to #97a6a4. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #97a6a0\n``#97a6a0` `rgb(151,166,160)``\n• #97a6a2\n``#97a6a2` `rgb(151,166,162)``\n• #97a6a3\n``#97a6a3` `rgb(151,166,163)``\n• #97a6a4\n``#97a6a4` `rgb(151,166,164)``\n• #97a6a5\n``#97a6a5` `rgb(151,166,165)``\n• #97a6a6\n``#97a6a6` `rgb(151,166,166)``\n• #97a4a6\n``#97a4a6` `rgb(151,164,166)``\nSimilar Colors\n\n# #97a6a4 Preview\n\nThis text has a font color of #97a6a4.\n\n``<span style=\"color:#97a6a4;\">Text here</span>``\n#97a6a4 background color\n\nThis paragraph has a background color of #97a6a4.\n\n``<p style=\"background-color:#97a6a4;\">Content here</p>``\n#97a6a4 border color\n\nThis element has a border color of #97a6a4.\n\n``<div style=\"border:1px solid #97a6a4;\">Content here</div>``\nCSS codes\n``.text {color:#97a6a4;}``\n``.background {background-color:#97a6a4;}``\n``.border {border:1px solid #97a6a4;}``\n\n# Shades and Tints of #97a6a4\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #010202 is the darkest color, while #f6f7f7 is the lightest one.\n\n• #010202\n``#010202` `rgb(1,2,2)``\n• #0a0c0c\n``#0a0c0c` `rgb(10,12,12)``\n• #141716\n``#141716` `rgb(20,23,22)``\n• #1d2121\n``#1d2121` `rgb(29,33,33)``\n• #262c2b\n``#262c2b` `rgb(38,44,43)``\n• #2f3736\n``#2f3736` `rgb(47,55,54)``\n• #384140\n``#384140` `rgb(56,65,64)``\n• #414c4a\n``#414c4a` `rgb(65,76,74)``\n• #4a5655\n``#4a5655` `rgb(74,86,85)``\n• #53615f\n``#53615f` `rgb(83,97,95)``\n• #5c6b69\n``#5c6b69` `rgb(92,107,105)``\n• #657674\n``#657674` `rgb(101,118,116)``\n• #6e817e\n``#6e817e` `rgb(110,129,126)``\n• #778b88\n``#778b88` `rgb(119,139,136)``\n• #829492\n``#829492` `rgb(130,148,146)``\n• #8c9d9b\n``#8c9d9b` `rgb(140,157,155)``\n• #97a6a4\n``#97a6a4` `rgb(151,166,164)``\n``#a2afad` `rgb(162,175,173)``\n• #acb8b6\n``#acb8b6` `rgb(172,184,182)``\n• #b7c1c0\n``#b7c1c0` `rgb(183,193,192)``\n• #c1cac9\n``#c1cac9` `rgb(193,202,201)``\n• #ccd3d2\n``#ccd3d2` `rgb(204,211,210)``\n• #d6dcdb\n``#d6dcdb` `rgb(214,220,219)``\n• #e1e5e5\n``#e1e5e5` `rgb(225,229,229)``\n• #eceeee\n``#eceeee` `rgb(236,238,238)``\n• #f6f7f7\n``#f6f7f7` `rgb(246,247,247)``\nTint Color Variation\n\n# Tones of #97a6a4\n\nA tone is produced by adding gray to any pure hue. In this case, #9e9f9f is the less saturated color, while #45f8e0 is the most saturated one.\n\n• #9e9f9f\n``#9e9f9f` `rgb(158,159,159)``\n• #97a6a4\n``#97a6a4` `rgb(151,166,164)``\n``#90ada9` `rgb(144,173,169)``\n• #88b5af\n``#88b5af` `rgb(136,181,175)``\n• #81bcb4\n``#81bcb4` `rgb(129,188,180)``\n• #79c4ba\n``#79c4ba` `rgb(121,196,186)``\n• #72cbbf\n``#72cbbf` `rgb(114,203,191)``\n``#6ad3c5` `rgb(106,211,197)``\n• #63daca\n``#63daca` `rgb(99,218,202)``\n• #5ce1d0\n``#5ce1d0` `rgb(92,225,208)``\n• #54e9d5\n``#54e9d5` `rgb(84,233,213)``\n• #4df0da\n``#4df0da` `rgb(77,240,218)``\n• #45f8e0\n``#45f8e0` `rgb(69,248,224)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #97a6a4 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.54666483,"math_prob":0.58032626,"size":3704,"snap":"2021-43-2021-49","text_gpt3_token_len":1718,"char_repetition_ratio":0.12216216,"word_repetition_ratio":0.011090573,"special_character_ratio":0.5510259,"punctuation_ratio":0.23430493,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9882664,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-26T04:31:53Z\",\"WARC-Record-ID\":\"<urn:uuid:98a8135b-833b-4f34-a064-45a53f2df1c2>\",\"Content-Length\":\"36222\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:377832c7-8dbd-41d5-ae7d-73c07984c812>\",\"WARC-Concurrent-To\":\"<urn:uuid:942753ad-f985-470a-8f0c-f7287844dbcf>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/97a6a4\",\"WARC-Payload-Digest\":\"sha1:NPKJULX6PUGKMGLMMMQP7OIMSBWVYK3Y\",\"WARC-Block-Digest\":\"sha1:WWYFGBC47SCMGR6SDDZID5POGYEHSGJY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323587799.46_warc_CC-MAIN-20211026042101-20211026072101-00256.warc.gz\"}"}
http://manual.conitec.net/avec_lenght.htm
[ "vec_length (vector);\n\nReturns the length or magnitude of a vector, i.e. its distance to the level origin.\n\nParameters:\n\nvector - whose length is to be calculated.\n\nReturns:\n\nMagnitude of vector\n\nFast\n\nExample:\n\n`distance = vec_length(my.x); // calculate the distance of the my entity to the level origin `" ]
[ null ]
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https://calculator.name/subtracting-fractions/16over2/23over4
[ "# 16/2 - 23/4 as a fraction\n\nWhat is 16/2 - 23/4 as a fraction? 16/2 - 23/4 in fraction form is equal to 9/4\n\nHere we will show you how to subtract 16/2 minus 23/4 written in maths equation as 16/2 - 23/4, answer in fraction and decimal form with step by step detailed solution.\n\n• 9/4\n• 2 1/4\n• 2.25\n\nTo subtract 16/2 - 23/4, follow these steps:\n\nSince the denominators are different find the least common denominator\n\nLCD = 4\n\nMultiply numerators and denominators to get the LCD as denominator for both fractions\n\n= 16 * 2/2 * 2 - 23 * 1/4 * 1 = 32/4 - 23/4\n\nThe denominators are same subtract the numerators, and put that answer over common denominator\n\n= 32 - 23/4 = 9/4\n\nMore Examples" ]
[ null ]
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http://osr507doc.xinuos.com/cgi-bin/pod2html/Math::BigInt::Calc
[ "DOC HOME SITE MAP MAN PAGES GNU INFO SEARCH\n\n# NAME\n\nMath::BigInt::Calc - Pure Perl module to support Math::BigInt\n\n# SYNOPSIS\n\nProvides support for big integer calculations. Not intended to be used by other modules. Other modules which sport the same functions can also be used to support Math::BigInt, like Math::BigInt::GMP or Math::BigInt::Pari.\n\n# DESCRIPTION\n\nIn order to allow for multiple big integer libraries, Math::BigInt was rewritten to use library modules for core math routines. Any module which follows the same API as this can be used instead by using the following:\n\n` use Math::BigInt lib => 'libname';`\n\n'libname' is either the long name ('Math::BigInt::Pari'), or only the short version like 'Pari'.\n\n# METHODS\n\nThe following functions MUST be defined in order to support the use by Math::BigInt v1.70 or later:\n\n``` api_version() return API version, minimum 1 for v1.70\n_new(string) return ref to new object from ref to decimal string\n_zero() return a new object with value 0\n_one() return a new object with value 1\n_two() return a new object with value 2\n_ten() return a new object with value 10```\n``` _str(obj) return ref to a string representing the object\n_num(obj) returns a Perl integer/floating point number\nNOTE: because of Perl numeric notation defaults,\nthe _num'ified obj may lose accuracy due to\nmachine-dependend floating point size limitations\n\n_mul(obj,obj) Multiplication of two objects\n_div(obj,obj) Division of the 1st object by the 2nd\nIn list context, returns (result,remainder).\nNOTE: this is integer math, so no\nfractional part will be returned.\nThe second operand will be not be 0, so no need to\ncheck for that.\n_sub(obj,obj) Simple subtraction of 1 object from another\na third, optional parameter indicates that the params\nare swapped. In this case, the first param needs to\nbe preserved, while you can destroy the second.\nsub (x,y,1) => return x - y and keep x intact!\n_dec(obj) decrement object by one (input is garant. to be > 0)\n_inc(obj) increment object by one```\n` _acmp(obj,obj) <=> operator for objects (return -1, 0 or 1)`\n``` _len(obj) returns count of the decimal digits of the object\n_digit(obj,n) returns the n'th decimal digit of object```\n``` _is_one(obj) return true if argument is 1\n_is_two(obj) return true if argument is 2\n_is_ten(obj) return true if argument is 10\n_is_zero(obj) return true if argument is 0\n_is_even(obj) return true if argument is even (0,2,4,6..)\n_is_odd(obj) return true if argument is odd (1,3,5,7..)```\n` _copy return a ref to a true copy of the object`\n``` _check(obj) check whether internal representation is still intact\nreturn 0 for ok, otherwise error message as string```\n``` _from_hex(str) return ref to new object from ref to hexadecimal string\n_from_bin(str) return ref to new object from ref to binary string\n\n_as_hex(str) return string containing the value as\nunsigned hex string, with the '0x' prepended.\n_as_bin(str) Like as_hex, only as binary string containing only\nzeros and ones. Leading zeros must be stripped and a\n'0b' must be prepended.\n\n_rsft(obj,N,B) shift object in base B by N 'digits' right\n_lsft(obj,N,B) shift object in base B by N 'digits' left\n\n_xor(obj1,obj2) XOR (bit-wise) object 1 with object 2\nNote: XOR, AND and OR pad with zeros if size mismatches\n_and(obj1,obj2) AND (bit-wise) object 1 with object 2\n_or(obj1,obj2) OR (bit-wise) object 1 with object 2```\n``` _mod(obj,obj) Return remainder of div of the 1st by the 2nd object\n_sqrt(obj) return the square root of object (truncated to int)\n_root(obj) return the n'th (n >= 3) root of obj (truncated to int)\n_fac(obj) return factorial of object 1 (1*2*3*4..)\n_pow(obj,obj) return object 1 to the power of object 2\nreturn undef for NaN\n_zeros(obj) return number of trailing decimal zeros\n_modinv return inverse modulus\n_modpow return modulus of power (\\$x ** \\$y) % \\$z\n_log_int(X,N) calculate integer log() of X in base N\nX >= 0, N >= 0 (return undef for NaN)\nreturns (RESULT, EXACT) where EXACT is:\n1 : result is exactly RESULT\n0 : result was truncated to RESULT\nundef : unknown whether result is exactly RESULT\n_gcd(obj,obj) return Greatest Common Divisor of two objects```\n\nThe following functions are optional, and can be defined if the underlying lib has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence slow) fallback routines to emulate these:\n\n```\n_signed_or\n_signed_and\n_signed_xor```\n\nInput strings come in as unsigned but with prefix (i.e. as '123', '0xabc' or '0b1101').\n\nSo the library needs only to deal with unsigned big integers. Testing of input parameter validity is done by the caller, so you need not worry about underflow (f.i. in `_sub()`, `_dec()`) nor about division by zero or similar cases.\n\nThe first parameter can be modified, that includes the possibility that you return a reference to a completely different object instead. Although keeping the reference and just changing it's contents is prefered over creating and returning a different reference.\n\nReturn values are always references to objects, strings, or true/false for comparisation routines.\n\nIf you want to port your own favourite c-lib for big numbers to the Math::BigInt interface, you can take any of the already existing modules as a rough guideline. You should really wrap up the latest BigInt and BigFloat testsuites with your module, and replace in them any of the following:\n\n` use Math::BigInt;`\n\nby this:\n\n``` use Math::BigInt lib => 'yourlib';\n\n```\n\nThis way you ensure that your library really works 100% within Math::BigInt.\n\n# AUTHORS\n\nOriginal math code by Mark Biggar, rewritten by Tels http://bloodgate.com/ in late 2000. Seperated from BigInt and shaped API with the help of John Peacock.\n\nFixed, speed-up, streamlined and enhanced by Tels 2001 - 2005." ]
[ null ]
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https://msp.org/agt/2013/13-2/p02.xhtml
[ "#### Volume 13, issue 2 (2013)\n\n Download this article", null, "For screen For printing", null, "", null, "Recent Issues", null, "", null, "The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals\nThe mod 2 homology of infinite loopspaces\n\n### Nicholas J Kuhn and Jason B McCarty\n\nAlgebraic & Geometric Topology 13 (2013) 687–745\n##### Abstract\n\nApplying mod 2 homology to the Goodwillie tower of the functor sending a spectrum $X$ to the suspension spectrum of its ${0}^{th}$ space, leads to a spectral sequence for computing ${H}_{\\ast }\\left({\\Omega }^{\\infty }X;ℤ∕2\\right)$, which converges strongly when $X$ is 0–connected. The ${E}^{1}$ term is the homology of the extended powers of $X$, and thus is a well known functor of ${H}_{\\ast }\\left(X;ℤ∕2\\right)$, including structure as a bigraded Hopf algebra, a right module over the mod 2 Steenrod algebra $\\mathsc{A}$, and a left module over the Dyer–Lashof operations. This paper is an investigation of how this structure is transformed through the spectral sequence.\n\nHopf algebra considerations show that all pages of the spectral sequence are primitively generated, with primitives equal to a subquotient of the primitives in ${E}^{1}$.\n\nWe use an operad action on the tower, and the Tate construction, to determine how Dyer–Lashof operations act on the spectral sequence. In particular, ${E}^{\\infty }$ has Dyer–Lashof operations induced from those on ${E}^{1}$.\n\nWe use our spectral sequence Dyer–Lashof operations to determine differentials that hold for any spectrum $X$. The formulae for these universal differentials then lead us to construct an algebraic spectral sequence depending functorially on an $\\mathsc{A}$–module $M$. The topological spectral sequence for $X$ agrees with the algebraic spectral sequence for ${H}_{\\ast }\\left(X;ℤ∕2\\right)$ for many spectra $X$, including suspension spectra and almost all Eilenberg–Mac Lane spectra. The ${E}^{\\infty }$ term of the algebraic spectral sequence has form and structure similar to ${E}^{1}$, but now the right $\\mathsc{A}$–module structure is unstable. Our explicit formula involves the derived functors of destabilization as studied in the 1980’s by W Singer, J Lannes and S Zarati, and P Goerss.\n\n##### Keywords\ninfinite loopspaces, Dyer–Lashof operations\n##### Mathematical Subject Classification 2010\nPrimary: 55P47\nSecondary: 55S10, 55S12, 55T99\n##### Publication", null, "" ]
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https://www.jnsciences.org/agri-biotech/16-volume-8/32-estimation-of-direct-and-maternal-variance-components-of-lamb-weights-at-90-days.html
[ "", null, "# Estimation of direct and maternal variance components of lamb weights at 90 days", null, "Volume 8, Article 3 [Volume 8, Article 3] 541 kB\n\nW. Mâaoui*\n\nA. Ben Gara\n\nB. Rekik\n\nLaboratory of improvement and integrated development of animal productivity and food resources, Higher School of Agriculture of Mateur, University of Carthage, Tunisia\n\nAbstract - Weights at 90 days were simulated for Barbarine lambs using various data and pedigree structures. The herd size, number of years and ram pedigree information were modified to cover probable structures of field data: Herds included between 100 and 2000 animals over 4 to 20 years with complete or missing ram information. Direct, maternal, permanent and residual variance components were estimated by Bayesian analysis via Gibbs sampling applied to an animal model that included the fixed effects of year and month of lambing, litter size, the age of the dam and sex of the lamb. A total of 30000 samples were generated. A burn-in period of 2000 rounds was used and then one out of 10 iterations was kept for subsequent analysis. Posterior means of direct and maternal variance effects ranged from 0,83 to 3,86 and from 2,30 to 4,34, respectively. Heritability estimates, in the same order, were between 0,06 and 0,29 and 0,16 and 0,28. In manner similar to direct estimates, maternal component estimates were closer to input parameters (3, 3,5, 9 and 7 for direct, maternal, permanent and residual variance, respectively) for increased herd sizes and number of years and complete ram pedigree.\n\nKey words: Barbarine / growth / maternal effect / Sheep breed.\n\n1. Introduction\n\nBarbarin is the major fat tail breed in Tunisia, Bedihaf-romdhani et al. (2008) indicate that they are 4 millions breeding ewes and 60% are fat tail Barbarin. Accurate estimation of these genetic parameters and in particular genetic correlations requires large across-generation data sets for each relevant population which are not always available. Pooling estimates from several populations may provide more reliable parameter estimates than those obtained from a single population if there is stability across populations. Under low input production systems, small heritability estimates were very often due to a large phenotypic variance and consequently the existing genetic variance (small or medium) is not exploited (Bedihaf-romdhani et Djemali 2006). A large results variability are observed for the direct heritability of weaning weight (90 days), Djemali et al. (1995) using three methods (MIVQUE(0), ML and REML) found 0,27 to 0,36, Ben Gara (2000) think that the heritability is about 0,24 and Bedihaf-romdhani and Djemali (2006) by means of an animal model with direct genetic effect and an animal model with direct and maternal effects between 0,307 and 0,369.\n\nSchenkel and Schaeffer (2000) indicated that selection may increase the mean square error of the estimates of variance components, amplifying the uncertainty about genetic parameters. The Bayesian methods can fully take into account the uncertainty about dispersion parameters by considering the marginal posterior density of those parameters (Gianola and Fernando1986; Wang et al.1993 and Sorensen et al., 1994)\n\nGibbs sampling is a Monte Carlo numerical integration method that allows inferences to be made about joint or marginal distributions, even if appropriate densities cannot be explicitly formed (Geman and Geman 1984). The great appeal of the Bayesian analyses via Gibbs sampling is that it yields Monte Carlo estimates of the full marginal posterior distribution of all parameters of interest, for instance breeding values, from which the probabilities that the parameter lies between specified values can be computed (Van Tassel et al.1994; Sorensen 1996).\n\nThe cycle of generating each parameter is repeated. Eventually, the Gibbs sampler converges to the posterior distribution, and the values drawn after that convergence are considered random samples from the posterior distribution. The number of rounds discarded before the values are considered samples from the posterior distribution is usually called the burn-in period (Van Tassell and Van Vleck 1996).\n\nBayesian analyses via Gibbs sampling are becoming more and more feasible as computer power increases and as better algorithms are developed. The applicability of Bayesian methods for genetic evaluation is already possible routinely for moderately sized problems (Schenkel et al. 2002).\n\nThe objective of this study was to determinate estimated variance components of lamb growth at 90 days with a simulated data (different scenarios) and using a Markov Chain Monte Carlo Bayesian method.\n\n2. Materials and methods\n\n2.1. Data Simulation\n\nSimulation of a Barbarin Herd:\n\n- Fertility: 0,9\n\n- Prolificacy: 1,3\n\n- Mortality: 0,0\n\n- Initial herd size: N\n\n- Sex ratio: 0,05\n\nVariance components:\n\n- Direct genetic additive variance: 3 Kg2\n\n- Maternal genetic additive variance: 3,5 Kg2\n\n- Direct-maternal covariance: -0,5 Kg2\n\n- Permanent environmental effect variance: 1 Kg2\n\n- Residual variance: 7 Kg2\n\n- h2d: 0,207\n\n- h2m: 0,241\n\nAnimal genetic value of the base herd:", null, "i= 1,……,N\n\nWith L’ such as G0=L’L and", null, "~N(02, 12)\n\nThe permanent maternal effect :", null, "With r~N(0,1)\n\nLambing year’s effect is determinate like this:\n\nan~N(0,1) and the effect of month, sex and type of birth and age of the ewe are taken from a Tunisian Barbarin semi-arid results (Ben Gara, no published references).\n\nDescendant generation’s simulation:\n\nThe descendants come from hazard mating of the reproductive animals kept every year with a phenotypic selection. The yearly reform rate is about 17%.\n\nThe breeding values of a descendant are calculated like this:\n\nThen", null, "with", null, "", null, "et", null, "where zj~N(0,1)\n\ns and d are respectively the sire and the dam of the animal i.\n\nThe phenotypic value of the animal i is calculated in this way:\n\nPhi=gi(1) + gd(2) + pd + ei + Σfi\n\nWith gi(1) Direct genetic additive effect of the animal i\n\ngd(2) Maternal genetic additive variance effect of the dam d\n\npd permanent environmental effect of the dam d\n\nei residual value of the animal i\n\nand Σfi The whole of fixed effects affecting the performance of the animal i (year, month, sex and type of birth , age of the ewe).\n\nWith", null, "and ri~N(0,1)\n\nThe table below gives us an idea about the number of lambs simulated, the base herd range between 100 and 2000, the number of years is between 4 and 20. Example for a base herd of 100 ewes and with 4 years of reproduction we obtain 495 lambs.\n\n Table 1. Description of the data simulated Base herd Number of years 4 6 8 10 12 20 100 250 300 500 1000 1200 1500 2000 495 1299 1518 2478 5025 6097 7446 10175 700 1859 2163 3534 7147 8684 10606 14645 914 2,398 2,819 4,597 9372 11414 13887 19106 1131 2969 3487 5693 11645 14120 17243 23698 1356 3509 4167 6826 13874 16833 20613 28280 2260 5714 6883 11364 22944 27716 34192 46478\n\n2.2. Analyses\n\nThe linear mixed model used in this analysis was:\n\ny= Xb + Wp + Zmm + Zaa +e (1)\n\nWith W = Zm\n\nm : Vector of maternal genetic additive effect q\n\na : Vector of direct genetic additive effect q\n\np : Vector permanent environnemental effect p\n\nN : Number of observation\n\nWe define :", null, "", null, "with", null, "produit de Kronecker\n\ny~N(Xb + Wp + Zmm + Zaa, I", null, ")", null, "~N(", null, "", null, "", null, "~N(0,", null, ")\n\ng’=(m’a’) with 2 q order.", null, "A priori distribution definition\n\np(b)~ a constant", null, "p(G0/V,v)", null, "IW2(V,v)\n\nwith v=-3 , V=0 in this way p(G0/V,v) is a uniform distribution", null, "", null, "Xb + Zmp + Zmm + Zaa = Wθ\n\nThen", null, "", null, "I\n\nWith :", null, "With\n\nb~N(", null, "p~N(", null, "m~N(", null, "a~N", null, "", null, "~", null, "", null, "~", null, "G0~", null, "And", null, "", null, "A Wishart distribution simulation\n\nWp(S,n)\n\nWe proceed with a Chodesky factorisation :\n\nS=L’L\n\nWe build an inferior triangle", null, "With", null, "", null, "Then Q=L’TT’L~Wp(S,n)\n\nAnd Q-1~I Wp(S,n)\n\nThe hyper parameter V(prior) is determinated in this way :\n\nE(G0/V,v)=", null, "We choose", null, "And", null, "establish the a priori information base.\n\n3. Results and discussions\n\n3.1. Variance component estimates\n\nMarginal distributions were used with herd’s size 100 and 500 to determine: direct, maternal, permanent environment and residual variances. Estimated posterior and standard deviation of all of these criteria are presented in Table 2. Posterior means for direct variance effect ranged from 0,83 to 3,83. This estimate is similar with Mandal et al. (2006) results who reported 3,23 for pre-weaning weight (75 days) with a Muzaffarnagari sheep. A similar result (3,99) was founded by Mokhtari et al. (2008) for weight at 6 months of Kermani sheep. A lower direct genetic variance for the weight at 90 days (0.57) was estimated by an animal model with direct and maternal effects with barbarin lambs (Bedhiaf-Romdhani and Djemali 2006).", null, "", null, "Figure 1. Posterior density function of direct variance (T100-G4) Complete ram information Figure 2. Posterior density function of direct variance (T100-SG-G4) sire ram missing information\n\nMarginal distributions of direct variance for a herd size of 100 ewes and 4 years with complete ram information (T100-G4) and a sire ram missing information (T100-SG-G4) are presented in Figures. 1-2, respectively. Direct variance ranged from -0,4 to 11,6 for the first design and from -0,5 to 10,9 for the second. With complete ram information the mode is about 0,78 and 0,43 with a sire ram missing information.", null, "", null, "Figure 3. Posterior density function of maternal variance (T100-G4) Complete ram information Figure 4. Posterior density function of direct variance (T100-SG-G4) sire ram missing information\n\n Table 2. Estimated posterior and standard deviation of direct, maternal, permanent environment and residual variances Design", null, "", null, "", null, "", null, "", null, "" ]
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", null, 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", null, 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", null, 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null, 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null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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null, 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", null, 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", null, 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null, 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", null, 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", null, 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null, 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wTsCbkFtiY/W53LsKQwUByffvqp/EGVVcGg1CC3wNaWlpYKe+GTJ0/Q3gJwJOQW2Jr8ZlU2yYIlhQEAO0BuAQAAT5BbwBlc5wAoccgtsDXxDcWCRCJhh3UaAcASyC2wNckNxczTp0+RW6XG5/NZXQSwC+QW2NrBgwflHYMzMzMdHR2WlAeK4PXr1/IHq6uri18SsCfkFtga1bLld2s9e/ZM/bZitugUFr/g1KtXr+QPfvXVV8UvCdgTcgtsrbKykqJL3uRqbW2Nx+OKyTQ9PR2JREZGRpBbnFpZWZE84vF40DMMAuQW2F1/f788t5LJZFNTk3xFwXA43NnZGQqFsHy2/dFuVRxi8/DhQ8kjQ0NDxSoUcAC5BXZXV1cXDAbla1s8e/Zs7969dEZraGig9KIzILW02OLudligGfJx4MABYf0thnai5GZzanBjdn8QQ24BB4aHh+lcRpkkeZxaXadOnRI/Que4y5cvF7FoUDjaWdQspujq7e0NBAJU+aDmcl9fn3gbr9d748YNq0oI9oTcAj5MTk6WlZWNjY3JZ35i3G43nf7Q0uIL7VbacdnmSqamM8bXgBxyC7hBmdTc3Pzo0aPbt28vLS2xAKOzXk1NzbFjx+gpnOB4RI1pamxNTEw8fPiQ3avn8XgaGxu//vprzIwMipBbwJPy8vKODKsLAkai3UoNL6tLAdxAbgEAAE+QWwAAwBPkFgAA8AS5BQAAPEFuAQAAT5BbAGCNjY0Nq4sAXEJuAYDpnjx5In8wmUym02ncdQdaIbcAwFzhcHhsbEzxqTNnzoyMjGASZNAEuQUAJvrggw9Uno1k0H9+//13zI4BeUJuAYCJ3r9/b3URwGmQWwAAwBPkFgAA8AS5BQAAPEFuAQAAT5BbAADAE+QWAADwBLkFAAA8QW4BAABPkFsAAMAT5BYAAPAEuQUAADxBbgEAAE+QWwAAwBPkFgAA8AS5BQAAPEFuAQAAT5BbAADAE+QWAADwBLkFAAA8QW4BAABPkFsAAMAT5BYAAPAEuQUAADxBbgEAAE+QWwAAwBPkFgAA8AS5BQAAPEFuAQAAT5BbAADAE+QWAADwBLkFAAA8QW4BAABPkFsAAMAT5BYAAPAEuQUAADxBbgEAAE+QWwAAwBPkFgAA8AS5BQAAPEFuAQAAT5BbAADAE+QWAADwBLkFAAA8QW4BAABPkFsAAMAT5BYAAPAEuQUAADxBbgEAAE+QWwBgsGg0Ojc39/Dhw2QyST+63e6amppjx441Nzdv27bN6tIB95BbAGCYRCLR1tb27Nkz8YObm5sPMvr6+kZHRzs6OqwqHjgDcgsAjBEOh0+dOqWyAQVYZ2cnZdvk5GTRSgXOg9wCAANEo1H10BJMTU2VlZX19PSYXSRwKuQWAOiVSqVaWlry3/7cuXPNzc3l5eXmFQkcDLkFAHpNTExsbm5qfQl6C6EwyC0A0IUaW1NTU/Qfn8/X2tra0NCwbdu2dDodj8d/+umnBw8eKL6KXoLcgsIgtwBAl9nZWfo3FAqJL1lRdB3O6O7uZqkmF4vF6urqilRKcBDkFgDoEolEgsFgtnEW1KiiBlm2VhdAAZBbAKBLe3u7+uDA/v5+xdz68MMPTSsUOBlyCwB0yTmiPVtnYGVlpQnFAedDbgGA6Xw+n6TJ5ff7rSpM0YTD4WvXri0tLbHBll6v98SJE4FAQDLZVTqd/vXXX2/fvi38iejPZdW0WFyUGbkFABY4evSo1UUo3AcffJDtKTY+JRaLtba2sukZBc8yxsbGFhYWhLZmNBptaWmR3EXApsWamZm5f/++UTHAY5mzQW4BgOmo/i7+0e12NzQ0WFUY/f78809qbXR2dio+qz7fFZ3uDxw4QGFQXl6uMtjSlcmMpqam5eVlA0rMZ5mzQW4BgLnS6bSkbt7b28v1xPBU+I6ODmpbSGYQJtQ0oV/W6/VeunSprq4ulUr5/X75RMMTExOuzE1sPp+PmjvUlKEtGxsb5c0dSpSTJ0+WZpmzyTe3qAlZX19v+MdL7vnIhgJc5zha+kNT61XPOwBAYeLxuPhHj8fjjMkJP/vsM3kGsAAQ+sqogRKJROhXlmzGmixdXV3Czde05dDQkLzRs7i4aGAG8FhmuXxzi0L4/fv37P+UsdTqv3Dhgvz3zwe7qb6mpib/2clY5NDnvnnzZm1tra+vL59JZdxuN/3tjhw58te//hUjlwCsMjc3J/7x1q1bVpXEWGVlZfIHxQHAZDvRiQOA2bFjh3wzOu/pKuV/47HMcoX0E5ZnUCSod3QqunnzZsE5zD6XErS5uZlaYOqpGQwGv/32W677IgAcIJ1Oh8Nh4ccrV644uxJ54sQJ+WlHPpySfP3115JHFG8YKMIt29yVWdf1La13wvv9fqM6an/44YcvvvhC8VlqZl2/fv3w4cP6PwgAdJqdnRV6R6i2jkUjQT+94zLOnj2bf279/e9/1/lxgi1btig+Tg3eSCSC9REA7IAaW2NjY+z/dGwODg5aWx5wBr25lS0/FO3du1fnxwlev34tf5Dac5cvX0bfIIBNXLx4kTW2PB5PEW7rgRKhN7c0Teds1LeWKnH9/f2SB+UXDAHAQrFYbGRkxJXpur916xZCC4zC5f1bAwMDkjsG9Az3AADDUeWytbXVlQkt8VQLAPrxl1vT09PiQYx0VFAzC6EFYCtnzpyhyiVCC8zAWW6Fw2HxPCUej+fWrVs4KgBshSqXkUgkZ2ixCfE2NjaKWTZwAJ5yS3K7mM/nu3HjBjrNAWyF0ogqlzlDi3Uker3eYpYNnIGP3KKv+JkzZ6gGJzwSDAaHh4ctLBIAyNGh+uWXX6qHFm0Tj8fPnz+fTCbb29uLXEJHorrC0NAQuyWJKvRnz5519g2sHORWIpFoa2sTz46BURgANkSB1NTUxAa+79mzJ5+X1NbWmlumEiCZyp2tJ+Ls8dV2zy3JQi+4zAtgWwMDA1rnLK2oqDCpMCWC6grd3d3yx6empo4cOeLUVpetc2t8fPzcuXPCj/LJHwHAJiQDffPh8XhwOOu0vr6ebZLx8+fPI7eKiioRVHcTHwbObvYCcC0ajWZbkFAF74My3r17l+eWdELLZzNjp1FXbPvavMx5smNuyVctwwUtANtKJBItLS0FvLCqqsrwwhTT8+fP5Q/Oz8/LVxdTjJAnT55I5hv6448/FD8oFotlm5lo+/btKiWUv9AOZdbPdrlFv+2XX36JC1oAKigq1tfXX716RWcc+nFjY0Myg4xRci64SrXy48eP57MenpxRgzLopEHnU/pTUGEkZ1sqP/1bXV29e/fuiooKo84k9EGzs7OKU4rTg9PT083NzawLlHUdKb7J2NjYrl27hK48di1fcctvvvlmZmZGsfDl5eXBYJDNp8VLmfWzV27R307c24DJ3QHE6AT9888/h8PhwnLCDGxejMJeq7M+nkql6EQ8NTWl8tdgp2mty0HlTOuPP/5Y5dnOjPfv36svE0/FZosx0ZbqS7pTGO/Zsyfb6vDDw8Nbt269evUq7QiPx9Pe3i4MCxAPe7FVmXWyUW5Jbivu6uoaHBzEZVsA1/9OLWFSo0qPcEaRP5QaBBcvXsynkWESYfF3deJl4tWpx2ROPRnCjyy3JMNe7FZmPWyRW+y2D3ED/8qVK1hfDsClNEapxCUSiePHj2eLcK/X+8MPP7COLNpydHRUPF9BSfH7/VYXwSzW5xZ9tw4cOCC+oHX37l3zLugBcER+032Jk1z/lpCMOq6srKS2YFVVlfh2GscTmr+BQMDakpjH4tyS3OlNent7EVoALlmVDugPonLpxePxKK6n3NPT88svv5RO9rO1CUOhkINHBliZW5ILWgzVjHw+HwYQQolLp9MILbFUKkV/EJUNhoaGsl0O/8c//iGpHwscdmMonVSTyST9UmaMhrAPa3KLjsnTp09nG4tC385//etfGJEBpUyY6E+d1+ttbGzct2/fli1bhI4KR17XoTOy+h+koaGhgKeo6lxWVuaAs7xwHdRhSazIgtxSv6zqygy1pIN2eXm5mKUCLkim/rLW77//blKfNv2aOfu16PT03XffKfYFses6R48eFRoZbrf75MmT2ba3P/p11Mey+3w+lZouPUUbZHsH+kbV1tZyfXmC/j6se/DevXtOndtJrNi5RX/fnPUmV2bsP23m+FoDgFwqlVLP5jyXS2VTzLDooiNuKiMUCgUCAe46My5cuKC+QXV1dc4NVJKP6+UrqZazsrIyNDRUOpMKFTW3NFWW6Rjbv39/6ewJAGZiYkLlWU2zS4uji6ED8OrVq9euXeOoeZFIJHK2Prdu3apng2QyGY1GOW2pOKCTU6ui5pbWHh463gycmgXA/qixpXKrltvtjkQimlpLFF2Li4vi96RzdH19PUcrrz59+jTnNjt37tS5wdzcHKe5VYKsv39LHcZoQEmZnZ1VeXZ0dLSAC1STk5PLy8uSJsvIyMjDhw+5WBiI2ls5t9mxY4fODeivoaFMYKli55bX693c3Mx/uhqM0QAxyXw2zqMyCNDj8RQ8iczMzIx8AWJKMjq47B9dxVkpw4ZzaEE2Rc0tn89348aN169fa7oxBWM0oERQw0Ll7Kln2p7KyspQKCTvqGfRhXoh8KWoucXmYaTKHYVQttsAFWGMBpSC9fV1lWcPHTqk580DgcDY2Ji8vkjR9f333/NyrQvAZdX1LUqgFy9eaJrOGWM0wPFevXql8qzOEYBUX6TjTnHQBx2JFIq2HWGoPoQdSpBl4zKofvf8+XNNX8fjx4/H43Gb98UDFOzly5fZnnK73frfv6OjI9tgRTvfwJRzKKAh2AqTwAUrxxPeuHHjb3/7W/4XupLJ5OnTpy1c9AXAVCoDEGpqavS/f2VlpcfjUbyERg+Gw2F7dsWrzNIkeP36tfoGa2tr6hvkvHMZ7MPK3KKW08LCgnyYkwpqn6EvHqBgjY2N2Zpc165ds2dulZeXq8zSxKh3sZJ3796pb/DVV19pLhlYxOL7t6gCePPmTU1jNEZGRnbv3m3PAwxAj48++sjsj1C5QkzBkE6n7dkP39/fr55bKysr6u+gvgHWoOCL9fcdy+/nz6m7uxtjNMB5qqqqst2/ZdTFp08//VTl2Xg8bs85I+rq6tSbXDknglK/rZhNSgu8sD63XFnu51exubmJMRpQUopzV+zq6qo9c8uV63I4/X1isVi2IZH0lMp19FAoZNuxlKDIFrnlytzahTEaUOJqa2tVnjWkE0/9BJ2zt81C7HK4ypQFQ0ND2U4I9FS2t3X8EouOZJfcwhgNyIez19+qqKhQeXZ9fd3sZsHbt29NfX+dKisr6SzR1tam2DdDJwTFiXXowWwdjKWwxKIj2SW3XJkv5ZUrVzo7O/N/CcZogJNQ7c3r9WbrMF9bW9OfW8WZ6888dJagRtXFixcVZy2YmpqiXzAUCrGL39Fo9KefflIMLbfbTYmFUwenbJRbrsx9kYlEAmM0oGQ1NjZmyy1qahQ8r67gzZs3Ks8WYUCjfpTuw8PDgUBgYmJCfq54kKH+DipLRQMX7JVbZHBwEGM0oGTR6Tjb/GdFWGijqqrK7I8wCqUONZgofhTTSxG1sSix6C+MxOKd7XKL4icSibDlTvJ8CcZogGOo3GNLR4T+KS2ePHmi8mxxZlQySjqd/vXXX+lvwn4UJmpaWloSzh6UVTU1NdXV1fv27bPtUEnQyna55cocunfv3q2vr8//JRijUSIcv/6WS/UeW/1TWqiPGDRkNqniGB8fF6a3D4VC1IpCj0vpsGNuuTKjdRWXC1KBMRrgDPTl9/v9ijcgU56p3KWUD5XORmqvcNGBlkgkxEMKb968iaO+1Ng0t1yZmvX8/LymCeMxRgOcgSphFDCKXeWtra0FX80Nh8Mq3e/0zgW8Z5FRaIlv4fJ6vQitEmTf3HJl5tHQdKGLtqSKmP3XHQdQxwYdKM7bmUwmBwYGCrvr6Nq1a9me4iIAJKFFTpw4YWF5wCq2zi06ekdHRzXd0fXs2bMzZ84Il2oBOKUyb2dhy39PT0+r9F5cunRJcxGLK51OHz9+XFKLVVmxDBzM1rnlytzR9eOPP2qanC0SifzlL3/BbfDAO/oOp1IpxbBhTbH8o4taKn19fdme5WKCvtnZWfl5gGqodIrApYFSoze3YrGYIeVQMTQ0pGmhE1ehFVIAu7lx40ZTU5Pi7Yx0ULx48SKfMbTy7jUxXiboGxsbkz9IvxT9ahTwDQ0NuDpQOvTmVs5lRsUKGwpF8dPd3Z3/VS5Ga4UUwIboXLy8vEzff8UOQzZ849KlSyqH1fT0tEpPOy8T9FH0ZjsD0OOa6rXsNq/y8vKysrLa2tqKigoEHnf05pbKlV65n3/+ubDuiJqaGk0DCxn6Ni8uLnJxWAKooO8wnWQVbwuhplh9fb3X621ra/v888+FHjOqI66tran3sQeDQV5uefz3v/9t1FvJzySUZK2trajjckRXbo2Pj2uKE6oz0nGldY41qmoVEFrCJ6ZSKTrsubgxBSCbnp4eOr1mmwr9WUb+7+Z2u69fv475Ixg2pSFVwYUJecHmCsktSoKlpSXazQXESWdn5+3bt6l2k/NGq3Q6vb6+/ttvv2maZleOCunxeLq6uo4cObJ37170CQCn6HhZXl4Oh8P9/f0FLyNJidXb28vd7BLbt283+yPoREGntYWFBUSX/eWbW7FYTNPESyokEza/f//e1I9jpjJcmT4Bo2YypDMIhbcwGZrX6z1x4oT8jMBmUaO0Fn5rKsOxY8eam5uLf+7gscwgdjKD9uOdO3cU59TIhvUlmr0HqVI7Ozv7/PlzY785KtM2GoiN8qCWK7pnbC7f3Kqrq1MMGJMU+eMkPvjgg2xPhUKhnp4eilVqMkrqvKyvZmxsTFxli0ajLS0tkkvKLLlnZmYMvEWaxzJDwVh6Xb58OR6Pr66uzs/PU1VD0lVIQUV7qrq6evfu3TU1NWafi6kAistisW9OX1/f3bt39Yy2V5m20UD0te/u7sYk3TZn9/u3LPHnn39SayPbKCyq6qqMXxJX2bINA2Nom6ampuXlZQNKzGeZQSeKpcMZlg9kp2aW3+8XgrOrq2twcJCKJ4xmpO9YfX29nrkEKfPo5VpviSmA/kkgwWzILQV0vHV0dFDbQn6tm01BTTVZNvhYcrgytMHExIQr0znp8/nYxV7asrGxUd7c0b8yBb9lBmeglpZ4Pjb6/giDeOk7+e7dO2EkJKXOjh07Co4E9q0r4K4YrQoe+QzFgdzK6rPPPpNnAAsAoa+MGiiRSMTj8Ug2Y00W8c0xtKXiDdSLi4sGZgCPZQbeURNcHCT9/f3iZwOBgHgEf2tr68bGRsGfRV+8mpqaYDCo6dqeVuhRsDnkVlZlZWXyB8UBwGS7bCC/o5NqmvLNqE2jq5T/jccyA9eo8S2uKlF9SNJSoS8ePSi02uk/etrr1LZ79OhRwcMp86TppgIoPuSWNidOnJCPSlAc6fT1119LHlHseSjCpWYeywy8kLSuPvnkE/k29KA4ae7cuVNAblFizc7OCmtFMm63mypbhw4d2r59u/rAE3ZfDfv/2tpaIpFQX9UF7Ay5BQAFikajkqbPwYMHc74qEoloXbGBUkc+T6O8I0EFbSZUwth/BgcHKQg1LU4LNoHcAoACPX78uLAXah2wJw8tamnpvCWDXtvT07N161b5KFxKxILfFooAuQUABXr+/LnkkXMZxn6K5BIa09XVZch9hB0dHX19fZIOw88++0z/O4N5kFsAUKClpaXCXvjkyZP821uLi4vyB6mdVNhHy8mn7d6/f79Rbw5mQG4BQIHk4xoMnEdNYPb4VUn6ejwe3OZhc8gtALC1jz76SP7g/Py8IbOExGIxSfoODQ3pf1swFXILAAxjxj0SR48eld9lTB+kf96WdDr9zTffiB/x+/1obNkfcgsACiS+oViQSCSMXQqEguTChQvyoRnd3d1btmwpeBUxKqdkPTOv13v58uXCCwrFgtyyu1gsNjQ0xKqxPp/v7NmzWO4PbEJyQzHz9OlTw5ewmpmZOXDggKRDj3784osvgsFgIBDQNNs9Jdb09LRk/mhNd4OBtZBbtiaZx50tCSGfjQnAEgcPHpR3DFLGaF3TPCcKwoWFBcXlnkcyqEpHhdm1axe1wCoqKiTxk0ql3rx58/r16xcvXkQiEXnWsrV+jC0zmAe5ZV/pdLq7u1v+ONUTjxw5glYXWI7SQn63FkWL+m3FbOUwrS0bttzz+Pj41atX5cEjWY02f1QL/O6777BQJF+QW/a1vr6ebf608+fPI7fAcpQlihNdtra2xuNxxWSanp6mFg+1kArrkevJiEajc3NzDx8+LGyCXbfb3djYePTo0YaGBnQM8gi5ldW7d+/y3JIaRvlsZuBtKNnmq7ZzmcGRFJchpjhpamqSXy4Kh8OdnZ2hUEhn+4atlunKfD//+OOP1dXVly9f0v/liz67MilVU1PjyvRq7ty5s6KiwvDLb1BkyK2s5HPYuLLcNaKYIvIZAegAU/ygbJ0q27dvVyme4qssLzOUGvoaBINBaj9JHqcv2N69e4eGhlibRhgK4ff7DbySVJ6BvodSg9xSwFZMUOwupwfp8GtubmYVSdpyYGBA8U3GxsZ27dolHFHRaLSlpUVxy2+++WZmZkZeB6QDUvGMYOcyQwkaHh7e3NyUDM9zZVpdkkVHfT4fBpqDfsgtBR9//LHKs50Z79+/pzZHfX19ts3YIF36D23Z1NSkctGYaqZ79uxRHNFEZ4StW7eyC9Eej6e9vV24DF5RUWHPMkMJmpycLCsrkyyOJeZ2u3t7e/FtAUMgtxTQWTufzerq6vLcUs+MbexCtPAjyy3KMMmVA1uVGUoQfUupTf/o0aPbt28vLS2xAGPXlo4dOyY09wH0Q25xye/3W10EAKny8vKODKsLAg6H3OKJsEpsIBCwtiQAAFZBbvGkv7/flbm3H7dJAkDJQm5xo7u7O5lMdnV14eI2AJQy5BYH2Mj1qakpzEwIAIDcsrtwOMy6B+/du4f7KwEAkFu2Nj4+vrKyMjQ0hLXsAAAY5Jat4VIWAIAEcgsAAHiC3AIAAJ4gtwAAgCfILQAA4AlyCwAAeILcAgAAniC3AACAJ8gtAADgCXILAAB4gtwCAACeILcAAIAnyC0AAOAJcgsAAHiC3AIAAJ4gtwAAgCfILQAA4AlyCwAAeILcAgAAniC3AACAJ8gtAADgCXILAAB4gtwCAACeILcAAIAnyC0AAOAJcgsAAHiC3AIAAJ4gtwAAgCfILQAA4AlyCwAAeILcAgAAniC3AACAJ8gtAADgCXILAAB4gtwCAACeILcAAIAnyC0AAOAJcgsAAHiC3AIAAJ4gtwAAgCfILQAA4AlyCwAAeILcAgAAniC3AACAJ8gtAADgCXILAAB4gtwCAACeILcAAIAnyC0AAOAJcgsAAHiC3AKArKLR6Nzc3MOHD5PJJP3odrtramqOHTvW3Ny8bds2q0sHJQq5BQAKEolEW1vbs2fPxA9ubm4+yOjr6xsdHe3o6LCqeFDKkFsAIBUOh0+dOqWyAQVYZ2cnZdvk5GTRSgXAILcA4L9Eo1H10BJMTU2VlZX19PSYXSQAMeQWAPyfVCrV0tKS//bnzp1rbm4uLy83r0gAEsgtAPg/ExMTm5ubWl+C3kIoJuQWAPwHNbampqboPz6fr7W1taGhYdu2bel0Oh6P//TTTw8ePFB8Fb0EuQXFhNwCgP+YnZ2lf0OhkPiSFUXX4Yzu7m6WanKxWKyurq5IpYSSh9wCgP+IRCLBYDDbOAtqVFGDLFurC6BokFsA8B/t7e3qgwP7+/sVc+vDDz80rVAAUsgtAPiPnCPas3UGVlZWmlAcAGXILQDQwOfzSZpcfr/fqsIUUzgcvnbt2tLSEhtv6fV6T5w4EQgEJPNdpdPpX3/99fbt28Jfif5iRZgZK5FI0CfOz89vbGywSbmIx+NpbGw8cuTI4cOHzfvo4kNuAYAuR48etboIunzwwQfZnmJDVGKxWGtrqxAGzLOMsbGxhYUFobkZjUZbWlokNxKwmbFmZmbu379vRnTRh54/f14yIxdDZZ7KoOycnJx0zG12yC0A0IAaHOIf3W53Q0ODVYUxxJ9//kktpM7OTsVn1ae8oog6cOAAZQZFgsp4S1cm55qampaXlw0o8f+itt2ZM2cikYgrsyMomditC6lUKhgMsscZCk5qIIojlmvILQDIF50oJY2J3t5e3ieGp/J3dHRQe0jeZKHmFP2+dMa/dOlSXV0d5YHf75fPNTwxMeHK3MdGzRpqolE20JaNjY3yJhql4MmTJ40q+enTp4XeyOvXrwudgRSi9EH06eKiUjnb2tqMDU6r5Jtb1FKur683/OMld4pkQ/UUnaNv6ftEjXQ97wAA8Xhc/KPH43HM5ISfffaZPLdYaAn9e5QH1Iih31qyGWtmdXV1Cfdf05ZDQ0Pyhtri4qJRuUXJJD4rPn78WHIR68SJE5LfiH6MRqMOuNaVb25RXeP9+/fs/1SVWFpaunDhgmKPak7sVvyampr8O1tZ5NDnvnnzZm1tra+vL5+paKjhTF+RI0eO/PWvf3VG6xjAWnNzc+Ifb926ZVVJDFdWViZ/UBxaTLazlji0mB07dsg3o5OYrlKK9Pf3i38cGRnZt29fzkxaXV0todwSK8+gSFDvz1V08+bNgqsb7HMpQZubm6kFpp6awWDw22+/5b0HA8A+0uk01fGFH69cueL46iA1WeTnEPmISvL1119LHlG8Z8DAu7YlnZDk/PnzDsikfOi6vqX1/nm/329IG5m+ST/88MMXX3yh+Cw1s8RdvQBgiNnZWaGfg5oXWDTSWnSik3Q7aZ0QmV96x2WcPXs2/9z6+9//rvPjBFu2bFF8nNr1kUjEMcM9AWyCGltjY2Ps/3SUDQ4OWlse6O3tPXfunPiR9vZ2qwpTZHpzK1t+KNq7d6/OjxO8fv1a/iC15y5fvoy+QQDDXbx4kVXnPR6PSfchgSY9PT1bt2798ccfk8kktb0oxsRjZGKx2Pz8vPxVKysrRSyjWfTmlqZJoI36rlPVT3JN0qV0XRQADEEnwZGREVemb+rWrVsILZvoyJA8SDtraGjowYMH8nGP5O3bt8Uomcm4vH9rYGBAck1Sz3APAFBB1cTW1lZXJrQcc+OqIwmJRXvq3r17q6urko5Ex+Avt6anp8WDGNld4ggtAJOcOXOG9UQhtGwrkUhQRLGhBsKeotyyulxm4Sy3wuGweDoWagjfunULxxKASaiaGIlEcoYWm8FvY2OjmGUDV6Y1fPHiRdaL6yqZNjFPuSW5Xczn8924cQNd7QAmoTSiamLOUyHrSPR6vcUsG7gyzay2tjbxnazXr193fGi5eMkt8fSRTDAYHB4etrBIAM5GB92XX36pHlq0TTweP3/+fDKZLJ1B2KYSrlG5MlXzs2fPZrsVNZVKHThwQHzPFm1fIvetcpBb8joFRmEAmIoCqampiZ0T9+zZk89LamtrzS1TCZDMPc8WQMk2Utrv90tuNKaQM72I9mD33JKsZ1MivbcA1hoYGNA6+2hFRYVJhSkRVFfo7u6WPz41NSVf+JFOjPIdpOluWq7ZOrfGx8fF4zjlc1wCgOEkQ3bz4fF4cGDqtL6+nm2iJvnEg48fP875hor3HTuDTXOLqh5U4xMfPLitGKAIqCKfbQVFFQ4YlPHu3bs8t6SzUz6bGTj1u7xp9fz5c/lmT548ESaCkKxy4jB2zC354my4oAVQBIlEoqWlpYAXVlVVGV6YIlNMAmqyyBcYU+xBFWcG88cffyh+UCwWU5xmaPv27SrFk7yqurpaHktjY2O1tbW0GVU+Lly4EAwGhfHxgo2NDcpd3hvHtsst2j1ffvklLmhBiaCoWF9ff/XqFevVodOKfH0KQ+RcOpVOZ8ePHy9sTnGjBmXQ4U8BQH8KKowkHqj8rsz5evfu3RUVFQaeE+izZmdnFVsn9OD09HRzczM70bN+IMU3oczYtWuX0JvHLswrbvnNN9/MzMzIy19eXq6YNIoOHTok35L2HVvdl+1rakHKt6Fv18cff8z7edVeuUVfEXEfBSZ3B6eiE/TPP/8cDofts/YEmxejsNdqmqdULpVKUXJMTU2p/DVYrmjt+8pnoXM6j6s825nx/v179TXfqeRsZSXaUn19dsrjPXv2KC71Pjw8vHXr1qtXr9KO8Hg87e3twgV+ybAX+oN3dXXJL0NSII2OjrJJCylrFYOQ99By2Sq3JLcV014ZHBzkvT0LIMGmljCpUaVHOKPIHyqZ7sESwkru6sRrvqvLmZQqejKEH1luKQ57mZyc3L9/v7DuPNXy29rahKYhQ0FIzVNhG3ofv9/vgAV1bZFb7GYRcbfAlStXsCodOIx8tFGJSyQSx48fzxbhdCL+4YcfWM8bbUnNCPHMAyWFwkbx8ZMZ6q/NZxvuWJ9b9I0U3/VNbdi7d+/q7HYAsBv57fMlTnIlW0IyfriyspLaglVVVU6d4FyR0PwNBALWlsRuLM4tyf3hrswinggtcBhJ5QzoD6Jyrcjj8Siup9zT0/PLL7+UTvazVQZDoRCu8UtYmVuSC1oM1ad8Ph/X1wwBxNLpNEJLjE2sp7LB0NBQtgsw//jHPyQ1XYHDbvGk02MymaRfSj58A6zJLTqST58+nW3IDX2n//Wvf/F+5RCAESb6U+f1ehsbG/ft27dlyxahy8GR13XojKz+B2loaCjgKaoEl5WVOeAsL1wHdVgSG8iC3FK/GOvKjCilQ315ebmYpYIik0ziZa3ff//dpN5p+jVz9mvR6em7775T7Ati13WOHj0qNDLcbvfJkyezbW9/Oedx8Pl8KnVWeoo2yPYO9I1iN97qLaV16O/Dugfv3btXIpO7F6DYuUV7JWdty5W5xYE2Q10DuJZKpdSzOc+FT9l4MBZddOxMZYRCoUAgwF23xIULF9Q3qK6uzrmBSvJxvXwl1XJWVlaGhoacNwLQWEXNLU1VbDoy9+/fj/0H/JqYmFB5VtM80eLoYuhQunr16rVr1zhqXiQSiZytz61bt+rZIJlMRqNRTlsqDujkLI6i5pbWfiE6So2d0AWgaKixpXKrltvtjkQimlpLFF2Li4vi96RzdH19PUdrqD59+jTnNjt37tS5wdzcHKe5BXmy/v4tdRijAZyanZ1VeXZ0dLSAC1STk5PLy8uSJsvIyMjDhw+5WOKH2ls5t9mxY4fODeivoaFMwKFi55bX693c3Mx/khuM0XAqyXw2zqMyCNDj8RQ8HczMzIx8AWJKMjpM7B9dBi7tocKGc2iBsYqaWz6f78aNG69fv9Z0OwvGaAB3qGGhcvbMNm1PPiorK0OhkLzLnUUXanhQCoqaW2y6SaoSUghlu3lQEcZoAF/W19dVnj106JCeNw8EAmNjY/KaH0XX999/z8u1LoCCWXN9ixLoxYsXmiaBxhgN4MirV69UntU5ApBqfnQEKQ76oGOKQtG2IwzVh7AD5MmycRlUK3z+/LmmL/Hx48fj8bjNe/AByMuXL7M95Xa79b9/R0dHtsGKdr6BKedQQEOwFSbBwawcT3jjxo2//e1v+V/oSiaTp0+f1rO2DUBxqAxAqKmp0f/+lZWVHo9H8RIaPRgOh+3Zqa4yS5Pg9evX6husra2pb5DzzmXgnZW5RS2nhYUF+eAoFdQ+Qw8+AGlsbMzW5Lp27Zo9c6u8vFxlliZGvYuVvHv3Tn2Dr776SnPJgCsW379F1cabN29qGqMxMjKye/duex6WAMxHH31k9keoXOulYEin0/bsUe/v71fPrZWVFfV3UN8Aq0mUAuvvO5bPApBTd3c3xmiAnVVVVWW7f8uoi0+ffvqpyrPxeNyec0bU1dWpN7lyTgSlflsxm5QWnM363HJlmQVAxebmJsZoAKeKc1fs6uqqPXPLlevCNv19YrFYtiGR9JTKFfFQKGTbsZRgIFvklitzaxfGaIBj1NbWqjxrSCee+gk6Z2+bhdiFbZXJB4aGhrId2vRUtrfFEoulwy65hTEapcbZ629VVFSoPLu+vm52s+Dt27emvr9OlZWVdLy3tbUp9rLQoa04RQ49mK2DEUsslhS75JYr81W+cuVKZ2dn/i/BGA2wJ6qHeb3ebF3fa2tr+nOrOHP9mYeOd2pUXbx4UXH+gampKfoFQ6EQu4wdjUZ/+uknxdByu92UWDgJlBQb5ZYrczdlIpHAGA1wgMbGxmy5RU2NgufVFbx580bl2SIMaNSP0n14eDgQCExMTMiP+gcZ6u+gslQ0OJi9cosMDg5ijAY4AJ2Os81kVoSFNqqqqsz+CKNQ6lCDieJHMb0UURuLEov+wkis0mS73KL4iUQibLmTPF+CMRpgQyr32NJ3W/+UFk+ePFF5tjgzKhklnU7/+uuv9DdhPwoTNS0tLQnnAcqqmpqa6urqffv22XaoJBSH7XLLlTng7969W19fn/9LMEaDO45ff8uleo+t/ikt1EcMGjKbVHGMj48L09uHQiFqRaHvBNTZMbdcmTG+iosMqcAYDbAb+hr7/X7FG5Apz1TuUsqHSmcjtVe46EBLJBLiIYU3b97E8Qv5sGluuTL18fn5eU0TxmOMBtgNVacoYBQ7vVtbWwu+LhsOh1U60umdC3jPIqPQEt/C5fV6EVqQJ/vmliszj4amC120JVXf7L9aOZQONuhAcQbOZDI5MDBQ2F1H165dy/YUFwEgCS1y4sQJC8sDfLF1btExPzo6qumOrmfPnp05c0a4wAtgOZUZOAtbyHt6elqlH+LSpUuai1hc6XT6+PHjkvqoyoplABK2zi1X5o6uH3/8UdOUbpFI5C9/+Qtungf7oG9jKpVSDBvWFMs/uqil0tfXl+1ZLibom52dlR/RVNekgx2d/JAPvbkVi8UMKYeKoaEhTQuduAqtxgKY58aNG01NTYo3JtLX+8WLF/mMhpV3r4nxMkHf2NiY/EH6pehXo4BvaGhAPz+o05tbORcnFStsABXFT3d3d/5XuRit1VgAU9G5eHl5mb7Jih2GbPjGpUuXVA6Q6elplT5zXiboo+jNdizT45pqqOw2r/Ly8rKystra2oqKCgReidCbWyrXh+V+/vnnwjoxampqNA0sZOgYWFxc5OJghhJB30Y6ySre4EFNsfr6eq/X29bW9vnnnws9ZlTbW1tbU+8tDwaDvNy8+O9//9uot5KfEyjJWltbUVt1PF25NT4+rilOqKZJR6PWmdmoglZAaAmfmEql6GTBxe0sUAp6enro9JptKvRnGfm/m9vtvn79OuaPYNiUhlSZFibkBUcqJLcoCZaWlujLUUCcdHZ23r59m+pEOW+0SqfT6+vrv/32m6ZpduWokB6Pp6ur68iRI3v37kVPAliOvvnLy8vhcLi/v7/gZSQpsXp7e7mbXWL79u1mfwQd8nSCWlhYQHQ5Vb65FYvFNE28pEIyzfP79+9N/ThmKsOV6UkwaiZDOu9QeAtTqHm93hMnTsjPI2zuNUpr4bemMhw7dqy5udnUMw5rp87Pz29sbAgnR4rwxsZGinDU0C13MoO+RXfu3FGcUyMb1pdo9veHqqezs7PPnz839nurMm2jgdgoD2q5oqPFkfLNrbq6OsWAMUmRP07igw8+yPZUKBTq6emhWKUmo6SmzHp4xsbGxBW9aDTa0tIiuRDNkntmZsakW6TpQ8+fP6/Y3URlZhFO5w50n9oBS6/Lly/H4/HV1VWqZ1BFR7LvKKjoe1JdXb179+6amhqz9xoVQHFZLPa97evru3v3rp7R9irTNhqIDrru7m5Mt+1Idr9/yxJ//vkntZCyjd2iCrLKqCdxRS/b4DGGtmlqalpeXjagxP+LzjhnzpxhlXe2nh4bVUx152AwKK7U04mDzoboS7EJ2keHMywfyE5fFb/fLwRnV1fX4OAgFU8YzUjf8Pr6ej1zCVLm0cu13txSAP2TQII9IbcU0FHa0dFB7SF5k4VNXE1nfDZkWXKQM7TBxMSEK9M5Sc0adomYtmxsbJQ30fSvZyF2+vRpoSYrvlxPIUofRJ8uLiqbFsvY4ASuUb1HPLMaa5Sz/9MR8e7dO2EkJKXOjh07Co4E9p0v4P4WrQoewwx2htzK6rPPPpPnFgstoX+P8oAaMR6PR7IZa2aJb6mhLRVvoF5cXDQqtyiZxN0vjx8/llzEOnHihOQ3oh+j0SiudQHT1NQkDpL+/n7xs4FAQDyCv7W1dWNjo+DPoq99TU2NpBvAcKiWORJyK6uysjL5g+LQYrJdbJDfB0r1U/lm1A7TVUoRyVlmZGQknxX2VldXkVvgytR7xNUaqo1JWir0tacHhT4D+o+e3gJq2z169Kjg4ZR50nRTAfACuaUNNVnkIykUx0d9/fXXkkcU+ysMvEAtPwWcP38emQR5ktR7PvnkE/k29KD4a3bnzp0CcosSa3Z2VlgrknG73VTVO3To0Pbt29UHnrA7ZNj/19bWEomE+qou4DzILeegI19y9OJghjxFo1FJvefgwYM5XxWJRLSuvUCpI5+nUd6NoYI2E6qA7D+Dg4MUhJqWmQWuIbeco7e3V3Lotre3W1UY4Mvjx48Le6HWAXvy0KL6ls4bQui1PT09W7dulY8BpkQs+G3BtpBbzsEOXTaRHZtMQTyoms4v8/Pz8letrKwUsYxgU8+fP5c8ci7D2E+RXEJjurq6DLmLsaOjo6+vT9LH8Nlnn+l/Z7Ab5JajdGRIHqTEGhoaYvNdyV/y9u3bYpQM7G1paamwFz558iT/9tbi4qL8QapsFfbRcvIJuPfv32/Um4N9ILecTEgsan7du3dvdXUV1wBAkfxSqIEzogkMHD2rSJK+VFHD3PCOhNxypkQiQRHF6p4UWmxeDMotq8sFJe2jjz6SPzg/P2/ILCFUS5OkL1Xa9L8t2BByy2kkk8sJoWVtqYA7ZkwhePToUfldxvRB+meNoa/9N998I37E7/ejseVUyC1HoWaWZGGn69evI7QgJ/ENxQL6Ohn75aEguXDhgnxoRnd395YtWwq+11D+tfd6vZcvXy68oGBvyC27E65RuTKXHM6ePZvt8E6lUgcOHBB3ldD2uO8Y8iG5oZh5+vSp4ZWemZkZybfUlbm69sUXXwSDwUAgoGm2e0qs6elpyezVmu4GAx4ht2xNMvc8W0hCPoMU4/f7JacDCjnTiwiOcPDgQXnHIGWM1tXJc6IgXFhYUFzueSSDKltUmF27dlELrKKiQhI/VDl78+bN69evX7x4EYlE5FnLVhoytsxgN8gt+0qn093d3fLHqXYpX/gxGo3KTwR05JtYPnAQSgv5WFP6RqnfVsxWDtPasmHLPY+Pj1+9elUePJJ1ZfNH9bnvvvsOS8qVAuSWfa2vr2ebqEk+8WA+8x0o3ncM4MpkieI0m62trfF4XDGZpqenqcVDLaTCeuR6Mqi+NTc39/Dhw8Im2HW73Y2NjUePHmXrzBXwDsAj5FZW7969y3NLahjls5mBN6/Im1by+Q5c/31PqGSVEwAJxWWIKU6amprkl4vo69TZ2RkKhXS2b9hqma7M0fHHH3+srq6+fPmS/i9f9NmVSamamhpXpldz586dFRUVGHNUmpBbWSkmgeK9JoprJcjnEaDDUvGDsnXFbN++XaV4kldVV1fLTzpjY2O1tbW0GdVqL1y4EAwG5Yuvb2xs0DkCdVWg74niN4S+3nv37h0aGmJtGmEohN/vN/BKUnkGhhFBPpBbCtg6C4qtE3qQDtrm5mZ2oqctBwYGFN+EMmPXrl3CcUjJ0dLSorjlN998MzMzI6850mGseB5RdOjQIfmWbEl11//OfUAtSPk2VKH++OOPcZsXkOHhYfrOSIbnuTJfEsmSp/SNwkBzsApySwGdx1We7cx4//49tXhYKihiQ3vpP7RlU1OTSh8d1Wf37NmjOA6KziNbt25ll689Hk97e7tw8byiokK8JVWWu7q65GccCqTR0VE2KoyyVjEIEVogmJycLCsrkyyOJSafshmgyJBbCihp8tmMoiLPLfXM88YuXws/styiDJP37NEZZ//+/cJ9nV6vt62tTWgaMhSEu3fvFrah9/H7/d9++y36CUFA3zf62jx69Oj27dtLS0sswNi1pWPHjkm+UQDFh9ziEoWN4uMnM9Rfm882UOLKy8sV1xYAsAPkFk+EtWUDgYC1JQEAsApyiyf9/f2uzIwAuLkSAEoWcosb3d3dyWSyq6sLl8QBoJQhtzjARttPTU1lm5kQAKB0ILfsLhwOs+7Be/fu4a5MAADklq2Nj4+vrKwMDQ1hBCAAAIPcsjVcygIAkEBuAQAAT5BbAADAE+QWAADwBLkFAAA8QW4BAABPkFsAAMAT5BYAAPAEuQUAADxBbgEAAE+QWwAAwBPkFgAA8AS5BQAAPEFuAQAAT5BbAADAE+QWAADwBLkFAAA8QW4BAABPkFsAAMAT5BYAAPAEuQUAADxBbgEAAE+QWwAAwBPkFgAA8AS5BQAAPEFuAQAAT5BbAADAE+QWAADwBLkFAAA8QW4BAABPkFsAAMAT5BYAAPAEuQUAADxBbgEAAE+QWwAAwBPkFgAA8AS5BQAAPEFuAQAAT5BbAADAE+QWAADwBLkFAAA8QW4BAABPkFsAAMAT5BYAAPAEuQUAADxBbgEAAE+QWwAAwBPkFgAA8AS5BQAAPEFuAZSKaDQ6Nzf38OHDZDJJP7rd7pqammPHjjU3N2/bts3q0gHkC7kF4HyJRKKtre3Zs2fiBzc3Nx9k9PX1jY6OdnR0WFU8AE2QWwAOFw6HT506pbIBBVhnZydl2+TkZNFKBVAw5BaAk0WjUfXQEkxNTZWVlfX09JhdJACdkFsAjpVKpVpaWvLf/ty5c83NzeXl5eYVCUA/5BaAY01MTGxubmp9CXoLweaQWwDORI2tqakp+o/P52ttbW1oaNi2bVs6nY7H4z/99NODBw8UX0UvQW6BzSG3AJxpdnaW/g2FQuJLVhRdhzO6u7tZqsnFYrG6uroilRJAO+QWgDNFIpFgMJhtnAU1qqhBlq3VBWBnyC0AZ2pvb1cfHNjf36+YWx9++KFphQIwAHILwJlyjmjP1hlYWVlpQnEADIPcAihdPp9P0uTy+/1WFcYMiUSCfsH5+fmNjQ02uxXxeDyNjY1Hjhw5fPiw4wvgSMgtAPg/R48etboIxohGo+fPn5dMbcVQfkxlUGxPTk6adL+a5QVwMOQWQOlaWloS/+h2uxsaGqwqjFHS6fSZM2cikYgr8xtRMLB7AFKpVDAYZI8z1BLyer0LCwvGdo1aXgDHQ24BlCg6vUruSu7t7XXAxPCnT58WOj+vX78u9MVRsyYcDlNbR9wGor9AW1vb8vKykwrgePnmViwWq6+vN/zjJTeXZNPU1KRzwC61x+/fv6/nHQAcJh6Pi3/0eDwOmJyQgkF8rnj8+LHkGtKJEyckfXf0YzQaNepSk+UFKAX55lZdXd379+/Z/6m1u7S0dOHCBcWu25zY3fs1NTX59+qyyKHPffPmzdraWl9fXz6z11AL/eTJk0eOHPnrX/+KZjiAxNzcnPjHW7duWVUSA/X394t/HBkZ2bdvX85IWF1dNSo2LC9AKSikn7A8gyJB5Zb7bG7evEkvLOBDhc+lBG1ubqYWmHpqBoPBb7/91gGdHgBmSKfT1DIQfrxy5Yoz6nbCmD3B+fPnixkJlhegFOi6vqX1lnu/319waIlRGv3www9ffPGF4rPUzBL3KQOA3OzsrNBp0dXV5ZhFI+nwl3TGaJ1ZmPcClAK94zLOnj2bf279/e9/1/lxgi1btig+7vV6I5EIxpUCqKDG1tjYGPs/HTKDg4PWlsdAvb29586dEz/S3t5eUgUoBXpzK1t+KNq7d6/OjxO8fv1a/iC15y5fvoy+QQB1Fy9eZI0Aj8dz//59Jx0yPT09W7du/fHHH5PJJDV9KEXEg01isdj8/Lz8VSsrK44pQCnQm1ua5o026vCg2qLk4qcr09eB9RcAcqJT58jIiCvTo3Xr1i0nhRbTkSF5kH7roaGhBw8eUFTLX/L27VsnFcDxuLx/a2BgQHLxU89wD4DSQXW+1tZWVya0SuR2VyEw6Fe+d+/e6uqqpB/P8QVwHv5ya3p6WjyIkd2OjtACyMeZM2dY/1UphFYikaCEYBfghV+ZYqN0CuBUnOVWOBzu7OwUfqQW961btxx/+AEYgup8kUgkZ2hR+4DaZBsbG8Usm7GoWXnx4kXWHeqyonFpeQGcjafcktwu5vP5bty44bzeeQAzUBpRnS/nCZR1JHq93mKWzVjUymlraxPf33n9+vViZoblBXA8PnJLPE8lEwwGh4eHLSwSAEfoCPryyy/VQ4u2icfj58+fTyaT/A7dTqVSBw4cEN8yRRVc/XdzCteo2BuePXs223uaVAAQ4yC35JUXjMIAyB8FUlNTEzuT7tmzJ5+X1NbWmlsm0/j9fsl9vpQxOt8zHA6fOnVK+PFBRrYBzGYUACTsnlvRaLSlpUX4HqCbGECrgYEBrVOJVlRUmFQYU9HpQv6barrHVI5Sv7u7W/741NSUfOFHMwoAcrbOrfHxcfGAUa/X67B7JAHMJhl/mw+Px8PpUfb48eOc2yje9qtifX0920RN8okHzSgAyNk0t6iOQ5VE8fGG24oBtKLqv3j8bZ74HZTx/Plz+YNPnjwRpkeQLDKik7xpVeQClCw75lYqlfL7/bigBaBHIpFoaWkp4IVVVVWGF6Y4qqur5akwNjZWW1tLyUEpfuHChWAwKAxPF2xsbFBdWbGVuX37dpVPjMVi4jmDzCgAyNkut+h78OWXX+KCFvCIomJ9ff3Vq1esL4hORvJVLQyRcx1UOgkeP368sJnIjRqUQccyNTXoT0GFkTRNqPyuzFl+9+7dFRUVRh3ghw4dkkcC/RHYmrfsj/bu3Tv5NrSbPv74Y8WzTXl5uWLSFK0AIGev3JqenhZ3a2Byd+ACnaB//vnncDhsnxUr2LwYhb1W06SjcqlUanZ2dmpqSuWvwRolWnvMcqY1lbyrq0t+PY/yYHR0lM0ZSG0axRxSyYzh4eGtW7devXqV/qQej6e9vV247i4ZwGJSAUDCRrklua2Ydv/g4CAazmBnbGoJkxpVeoQzivyhkkkiLDE5Obl//35hNXaq+7a1tTU3N4vPJJRD1M4TtqEo8vv96svM9mQIP7LcUhzAYlIBQMwWucXuLxH3JFy5csUxC9mBI8mHDpW4RCJx/PjxbBFOp+8ffviBjb6jLanxIZ5GwFgnM/RvkxOFjbUFKFnW5xZ9icW3l1Nj+e7duzp7KgBMJb8XvsRJLktLSAYDV1ZWUluwqqqK02nRhYZsIBCwtiQly+LcktyI7sqsForQAjuT1LSA/iBs3IEij8ejuJ5yT0/PL7/8wmP2s8X/QqEQLr1bxcrcklzQYqgK5vP5cHES7CmdTiO0xNh0fCobDA0NZbts849//ENSbRXY9n5NOmslk0kqnvhyFxSZNblFB//p06ezjSaiw+Bf//oXLlGCDQkT/anzer2NjY379u3bsmWL0H9g9nUdS9B5XP0P0tDQUMBTVKMtKyuzVTYIVzRtm6mlw4LcUr9+68rc7kBnh+Xl5WKWCvSQzMhlrd9//92krmb6NXP2a9FJ7bvvvlPsQWLXdY4ePSo0Mtxu98mTJ7Ntb385Z3/w+XwqFVB6ijbI9g70jWK36+otpRHoN2Xdg/fu3cPk7pYrdm7R7s9ZQXNlJlChzVCpAftIpVLq2ZznKqZsFBmLLjoQpjJCoVAgEOCuj+HChQvqG1RXV+fcQCX5bLJ8JdVXVlZWhoaGMALQJoqaW5pq5XQw79+/H18UsImJiQmVZzVN+iyOLoaOi6tXr167ds0mzYt8JBKJnK3PrVu36tkgmUxGo1HL2ze26q4EV5FzS2tXEh3YBs4BA1Awamyp3KrldrsjkYim1hJF1+Liovg96RxdX1/P0YKoT58+zbnNzp07dW4wNzdneW6B3Vh//5Y6jNEAO5idnVV5dnR0tIALVJOTk8vLy5Imy8jIyMOHD7lYr4faWzm32bFjh84N6K+hoUxQGoqdW16vd3NzM/95cTBGgwuSWXCcR2UQoMfjKXhul5mZGfkCxJRk9J23f3RRG7QIn2LDObTAckXNLZ/Pd+PGjdevX2u6AwZjNMBa1LBQOXtmm+wnH5WVlaFQSN5/zqIL1TUARUXNLTaXM9UiKYSy3W+oCGM0wELr6+sqzx46dEjPmwcCgbGxMXk1jqLr+++/5+VaF0AxWXN9ixLoxYsXmuaNxhgNsMqrV69UntU5ApCqcXQ4KA76oAOEQtG2IwzVh7ADmMeycRlUkXz+/Lmm7/3x48fj8bjNO/3BeV6+fJntKbfbrf/9Ozo6sg1WtMkNTIpyDgU0BFthEkDMyvGEN27c+Nvf/pb/ha5kMnn69Gn1heMADKcyAKGmpkb/+1dWVno8HsVLaPRgOBy2Zw+5yixNgtevX6tvsLa2pr5BzjuXoQRZmVvUclpYWJCPp1JB7TN0+oPzNDY2ZmtyXbt2zZ65VV5erjJLE6PexUrevXunvsFXX32luWTgdBbfv0U1zZs3b2oaozEyMrJ79257HsngSB999JHZH6Fy4ZaCIZ1O27N7vL+/Xz23VlZW1N9BfQMsDQGKrL/vWD5xQE7d3d0YowFFU1VVle3+LaMuPn366acqz8bjcXvOGVFXV6fe5Mo5EZT6bcVsKlsACetzy5Vl4gAVm5ubGKMBdlCcu2JXV1ftmVuuXFep6e8Ti8WyDYmkp1Qub4dCIduOpQRr2SK3XJlbuzBGA+yptrZW5VlDOvHUT9A5e9ssxK5Sq8wkMDQ0lO04paeyvS0WZgQVdsktjNHgmrPX36qoqFB5dn193exmwdu3b019f50qKyvp4G1ra1PsMqHjVHG+G3owWwcjFmYEdXbJLVfm23/lypXOzs78X4IxGlAEVKnyer3Z+rHX1tb051Zx5vozDx281Ki6ePGi4mQCU1NT9AuGQiF2TToajf7000+KoeV2uymxcESDOhvllitzA2YikcAYDbCbxsbGbLlFTY2C59UVvHnzRuXZIgxo1I/SfXh4OBAITExMyA/hBxnq76CyVDSAmL1yiwwODmKMBtgNnY6zTUtWhIU2qqqqzP4Io1DqUIOJ4kcxvRRRG4sSi/7CSCzIk+1yi+InEomw5U7yfAnGaIDZVO6xpS+q/iktnjx5ovJscWZUMko6nf7111/pb8J+FCZqWlpaEg5qyqqamprq6up9+/bZdqgk2JbtcsuVOUfcvXu3vr4+/5dgjIa1HL/+lkv1Hlv9U1qojxg0ZDap4hgfHxemtw+FQtSKQkcIGM6OueXKDAtWXJdIBcZogKnoO+n3+xVvQKY8U7lLKR8qnY3UXuGiAy2RSIiHFN68eRMHI5jEprnlylTh5+fnNU0YjzEaYCqqG1HAKPZgt7a2FnyRNRwOq/SK0zsX8J5FRqElvoXL6/UitMA89s0tV2YeDU0XumhLqvHZf4Fz4BQbdKA4nWYymRwYGCjsrqNr165le4qLAJCEFjlx4oSF5QHHs3Vu0WlidHRU0x1dz549O3PmjHBNGMBYKtNpFrYq9/T0tEqnwqVLlzQXsbjS6fTx48cllUuVFcsA9LN1brkyd3T9+OOPmmaBi0Qif/nLX3C/PZiEvlqpVEoxbFhTLP/oopZKX19ftme5mKBvdnZWfnhSxZGOXPTYg0n05lYsFjOkHCqGhoY0LXTiKrTmC5CnGzduNDU1Kd5lSN/VFy9e5DO0Vd69JsbLBH1jY2PyB+mXol+NAr6hoQGd9mA4vbmVcz1TscLGXFH8dHd353+Vi9Fa8wXIH52Ll5eX6Wup2GHIhm9cunRJ5ds+PT2t0gHOywR9FL3ZDkx6XFN1k93mVV5eXlZWVltbW1FRgcCDbPTmlsolZbmff/65sH6PmpoaTQMLGTpsFhcXuTj+gUf01aKTrOLdGtQUq6+v93q9bW1tn3/+udBjRlW3tbU19a7vYDDIy52I//73v416K/kBTknW2tqKqifI6cqt8fFxTXFClVM6gLVO5kZ1ugJCS/jEVCpF5xcu7oAB7vT09NDpNdtU6M8y8n83t9t9/fp1zB/BsCkNqWYsTMgLwBSSW5QES0tL9H0qIE46Oztv375N1aicN1ql0+n19fXffvtN0zS7clRIj8fT1dV15MiRvXv3ovMBjEVf4+Xl5XA43N/fX/AykpRYvb293M0usX37drM/go5fOtssLCwgukCQb27FYjFNEy+pkMwM/f79e1M/jpnKcGU6HwqYyZC1+ebn5zc2NoRzE8VhY2MjxaHZFWRrPx3ycTKD0uvOnTuKc2pkw/oSm5ubTU0sqmvOzs4+f/5cOPToQDh27JjOz1WZttFAbJQHtVzRawJMvrlVV1enGDAmKfLHqYhGo+fPn1fs7aEIYXFIh65JXZHWfjpoxdLr8uXL8Xh8dXWVqhrpdFqy+yioKCqqq6t3795dU1Nj9o6jAigui8Wqj319fXfv3tUz2l5l2kYDUXR1d3dj7mxg7H7/loXogD9z5gyrO7Pl7NigXqq6BoNBcZ2ajls6GRnblWHtp4MetJsOZ1g+kJ2+LX6/XwjOrq6uwcFBKp4wmpHyoL6+Xs9cgpR59HKtd6oUQP8kkOAYyK2sTp8+LVQkxVfLqYIcDoepuSOuR7MpppaXl53x6eAAVPURT5PG2uXs/x0dHe/evRNGQlLq7Nixo+BIYJlXwM0qWhU8IBkcBrmljLJB3Pvx+PFjyWWkEydOSPp/6MdoNGrI1SZrPx2coampSRwk/f394mcDgYB4BH9ra+vGxkbBn0XRVVNTI+kJMBxqZsAgt5RJDvKRkZF8FrhbXV01JDms/XRwAKr6iGs2Ho9H0lLZtm0bPSgM86H/6Fn9ktp2jx49Kng4ZZ403VQADobcUiY/As+fP1+0VLD208EBJFWfTz75RL4NPSj+pt25c6eA3KLEmp2dFdaKZNxud1dX16FDh7Zv364+8ITd7sL+v7a2lkgk1Fd1AXAht7KhA09y8BTzWLL204F30WhUUvU5ePBgzldFIhGtCylQ6sjnafR6vfmvJUSbCQ1B9p/BwUEKQk1rxkKpQW4p6+3tlRw57e3tJfLpwLvHjx8X9kKtA/bkoUVVLp0L4NFre3p6tm7dKp+/kRKx4LcFJ0FuKWNHDptHjs1lIB7TTIf3/Py8/FUrKysO+HTg3fPnzyWPnMsw9lMkl9CYrq4uQ26g7ujo6Ovrk3QzfPbZZ/rfGRwAuZVVR4bkQcqMoaEhNneU/CVv3751xqcD15aWlgp74ZMnT/Jvby0uLsofpPpWYR8tJ59Ne//+/Ua9OXANuZUvITOoAXTv3r3V1dVidsFb++nAF/nV0MKmN1OXSqWMfUMJSfpSXQ1zwwOD3MotkUhQSLCqH8UGm5mCkqMUPh0gm48++kj+4Pz8vCGzhFBFTZK+VG/T/7bgDMgtNZK53YTYKIVPBycxYwrBo0ePyu8ypg/Scx8YQ9/8b775RvyI3+9HYwsEyK2sqKEjWVfp+vXrRYsNaz8duCa+oVhA3yhjvz8UJBcuXJAPzeju7t6yZUvBtxvKv/ler/fy5cuFFxQcB7mlLJVKHThwQNxT4fP59N/5K1ymYm949uxZxfc06dOhREhuKGaePn1qeL1nZmZG8kV1Za6uffHFF8FgMBAIaJrtnhJrenpast6eprvBoEQgt5T5/X7J0UgZo/M9w+GweNpstpBEV1eXMNupqZ8OpePgwYPyjkHKGK1LjedEQbiwsKC43PNIBtW3qDC7du2iFlhFRYUkfqh+9ubNm9evX7948SISicizNhQKWT6nPtgQcktBNBqVH4d04Ol5z3Q63d3dLX+capeStR/N+HQoKZQW8uGm9KVSv62YrRymtWXDlnseHx+/evWqPHgki8Tmj+pz3333HVaVA0XILQX5TDegeOevivX19WxzNUnmHjTj06GkUJYoLkPc2toaj8cVk2l6eppaPNRCKqxHrieDqlxzc3MPHz4sbIJdt9vd2Nh49OhRttRcAe8AJQK5pUA+3YDrv2/JlKwzopOkdVXkTwdHUlyGmOKkqalJfrmIvlGdnZ2hUEhn+4atlunKdAD+8ccfq6urL1++pP/LF312ZVKqpqbGlenV3LlzZ0VFBYYdQZ6QWwqqq6vlx/zY2FhtbS2FB1UqL1y4EAwG5Wufb2xs0CGqWFXcvn27yieKO3DM+HQoNfRVUfySUH7s3bt3aGiItWmEoRB+v9/AK0nlGRhJBCZBbik4dOiQ/IBnK5q7/nfqgXfv3sm3ofrsxx9/rHijFR3GiueR4nw6lKDh4WH62kiG57ky3xPx+CBX5kuFgebAEeSWAqqrdnV1yQ94ioTR0VE2KIvqqoo5pBIbdB7ZunUru3zt8Xja29uFi+cVFRVmfzqUoMnJybKyMsniWGLyWZsB7A+5pYwO+P379wu3VXq93ra2tubmZnEvHOXQ7t27hW0oivx+/7fffqvSU8cuXws/styiF0peYtKnQwmi7xt9cx49enT79u2lpSUWYOza0rFjxyRfKgAuILeyOpmhf5ucKG8s/HRwvPLycsXlBQA4hdyyjLC2bCAQsLYkAAAcQW5Zpr+/35WZEQA3VwIA5A+5ZY3u7u5kMtnV1YVL4gAAmiC3ii2dTg8MDExNTSnOTAgAAOqQW0UVDodZ9+C9e/dwVyYAQAGQW8UzPj6+srIyNDSEQYAAAAVDbhUPLmUBAOiH3AIAAJ4gtwAAgCfILQAA4AlyCwAAeILcAgAAniC3AACAJ8gtAADgCXILAAB4gtwCAACeILcAAIAnyC0AAOAJcgsAAHiC3AIAAJ4gtwAAgCfILQAA4AlyCwAAeILcAgAAniC3AACAJ8gtAADgCXILAAB4gtwCAACe/H9UNfVT1JerCwAAAABJRU5ErkJggg==", null, 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null, 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null, 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", null, 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", null, 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null, 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null, 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", null, 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", null, 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null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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null, 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lpdXr927dpVGfKNq1smSUlJWSRToUKFLl26kP+FjGX+CfJdTgIPMjmwoOo0W2ZiWAC0bNmy/jIXLlyYOnUqSQL819CiRQsy4BDzbVE5cuRwlBkxYgT5LCJf4hs3btS/WzL0HzJkiCA3goNkkSG+nZ2dj4/P2bNnlTYgn107duyIjo4mbXiujTWBJ9jVrVt3586d06ZNI58jwlYCVLx69crPz0/9l31wcPC8efP4qkhr8fHxZOiv5n5lHZQrV65Pnz4dOnSoX7++zp3UkZGfkCNfuvtlTpw4oUNXjx8/niNjZmZWo0YN8qt8kzKdawNQI2PJWjXKly9foEABHorhiIy/yYcAicSBgYF8HpeMqo8fP87nEfVka2u7YcMGLxmdP0NIoiD/1L6+vnRrA+CiWrVqZ86cIT/p5E2otEF6ejp5c166dCkqKipnzpw8l8eOKO6wGT58eFpa2rhx41gfaO7cuaVLl1b6VLZs2Uz/K3v27N8zIbXJf5X7+PHjK5nk5GTyeWegC0izQLKcv7+/+u8AEqNF+yn//v17MvSnu/pNly5d+vXr17FjR4p9msi+dImhQ4feunVr9erVa9asIW9IHfoh7+erV6/SrQ0gCy63zovh9L+igICAokWLuru783bERYsW8XYsitq0abNv37727duTr0VtX+vk5EQGXjovWQZAxYIFCypXrhwUFKSqwfLly+UZgKR0PgtjRxQBgIiIiHj48OHatWuZHoV8SJFhE90+SQD4559/7t27d+HChdOnT1+5coVu/4aCpLjp06eraUBi1fbt2zt37sxbSVrZuHGjn58fyQC0OiR/09DQUNY7HNesWXOmDElWs2bNevToEdPDAehg8+bNGtuIMwAQbm5uly9fnjNnDg/HIj/OtWvX5uFALNjZ2UVGRrq6umr1Kg8Pj1WrVjEqCUArgYGBefLk8fb2VtXg1q1bTZo0IZ8GgwcP5rMwRsQSAExk//SsAwALhQoVqinTrVs3E9kOaOtlbt68KXRp/OnZs+eGDRvUNChcuPC2bdtatmzJW0laCQ4Onj9/Pq3eatWqNXny5A4dOtDqkIuBMgsWLCBhQIQrmYBknTt3TukNdpmRT9EyZcrwU48OZs+effjwYR4Wr+NhVR+munfvTr4LyNcfx/YY/YPYDBgwIG/evL169VLTZsiQIa9evZo2bRpvVTEiogBQv379zp07G/oNwdbW1sNkzpw5Qz4Ho6Ojha6IraSkJPKJr36JTPJvsn37dgcHB96q4u7KlSt+fn6XL1+m1SEZ+qtaXZgHJEWTGBARESH+xVVBIsS8/g9348ePz1gpiJ13796xPgRrISEhHAMARv8gTmRIkz17dvUT/6ZPn/7mzZtly5bxVhULIgoABEldhh4AMjSVGTp0KImJhv4uUYWMm8mPysOHD9U3I98H4hz9L1iwQM2EP21ZWFjExsZSn+6vrZw5c06ZMoX8KJEYsG3bNmGLATCOAODi4tKiRQvd7rnn7smTJ0z750G9evXy5s375csX9c2cnJww+gfRcnNze/bsWXh4uJo2y5cvf/v27ebNmw33tmBxBQDqE/QFZ2NjExMT4+fnJ99UQuhyaCJRjUTkr1+/qm+2cuXKJk2a8FOSVvr160dqo9Wbvb39xo0bK1WqRKtDPVWvXn3r1q3R0dEk4fz48UPockCi/v77by4rw9jZ2bGvRV9hYWGsA0BycnJCQoKhfw9WqVLl2rVrahrkyJGDfC3yVg+ADsjPO8kACxYsUNNm586dLVu2JEM7Ma9proa4AkChQoWELoGJOnXqbNq0qXHjxiEhIULXQsfevXu7dOmisdno0aNFeG7v27dv3bt3J38FWh2S0f++ffuKFy9Oq0NaBg4c2Lx5c5IBjh49KnQtIEVcTv97eHjwUIn+nGUOHDjA9CgnT5409ABQpkwZ9QFgxowZFStW5K0eAN3Mnz//wYMHBw8eVNPm7NmzHTp02L9/v5WVFW+F0SKuAJAnTx6hS2AoODi4bt26vr6+jHaW5Q35eejUqZPGZm3btp04cSIP9WiFZHpXV9e4uDhaHZL/U5IlRDj6l6tWrdqRI0dCQ0P5WcYEIDPjmP+TISwsjHUA2L59u5+fH9NDsJaSkqLm2ebNmxvHCiogBeR78/Dhw79//1bTJj4+vmPHjiQDFC1alLfCqBBXAMidO7fQJbDVpEkTkhddXFxOnjwpdC06IqNJ8l5PT09X38zU1HTu3Ln8lMTdtWvXunfvTnGtTJGP/jPMnj27TJkyRnMBCgzCP//8c+fOHY3NWrRowUMxVJBS27RpQwYE7A5x7NixxMREg14OSH0AwPoEYECqVatGvj01RtbLly/LM4C5uTk/hVEhrgBgZmYmdAnMkffH7t27nZ2dz507J3QtWjt+/Dh5l//8+VNjSzL6Jz85PJTEHfnadnV1pbhxm6GM/uWCg4PJqKJHjx7fv38XuhaQBC6n/3leLVd/gYGBTAMAsWrVqrFjxzI9BDtpaWmPHz9W9eyQIUMaNWrEZz0AegoJCTl06JD6iUBEXFxcp06dSAYQ1Y7m6okrAOTIkcPU1PTXr19CF8IWeX/IM8ClS5eErkULV69eJaN/8vmusWXnzp3J1yQPJXF34sQJ8g+u/kKeVnLnzr1u3TpDGf3LdenShSQWMuRCBgAeGO4GwGqQHx8yhL1w4QK7Q8TGxhpuADhz5oyq68PkM3PYsGE81wOgP/lOIBrHD2fPniVjJAOa3yGuAEDkypVL48IyRsDCwmLDhg0ODg4Ut55l6s2bN71799a4uJuJLMWJbfJPfHz8X3/9RXH0byJbQrRKlSoUO+RH69atkQGAB6mpqVzutOFhcX3q/P39mQaAJ0+ebN68WdstdUXi9OnTqp4aPny4paUln8UAUGFra8tlIhBx6tSpPn36rFmzhoeq9Ce6AJAzZ04pBACiQoUKS5YsMZRPeTL6v3v3LpeWYWFh5cuXZ10Pdw8fPiSDDLpBy8PDY8CAARQ75JM8A7Rp00boQsCYcZn/4+joyEMl1PXq1Wvy5Mlcbm/Q2bJlywzlqyELVZtCFilSRP2q6gBiFhISsmDBAjXT2zKsXbuWDIEmTJjAQ1V6EmMAELoE/nTv3p0MrMnbRehCNPD19T106BCXlvny5Rs6dCjrerh7/fp1t27dnj59SrFP8rOtfm1g8SMZYN26dep3OwfQh5Gt/5OFv79/QEAAu/6PHDkSHx9vb2/P7hAsJCYmqroCEBYWZtyr/IHRCw0NJT/4XFpOnDixQoUK4v98QwAQ2OTJk0UeAKZMmbJ06VKOjcmnvIWFBdN6uPv+/TsZ/d+4cYNut2T0X7BgQbp98q9nz55JSUnk/0voQsAIpaenc7lT1nAjqJ+f3/jx41+/fs3uECtWrDC4ALBjxw6lj5coUUJUJ4YAdEB+6ufNm/fgwQMujb28vEgGaNasGeuq9CG6AGBqaip0CbwqU6ZMcHBwZGSk0IUot3nz5lGjRnFsTIb+ovqU7927t5oJqboJCAj4888/6fYpFPKflZycjP0BgDoup/9tbW0N95RwtmzZfHx8Jk+ezO4QsbGxs2bNMqylsVVNfQ4NDZXaNzsYJfJOHjhwIMfGffr0OX/+fKlSpZiWpA/RBQAJEm0AePHihVaXucPCwvLly8euHq1MmTKFyyhEW6JKOPqbPXv2lStXqMckkDijXP8nC9YB4PPnzyQDcB9tCO7MmTPx8fGKj5csWXLIkCH81wNAna+v79y5c+/du8el8T///DNo0KDdu3ezrkpnCADCK1++PPkuJJ/1QheSFRn9c7/GLT8lxrQe7g4cOMD9wgV3ISEhBr1Bj1LR0dH29vbfvn0TuhAwHlyyd+/evXmohJ0yZcp4eHisXr2a3SGWLVtmQAFA1T8FGf2TbweeiwFgZOjQod7e3hwb79mzZ8qUKSNHjmRaks4QAESBxESxBYDZs2fv3LmTe/u+ffuKZPZ/cnIy959PrYSGhrLoVljVqlUjGcDQT8eCeHBZMKB48eIlSpTgoRimfHx8mAaAq1evkn/Mtm3bsjsELe/fv1+5cqXi41ZWVjj9D8akT58+wcHBXJZElxs1alTDhg1btmzJtCrdIACIQv369Rs3bnz+/HmhC/n/4uLitJ3rQgIAo2K0RUb/L168oN4tGf2XLl2aerdiQP7vjhw5sm7dOqELAWNg3Ov/ZObo6PjHH38cO3aM3SGWLl1qEAGAjP6V7uAZGBiI0/9gTMzMzEgGWLJkCfeX+Pn5xcfH582bl11VukEAEIu//vpLPAFA2xXu7O3tnZyc2NSinTFjxuzbt496t9mzZzfK0/8ZJk2aRMZt2B0M9Ld+/XqNbTw8PHiohAe+vr5MA8D27dvv3r1btWpVdoegYvny5YoP5smTh+OyiQAGRNsAcO/ePZIBxDbLwwQBQDxIABDJEDM8PPzq1atavUQkp/8vX75MBrIseg4KCjKCGQtqlCtXjvzTYace0FNcXJzGnRzNzMyqVavGTz2sde/enfxdmG4KFhMTM3v2bHb962/fvn0JCQmKjwcEBBQuXJj3cgDYcnR0rFu3rlbDpFWrVjVp0kRs+4ciAOhlzJgx5E3w+/fv9PT0iRMn1q9fX+euypYtK4ZZQKSAmTNnavUSU1NTkVzQHz58OKOeSTxj1LN4hIWFbdmyhYQooQsBAyad+T8ZfH19Q0JC2PW/dOnSKVOmkNTE7hB6IhFF6eM4/Q/Gqk+fPtqeJx01alS3bt1EFYkRAPRy5cqVgwcPyn9PAoCevbVv317wAKDDGLpTp05i2Bhr4cKFx48fZ9FzpUqVSHZn0bPYkE+oLl26CF0FGDAu839EcsGQFm9vb/KD8/nzZ0b9f/r0acmSJUFBQYz619Pt27d37dql+DiJeca3ZhqAHAkA2sb+lJQU8kGxaNEiNhXpAgFALw8fPqTY259//jl69GiKHWprzpw5Z86c0fZVJACwKEYrz58/Z3f6n6R2Rj2LTefOnZ2dnQ8cOCB0IWCQEhISXr58qbFZo0aNeCiGN3nz5iUZYN68eewOsXTpUtEGAFWn/wcNGsRzJQC8sbCwIAMDLhueZLZ48WLyqhYtWjCqSlsIAHr5559/KPZmZ2dXsmTJpKQkin1y9+jRI93G0B07dqRejLZI5ezOwElh/k+GESNGIACAbrjM/+nevTsPlfCMdQCQn2Un+ZzdIXTz5csXpQHA2dlZnwmxAOLXvn17bQOAiewyu+ATPTIgAOguNTWV+qopJBoKtRojGfn9+PFD21e1bdu2SJEiLOrh7tChQ+z+0WrVqlW3bl1GnYtQ06ZNe/fuvXbtWqELAcOzceNGjW2M7AYAOVtb2y5dumi1cYq2li5dKsIAsGTJEqULouP0Pxg9EgB0eNWFCxfmzJkjks0xEAB0x3E7aK0IFQD27NnD5eydIjHM/5k/fz67ziV1+l9u4MCBCACgrRcvXty9e1djM92+NcXP29ubaQDYv3//9evX7ezs2B1CB9HR0YoP2tvbi+GyMABTVlZWzZo1O336tLYvHDlypJubW8mSJVlUpRUEAN09efKEep8NGzak3icXM2bM0O2FggeAc+fOka9Gdv0L/hfkn6OjY/PmzU+dOiV0IWBIuJxBaNWqFQ+VCIIEGzI6J2N0dodYunTp4sWL2fWvrU2bNt2/f1/xcZz+B4kgP/U6BIC0tLSZM2fOnTuXRUlaQQDQ3dOnT6n3Wb16dep9arRhw4azZ8/q8MI6deoIvjnuggUL2HVeqFAhsZ1y44ePjw8CAGiFDAc1tjHK+T8ZvL29mS58GRMTQwYN4lkPVOnp/1KlSoltsXMARv7880/d7pycN29eQECAjY0N9ZK0ggCgOx2SHxf29vbx8fEselZF59P/gi+OeePGDS7DDp01btyYXedi1rNnz1GjRrGIuGCUPn78GBcXp7GZq6srD8UIRb4e6L///suo/58/f5Jxw7Bhwxj1rxXy9Xfy5EnFx3H6H6SjRo0aOu8DOHPmTKURmk8IALpjFAB4XoMlJiZG58vWjo6OVGvRGtPT/yYSDgAmssXax48fL3QVYBi4rIZhb2+fM2dOHooRCvnbkQyg7UaKWiEf1yIJAErHLjly5EAAAElp3769bgFgyZIlgYGBgkz6yIAAoKMLFy58+vSJRc+WlpYsulVF59P/JkJfAXj16tXy5cuZHsLIFizXSq9evRAAgKPNmzdrbGPc83/kWAeAR48ebdy40c3Njd0huHjw4MGGDRsUHyejfwsLC/7rkZpv374JXcL/5M6dW4dXMfor6FaMPpo1azZ79mzdXktGX6tWraJbj1YQAHTE6PQ/z6Kjo3Xey6xSpUqlSpWiW49WmE7+kZNyACD/v7gVGDjK2BBdDcGHrTwgPzXdu3fXbUU1jmJiYgT/l1yyZInSx3H6nwcXLlwQ1aXpf/75x9raWquXREVF+fn5Ua8kf/78Hz9+pN6tevrMg1i9enVgYKCDgwPFerSCAKAj4wgAqjZx5KJWrVoUK9EBl5OO+qhfv37evHmZHkLk+vbtiwAAGm3btk1jm/LlyxcrVoyHYgTn7e3NNAAcP3784sWLDRo0YHcI9T5//qz0lKerq2u1atX4rwdALkcOAQa0RYoU0Wf5r2XLliEAGB4jCAAHDx7U527j2rVrUyxGWwkJCefOnWN6CCmf/pcjAeD169fkN79+/TI3Nxe6HBApLuNdKcz/kWvdunW9evUuX77M7hBLliwRMACounMRp/9BWKampoIc19HRUecAsHLlyhkzZhQsWJBqRVwhAOhi8+bNjG4A4JM+p/9NhA4ArE//EzVr1mR9CJHLnj17eHi40FWA2HGZjOfu7s5DJSLh7e3NNACQQUNUVJRQ64EuWrRI8cHmzZs7OTnxXosUFSlShIRMdnchclFJxtraOm/evDoMXm1sbDw8PD58+PD69WsydP78+bOe9eTLl69+/fpVq1bVsx/d6LNW+Pfv38mPc3BwML1ytIAAoAul9z8Zlnv37m3fvl2fHow+ANSoUYP1IQAM3dGjRzW2KVy4MBku8FCMSJAAMHLkyDdv3rA7xLRp0yIiItj1rwr57lO6AyZO//OmcuXKhw8fNpFdeYuJiTly5AifR2/RosWIESNIAtGnkzYyGX8kaXnHjh2RkZFfvnzRtqvq1asHBgZ6enoKuD+GntOhEQAMSVJSEtMt3/mh5+l/8o1etmxZWsVo6+zZs7otvKUVXAEA0Ajzf5Ty8fGZMmUKu/7JB7ggAUDp/J+qVav26NGD/2IkrrvMxo0bhwwZkpyczMMRvby8VqxYQb3bejLkU6Jfv35azeydO3duSEgI9Xq0pedQ4caNGyTRZU5EvEEA0JoRnP7/+fOnngFAqGttcqxn/5vIzrJI/A5gAC64LGPXs2dPHioRFW9vb6YB4MWLF7GxsTwnq5MnTyq9+Q2n/wXk5uZGBqAuLi73799neqC6deuyGP1nIN+5+/btc3Jy4jKf3srKatOmTc2bN2dXD3d58uTReTswuZUrVyIAGIZ169YJXYK+du7c+eHDB316qFKlCq1idHD+/HnWh8D8HwCNLl26lJaWprFZvXr1eChGVMqVK0diz/r169kdIiYmhucAoPT0v7m5ub+/P59lQBbVq1ffsGEDGaAzPQoPi88WKlQoIiKia9euGluuWrVKJKN/OfJfoE8A2Lhx4/z58/lfJw0BQDtr1qy5du2a0FXoS/8pTMIGAB6uACAAAGjEZf6Ph4cHD5WIkLe3N9MAcP78eT7XA71//77Su70HDRok1OorkMHe3n7evHns5sMUKVJk6NChjDrPrEuXLtbW1s+ePVPTZuzYsW3btuWhGO4qV66sZw87duzw8fGhUgx3CABaSE9PF2TaJV3kb2HQAeDmzZtv375lfRQEAACNVq9erbFN7969eahEhJycnBo3bsz0cmVkZCTTjJGZqtU/WezoBDoIDg4m3+wnT55k0XmFChVYdKtU7dq11QQABwcHEW5Rr/8iB9u3b0cAEDUy+le6AIJhIZ8R+q+6JWAA4GH+jwm/n3cAhujevXspKSkam+m5YIhB8/b2Zvp5tWHDhpUrV/Kw/snHjx/nzp2r+Hj//v2F3Q8eMps2bVrDhg2FrkJflpaWap6dOHEib5Vwp/8VgEOHDr18+bJ48eJU6uEIAYAr8m0nzneetqgsYaTt1t8U8RMASpQowcNRAAwXl/k/HTt25KES0fL09Bw+fPirV6/YHWLcuHFTp05l178cNv8yCA0aNPD391e6UYOeWN9hnNnz589VPeXm5tauXTveKuFO/wBgIpsFxPMPFAIAJ+np6YGBgUJXQceuXbv07MHc3FyojeuIK1eusD5EtmzZEAAA1FuzZo3GNn369OGhEjEbOHAg0xkLS5cu5SEAKD351aFDB9Y3noK2xo4du2zZMi635mslNTX1yZMn5cuXp9utUi9evFD1FD/3IeigaNGihQoVIv9K+nSyfft2BAAx6ty5M8/bbTBy8OBBPd+jJoKe/icePnzI+hBk9E8yAOujABiu5ORkLicFu3XrxkMxYubt7c00ALx7927JkiW+vr7sDrFu3bqPHz8qPo7T/yJkaWk5ZMgQFpnw9OnT/AQAVTcA9OzZU8yBs1SpUnoOro4ePZqUlFSyZElaJWmEAKBZjx499uzZI3QVdChdxVlbZcqU0b8T3Tx+/PjHjx+sj8LzPDwAg7N161aNbRwdHRGkybCgb9++XHZL0BnrADBjxgzFB+vVq9e+fXt2BwWdkQAwe/bs79+/0+2WDB7IO5lun4ouXryoao1yka82W7p06YSEBD07OXz4MJ9r+yIAqEPeiEFBQZs3bxa6EGqoBAABrwDwcPrfBDcAAGiydu1ajW14GC4YBG9vb6YB4Nq1a+zWAz1+/PjNmzcVH8fpf9EqWrRocHDwzJkz6XZ77Ngxuh0qpWqI0rp168aNG/NQgM6o3A1/5swZBABRWLFixciRI5nev8WzL1++UFlBX8AT5AgAAIIjnySXLl3S2Azzf+QcHR2bNWtG5eSLKtOmTduxYweLniMjIxUfLFOmjJeXF4vDARUsAkBiYuKRI0dYL+ql6sdk4MCBTI+rP1oBQP9OuEMAUOLatWtk6H/w4EGhC6GM1jcQ//vVZeAnAGAKEIAaXNb/sbW1NTc356EYg+Dj48M0AOzcuTMtLY36eqB3797dvXu34uM4/S9yZDAaFBQ0f/58ut1u3ryZdQA4deqU4oO1a9d2cXFhelz9UZm7/+DBg6dPn5YrV07/rrhAAPifs2fPHj58mGTcuLg4oWthAgGAo9y5c/NwFAADxWXzKT4vZItfr169hg0bpmZ5E/2R/ufNm0e3z6ioKMUHScwwmjXxjFhwcDD1AECSf0xMDN0+M9u7d6/h3m6ufvsC7s6cOYMAwASJVjly/Oev/P79+xSZ169fk19fvnxJhv487C8rLFoBoGjRolT60UFycjIPR0EAAFCDfFpqbIP5P1mQQczo0aPZ9U9GZnQDQGpqqtIRJPmL5MuXj+KBgIUKFSr4+vouWbKEYp/kLREbG8su2ytdbaV48eJM73GnhWIA4G31ZGkFgD///FPoEgTz+/dvWlc2BLwCoP8exlwgAACowmUnQfKdzc+KgQbE29ubaQD48uUL3eWAVG3+JfLFWCCDj48P3QBgIrs3kucAYBCjfxN6AYDpXMEspBUApOzmzZu/fv2i0pWAVwA+ffrEw1EQAABU2bBhg8Y2mP+jiIwPBgwYsGzZMnaHiIyMpDhaGj58uOKDbm5uFStWpHUIYMre3t7Z2fnAgQMU+zxz5sz58+dZLMhz4sQJpVf4xX/7rxytE6P37t179+6dhYUFld7UQwCQCqVLuelGwHv7+LkCkCdPHh6OAmCIuCyL7OrqykMlBsfb25tpALhz5w6t9UBVbfOM0/+Ghbzl6AYAE9lFABYBYNu2bYoPenl5GcqaHGTInjNnTir7FN26dat58+b696MRAoBU0AoAZmZmuXLlotKVDnAFAEBAx48f19iGfETUqVOHh2IMTv369Vu2bMnl31Bn48aNozLgU3r6v0WLFk2aNNG/c+BN165dq1WrRpIhxT5JAJg6dSrdmcBk3Lx69WrFxwcMGEDxKKyZm5unpKTo3w8ZrSEAAE20AkCBAgWo9KOD7zI8HAgBAECpjRs3amyD+T9q+Pr6Mg0ABw8e1H890KNHjyYlJSk+bhCLsUAWPj4+gwcPpthhenp6VFTU2LFjKfa5atUqxfV/mjVrJvLNv7IoWLAglQBw69Yt/TvhAgFAKowgAPBz+p/Inj07PwcCMCyxsbEa2/To0YN9IYbK1dU1PDw8MTGR3SFCQkKULt/JXUREhOKDtra23bt316dbEIS3t/eoUaO+fPlCsc/o6GjqAUDxwf79+1M8BA9IAKDSD8UJ2+ohAEjC8+fPaW1pnD9/fir96IDWTcwapaWl8XMgAANy9epVLjNcW7RowUMxhsvPz2/YsGHs+l+6dKk+ASAhIeH8+fOKj+P0v4HKly+fj48P3SVik5OTY2JiSLSg0tvly5fPnj2b5cGSJUt6eHhQ6Z83CACiRv5Zra2tP3/+/OnTJ/JN9uTJk6cy9+/fj4uLe/PmjdAFsvLgwQNaXQl4BYC3QyMAACjatGmTxjY4SawRGTYxDQC/f//WZz3QyZMnKz5YpEiRgIAA/eoCwZC3HItN4mgFAOM4/W9CLwB8/fr1zp071apVo9KbGtIKADlz5iwsI/9jjRo1Mj+bkJAwa9asx48fK92M2qBR3D9LwCsAuXPnzpUrFw+3AfBzpwGAYVm5cqXGNu7u7jxUYtDMzc0HDhyoapV9KqZPn65bAHj//r3SbZ5x+t+g2dradu3adceOHRT7vHbt2p49ezp27KhnP+TbVmkAMKzbf+VoBQDi0aNHCACUZcuWTc2z5IdkxYoV5DfXr19fsGCB/PfGQekdXboRdonMAgUK8LBhM64AAGTx4MEDLtdIyTiDh2IMnbe3N9MA8OTJE93WA509e7bSx4ODg/UuCoTk4+NDNwCYyC4C6B8AYmNjFe/uc3d3L1OmjJ498y9v3ry0uqJ40lYNBAAl7Ozsli9f7uzsHBYW9vTpU8ZF8YHimwkBAECCtmzZorFNq1ateKjECNjb27dp0+bw4cPsDjF8+PATJ05o+yql839IXBFw80egol27duRdFx8fT7HPAwcOXLlyxcHBQZ9OlK4rYIin/wmKK6QjANDHMQDIdevWrXnz5i4uLoq3pxgcYwoAPBwFAQAgCy7zf3r27MlDJcbB19eXaQA4efLkt2/ftFrRWNUmZYGBgZSKAiH5+PhQ31U3Kipq+fLlOr/8gkyWB+XbZehXlzD0XH43MwQA+rQKACayvZ2PHj1KMsD+/fsZlcQPilOAKF7k0gECAAD/UlJSHj58qLFZt27deCjGOJCvlQoVKjx+/JjdIQYPHqzVckBKd/nt1KlTzZo16RUFgvH29h45cuS7d+8o9rlixYoFCxboPCpQevrfEG//lcMVAGNDIt3evXsbNGhw+fJloWvRHa4AaAUBACAzLvN/6tatK+ASYYaIDLhDQ0PZ9R8dHc09ABw+fFjp4gdY/MdoZM+e3dfXd+rUqXS7nSyjwws/fvy4dOnSLA9aWFj4+PjQqEsAuAJghLJly0ZibsOGDT9//ix0LToymgBQokQJHo6SmprKw1E0unHjhtAl6K527dpClwDUcNn/q1evXuwLMSre3t5MAwDBfT1QpfN8GjRo0Lp1a9pFgWDI2Jp6ACA5U7cAYGSn/01wBcBY1ahRg2QAw93h8tu3b7S6ophxdVC9enUejvLixQsejqLep0+f7OzshK5CR3Xr1r1y5YrQVQAdaWlpXP43Mf9HWwUKFCDD7gULFrA7xLhx47gEgL///vv+/fuKj/v5+TEoCgRTrly5nj17Kl3pVWfv3r0j72EdbhQh6VTxQVp7CwiCYgB4+fIlra7UQADgytXVdceOHRs3bhS6EK39/PmTy/6dHJmamtLqSgdZtm5ghOItE9KUPXt2oUsAarjM/ylfvry1tTUPxRgZMtxhGgDIMILLeqBDhw5VfJAMFg1uK1bQyMfHh24AMJFdBNA2AJw8efL27dtZHnRxcalUqRK9uvhGcXRExmxk5JYjB9shOgKAFiIiIgwxAFA8/W8idACQzhUAg4YAYEyUbtOTRZ8+fXioxPjUrFnT2dn5wIED7A4REhKiuNBKZm/fvj106JDi49j8yyg1b97c0dHx3LlzFPtMSEjYv39/+/btub/E+Ob/mNAeHZGRG+t9VxEAtFC1atURI0ZQn0LH2tevXyn2JmwAsLa2trCwoLuOgSIxBADykx8TE2Mi276a/Js/e/bs+fPnz2SuX78udHVZkf+USpUqVaxYsXjx4sWKFcvYbBuMwNGjRzW2wfwfnZFxNtMAEBcXp3490FGjRik+mCdPniFDhrCrCgTk4+NDNwCYyLaQ4x4A3rx5o3haoVatWlpFCBFCADBy4eHhBhcAjOkKgInsIsCZM2eYHuL79+8pKSmWlpZMj6KRqs1QEhISNsvcuXOH55IyK1CgQI8ePZycnFq0aFGyZEkBKwF2du/erbENyXtYKVJnHTt2rFy5stIp+LSoXw9U6VRsEktYTz8AoXh4eIwYMYLuTNfjx48/ffq0XLlyXBob5el/EwYBgGJvSuEnXDvkq458mM6dO1foQrRA920k+OyOGjVqsA4AJrKLAIIHAFVsbW3HyWzbti00NDQxMZH/GiIjI/39/QVPg8DamjVrNLbBTHE9BQQEBAUFsetfzXqg06ZNU/p4SEgIu3pAcAMHDhw7dizdPkePHr127VouLSdNmpTlkbx58xrBlDO6X4h0524ohQCgNT8/PykHAMHHfLzdBlCnTh0eDqSPv/76q02bNp6entu3b+ftoOXLlyfBQ/z/OEDF1q1bNbbB/B89eXt7kwH379+/2R1C1XqgI0aMUHywV69euKXbuPn4+FAPAOvWreMSAA4dOqS40PaAAQNy5sxJtx7+4QqA8atYsaLQJWhH2/2P1RM8ADg5OfFwFDHcBsBFgQIFyHCcZAAud2rqL0+ePDExMRj9S8SpU6e4NGvatCnrSoxb7ty5g4KC5s2bx+4Qw4cPVwwAmzZtUto4ODiYXSUgBlZWVv3791++fDndbsPDw2fMmKG+zZw5cxQfNNzNvzKjOz8CAUCkduzY0bVrV6Gr4ErN7V86YHqaiovq1atXqlTpwYMHTI8i7PR6bcXGxt64cYOHm4MXLFjwxx9/sD4KiATm//CGjM6ZBoB///1XcT1Qf39/xZatWrWqV68eu0pAJMiYm3oAWLRokfoAkJSUdPjw4SwPtm/fnp8L+6z9+vVL6BK0gwCgi06dOgldghboBgAxvMXbtGnDOgAkJCQw7Z+60NBQ1ksxNm3a1Aju0wLuuGwAjPk/VFStWrVjx4579uxhd4gs64GSPPD27VvFZjrs6ASGqH79+n/88cexY8co9vnlyxfyoeHp6amqgdI7zo3ma4Xu6ChPnjwUe1MKAUAX2bNnd3NzM5Q9AegGgJ8/f1LsTTetW7detGgR00MYXAAg/yasD4H7AiXl+vXrXL7PyLCVh2KkwM/Pj2kAyLIeqNLT/zVr1jSs01ugD19fX7oBwER2g6+aADBhwoQsj1SuXNnFxYVuDUKhOz+C7shNKQQAHZFPSWkGAJFcAWB9iBcvXrx7987CwoL1gWixsrKysbF59OgRu0O0bNmSXecgNlzu58Pon6J27drZ2toyPfWQsR5oSkrK1atXFRsEBASwOzqITffu3cuXL//kyROKfZLvIFWbTytdU1jVateGiO7oCAFAvISaCf3582f5b/Lly8fxJcYXAPLkyUMygOJUQrrIN3GTJk2YHoKu2rVrswsA5cqVw/ZekrJy5UqNbcgAgodKpCMwMJDpYogZ64H6+fkpPmtpaWkc92ICd+SdEBYWRrfP0NDQs2fPKj6uuORU9uzZlb4VDRQCgFSQz0rWJ1wVxcTEZHxA79+/39nZmcurcuTIkTNnzh8/flCpQQwBwER2EQABIAsrKyt2nVeuXJld5yA2jx8/5rLfNgIAXd7e3sHBwd+/f2d3CPl6oNu2bVN8ypiGYsARGVFQDwDnzp37+PFjgQIFMj/45MkTxatbAwYM4H4qU/wwBUhCHBwceA4AmdfkrlGjBvcXkneSkQUAd3f3oUOHMj2Ewd0GUKhQIXadm5ubs+scxGb9+vUa25B4zMNXlKSYmpoGBQXNmjWL3SFCQkIePnyo9KkhQ4awOy6IU8GCBQMCAhYuXEi328DAwCxLCChu/mUi24+M7nGFhSsAElK3bl1V6yizkJ6envmct1YbtRQvXpwkciplMD07xV3JkiW9vLy4zFLQ2d9//82ucxYQAIAWLj9Zrq6uPFQiNWRIxDQAfPv2TWn/5LhZTtmCRPj4+FAPAKtWrcoSAFasWJGlTcuWLY1sSxmKK/fnzJkzRw7m43MEAN05ODjwebidO3dm/F7b9aFKlChBa93MtLQ0Kv3oz9vbm2kAOH78OPnLmpmZsTsEXUxLzZUrF7vOQVTevn37+PFjjc0w/4cFGxubrl277tixg+fj4vS/ZNWsWfPPP//ct28f3W6nT58+bNgw+e9jYmIUG5BvcLpHFNyXL19odVWyZElaXamBAKC7KlWq8Hm4zHfQa7trBgkAtMoQyRUAolGjRi1btiTDdEb9p6enk8453mghBhijAxUbNmzQ2MbW1rZ48eI8FCNB/v7+PAcAEjkqVarE5xFBVAYOHEg9AIwaNSojACjO1y1TpoybmxvdIwru69evtLqiOGZTAwFAd/xENDmSLDN/K2t1A4AJ1TeTeK4AmMhOIbALACayiwAIACA1XC6sGd+Xt3j88ccfNWvWvHXrFm9HxBYfEtehQ4dq1arduXOHYp+/fv3as2dPx44db968+eHDhyzPGtPqnxkoBgBcATAA1NfQVYWM/jOPvLUNABTfTOK5AmAiG4WMHj2a3a3YTNMFdaampuw6T09PZ9c5iMePHz/i4+M1NsP8H6aCgoJ4myDRuHHjZs2a8XMsEC1/f3/qu0AEBgaSAKB0uQ6j3HECVwCkhc8AkPmPAl4BEFUAMJFdBBg+fDijzslI6OXLl5jqYIIAIBlcFjYgnydVq1bloRjJGjBgQHBwMMUpxWqQA/FwFBA5Hx+f0NBQulf4ExMTHz16dOTIkSyPe3h4GOWqErgCIC0kAPBwlEuXLmXZr1vAewA+ffpEqysqhg0bFhsbe/fuXUb9nzhxwt3dnVHnAGLDZf4PfiJ4EBQUNG3aNNZHsbGxwWpOYCJbdoa85WbOnEm323bt2ik+yHS3OwHhJmBpWSbD+ijz58/P8kjp0qW16oF8ytMqhtZyohRFRESwG5EcP34cwx0TXAGQDC7T3jD/hwdkkMRDAAgMDGR9CDAUPj4+1AOA4qYTjRs3btiwId2jiATF06OYAgT/8ffff69bty7zIzrsnFeuXDkLCwsuW3tqpHg3j+Dc3NxWrVp18OBBFp1v2rQpKiqKhxV5RQ4BQAr27NmjsY2ZmZmxfn+LSpkyZbp165Z580fq8ufPj/k/kKFixYouLi7bt29nehRfX1+m/QuI4ulRfuZYSn1YI34LFizI8oi2NwDI1axZ89SpU/rXI8IAQIwbN45RACA/0mvXrvX09GTRuQFBAJCCLHv3KNWrVy/2hcB/BAYGMg0A/v7+7Do3CGlpaUlJScnJycWLFy9ZsiR2tvbz82MaACwtLT08PNj1LyxaAaBIkSJly5al0pV6CACidunSpaVLl2Z5ULcAUKtWLSoBQIRTgIgGDRqQT67Fixez6BwBwMS4AsCXL1/y5s0rdBVixOW7H/N/eNOsWbM6depcu3aNUf+hoaGMehazly9fHpA5fvz427dvMz9lYWFhbW3dQUaal7n++OMPOzu769evM+rf+Db/yozW6IiM1qj0oxECgKhNmjRJ8UGdA4De5fyHOK8AEIsWLbpw4QKLL8tjx44lJCTY2tpS79mAGG4A+P379zGZM2fOvJL59OlTwYIFLS0traysmjZtSr7zWrVqJXSZwiP/PlyaKb2rDxgJCgry8vJi0XPfvn2LFSvGomfRSkxMnDZtWnR0tKoG72Ru3LgxefLksmXL9u/ff8yYMXxWKAaBgYHkL86uc0Y9iwGtAFC7dm0q/WiEACBeO3bsUDolV7eRaM2aNfWu6D/IW/z79+/i3HNq8eLFjRo1YtHzmjVrpk6dyqJnYOfevXsLFy6MiYlRXNvug8zDhw/PnTtHxgS5c+f29fUNCAioWLGiIKWKAZf1f1xcXHioBDJ4enoGBwezOO0yZMgQ6n2K2YgRI7S6qZqkhbFjx27ZsoWEgY4dO7IrTGz69es3ePBgFm85V1dXKysr6t2KB64AAB3p6emjRo1S+lS1atV06JDiWyolJUXbZYj40bBhwzlz5rD4Ylu7dq3EA4BhXQF4+vQp+fImsY1j+2/fvkXKkPHWhAkTrK2tmZYnTlxuAMD8H/4FBQUpvRSsj7Zt2/I2yBCDvn37rl69WocX3rp1q1OnTl5eXitWrKBelWixeMuZGPs9J1QWWZFDAJC6oUOHqtqXW7fRSZ48eWjN7Xv9+rU4AwAxePDgCxcubNmyhW63z58/X7lyJaNr8QbBgAJATEwMCYG6rchGBsHbt2+fPXu2Ue5Ur8bNmze5/Bd369aNh2IgMz8/P+qjMfI5SbdD0fr+/XuHDh0U96LSCvnwf/PmDflaMTMzo1WYmA0cOJD6W87e3t64N5wm7xBaXSEASNrRo0fnzJmj9KkCBQro3G3Tpk2pBICUlBT9O2Fn8eLFt2/fTkhIoNvthAkTEABE7sePH3369FG1l+2YMWMCAgIsLS3lf7x7925kZKTihOAPHz54e3sfPnx448aN2bNnZ1uxaHA5/d+yZUush8u/EiVKuLm5kXcjrQ7t7Ozatm1LqzeRc3d313P0L7dnz54WLVqQDFCqVCn9exM58nfs2bPn+vXrKfZprJt/ZaAVABo1apQzZ04qXWkkrU9zMj4QugTNyPBazY+KbncAy5H8rbioqA5EHgCKFi1KviydnJwoXpIzkc0qIRlg7NixFPs0IOIPAOS/28XFRdVSV5cuXapXr17mR6pWrRoVFdWgQQOluY580799+3b79u2FChViUq7IcLkBAKf/hRIUFEQxAISEhNDqSuRI4Ke4qOWFCxc6dep09epVWh2Kmb+/P8UAULBgQaO/pvr69Wsq/fB5nUR0AeDXr1/sOv/69Su7zmnx8PBQ3Dwvgz4BoGnTpjq/NjORBwAT2R3P5PuyTZs2dLuVXwSQ5gRxkQcAEs/I6F/VGlALFy7MMvrP4OnpeejQIaWjq+PHj7du3ZoMIEQ74Y2WxMTEf//9V2Mz3AAglEaNGpE38OXLl/Xvqnjx4n379tW/H/EjGX7RokV0+4yPjw8MDKRyHk3k5Pv1xsXFUenNx8eHSj9iRusKgKQDANOT9IqLgYgNid1kOKKmQfXq1XXu3MrKioyMb926pXMPcklJSXr2wAMydFu1ahXdrzqSTkkGiImJodgn6O/3799kbKpq9F++fHn1N58NHz5c1elVMuRydXU9f/48hSpFjPykaGxjb29ftGhRHooBpYKCgvr06aN/P9LZ+nfKlCksul24cCHJYz179mTRuaiQtxytAGDcq3/KIQBQ8PPnT6FLEMyIESM0bmWl2xJAGch7S/8A8Pz5cz174IeHh8fLly+HDRtGsc9ly5Z5eXk1btyYYp8GQcxXAPr373/lyhVVz2qcuFJb5saNG0qfvXDhQu/evdeuXatXieKG+T/iR96EZED2/v17fTrJli2bRFb/jIqKYreblb+/v5OTU8mSJRn1LxLu7u4hISH6X/Dv1KlTmTJlqJQkZsnJyfp3QoYW+fPn178fjkQXAJheAfj+/Tu7zvUUERHBZZViPQNA06ZN9b8q+uLFCz174E14eDj5lW4GIMPNc+fOWVhYUOxT/EQbAGbPnq3+BlZnZ2eNnXTp0kVVACDWrVtXoUKFCRMm6FCe+JEx5dOnTzU2w/wfwZEAMH78eD17EOcWLtRt3bqVXef//vsvCRgTJ05kdwiRIG+Y0aNH69mJFE7/E8+ePdO/E54XShJdAGA6Rn/16hW7zvUxZswYjqtu6TkBvXXr1vq8XM6AAoCJLAOYmZlRvO/t7t27ffr02bdvH60OQWcJCQlDhw5V38bR0VFjP3Xr1lXfgHzZ//XXX7xt0MgnLrsllC9fXspbpImEv7+/ngFAIqf/U1JSjh8/zvQQJACQ/wujXyVs0KBBegYAW1tbieyz/s8//+jfCa0bNTkSVwD4+vUr0ylAb9++Zde5zjw8PDjuWKT/giQWFhYdO3ZUusEwd4YyBShDcHBwrly5/Pz8aHW4f/9+Ed4KJtqT9OxoPCvv4ODA5ZSnnZ2dxjYRERE7d+7kVpch4TL/B6f/xaBYsWL6zEZzdXWVwkwMYu/evawPQcYSJAMY985WJrIBQ79+/fTZBI3i167I6X8FoEiRIu3bt6dSDEfiCgC67d3DXWpqKtP+tXXnzh2SsFUtXKhInyWAMri4uOgZAEhIS0xMLFu2rP7F8Ib8O5uZmfXv359WhwsXLqxQoYKo9tP5/fu30CXw6uDBg6qW/M/AccqctbW1lZWV+iuEu3bt2rx5MxlFaVGi6JH3DJep0ggAIhEUFKRzAJDI6X8Tvk5RSSEAmMiWUtU5AOTKlUsK/0Qmsr3k9Z9g8tdff1EphjtpBYAnT54w7V8rixYtCgkJ0eqKhz5LAGXo2rWr/hta3b9/37ACANGvXz9LS8u+ffvS2h+AfKHK9+ih0pv+pHYFgMt0CO6nPEuVKqXxEzwyMtLIAgCX0WThwoUdHBx4KAY0qlevnm6LMzZr1qxBgwYsShIhfiap3r59+/HjxxUqVODhWAKqU6dO8+bNuZ+mzGzgwIHU6xEnKvN/pB4AWP/c3rlzh2n/HN28eZOMXXTYoETPO4DlChUq1KVLFz0nM5AAQOV2Ap516NDh3Llznp6eFy9epNKhu7v7o0ePRo0aRaU3PUkqAJw8eZLLMIj7igqlS5eOj49X3+b8+fNnzpzheZomU1zm/xhZ5jF0ui3OKJ3T/yY83qVGPg2MPgCYyObQ6hYAJHL7L3Hv3j09eyhVqhT1nYs0ElcAYH2Gnvy4kv+nKlWqMD2KGq9evZo8ebLOc8epBAAT2UUA/QMAlUr4V7VqVXkGoLWw4+jRox8+fMhlIMWapAKA+pV/MuTNm5djhxx3+1q+fLkxBQCSozS2wfwfUXF3dycDMq22Ha1UqVLnzp3ZlSQ25ubm/ByIjCiksKsaGTBYW1trO8e9Xbt20lk5QP8AIMg6y+IKADycoR8zZszmzZtZH0XR48ePFy9evGjRom/fvuncCa0A4OLiQkbA+owXDTcAEKampmvWrCGfTePGjaPSIRmMPnr0aPXq1eXKlaPSoW6kEwDevn3LZe8qIk+ePBz7LFiwIJdm5LizZs0yji2xdu3axaWZRBbxMCBBQUHki4x7e0md/icsLS35ORAJAPwcSHDkLRcWFqbVS6Rz+t9Etjagnj3wP//HRGwBYP/+/awPsWXLlmHDhk2fPp31gTIcPnx47dq1HNf5UY/WGg758+cnAUCfk9a3b9+mUomAIiIimjRpQj7UVO0gqxXyTeDo6Dhx4sR+/frp35tupBMAOJ7+J3Lnzs2xZc6cOTm23L17t4D/yxRx+WfE/B8RCggI4B4ASLKVzlRsOSsrK34OdP/+/Q8fPnA8d2DQ/P39tQoAFSpU4HlBG2HpeQWgevXqglxYFlEA2L59u5q9eCiaMWOGubn58OHD2R3i06dPR48eJQOFPXv20Nogmu5lTS8vL30CwLNnz16/fl2sWDGKJfHvjz/+iI+PHzVqFJVN45OSkvr3779q1aqxY8eSnvXvUFvSCQCHDh3i2JJ7AChcuDDHlkYTALjMA8T8HxEi71VPT0+OMVhUK5Xx488//6S7+aMaqampUggAefLkGTRoUFRUFMf2JKMyrUds9AwAQn2hiCgAaHVNU08jRoy4efMm+YyguLNPcnLynTt3Tp8+feLECfIrrW4zUFkCKAOJm7qtJpHh1q1bLVu2pFiSUCZPnuzs7Dx06FAqdwaT//pWrVp5eHiQGGBjY6N/h9x9/PiRz8MJ5cuXL0eOHOHYmPsUIO57+pAA8Pnz53z58nFsL04c7+oTZGYqaBQYGMgxAEht/o+J7LuyWrVq/Kz58e+//+q5O6ehCAoK4h4AJDX/5/nz51rdk5NFjhw5pB4ApkyZkpCQwOcRN8jY2dk1atSoatWqlStXNjc3z507t5mZmdL2v3///vnz548fP8ivV69eLVas2MuXL8mgn/z64MED8lnDepcxW1tbuh16eXnpEwBIgjKOAEA0adKE/FPMmDFj0qRJVIbRq2U8PT3d3Nzatm2rf4dqkI8e8k7euHHjhQsXWPRfr169gQMHiuec9+HDh7k3LlCgAPUC0tPTSQZwd3en3jOfuAwf+V+VAjiyt7cnn1pnz55V38zHx0cK56cVeXh4jBgxgocDkQDAw1HEgAyTyHcZl6uv5PuCDGp5KEkk9Jy6Qr5buV9/pksU/0lDhgyZO3euIIe+LiPIobVF6w7gDCQAhIWFffjwQbeXU5k6Lyrh4eHkR5FkgMjISCodxsqUL1/eTaZWrVpUupUjsfPUqVNbt27lPh9GK9myZfP19SVvkvr167PoX2da/X25LwOqKvkrtWvXLikEAMz/EbOgoCCNAUCCp//lhg8fHhUVRWV1dvXEtrsoU+Qtx+XjV1Kn/01kJ0P1eTnF/Um1JXAAuHTpEhlv6bkxrURQDwA5c+Yk49158+bp9vJz585RLUcUihYtSv5B5DFgy5YtVPp88uTJVBkHBwf7TExNTbXq5+fPn/fv3z/zX+y+2xo2bNijRw/yjyDOc4daXQHgHgC4TxYyMfzVPziessL8HzEj8axEiRLJycmqGnTq1EnANa8FRzKAn58f66NI5woA0b59+0qVKj148EBNmxYtWlCfrSBy+lwBcHJyEvAUmzAB4PXr1/v27du1a5eeq9FLCvUAQAwYMEDnAPDo0SMyBqW1MJGo1KpVa/PmzQcPHpw/f/6BAwdodXtFRv77bNmyyWOAuUzhTMhTHz58+ChDfkPyw30Z9R+7+iNvsO4yNWrUYHogfTx//vzx48fc23M/r69VAEhKSnr27Jnhzv3lsgAA+VoS6sI0cBQUFKRmootkT//LDRo06Nq1azExMUyPkitXLqb9iw15y6k/wS+10/8m+gUAYefWsgoAZIg/adKkfPnyyb+Af/z4kSpDvr/lA0dGxzViLIba1atX9/X1XbJkiW4vP3/+vFEGALl2MmfPnl2wYAH1vSPS09OvytDtVgfkf7BLly6urq6Ojo5C16KZeCbskf87ww0AmP9jHMhgS1UAqFevXvPmzXmuR2yWLl16+/Zt8j3F7hBaTR00AgEBASEhIb9+/VL6bKlSpbp27cpzScJ6+fKlzpsA2NnZ9enTh249WmEVAL59+zZ//nxGnUtQkSJFGPUcHh6ucwAgg2M3Nze69YhNE5mRI0eSGLB8+XKhy6GGDA7atm3bpk2bunXrCl2LFvhZKZgLEgBIcBK6Cl0kJiZymbiM+T/ily9fvv79+yv9XJL46f8M+/btc3V15b5umLakdgXARHYRQNVNmxI8/a/xPhw1yOiLYiU6EMVNwKARi/k/chUqVCCBXreJQOSzdeHChbQrEqPatWsvW7YsIiJi165du3fvZvd1wlSlSpVImCGDfjL0p7utBG9EdQVA6BJ0xGX+T+XKlYXd1ho4IqMxxQBQunRpoz81w1HhwoUPHz7cq1ev9evXs+ift03HxAMBIDOdA0CjRo0EX0kCAcAwsAsARFhY2IIFC1Rd1FPj6dOnFy9ebNCgAYuqRMja2jpA5tWrVyQGkDBAIpDQRWng4ODQuHFjR0dH8isZFghdjr7EcwUgPj5e6BJ0xCUAYP6PoahVq5aTk9PJkyczPxgaGipQOSK1bt269u3bjxo1KjExUX3L+vXre3t79+zZ88KFC506dfry5Yv69hLMyeSv3LlzZ/L1l+Xxfv365c2bV5CSBKRzABD89L8JuwBAhkrS2ZfU0JUsWZJkgGnTpunwWjIClk4AyGBlZeUt8++//x4/fjwuLo4EIfLr9+/fhS7tP/d12NnZ1alTh/xK/mu4L4Mjfp8/f9b2Tmh2y1GTEPjt2zfuOw2LRGpqKpdbsDD/x4AEBQVlDgDkPR8SEiJYNWLVq1cvEmtJEtgrk/mz2tTUtHTp0u3atfPw8GjcuLH8wT/++CMgIGDGjBlq+ixUqJCFhQXbukWJvOUUA4AET/+/ePFCt0vBLVu2FMMMUlwBgP8gYTQ6OlqHFc1IAJgwYQKDigxD4cKFXWRMZPf1ZiSBa9euPX/+XOPZIz1ZWlqSpF1GpnLlynYyRnwO5tmzZ9q+hOl+NKSeSpUqseufBS6n/8n7iryR2NcCdHTt2pWMX8kHjvyPmP2vSq5cubxkyO9TUlJIhk9LSyP/dMWLF1fa3t7eXn2HTK/MixkZv9aoUePvv//OeMTR0VGCHxo6L2EfFhZGtxLdIADAf5ibm0+ePNnf31/bF8bHxz98+LBixYosqjIs2bJlayST8cjr16+f/18vX74kqeDr16+ZfyV+/vwpfwkZsObMmTPXf+XLl69YsWJFixYtJiP/jZWVlXzQb8RjfaV0CADkH5NFJXLGGgAw/8fgBAUFZcwoQADgwlJGfZtChQqpb+Dg4ECvIgMTHByceTExCZ7+N9E1APTq1atdu3bUi9EBAgD8f35+flu3bj1x4oS2L9y3bx/5LGBRkqGTj9rr1KmjseX3799///5NRvzZs2fnoTADJcIrAOw6Z0Q8N1EARWEyQldhbFJSUtQ3MKwl1OgaICN0FUJKTU3dv3+/tq/Kly+fbtOtWUAAgP+ZMmVK5hPYHCEA6E+Ca8npQIRXANh1DgDCev36tfoGErz/DTLodvqfjP7FsxoHAgD8T8OGDYcMGTJnzhytXnXkyJHHjx9XqFCBUVUAcjpsIGhqasqiErnk5GR2nQOAsNQHgKpVq0r2HgAw0SkAyO8sZ1GMbhAA4P+YMmXKtm3bNK6VlsWaNWsiIiIYlQQgp/GKPM8+ffokdAkAwMrjx4/VPNumTRveKgGx+fr1qw4BQDyTf+QQAOD/MDMzmzx5cu/evbV6FQIA8ODbt29Cl/B/IAAAGLELFy6oedbZ2Zm3SkBsYmNjSQbQ6iWjRo0S213jCACQVa9evc6ePRsdHc39JY8ePdq3b9+ff/7JrioABAAA4MfDhw8zVlZVZGNjI5KFXEAQXJZTy6xZs2aTJk1iVIzOEABAicWLF8fFxV2/fp37S9asWYMAAEwhAAAAP9Sf/u/VqxdvlYDYnD59+vLly9zb58mTJyoqil09OkMAACWyZctGMkDGnohcbNq0KTIy0srKil1VIHEIAADAj71796p5tmfPnrxVAmKTeQMELsjo39bWlk0tekEAAOUaNWo0Z84crfaUWbVqVcZmNADUaTvnkrW0tDShSwAA+p4/f75582ZVz/r5+VWpUoXPekA83r59q9X8H39//759+7KrRx8IAKDS4MGD4+Li1HwOZjFr1qyQkBAsaQ+MpKens+v89+/f2r4kT548LCoBAGGpP8WLPdekTKvJPPXr11+4cCG7YvSEAADqLF68+ObNm3fv3uXS+PXr17Nnzx4xYgTrqkCa8uXLx65zBAAAkFMTAIYNG1auXDn+SgEx+fDhw8yZMzk2NjMzE+fU/wwIAKBOkSJF1q5d27RpU46zL+QXATAwAhbEFgBy587NohIAENCiRYsePXqk9KnSpUuPHz+e53pAPMjon2QAjo3J2Mne3p5pPXpCAAAN6tatS97Hf/31F5fG7969mz179ujRo1lXBRIktgCAoAtgZD5+/KhmiE+eMjMz47MeEI/Xr19zP/0/a9asbt26Ma1HfwgAoJmLiwv3G4LlFwHy58/PuiqQGgQAAGCKDPHJOE/pUz169OjXrx/P9YB4zJgxg+PCD4GBgaGhoazr0R8CAHAyePDgxMTEyMhIjS1TU1OnTZsmwj0vwNAVLVqUXee/fv3S9iUlSpRgUQkACOLGjRuzZ89W+lTZsmUXL17Mcz0gHnfv3p01axaXlp06dZo/fz7reqhAAACu5s2bl5SUtGXLFo0tJ0+e7Ozs7OjoyENVIB2WlpbsOtfhCgAZE7CoBAD4l5aW5uXlperZRYsWWVhY8FkPiEpISAiXZvb29uvWrWNcCzUIAKCFzZs3d+7ceffu3RpbDh06VP1OigDaQgAAAEbI6P/atWtKn5o3bx72uZeyWbNmHTp0SGOz2rVr79mzx4DmPyMAgHZ27drl7Ox88OBB9c3i4uImTpw4ZswYfqoCKShWrBi7zhEAACRr/PjxGzZsUPrUkCFDgoODea4HxOP69etcdn6oUaMGGf2XLFmSh5JoQQAArZEM0K5duxMnTqhvNnbsWBIVHBwc+KkKjF6ZMmXYdY4AACBNS5cuHTdunNKnPD09Vd0VABIxePBgjW2qVatGRv/W1tY81EMRAgBoLVeuXLt37yYZ4Ny5c+pbDh069OTJk7wUBcavRo0a7DrXNgAULlzYysqKUTEAwI9p06ap2rzS19c3Ojqa53pAVIYMGaJxDFOpUiUy+jfE7eEQAEAX+fPnJ+94V1fXo0ePqml26tQpb2/vmJgY3goDI2ZhYWFtbf3s2TMWnWsbAGrVqsWiDADgzbBhw2bMmKH0qcDAQENZywUYmTdv3ty5c9W3qVOnzqZNm2xsbPgpiS4EANCRubn5kSNH3N3dN27cqKbZsmXLyKBt7NixvBUGRqxGjRoIAACgp7S0NDLEV3Vyioz8MO9f4nbs2KFx8k+7du3I6L9gwYL8lEQdAgDoZcOGD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null, 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null, 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C0tUdlVu91cmskUUEOLOwNGomQj4dFatg+kPTIO/NaLU+jQtf1GLoRRdvQvOMtmD8Evc9VGuXwrFZJNzT/noe4f5kJAGAAYgTAAMABhAGAAwgDAAIQBgAEIAwADEAYABiAMAAxAGAAYgDAAMABhAGAAwgDAAIQBgAEIAwADEAYABiAMAAxAGAAYgDAAMABhAGDgf7aMpXJ9IvH4AAAAAElFTkSuQmCC", null, 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null, 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null, 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", null, 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", null, 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", null, 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", null, 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https://www.colorhexa.com/00d9a7
[ "# #00d9a7 Color Information\n\nIn a RGB color space, hex #00d9a7 is composed of 0% red, 85.1% green and 65.5% blue. Whereas in a CMYK color space, it is composed of 100% cyan, 0% magenta, 23% yellow and 14.9% black. It has a hue angle of 166.2 degrees, a saturation of 100% and a lightness of 42.5%. #00d9a7 color hex could be obtained by blending #00ffff with #00b34f. Closest websafe color is: #00cc99.\n\n• R 0\n• G 85\n• B 65\nRGB color chart\n• C 100\n• M 0\n• Y 23\n• K 15\nCMYK color chart\n\n#00d9a7 color description : Pure (or mostly pure) cyan.\n\n# #00d9a7 Color Conversion\n\nThe hexadecimal color #00d9a7 has RGB values of R:0, G:217, B:167 and CMYK values of C:1, M:0, Y:0.23, K:0.15. Its decimal value is 55719.\n\nHex triplet RGB Decimal 00d9a7 `#00d9a7` 0, 217, 167 `rgb(0,217,167)` 0, 85.1, 65.5 `rgb(0%,85.1%,65.5%)` 100, 0, 23, 15 166.2°, 100, 42.5 `hsl(166.2,100%,42.5%)` 166.2°, 100, 85.1 00cc99 `#00cc99`\nCIE-LAB 77.527, -56.077, 12.279 31.785, 52.412, 44.998 0.246, 0.406, 52.412 77.527, 57.406, 167.649 77.527, -64.93, 26.866 72.396, -48.324, 13.825 00000000, 11011001, 10100111\n\n# Color Schemes with #00d9a7\n\n• #00d9a7\n``#00d9a7` `rgb(0,217,167)``\n• #d90032\n``#d90032` `rgb(217,0,50)``\nComplementary Color\n• #00d93b\n``#00d93b` `rgb(0,217,59)``\n• #00d9a7\n``#00d9a7` `rgb(0,217,167)``\n• #009fd9\n``#009fd9` `rgb(0,159,217)``\nAnalogous Color\n• #d93b00\n``#d93b00` `rgb(217,59,0)``\n• #00d9a7\n``#00d9a7` `rgb(0,217,167)``\n• #d9009f\n``#d9009f` `rgb(217,0,159)``\nSplit Complementary Color\n• #d9a700\n``#d9a700` `rgb(217,167,0)``\n• #00d9a7\n``#00d9a7` `rgb(0,217,167)``\n• #a700d9\n``#a700d9` `rgb(167,0,217)``\n• #32d900\n``#32d900` `rgb(50,217,0)``\n• #00d9a7\n``#00d9a7` `rgb(0,217,167)``\n• #a700d9\n``#a700d9` `rgb(167,0,217)``\n• #d90032\n``#d90032` `rgb(217,0,50)``\n• #008d6c\n``#008d6c` `rgb(0,141,108)``\n• #00a680\n``#00a680` `rgb(0,166,128)``\n• #00c093\n``#00c093` `rgb(0,192,147)``\n• #00d9a7\n``#00d9a7` `rgb(0,217,167)``\n• #00f3bb\n``#00f3bb` `rgb(0,243,187)``\n• #0dffc7\n``#0dffc7` `rgb(13,255,199)``\n• #27ffcd\n``#27ffcd` `rgb(39,255,205)``\nMonochromatic Color\n\n# Alternatives to #00d9a7\n\nBelow, you can see some colors close to #00d9a7. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #00d971\n``#00d971` `rgb(0,217,113)``\n• #00d983\n``#00d983` `rgb(0,217,131)``\n• #00d995\n``#00d995` `rgb(0,217,149)``\n• #00d9a7\n``#00d9a7` `rgb(0,217,167)``\n• #00d9b9\n``#00d9b9` `rgb(0,217,185)``\n• #00d9cb\n``#00d9cb` `rgb(0,217,203)``\n• #00d5d9\n``#00d5d9` `rgb(0,213,217)``\nSimilar Colors\n\n# #00d9a7 Preview\n\nThis text has a font color of #00d9a7.\n\n``<span style=\"color:#00d9a7;\">Text here</span>``\n#00d9a7 background color\n\nThis paragraph has a background color of #00d9a7.\n\n``<p style=\"background-color:#00d9a7;\">Content here</p>``\n#00d9a7 border color\n\nThis element has a border color of #00d9a7.\n\n``<div style=\"border:1px solid #00d9a7;\">Content here</div>``\nCSS codes\n``.text {color:#00d9a7;}``\n``.background {background-color:#00d9a7;}``\n``.border {border:1px solid #00d9a7;}``\n\n# Shades and Tints of #00d9a7\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000101 is the darkest color, while #edfffb is the lightest one.\n\n• #000101\n``#000101` `rgb(0,1,1)``\n• #001510\n``#001510` `rgb(0,21,16)``\n• #00281f\n``#00281f` `rgb(0,40,31)``\n• #003c2e\n``#003c2e` `rgb(0,60,46)``\n• #00503d\n``#00503d` `rgb(0,80,61)``\n• #00634c\n``#00634c` `rgb(0,99,76)``\n• #00775c\n``#00775c` `rgb(0,119,92)``\n• #008b6b\n``#008b6b` `rgb(0,139,107)``\n• #009e7a\n``#009e7a` `rgb(0,158,122)``\n• #00b289\n``#00b289` `rgb(0,178,137)``\n• #00c598\n``#00c598` `rgb(0,197,152)``\n• #00d9a7\n``#00d9a7` `rgb(0,217,167)``\n• #00edb6\n``#00edb6` `rgb(0,237,182)``\n• #01ffc5\n``#01ffc5` `rgb(1,255,197)``\n• #15ffc9\n``#15ffc9` `rgb(21,255,201)``\n• #28ffce\n``#28ffce` `rgb(40,255,206)``\n• #3cffd2\n``#3cffd2` `rgb(60,255,210)``\n• #50ffd7\n``#50ffd7` `rgb(80,255,215)``\n• #63ffdb\n``#63ffdb` `rgb(99,255,219)``\n• #77ffe0\n``#77ffe0` `rgb(119,255,224)``\n• #8bffe4\n``#8bffe4` `rgb(139,255,228)``\n• #9effe9\n``#9effe9` `rgb(158,255,233)``\n• #b2ffed\n``#b2ffed` `rgb(178,255,237)``\n• #c5fff2\n``#c5fff2` `rgb(197,255,242)``\n• #d9fff6\n``#d9fff6` `rgb(217,255,246)``\n• #edfffb\n``#edfffb` `rgb(237,255,251)``\nTint Color Variation\n\n# Tones of #00d9a7\n\nA tone is produced by adding gray to any pure hue. In this case, #647571 is the less saturated color, while #00d9a7 is the most saturated one.\n\n• #647571\n``#647571` `rgb(100,117,113)``\n• #5c7d76\n``#5c7d76` `rgb(92,125,118)``\n• #53867a\n``#53867a` `rgb(83,134,122)``\n• #4b8e7f\n``#4b8e7f` `rgb(75,142,127)``\n• #439683\n``#439683` `rgb(67,150,131)``\n• #3a9f88\n``#3a9f88` `rgb(58,159,136)``\n• #32a78c\n``#32a78c` `rgb(50,167,140)``\n• #2aaf91\n``#2aaf91` `rgb(42,175,145)``\n• #21b895\n``#21b895` `rgb(33,184,149)``\n• #19c09a\n``#19c09a` `rgb(25,192,154)``\n• #11c89e\n``#11c89e` `rgb(17,200,158)``\n• #08d1a3\n``#08d1a3` `rgb(8,209,163)``\n• #00d9a7\n``#00d9a7` `rgb(0,217,167)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #00d9a7 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
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https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_4B%3A_General_Chemistry_for_Majors_(Larsen)/Text/Unit_III%3A_Chemical_Equilibria/VII%3A_Solubility_and_Precipitation_Equilibria/7.3%3A_Precipitation_and_the_Solubility_Product
[ "# 7.3: Precipitation and the Solubility Product\n\n$$\\newcommand{\\vecs}{\\overset { \\rightharpoonup} {\\mathbf{#1}} }$$ $$\\newcommand{\\vecd}{\\overset{-\\!-\\!\\rightharpoonup}{\\vphantom{a}\\smash {#1}}}$$$$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$\n\nLearning Objectives\n\n• Define Ksp, the solubility product.\n• Explain solid/solution equilibria using $$K_{sp}$$ and Qsp.\n• Calculate molarity of saturated solution from Ksp.\n• Calculate $$K_{sp}$$ from molarity of saturated solution.\n\nPrecipitation reactions occur when cations and anions in aqueous solution combine to form an insoluble ionic solid called a precipitate. Whether or not such a reaction occurs can be determined by using the solubility rules for common ionic solids. Because not all aqueous reactions form precipitates, one must consult the solubility rules before determining the state of the products and writing a net ionic equation. The ability to predict these reactions allows scientists to determine which ions are present in a solution, and allows industries to form chemicals by extracting components from these reactions.\n\n## Properties of Precipitates\n\nPrecipitates are insoluble ionic solid products of a reaction, formed when certain cations and anions combine in an aqueous solution. The determining factors of the formation of a precipitate can vary. Some reactions depend on temperature, such as solutions used for buffers, whereas others are dependent only on solution concentration. The solids produced in precipitate reactions are crystalline solids, and can be suspended throughout the liquid or fall to the bottom of the solution. The remaining fluid is called supernatant liquid (or just the supernate). The two components of the mixture (precipitate and supernate) can be separated by various methods, such as filtration, centrifuging, or decanting.", null, "Figure $$\\PageIndex{1}$$: Above is a diagram of the formation of a precipitate in solution. (Public Domain; ZabMilenko)\n\nThe use of solubility rules require an understanding of the way that ions react. Most precipitation reactions are single replacement reactions or double replacement reactions. A double replacement reaction occurs when two ionic reactants dissociate and bond with the respective anion or cation from the other reactant. The ions replace each other based on their charges as either a cation or an anion. This can be thought of as a double displacement reaction where the partners \"switching; that is, the two reactants each \"lose\" their partner and form a bond with a different partner:", null, "Figure $$\\PageIndex{2}$$: A double replacement reaction\n\nA double replacement reaction is specifically classified as a precipitation reaction when the chemical equation in question occurs in aqueous solution and one of the of the products formed is insoluble. An example of a precipitation reaction is given below:\n\n$\\ce{CdSO4(aq) + K2S (aq) \\rightarrow CdS (s) + K2SO4(aq)}$\n\nBoth reactants are aqueous and one product is solid. Because the reactants are ionic and aqueous, they dissociate and are therefore soluble. However, there are six solubility guidelines used to predict which molecules are insoluble in water. These molecules form a solid precipitate in solution.\n\nSolubility Rules\n\nWhether or not a reaction forms a precipitate is dictated by the solubility rules. These rules provide guidelines that tell which ions form solids and which remain in their ionic form in aqueous solution. The rules are to be followed from the top down, meaning that if something is insoluble (or soluble) due to rule 1, it has precedence over a higher-numbered rule.\n\n1. Salts formed with group 1 cations and $$\\ce{NH_4^{+}}$$ cations are soluble. There are some exceptions for certain $$Li^+$$ salts.\n2. Acetates ($$\\ce{C2H3O2^{-}}$$), nitrates ($$\\ce{NO3^{-}}$$), and perchlorates ($$\\ce{ClO4^{-}}$$) are soluble.\n3. Bromides, chlorides, and iodides are soluble.\n4. Sulfates ($$\\ce{SO4^{2-}}$$) are soluble with the exception of sulfates formed with $$\\ce{Ca^{2+}}$$, $$\\ce{Sr^{2+}}$$, and $$\\ce{Ba^{2+}}$$.\n5. Salts containing silver, lead, and mercury (I) are insoluble.\n6. Carbonates ($$\\ce{CO3^{2-}}$$), phosphates ($$\\ce{PO4^{3-}}$$), sulfides, oxides, and hydroxides ($$\\ce{OH^{-}}$$) are insoluble. Sulfides formed with group 2 cations and hydroxides formed with calcium, strontium, and barium are exceptions.\n\nIf the rules state that an ion is soluble, then it remains in its aqueous ion form. If an ion is insoluble based on the solubility rules, then it forms a solid with an ion from the other reactant. If all the ions in a reaction are shown to be soluble, then no precipitation reaction occurs.\n\n## Net Ionic Equations\n\nTo understand the definition of a net ionic equation, recall the equation for the double replacement reaction. Because this particular reaction is a precipitation reaction, states of matter can be assigned to each variable pair:\n\n$\\color{blue}{A}\\color{red}{B}\\color{black} (aq) + \\color{blue}{C}\\color{red}{D}\\color{black} (aq) → \\color{blue}{A}\\color{red}{D}\\color{black} (aq) \\color{black}+ \\color{blue}{C}\\color{red}{B}\\color{black} (s)$\n\nThe first step to writing a net ionic equation is to separate the soluble (aqueous) reactants and products into their respective cations and anions. Precipitates do not dissociate in water, so the solid should not be separated. The resulting equation looks like that below:\n\n$\\color{blue}{A}^+ \\color{black} (aq) + \\color{red}{B}\\color{black}^- (aq) + \\color{blue}{C}\\color{black}^+ (aq) + \\color{red}{D}^-\\color{black} (aq) → \\color{blue}{A}^+\\color{black} (aq) + \\color{red}{D}^-\\color{black} (aq) + \\color{blue}{C}\\color{red}{B}\\color{black} (s)$\n\nIn the equation above, A+ and D- ions are present on both sides of the equation. These are called spectator ions because they remain unchanged throughout the reaction. Since they go through the equation unchanged, they can be eliminated to show the net ionic equation:\n\n$\\color{red}{B}\\color{black}^- (aq) + \\color{blue}{C}\\color{black}^+ (aq) → + \\color{blue}{C}\\color{red}{B}\\color{black} (s)$\n\nThe net ionic equation only shows the precipitation reaction. A net ionic equation must be balanced on both sides not only in terms of atoms of elements, but also in terms of electric charge. Precipitation reactions are usually represented solely by net ionic equations. If all products are aqueous, a net ionic equation cannot be written because all ions are canceled out as spectator ions. Therefore, no precipitation reaction occurs\n\n## Equilibrium and non-Equilibrium Conditions\n\nThe ion product (Q) of a salt is the product of the concentrations of the ions in solution raised to the same powers as in the solubility product expression. It is analogous to the reaction quotient (Q) discussed for gaseous equilibria. Whereas Ksp describes equilibrium concentrations, the ion product describes concentrations that are not necessarily equilibrium concentrations. An ion product can in principle have any positive value, depending on the concentrations of the ions involved. Only in the special case when its value is identical with Ks does it become the solubility product. A solution in which this is the case is said to be saturated. Thus when\n\n$[\\ce{Ag^{+}}]^2 [\\ce{CrO4^{2-}}] = 2.76 \\times 10^{-12}$\n\nat the temperature and pressure at which this value $$K_{sp}$$ of applies, we say that the \"solution is saturated in silver chromate\".\n\nThe ion product $$Q$$ is analogous to the reaction quotient $$Q$$ for gaseous equilibria.\n\nAs summarized in Figure $$\\PageIndex{3}$$, there are three possible conditions for an aqueous solution of an ionic solid:\n\n• $$Q < K_{sp}$$. The solution is unsaturated, and more of the ionic solid, if available, will dissolve.\n• $$Q = K_{sp}$$. The solution is saturated and at equilibrium.\n• $$Q > K_{sp}$$. The solution is supersaturated, and ionic solid will precipitate.", null, "Figure $$\\PageIndex{3}$$: The Relationship between Q and Ksp. If Q is less than Ksp, the solution is unsaturated and more solid will dissolve until the system reaches equilibrium (Q = Ksp). If Q is greater than Ksp, the solution is supersaturated and solid will precipitate until Q = Ksp. If Q = Ksp, the rate of dissolution is equal to the rate of precipitation; the solution is saturated, and no net change in the amount of dissolved solid will occur. (CC BY-SA-NC; Anonymous)\n\nThe process of calculating the value of the ion product and comparing it with the magnitude of the solubility product is a straightforward way to determine whether a solution is unsaturated, saturated, or supersaturated. More important, the ion product tells chemists whether a precipitate will form when solutions of two soluble salts are mixed.\n\nExample $$\\PageIndex{3}$$: barium milkshakes\n\nBarium sulfate is used in medical imaging of the gastrointestinal tract. Its solubility product is $$1.08 \\times 10^{−10}$$ at 25°C, so it is ideally suited for this purpose because of its low solubility when a “barium milkshake” is consumed by a patient. The pathway of the sparingly soluble salt can be easily monitored by x-rays. Will barium sulfate precipitate if 10.0 mL of 0.0020 M Na2SO4 is added to 100 mL of 3.2 × 10−4 M BaCl2? Recall that $$\\ce{NaCl}$$ is highly soluble in water.\n\nGiven: Ksp and volumes and concentrations of reactants\n\nAsked for: whether precipitate will form\n\nStrategy:\n\n1. Write the balanced equilibrium equation for the precipitation reaction and the expression for Ksp.\n2. Determine the concentrations of all ions in solution when the solutions are mixed and use them to calculate the ion product (Q).\n3. Compare the values of Q and Ksp to decide whether a precipitate will form.\n\nSolution\n\nA The only slightly soluble salt that can be formed when these two solutions are mixed is $$\\ce{BaSO4}$$ because $$\\ce{NaCl}$$ is highly soluble. The equation for the precipitation of $$\\ce{BaSO4}$$ is as follows:\n\n$\\ce{BaSO4(s) <=> Ba^{2+} (aq) + SO^{2−}4(aq)} \\nonumber$\n\nThe solubility product expression is as follows:\n\n$K_{sp} = [\\ce{Ba^{2+}}][\\ce{SO4^{2−}}] = 1.08 \\times 10^{−10} \\nonumber$\n\nB To solve this problem, we must first calculate the ion product:\n\n$Q = [\\ce{Ba^{2+}}][\\ce{SO4^{2−}}] \\nonumber$\n\nusing the concentrations of the ions that are present after the solutions are mixed and before any reaction occurs. The concentration of Ba2+ when the solutions are mixed is the total number of moles of Ba2+ in the original 100 mL of $$\\ce{BaCl2}$$ solution divided by the final volume (100 mL + 10.0 mL = 110 mL):\n\n\\begin{align*} \\textrm{moles Ba}^{2+}=\\textrm{100 mL}\\left(\\dfrac{\\textrm{1 L}}{\\textrm{1000 mL}}\\right)\\left(\\dfrac{3.2\\times10^{-4}\\textrm{ mol}}{\\textrm{1 L}} \\right )=3.2\\times10^{-5}\\textrm{ mol Ba}^{2+} \\\\[4pt] [\\mathrm{Ba^{2+}}]=\\left(\\dfrac{3.2\\times10^{-5}\\textrm{ mol Ba}^{2+}}{\\textrm{110 mL}}\\right)\\left(\\dfrac{\\textrm{1000 mL}}{\\textrm{1 L}}\\right)=2.9\\times10^{-4}\\textrm{ M Ba}^{2+} \\end{align*}\n\nSimilarly, the concentration of SO42− after mixing is the total number of moles of SO42− in the original 10.0 mL of Na2SO4 solution divided by the final volume (110 mL):\n\n\\begin{align*} \\textrm{moles SO}_4^{2-} &=\\textrm{10.0 mL}\\left(\\dfrac{\\textrm{1 L}}{\\textrm{1000 mL}}\\right)\\left(\\dfrac{\\textrm{0.0020 mol}}{\\textrm{1 L}}\\right)=2.0\\times10^{-5}\\textrm{ mol SO}_4^{2-} \\\\[4pt] [\\mathrm{SO_4^{2-}}] &=\\left(\\dfrac{2.0\\times10^{-5}\\textrm{ mol SO}_4^{2-}}{\\textrm{110 mL}} \\right )\\left(\\dfrac{\\textrm{1000 mL}}{\\textrm{1 L}}\\right)=1.8\\times10^{-4}\\textrm{ M SO}_4^{2-} \\end{align*}\n\nWe can now calculate $$Q$$:\n\n$Q = [\\ce{Ba^{2+}}][\\ce{SO4^{2−}}] = (2.9 \\times 10^{−4})(1.8 \\times 10^{−4}) = 5.2 \\times 10^{−8} \\nonumber$\n\nC We now compare $$Q$$ with the $$K_{sp}$$. If Q > Ksp, then $$\\ce{BaSO4}$$ will precipitate, but if Q < Ksp, it will not. Because Q > Ksp, we predict that $$\\ce{BaSO4}$$ will precipitate when the two solutions are mixed. In fact, $$\\ce{BaSO4}$$ will continue to precipitate until the system reaches equilibrium, which occurs when\n\n$[\\ce{Ba^{2+}}][\\ce{SO4^{2−}}] = K_{sp} = 1.08 \\times 10^{−10}. \\nonumber$\n\nExercise $$\\PageIndex{3}$$\n\nThe solubility product of calcium fluoride ($$\\ce{CaF2}$$) is $$3.45 \\times 10^{−11}$$. If 2.0 mL of a 0.10 M solution of $$\\ce{NaF}$$ is added to 128 mL of a $$2.0 \\times 10^{−5}\\,M$$ solution of $$\\ce{Ca(NO3)2}$$, will $$\\ce{CaF2}$$ precipitate?\n\nYes, since $$Q_{sp} = 4.7 \\times 10^{−11} > K_{sp}$$.\n\nA solution must be saturated to be in equilibrium with the solid. This is a necessary condition for solubility equilibrium, but it is not by itself sufficient. True chemical equilibrium can only occur when all components are simultaneously present. A solubility system can be in equilibrium only when some of the solid is in contact with a saturated solution of its ions. Failure to appreciate this is a very common cause of errors in solving solubility problems.\n\nUndersaturated and supersaturated solutions\n\nIf the ion product is smaller than the solubility product, the system is not in equilibrium and no solid can be present. Such a solution is said to be undersaturated. A supersaturated solution is one in which the ion product exceeds the solubility product. A supersaturated solution is not at equilibrium, and no solid can ordinarily be present in such a solution. If some of the solid is added, the excess ions precipitate out and until solubility equilibrium is achieved.\n\nHow to know the saturation status of a solution? Just comparing the ion product Qs with the solubility product Ksp. as shown in Table $$\\PageIndex{1}$$.\n\nTable $$\\PageIndex{1}$$: relationship among $$Q_{sp}$$, $$K_{sp}$$ and saturation\n$$Q_{sp}/K_{sp}$$ Status\n> 1 Product concentration too high for equilibrium; net reaction proceeds to left.\n= 1 System is at equilibrium; no net change will occur.\n< 1 Product concentration too low for equilibrium; net reaction proceeds to right.\n\nFor example, for the system\n\n$\\ce{Ag2CrO4(s) <=> 2 Ag^{+} + CrO_4^{2–}} \\label{4ba}$\n\na solution in which Qs < Ks (i.e., Ks /Qs > 1) is undersaturated (blue shading) and the no solid will be present. The combinations of [Ag+] and [CrO42–] that correspond to a saturated solution (and thus to equilibrium) are limited to those described by the curved line. The pink area to the right of this curve represents a supersaturated solution.", null, "Figure $$\\PageIndex{4}$$: Equilibrium vs. non-equilibrium states for $$\\ce{Ag2CrO4(s)}$$. (CC BY; Stephen Lower).\n\nFor some substances, formation of a solid or crystallization does not occur automatically whenever a solution is saturated. These substances have a tendency to form oversaturated solutions. For example, syrup and honey are oversaturated sugar solutions, containing other substances such as citric acids. For oversatureated solutions, Qsp is greater than Ksp. When a seed crystal is provided or formed, a precipitate will form immediately due to equilibrium of requiring $$Q_{sp}$$ to approach $$K_{sp}$$. For example Sodium acetate trihydrate, $$\\ce{NaCH3COO\\cdot 3H2O}$$, when heated to 370 K will become a liquid and stays as a liquid when cooled to room temperature or even below 273 K (Video $$\\PageIndex{1}$$). As soon as a seed crystal is present, crystallization occurs rapidly. In such a process, heat is released since this is an exothermic process $$\\Delta H < 0$$.\n\nVideo $$\\PageIndex{1}$$: \"hot ice\" (sodium acetate) crystallized from a non-equilibrium supersaturated ($$Q_{sp} > K_{sp}$$) solution\n\nExample $$\\PageIndex{1}$$\n\nA sample of groundwater that has percolated through a layer of gypsum ($$\\ce{CaSO4}$$) with $$K_{sp} = 4.9 \\times 10^{–5} = 10^{–4.3}$$) is found to have be $$8.4 \\times 10^{–5}\\; M$$ in Ca2+ and $$7.2 \\times 10^{–5}\\; M$$ in SO42–. What is the equilibrium state of this solution with respect to gypsum?\n\nSolution\n\nThe ion product\n\n$Q_s = (8.4 \\times 10^{–5})(7.2 \\times 10^{-5}) = 6.0 \\times 10^{–4} \\nonumber$\n\nexceeds $$K_{sp}$$, so the ratio $$K_{sp} /Q_{sp} > 1$$ and the solution is supersaturated in $$\\ce{CaSO_4}$$.\n\n## Relating Solubilities to Solubility Constants\n\nThe solubility (by which we usually mean the molar solubility) of a solid is expressed as the concentration of the \"dissolved solid\" in a saturated solution. In the case of a simple 1:1 solid such as AgCl, this would just be the concentration of Ag+ or Cl in the saturated solution. But for a more complicated stoichiometry such as as silver chromate, the solubility would be only one-half of the Ag+ concentration.\n\nFor example, let us denote the solubility of Ag2CrO4 as S mol L–1. Then for a saturated solution, we have\n\n• $$[Ag^+] = 2S$$\n• $$[CrO_4^{2–}] = S$$\n\nSubstituting this into Eq 5b above,\n\n$(2S)^2 (S) = 4S^3 = 2.76 \\times 10^{–12}$\n\n$S= \\left( \\dfrac{K_{sp}}{4} \\right)^{1/3} = (6.9 \\times 10^{-13})^{1/3} = 0.88 \\times 10^{-4} \\label{6a}$\n\nthus the solubility is $$8.8 \\times 10^{–5}\\; M$$.\n\nNote that the relation between the solubility and the solubility product constant depends on the stoichiometry of the dissolution reaction. For this reason it is meaningless to compare the solubilities of two salts having the formulas A2B and AB2, say, on the basis of their Ks values.\n\nIt is meaningless to compare the solubilities of two salts having different formulas on the basis of their Ks values.\n\nExample $$\\PageIndex{2}$$\n\nThe solubility of CaF2 (molar mass 78.1) at 18°C is reported to be 1.6 mg per 100 mL of water. Calculate the value of Ks under these conditions.\n\nSolution\n\nmoles of solute in 100 mL; S = 0.0016 g / 78.1 g/mol = $$2.05 \\times 10^{-5}$$ mol\n\n$S = \\dfrac{2.05 \\times 10^{ –5} mol}{0.100\\; L} = 2.05 \\times 10^{-4} M$\n\n$K_{sp}= [Ca^{2+}][F^–]^2 = (S)(2S)^2 = 4 × (2.05 \\times 10^{–4})^3 = 3.44 \\times 10^{–11}$\n\nExample $$\\PageIndex{3}$$\n\nEstimate the solubility of La(IO3)3 and calculate the concentration of iodate in equilibrium with solid lanthanum iodate, for which Ks = 6.2 × 10–12.\n\nSolution\n\nThe equation for the dissolution is\n\n$La(IO_3)_3 \\rightleftharpoons La^{3+ }+ 3 IO_3^–$\n\nIf the solubility is S, then the equilibrium concentrations of the ions will be\n\n[La3+] = S and [IO3] = 3S. Then Ks = [La3+][IO3]3 = S(3S)3 = 27S4\n\n27S4 = 6.2 × 10–12, S = ( ( 6.2 ÷ 27) × 10–12 )¼ = 6.92 × 10–4 M\n\n[IO3] = 3S = 2.08 × 10–5 (M)\n\nExample $$\\PageIndex{4}$$: Cadmium\n\nCadmium is a highly toxic environmental pollutant that enters wastewaters associated with zinc smelting (Cd and Zn commonly occur together in ZnS ores) and in some electroplating processes. One way of controlling cadmium in effluent streams is to add sodium hydroxide, which precipitates insoluble Cd(OH)2 (Ks = 2.5E–14). If 1000 L of a certain wastewater contains Cd2+ at a concentration of 1.6E–5 M, what concentration of Cd2+ would remain after addition of 10 L of 4 M NaOH solution?\n\nSolution\n\nAs with most real-world problems, this is best approached as a series of smaller problems, making simplifying approximations as appropriate.\n\nVolume of treated water: 1000 L + 10 L = 1010 L\n\nConcentration of OH on addition to 1000 L of pure water:\n\n(4 M) × (10 L)/(1010 L) = 0.040 M\n\nInitial concentration of Cd2+ in 1010 L of water:\n\n$(1.6 \\times 10^{–5}\\; M) \\left( \\dfrac{100}{101} \\right) \\approx 1.6 \\times 10^{–5}\\; M$\n\nThe easiest way to tackle this is to start by assuming that a stoichiometric quantity of Cd(OH)2 is formed — that is, all of the Cd2+ gets precipitated.\n\nConcentrations $$[\\ce{Cd^{2+}}],\\, M$$ $$[\\ce{OH^{–}}],\\, M$$\ninitial 1.6E–5 0.04\nchange –1.6E–5 –3.2E–5\nfinal: 0 0.04 – 3.2E–5 ≈ .04\n\nNow \"turn on the equilibrium\" — find the concentration of Cd2+ that can exist in a 0.04M OH solution:\n\nConcentrations $$[\\ce{Cd^{2+}}],\\, M$$ $$[\\ce{OH^{–}}],\\, M$$\ninitial o 0.04\nchange +x +2x\nat equilibrium x .04 + 2x.04\n\nSubstitute these values into the solubility product expression:\n\nCd(OH)2(s) = [Cd2+] [OH]2 = 2.5E–14\n\n[Cd2+] = (2.5E–14) / (16E–4) = 1.6E–13 M\n\nNote that the effluent will now be very alkaline:\n\n$pH = 14 + \\log 0.04 = 12.6$\nso in order to meet environmental standards an equivalent quantity of strong acid must be added to neutralize the water before it is released.\n\n## The Common Ion Effect\n\nIt has long been known that the solubility of a sparingly soluble ionic substance is markedly decreased in a solution of another ionic compound when the two substances have an ion in common. This is just what would be expected on the basis of the Le Chatelier Principle; whenever the process\n\n$CaF_{2(s)} \\rightleftharpoons Ca^{2+} + 2 F^– \\label{7}$\n\nis in equilibrium, addition of more fluoride ion (in the form of highly soluble NaF) will shift the composition to the left, reducing the concentration of Ca2+, and thus effectively reducing the solubility of the solid. We can express this quantitatively by noting that the solubility product expression\n\n$[Ca^{2+}][F^–]^2 = 1.7 \\times 10^{–10} \\label{8}$\n\nmust always hold, even if some of the ionic species involved come from sources other than CaF2(s). For example, if some quantity x of fluoride ion is added to a solution initially in equilibrium with solid CaF2, we have\n\n• $$[Ca^{2+}] = S$$\n• $$[F^–] = 2S + x$$\n\nso that\n\n$K_{sp} = [Ca^{2+}][ F^–]^2 = S (2S + x)^2 . \\label{9a}$\n\nUniversity-level students should be able to derive these relations for ion-derived solids of any stoichiometry. In most practical cases x will be large compared to S so that the 2S term can be dropped and the relation becomes\n\n$K_{sp} ≈ S x^2$\n\n$S = \\dfrac{K_{sp}}{x^2} \\label{9b}$\n\nThe plots shown below illustrate the common ion effect for silver chromate as the chromate ion concentration is increased by addition of a soluble chromate such as Na2CrO4.", null, "", null, "What's different about the plot on the right? If you look carefully at the scales, you will see that this one is plotted logarithmically (that is, in powers of 10.) Notice how a much wider a range of values can display on a logarithmic plot. The point of showing this pair of plots is to illustrate the great utility of log-concentration plots in equilibrium calculations in which simple approximations (such as that made in Equation $$\\ref{9b}$$) can yield straight-lines within the range of values for which the approximation is valid.\n\nExample $$\\PageIndex{5}$$: strontium sulfate\n\nCalculate the solubility of strontium sulfate (Ks = 2.8 × 10–7) in\n\n1. pure water and\n2. in a 0.10 mol L–1 solution of Na2SO4.\n\nSolution:\n\n(a) In pure water, Ks = [Sr2+][SO42–] = S2\n\nS = √Ks = (2.8 × 10–7)½ = 5.3 × 10–4\n\n(b) In 0.10 mol L–1 Na2SO4, we have\n\nKs = [Sr2+][SO42–] = S × (0.10 + S) = 2.8 × 10–7\n\nBecause S is negligible compared to 0.10 M, we make the approximation\n\nKs = [Sr2+][SO42–] ≈ S × (0.10 M) = 2.8 × 10–7\n\nso S ≈ (2.8 × 10–7) / 0.10M = 2.8 × 10–6 M — which is roughly 100 times smaller than the result from (a).\n\nNote\n\nThe common ion effect usually decreases the solubility of a sparingly soluble salt.\n\nExample $$\\PageIndex{6}$$\n\nCalculate the solubility of calcium phosphate [Ca3(PO4)2] in 0.20 M CaCl2.\n\nGiven: concentration of CaCl2 solution\n\nAsked for: solubility of Ca3(PO4)2 in CaCl2 solution\n\nStrategy:\n\n1. Write the balanced equilibrium equation for the dissolution of Ca3(PO4)2. Tabulate the concentrations of all species produced in solution.\n2. Substitute the appropriate values into the expression for the solubility product and calculate the solubility of Ca3(PO4)2.\n\nSolution\n\nA The balanced equilibrium equation is given in the following table. If we let x equal the solubility of Ca3(PO4)2 in moles per liter, then the change in [Ca2+] is once again +3x, and the change in [PO43−] is +2x. We can insert these values into the ICE table.\n\n$Ca_3(PO_4)_{2(s)} \\rightleftharpoons 3Ca^{2+} (aq) + 2PO^{3−}_{4(aq)}$\n\n$$\\ce{Ca3(PO4)2}$$ $$\\ce{[Ca2+]}$$ $$\\ce{[PO43−]}$$\ninitial pure solid 0.20 0\nchange +3x +2x\nfinal pure solid 0.20 + 3x 2x\n\nB The Ksp expression is as follows:\n\nKsp = [Ca2+]3[PO43−]2 = (0.20 + 3x)3(2x)2 = 2.07×10−33\n\nBecause Ca3(PO4)2 is a sparingly soluble salt, we can reasonably expect that x << 0.20. Thus (0.20 + 3x) M is approximately 0.20 M, which simplifies the Ksp expression as follows:\n\n\\begin{align}K_{\\textrm{sp}}=(0.20)^3(2x)^2&=2.07\\times10^{-33} \\\\x^2&=6.5\\times10^{-32} \\\\x&=2.5\\times10^{-16}\\textrm{ M}\\end{align}\n\nThis value is the solubility of Ca3(PO4)2 in 0.20 M CaCl2 at 25°C. It is approximately nine orders of magnitude less than its solubility in pure water, as we would expect based on Le Chatelier’s principle. With one exception, this example is identical to Example $$\\PageIndex{2}$$—here the initial [Ca2+] was 0.20 M rather than 0.\n\nExercise $$\\PageIndex{6}$$\n\nCalculate the solubility of silver carbonate in a 0.25 M solution of sodium carbonate. The solubility of silver carbonate in pure water is 8.45 × 10−12 at 25°C.\n\n2.9 × 10−6 M (versus 1.3 × 10−4 M in pure water)\n\n## Applications and Examples\n\nPrecipitation reactions are useful in determining whether a certain element is present in a solution. If a precipitate is formed when a chemical reacts with lead, for example, the presence of lead in water sources could be tested by adding the chemical and monitoring for precipitate formation. In addition, precipitation reactions can be used to extract elements, such as magnesium from seawater. Precipitation reactions even occur in the human body between antibodies and antigens; however, the environment in which this occurs is still being studied.\n\nExample $$\\PageIndex{7}$$\n\nComplete the double replacement reaction and then reduce it to the net ionic equation.\n\n$NaOH (aq) + MgCl_{2 \\;(aq)} \\rightarrow \\nonumber$\n\nFirst, predict the products of this reaction using knowledge of double replacement reactions (remember the cations and anions “switch partners”).\n\n$2NaOH (aq) + MgCl_{2\\;(aq)} \\rightarrow 2NaCl + Mg(OH)_2 \\nonumber$\n\nSecond, consult the solubility rules to determine if the products are soluble. Group 1 cations ($$Na^+$$) and chlorides are soluble from rules 1 and 3 respectively, so $$NaCl$$ will be soluble in water. However, rule 6 states that hydroxides are insoluble, and thus $$Mg(OH)_2$$ will form a precipitate. The resulting equation is the following:\n\n$2NaOH(aq) + MgCl_{2\\;(aq)} \\rightarrow 2NaCl (aq) + Mg(OH)_{2\\;(s)} \\nonumber$\n\nThird, separate the reactants into their ionic forms, as they would exist in an aqueous solution. Be sure to balance both the electrical charge and the number of atoms:\n\n$2Na^+ (aq) + 2OH^- (aq) + Mg^{2+} (aq) + 2Cl^- (aq) \\rightarrow Mg(OH)_{2\\;(s)} + 2Na^+ (aq) + 2Cl^- (aq) \\nonumber$\n\nLastly, eliminate the spectator ions (the ions that occur on both sides of the equation unchanged). In this case, they are the sodium and chlorine ions. The final net ionic equation is:\n\n$Mg^{2+} (aq) + 2OH^- (aq) \\rightarrow Mg(OH)_{2(s)} \\nonumber$\n\nExample $$\\PageIndex{8}$$\n\nComplete the double replacement reaction and then reduce it to the net ionic equation.\n\n$CoCl_{2\\;(aq)} + Na_2SO_{4\\;(aq)} \\rightarrow \\nonumber$\n\nSolution\n\nThe predicted products of this reaction are $$CoSO_4$$ and $$NaCl$$. From the solubility rules, $$CoSO_4$$ is soluble because rule 4 states that sulfates ($$SO_4^{2-}$$) are soluble. Similarly, we find that $$NaCl$$ is soluble based on rules 1 and 3. After balancing, the resulting equation is as follows:\n\n$CoCl_{2\\;(aq)} + Na_2SO_{4\\;(aq)} \\rightarrow CoSO_{4\\;(aq)} + 2 NaCl (aq) \\nonumber$\n\nSeparate the species into their ionic forms, as they would exist in an aqueous solution. Balance the charge and the atoms. Cancel out all spectator ions (those that appear as ions on both sides of the equation.):\n\nCo2- (aq) + 2Cl-(aq) + 2Na+ (aq) + SO42-(aq) Co2- (aq) + SO42-(aq) + 2Na+ (aq) + 2Cl-(aq)\n\nNo precipitation reaction\n\nThis particular example is important because all of the reactants and the products are aqueous, meaning they cancel out of the net ionic equation. There is no solid precipitate formed; therefore, no precipitation reaction occurs.\n\nExample $$\\PageIndex{9}$$\n\nWrite the net ionic equation for the potentially double displacement reactions. Make sure to include the states of matter and balance the equations.\n\n1. $$Fe(NO_3)_{3\\;(aq)} + NaOH (aq) \\rightarrow$$\n2. $$Al_2(SO_4)_{3\\;(aq)} + BaCl_{2\\;(aq)} \\rightarrow$$\n3. $$HI (aq) + Zn(NO_3)_{2\\;(aq)} \\rightarrow$$\n4. $$CaCl_{2\\;(aq)} + Na_3PO_{4\\;(aq)} \\rightarrow$$\n5. $$Pb(NO_3)_{2\\;(aq)} + K_2SO_{4 \\;(aq)} \\rightarrow$$\n\nSolutions\n\na. Regardless of physical state, the products of this reaction are $$Fe(OH)_3$$ and $$NaNO_3$$. The solubility rules predict that $$NaNO_3$$ is soluble because all nitrates are soluble (rule 2). However, $$Fe(OH)_3$$ is insoluble, because hydroxides are insoluble (rule 6) and $$Fe$$ is not one of the cations which results in an exception. After dissociation, the ionic equation is as follows:\n\n$Fe^{3+} (aq) + NO^-_{3\\;(aq)} + Na^+ (aq) + 3OH^- (aq) \\rightarrow Fe(OH)_{3\\;(s)} + Na^+ (aq) + NO^-_{3\\;(aq)} \\nonumber$\n\nCanceling out spectator ions leaves the net ionic equation:\n\n$Fe^{3+} (aq) + OH^- (aq) \\rightarrow Fe(OH)_{\\;3(s)} \\nonumber$\n\nb. From the double replacement reaction, the products are $$AlCl_3$$ and $$BaSO_4$$. $$AlCl_3$$ is soluble because it contains a chloride (rule 3); however, $$BaSO_4$$ is insoluble: it contains a sulfate, but the $$Ba^{2+}$$ ion causes it to be insoluble because it is one of the cations that causes an exception to rule 4. The ionic equation is (after balancing):\n\n$2Al^{3+} (aq) + 6Cl^- (aq) + 3Ba^{2+} (aq) + 3SO^{2-}_{4\\;(aq)} \\rightarrow 2 Al^{3+} (aq) +6Cl^- (aq) + 3BaSO_{4\\;(s)} \\nonumber$\n\nCanceling out spectator ions leaves the following net ionic equation:\n\n$Ba^{2+} (aq) + SO^{2-}_{4\\;(aq)} \\rightarrow BaSO_{4\\;(s)} \\nonumber$\n\nc. From the double replacement reaction, the products $$HNO_3$$ and $$ZnI_2$$ are formed. Looking at the solubility rules, $$HNO_3$$ is soluble because it contains nitrate (rule 2), and $$ZnI_2$$ is soluble because iodides are soluble (rule 3). This means that both the products are aqueous (i.e. dissociate in water), and thus no precipitation reaction occurs.\n\nd. The products of this double replacement reaction are $$Ca_3(PO_4)_2$$ and $$NaCl$$. Rule 1 states that $$NaCl$$ is soluble, and according to solubility rule 6, $$Ca_3(PO_4)_2$$ is insoluble. The ionic equation is:\n\n$Ca^{2+} (aq) + Cl^- (aq) + Na^+ (aq) + PO^{3-}_{4\\;(aq)} \\rightarrow Ca_3(PO_4)_{2\\;(s)} + Na^+ (aq) + Cl^- (aq) \\nonumber$\n\nAfter canceling out spectator ions, the net ionic equation is given below:\n\n$Ca^{2+} (aq) + PO^{3-}_{4\\;(aq)} \\rightarrow Ca_3(PO_4)_{2\\;(s)} \\nonumber$\n\ne. The first product of this reaction, $$PbSO_4$$, is soluble according to rule 4 because it is a sulfate. The second product, $$KNO_3$$, is also soluble because it contains nitrate (rule 2). Therefore, no precipitation reaction occurs.\n\n## References\n\n1. Campbell, Dan, Linus Pauling, and Davis Pressman. \"The Nature of the Forces Between Antigen and Antibody and of the Precipitation Reaction.\" Physiological Reviews 23.3 (1943): 203-219. Online.\n2. Harwood, William, F Herring, Jeffry Madura, and Ralph Petrucci. General Chemistry. 9th ed. Upper Saddle River: Pearson Pretence Hall, 2007. Print.\n3. Freeouf, J.L, Grischkowsky, D., McInturff, D.T., Warren, A.C., & Woodall, J.M. (1990). Arsenic precipitates and the semi-insulating properties of gaas buffer layers grown by low-temperature molecular beam epitaxy. Applied Physics Letters, 57(13)\n4. Petrucci, et al. General Chemistry: Principles & Modern Applications. 9th ed. Upper Saddle River, New Jersey 2007.\n\n7.3: Precipitation and the Solubility Product is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts." ]
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http://www.numbersaplenty.com/2022012
[ "Search a number\nBaseRepresentation\nbin111101101101001111100\n310210201200100\n413231221330\n51004201022\n6111201100\n723121036\noct7555174\n93721610\n102022012\n111161193\n12816190\n1355a475\n143a8c56\n1529e1ac\nhex1eda7c\n\n2022012 has 18 divisors (see below), whose sum is σ = 5111288. Its totient is φ = 673992.\n\nThe previous prime is 2022011. The next prime is 2022017. The reversal of 2022012 is 2102202.\n\nAdding to 2022012 its reverse (2102202), we get a palindrome (4124214).\n\nIt is a tau number, because it is divible by the number of its divisors (18).\n\nIt is a Harshad number since it is a multiple of its sum of digits (9).\n\nIt is a junction number, because it is equal to n+sod(n) for n = 2021985 and 2022003.\n\nIt is a congruent number.\n\nIt is not an unprimeable number, because it can be changed into a prime (2022011) by changing a digit.\n\nIt is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 28048 + ... + 28119.\n\n22022012 is an apocalyptic number.\n\nIt is an amenable number.\n\n2022012 is an abundant number, since it is smaller than the sum of its proper divisors (3089276).\n\nIt is a pseudoperfect number, because it is the sum of a subset of its proper divisors.\n\n2022012 is a wasteful number, since it uses less digits than its factorization.\n\n2022012 is an evil number, because the sum of its binary digits is even.\n\nThe sum of its prime factors is 56177 (or 56172 counting only the distinct ones).\n\nThe product of its (nonzero) digits is 16, while the sum is 9.\n\nThe square root of 2022012 is about 1421.9746833189. The cubic root of 2022012 is about 126.4526425761.\n\nThe spelling of 2022012 in words is \"two million, twenty-two thousand, twelve\"." ]
[ null ]
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https://www.nature.com/articles/s41467-022-29686-7?error=cookies_not_supported&code=1a114c9e-3dfc-4afc-8bba-0290fd86ac98
[ "## Introduction\n\nThe strong interaction between Rydberg atoms and microwave (MW) fields that results from their high polarizability means that the Rydberg atom is a candidate medium for MW fields measurement, e.g., using electromagnetically induced absorption1, electromagnetically induced transparency (EIT)2,3 and the Autler–Townes effect3,4,5,6. The amplitudes7,8,9,10, phases10,11 and frequencies9,10 of MW fields could then be measured with high sensitivity. Based on this measurement sensitivity for MW fields, the Rydberg atom has been used in communications7,8,12,13 and radar14 as an atom-based radio receiver. In the communications field, the Rydberg atom replaces the traditional antenna with superior performance aspects that include sub-wavelength size, high sensitivity, system international (SI) traceability to Planck’s constant, high dynamic range, self-calibration and an operating range that spans from MHz to THz frequencies7,9,10,15,16. One application is analogue communications, e.g., real-time recording and reconstruction of audio signals13. Another application is digital communications, e.g., phase-shift keying and quadrature amplitude modulation7,8,12. The channel capacity of MW-based communications is limited by the standard quantum limited phase uncertainty7. Furthermore, a continuously tunable radio-frequency carrier has been realized based on Rydberg atoms17, thus paving the way for concurrent multichannel communications. Detection and decoding of multifrequency MW fields are highly important in communications for acceleration of information transmission and improved bandwidth efficiency. Additionally, MW fields recognition enables simultaneous detection of multiple targets with different velocities from the multifrequency spectrum induced by the Doppler effect. However, because of the sensitivity of Rydberg atoms, the noise is superimposed on the message, meaning that the message cannot be recovered efficiently. Additionally, it is difficult to generalize and scale the band-pass filters to enable demultiplexing of multifrequency signals with more carriers16.\n\nTo solve these problems, we use a deep learning model for its accurate signal prediction capability and its outstanding ability to recognize complex information from noisy data without use of complex circuits. The deep learning model updates the weights via backpropagation and then extracts features from massive data without human intervention or prior knowledge of physics and the experimental system. Because of these advantages, physicists have constructed complex neural networks to complete numerous tasks, including far-field subwavelength acoustic imaging18, value estimation of a stochastic magnetic field19, vortex light recognition20,21, demultiplexing of an orbital angular momentum beam22,23 and automatic control of experiments24,25,26,27,28,29.\n\nHere, we demonstrate a deep learning enhanced Rydberg receiver for frequency-division multiplexed digital communication. In our experiment, the Rydberg atoms act as a sensitive antenna and a mixer to receive multifrequency MW signals and extract information9,11,12. The modulated signal frequency is reduced from several gigahertz to several kilohertz via the interaction between the Rydberg atoms and the MWs, thus allowing the information to be extracted using simple apparatus. These interference signals are then fed into a well-trained deep learning model to retrieve the messages. The deep learning model extracts the multifrequency MW signal phases, even without knowing anything about the Lindblad master equation, which describes the interactions between atoms and light beams in an open system theoretically. The solution of the master equation is often complex because the higher-order terms and the noises from the environment and from among the atoms are taken into consideration. However, the deep learning model is robust to the noise because of its generalization ability, which takes advantage of the sensitivity of the Rydberg atoms while also reducing the impact of the noise that results from this sensitivity. Our deep learning model is scalable, allowing it to recognize the information carried by more than 20 MW bins. Additionally, when the training is complete, the deep learning model extracts the phases more rapidly than via direct solution of the master equation.\n\n## Results\n\n### Setup\n\nWe adapt a two-photon Rydberg-EIT scheme to excite atoms from a ground state to a Rydberg state. A probe field drives the atomic transition $$|5{S}_{1/2},F=2\\rangle \\to |5{P}_{1/2},F^{\\prime} =3\\rangle$$ and a coupling light couples the transition $$|5{P}_{1/2},F^{\\prime} =3\\rangle \\to |51{D}_{3/2}\\rangle$$ in rubidium 85, as shown in Fig. 1a. Multifrequency MW fields drive a radio-frequency (RF) transition between the two different Rydberg states $$|51{D}_{3/2}\\rangle$$ and $$|50{F}_{5/2}\\rangle$$. The energy difference between these states is 17.62 GHz. The multifrequency MW fields consist of multiple MW bins (more than three bins) with frequency differences of several kilohertz from the resonance frequency. The amplitudes, frequencies, and phases of the multiple MW bins can be adjusted individually (further details are provided in the “Methods” section). The detunings of the probe, coupling and MW fields are Δp, Δc and Δs, respectively. The Rabi frequencies of the probe, coupling and MW fields are Ωp, Ωc and Ωs, respectively. The experimental setup is depicted in Fig. 1b. We use MW fields to drive the Rydberg states constantly, producing modulated EIT spectra, i.e., the probe transmission spectra, as shown in the inset of Fig. 1b. The phases of the MW fields correlate with the modulated EIT spectra and can be recovered from these spectra with the aid of deep learning. Specifically, the probe transmission spectra are fed into a well-trained deep learning model that consists of a one-dimensional convolution layer (1D CNN), a bi-directional long–short-term memory layer (Bi-LSTM) and a dense layer to extract the phases of the MW fields. Figure 1c–e shows these components of the neural network (further details are presented in the “Methods” section). Finally, the bin phases are recovered and the data are read out.\n\n### Frequency-division multiplexed signal encoding and receiving\n\nIn the experiments, we use a four-bin frequency-division multiplexing (FDM) MW signal for demonstration, where one of the four MW bins is used as the reference bin. The relative phase differences between the reference bin and the other bins are modulated by the message signal. Specifically, for the four-bin MW signal,\n\n$$E= \\;{A}_{1}\\cos [({\\omega }_{0}+{\\omega }_{1})t+{\\varphi }_{1}]+{A}_{2}\\cos [({\\omega }_{0}+{\\omega }_{2})t+{\\varphi }_{2}]\\\\ +{A}_{3}\\cos [({\\omega }_{0}+{\\omega }_{3})t+{\\varphi }_{3}]+{A}_{4}\\cos [({\\omega }_{0}+{\\omega }_{4})t+{\\varphi }_{4}],$$\n\nwhere ω0 is the resonant frequency, ω1,2,3 are the relative frequencies, the carrier frequencies are 2π(ω0 + ω1) = 17.62 GHz − 3 kHz, 2π(ω0 + ω2) = 17.62 GHz − 1 kHz, 2π(ω0 + ω3) = 17.62 GHz + 1 kHz and 2π(ω0 + ω4) = 17.62 GHz + 3 kHz, the frequency difference between two frequency-adjacent bins is Δf = 2 kHz and the message signal is φ1,2,3 = 0 or π, standing for 3 bits (0 or 1), and the reference phase is φ4 = 0 (which remains unchanged). The phase list $$\\left({\\varphi }_{1},\\,{\\varphi }_{2},\\,{\\varphi }_{3},\\,{\\varphi }_{4}\\right)$$ is a bit string for time t0. By varying the phase of φ1,2,3 with time, we then obtain the FDM signal for binary phase-shift keying (2PSK). Additionally, the amplitudes of the four bins are 0.1A 4 = A1,2,3 to solve the problem that results from the nonlinearity of the atom, where the probe transmission spectra of two different bit strings, e.g. (0, 0, π, 0) and (0, π, 0, 0), are the same (further details are presented in the “Methods” section). By increasing the frequency difference Δf, we can obtain higher information transmission rates. For four bins with Δf = 2 kHz, the information transmission rate is nb × Δf = (4 − 1) × 2 × 103 bps = 6 kbps, where nb is the number of bits. In the experiments, disturbances originate from the environment and atomic collisions. Because of the sensitivity of Rydberg atoms to MW fields, the resulting noise submerges our signal. To use the sensitivity of the Rydberg atoms and simultaneously minimize the effects of noise, the deep learning model is used to extract the relative phases $$\\left({\\varphi }_{1},\\,{\\varphi }_{2},\\,{\\varphi }_{3}\\right)$$.\n\n### Deep learning\n\nTo improve the robustness and speed of our receiver, we use a deep learning model to decode the probe transmission signal. The complete encoding and decoding process is illustrated in Fig. 2a. The Rydberg antenna receives the FDM-2PSK signal and down-converts this signal into the probe transmission spectrum. The information is then retrieved from the spectrum using the deep learning model. The precondition is that the different bit strings correspond to distinct probe spectra; this is resolved by setting 0.1A4 = A1,2,3, as discussed earlier. Then, we combine the 1D CNN layer, the Bi-LSTM layer and the dense layer to form the deep learning model (see the “Methods” section for further details)30,31. One of the reasons for using the 1D CNN layer and the Bi-LSTM layer is that the data sequences are long, which means that prediction of the phases $${{{{{\\boldsymbol{\\varphi }}}}}}=\\left({\\varphi }_{1},\\,{\\varphi }_{2},\\,{\\varphi }_{3},\\,0\\right)$$ from the spectrum is a regression task and requires a long-term memory for our model. Another reason is to combine the convolution layer’s speed with the sequential sensitivity of the Bi-LSTM layer32. The input sequence is first processed by the 1D CNN to extract the features, meaning that a long sequence is converted into a shorter sequence with higher-order features. This process is visualized to show how the deep learning model treats the transmission spectrum; more details are presented in the Supplementary Materials. The shorter sequence is then fed into the Bi-LSTM layer and resized by the dense layer to match the label size (see the “Methods” section for further details). Specifically, the probe spectrum $${{{{{\\bf{T}}}}}}=\\left\\{{T}_{0},\\,{T}_{\\tau },\\,{T}_{2\\tau },\\,\\cdots \\,,\\,{T}_{{{{{{\\rm{i}}}}}}\\cdot \\tau }\\cdots \\,,\\,{T}_{{{{{{\\rm{N}}}}}}\\cdot \\tau }\\right\\}$$ and the corresponding phases $${{{{{\\boldsymbol{\\varphi }}}}}}=\\left({\\varphi }_{1},\\,{\\varphi }_{2},\\,{\\varphi }_{3},\\,{\\varphi }_{4}=0\\right)$$ are collected to form the data set, where Tiτ is the ith data point of a probe spectrum and the fourth bit φ4 = 0 is the reference bit. Both the spectra and the phases are 1D vectors with dimensions of N + 1 and 4, respectively. These independent, identically distributed data {{T}, {φ}} are fed into our model as a data set. By shuffling this data set and splitting it into three sets, i.e., a training set, a validation set and a test set, we train our model on the training set (feeding both the waveforms and labels {{T}, {φ}}), validate, and test our model on the validation and test sets, respectively (by feeding waveforms without labels and comparing the predictions with ground truth labels). The validation set is used to determine whether there is either overfitting or underfitting during training. Finally, the performance (i.e., accuracy) of the model is estimated by predicting the test set.", null, "Fig. 2: Flow chat of recognizing the multifrequency MWs and results.\n\nThe performance of our deep learning model is affected by the training epochs and the training and validation set sizes. The training curves on different training sets and validation sets are shown in Fig. 2b, c. Initially, our model performs well on the training set only, implying overfitting. The curves then converge (dashed line) and our model performs well on both the training set and the validation set. The sudden jump in the loss curve in Fig. 2c is caused by the change in the learning rate (further details are presented in the “Methods” section). Use of more training and validation data causes the curves to converge more quickly. The deep learning model performs well after these few-sample training. In Fig. 2d, we show a confusion matrix for prediction of a uniformly distributed test set, which demonstrates accuracy of 99.38%.", null, "Fig. 3: Reconstruction of the QR code after different epochs of training of the deep learning model.\n\n### Comparison between deep learning method and the master equation\n\nIn our case, the master equation that we employed is the commonly used one without considering the noise spectrum. The accuracies of the deep learning model and the master equation fitting on noisy data are different. Figure 4 shows the accuracies obtained by the two methods. The deep learning model is trained on a training set without additional noise, and tested on a test set with additional white noise whose standard deviation is σ (the transmission spectra with noise are given in Supplementary Materials). Here for simplicity, the data set is composed of the transmission of four MW bins only (one of them is reference bin) and the frequency difference between the adjoin bins is Δf = 2kHz. On the other hand, the result of the master equation is given based on the same test set as that of the deep learning model. The deep learning method outperforms the fitting of the master equation on the noisy data set.", null, "Fig. 4: Prediction accuracy of deep learning model and the master equation on the noisy test set.\n\nApart from the robutness to the noise, when the transmission rate is increased by increasing the number of MW bins or the frequency difference Δf, the deep learning model performs well, while it is difficult to retrieve the messages with high accuracy using the master equation. Specifically, to increase the bandwidth efficiency and the transmission rate, the number of MW bins used to carry the messages must be increased, but the information is still recognizable because of the scalability of the deep learning model. For 20 MW bins, the number of bits is (20 − 1) with one reference bit, giving a $$\\left(20-1\\right)\\times 2\\,{{{{{\\rm{kbps}}}}}}=38\\,{{{{{\\rm{kbps}}}}}}$$ transmission rate. The number of combinations of these bits is 219, which increases exponentially as the number of MW bins increases. Here, for demonstration purposes, only the first 3 bits of the total of 19 bits carry the messages and the other bits, including the reference, are set to be 0. To show how well our model performs, we train, validate and test the model on this new data set without varying the other parameters, with the exception of the training epochs of our model. The loss curves for training and validation are shown in Fig. 5a. A confusion matrix for epoch 78 is shown in Fig. 5b. The model performs well on this new test set, which was sampled uniformly from eight categories with an accuracy of 100%. Another method that can be used to increase the information transmission rate involves increasing the frequency difference. In our case, the frequency difference is increased from Δf = 2 kHz to Δf = 200 kHz. The transmission rate increases correspondingly, from (4 − 1) × 2 kbps = 6 kbps to (4 − 1) × 200 kbps = 0.6 Mbps. To detect the high-speed signal, the DD bandwidth is increased, which inevitably leads to increased noise. After the model is trained on this new data set, the training and validation loss curves are as shown in Fig. 5c. A confusion matrix for epoch 83 is shown in Fig. 5d. Increasing the number of training epochs allows the model to perform well on this new data set, with an accuracy of 98.83% on a uniformly sampled test set.", null, "Fig. 5: Loss curves and confusion maps of the deep learning method and the master equation fitting method for MWs with 20 bins and frequency difference Δf.\n\nTo compare the performances of the deep learning model and the master equation, we fitted the probe spectra for 20 bins with a frequency difference Δf = 2 kHz and four bins with a frequency difference Δf = 200 kHz by solving the master equation without considering the higher-order terms and the effects of noise. In each case, 160 probe spectra were fitted that were sampled uniformly from every category. The prediction results are shown in Fig. 5(e) and (f). The prediction accuracy of the master equation is lower than that of the deep learning model. In our case, the impact of increasing the number of bins is greater than increasing the DD bandwidth for high-speed signals on the fitting accuracy. The prediction accuracy for a 20-bin carrier with frequency difference Δf = 2 kHz is 20.63%, which is like to the accuracy of guessing, i.e., 1/8. This implies that there is a disadvantage that comes from the fitting method itself, i.e., it can easily become trapped by local minima. Some type of prior knowledge is required to overcome this disadvantage, e.g., provision of the initial values of the phases before fitting. In contrast, the deep learning model is data driven and does not require any prior knowledge. The local minima problem of deep learning can be overcome using some well-known techniques, including learning rate scheduling and design of a more effective optimizer32. Additionally, the accuracy difference for the 200-kHz-difference MW bins between the deep learning model and the master equation means that the deep learning model is more robust to noise. Furthermore, the prediction time for the master equation is 25 s per spectrum, while the time for the deep learning model is 1.6 ms per spectrum. The master equation is solved by “FindFit” function in Mathematica 11.1 with both “AccuracyGoal” and “PrecisionGoal” default, while the deep learning code is written in Python 3.7.6. These codes are run on the same computer with NVIDIA GTX 1650 and Intel®$${{{{{{\\rm{Core}}}}}}}^{{{{{{\\rm{TM}}}}}}}$$ i7-9750H.\n\nAnother method to decode the signal is available that uses an in-phase and quadrature (I–Q) demodulator or a lock-in amplifier7,12. However, the carrier frequency must be given when decoding the signal in this case. Additionally, for multiple MW bins, numerous bandpass filters are required. The deep learning method is thus much more convenient.\n\n## Discussion\n\nWe report a work on Rydberg receiver enhanced via deep learning to detect multifrequency MW fields. The results show that the deep learning enhanced Rydberg mixer receives and decodes multifrequency MW fields efficiently; these fields are often difficult to decode using theoretical methods. Using the deep learning model, the Rydberg receiver is robust to noise induced by the environment and atomic collisions and is immune to the distortion that results from the limited bandwidths of the Rydberg atoms (from dipole-dipole interactions and the EIT pumping rate, as studied in ref. 7) for high-speed signals (Δf = 200 kHz). In addition to increasing the transmission speed of the signals, further increments in the information transmission rate are achieved by using more bins, which is feasible because of the scalability of our model. Besides the transmission rate, this deep learning enhanced Rydberg system promises for use in studies of the channel capacity limitations. Because spectra that are difficult for humans to recognize as a result of noise and distortion are distinguishable when using the deep learning model, Rydberg systems enhanced by deep learning could take steps toward the realization of the capacity limit proposed in the literature ref. 34. To obtain high performance (i.e. high signal-to-noise ratio, information transmission rate, channel capacity and accuracy), the training epochs and training set must be extended and enlarged.\n\n## Methods\n\n### Generation and calibration of MW fields\n\nThe MW fields used in our experiments were synthesized by the signal generator (1465F-V from Ceyear) and a frequency horn. Each bin in the multifrequency MW field is tunable in terms of frequency, amplitude and phase. The RF source operates in the range from DC to 40 GHz. The frequency horn is located close to the Rb cell. We used an antenna and a spectrum analyser (4024F from Ceyear) to receive the MW fields and then calibrated the amplitudes of the MW fields at the centre of the Rb cell.\n\nThe probe transmission spectrum in the time domain when Δp = 0, Δc = 0 and Δs = 0 reflects the interference among the multifrequency MW bins, which results from the beat frequencies of the bins that occur through the interaction between the atoms and light. The Rydberg atoms receive the MW bins by acting as an antenna and a mixer9,11,12. After reception by the atoms, the frequency spectrum of the probe transmission shows that we can obtain the frequency differential signal from the probe transmission spectrum. This represents an application of our atoms to reduce the modulated signal frequency (from terahertz to kilohertz magnitude), which allows the signal to be received and decoded using simple apparatus. In our experiment, more than 20 frequency bins can be added to the atoms, for which the dynamic range is greater than 30 dBm. The amplitudes, phases and frequencies of these bins can be tuned individually. When the bandwidth is increased to detect an increasing frequency difference Δf signal, more noise is involved, but this noise is suppressed by the deep learning model. In other words, the signal can be recognized using the deep learning model when the information transmission rate is increased by raising the frequency difference Δf. These bins are used to send FDM-PSK signals in the “FDM signal encoding and receiving ” section of the main text.\n\n### Master equation\n\nThe Lindblad master equation is given as follows: $${{{{{\\rm{d}}}}}}\\rho /{{{{{\\rm{d}}}}}}t=-i\\left[H,\\rho \\right]/\\hslash +L/\\hslash$$, where ρ is the density matrix of the atomic ensemble and H = ∑kH[ρ(k)] is the atom–light interaction Hamiltonian when summed over all the single-atom Hamiltonians using the rotating wave approximation. This Hamiltonian has the following matrix form:\n\n$$H=\\hslash \\left(\\begin{array}{llll}0&-\\frac{{{{\\Omega }}}_{{{{{{\\rm{p}}}}}}}}{2}&0&0\\\\ -\\frac{{{{\\Omega }}}_{{{{{{\\rm{p}}}}}}}}{2}&{{{\\Delta }}}_{{{{{{\\rm{p}}}}}}}&-\\frac{{{{\\Omega }}}_{{{{{{\\rm{c}}}}}}}}{2}&0\\\\ 0&-\\frac{{{{\\Omega }}}_{{{{{{\\rm{c}}}}}}}}{2}&{{{\\Delta }}}_{{{{{{\\rm{c}}}}}}}+{{{\\Delta }}}_{{{{{{\\rm{p}}}}}}}&-\\frac{{{{\\Omega }}}_{{{{{{\\rm{s}}}}}}}(t)}{2}\\\\ 0&0&-\\frac{{{{\\Omega }}}_{{{{{{\\rm{s}}}}}}}(t)}{2}&{{{\\Delta }}}_{{{{{{\\rm{c}}}}}}}+{{{\\Delta }}}_{{{{{{\\rm{p}}}}}}}+{{{\\Delta }}}_{{{{{{\\rm{s}}}}}}}\\end{array}\\right),$$\n(1)\n\nwhere for the MW signal $$E={A}_{1}\\cos [\\left({\\omega }_{0}+{\\omega }_{1}\\right)t+{\\varphi }_{1}]+{A}_{2}\\cos [\\left({\\omega }_{0}+{\\omega }_{2}\\right)t+{\\varphi }_{2}]+{A}_{3}\\cos [\\left({\\omega }_{0}+{\\omega }_{3}\\right)t+{\\varphi }_{3}]+{A}_{4}\\cos [\\left({\\omega }_{0}+{\\omega }_{4}\\right)t+{\\varphi }_{4}]$$, we have the Rabi frequency $${{{\\Omega }}}_{{{{{{\\rm{s}}}}}}}(t)=\\sqrt{{E}_{1}^{2}+{E}_{2}^{2}}$$, where $${E}_{1}={A}_{1}\\sin [{\\omega }_{1}t+{\\varphi }_{1}]+{A}_{2}\\sin [{\\omega }_{2}t+{\\varphi }_{2}]+{A}_{3}\\sin [{\\omega }_{3}t+{\\varphi }_{3}]+{A}_{4}\\sin [{\\omega }_{4}t+{\\varphi }_{4}]$$ and $${E}_{2}={A}_{1}\\cos [{\\omega }_{1}t+{\\varphi }_{1}]+{A}_{2}\\cos [{\\omega }_{2}t+{\\varphi }_{2}]+{A}_{3}\\cos [{\\omega }_{3}t+{\\varphi }_{3}]+{A}_{4}\\cos [{\\omega }_{4}t+{\\varphi }_{4}]$$. The Rabi frequency can be derived as follows:\n\n$$E =\\mathop{\\sum }\\limits_{i=1}^{4}{A}_{i}\\cos \\left[\\left({\\omega }_{0}+{\\omega }_{i}\\right)t+{\\varphi }_{i}\\right]\\\\ =\\sqrt{{E}_{1}^{2}+{E}_{2}^{2}}\\cos \\left({\\omega }_{0}t+\\arctan \\frac{\\mathop{\\sum }\\nolimits_{i = 1}^{4}{A}_{i}\\sin \\left({\\omega }_{i}t+{\\varphi }_{i}\\right)}{\\mathop{\\sum }\\nolimits_{i = 1}^{4}{A}_{i}\\cos \\left({\\omega }_{i}t+{\\varphi }_{i}\\right)}\\right),$$\n(2)\n\nwhere the second term (which resonates with the energy levels of the Rydberg atoms) induces the normal EIT spectrum and the first term modulates that spectrum. In the interaction between the atoms and the MW fields, the atoms act as a mixer such that the output signal frequency (ω1, ω2, ω3) is less than the input signal frequency (ω0 + ω1, ω0 + ω2, ω0 + ω3). The modulation signal’s nonlinearity is reduced by setting the reference and increasing its amplitude as shown in Eq. (3), which is a precondition for recognition of these phases via deep learning.\n\n$$\\sqrt{{E}_{1}^{2}+{E}_{2}^{2}} \\\\ \\approx {A}_{4}\\sqrt{1+2\\mathop{\\sum }\\limits_{i=1}^{3}\\frac{{A}_{i}}{{A}_{4}}\\cos \\left[\\left({\\omega }_{4}-{\\omega }_{i}\\right)t+\\left({\\varphi }_{4}-{\\varphi }_{i}\\right)\\right]}\\\\ \\approx {A}_{4}+\\mathop{\\sum }\\limits_{i=1}^{3}{A}_{i}\\cos \\left[\\left({\\omega }_{4}-{\\omega }_{i}\\right)t+\\left({\\varphi }_{4}-{\\varphi }_{i}\\right)\\right],$$\n(3)\n\nwhere the condition for the approximations on the second line and the third line is A4A1,2,3.\n\nThe Lindblad superoperator L = ∑kL[ρ(k)] is composed of single-atom superoperators, where L[ρ(k)] represents the Lindbladian and has the following form: $$\\frac{L[{\\rho }^{(k)}]}{\\hslash }=-\\frac{1}{2}{\\sum }_{m}\\left({C}_{m}^{{{\\dagger}} }{C}_{m}\\rho +\\rho {C}_{m}^{{{\\dagger}} }{C}_{m}\\right)+{\\sum }_{m}{C}_{m}\\rho {C}_{m}^{{{\\dagger}} }$$ where $${C}_{1}=\\sqrt{{{{\\Gamma }}}_{{{{{{\\rm{e}}}}}}}}\\left|g\\right\\rangle \\left\\langle e\\right|$$, $${C}_{2}=\\sqrt{{{{\\Gamma }}}_{{{{{{\\rm{r}}}}}}}}\\left|e\\right\\rangle \\left\\langle r\\right|$$ and $${C}_{3}=\\sqrt{{{{\\Gamma }}}_{{{{{{\\rm{s}}}}}}}}\\left|r\\right\\rangle \\left\\langle s\\right|$$ are collapse operators that stand for the decays from state $$\\left|e\\right\\rangle$$ to state $$\\left|g\\right\\rangle$$, from state $$\\left|r\\right\\rangle$$ to state $$\\left|e\\right\\rangle$$ and from state $$\\left|s\\right\\rangle$$ to state $$\\left|r\\right\\rangle$$ with rates Γe, Γr and Γs, respectively. Because we are only concerned with the steady state here, i.e. t → , the Lindblad master equation can be solved using dρ/dt = 0. The complex susceptibility of the EIT medium has the form χ(v) = (μge2/ϵ0)ρeg, where ρeg is the element of density matrix solved using the master equation. The spectrum of the EIT medium can be obtained from the susceptibility using $$T \\sim {e}^{-{{{{{\\rm{Im}}}}}}[\\chi ]}.$$\n\n### Deep learning layers\n\nOur deep learning model consists of a 1D CNN layer, a Bi-LSTM layer and a dense layer. The mathematical sketches for these layers are given as follows.\n\nThe 1D CNN layer is illustrated in Fig. 1c. The input signal convolutes the kernel in the following form:\n\n$$f\\otimes g=\\mathop{\\sum }\\limits_{m=0}^{N-1}{f}_{m}{g}_{(n-m)}.$$\n(4)\n\nwhere f represents the input data, g is the convolution kernel, m is the input data index and n is the kernel index. The 1D CNN extracts the higher-order features from the input data to reduce the lengths of the sequences fed into the Bi-LSTM layer. Before flowing into the Bi-LSTM layer, the data pass through the batch normalization layer, the ReLU activation layer and the max-pooling layer, in that sequence. For a mini-batch $${{{{{\\mathcal{B}}}}}}=\\left\\{{x}_{1\\cdots m}\\right\\}$$, the output from the batch normalization layer is yi = BNγ,β(xi) and the learning parameters are γ and β40. The update rules for the batch normalization layer are:\n\n$${\\mu }_{{{{{{\\mathcal{B}}}}}}}\\leftarrow \\frac{1}{m}\\mathop{\\sum }\\limits_{i=1}^{m}{x}_{i},$$\n(5)\n$${\\sigma }_{{{{{{\\mathcal{B}}}}}}}^{2}\\leftarrow \\frac{1}{m}\\mathop{\\sum }\\limits_{i=1}^{m}{\\left({x}_{i}-{\\mu }_{{{{{{\\mathcal{B}}}}}}}\\right)}^{2},$$\n(6)\n$${\\hat{x}}_{i}\\leftarrow \\frac{{x}_{i}-{\\mu }_{{{{{{\\mathcal{B}}}}}}}}{\\sqrt{{\\sigma }_{{{{{{\\mathcal{B}}}}}}}^{2}+\\epsilon}},$$\n(7)\n$${y}_{i}\\leftarrow \\gamma {\\hat{x}}_{i}+\\beta \\equiv B{N}_{\\gamma ,\\beta }({x}_{i}),$$\n(8)\n\nwhere Eqs. (5) and (6) evaluate the mean and the variance of the mini-batch, respectively; the data are normalized using the mean and the variance in Eq. (7) and the results are then scaled and shifted in Eq. (8). The training is accelerated using the batch normalization layer and the overfitting is also weakened by this layer. The output then passes through the ReLU activation layer. The activation function of this layer is $${f}_{{{{{{\\rm{ReLU}}}}}}}(x)=\\max (x,0)$$. The vanishing gradient problem is diminished by this activation function. Next, the inputs are downsampled in a max-pooling layer30.\n\nThe LSTM layer and an LSTM cell are shown schematically in Figs. 1d and 6a, respectively. The equations for the LSTM are shown as Eqs. (9)–(14)32,41. At a time t, the input xt and two internal states Ct−1and ht−1 are fed into the LSTM cell. The first thing to be decided by the LSTM cell is whether or not to forget in Eq. (9), which outputs a number between 0 and 1 that represents retaining or forgetting. Next, an input gate (Eq. (10)) decides which values are to be updated from a vector of new candidate values created using Eq. (11). The new value is then added to the cell state and the old value is forgotten in Eq. (12). Finally, the cell decides what to output using Eqs. (13) and (14).\n\n$${f}_{t}=\\sigma \\left({W}_{f}\\cdot \\left[{h}_{t-1},{x}_{t}\\right]+{b}_{f}\\right),$$\n(9)\n$${i}_{t}=\\sigma \\left({W}_{i}\\cdot \\left[{h}_{t-1},{x}_{t}\\right]+{b}_{i}\\right),$$\n(10)\n$${\\tilde{C}}_{t}=\\tanh \\left({W}_{C}\\cdot \\left[{h}_{t-1},{x}_{t}\\right]+{b}_{C}\\right),$$\n(11)\n$${C}_{t}={f}_{t}\\times {C}_{t-1}+{i}_{t}\\times {\\tilde{C}}_{t},$$\n(12)\n$${o}_{t}=\\sigma \\left({W}_{o}\\left[{h}_{t-1},{x}_{t}\\right]+{b}_{o}\\right),$$\n(13)\n$${h}_{t}={o}_{t}\\times \\tanh \\left({C}_{t}\\right),$$\n(14)\n\nwhere σ(x) = 1/(1 + ex) is the sigmoid function. The sigmoid and $$\\tanh$$ functions are applied in an element-wise manner. The LSTM is followed by a time-reversed LSTM to constitute a Bi-LSTM layer that improves the memory for long sequences.\n\nThe dense layer and a neuron are drawn in Figs. 1e and 6b, respectively, and the corresponding equations are\n\n$${{{{{\\bf{a}}}}}}={{{{{\\bf{w}}}}}}\\cdot {{{{{\\bf{x}}}}}}+b,$$\n(15)\n$${{{{{\\bf{y}}}}}}=g({{{{{\\bf{a}}}}}}),$$\n(16)\n\nwhere w is the vector of weights, b is the bias, x represents the input data, g(a) = 1/(1 + ea) is the sigmoid activation function used to limit the output values to between 0 and 1, and y is the output. The dense layer resizes the shape of the data obtained from the Bi-LSTM to match the size of the label.\n\nThe training consists of both forward and backward propagation. A batch of probe spectra propagates through the 1D CNN layer, the Bi-LSTM layer, and dense layer during the forward training process. The differentiable loss function is then calculated. In our case, the differentiable loss function is the mean squared error (MSE) between the predictions and the ground truth, which is used widely in the regression task32. The equation for the MSE is\n\n$${L}_{{{{{{\\rm{MSE}}}}}}}=\\frac{1}{m\\cdot n}\\mathop{\\sum }\\limits_{j=1}^{n}\\mathop{\\sum }\\limits_{i=1}^{m}{\\left({\\varphi }_{i,j}-f({T}_{i,j})\\right)}^{2},$$\n(17)\n\nwhere m is the number of data points in one spectrum, n is the mini-batch size, φi is the ground truth and f(Ti) is the model prediction. In backpropagation, the trainable weights of each layer are updated based on the learning rate and the derivative of the MSE loss function with respect to the weights to minimize the loss LMSE, such that\n\n$$W\\leftarrow W-\\eta \\frac{\\partial {L}_{{{{{{\\rm{MSE}}}}}}}}{\\partial W},$$\n(18)\n\nwhere η is the learning rate and W is the trainable weight for each layer. The weights of each layer are then updated according to the RMSprop optimizer42.\n\nThe network is implemented using the Keras 2.3.1 framework on Python 3.6.11 (ref. 30). All weights are initialized with the Keras default. The hyper-parameters of the deep learning model (including the convolution kernel length, the number of hidden variables and the learning rate) are tuned using Optuna43.\n\n### Deep learning pipeline\n\nTo obtain better fitting results, the data are scaled based on their maximum and minimum values, i.e., $$T^{\\prime} =({T}_{i}-\\min(T))/(\\max(T)-\\min(T))$$. The labels are encoded in dense vectors with four elements rather than in one-shot encoding vectors to save space32. Each of these elements is either 0 or 1, representing the relative phase 0 or π of each bin, respectively.\n\nA one-dimensional convolution layer (1D CNN), a bidirectional long–short-term memory layer (Bi-LSTM) and a dense layer are used in our deep learning model. The deep learning model structure is shown in Fig. 7. The data size for the input layer is given in the form (batch size, length of probe spectrum, number of features). The batch size is 64 in our case. Because the duration of the spectrum ranges from t = 0 to t = 0.999 ms with a time difference of τ = 1 μs, the spectrum length is 1000. For a 1D input, the number of features is 1. Therefore, the data size for the input layer is (64, 1000, 1).", null, "Fig. 7: Structure of our deep learning model and size of the data.\n\nDuring training of this model, fourfold cross-validation is used to save the amount of training data.The data set is split as shown in Fig. 8. First, the data set is split into two parts. The first is the test set (red), which remains untouched during training. The second (purple) is used to train the model. In the cross-validation process, the rest data set (purple) is copied four times and is divided equally into four parts each. One of these parts is the validation data set (green) and the others are used as training sets (blue). Four models are trained on the different training sets and validation sets. Then the best model is chosen according to the validation set and is tested on the test set. After splitting, the training set, the validation set, and the test set all remain unchanged. In every epoch, each model iterates the training set only once. There is no new set being taken; instead, the same training set is iterated once each epoch." ]
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https://www.hercampus.com/school/western/why-stats-pretty-much-magic/
[ "", null, "", null, "", null, "# Why Stats is Pretty Much Magic\n\nThe methods provided by the field of statistics are more powerful than most people are aware. They allow for testing of various hypotheses, if a hypothesis is likely, it can then be used to predict what is likely to happen in the future. I say likely because there is always some uncertainty that is impossible to get rid of. But when different methods yield the same prediction, there is a good chance that you have an idea of what is going to happen in the future! That’s HUGE!!! I am going to go through two ways that allow us to test hypotheses and how credible they are: the Frequentist and the Bayesian approach.\n\n### 1.     Randomization test (The Frequentist)\n\nSo many factors out there could be correlated. There could be a correlation between the number of times I eat out and the number of birds on campus. But obviously, it is unreasonable to think the correlation suggests causation of the two. It is definitely a possibility, but no such inferences can be drawn from the correlation alone.\n\nSay that we go to Western students and collect data in the form of a survey. We then create a database of these surveys. We notice something interesting: sleep hours and student grades show a very high degree of correlation. As much as we think that it is intuitive to say sleeping less can cause students to perform more poorly on a test, we can’t prove it and hence cannot conclude that for the same reasons in the case of the example stated above. So then… how do we back up our intuition?\n\nWe run a randomization test! We can use this test to keep information about every single student in our dataset constant but shuffle up their hours of sleep. And each time, we can calculate the mean difference in grades between students that sleep 6 hours or more and students that sleep less than 6 hours. If we do this 1000 times, we end up with 1000 differences and that in itself will be used as our stats. Through calculation of a p-value (a type of conditional probability that I will not go into detail about) of the column containing the 1000 stats, we can see if we were right that the two have a significant relationship, or that we were wrong and in fact the relationship observed between the two was due to random chance and the difference observed was from some other characteristic of the students surveyed. Powerful, huh? That’s only one of the uses of a randomization test.\n\n### 2.     Baye’s theorem\n\nIt is again a method of testing that can help us find out if our hypothesis was correct or if all the relationships seen are just due to random chance. To demonstrate the power of Bayesian way of thinking, consider the following probability: P(A|B). That means the probability of A happening under the assumption of B. Now, in the case of hypothesizing based on data, A is our data and B is our hypothesis. Measuring the probability of the data happening under our hypothesis is not that difficult. What we are interested in is P(B|A), the probability of our hypothesis occurring under the data we have. The Bayesian theorem can calculate this probability!!\n\nHowever, it does need some starting point. In other words, it needs P(B). Once this challenge is overcome—if nothing else is known, the P(B) can be assigned a value of 50%—the P(B|A) can be calculated which can be interpreted as the updated probability in light of new evidence; we now have an updated “posterior” probability. We can calculate two posterior probabilities: one for our hypothesis that amount of sleep can affect academic performance and the other for the opposite (null) hypothesis, which states that sleep and grades are not related and the data observed is due to random chance. Bayes Factor is then just the ratio of the updated probabilities for the suggested hypothesis over null. If this ratio is 3 or greater (a universal standard) then our hypothesis can be used to explain the data.\n\nI hope that by now, I was able to give you a glimpse of why the field of stats is powerful enough to be known as the closest tool we have to magic. Prediction is one of the many interests explored by this field, and the methods noted above are only two ways of many—some of which that are more direct than the ones explained here—that statisticians have developed for the prediction of unseen.\n\n### Related Articles\n\nWant more HCW? Check us out on social media!\n\nI am a second-year student in integrated science with specilization in physics. I aim to write about topics that are most relatable to students on campus. So if you are excited/bothered by something and want others to know about it, don't hesitate to contact me for a potential article :)" ]
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http://cloud.originlab.com/doc/en/OriginC/ref/matrixbase-GetMean
[ "# 2.2.3.9.33 matrixbase::GetMean\n\n## Description\n\nGet the mean cell value of the matrix (as a double).\n\n## Syntax\n\ndouble GetMean( )\n\n## Return\n\nReturns the mean cell value of the matrix (as a double).\n\nNote that the missing values (NANUMs) in the matrix are ignored in computation.\n\n## Examples\n\nEX1\n\n// Compute the mean value of cells of a matrix\nvoid matrixbase_GetMean_ex1()\n{\nmatrix<double> mat1 = {\n{1, 1, 1, 1},\n{2, 4, 6, 8},\n{3, 6, 9, 12}\n};\n// Output of this program will be like following:\n// The mean value of cells in Matrix1 is: 4.5 .\n\nMatrixPage MatPg1;\nMatPg1.Create(\"Origin\");\nMatrixLayer MatLy1 = MatPg1.Layers(0);\nMatrix Mat1(MatLy1);\nMat1 = mat1;\n\ndouble dMean;\ndMean = Mat1.GetMean(); // Compute the mean value by GetMean\nprintf(\" The mean value of cells in %s is: %g .\\n\",\nMat1.GetName(), dMean);\n}\n\nEX2\n\n// Compute the mean value of cells of a matrix including NANUMs\nvoid matrixbase_GetMean_ex2()\n{\nmatrix<double> mat1 = {\n{99, 99, 99},\n{ 2, 3, 4}\n};\nmat1=NANUM; // set row=1,col=1 to NANUM\nmat1=NANUM; // set row=1,col=2 to NANUM\nmat1=NANUM; // set row=1,col=3 to NANUM\n// Input matrix is:\n// {--, --, --}\n// { 2, 3 4}\n//\n// Output of this program will be like following:\n// The mean value of cells in Matrix1 is: 3 .\n\nMatrixPage MatPg1;\nMatPg1.Create(\"Origin\");\nMatrixLayer MatLy1 = MatPg1.Layers(0);\nMatrix Mat1(MatLy1);\nMat1 = mat1;\n\ndouble dMean;\ndMean = Mat1.GetMean(); // Compute the mean value by GetMean\nprintf(\" The mean value of cells in %s is: %g .\\n\",\nMat1.GetName(), dMean);\n}\n\n## Remark\n\nGet the mean value of the matrix (as a double)." ]
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https://maffsguru.com/videos/triangle-angle-sum/
[ "Triangle angle sum\nPolygons, solids and transformations\nEssential Mathematics Year 7\nShare:\n##### Videos in this series\nPlease select a video from the same chapter\nIntroduction\nThis video looks at how to find the missing angles from any triangle using nothing but some basic maths and a calculator (or your brain!). We look at all the different types of triangles there are and the fact that, no matter what they look like, they all have 180 degrees inside of them. We use this rule to find the missing angles without the use of a protractor. I then make things a little more complicated by adding straight lines into the diagrams! This is funky but uses another rule that angles on a straight line add to 180 degrees. With lots of examples, I finish by looking at FUZX! If you don't know what that means, then watch the video. It's an awesome area of Mathematics!!! So much fun had sitting in front of a camera. I hope you enjoy the video. Let me know what you think by leaving a comment below.\nThere are no current errors with this video ... phew!\nThere are currently no lesson notes at this time to download. I add new content every week.\nVideo tags\n\nsum of angles of triangle is 180 proof sum of angles on a straight line triangle angle sum triangle angles FUZX alternate angles in maths alternate angles on parallel lines alternate angles examples Year 7 Maths angles on a straight line angles on a straight line add up to angles questions angles questions and answers angles in a triangle" ]
[ null ]
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https://www.hackmath.net/en/math-problem/130
[ "Tournament\n\nDetermine how many ways can be chosen two representatives from 34 students to school tournament.\n\nResult\n\nn =  561\n\nSolution:", null, "Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):", null, "Be the first to comment!", null, "To solve this verbal math problem are needed these knowledge from mathematics:\n\nWould you like to compute count of combinations?\n\nNext similar math problems:\n\n1. Examination", null, "The class is 21 students. How many ways can choose two to examination?\n2. Fish tank", null, "A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?\n3. Confectionery", null, "The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.\n4. Teams", null, "How many ways can divide 16 players into two teams of 8 member?\n5. Ice cream", null, "Annie likes much ice cream. In the shop are six kinds of ice cream. In how many ways she can buy ice cream to three scoop if each have a different flavor mound and the order of scoops doesn't matter?\n6. Trinity", null, "How many different triads can be selected from the group 43 students?\n7. MATES", null, "In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is?\n8. Volleyball", null, "8 girls wants to play volleyball against boys. On the field at one time can be six players per team. How many initial teams of this girls may trainer to choose?\n9. Chords", null, "How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?\n10. Class pairs", null, "In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) we can create? By what formula?\n11. Blocks", null, "There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?\n12. Theorem prove", null, "We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?\n13. Calculation of CN", null, "Calculate: ?\n14. Cancel fractions", null, "Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!\n15. Functions f,g", null, "Find g(1) if g(x) = 3x - x2 Find f(5) if f(x) = x + 1/2\n16. Powers", null, "Express the expression ? as the n-th power of the base 10.\n17. First man", null, "What is the likelihood of a random event where are five men and seven women first will leave the man?" ]
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https://juliuso.com/2019/07/05/induction.html
[ "# Induction\n\n05 Jul 2019\n\nConsider the formula for computing the sum of squares:\n\nThe formula says there are two ways to find a solution. The conventional way, shown by the left-hand side (LHS) of the equation, says that starting from 0, square 0, then add to it the square of 1, then add to it the square of 2, and continue adding subsequent squares to the series, finally stopping after the n-th number is squared and added. Then just add all the terms in the series together and get an answer.\n\nFor example, in calculating the sum of the squares up to and including 10, the LHS method is applied to yield:\n\nNow the right-hand side (RHS) claims to get the same answer as the LHS simply by substituting the highest term ($$10$$ in for $$n$$), and evaluating the expression. With skepticism, substituting and evaluating the RHS yields:\n\nSo while the formula appears to work for a specific example, does it also work with other numbers? Can we be absolutely sure it would work for the first thousand, million, billion, or even trillion square numbers? A reasonable idea would be to keep a continuously expanding (and large and dusty) book of calculations in the library that we could look up to be sure the formula works for a particular example. Just have a computer continuously calculate the sums of the squares using the LHS and RHS methods, and check to see if both sides equal each other. Surely, performing continuous calculations using larger and larger numbers provides more than ample evidence in proving that the formula is true and universal for other numbers!\n\nIn 1910, mathematicians Alfred North Whitehead and Bertrand Russell published Principia Mathematica to build and prove mathematical foundations from first principles. It took nearly 400 pages of symbolic logic to prove that $$1+1=2$$.It turns out that in math, specific examples can't be used as proofs. In writing proofs, only variables, symbols, and previously proven ideas such as axioms, corollaries, lemmas, and theorems can be used as building blocks to show the truth or falsity of a statement. So how do we prove this? The good news is we have a powerful tool at our disposal which will rigorously prove and answer this question.\n\nThat tool, is INDUCTION. And here's my take on what it means:\n\n\"If you can show that the next thing exists in the current thing, then you've proved that the current thing works for all subsequent things.\"\n\nIn the next post, we'll see induction in action, and apply it in proving the sum of squares formula." ]
[ null ]
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https://ask.sagemath.org/question/51834/why-does-the-code-not-work/
[ "# Why does the code not work?\n\nI want to write a program which gives me all prime ideals in the ring of integers $\\mathcal{O}_K$, $K= \\mathbb{Q}(\\sqrt{-5})$ . They should have the property to be principal. My problem is that the condition if(J.gens()-1 in L): does not really work. By this I want that the generator of the principal ideal minus 1 is contained in the ideal L.\n\n sage: K.<a> = QuadraticField(-5)\ncl = K.class_group()\ng = cl.gens()\nL=K.fractional_ideal(-a-1)\nsage: for norm, ideals in K.ideals_of_bdd_norm(10).items():\nfor J in ideals:\nif (J.is_prime()):\nif (cl(J)==g^4):\nif(J.gens()-1 in L):\nprint norm,J\n\nedit retag close merge delete\n\nHave you look at what J.gens() looks like for the various ideals J you are considering?\n\nIf i leave out the condtion if(J.gens()-1 in L):, then it prints this: 5 Fractional ideal (-a). Now -a is the generator of the principal ideal (-a). If I take again the condition if(J.gens()-1 in L), then this means whether -a-1 is in L and it is but sage does not print me out J.\n\n1\n\nThat -a-1 lies in L should hold, and sage does seem to agree with that. However, J.gens()-1 apparently doesn't, so you should probably print J.gens(), or more generally J.gens(), to see why that is the case. That's either going to give you a good, reportable, bug or it shows you what's going wrong.\n\nSort by » oldest newest most voted", null, "What you are looking for is J.gens_reduced() instead of J.gens().\n\nInstead of g^4 you can just write cl.one(). The class group has order $2$ so g^2 is already cl.one(). Instead of comparing classes you can also just ask J.is_principal().\n\nmore\n\nWhat is the difference between J.gens_reduced() and J.gens()?\n\nSee the documentation of gens_reduced: \"Express this ideal in terms of at most two generators, and one if possible\". By contrast, gens() are just the generators which were given when the ideal was constructed (in this case, by Sage)." ]
[ null, "https://www.gravatar.com/avatar/dab2f5dc05d812841ee7e10d04e29e7c", null ]
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https://docs.ropensci.org/unifir/reference/add_light.html
[ "", null, "This function creates light objects within a Unity scene. This function can only add one light at a time -- call the function multiple times to add more than one light.\n\n## Usage\n\n``````add_light(\nscript,\nlight_type = c(\"Directional\", \"Point\", \"Spot\", \"Area\"),\nmethod_name = NULL,\nlight_name = \"Light\",\nx_position = 0,\ny_position = 0,\nz_position = 0,\nx_scale = 1,\ny_scale = 1,\nz_scale = 1,\nx_rotation = 50,\ny_rotation = -30,\nz_rotation = 0,\nexec = TRUE\n)``````\n\n## Arguments\n\nscript\n\nA `unifir_script` object, created by make_script or returned by an `add_prop_*` function.\n\nlight_type\n\nOne of \"Directional\", \"Point\", \"Spot\", or \"Area\". See https://docs.unity3d.com/Manual/Lighting.html for more information.\n\nmethod_name\n\nThe internal name to use for the C# method created. Will be randomly generated if not set.\n\nlight_name\n\nThe name to assign the Light object.\n\nx_position, y_position, z_position\n\nThe position of the GameObject in world space.\n\nx_scale, y_scale, z_scale\n\nThe scale of the GameObject (relative to its parent object).\n\nx_rotation, y_rotation, z_rotation\n\nThe rotation of the GameObject to create, as Euler angles.\n\nexec\n\nLogical: Should the C# method be included in the set executed by MainFunc?\n\n## Value\n\nThe `unifir_script` object passed to `script`, with props for adding lights appended.\n\nOther props: `add_default_player()`, `add_prop()`, `add_texture()`, `create_terrain()`, `import_asset()`, `instantiate_prefab()`, `load_png()`, `load_scene()`, `new_scene()`, `read_raw()`, `save_scene()`, `set_active_scene()`, `validate_path()`\n\n## Examples\n\n``````# First, create a script object.\n# CRAN doesn't have Unity installed, so pass\n# a waiver object to skip the Unity-lookup stage:\nscript <- make_script(\"example_script\", unity = waiver())" ]
[ null, "https://ropensci.matomo.cloud/matomo.php", null ]
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https://docs.eazybi.com/eazybi/analyze-and-visualize/calculated-measures-and-members/mdx-function-reference/tuple
[ "All eazyBI for Jira eazyBI for Confluence Private eazyBI\n\n# Tuple\n\nA tuple is a collection of member(s) with the restriction that only one member in the tuple can be from the same dimension. A tuple uniquely identifies a slice of data from a cube, and it represents a single data cell if all dimensions are represented.\n\n## Syntax\n\n` ( tuple )`\n\n## Arguments\n\ntuple Combination of members from different dimensions in MDX syntax (member_1, member_2, ..., member n)\n\n## Examples\n\nTuples can be useful when creating new calculated measures to calculate results for a specific set of members from dimensions, even if dimensions are not used in the report context directly (rows/pages/columns).\n\nThere are several ways to create reports with tuples. For example, to compare the results from the filtered report context with results from a specific set.\n\n### Example 1\n\nThe Issues created measure, in this example, would calculate the Issues created value for Issue type dimension member Bug and Priority dimension member High regardless of the report context (other dimensions used as filters).\n\n```(\n[Issue Type].[Bug],\n[Priority].[High],\n[Measures].[Issues created]\n)```\n\n### Example 2\n\nThe Issues resolved measure, in this example, would calculate the Issues resolved value for Issue type dimension member Bug and a calculated member from \"Priority\" dimension that aggregates two priorities \"High\" and \"Highest\".\n\n```(\n[Issue Type].[Bug],\n[Priority].[High & Highest], --calculated member from Priority dimension\n[Measures].[Issues resolved]\n)```" ]
[ null ]
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http://slicot.org/objects/software/shared/doc/MB04DL.html
[ "## MB04DL\n\n### Balancing a real pencil, optionally avoiding large norms for the scaled (sub)matrices\n\n[Specification] [Arguments] [Method] [References] [Comments] [Example]\n\nPurpose\n\n``` To balance a pair of N-by-N real matrices (A,B). This involves,\nfirst, permuting A and B by equivalence transformations to isolate\neigenvalues in the first 1 to ILO-1 and last IHI+1 to N elements\non the diagonal of A and B; and second, applying a diagonal\nequivalence transformation to rows and columns ILO to IHI to make\nthe rows and columns as close in 1-norm as possible. Both steps\nare optional. Balancing may reduce the 1-norms of the matrices,\nand improve the accuracy of the computed eigenvalues and/or\neigenvectors in the generalized eigenvalue problem\nA*x = lambda*B*x.\n\nThis routine may optionally improve the conditioning of the\nscaling transformation compared to the LAPACK routine DGGBAL.\n\n```\nSpecification\n``` SUBROUTINE MB04DL( JOB, N, THRESH, A, LDA, B, LDB, ILO, IHI,\n\\$ LSCALE, RSCALE, DWORK, IWARN, INFO )\nC .. Scalar Arguments ..\nCHARACTER JOB\nINTEGER IHI, ILO, INFO, IWARN, LDA, LDB, N\nDOUBLE PRECISION THRESH\nC .. Array Arguments ..\nDOUBLE PRECISION A(LDA,*), B(LDB,*), DWORK(*), LSCALE(*),\n\\$ RSCALE(*)\n\n```\nArguments\n\nMode Parameters\n\n``` JOB CHARACTER*1\nSpecifies the operations to be performed on A and B:\n= 'N': none: simply set ILO = 1, LSCALE(I) = 1.0 and\nRSCALE(I) = 1.0 for I = 1,...,N.\n= 'P': permute only;\n= 'S': scale only;\n= 'B': both permute and scale.\n\n```\nInput/Output Parameters\n``` N (input) INTEGER\nThe order of matrices A and B. N >= 0.\n\nTHRESH (input) DOUBLE PRECISION\nIf JOB = 'S' or JOB = 'B', and THRESH >= 0, threshold\nvalue for magnitude of the elements to be considered in\nthe scaling process: elements with magnitude less than or\nequal to THRESH*MXNORM are ignored for scaling, where\nMXNORM is the maximum of the 1-norms of the original\nsubmatrices A(s,s) and B(s,s), with s = ILO:IHI.\nIf THRESH < 0, the subroutine finds the scaling factors\nfor which some conditions, detailed below, are fulfilled.\nA sequence of increasing strictly positive threshold\nvalues is used.\nIf THRESH = -1, the condition is that\nmax( norm(A(s,s),1)/norm(B(s,s),1),\nnorm(B(s,s),1)/norm(S(s,s),1) ) (1)\nhas the smallest value, for the threshold values used,\nwhere A(s,s) and B(s,s) are the scaled submatrices.\nIf THRESH = -2, the norm ratio reduction (1) is tried, but\nthe subroutine may return IWARN = 1 and reset the scaling\nfactors to 1, if this seems suitable. See the description\nof the argument IWARN and FURTHER COMMENTS.\nIf THRESH = -3, the condition is that\nnorm(A(s,s),1)*norm(B(s,s),1) (2)\nhas the smallest value for the scaled submatrices.\nIf THRESH = -4, the norm reduction in (2) is tried, but\nthe subroutine may return IWARN = 1 and reset the scaling\nfactors to 1, as for THRESH = -2 above.\nIf THRESH = -VALUE, with VALUE >= 10, the condition\nnumbers of the left and right scaling transformations will\nbe bounded by VALUE, i.e., the ratios between the largest\nand smallest entries in LSCALE(s) and RSCALE(s), will be\nat most VALUE. VALUE should be a power of 10.\nIf JOB = 'N' or JOB = 'P', the value of THRESH is\nirrelevant.\n\nA (input/output) DOUBLE PRECISION array, dimension (LDA,N)\nOn entry, the leading N-by-N part of this array must\ncontain the matrix A.\nOn exit, the leading N-by-N part of this array contains\nthe balanced matrix A.\nIn particular, the strictly lower triangular part of the\nfirst ILO-1 columns and the last N-IHI rows of A is zero.\n\nLDA INTEGER\nThe leading dimension of the array A. LDA >= MAX(1,N).\n\nB (input/output) DOUBLE PRECISION array, dimension (LDB, N)\nOn entry, the leading N-by-N part of this array must\ncontain the matrix B.\nOn exit, the leading N-by-N part of this array contains\nthe balanced matrix B.\nIn particular, the strictly lower triangular part of the\nfirst ILO-1 columns and the last N-IHI rows of B is zero.\nIf JOB = 'N', the arrays A and B are not referenced.\n\nLDB INTEGER\nThe leading dimension of the array B. LDB >= MAX(1, N).\n\nILO (output) INTEGER\nIHI (output) INTEGER\nILO and IHI are set to integers such that on exit\nA(i,j) = 0 and B(i,j) = 0 if i > j and\nj = 1,...,ILO-1 or i = IHI+1,...,N.\nIf JOB = 'N' or 'S', ILO = 1 and IHI = N.\n\nLSCALE (output) DOUBLE PRECISION array, dimension (N)\nDetails of the permutations and scaling factors applied\nto the left side of A and B. If P(j) is the index of the\nrow interchanged with row j, and D(j) is the scaling\nfactor applied to row j, then\nLSCALE(j) = P(j) for j = 1,...,ILO-1\n= D(j) for j = ILO,...,IHI\n= P(j) for j = IHI+1,...,N.\nThe order in which the interchanges are made is N to\nIHI+1, then 1 to ILO-1.\n\nRSCALE (output) DOUBLE PRECISION array, dimension (N)\nDetails of the permutations and scaling factors applied\nto the right side of A and B. If P(j) is the index of the\ncolumn interchanged with column j, and D(j) is the scaling\nfactor applied to column j, then\nRSCALE(j) = P(j) for j = 1,...,ILO-1\n= D(j) for j = ILO,...,IHI\n= P(j) for j = IHI+1,...,N.\nThe order in which the interchanges are made is N to\nIHI+1, then 1 to ILO-1.\n\n```\nWorkspace\n``` DWORK DOUBLE PRECISION array, dimension (LDWORK) where\nLDWORK = 0, if JOB = 'N' or JOB = 'P', or N = 0;\nLDWORK = 6*N, if (JOB = 'S' or JOB = 'B') and THRESH >= 0;\nLDWORK = 8*N, if (JOB = 'S' or JOB = 'B') and THRESH < 0.\nOn exit, if JOB = 'S' or JOB = 'B', DWORK(1) and DWORK(2)\ncontain the initial 1-norms of A(s,s) and B(s,s), and\nDWORK(3) and DWORK(4) contain their final 1-norms,\nrespectively. Moreover, DWORK(5) contains the THRESH value\nused (irrelevant if IWARN = 1 or ILO = IHI).\n\n```\nWarning Indicator\n``` IWARN INTEGER\n= 0: no warning;\n= 1: scaling has been requested, for THRESH = -2 or\nTHRESH = -4, but it most probably would not improve\nthe accuracy of the computed solution for a related\neigenproblem (since maximum norm increased\nsignificantly compared to the original pencil\nmatrices and (very) high and/or small scaling\nfactors occurred). The returned scaling factors have\nbeen reset to 1, but information about permutations,\nif requested, has been preserved.\n\n```\nError Indicator\n``` INFO INTEGER\n= 0: successful exit.\n< 0: if INFO = -i, the i-th argument had an illegal\nvalue.\n\n```\nMethod\n``` Balancing consists of applying an equivalence transformation\nto isolate eigenvalues and/or to make the 1-norms of the rows\nand columns ILO,...,IHI of A and B nearly equal. If THRESH < 0,\na search is performed to find those scaling factors giving the\nsmallest norm ratio or product defined above (see the description\nof the parameter THRESH).\n\nAssuming JOB = 'S', let Dl and Dr be diagonal matrices containing\nthe vectors LSCALE and RSCALE, respectively. The returned matrices\nare obtained using the equivalence transformation\n\nDl*A*Dr and Dl*B*Dr.\n\nFor THRESH = 0, the routine returns essentially the same results\nas the LAPACK subroutine DGGBAL . Setting THRESH < 0, usually\ngives better results than DGGBAL for badly scaled matrix pencils.\n\n```\nReferences\n``` Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J.,\nDu Croz, J., Greenbaum, A., Hammarling, S., McKenney, A.,\nOstrouchov, S., and Sorensen, D.\nLAPACK Users' Guide: Second Edition.\n\n```\nNumerical Aspects\n``` No rounding errors appear if JOB = 'P'.\n\n```\n``` If THRESH = -2, the increase of the maximum norm of the scaled\nsubmatrices, compared to the maximum norm of the initial\nsubmatrices, is bounded by MXGAIN = 100.\nIf THRESH = -2, or THRESH = -4, the maximum condition number of\nthe scaling transformations is bounded by MXCOND = 1/SQRT(EPS),\nwhere EPS is the machine precision (see LAPACK Library routine\nDLAMCH).\n\n```\nExample\n\nProgram Text\n\n```* MB04DL EXAMPLE PROGRAM TEXT\n* Copyright (c) 2002-2017 NICONET e.V.\n*\n* .. Parameters ..\nINTEGER NIN, NOUT\nPARAMETER ( NIN = 5, NOUT = 6 )\nINTEGER NMAX\nPARAMETER ( NMAX = 10 )\nINTEGER LDA, LDB\nPARAMETER ( LDA = NMAX, LDB = NMAX )\n* .. Local Scalars ..\nCHARACTER*1 JOB\nINTEGER I, ILO, INFO, IWARN, J, N\nDOUBLE PRECISION THRESH\n* .. Local Arrays ..\nDOUBLE PRECISION A(LDA, NMAX), B(LDB, NMAX), DWORK(8*NMAX),\n\\$ LSCALE(NMAX), RSCALE(NMAX)\n* .. External Functions ..\nLOGICAL LSAME\nEXTERNAL LSAME\n* .. External Subroutines ..\nEXTERNAL MB04DL\n* .. Executable Statements ..\nWRITE ( NOUT, FMT = 99999 )\n* Skip the heading in the data file and read the data.\nREAD ( NIN, FMT = '()' )\nREAD ( NIN, FMT = * ) N, JOB, THRESH\nIF( N.LE.0 .OR. N.GT.NMAX ) THEN\nWRITE ( NOUT, FMT = 99985 ) N\nELSE\nREAD ( NIN, FMT = * ) ( ( A(I,J), J = 1,N ), I = 1,N )\nREAD ( NIN, FMT = * ) ( ( B(I,J), J = 1,N ), I = 1,N )\nCALL MB04DL( JOB, N, THRESH, A, LDA, B, LDB, ILO, IHI, LSCALE,\n\\$ RSCALE, DWORK, IWARN, INFO )\nIF ( INFO.NE.0 ) THEN\nWRITE ( NOUT, FMT = 99998 ) INFO\nELSE\nWRITE ( NOUT, FMT = 99997 )\nDO 10 I = 1, N\nWRITE ( NOUT, FMT = 99995 ) ( A(I,J), J = 1,N )\n10 CONTINUE\nWRITE ( NOUT, FMT = 99996 )\nDO 40 I = 1, N\nWRITE ( NOUT, FMT = 99995 ) ( B(I,J), J = 1,N )\n40 CONTINUE\nWRITE ( NOUT, FMT = 99994 ) ILO\nWRITE ( NOUT, FMT = 99993 ) IHI\nWRITE ( NOUT, FMT = 99991 )\nWRITE ( NOUT, FMT = 99995 ) ( LSCALE(I), I = 1,N )\nWRITE ( NOUT, FMT = 99990 )\nWRITE ( NOUT, FMT = 99995 ) ( RSCALE(I), I = 1,N )\nIF ( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN\nIF ( .NOT.( THRESH.EQ.-2 .OR. THRESH.EQ.-4 ) ) THEN\nWRITE ( NOUT, FMT = 99989 )\nWRITE ( NOUT, FMT = 99995 ) ( DWORK(I), I = 1,2 )\nWRITE ( NOUT, FMT = 99988 )\nWRITE ( NOUT, FMT = 99995 ) ( DWORK(I), I = 3,4 )\nWRITE ( NOUT, FMT = 99987 )\nWRITE ( NOUT, FMT = 99995 ) ( DWORK(5) )\nELSE\nWRITE ( NOUT, FMT = 99986 ) IWARN\nEND IF\nEND IF\nEND IF\nEND IF\n*\n99999 FORMAT (' MB04DL EXAMPLE PROGRAM RESULTS',/1X)\n99998 FORMAT (' INFO on exit from MB04DL = ',I2)\n99997 FORMAT (' The balanced matrix A is ')\n99996 FORMAT (/' The balanced matrix B is ')\n99995 FORMAT (20(1X,G12.4))\n99994 FORMAT (/' ILO = ',I4)\n99993 FORMAT (/' IHI = ',I4)\n99991 FORMAT (/' The permutations and left scaling factors are ')\n99990 FORMAT (/' The permutations and right scaling factors are ')\n99989 FORMAT (/' The initial 1-norms of the (sub)matrices are ')\n99988 FORMAT (/' The final 1-norms of the (sub)matrices are ')\n99987 FORMAT (/' The threshold value finally used is ')\n99986 FORMAT (/' IWARN on exit from MB04DL = ',I2)\n99985 FORMAT (/' N is out of range.',/' N = ',I5)\nEND\n```\nProgram Data\n```MB04DL EXAMPLE PROGRAM DATA\n4 B -3\n1 0 -1e-12 0\n0 -2 0 0\n-1 -1 -1 0\n-1 -1 0 2\n1 0 0 0\n0 1 0 0\n0 0 1 0\n0 0 0 1\n\n```\nProgram Results\n``` MB04DL EXAMPLE PROGRAM RESULTS\n\nThe balanced matrix A is\n2.000 -1.000 0.000 -1.000\n0.000 1.000 -0.1000E-11 0.000\n0.000 -1.000 -1.000 -1.000\n0.000 0.000 0.000 -2.000\n\nThe balanced matrix B is\n1.000 0.000 0.000 0.000\n0.000 1.000 0.000 0.000\n0.000 0.000 1.000 0.000\n0.000 0.000 0.000 1.000\n\nILO = 2\n\nIHI = 3\n\nThe permutations and left scaling factors are\n2.000 1.000 1.000 2.000\n\nThe permutations and right scaling factors are\n2.000 1.000 1.000 2.000\n\nThe initial 1-norms of the (sub)matrices are\n2.000 1.000\n\nThe final 1-norms of the (sub)matrices are\n2.000 1.000\n\nThe threshold value finally used is\n0.2500E-12\n```" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.76476717,"math_prob":0.98967576,"size":10682,"snap":"2019-51-2020-05","text_gpt3_token_len":3394,"char_repetition_ratio":0.13841544,"word_repetition_ratio":0.22335026,"special_character_ratio":0.34431756,"punctuation_ratio":0.1945462,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9974011,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-24T13:19:58Z\",\"WARC-Record-ID\":\"<urn:uuid:600fdeca-b18f-4abb-a927-22af1f3169dc>\",\"Content-Length\":\"15123\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4ab2d5f4-040a-4242-9227-f2182bc2f61b>\",\"WARC-Concurrent-To\":\"<urn:uuid:7a4a0875-9bf5-4d4d-8774-0e4eda6bcabf>\",\"WARC-IP-Address\":\"159.69.82.252\",\"WARC-Target-URI\":\"http://slicot.org/objects/software/shared/doc/MB04DL.html\",\"WARC-Payload-Digest\":\"sha1:LCKELHRT26POX6UM3DK6PYKDTXHWUIRU\",\"WARC-Block-Digest\":\"sha1:STG626OBH7KVMT7NEINXEQRVD4RD4DEM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250620381.59_warc_CC-MAIN-20200124130719-20200124155719-00420.warc.gz\"}"}
https://kr.mathworks.com/matlabcentral/cody/problems/230-project-euler-problem-1-multiples-of-3-and-5/solutions/1681280
[ "Cody\n\n# Problem 230. Project Euler: Problem 1, Multiples of 3 and 5\n\nSolution 1681280\n\nSubmitted on 27 Nov 2018 by Luca Balbi\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1   Pass\nx = 1000; y_correct = 233168; assert(isequal(euler001(x),y_correct))\n\n2   Pass\nx = 4000; y_correct = 3732668; assert(isequal(euler001(x),y_correct))\n\n3   Pass\nx = 2340; y_correct = 1276470; assert(isequal(euler001(x),y_correct))\n\n4   Pass\nx = 2341; y_correct = 1278810; assert(isequal(euler001(x),y_correct))" ]
[ null ]
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https://uk.mathworks.com/matlabcentral/cody/problems/1988-remove-the-middle-element-from-a-vector/solutions/1043396
[ "Cody\n\n# Problem 1988. Remove the middle element from a vector\n\nSolution 1043396\n\nSubmitted on 3 Nov 2016 by JAEHYUK WOO\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1   Pass\nx = [1,2,3]; y_correct = 2; assert(isequal(remove_middle(x),y_correct))\n\n2   Pass\nx = [1,2,3,4]; y_correct = 2; assert(isequal(remove_middle(x),y_correct))\n\n3   Pass\nx = []; y_correct = []; assert(isequal(remove_middle(x),y_correct))\n\ny = []" ]
[ null ]
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https://www.geeksforgeeks.org/common-elements-in-all-rows-of-a-given-matrix/?ref=rp
[ "Related Articles\nCommon elements in all rows of a given matrix\n• Difficulty Level : Medium\n• Last Updated : 22 Mar, 2021\n\nGiven an m x n matrix, find all common elements present in all rows in O(mn) time and one traversal of matrix.\nExample:\n\n```Input:\nmat = {{1, 2, 1, 4, 8},\n{3, 7, 8, 5, 1},\n{8, 7, 7, 3, 1},\n{8, 1, 2, 7, 9},\n};\n\nOutput:\n1 8 or 8 1\n8 and 1 are present in all rows.```\n\nA simple solution is to consider every element and check if it is present in all rows. If present, then print it.\nA better solution is to sort all rows in the matrix and use similar approach as discussed here. Sorting will take O(mnlogn) time and finding common elements will take O(mn) time. So overall time complexity of this solution is O(mnlogn)\nCan we do better than O(mnlogn)?\nThe idea is to use maps. We initially insert all elements of the first row in an map. For every other element in remaining rows, we check if it is present in the map. If it is present in the map and is not duplicated in current row, we increment count of the element in map by 1, else we ignore the element. If the currently traversed row is the last row, we print the element if it has appeared m-1 times before.\nBelow is the implementation of the idea:\n\n## C++\n\n `// A Program to prints common element in all``// rows of matrix``#include ``using` `namespace` `std;` `// Specify number of rows and columns``#define M 4``#define N 5` `// prints common element in all rows of matrix``void` `printCommonElements(``int` `mat[M][N])``{``    ``unordered_map<``int``, ``int``> mp;` `    ``// initalize 1st row elements with value 1``    ``for` `(``int` `j = 0; j < N; j++)``        ``mp[mat[j]] = 1;` `    ``// traverse the matrix``    ``for` `(``int` `i = 1; i < M; i++)``    ``{``        ``for` `(``int` `j = 0; j < N; j++)``        ``{``            ``// If element is present in the map and``            ``// is not duplicated in current row.``            ``if` `(mp[mat[i][j]] == i)``            ``{``               ``// we increment count of the element``               ``// in map by 1``                ``mp[mat[i][j]] = i + 1;` `                ``// If this is last row``                ``if` `(i==M-1 && mp[mat[i][j]]==M)``                  ``cout << mat[i][j] << ``\" \"``;``            ``}``        ``}``    ``}``}` `// driver program to test above function``int` `main()``{``    ``int` `mat[M][N] =``    ``{``        ``{1, 2, 1, 4, 8},``        ``{3, 7, 8, 5, 1},``        ``{8, 7, 7, 3, 1},``        ``{8, 1, 2, 7, 9},``    ``};` `    ``printCommonElements(mat);` `    ``return` `0;``}`\n\n## Java\n\n `// Java Program to prints common element in all``// rows of matrix``import` `java.util.*;` `class` `GFG``{` `// Specify number of rows and columns``static` `int` `M = ``4``;``static` `int` `N =``5``;` `// prints common element in all rows of matrix``static` `void` `printCommonElements(``int` `mat[][])``{` `    ``Map mp = ``new` `HashMap<>();``    ` `    ``// initalize 1st row elements with value 1``    ``for` `(``int` `j = ``0``; j < N; j++)``        ``mp.put(mat[``0``][j],``1``);``        ` `    ``// traverse the matrix``    ``for` `(``int` `i = ``1``; i < M; i++)``    ``{``        ``for` `(``int` `j = ``0``; j < N; j++)``        ``{``            ``// If element is present in the map and``            ``// is not duplicated in current row.``            ``if` `(mp.get(mat[i][j]) != ``null` `&& mp.get(mat[i][j]) == i)``            ``{``                ``// we increment count of the element``                ``// in map by 1``                ``mp.put(mat[i][j], i + ``1``);` `                ``// If this is last row``                ``if` `(i == M - ``1``)``                    ``System.out.print(mat[i][j] + ``\" \"``);``            ``}``        ``}``    ``}``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `mat[][] =``    ``{``        ``{``1``, ``2``, ``1``, ``4``, ``8``},``        ``{``3``, ``7``, ``8``, ``5``, ``1``},``        ``{``8``, ``7``, ``7``, ``3``, ``1``},``        ``{``8``, ``1``, ``2``, ``7``, ``9``},``    ``};` `    ``printCommonElements(mat);``}``}` `// This code contributed by Rajput-Ji`\n\n## Python3\n\n `# A Program to prints common element``# in all rows of matrix` `# Specify number of rows and columns``M ``=` `4``N ``=` `5` `# prints common element in all``# rows of matrix``def` `printCommonElements(mat):` `    ``mp ``=` `dict``()` `    ``# initalize 1st row elements``    ``# with value 1``    ``for` `j ``in` `range``(N):``        ``mp[mat[``0``][j]] ``=` `1` `    ``# traverse the matrix``    ``for` `i ``in` `range``(``1``, M):``        ``for` `j ``in` `range``(N):``            ` `            ``# If element is present in the``            ``# map and is not duplicated in``            ``# current row.``            ``if` `(mat[i][j] ``in` `mp.keys() ``and``                             ``mp[mat[i][j]] ``=``=` `i):``                                 ` `            ``# we increment count of the``            ``# element in map by 1``                ``mp[mat[i][j]] ``=` `i ``+` `1` `                ``# If this is last row``                ``if` `i ``=``=` `M ``-` `1``:``                    ``print``(mat[i][j], end ``=` `\" \"``)``            ` `# Driver Code``mat ``=` `[[``1``, ``2``, ``1``, ``4``, ``8``],``       ``[``3``, ``7``, ``8``, ``5``, ``1``],``       ``[``8``, ``7``, ``7``, ``3``, ``1``],``       ``[``8``, ``1``, ``2``, ``7``, ``9``]]` `printCommonElements(mat)` `# This code is conteibuted``# by mohit kumar 29`\n\n## C#\n\n `// C# Program to print common element in all``// rows of matrix to another.``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{` `// Specify number of rows and columns``static` `int` `M = 4;``static` `int` `N = 5;` `// prints common element in all rows of matrix``static` `void` `printCommonElements(``int` `[,]mat)``{` `    ``Dictionary<``int``, ``int``> mp = ``new` `Dictionary<``int``, ``int``>();``    ` `    ``// initalize 1st row elements with value 1``    ``for` `(``int` `j = 0; j < N; j++)``    ``{``        ``if``(!mp.ContainsKey(mat[0, j]))``            ``mp.Add(mat[0, j], 1);``    ``}``    ` `    ``// traverse the matrix``    ``for` `(``int` `i = 1; i < M; i++)``    ``{``        ``for` `(``int` `j = 0; j < N; j++)``        ``{``            ``// If element is present in the map and``            ``// is not duplicated in current row.``            ``if` `(mp.ContainsKey(mat[i, j])&&``               ``(mp[mat[i, j]] != 0 &&``                ``mp[mat[i, j]] == i))``            ``{``                ``// we increment count of the element``                ``// in map by 1``                ``if``(mp.ContainsKey(mat[i, j]))``                ``{``                    ``var` `v = mp[mat[i, j]];``                    ``mp.Remove(mat[i, j]);``                    ``mp.Add(mat[i, j], i + 1);``                ``}``                ``else``                    ``mp.Add(mat[i, j], i + 1);` `                ``// If this is last row``                ``if` `(i == M - 1)``                    ``Console.Write(mat[i, j] + ``\" \"``);``            ``}``        ``}``    ``}``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[,]mat = {{1, 2, 1, 4, 8},``                  ``{3, 7, 8, 5, 1},``                  ``{8, 7, 7, 3, 1},``                  ``{8, 1, 2, 7, 9}};` `    ``printCommonElements(mat);``}``}` `// This code is contributed by 29AjayKumar`\n\nOutput:\n\n`8 1`\n\nThe time complexity of this solution is O(m * n) and we are doing only one traversal of the matrix.\nThis article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to [email protected]. See your article appearing on the GeeksforGeeks main page and help other Geeks.\nPlease write comments if you find anything incorrect, or you want to share more information about the topic discussed above.\n\nAttention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.\n\nMy Personal Notes arrow_drop_up" ]
[ null ]
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http://www.databison.com/tag/vlookup/
[ "## VLOOKUP Formula Excel – How to use Excel VLOOKUP Function\n\nSyntax of VLOOKUP Formula Example of VLOOKUP Formula Possible Errors returned by the VLOOKUP Formula VLOOKUP formula matches a string against the 1st column of a range and returns any cell value from the matched row. VLOOKUP Formula Syntax VLOOKUP Formula has three parts: VLOOKUP (value_to_find, range_to_search_in, column_number_to_return, match_type) value_to_find value_to_find is the value that we would like to find. You can specify a string, ...", null, "## VLOOKUP Function Error\n\nPosted on 18 October 2008", null, "You think you've entered the right formula and yet you get the dreaded #N/A error on the sheet.....well....here are some useful tips to get you through the vlookup blues! =vlookup(value_to_match, range_to_find_this_value, which_column_to_return , try_to_approximate_if_no_match) (Delimited) text being compared to numbers If you have imported data from a plain text file (a .txt file), your data may most likely have numbers which have been converted to string. Excel will still display the values ...\n\n## 60 Useful Excel Formulas That Are Good To Know\n\nPosted on 23 August 2008\n\n60 useful excel formulas that are a good to know DATE = Returns the serial number of a particular date DATEVALUE = Converts a date in the form of text to a serial number DAY = Converts a serial number to a day of the month EOMONTH = Returns the serial number of the last day of the month before or after a specified number of months MONTH = Converts a serial number to a month NOW = ..." ]
[ null, "http://www.databison.com/wp-content/uploads/2009/07/vlookup-formula-300x300.png", null, "http://www.databison.com/wp-content/uploads/2008/10/changeinreference-150x150.png", null ]
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http://mathandmultimedia.com/tag/damath-board-game/
[ "## Introduction to the DaMath Board Game Part 3\n\nThis is the third part of our series on learning how to play Damath. In the first part, we learned about the basics of Damath and in the second part, we learned how to capture multiple pieces.\n\nThe Dama Piece\n\nA piece can be promoted when it reaches the last row (the first row of the opponent’s area) on the board. In the next figure, if it is the Red Player’s turn, then he can promote 2 by moving it to (6,7) as indicated by the arrow. In the same way, the Blue Player’s 8 is just two moves away from being promoted. Promoted pieces are called dama (roughly equivalent of Queen in chess). Each player can have more than one dama.", null, "Moving the Dama\n\nThe dama can move forward and backward on unobstructed diagonals. For example, if the Red Player’s 2 becomes a dama on (6,7) as shown in the next figure, it can move to any of the four squares indicated by the red lines. It cannot move to (1,2) and (0,1) because 8 is obstructing the path.  » Read more\n\n## Introduction to the DaMath Board Game Part 1\n\nDaMath is a math board game coined from the word dama, a Filipino checker game, and mathematics. It was invented by Jesus Huenda, a high school teacher from Sorsogon, Philippines. It became very popular in the 1980s and until now played in many schools in the Philippines.\n\nDaMath can be used to practice the four fundamental operations and also the order of operations. It has numerous variations, but in the tutorial below, we will discuss the Integers DaMath. Note that explaining this game is quite complicated, so I have divided the tutorial into three posts.\n\nThe DaMath Board\n\nThe board is composed of 64 squares in alternating black and white just like the chessboard. The four basic mathematical operations are written on white squares as shown in Figure 1. Each square is identified by a (column, row) notation. The top-left square, for example, is in column 0 and row 7, so it is denoted by (0,7).  » Read more", null, "" ]
[ null, "http://mathandmultimedia.com/wp-content/uploads/2017/01/figure-1-253x300.png", null, "http://www.linkwithin.com/pixel.png", null ]
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https://calculatorsonline.org/scientific-notation-to-decimal/-7e-12
[ "# Convert -7e-12 to decimal number\n\nHere you will see step by step solution to convert -7e-12 scientific number to decimal. -7e-12 conversion to decimal is -0.000000000007, please check the explanation that how to convert -7e-12 to as a decimal.\n\n## Answer: -7e-12 as a decimal is\n\n= -0.000000000007\n\n### How to convert -7e-12 to number?\n\nTo convert the scientific notation -7e-12 number simply multiply the coefficient part[-7] with by 10 to the power of exponent[-12]. Scientific notation -7e-12 is same as -7 × 10-12.\n\n#### Solution for -7e-12 to number\n\nFollow these easy steps to convert -7e-12 to number-\n\nGiven scientific notation is => -7e-12\n\ne = 10\n\n-7 = Coefficient\n\n-12 = Exponent\n\n=> -7e-12 = -7 × 10-12\n= -0.000000000007\n\nHence, the -7e-12 is in decimal number form is -0.000000000007." ]
[ null ]
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https://topbtcxqehhbbq.netlify.app/bormet31187wov/calculate-steady-state-capital-stock-neso.html
[ "## Calculate steady state capital stock\n\n19 Feb 2018 Steady-state ratios of government sector capital stock to potential output in for the private saving rate, and total savings was calculated by  away it is from its steady state (i.e., lnkt+1 − lnkt is increasing in the distance lnk* − lnkt). Second, it tells us that every time the capital stock increases by 1 percent\n\nb) The reduction in the labor force means that the capital stock per worker is higher after the war. Therefore, if the economy were in a steady state prior to the war  The change in the capital stock per worker (known as capital deepening) is equal to per worker gross The capital stock rises eventually to a new steady state equilibrium, at k2*. During the estimate 7 ½%, p 11), reflecting risk premiums. 1 Nov 2011 Equilibrium path: not simply steady state, but entire path of capital stock, output, consumption and factor prices. In engineering and physical  Note that if depreciation were only 10 percent of capital stock, the equilibrium condition would We can use the production function to calculate that q = 1000. We can find steady state equilibrium by making use of the equilibrium condition :  1.3 Law of Motion for the Capital Stock Steady-state in the Solow model: in long-run equilibrium, capital per worker (the capital-labor ratio) is con- stant. 19 Feb 2018 Steady-state ratios of government sector capital stock to potential output in for the private saving rate, and total savings was calculated by\n\n## A savings rate of 0% implies that no new investment capital is being created, so that the capital stock depreciates without replacement. This makes a steady state\n\ninvestment. An increase in saving and investment raises the capital stock and thus raises the In the long run, there is steady-state economic growth. Since the   Finding the Solow steady state. • In the Solow model, we o Capital per effective labor unit k is unchanging over time in the steady state. o Since output per effective current capital stock, but k will fall over time so y will fall and. C cannot be  for t = 0, 1,. The question is to determine the equilibrium dynamic allocation among the sponding steady-state golden rule capital stock is defined as k. ∗ gold. for the finding that the depreciation rate of fixed capital tends to be higher in is available; StSt indicates the steady-‐state capital stock based on equation (6) is  10 Oct 2006 f(k)=δk be the steady state capital stock. At any To calculate the wage in the open economy, we just look at what is left after capital it paid. 30 Jul 2019 This function allows you to compute a Cobb-Douglas production/ utility This function computes steady state income, capital and human capital per worker given relevant is the physical capital stock's depreciation rate.\n\n### 30 Jul 2019 This function allows you to compute a Cobb-Douglas production/ utility This function computes steady state income, capital and human capital per worker given relevant is the physical capital stock's depreciation rate.\n\nand country B with saving rate s = 0.2 has steady state capital stock k∗ = 16.2 If we had continued with the calculations for the next several years, we would  That is, it makes the capital stock an endogenous variable. Output stops growing as well, and the economy settles down to a steady state. The Solow growth model is the starting point to determine why growth differs across similar\n\n### Then find the steady state levels of income per worker and consumption per worker. 18:10 d. Suppose that both countries start off with a capital stock per worker of 2.\n\n19 Feb 2018 Steady-state ratios of government sector capital stock to potential output in for the private saving rate, and total savings was calculated by  away it is from its steady state (i.e., lnkt+1 − lnkt is increasing in the distance lnk* − lnkt). Second, it tells us that every time the capital stock increases by 1 percent   for the existence of a steady-state. Y = AKβL(1-β). (1) with A an arbitrary constant to model exogenous technical, K the capital stock, L is labor and β is the share  and country B with saving rate s = 0.2 has steady state capital stock k∗ = 16.2 If we had continued with the calculations for the next several years, we would  That is, it makes the capital stock an endogenous variable. Output stops growing as well, and the economy settles down to a steady state. The Solow growth model is the starting point to determine why growth differs across similar  determine their steady state capital/labor ratios (ie., productivity, saving, population growth, depreciation rates, etc). If they don't, then poor countries may actually\n\n## However, to determine equilibrium prices we need to determine demand for labor and The steady state capital stock is, thus, the capital stock for which actual.\n\nFor this economy, the savings rate is 25 perent, the depreciation rate is 5 percent, the population growth rate is 2 perscent, and the technology growth rate is 3percent. calculate the steady-state capital stock per effective worker, output per effective worker, and consumption per effective worker. c.\n\nTo determine whether an economy is operating at its Golden Rule level of capital stock, a policymaker must determine the steady-state saving rate that produces  (2) Might a policymaker choose a steady state with more capital than in the. Golden Rule (d) Suppose that both countries start off with a capital stock per worker of 2. What are year, calculate income per worker and consumption per worker. An obvious problem of this ''Steady State Approach'' is that the estimate of the initial capital stock depends crucially on the investments and the growth rate of" ]
[ null ]
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http://www.viaggiegyptalia.com/what-you-should-do-about-what-is-a-coefficient-in-math-beginning-in-the-next-10-minutes/
[ "What You Should Do About What Is a Coefficient in Math Beginning in the Next 10 Minutes\n\nThe very first step is to compose this as a linear system. The sample set could be each of these 3 data sets for the last 20 decades. If you’re lucky, you can locate math grinds for a very low price.\n\nA course like Mastering Excel will teach you all the basics you should begin with Excel, as well as teaching you more advanced functions which are included within the application. Case of a Continuous Function Now that we’ve considered a couple counterexamples, we’re in a better position to examine a continuous function and consider how it’s different. Setting Up the Problem Here are some fundamental facts.\n\nType of What Is a Coefficient in Math\n\nThere are a lot of methods to instantiate and use statistics. There are a few requirements that have to be met for the CV to be interpreted in the ways we’ve described. It comes into play when you have a dataset with various capabilities.\n\nA source of information, and the question you’re attempting to answer. If you’ve got other books you’d love to recommend regarding math, company, http://www.umm.edu/programs/psychiatry or computer science, I’d like to hear about them. A regular task in math is to compute what is known as the absolute value of a particular number.\n\nYou will discover urge for constant involvement in your house’s construction. Firstly, you ought to look for assistance with term paper somebody who’s well trained and has the capacity to evaluate your child’s needs properly. The very first idea to be thought about is continuity.\n\nHow to Find What Is a Coefficient in Math on the Web\n\nSee that the factors are identicle but for the sign. In the newest instance, a soft memory error looks like the culprit. A composite expression is comparable as it can be written as the product of a few expressions.\n\nIt’s apparent that a single particpant can’t opt for a weak signature. Instead of unique letters in every single pair of parentheses, we’re now repeating the very same letters over and over again. It is referred to as a Constant.\n\nSometimes in case you’d love to do just a bit of research on what a particular fabric or leather is created of and how the texture would affect the durability, some unfamiliar terms might be used. write essay for me For Airbnb, a common person stays a number of nights in a number of cities. The degree of a polynomial is the sum of the most degree term.\n\nAttic insulation is likewise an important issue as to your house’s energy efficiency. The bigger The variance the bigger the quantity of information the variable contains. The beta coefficient can be beneficial in attempting to predict a specific stock’s tendencies and calculate the total risk.\n\nMath concepts might also be reinforced for the children during the day on a usual basis. For the reason, you should be mindful to pick a math tutor that won’t only help your child to complete homework and find math solutions, but also challenge her or him to work on the most difficult math difficulties. One has to be sound in mathematics to be able to start machine learning.\n\nThe Correlation Coefficient may be used to recognize non-correlated securities, which is important in creating a diversified portfolio. Actually, several critical concepts like the function of eigenvectors and eigenvalues have never been mentioned even though they play an essential role in PCA. Elementary algebra differs from arithmetic in the usage of abstractions, including using letters to stand for numbers which are either unknown or permitted to take on several values.\n\nThe outcomes are the precise same but the methods are very different. There are a lot of combinations here! Now the fourth and fifth items within this equation should make a bit more sense.\n\nThere are some decisions that will want to go made when putting groups together. The answer, in fact, lies somewhere in the center. Regardless of what level of control you’ve got over the topic matter, it’s important to get some crystal clear and specific goals in mind as you’re creating educational experiences for people.\n\nThe 5-Minute Rule for What Is a Coefficient in Math\n\nA different sign on the top coefficient altered the direction of this graph too. The arguments necessary to work out the correlation coefficient are the 2 ranges of information which will want to go compared. For the time being, let’s just center on the top portion of this equation.\n\nThe denominator contains the determinant of the coefficients. In case the coefficient is negative, the inequality will be reversed. This equation involves the slope.\n\nBased on what kind of shrinkage is performed, a number of the coefficients could be estimated to be exactly zero. Moreover, in the event the slope has a negative price, then there’s a negative correlation between two variables. The coefficient of the most significant term is called the major coefficient.\n\nWhatever They Told You About What Is a Coefficient in Math Is Dead Wrong…And Here’s Why\n\nFor example, a normal propane compressor may have a k-value at suction conditions of 1.195. This function is therefore not continuous at this time and so isn’t continuous. Providing Z is an excellent figure, p-value should be calculated via the area of space under the traditional normal distribution after point Z.\n\nWhat Is a Coefficient in Math Can Be Fun for Everyone\n\nSometimes one wants to address a system of equations with regard to a set of unknown parameters. These functions are supplied via this module. In many instances, introducing heuristics may raise the random algorithm.\n\nQuite simply, it’s a tangent function analysis. It is just the choice of input variables. You’re able to interactively explore graphs similar to this at Quadratic explorer." ]
[ null ]
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https://www.rdocumentation.org/packages/lattice/versions/0.3-1/topics/bwplot
[ "# bwplot\n\n0th\n\nPercentile\n\n##### Box and Whisker Plots\n\nDraw Box and Whisker Plots\n\nKeywords\nhplot\n##### Usage\nbwplot(formula, box.ratio = 1, ...)\n##### Arguments\nformula\na formula describing the form of conditioning plot. A formula of the form y ~ x | g1 * g2 * ... indicates that plots of y versus x should be produced conditional on the variables g1,g2,....\nbox.ratio\ngives the ratio of the width of the rectangles to the inter rectangle space.\n...\nother arguments\n##### Details\n\nsee the documentation for trellis.args. Behaviour when trying to modify the y-axis via scales\\$y is not defined. (It might give what you want, but again, it might not.) The default value of ylim is an interval containing c(1,number of levels of y), with the extra amount calculated based on box.ratio (not 7%, the usual default) .\n\n##### Value\n\n• An object of class trellis'', plotted by default by print.trellis.\n\n##### synopsis\n\nbwplot(formula, data = parent.frame(), aspect = \"fill\", layout = NULL, panel = panel.bwplot, prepanel = NULL, scales = list(), strip = TRUE, groups = NULL, xlab, xlim, ylab, ylim, box.ratio = 1, ..., subscripts = !missing(groups), subset = TRUE)\n\ntrellis.args, panel.bwplot,Lattice\ndata(singer)\nbwplot(voice.part ~ height, data=singer, xlab=\"Height (inches)\")" ]
[ null ]
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https://katjaas.nl/bitreversal/bitreversal.html
[ "# Bit Reversal and Permutation\n\nIn order to use the FFT schemes of the preceding pages, I need a method for bitreversed permutation of the output arrays. Although bitreversal is generally considered a rather trivial aspect, I find it more complicated than the FFT proper. In every FFT stage, the array entries are intertwined in a systematical way, the pattern of which is quite clear. But in the decimated end result, things appear shuffled beyond comprehension. To unravel, you would not want to spend so many iterations as in the whole FFT, like the naivest bit-reversed permutation methods do. More efficient methods tend to be rather enigmatic however.\n\nOn this page I want to develop a visual sense of bit-patterns and ways to manipulate these. I will start from scratch. First find a routine to reverse the bitpattern of one integer. Then figure out a way of swapping the relevant components within an array of length 2n.", null, "Here is an example of a bit-reverse ordered output array like it could result from an FFT routine. The figure is copied from the page Phase Decomposition, where I illustrated how repeated downsampling shuffles the entries in an array. It needs reorganisation before it makes sense as being harmonics within a spectrum. Let us take one example pair of entries that must be swapped. Harmonic number 6 is at the location where 3 should be, and 3 is where 6 belongs.\n\nBelow I have expanded both entries as binary numbers. So we are looking at individual bits now. An integer datatype can have 32 bits for example, but here we would need only three of these.", null, "General-purpose CPU's have no bit-reversal instruction, as far as I know. Anyway there is no ANSI C operator to addres such an instruction if it would exist. It would be so convenient if you could just write something like n ><= 3, to do the above sketched bit reversal. Instead, we have to write a loop to reverse the bits in one integer number. Let us do it then.\n\nTo start, we store a copy of n in a separate variable.", null, "The bit-pattern of n must be shifted right one position, and it's least significant bit falls off.", null, "At the same time, copy-of-n is shifted left by one position. The vacant positions in n and copy-of-n are filled with zero's.", null, "", null, "It seems that the bit-reverse of n is already found. But that is coincidence. We must continue systematically till all is done.\n\nWe will now scan the least significant bit of the shifted n. That is the second-least significant bit of the original. The scanning can be done by a bitwise-and operation. The unsigned integer value 1 masks everything but the LSB.", null, "This bit-of-n is then transferred to copy-of-n by inclusive bitwise-or. This works because copy-of-n always has a shifted-in zero at that position. It takes the true value when bit-of-n is one, or remains zero when the bit-of-n is zero.", null, "The series of operations is repeated:\nshift n one position right,\nshift copy-of-n one position left,\ngive the LSB of n to copy-of-n.", null, "After two iterations we have the LSB of the original three-bit n at the MSB position of our copy-of-n. The loop of operations should end here. But one thing remains to be done after that. The variable copy-of-n has now decimal value 27. A last bitwise-and operation is required to mask everything but the three least significant bits that we use. The mask has value 7, which is N-1. The result of this masking is that we finally have the bitpattern 011.", null, "Notice that the count of iterations is one less than the count of bits used for the values, because the LSB of n is the most significant relevant bit in copy-of-n. Here we have the above sketched bit-reversal written as a C function:\n\n unsigned int bitrev(unsigned int n, unsigned int bits) {     unsigned int i, nrev;   // nrev will store the bit-reversed pattern     N = 1<>= 1;         nrev <<= 1;         nrev |= n & 1;   // give LSB of n to nrev     }     nrev &= N-1;         // clear all bits more significant than N-1         return nrev; }\n\nThis loop could perform redundant iterations. Imagine you have N=1024 which uses 10 bits, and do a bitreversal for n=3 which turns bit pattern 0000000011 into 1100000000. After one iteration you already have the set bits, but 8 more iterations will follow. From the page 'Bit Twiddling Hacks' by Sean Eron Anderson I learnt a modification to avoid that redundancy. The loop can end when the shifted n has become zero.\n\n // modification of the preceding code unsigned int bitrev(unsigned int n, unsigned int bits) {     unsigned int nrev, N,;     unsigned int count;       N = 1<>=1; n; n>>=1)     {         nrev <<= 1;         nrev |= n & 1;         count--;     }     nrev <<= count;     nrev &= N - 1;     return nrev; }\n\nWith this code, the loop will end as soon as all high bits of n are shifted out, and nrev receives a compensating shift after the loop end. Later I understood that this will save only one iteration on average. But never mind, we need a count variable of some sort anyway.\n\nSo far we have code to compute a bit-reversed version of only one integer. To visually check what happens to bitpatterns, I have plotted the indexes 0 till 63 with their bits separately shown. Here is the plot for n with the bits in their orignal order:", null, "Below is a plot of the indexes with their bitpatterns reversed. For example:\n\nat index 000001, 100000 is plotted with it's individual bits\nat index 110110, 011011 is plotted with it's individual bits\n\nAll the bits representing decimal 1 are now regrouped in the second half of the plot. So all odd numbers are in that part. All bits representing 32 are now spread evenly over the range. Etcetera.", null, "Now we are going to reorganise an array according to the bit-reversed indexes of the components. That means swapping the contents of pairs with bit-mirrored index, if we want to recycle the array x[n]. While doing this, we should avoid swapping content of entries on the identity diagonal (optional), and avoid swapping content twice (obligatory).\n\nLet us take a look at the bit-reversed permutation matrix for N=8. Four entries are on the identity diagonal, and we would prefer to skip these. Only two pairs have to be swapped. x with x and x with x.", null, "Iterating over n, how do we decide whether to swap contents or not? Well.... if n=nrev we have an identity, and we can skip the swapping. And if n>nrev we will skip as well. Then we are sure that a pair is only swapped once. For this to work, we have to compute all nrev, even for the cases where we do not take action. Redundancy again. So be it. Let us for the moment just check whether a test routine will give correct output.\n\nWe need a loop iterating over n, and within that, a loop which computes nrev. A conditional check will tell whether the swap shall be performed or not.\n\n /****** radix 2 bit-reversed-permutation test routine for N = 32 **********/ // .... this code goes in main unsigned int N = 32, bits = 5;    // array length and number of bits used unsigned int x;               // test array unsigned int n;                   // index unsigned int nforward, nreversed; unsigned int count; unsigned int temp;                // to store x[n] during swap for(n=0; n>1; nforward; nforward>>=1)        {        nreversed <<= 1;        nreversed |= nforward & 1;   // give LSB of nforward to nreversed        count--;     }     nreversed <<=count;      // compensation for missed iterations     nreversed &= N-1;        // clear all bits more significant than N-1     if(n\n\nI have checked that this code does the job. It may be utterly inefficient, but at least I now have a basic understanding of bit-reversed permutation. I just needed to go through this, before checking more advanced methods.\n\nWhile staring at the bit-reversal matrices (I have bigger ones that do not fit on this page) I stumbled upon the 'not-identity-diagonal'. It is perpendicular to the identity diagonal, and the column index is the bitwise negation of the row index. All bit-reversed pairs seem to be mirrored over this not-I diagonal. Actually they are 180 degree rotations within the matrix. That means, once you have a bitreversed pair it is easy to identify the corresponding bit-wise-not pair that must be swapped as well.", null, "Straightforward exploitation of this symmetry could save half of the iterations and bit-reversal computations. The illustration below shows where the bitreversed values and the bitwise negated values are located for n<nrev and n<~nrev. Iterating over n till only N/2 will suffice to compute the swaps for the whole matrix. There is one condition however: no entries should be precisely on the not-I-diagonal. They would be swapped twice if they are included.", null, "I wrote code for this, but it turned out that it only works for N being an odd power of 2. For an even power, some entries are on the not-I-diagonal apparently. I was disappointed with the keen yet inconvenient modification.\n\nStill, it was a stepping stone to a more fruitful reorganisation of the loop. After gazing at my permutation matrices a couple more times, I finally perceived the decisive pattern. The lower-left and upper-right quarters are coupled, while the upper-left and lower-right quarters are mirrored. They ask for separate treatment.", null, "The upper left quarter entries must be checked against double swapping as the bitmirrored pairs are within the region itself. Furter, the identities are here. But then, once a bitmirrored pair is found and checked, the bitwise negation of it can be done simultaneously, thereby covering the lower right quarter.\n\nThe lower left quarter has it's bitreversed counterparts all in the upper right quarter and never in it's own region. These entries can be swapped unconditionally, since it happens to be the case that all the lower left entries have n=odd.\n\nFurther, it is very easy to create an odd bitmirrored pair from an even pair or vice versa. Therefore, we only have to find half of the bitreversed pairs inbetween n=0 and n=N/2. That means, N/4 iterations over the outer loop will suffice, N/4 bitreversal computations, and N/4 conditional checks. Now we are getting somewhere.\n\nComputing bitwise-not of n can be done in C with ~n but it must be masked by bitwise-and: (~n)&(N-1). It is also N-1-n (for N being a power of 2), and n^(N-1) which is an exclusive-or.\n\n /****** radix 2 bit-reversed-permutation test routine for N = 32 **********/ // .... this code goes in main unsigned int N = 32, bits = 5;     unsigned int NMIN1 = N-1; unsigned int x;                // test array unsigned int n;                    // index unsigned int count; unsigned int nforward, nreversed; unsigned int notn, notnreversed;   // for bitwise negated values unsigned int temp;                 // to store x[n] during swap for(n=0; n>1; n++)   // only N/4 iterations, extra increment within loop {     count = bits-1;     nreversed = n;         for(nforward=n>>1; nforward; nforward>>=1) // reverses the bit-pattern of n     {        nreversed <<= 1;        nreversed |= nforward & 1;   // give LSB of nforward to nreversed        count--;     }     nreversed <<= count;       // compensation for skipped iterations     nreversed &= NMIN1;        // cut off all bits more significant than N-1        if(n>1;                   // set highest bit in nreversed         temp = x[n];     x[n] = x[nreversed];     x[nreversed] = temp; } // end of the bitreversed permutation loop // ......print the values of x[n] and x[nrev] to stdout for check\n\nOf this I have a decrementing version as well:\n\n /****** radix 2 bit-reversed-permutation test routine for N = 32 **********/ // .... this code goes in main unsigned int N = 32, bits = 5;     unsigned int NMIN1 = N-1; unsigned int x;                // test array unsigned int n;                    // index unsigned int count; unsigned int nforward, nreversed; unsigned int nodd, noddrev;        // for odd or bitwise negated values unsigned int temp;                 // to store x[n] during swap for(n=0; n>1; n; )              // permutation loop, only N/4 iterations {     n -= 2;                   // decrement at unusual place     nreversed = n;     count = bits-3;           // bitreversal loop now optimized for n=even     for(nforward=n>>2; nforward; nforward>>=1) // reverses the bit-pattern of n     {        nreversed |= nforward & 1;   // give LSB of nforward to nreversed        nreversed <<= 1;             // notice: order of operations has changed        count--;     }     nreversed <<= count;       // compensation for skipped iterations     nreversed &= NMIN1>>1;     // cut off all bits more significant than (N/2)-1        if(n>1;    // set highest bit in nreversed         temp = x[nodd];     x[nodd] = x[noddrev];     x[noddrev] = temp; } // end of the bitreversed permutation loop // ......print the values of x[n] and x[nrev] to stdout for check\n\nThis modification speeds up the routine by a factor two, according to time profiler results. I would think there is still more gain possible.\n\nGenerally, a permutation routine would compute the bitreversed values as a running sum, rather than starting from scratch in every iteration over the outer loop. The result can be updated with helper variables of some sort. Unfortunately, the inner mechanism of such code is hard to follow.\n\nIt would be more elegant to decouple the bit-mirrored pairs from the loop index, and compute both as running sums in a symmetric fashion. The beautifullest algorithm that I have seen so far, does exactly this. It is invented and published by Jennifer E. Elaan. See: http://caladan.nanosoft.ca/index.php.\n\nAt the heart of Jennifer's technique is a Gray code generator. That is supercool! The trigger for such a generator is hidden within a natural number sequence. Below I have plotted the pattern of the trigger or toggle for N=64. Every value is a pure power of two. This universal pattern can be extracted in various ways. Illustrations of bit-patterns and extraction are on the page Bitwise&Poundfoolish.", null, "When N/2 is divided by the values in the plot above, you get the bit-reversed values, as plotted below. It is a multiplicative reflection.", null, "Using these patterns you can toggle-switch bits of variables initialized at zero, one at a time. That is done by exclusive-or. Then you get a Gray code sequence and it's bit-reversed version. A Gray code sequence plotted looks like this:", null, "It looks freaky. But now watch the pattern of it's individual bits plotted, like it was done earlier for a natural sequence:", null, "And here is the Gray code with it's bit-patterns reversed:", null, "Despite the differences between Gray code and the 'powers-of-two' binary sequence, there is also a striking resemblance. The bits appear in blocks of sizes proportional to their value. For several reasons, both sequences work equally well in my odd-nodd-skippy permutation structure that was described earlier.\n\nBitmirrored pairs can now be computed as running sums with help of a loop that counts trailing zero's, a count which coincides with the base 2 logarithms of the 'toggle' pattern values. Iterating over a natural index sequence i, I add an extra shift in the reconstructions to derive even values of the forward variable exclusively. The initialisation of forward and reversed is adapted to the decrementing direction of the loop.\n\nvoid bitrev(double *real, unsigned int logN)\n{\nunsigned int i, forward, rev, zeros;\nunsigned int nodd, noddrev;        // to hold bitwise negated or odd values\nunsigned int N, halfn, quartn, nmin1;\ndouble temp;\n\nN = 1<<logN;\nhalfn = N>>1;            // frequently used 'constants'\nquartn = N>>2;\nnmin1 = N-1;\n\nforward = halfn;         // variable initialisations\nrev = 1;\n\nfor(i=quartn; i; i--)    // start of bitreversed permutation loop, N/4 iterations\n{\n // Gray code generator for even values:      nodd = ~i;                                  // counting ones is easier      for(zeros=0; nodd&1; zeros++) nodd >>= 1;   // find trailing zero's in i      forward ^= 2 << zeros;                      // toggle one bit of forward      rev ^= quartn >> zeros;                     // toggle one bit of reversed\n\nif(forward<rev)                  // swap even and ~even conditionally\n{\ntemp = real[forward];\nreal[forward] = real[rev];\nreal[rev] = temp;\n\nnodd = nmin1 ^ forward;           // compute the bitwise negations\nnoddrev = nmin1 ^ rev;\n\ntemp = real[nodd];                // swap bitwise-negated pairs\nreal[nodd] = real[noddrev];\nreal[noddrev] = temp;\n}\n\nnodd = forward ^ 1;                   // compute the odd values from the even\nnoddrev = rev ^ halfn;\n\ntemp = real[nodd];                    // swap odd unconditionally\nreal[nodd] = real[noddrev];\nreal[noddrev] = temp;\n}\n// end of the bitreverse permutation loop\n}\n// end of bitrev function\n\nAnother factor 1.5 speed gain is the result of inserting Jennifer's method. It works because there are only N-1 trailing zero's over N indexes, which means 1 zero on average per index. A zero's-counting-loop is therefore not quite so demanding as a loop that reverses a whole bitpattern.\n\nFor some architectures, instructions are available for counting trailing and leading zero's. Major compilers have C extensions, giving access to such instructions. GNU has __builtin_ctz() for example. It should be faster theoretically, or not? I have checked that the function is expanded inline and it accesses Intel's bsfl instruction. But for some reason, I have no profit from it.\n\nAfter all these bitwise exercises, I got more confident and finally grasped how the more traditional update of the bitreversed index works. You could say that it counts and toggles 'leading ones' in the reversed index, parallel to the flipping of 'trailing ones' in an incremented forward index. And instead of shifting the index when counting, the toggle variable is shifted rightward. The toggle can also be used as a bitmask. I have adapted this method to my particular iteration scheme, and it works just as fine:\n\nvoid bitrev(double *real, unsigned int logN)\n{\nunsigned int i, forward, rev, toggle;\nunsigned int nodd, noddrev;               // to hold bitwise negated or odd values\nunsigned int N, halfn, quartn, nmin1;\ndouble temp;\n\nN = 1<<logN;\nhalfn = N>>1;            // frequently used 'constants'\nquartn = N>>2;\nnmin1 = N-1;\n\nforward = halfn;         // variable initialisations\nrev = 1;\n\nwhile(forward)           // start of bitreversed permutation loop, N/4 iterations\n{\n // adaptation of the traditional bitreverse update method      forward -= 2;                                         toggle = quartN;               // reset the toggle in every iteration      rev ^= toggle;                 // toggle one bit in reversed unconditionally      while(rev&toggle)              // check if more bits in reversed must be toggled      {          toggle >>= 1;          rev ^= toggle;                                 }\n\nif(forward<rev)                       // swap even and ~even conditionally\n{\ntemp = real[forward];\nreal[forward] = real[rev];\nreal[rev] = temp;\n\nnodd = nmin1 ^ forward;           // compute the bitwise negations\nnoddrev = nmin1 ^ rev;\n\ntemp = real[nodd];                // swap bitwise-negated pairs\nreal[nodd] = real[noddrev];\nreal[noddrev] = temp;\n}\n\nnodd = forward ^ 1;                   // compute the odd values from the even\nnoddrev = rev ^ halfn;\n\ntemp = real[nodd];                    // swap odd unconditionally\nreal[nodd] = real[noddrev];\nreal[noddrev] = temp;\n}\n// end of the bitreverse permutation loop\n}\n// end of bitrev function\n\nIn practical applications the bitreverse permutation will be used for complex data. For now, I am working with separate real and imaginary arrays. (I will switch to a complex datatype later.) In order to keep code transparent, I have a swap function, defined static inline.\n\nstatic inline void swap(unsigned int forward, unsigned int rev, double *real, double *im)\n{\ndouble temp;\n\ntemp = real[forward];\nreal[forward] = real[rev];\nreal[rev] = temp;\n\ntemp = im[forward];\nim[forward] = im[rev];\nim[rev] = temp;\n}\n\nvoid complexbitrev(double *real, double *im, unsigned int logN)\n{\nunsigned int i, forward, rev, zeros;\nunsigned int nodd, noddrev;        // to hold bitwise negated or odd values\nunsigned int halfn, quartn, nmin1;\n\nN = 1<<logN;\nhalfn = N>>1;            // frequently used 'constants'\nquartn = N>>2;\nnmin1 = N-1;\n\nforward = halfn;         // variable initialisations\nrev = 1;\n\nfor(i=quartn; i; i--)    // start of bitreversed permutation loop, N/4 iterations\n{\n // Gray code generator for even values:      nodd = ~i;                                  // counting ones is easier      for(zeros=0; nodd&1; zeros++) nodd >>= 1;   // find trailing zero's in i      forward ^= 2 << zeros;                      // toggle one bit of forward      rev ^= quartn >> zeros;                     // toggle one bit of rev\n\nif(forward<rev)                          // swap even and ~even conditionally\n{\nswap(forward, rev, real, im);\nnodd = nmin1 ^ forward;              // compute the bitwise negations\nnoddrev = nmin1 ^ rev;\nswap(nodd, noddrev, real, im);       // swap bitwise-negated pairs\n}\n\nnodd = forward ^ 1;                      // compute the odd values from the even\nnoddrev = rev ^ halfn;\nswap(nodd, noddrev, real, im);           // swap odd unconditionally\n}\n// end of the bitreverse permutation loop\n}\n// end of complexbitrev function\n\nWhile optimizing the bitreversal, memory access becomes more and more the factor determining processing time. After all, these samples have to be swapped no matter how. I can bitreverse-sort one million real-and-imaginary arrays of length N=1024 in some 6 seconds, on an Intel core2duo 2 GHz. That is about 6 microseconds per vector pair. That will do for the moment. I must quit this topic now. In the time that I have spent on it I could have done a zillion times zillion bitreversals with whatever wasteful routine.\n\nAt last. I can add bit-reversed sorting to my FFT routines and have intelligible output from it. I will do some plots on an upcoming page. It is cool to finally have real and imaginary output plotted. Regular analysers show amplitudes or decibels, that is fine for audio engineers, but I want to see complex numbers." ]
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https://www.researchgate.net/publication/2559820_Transducers_from_Rewrite_Rules_with_Backreferences
[ "ArticlePDF Available\n\n## Abstract\n\nContext sensitive rewrite rules have been widely used in several areas of natural language processing, including syntax, morphology, phonology and speech processing.\nProceedings of EACL '99\nTransducers from Rewrite Rules with Backreferences\nDale Gerdemann\nUniversity of Tuebingen\nK1. Wilhelmstr. 113\nD-72074 Tuebingen\ndg@sf s. nphil, uni-tuebingen,\nde\nGertjan van Noord\nGroningen University\nPO Box 716\nNL 9700 AS Groningen\nvannoord@let, rug. nl\nAbstract\nContext sensitive rewrite rules have been\nwidely used in several areas of natural\nlanguage processing, including syntax,\nmorphology, phonology and speech pro-\ncessing. Kaplan and Kay, Karttunen,\nand Mohri & Sproat have given vari-\nous algorithms to compile such rewrite\nrules into finite-state transducers. The\npresent paper extends this work by al-\nlowing a limited form of backreferencing\nin such rules. The explicit use of backref-\nerencing leads to more elegant and gen-\neral solutions.\n1 Introduction\nContext sensitive rewrite rules have been widely\nused in several areas of natural language pro-\ncessing. Johnson (1972) has shown that such\nrewrite rules are equivalent to finite state trans-\nducers in the special case that they are not al-\nlowed to rewrite their own output. An algo-\nrithm for compilation into transducers was pro-\nvided by Kaplan and Kay (1994). Improvements\nand extensions to this algorithm have been pro-\nvided by Karttunen (1995), Karttunen (1997),\nKarttunen (1996) and Mohri and Sproat (1996).\nIn this paper, the algorithm will be ex-\ntended to provide a limited form of back-\nreferencing. Backreferencing has been im-\nplicit in previous research, such as in the\n\"batch rules\" of Kaplan and Kay (1994), brack-\neting transducers for finite-state parsing (Kart-\ntunen, 1996), and the \"LocalExtension\" operation\nof Roche and Schabes (1995). The explicit use of\nbackreferencing leads to more elegant and general\nsolutions.\nBackreferencing is widely used in editors, script-\ning languages and other tools employing regular\nexpressions (Friedl, 1997). For example, Emacs\nuses the special brackets \\( and \\) to capture\nstrings along with the notation \\n to recall the nth\nsuch string. The expression \\(a*\\)b\\l matches\nstrings of the form\nanba n.\nUnrestricted use of\nbackreferencing thus can introduce non-regular\nlanguages. For NLP finite state calculi (Kart-\ntunen et al., 1996; van Noord, 1997) this is unac-\nceptable. The form of backreferences introduced\nin this paper will therefore be restricted.\nThe central case of an allowable backreference\nis:\nx ~ T(x)/A__p\n(1)\nThis says that each string x preceded by A and\nfollowed by p is replaced by T(x), where A and p\nare arbitrary regular expressions, and T is a trans-\nducer) This contrasts sharply with the rewriting\n¢ ~ ¢l:~__p\n(2)\nIn this case, any string from the language ¢ is\nreplaced by any string independently chosen from\nthe language ¢.\nWe also allow multiple (non-permuting) back-\nreferences of the form:\n~The syntax at this point is merely suggestive. As\nan example, suppose that T,c,. transduces phrases into\nacronyms. Then\nx =¢~ T=cr(x)/(abbr)__(/abbr>\nwould transduce\n<abbr>non-deterministic finite\nautomaton</abbr> into <abbr>NDFA</abbr>.\nTo compare this with a backreference in Perl,\nsuppose that T~cr is a subroutine that con-\nverts phrases into acronyms and that R~¢,. is\na regular expression matching phrases that can\nbe converted into acronyms. Then (ignoring\nthe left context) one can write something\nlike:\ns/(R~c,.)(?=(/ASBR))/T,,c~(\\$1)/ge;.\nThe backrefer-\nence variable, \\$1, will be set to whatever string R~c,.\nmatches.\n126\nProceedings of EACL '99\nxlx2.., xn ~ Tl(xl)T2(x2)...Tn(x,O/A--p (3)\nSince transducers are closed under concatenation,\nhandling multiple backreferences reduces to the\nproblem of handling a single backreference:\nx ~ (TI\" T2..... T,O(x)/A--p (4)\nA problem arises if we want capturing to fol-\nlow the POSIX standard requiring a longest-\ncapture strategy. ~riedl (1997) (p. 117), for\nexample, discusses matching the regular expres-\nsion (toltop)(olpolo)?(gicallo?logical) against the\nword: topological. The desired result is that\n(once an overall match is established) the first set\nof parentheses should capture the longest string\npossible (top); the second set should then match\nthe longest string possible from what's left (o),\nand so on. Such a left-most longest match con-\ncatenation operation is described in §3.\nIn the following section, we initially concentrate\non the simple Case in (1) and show how (1) may be\ncompiled assuming left-to-right processing along\nwith the overall longest match strategy described\nby Karttunen (1996).\nThe major components of the algorithm are\nnot new, but straightforward modifications of\ncomponents presented in Karttunen (1996) and\nMohri and Sproat (1996). We improve upon ex-\nisting approaches because we solve a problem con-\ncerning the use of special marker symbols (§2.1.2).\nA further contribution is that all steps are imple-\nmented in a freely available system, the FSA Util-\nities of van Noord (1997) (§2.1.1).\n2 The Algorithm\n2.1 Preliminary Considerations\nBefore presenting the algorithm proper, we will\ndeal with a couple of meta issues. First, we in-\ntroduce our version of the finite state calculus in\n§2.1.1. The treatment of special marker symbols\nis discussed in §2.1.2. Then in §2.1.3, we discuss\nvarious utilities that will be essential for the algo-\nrithm.\n2.1.1 FSA Utilities\nThe algorithm is implemented in the FSA Util-\nities (van Noord, 1997). We use the notation pro-\nvided by the toolbox throughout this paper. Ta-\nble 1 lists the relevant regular expression opera-\ntors. FSA Utilities offers the possibility to de-\nfine new regular expression operators. For exam-\nple, consider the definition of the nullary operator\nvowel as the union of the five vowels:\n[] empty string\n[El,... En] concatenation of E1 ... En\n{} empty language\n<El,...En} union of El,...En\nE* Kleene closure\nE ^ optionality\n-E\ncomplement\nEI-E2\ndifference\n\\$ E containment\nE1 ~\nE2 intersection\nany symbol\nA : B pair\nE1 x E2\ncross-product\nA o B composition\ndomain(E) domain of a transduction\nrange (E) range of a transduction\nident ity (E) identity transduction\ninverse (E) inverse transduction\nTable 1: Regular expression operators.\nmacro (vowel, {a, e, i,o,u}).\nIn such macro definitions, Prolog variables can be\nused in order to define new n-ary regular expres-\nsion operators in terms of existing operators. For\ninstance, the lenient_composition operator (Kart-\ntunen, 1998) is defined by:\nmacro (priorityiunion (Q ,R),\n{Q, -domain(Q) o R}).\nmacro (lenient_composition (R, C),\npriority_union(R o C,R)).\nHere, priority_union of two regular expressions\nQ and R is defined as the union of Q and the compo-\nsition of the complement of the domain of Q with\nR. Lenient composition of R and C is defined as the\npriority union of the composition of R and C (on\nthe one hand) and R (on the other hand).\nSome operators, however, require something\nmore than simple macro expansion for their def-\ninition. For example, suppose a user wanted to\nmatch n occurrences of some pattern. The FSA\nUtilities already has the '*' and '+' quantifiers,\nbut any other operators like this need to be user\ndefined. For this purpose, the FSA Utilities sup-\nplies simple Prolog hooks allowing this general\nquantifier to be defined as:\nmacro (mat chn (N, X), Regex) -\nmat ch_n (N, X, Regex).\nmatch_n(O, _X, [] ) .\nmatch_n(N,X, [XIRest]) :-\nN>O,\nN1 is N-l,\nmat ch_n (NI, X, Rest) .\n127\nProceedings of EACL '99\nFor example: match_n(3,a) is equivalent to the\nordinary finite state calculus expression [a, a, a].\nFinally, regular expression operators can be\ndefined in terms of operations on the un-\nderlying automaton. In such cases, Prolog\nhooks for manipulating states and transitions\nmay be used. This functionality has been\nused in van Noord and Gerdemann (1999) to pro-\nvide an implementation of the algorithm in\nMohri and Sproat (1996).\n2.1.2 Treatment of Markers\nPrevious algorithms for compiling rewrite\nrules into transducers have followed\nKaplan and Kay (1994) by introducing spe-\ncial marker symbols\n(markers)\ninto strings in\norder to mark off candidate regions for replace-\nment. The assumption is that these markers are\noutside the resulting transducer's alphabets. But\nprevious algorithms have not ensured that the\nassumption holds.\nThis problem was recognized by\nKarttunen (1996), whose algorithm starts with\na filter transducer which filters out any string\ncontaining a marker. This is problematic for two\nreasons. First, when applied to a string that does\nhappen to contain a marker, the algorithm will\nsimply fail. Second, it leads to logical problems in\nthe interpretation of complementation. Since the\ncomplement of a regular expression R is defined\nas E - R, one needs to know whether the marker\nsymbols are in E or not. This has not been\nWe have taken a different approach by providing\na contextual way of distinguishing markers from\nnon-markers. Every symbol used in the algorithm\nis replaced by a pair of symbols, where the second\nmember of the pair is either a 0 or a 1 depending\non whether the first member is a marker or not. 2\nAs the first step in the algorithm, O's are inserted\nafter every symbol in the input string to indicate\nthat initially every symbol is a non-marker. This\nis defined as:\nmacro (non_markers, [?, [] :0] *) .\nSimilarly, the following macro can be used to\ninsert a 0 after every symbol in an arbitrary ex-\npression E.\n2This approach is similar to the idea of laying down\ntracks as in the compilation of monadic second-order\nlogic into automata Klarlund (1997, p. 5). In fact, this\ntechnique could possibly be used for a more efficient\ntransitions over 0 and 1, one could represent the al-\nphabet as bit sequences and then add a final 0 bit for\nany ordinary symbol and a final 1 bit for a marker\nsymbol.\nmacro (non_markers (E),\nrange (E o non_markers)).\nSince E is a recognizer, it is first coerced to\nidentity(E). This form of implicit conversion is\nstandard in the finite state calculus.\nNote that 0 and 1 are perfectly ordinary alpha-\nbet symbols, which may also be used within a re-\nplacement. For example, the sequence [i,0] repre-\nsents a non-marker use of the symbol I.\n2.1.3 Utilities\nBefore describing the algorithm, it will be\nhelpful to have at our disposal a few general\ntools, most of which were described already in\nKaplan and Kay (1994). These tools, however,\nhave been modified so that they work with our\napproach of distinguishing markers from ordinary\nsymbols. So to begin with, we provide macros to\ndescribe the alphabet and the alphabet extended\nwith marker symbols:\nmacro (sig, [?, 0] ).\nmacro (xsig, [?, {0,1}] ).\nThe macro xsig is useful for defining a special-\nized version of complementation and containment:\nmacro(not (X) ,xsig* - X).\nmacro (\\$\\$ (X), [xsig*, X, xsig*] ).\nThe algorithm uses four kinds of brackets, so\nit will be convenient to define macros for each of\nthese brackets, and for a few disjunctions.\nmacro (lbl, [' <1 ', 1] )\nmacro (lb2, [' <2', 1] )\nmacro (rb2, [' 2> ', 1] )\nmacro (rbl, [' 1> ', 1] )\nmacro (lb, {lbl, lb2})\nmacro (rb, {rbl ,rb2})\nmacro (bl, {lbl, rbl})\nmacro (b2, {lb2, rb2})\nmacro (brack, {lb, rb}).\nAs in Kaplan & Kay, we define an Intro(S) op-\nerator that produces a transducer that freely in-\ntroduces instances of S into an input string. We\nextend this idea to create a family of Intro oper-\nators. It is often the case that we want to freely\nintroduce marker symbols into a string at any po-\nsition\nexcept\nthe beginning or the end.\n%% Free introduction\nmacro(intro(S) ,{xsig-S, [] x S}*) .\n~.7. Introduction, except at begin\nmacro (xintro (S) , ( [] , [xsig-S, intro (S) ] }) .\n°/.~. Introduction, except at end\nmacro (introx (S) , ( [] , [intro (S) , xsig-S] }) .\n128\nProceedings of EACL '99\n%% Introduction, except at begin & end\nmacro (xintrox (S), { [], [xsig-S] ,\n[xsig-S, intro (S), xsig-S] }).\nThis family of Intro operators is useful for defin-\ning\na family of Ignore operators:\nmacro( ign( E1,S),range(E1 o intro(S))).\nmacro(xign(El,S) ,range(E1 o xintro(S))).\nmacro( ignx(E1,S),range(E1 o introx(S))).\nmacro (xigax (El, S), range (El o xintrox (S)) ).\nIn order to create filter transducers to en-\nsure that markers are placed in the correct po-\nsitions, Kaplan & Kay introduce the operator\nP-iff-S(L1,L2). A string is described by this\nexpression iff each prefix in L1 is followed by a\nsuffix in L2 and each suffix in L2 is preceded by a\nprefix in L1. In our approach, this is defined as:\nmacro(if_p then s(L1,L2),\nnot(\niLl\n,not (L2) ] )).\nmacro (if s then_p (L1,L2),\nnot ( [not (al), L2] ) ).\nmacro (p_iff_s (LI, L2),\nif_p_then_s (LI, L2)\nif_s_then_p (LI ,L2) ).\nTo make the use ofp_iff_s more convenient, we\nintroduce a new operator l_if f_r (L, R), which de-\nscribes strings where every string position is pre-\nceded by a string in L just in case it is followed by\na string in R:\nmacro (l_iff_r (L ,R),\np_iff_s([xsig*,L] , [R,xsig*])) .\nFinally, we introduce a new operator\nif (Condit ion, Then, Else) for conditionals.\nThis operator is extremely useful, but in order\nfor it to work within the finite state calculus, one\nneeds a convention as to what counts as a boolean\ntrue or false for the condition argument. It is\npossible to define true as the universal language\nand false as\nthe empty language:\nmacro(true,? *). macro(false,{}).\nWith these definitions, we can use the comple-\nment operator as negation, the intersection opera-\ntor as conjunction and the union operator as dis-\njunction. Arbitrary expressions may be coerced\nto booleans\nusing\nthe following macro:\nmacro (coerce_t oboolean (E),\nrange(E o (true x true))).\nHere, E should describe a recognizer. E is com-\nposed with the universal transducer, which trans-\nduces from anything (?*) to anything (?*). Now\nwith this background, we can define the condi-\ntionah\nmacro ( if (Cond, Then, Else),\n{ coerce_to_boolean(Cond) o Then,\n-coerce_to_boolean(Cond) o Else\n}).\n2.2 Implementation\nA rule of the form\nx ~ T(x)/A__p\nwill be written\nas replace(T,Lambda,Rho). Rules of the more\ngeneral form\nxl ...z,, ~ Tl(xl)...T,~(Xn)/A_-p\nwill be discussed in §3. The algorithm consists\nof nine steps composed as in figure 1.\nThe names of these steps are mostly\nderived from Karttunen (1995) and\nMohri and Sproat (1996) even though the\ntransductions involved are not exactly the same.\nIn particular, the steps derived from Mohri &\nSproat (r, f, 11 and 12) will all be defined in\nterms of the finite state calculus as opposed to\nMohri & Sproat's approach of using low-level\nmanipulation of states and transitions, z\nThe first step, non_markers, was already de-\nfined above. For the second step, we first consider\na simple special case. If the empty string is in\nthe language described by Right, then r(Right)\nshould insert an rb2 in every string position. The\ndefinition of r(Right) is both simpler and more\nefficient if this is treated as a special case. To in-\nsert a bracket in every possible string position, we\nuse:\n[[[] x rb2,sig]*,[] x rb2]\nIf the empty string is not in Right, then we\nmust use intro(rb2) to introduce the marker\nrb2, fol]owed by l_iff_r to ensure that such\nmarkers are immediately followed by a string in\nRight, or more precisely a string in Right where\nadditional instances of rb2 are freely inserted in\nany position other than the beginning. This ex-\npression is written as:\nintro (rb2)\no\ni_ if f _r (rb2, xign (non_markers (Right) , rb2) )\nPutting these two pieces together with the con-\nditional yields:\nmacro (r (R),\nif([] ~ R, % If: [] is in R:\n[[[] x rb2,sig]*,[] x rb2],\nintro (rb2) % Else:\no\nl_iff_r (rb2, xign (non_markers (R) , rb2) ) ) ) .\nThe third step,\nf(domain(T))\nis implemented\nas:\n3The alternative implementation is provided in\nvan Noord and Gerdemann (1999).\n129\nmacro(replace(T,Left,Right),\nnon_markers\n0\nr(Right)\n0\nf(domain(T))\n0\nleft_toright (domain(T))\n0\nlongest_match(domain(T))\n0\naux_replace(T)\n0\nll(Left)\n0\n12(Left)\nO\ninverse(non_markers)).\nProceedings of EACL '99\n% introduce 0 after every symbol\n% (a b c => a 0 b 0 c 0).\n% introduce rb2 before any string\n% in Right.\n% introduce ib2 before any string in\n% domain(T) followed by rb2.\n% ib2 ... rb2 around domain(T) optionally\n% replaced by Ibl ... rbl\n% filter out non-longest matches marked\n% in previous step.\n% perform T's transduction on regions marked\n% off by bl's.\n% ensure that Ibl must be preceded\n% by a string in Left.\n% ensure that Ib2 must not occur preceded\n% by a string in Left.\n% remove the auxiliary O's.\nFigure 1: Definition of replace operator.\nmacro (f (Phi), intro (lb2)\nO\nl_iff_r (Ib2, [xignx (non_markers (Phi), b2),\nlb2\", rb2] ) ).\nThe lb2 is first introduced and then, using\nt_i f f_.r, it is constrained to occur immediately be-\nfore every instance of (ignoring complexities) Phi\nfollowed by an rb2. Phi needs to be marked as\nnormal text using non_markers and then xign_x\nis used to allow freely inserted lb2 and rb2 any-\nwhere except at the beginning and end. The fol-\nlowing lb2\" allows an optional lb2, which occurs\nwhen the empty string is in Phi.\nThe fourth step is a guessing component which\n(ignoring complexities) looks for sequences of the\nform lb2 Phi rb2 and converts some of these\ninto lbl Phi rbl, where the bl marking indicates\nthat the sequence is a candidate for replacement.\nThe complication is that Phi, as always, must\nbe converted to non_markers (Phi) and instances\nof b2 need to be ignored. Furthermore, between\npairs of lbl and rbl, instances of lb2 are deleted.\nThese lb2 markers have done their job and are\nno longer needed. Putting this all together, the\ndefinition is:\nmacro (left_to_right (Phi),\n[ [xsig*,\nlib2 x ibl,\n( ign (non_markers (Phi) , b2)\nO\ninverse (intro (ib2))\n),\nrb2 x rbl]\n]*, xsig*]).\nThe fifth step filters out non-longest matches\nproduced in the previous step. For example (and\nsimplifying a bit), if Phi is ab*, then a string of\nthe form ... rbl a b Ibl b ... should be ruled out\nsince there is an instance of Phi (ignoring brackets\nexcept at the end) where there is an internal Ibl.\nThis is implemented as:~\nmacro (longest_mat ch (Phi),\nnot (\\$\\$ ( [lbl,\n(ignx (non_markers (Phi) , brack)\n\\$\\$(rbl)\n), % longer match must be\nrb % followed by an rb\n])) % so context is ok\n0\n~, done with rb2, throw away:\ninverse (intro (rb2)) ) .\nThe sixth step performs the transduction de-\nscribed by\nT.\nThis step is straightforwardly imple-\nmented, where the main difficulty is getting T to\napply to our specially marked string:\nmacro (aux_replace (T),\n{{sig, Ib2},\n[Ibl,\ninverse (non_markers)\n4The line with \\$\\$ (rbl) (:an be oI)ti-\nmized a bit: Since we know that an rbl\nmust be preceded by Phi, we can write!\n[ign_ (non_markers (Phi) , brack) , rb 1, xs ig*] ).\nThis may lead to a more constrained (hence smaller)\ntransducer.\n130\nProceedings of EACL '99\noTo\nnon_markers,\nrbl x []\n]\n}*).\nThe seventh step ensures that lbl is preceded\nby a string in Left:\nmacro\n(ii (L),\nign ( if _s_then p (\nignx ( [xsig*, non_markers (L) ], lbl),\n[lbl,xsig*] ),\nib2)\nO\ninverse (intro (ib i) ) ).\nThe eighth step ensures that ib2 is not preceded\nby a string in Left. This is implemented similarly\nto the previous step:\nmacro\n(12 (L),\nif_s_then_p (\nignx (not ( [xsig*,non_markers (L) ] ), lb2),\n[lb2, xsig*] )\n0\ninverse\n( intro (lb2) ) ).\nFinally the ninth step, inverse (non_markers),\nremoves \"the O's so that the final result in not\nmarked up in any special way.\n3 Longest Match Capturing\nAs discussed in §1 the POSIX standard requires\nthat multiple captures follow a longest match\nstrategy. For multiple captures as in (3), one es-\ntablishes first a longest match for domain(T1).\n.... domain( T~ ). Then we ensure that each of\ndomain(Ti) in turn is required to match as long\nas possible, with each one having priority over its\nrightward neighbors. To implement this, we define\na macro lm_concat(Ts) and use it as:\nreplace (lm_concat (Ts), Left, Right)\nEnsuring the longest overall match is delegated\nto the replace macro, so lm_concat(Ts) needs\nonly ensure that each individual transducer within\nTs gets its proper left-to-right longest matching\npriority. This problem is mostly solved by the\nsame techniques used to ensure the longest match\nwithin the replace macro. The only complica-\ntion here is that Ts can be of unbounded length.\nSo it is not possible to have a single expression in\nthe finite state calculus that applies to all possi-\nble lenghts. This means that we need something\na little more powerful than mere macro expan-\nsion to construct the proper finite state calculus\nexpression. The FSA Utilities provides a Prolog\nhook for this purpose. The resulting definition of\nlm_concat is given in figure 2.\nSuppose (as in Friedl (1997)), we want to match\nthe following list of recognizers against the string\ntopological\nand insert a marker in each bound-\nary position. This reduces to applying:\nim_concat\n(\n[\n[{[t,o],[t,o,p]},[] : '#'],\n[{o,[p,o,l,o]},[]: '#'],\n{ [g,i,c,a,l], [o',l,o,g,i,c,a,l] }\n])\nThis expression transduces the string\ntopological\nonly to the string top#o#1ogical. 5\n4 Conclusions\nThe algorithm presented here has extended previ-\nous algorithms for rewrite rules by adding a lim-\nited version of backreferencing. This allows the\noutput of rewriting to be dependent on the form of\nthe strings which are rewritten. This new feature\nbrings techniques used in Perl-like languages into\nthe finite state calculus. Such an integration is\nneeded in practical applications where simple text\nprocessing needs to be combined with more so-\nphisticated computational linguistics techniques.\nOne particularly interesting example where\nbackreferences are essential is cascaded determin-\nistic (longest match) finite state parsing as de-\nscribed for example in Abney (Abney, 1996) and\nvarious papers in (Roche and Schabes, 1997a).\nClearly, the standard rewrite rules do not apply in\nthis domain. If NP is an NP recognizer, it would\nnot do to.say NP ~ [NP]/A_p. Nothing would\nforce the string matched by the NP to the left of\nthe arrow to be the same as the string matched\nby the NP to the right of the arrow.\nOne advantage of using our algorithm for fi-\nnite state parsing is that the left and right con-\ntexts may be used to bring in top-down filter-\ning. 6 An often cited advantage of finite state\n5An anonymous reviewer suggested theft\nlm_concat\ncould be implemented in the frame-\nwork of Karttunen (1996) as:\n[toltoplolpolo]-+... #;\nIndeed the resulting transducer from this expression\nwould transduce topological into top#o#1ogical.\nBut unfortunately this transducer would also trans-\nduce polotopogical into polo#top#o#gical, since\nthe notion of left-right ordering is lost in this expres-\nsion.\n6The bracketing operator of Karttunen (1996), on\nthe other hand, does not provide for left and right\ncontexts.\n131\nProceedings of EACL '99\nmacro(im_concat(Ts),mark_boundaries(Domains) o ConcatTs):-\ndomains(Ts,Domains), concatT(Ts,ConcatTs).\ndomains([],[]).\ndomains([FIRO],[domain(F) IR]):- domains(RO,R).\nconcatT([],[]).\nconcatT([TlTs], [inverse(non_markers) o T,ibl x []IRest]):- concatT(Ts,Rest).\n%% macro(mark_boundaries(L),Exp): This is the central component of im_concat. For our\n%% \"toplological\" example we will have:\n%% mark_boundaries ([domain( [{ [t, o] , [t, o ,p] }, [] : #] ),\n%% domain([{o,[p,o,l,o]},[]: #]),\n%% domain({ [g,i, c,a, i] , [o^,l,o,g,i,c,a,l] })])\n%% which simplifies to:\n%% mark_boundaries([{[t,o],[t,o,p]}, {o,[p,o,l,o]}, {[g,i,c,a,l],[o^,l,o,g,i,c,a,l]}]).\n%% Then by macro expansion, we get:\n%% [{[t,o], [t,o,p]} o non_markers,[]x ibl,\n%% {o,[p,o,l,o]} o non_markers,[]x ibl,\n%% {[g,i,c,a,l],[o',l,o,g,i,c,a,l]} o non_markers,[]x ibl]\n%%\no\n%%\n%\nFilter i: {[t,o],[t,o,p]} gets longest match\n%%\n-\n[ignx_l(non_markers({ [t,o] , [t,o,p] }),ibl) ,\n%% ign(non_markers({o, [p,o,l,o] }) ,ibl) ,\n%% ign(non_markers({ [g,i,c,a,l] , [o^,l,o,g,i,c,a,l] }) ,ibl)]\n%%\no\n%% % Filter 2: {o,[p,o,l,o]} gets longest match\n%%\n~\n[non_markers ({ [t, o] , [t, o, p] }) , Ib i,\n%% ignx_l(non_markers ({o, [p,o,l,o] }) ,ibl),\n%% ign(non_markers({ [g, i,c,a,l] , [o',l,o,g,i,c,a,l] }) ,ibl)]\nmacro(mark_boundaries(L),Exp):-\nboundaries(L,ExpO), % guess boundary positions\ngreed(L,ExpO,Exp). % filter non-longest matches\nboundaries([],[]).\nboundaries([FIRO],[F o non_markers, [] x ibl ]R]):- boundaries(RO,R).\ngreed(L,ComposedO,Composed) :-\naux_greed(L,[],Filters), compose_list(Filters,ComposedO,Composed).\naux_greed([HIT],Front,Filters):- aux_greed(T,H,Front,Filters,_CurrentFilter).\naux_greed([],F,_,[],[ign(non_markers(F),Ibl)]).\naux_greed([HlRO],F,Front,[-LiIR],[ign(non_markers(F),ibl)IRl]) \"-\nappend(Front,[ignx_l(non_markers(F),Ibl)IRl],Ll),\nappend(Front,[non_markers(F),ibl],NewFront),\naux_greed(RO,H,NewFront,R,Rl).\n%% ignore at least one instance of E2 except at end\nmacro(ignx_l(E1,E2), range(El o [[? *,[] x E2]+,? +])).\ncompose_list([],SoFar,SoFar).\ncompose_list([FlR],SoFar,Composed):- compose_list(R,(SoFar o F),Composed).\nFigure 2: Definition of lm_concat operator.\n132\nProceedings of EACL '99\nparsing is robustness. A constituent is found bot-\ntom up in an early level in the cascade even if\nthat constituent does not ultimately contribute\nto an S in a later level of the cascade. While\nthis is undoubtedly an advantage for certain ap-\nplications, our approach would allow the intro-\nduction of some top-down filtering while main-\ntaining the robustness of a bottom-up approach.\nA second advantage for robust finite state pars-\ning is that bracketing could also include the no-\ntion of \"repair\" as in Abney (1990). One might,\nfor example, want to say something like:\nxy\n[NP\nRepairDet(x) RepairN(y) ]/)~__p 7\nso that an\nNP\ncould be parsed as a slightly malformed\nDet\nfollowed by a slightly malformed N. RepairDet\nand RepairN, in this example, could be doing a\nvariety of things such as: contextualized spelling\ncorrection, reordering of function words, replace-\nment of phrases by acronyms, or any other oper-\nation implemented as a transducer.\nFinally, we should mention the problem of com-\nplexity. A critical reader might see the nine steps\nin our algorithm and conclude that the algorithm\nis overly complex. This would be a false conclu-\nsion. To begin with, the problem itself is complex.\nIt is easy to create examples where the resulting\ntransducer created by any algorithm would be-\ncome unmanageably large. But there exist strate-\ngies for keeping the transducers smaller. For ex-\nample, it is not necessary for all nine steps to\nbe composed. They can also be cascaded. In\nthat case it will be possible to implement different\nsteps by different strategies, e.g. by determinis-\ntic or non-deterministic transducers or bimachines\n(Roche and Schabes, 1997b). The range of possi-\nbilities leaves plenty of room for future research.\nReferences\nSteve Abney. 1990. Rapid incremental parsing\nwith repair. In\nProceedings of the 6th New OED\nConference: Electronic Text Rese arch,\npages\n1-9.\nSteven Abney. 1996. Partial parsing via finite-\nProceedings of the ESSLLI\n'96 Robust Parsing Workshop.\n.Jeffrey Friedl. 1997.\nMastering Regular Expres-\nsions.\nO'Reilly & Associates, Inc.\nC. Douglas Johnson. 1972.\nFormal Aspects\nof Phonological Descriptions.\nMouton, The\nHague.\n7The syntax here has been simplified. The rule\nshould be understood as: replace(lm_concat([[]:'[np',\nrepair_det, repair_n, []:']'],lambda, rho).\nRonald Kaplan and Martin Kay. 1994. Regular\nmodels of phonological rule systems.\nComputa-\ntional Linguistics,\n20(3):331-379.\nL. Karttunen, J-P. Chanod, G. Grefenstette, and\nA. Schiller. 1996. Regular expressions for lan-\nguage engineering.\nNatural Language Engineer-\ning,\n2(4):305-238.\nLauri Karttunen. 1995. The replace operator.\nIn\n33th Annual Meeting of the Association for\nComputational Linguistics,\nM.I.T. Cambridge\nMass.\nLauri Karttunen. 1996. Directed replacement.\nIn\n34th Annual Meeting of the Association for\nComputational Linguistics,\nSanta Cruz.\nLauri Karttunen. 1997. The replace operator.\nIn Emannual Roche and Yves Schabes, editors,\nFinite-State Language Processing,\npages 117-\nLauri Karttunen. 1998. The proper treatment\nof optimality theory in computational phonol-\nogy. In\nFinite-state Methods in Natural Lan-\nguage Processing,\npages 1-12, Ankara, June.\nNils Klarlund. 1997. Mona & Fido: The logic\nautomaton connection in practice. In\nCSL '97.\nMehryar Mohri and Richard Sproat. 1996. An\nefficient compiler for weighted rewrite rules.\nIn\n3~th Annual Meeting of the Association for\nComputational Linguistics,\nSanta Cruz.\nEmmanuel Roche and Yves Schabes. 1995. De-\nterministic part-of-speech tagging with finite-\nstate transducers.\nComputational Linguistics,\n21:227-263. Reprinted in Roche & Schabes\n(1997).\nEmmanuel Roche and Yves Schabes, editors.\n1997a.\nFinite-State Language Processing.\nMIT\nPress, Cambridge.\nEmmanuel Roche and Yves Schabes. 1997b. In-\ntroduction. In Emmanuel Roche and Yves Sch-\nabes, editors,\nFinite-State Language Processing.\nMIT Press, Cambridge, Mass.\nGertjan van Noord and Dale Gerdemann. 1999.\nAn extendible regular expression compiler for\nfinite-state approaches in natural language pro-\ncessing. In\nWorkshop on Implementing Au-\ntomata 99,\nPotsdam Germany.\nGertjan van Noord. 1997. Fsa utilities.\nThe\nFSA Utilities\ntoolbox is available free of\ncharge under Gnu General Public License at\nhttp://www.let.rug.nl/-vannoord/Fsa/.\n133" ]
[ null ]
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https://www.freetutes.com/systemanalysis/sa9-measurement-sqa.html
[ "", null, "Other Tutorials by Freetutes.com\n\nVisual Basic - Visual Basic tutorials\n\nVB6 beginners tutorial - Learn VB6\n\nYou are here: Freetutes.com > Systems Analysis and Design\n\n# Measurement - Software Quality Assurance Activities\n\nEarlier in this chapter we discussed what is the objective and meaning of the quality with respect to software development. We defined a set of qualitative factors of the software quality measurement. Since there is no such thing as absolute knowledge we can’t expect to measure software quality exactly. Therefore SQ metrics is developed and employed to figure out the measure, content of the quality. A set of software metrics is applied to the quantitative assessment of software quality. In all cases these metrics use indirect measures therefore quality as such in itself is never measured but rather some manifestation of it.\n\nThere are a number of software quality indicators that are based on the measurable design characteristics of a computer program. Design structural quality index (DSQI) is one such measure. The following values must be ascertained to compute the DSQI\n\nS1 = the total number of modules defined in the program architecture\n\nS2 = the number of modules whose correct function depends on the source of data input or that produces data to be used elsewhere {in general control modules (among others) would not be counted as part of S2}\n\nS3 = the number of modules whose correct function depends on prior processing\n\nS4 = the number of database items (includes data objects and all attributes that define objects)\n\nS5 = the total number of unique database items\n\nS6 = the number of database segments ( different records or individual objects)\n\nS7 = the number of modules with a single entry and exit ( exception processing is not considered to be a multiple exit)\n\nWhen all these values are determined for a computer program, the following intermediate values can be computed:\n\nProgram structure: D1, where D1 is defined as follows:\n\nIf the architectural design was developed using a distinct method( e.g., data flow-oriented design or object oriented design), then D1 = 1; otherwise D1 = 0.\n\nModule independence: D2 = 1 -(S2/S1)\n\nModule not dependent on prior processing: D3 = 1- (S3/S1)\n\nDatabase size : D4 = 1- (S5/S4)\n\nDatabase compartmentalization: D5 = 1- (S6/S4)\n\nModule entrance/exit characteristic: D6 = 1- (S7/S1)\n\nWith the intermediate values determined, the DSQI is computed in the following manner: DSQI = Swi Di\n\nWhere i = 1 to 6, wi is the relative weighting of the importance of each of the intermediate values, and Swi = 1 ( if all Di are weighted equally, then wi = 0.167).\n\nThe value of DSQI for past designs can be determined and compared to a design that is currently under development. If the DSQI is significantly lower than average, further design work and review is indicated. Similarly, if major changes are to be made to an existing design, the effect of those changes on DSQI can be calculated.\n\nIEEE Standard 982.1-1988 suggests a software maturity index (SMI) that provides an indication of the stability of a software product ( based on changes that occur for each release of the product). The following information is determined:\n\nMT = the number of modules in the current release\n\nFc = the number of modules in the current release that have been changed\n\nFa = the number of modules in the current release that have been added\n\nFd = the number of modules from the preceding release that were deleted in the current release\n\nThe software maturity index is computed as :", null, "As SMI approaches 1.0, the product begins to stabilize" ]
[ null, "https://www.freetutes.com/logo.gif", null, "https://www.freetutes.com/systemanalysis/images/smi.jpg", null ]
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https://www.colorhexa.com/032c60
[ "# #032c60 Color Information\n\nIn a RGB color space, hex #032c60 is composed of 1.2% red, 17.3% green and 37.6% blue. Whereas in a CMYK color space, it is composed of 96.9% cyan, 54.2% magenta, 0% yellow and 62.4% black. It has a hue angle of 213.5 degrees, a saturation of 93.9% and a lightness of 19.4%. #032c60 color hex could be obtained by blending #0658c0 with #000000. Closest websafe color is: #003366.\n\n• R 1\n• G 17\n• B 38\nRGB color chart\n• C 97\n• M 54\n• Y 0\n• K 62\nCMYK color chart\n\n#032c60 color description : Very dark blue.\n\n# #032c60 Color Conversion\n\nThe hexadecimal color #032c60 has RGB values of R:3, G:44, B:96 and CMYK values of C:0.97, M:0.54, Y:0, K:0.62. Its decimal value is 207968.\n\nHex triplet RGB Decimal 032c60 `#032c60` 3, 44, 96 `rgb(3,44,96)` 1.2, 17.3, 37.6 `rgb(1.2%,17.3%,37.6%)` 97, 54, 0, 62 213.5°, 93.9, 19.4 `hsl(213.5,93.9%,19.4%)` 213.5°, 96.9, 37.6 003366 `#003366`\nCIE-LAB 18.649, 9.523, -34.578 3.049, 2.665, 11.419 0.178, 0.156, 2.665 18.649, 35.865, 285.398 18.649, -9.703, -38.3 16.325, 4.771, -30.047 00000011, 00101100, 01100000\n\n# Color Schemes with #032c60\n\n• #032c60\n``#032c60` `rgb(3,44,96)``\n• #603703\n``#603703` `rgb(96,55,3)``\nComplementary Color\n• #035b60\n``#035b60` `rgb(3,91,96)``\n• #032c60\n``#032c60` `rgb(3,44,96)``\n• #080360\n``#080360` `rgb(8,3,96)``\nAnalogous Color\n• #5b6003\n``#5b6003` `rgb(91,96,3)``\n• #032c60\n``#032c60` `rgb(3,44,96)``\n• #600803\n``#600803` `rgb(96,8,3)``\nSplit Complementary Color\n• #2c6003\n``#2c6003` `rgb(44,96,3)``\n• #032c60\n``#032c60` `rgb(3,44,96)``\n• #60032c\n``#60032c` `rgb(96,3,44)``\n• #036037\n``#036037` `rgb(3,96,55)``\n• #032c60\n``#032c60` `rgb(3,44,96)``\n• #60032c\n``#60032c` `rgb(96,3,44)``\n• #603703\n``#603703` `rgb(96,55,3)``\n• #010a16\n``#010a16` `rgb(1,10,22)``\n• #01152f\n``#01152f` `rgb(1,21,47)``\n• #022147\n``#022147` `rgb(2,33,71)``\n• #032c60\n``#032c60` `rgb(3,44,96)``\n• #043779\n``#043779` `rgb(4,55,121)``\n• #054391\n``#054391` `rgb(5,67,145)``\n• #054eaa\n``#054eaa` `rgb(5,78,170)``\nMonochromatic Color\n\n# Alternatives to #032c60\n\nBelow, you can see some colors close to #032c60. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #034360\n``#034360` `rgb(3,67,96)``\n• #033c60\n``#033c60` `rgb(3,60,96)``\n• #033460\n``#033460` `rgb(3,52,96)``\n• #032c60\n``#032c60` `rgb(3,44,96)``\n• #032460\n``#032460` `rgb(3,36,96)``\n• #031d60\n``#031d60` `rgb(3,29,96)``\n• #031560\n``#031560` `rgb(3,21,96)``\nSimilar Colors\n\n# #032c60 Preview\n\nThis text has a font color of #032c60.\n\n``<span style=\"color:#032c60;\">Text here</span>``\n#032c60 background color\n\nThis paragraph has a background color of #032c60.\n\n``<p style=\"background-color:#032c60;\">Content here</p>``\n#032c60 border color\n\nThis element has a border color of #032c60.\n\n``<div style=\"border:1px solid #032c60;\">Content here</div>``\nCSS codes\n``.text {color:#032c60;}``\n``.background {background-color:#032c60;}``\n``.border {border:1px solid #032c60;}``\n\n# Shades and Tints of #032c60\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000001 is the darkest color, while #edf5fe is the lightest one.\n\n• #000001\n``#000001` `rgb(0,0,1)``\n• #010914\n``#010914` `rgb(1,9,20)``\n• #011227\n``#011227` `rgb(1,18,39)``\n• #021b3a\n``#021b3a` `rgb(2,27,58)``\n• #02234d\n``#02234d` `rgb(2,35,77)``\n• #032c60\n``#032c60` `rgb(3,44,96)``\n• #043573\n``#043573` `rgb(4,53,115)``\n• #043d86\n``#043d86` `rgb(4,61,134)``\n• #054699\n``#054699` `rgb(5,70,153)``\n• #054fac\n``#054fac` `rgb(5,79,172)``\n• #0658bf\n``#0658bf` `rgb(6,88,191)``\n• #0760d2\n``#0760d2` `rgb(7,96,210)``\n• #0769e5\n``#0769e5` `rgb(7,105,229)``\n• #0972f7\n``#0972f7` `rgb(9,114,247)``\n• #1c7df8\n``#1c7df8` `rgb(28,125,248)``\n• #2f88f8\n``#2f88f8` `rgb(47,136,248)``\n• #4293f9\n``#4293f9` `rgb(66,147,249)``\n• #559dfa\n``#559dfa` `rgb(85,157,250)``\n• #68a8fa\n``#68a8fa` `rgb(104,168,250)``\n• #7bb3fb\n``#7bb3fb` `rgb(123,179,251)``\n• #8ebefb\n``#8ebefb` `rgb(142,190,251)``\n• #a1c9fc\n``#a1c9fc` `rgb(161,201,252)``\n• #b4d4fd\n``#b4d4fd` `rgb(180,212,253)``\n• #c7dffd\n``#c7dffd` `rgb(199,223,253)``\n• #daeafe\n``#daeafe` `rgb(218,234,254)``\n• #edf5fe\n``#edf5fe` `rgb(237,245,254)``\nTint Color Variation\n\n# Tones of #032c60\n\nA tone is produced by adding gray to any pure hue. In this case, #313132 is the less saturated color, while #032c60 is the most saturated one.\n\n• #313132\n``#313132` `rgb(49,49,50)``\n• #2d3136\n``#2d3136` `rgb(45,49,54)``\n• #29313a\n``#29313a` `rgb(41,49,58)``\n• #25303e\n``#25303e` `rgb(37,48,62)``\n• #213042\n``#213042` `rgb(33,48,66)``\n• #1e2f45\n``#1e2f45` `rgb(30,47,69)``\n• #1a2f49\n``#1a2f49` `rgb(26,47,73)``\n• #162e4d\n``#162e4d` `rgb(22,46,77)``\n• #122e51\n``#122e51` `rgb(18,46,81)``\n• #0e2d55\n``#0e2d55` `rgb(14,45,85)``\n• #0b2d58\n``#0b2d58` `rgb(11,45,88)``\n• #072c5c\n``#072c5c` `rgb(7,44,92)``\n• #032c60\n``#032c60` `rgb(3,44,96)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #032c60 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
[ null ]
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https://machinelearningknowledge.ai/matplotlib-scatter-plot-complete-tutorial/
[ "# Matplotlib Scatter Plot – Complete Tutorial for Beginners\n\n## Introduction\n\nA lot of times we are required to present results in the form of visualizations that are easy to build and conveys a good amount of information. In this article, we will go through Matplotlib scatter plot tutorial, with practical hands-on of creating different types of scatter plots with several features. We will cover those examples of scattere plot in matplotlib that you may not have usually seen.\n\n### Importing Matplotlib Library\n\nBefore starting to plot different values, we’ll need the Matplotlib Library. So let’s import Matplotlib\n\nIn :\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n\n## Matplotlib Scatter Plot\n\nA Scatter Plot is used for plotting two different sets of values, helping in finding out correlation amongst the values.\n\nThe following section tells about the syntax of the scatter plot function.\n\n### Syntax\n\nmatplotlib.pyplot.scatter(x, y, s=None, c=None, marker=None, cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None edgecolors=None, *, plotnonfinite=False, data=None, **kwargs)\n\n• x,y : Float or array-like, shape(n,) – These are the two sets of values provided to the scatter function for plotting.\n• s : Float or array-like, shape(n,) – This parameter specifies the size of the marker\n• c : Array-like or List of Color or Color – This specifies the color of the marker\n• marker : MarkerStyle – For setting the marker style, this parameter comes handy\n• cmap : str or Colormap, default: ‘viridis’ – Used when we provide c an array of floats\n• norm : Normalize, default: None – It helps in normalization of color data for the c.\n• vmin, vmax : Float, default: None – When norm is given these parameters aren’t used, but otherwise they help in mapping of color array c to colormap cmap.\n• alpha : Float, default: None – It’s a blending value where the range is between 0(transparent) and 1(opaque).\n• lindwidths : Float or array-like, default:1.5 – The linewidth of marker is set using this parameter.\n• edgecolors : {‘face’,’none’, None} or Color or Color Sequence – The edge color of the marker is set with this parameter. With ‘face’, the edge color will always be same as face color. With ‘none’, No patch boundary will be drawn.\n\nThe function returns a plot with desired axes and other parameters.\n\n### Example 1: Simple Scatter Plot\n\nThis first example is a simple scatter plot that uses randomly generated data.\n\nThe data is generated using numpy’s random seed function which helps in generating pseudo numbers.\n\nThe color and size of the markers(dots) is decided by the random number they represent.\n\nThe scatter function is provided with the data points through ‘x’ and ‘y’ parameter. The ‘s’ and ‘c’ parameters specify the size and color of the markers. Lastly, the ‘alpha’ parameter is used for increasing the transparency of the markers. The range of alpha parameter ranges from 0 to 1.\n\nThe cmap or colormap parameter is used for giving different colors to the markers.\n\nIn :\nnp.random.seed(11808096)\n\nN = 75\nx = np.random.rand(N)\ny = np.random.rand(N)\ncolors = np.random.rand(N)\narea = (25 * np.random.rand(N))**2\n\nplt.scatter(x, y, s=area, c=colors, cmap = 'Spectral_r', alpha=0.9)\nplt.show()\n\nOutput:", null, "### Example 2: Scatter Plot Masked\n\nIn this sort of example, some of the data points are masked(hidden) and there is a line been made for demarking the masked regions.\n\nIn masked scatter plot, we create a boundary in which the data points are represented differently (masked) and other data points are represented differently.\n\nThe scatter function is called for both the areas. To make the two regions standout, there is a boundary created with the help of plt.plot function.\n\nTo determine the angle of the boundary, numpy’s arange function is used.\n\nIn :\nnp.random.seed(11808096)\n\nN = 75\nr0 = 0.5\nx = 0.9 * np.random.rand(N)\ny = 0.9 * np.random.rand(N)\narea = (30 * np.random.rand(N))**2\nc = np.sqrt(area)\nr = np.sqrt(x ** 2 + y ** 2)\n\n# Defining the two different areas\narea1 = np.ma.masked_where(r < r0, area)\narea2 = np.ma.masked_where(r >= r0, area)\nplt.scatter(x, y, s=area1, marker='o', c=c, cmap= 'gist_rainbow_r')\nplt.scatter(x, y, s=area2, marker='*', c=c, cmap= 'tab20_r')\n\n# Code for building a boundary between the regions\ntheta = np.arange(0, np.pi / 2, 0.01)\nplt.plot(r0 * np.cos(theta), r0 * np.sin(theta))\n\nplt.show()\n\nOutput:", null, "### Example 3: Scatter Plot with Pie Chart Markers\n\nIn this type of scatter plot, the markers are made in the form of pie chart that depict an extra information about the data.\n\nFor the 3rd example, we’ll be combining two different plots into a single plot for conveying more information. In the previous example, the markers made for scatter plots were simple dots that presented a value, but here the markers is represented with the help of pie charts.\n\nInitially, we define the ratios for the radii of the pie chart markers. After this, we randomly provide the relative sizes for the pie charts in the form of an array. After this, the pie chart sections are created with the help of numpy’s sin and cos functions.\n\nThe penultimate step is to call the subplots function for plotting the pie chart along with the scatter plot. At last, the scatter function is called for building the scatter plot with pie charts as markers.\n\nIn :\n# Defining the ratios for radius of pie chart markers\nr1 = 0.2 # 20%\nr2 = r1 + 0.2 # 40%\nr3 = r2 + 0.4 # 80%\n\n# define some sizes of the scatter marker\nsizes = np.array([45, 90, 135, 180, 225, 270, 315, 360])\n\n# calculate the points of the first pie marker\n# these are just the origin (0, 0) + some (cos, sin) points on a circle\nx1 = np.cos(2 * np.pi * np.linspace(0, r1))\ny1 = np.sin(2 * np.pi * np.linspace(0, r1))\nxy1 = np.row_stack([[0, 0], np.column_stack([x1, y1])])\ns1 = np.abs(xy1).max()\n\nx2 = np.cos(2 * np.pi * np.linspace(r1, r2))\ny2 = np.sin(2 * np.pi * np.linspace(r1, r2))\nxy2 = np.row_stack([[0, 0], np.column_stack([x2, y2])])\ns2 = np.abs(xy2).max()\n\nx3 = np.cos(2 * np.pi * np.linspace(r2, r3))\ny3 = np.sin(2 * np.pi * np.linspace(r2, r3))\nxy3 = np.row_stack([[0, 0], np.column_stack([x3, y3])])\ns3 = np.abs(xy3).max()\n\nx4 = np.cos(2 * np.pi * np.linspace(r3, 1))\ny4 = np.sin(2 * np.pi * np.linspace(r3, 1))\nxy4 = np.row_stack([[0, 0], np.column_stack([x4, y4])])\ns4 = np.abs(xy4).max()\n\nfig, ax = plt.subplots()\nax.scatter(range(8), range(8), marker=xy1, s=s1**2 * sizes, facecolor='blue')\nax.scatter(range(8), range(8), marker=xy2, s=s2**2 * sizes, facecolor='green')\nax.scatter(range(8), range(8), marker=xy3, s=s3**2 * sizes, facecolor='red')\nax.scatter(range(8), range(8), marker=xy4, s=s3**2 * sizes, facecolor='orange')\n\nplt.show()\n\nOutput:", null, "### Example 4: Scatter Plot with different marker style\n\nHere in this example, a different type of marker will be used in the plot.\n\nThe fourth example of this matplotlib tutorial on scatter plot will tell us how we can play around with different marker styles.\n\nHere in this example, we have used two different marker styles. You can explore various types of markers from here.\n\nWe have to use the $symbol to specify the type of marker we desire in our scatter plot. Apart from this, we are using numpy’s arange and random function for generating pseudo numbers for plotting scatter plot. The color of the two markers are passed in the c parameter and alpha parameter ensures that the transparency level is correct. In : np.random.seed(11808096) x1 = np.arange(0.0, 50.0, 2.0) y1 = x1 ** 1.3 + np.random.rand(*x1.shape) * 30.0 s1 = np.random.rand(*x1.shape) * 800 + 500 x2 = np.arange(0.0, 50.0, 2.0) y2 = x2 ** 0.3 + np.random.rand(*x2.shape) * 25.0 s2 = np.random.rand(*x2.shape) * 800 + 500 plt.scatter(x1, y1, s1, c=\"g\", alpha=0.7, marker=r'$\\star$',label=\"Fortune\") plt.scatter(x2, y2, s2, c=\"r\", alpha=0.8, marker=r'$\\diamondsuit\\$',label=\"Fortune\")\n\nplt.xlabel(\"Area Covered\")\nplt.ylabel(\"Diamnonds and Stars Found\")\nplt.legend(loc='upper left')\nplt.show()\n\nOutput:", null, "### Example 5: Scatter Plots on a Polar Axis\n\nIn the case of polar axis, the size of the marker increases radially, and also the color increases with an increase in angle.\n\nThe last example of this matplotlib scatter plot tutorial is a scatter plot built on the polar axis. Polar axes are generally different from normal axes, here in this case we have the liberty to place the values across 360 degrees.\n\nAfter specifying the count of markers with the parameter “N”, we will be assigning radius, angle, area, and colors with the help of the random function of numpy.\n\nThrough figure function, we are able to print the plot, and figsize help in increasing or decreasing the size of plot. Subplot function helps in plotting the scatter plot over polar axis.\n\nLastly, scatter function is called where we also specify the cmap or color map parameter for assigning different colors to the markers.\n\nIn :\nnp.random.seed(11808096)\n\n# Compute areas and colors\nN = 150\nr = 2 * np.random.rand(N)\ntheta = 2 * np.pi * np.random.rand(N)\narea = 400 * r**2\ncolors = theta\n\nfig = plt.figure(figsize=(10,8))", null, "" ]
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https://jp.mathworks.com/matlabcentral/cody/problems/12-fibonacci-sequence/solutions/1727429
[ "Cody\n\n# Problem 12. Fibonacci sequence\n\nSolution 1727429\n\nSubmitted on 15 Feb 2019 by James Campbell\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1   Pass\nn = 1; f = 1; assert(isequal(fib(n),f))\n\n2   Pass\nn = 6; f = 8; assert(isequal(fib(n),f))\n\n3   Pass\nn = 10; f = 55; assert(isequal(fib(n),f))\n\n4   Pass\nn = 20; f = 6765; assert(isequal(fib(n),f))\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]
[ null ]
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https://www.coursehero.com/file/p2t0c9i/The-investor-has-two-alternatives-Investment-theory-class-2-Page-15-of-22-All/
[ "The investor has two alternatives investment theory\n\n• Notes\n• 22\n\nThis preview shows page 14 - 19 out of 22 pages.\n\nThe investor has two alternatives:\nInvestment theory, class #2 Page 15 of 22 ® All rights reserved to Tal Mofkadi Invest δ in the market portfolio Invest δ in stock A Additional return: ] ) ( [ ) ( f m r r E r E = Δ δ New portfolio risk: { ( ) ( 2 2 2 2 2 2 0 0 2 2 2 2 2 ) 2 ( ) 1 ( , cov 1 2 ) 1 ( m m m f rf m r M σ δ δ σ σ δ σ δ δ σ δ σ δ σ + + = + = + + + = 43 42 1 and since δ is very small, we can omit 2 δ and get that the additional portfolio risk is: 2 2 2 m σ δ σ = Δ The compensation on risk for the individual is therefore: 2 2 2 2 ) ( 2 ] ) ( [ ) ( m f m m f m r r E r r E r E σ σ δ δ σ = = Δ Δ Additional return: ] ) ( [ ) ( f A r r E r E = Δ δ New portfolio risk: ( ) { ( ) ( ) ) , ( 1 2 1 , 1 2 , 2 ) , ( 1 2 1 2 2 2 2 0 0 0 2 2 2 2 2 2 M A Cov r M Cov r A Cov M A Cov A m f f rf A m + + = + + + = δ σ δ σ σ δ δ δ δ σ δ σ δ σ σ 43 42 1 43 42 1 and since δ is very small, we can omit 2 δ and get that the additional portfolio risk is: ) , ( 2 2 M A COV = Δ δ σ The compensation on risk for the individual is therefore: ) , ( 2 ) ( ) , ( 2 ] ) ( [ ) ( 2 M A COV r r E M A COV r r E r E f A f A = = Δ Δ δ δ σ Key: the two “compensation on risk” should equal, and we get: ) , ( 2 ) ( 2 ) ( ) ( 2 2 M A Cov r r E r r E r E f A M f M = = Δ Δ σ σ If, for example, the RHS is larger than the LHS, the investor should sell short M and buy A, and increase his return and not the risk. From this we get:\nInvestment theory, class #2 Page 16 of 22 ® All rights reserved to Tal Mofkadi [ ] f M M f A r r E M A Cov r r E + = ) ( ) , ( ) ( 2 σ and if we define 2 ) , ( M A M A Cov σ β = , we get: [ ] f M A f A r r E r r E + = ) ( ) ( β 3.4 Calculating Beta If we use a linear regression (OLS) of the form: [ ] f M A f A r r E r r E = ) ( ) ( β or alternatively: ( ) { { ) ( ) ( 1 M r A r E r E A f A β β β α + = . This is also known as the “market model” Statistics tell us that in this model: ( ) ( ) ( ) ( ) x Var Y X Cov X n X Y X n Y X i i i , 2 2 = = β . Technically, this is done using statistical program or by using Excel’s regression capabilities or “Slope” worksheet function. Will be seen in the tutorial! 3.4.1 The meaning of Beta Beta is a measure of the additional risk of an asset to the overall market portfolio. In other words, Beta is a proxy of an asset’s risk due to market “shocks”. For example, if the beta of asset i is 0.5 this means that when the market portfolio absorbs a shock of 1% (i.e. r m -r f is grater in 1%) asset i expect to absorb a shock of 0.5% (i.e. r i -r f is expected to be grater in 0.5%). This makes asset i less risky than the market portfolio (why?) and therefore we should expect it to yield lower rate of return. Note that the beta of a portfolio is a weighted sum of its asset’s betas, that is: = = n i i i p x 1 β β\nInvestment theory, class #2 Page 17 of 22 ® All rights reserved to Tal Mofkadi 3.5 Variance decomposition For any asset, the total variance can be expressed as follows: () ( ) ( ) { risk Specific 2 risk Systematic 2 2 risk Specific risk Systematic 2 risk Total ε σ σ β ε β + = + = 3 2 1 3 2 1 43 42 1 3 2 1 m i i Var m Var i Var 3.6 The SML (security market line) [ ] f M A f A r r E r r E + = ) ( ) ( β Note that: 1. 1 = m β since 1 1 2 = = m m m m σ σ σ β 2. 0 = rf β since 0 0 0 2 = = m m rf σ σ β Thus we can graphically present the SML formula: CML Stock A Standard deviation- σ Expected return - E(r) R f Specific risk Market risk Stupidity Dreams\nInvestment theory, class #2\n•", null, "•", null, "•", null, "" ]
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https://mcqslearn.com/math/trigonometry-problems-multiple-choice-questions.php
[ "College Degrees Online Courses\n\nCollege Math MCQs\n\nCollege Math MCQs - Topic\n\n# Trigonometry Problems MCQ with Answers PDF\n\nPractice Trigonometry Problems Multiple Choice Questions (MCQ), college math quiz answers PDF with live worksheets for online degrees. Solve fundamentals of trigonometry Multiple Choice Questions and Answers (MCQs), Trigonometry Problems quiz questions bank for SAT prep classes. \"Trigonometry Problems MCQ\" PDF book: math problems, radian to degree conversion, fundamental identities test prep for GRE test prep classes.\n\n\"1 + tan²2θ =\" Multiple Choice Questions (MCQ) on trigonometry problems with choices sec²θ, csc²θ, csc²2θ, and sec²2θ for SAT prep classes. Solve trigonometry problems quiz questions for merit scholarship test and certificate programs for schools that offer online degrees.\n\n## MCQs on Trigonometry Problems\n\n1.\n\n1 + tan²2θ =\n\nsec²θ\ncsc²θ\ncsc²2θ\nsec²2θ\n\n2.\n\ncos²2θ =\n\n1 - sin²θ\n1 + sin²θ\n1 - sin²2θ\n1 - sinθ\n\n3.\n\ncsc²θ/2-cot²θ/2 =\n\n1\n−1\n0\nsec²2θ\n\n4.\n\nsec²θ-tan²θ =\n\n1\n−1\n0\nsec²2θ\n\n5.\n\n1 + cot²2θ =\n\nsec²θ\ncsc²θ\ncsc²2θ\nsec²2θ" ]
[ null ]
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https://www.jpost.com/international/eu-too-early-to-decide-on-pa-govt-aid
[ "(function (a, d, o, r, i, c, u, p, w, m) { m = d.getElementsByTagName(o), a[c] = a[c] || {}, a[c].trigger = a[c].trigger || function () { (a[c].trigger.arg = a[c].trigger.arg || []).push(arguments)}, a[c].on = a[c].on || function () {(a[c].on.arg = a[c].on.arg || []).push(arguments)}, a[c].off = a[c].off || function () {(a[c].off.arg = a[c].off.arg || []).push(arguments) }, w = d.createElement(o), w.id = i, w.src = r, w.async = 1, w.setAttribute(p, u), m.parentNode.insertBefore(w, m), w = null} )(window, document, \"script\", \"https://95662602.adoric-om.com/adoric.js\", \"Adoric_Script\", \"adoric\",\"9cc40a7455aa779b8031bd738f77ccf1\", \"data-key\");\nvar domain=window.location.hostname; var params_totm = \"\"; (new URLSearchParams(window.location.search)).forEach(function(value, key) {if (key.startsWith('totm')) { params_totm = params_totm +\"&\"+key.replace('totm','')+\"=\"+value}}); var rand=Math.floor(10*Math.random()); var script=document.createElement(\"script\"); script.src=`https://stag-core.tfla.xyz/pre_onetag?pub_id=34&domain=\\${domain}&rand=\\${rand}&min_ugl=0\\${params_totm}`; document.head.append(script);" ]
[ null ]
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http://xavierdupre.fr/app/onnxcustom/helpsphinx/gyexamples/plot_bbegin_measure_time.html
[ "# Benchmark ONNX conversion#\n\nExample Train and deploy a scikit-learn pipeline converts a simple model. This example takes a similar example but on random data and compares the processing time required by each option to compute predictions.\n\n## Training a pipeline#\n\n```import numpy\nfrom pandas import DataFrame\nfrom tqdm import tqdm\nfrom sklearn import config_context\nfrom sklearn.datasets import make_regression\nfrom sklearn.ensemble import (\nVotingRegressor)\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.model_selection import train_test_split\nfrom mlprodict.onnxrt import OnnxInference\nfrom onnxruntime import InferenceSession\nfrom skl2onnx import to_onnx\nfrom onnxcustom.utils import measure_time\n\nN = 11000\nX, y = make_regression(N, n_features=10)\nX_train, X_test, y_train, y_test = train_test_split(\nX, y, train_size=0.01)\nprint(\"Train shape\", X_train.shape)\nprint(\"Test shape\", X_test.shape)\n\nreg2 = RandomForestRegressor(random_state=1)\nreg3 = LinearRegression()\nereg = VotingRegressor([('gb', reg1), ('rf', reg2), ('lr', reg3)])\nereg.fit(X_train, y_train)\n```\n```Train shape (110, 10)\nTest shape (10890, 10)\n```\n```VotingRegressor(estimators=[('gb', GradientBoostingRegressor(random_state=1)),\n('rf', RandomForestRegressor(random_state=1)),\n('lr', LinearRegression())])```\nIn a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.\n\n## Measure the processing time#\n\nWe use function `measure_time`. The page about assume_finite may be useful if you need to optimize the prediction. We measure the processing time per observation whether or not an observation belongs to a batch or is a single one.\n\n```sizes = [(1, 50), (10, 50), (1000, 10), (10000, 5)]\n\nwith config_context(assume_finite=True):\nobs = []\nfor batch_size, repeat in tqdm(sizes):\ncontext = {\"ereg\": ereg, 'X': X_test[:batch_size]}\nmt = measure_time(\n\"ereg.predict(X)\", context, div_by_number=True,\nnumber=10, repeat=repeat)\nmt['size'] = context['X'].shape\nmt['mean_obs'] = mt['average'] / mt['size']\nobs.append(mt)\n\ndf_skl = DataFrame(obs)\ndf_skl\n```\n``` 0%| | 0/4 [00:00<?, ?it/s]\n25%|##5 | 1/4 [00:15<00:45, 15.00s/it]\n50%|##### | 2/4 [00:29<00:29, 14.83s/it]\n75%|#######5 | 3/4 [00:34<00:10, 10.20s/it]\n100%|##########| 4/4 [00:42<00:00, 9.37s/it]\n100%|##########| 4/4 [00:42<00:00, 10.63s/it]\n```\naverage deviation min_exec max_exec repeat number size mean_obs\n0 0.029989 0.000107 0.029839 0.030542 50 10 1 0.029989\n1 0.029418 0.000125 0.029245 0.030009 50 10 10 0.002942\n2 0.046801 0.003460 0.043296 0.053204 10 10 1000 0.000047\n3 0.162123 0.000081 0.162050 0.162258 5 10 10000 0.000016\n\nGraphe.\n\n```df_skl.set_index('size')[['mean_obs']].plot(\ntitle=\"scikit-learn\", logx=True, logy=True)\n```", null, "```<AxesSubplot: title={'center': 'scikit-learn'}, xlabel='size'>\n```\n\n## ONNX runtime#\n\nThe same is done with the two ONNX runtime available.\n\n```onx = to_onnx(ereg, X_train[:1].astype(numpy.float32),\ntarget_opset={'': 14, 'ai.onnx.ml': 2})\nsess = InferenceSession(onx.SerializeToString(),\nproviders=['CPUExecutionProvider'])\noinf = OnnxInference(onx, runtime=\"python_compiled\")\n\nobs = []\nfor batch_size, repeat in tqdm(sizes):\n\n# scikit-learn\ncontext = {\"ereg\": ereg, 'X': X_test[:batch_size].astype(numpy.float32)}\nmt = measure_time(\n\"ereg.predict(X)\", context, div_by_number=True,\nnumber=10, repeat=repeat)\nmt['size'] = context['X'].shape\nmt['skl'] = mt['average'] / mt['size']\n\n# onnxruntime\ncontext = {\"sess\": sess, 'X': X_test[:batch_size].astype(numpy.float32)}\nmt2 = measure_time(\n\"sess.run(None, {'X': X})\", context, div_by_number=True,\nnumber=10, repeat=repeat)\nmt['ort'] = mt2['average'] / mt['size']\n\n# mlprodict\ncontext = {\"oinf\": oinf, 'X': X_test[:batch_size].astype(numpy.float32)}\nmt2 = measure_time(\n\"oinf.run({'X': X})['variable']\", context, div_by_number=True,\nnumber=10, repeat=repeat)\nmt['pyrt'] = mt2['average'] / mt['size']\n\n# end\nobs.append(mt)\n\ndf = DataFrame(obs)\ndf\n```\n``` 0%| | 0/4 [00:00<?, ?it/s]\n25%|##5 | 1/4 [00:20<01:00, 20.20s/it]\n50%|##### | 2/4 [00:42<00:43, 21.63s/it]\n75%|#######5 | 3/4 [01:12<00:25, 25.23s/it]\n100%|##########| 4/4 [02:34<00:00, 47.79s/it]\n100%|##########| 4/4 [02:34<00:00, 38.68s/it]\n```\naverage deviation min_exec max_exec repeat number size skl ort pyrt\n0 0.030600 0.000161 0.030286 0.031162 50 10 1 0.030600 0.000234 0.009540\n1 0.030283 0.000084 0.030121 0.030600 50 10 10 0.003028 0.000057 0.001440\n2 0.045175 0.001052 0.044146 0.047618 10 10 1000 0.000045 0.000006 0.000244\n3 0.164668 0.000791 0.163987 0.166081 5 10 10000 0.000016 0.000003 0.000145\n\nGraph.\n\n```df.set_index('size')[['skl', 'ort', 'pyrt']].plot(\ntitle=\"Average prediction time per runtime\",\nlogx=True, logy=True)\n```", null, "```<AxesSubplot: title={'center': 'Average prediction time per runtime'}, xlabel='size'>\n```\n\nONNX runtimes are much faster than scikit-learn to predict one observation. scikit-learn is optimized for training, for batch prediction. That explains why scikit-learn and ONNX runtimes seem to converge for big batches. They use similar implementation, parallelization and languages (C++, openmp).\n\nTotal running time of the script: ( 3 minutes 22.568 seconds)\n\nGallery generated by Sphinx-Gallery" ]
[ null, "http://xavierdupre.fr/app/onnxcustom/helpsphinx/_images/sphx_glr_plot_bbegin_measure_time_001.png", null, "http://xavierdupre.fr/app/onnxcustom/helpsphinx/_images/sphx_glr_plot_bbegin_measure_time_002.png", null ]
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https://pymatgen.org/pymatgen.analysis.phase_diagram.html
[ "# pymatgen.analysis.phase_diagram module¶\n\nThis module defines tools to generate and analyze phase diagrams.\n\nclass CompoundPhaseDiagram(entries, terminal_compositions, normalize_terminal_compositions=True)[source]\n\nGenerates phase diagrams from compounds as terminations instead of elements.\n\nInitializes a CompoundPhaseDiagram.\n\nParameters\n• entries ([PDEntry]) – Sequence of input entries. For example, if you want a Li2O-P2O5 phase diagram, you might have all Li-P-O entries as an input.\n\n• terminal_compositions ([Composition]) – Terminal compositions of phase space. In the Li2O-P2O5 example, these will be the Li2O and P2O5 compositions.\n\n• normalize_terminal_compositions (bool) – Whether to normalize the terminal compositions to a per atom basis. If normalized, the energy above hulls will be consistent for comparison across systems. Non-normalized terminals are more intuitive in terms of compositional breakdowns.\n\namount_tol = 1e-05[source]\nas_dict()[source]\nReturns\n\nMSONable dict\n\nclassmethod from_dict(d)[source]\nParameters\n\nd – Dict Representation\n\nReturns\n\nCompoundPhaseDiagram\n\ntransform_entries(entries, terminal_compositions)[source]\n\nMethod to transform all entries to the composition coordinate in the terminal compositions. If the entry does not fall within the space defined by the terminal compositions, they are excluded. For example, Li3PO4 is mapped into a Li2O:1.5, P2O5:0.5 composition. The terminal compositions are represented by DummySpecies.\n\nParameters\n• entries – Sequence of all input entries\n\n• terminal_compositions – Terminal compositions of phase space.\n\nReturns\n\nSequence of TransformedPDEntries falling within the phase space.\n\nclass GrandPotPDEntry(entry, chempots, name=None)[source]\n\nA grand potential pd entry object encompassing all relevant data for phase diagrams. Chemical potentials are given as a element-chemical potential dict.\n\nParameters\n• entry – A PDEntry-like object.\n\n• chempots – Chemical potential specification as {Element: float}.\n\n• name – Optional parameter to name the entry. Defaults to the reduced chemical formula of the original entry.\n\nas_dict()[source]\nReturns\n\nMSONAble dict\n\nclassmethod from_dict(d)[source]\nParameters\n\nd – Dict representation\n\nReturns\n\nPDStructureEntry\n\nproperty is_element[source]\n\nTrue if the entry is an element.\n\nclass GrandPotentialPhaseDiagram(entries, chempots, elements=None)[source]\n\nA class representing a Grand potential phase diagram. Grand potential phase diagrams are essentially phase diagrams that are open to one or more components. To construct such phase diagrams, the relevant free energy is the grand potential, which can be written as the Legendre transform of the Gibbs free energy as follows\n\nGrand potential = G - u_X N_X\n\nThe algorithm is based on the work in the following papers:\n\n1. S. P. Ong, L. Wang, B. Kang, and G. Ceder, Li-Fe-P-O2 Phase Diagram from First Principles Calculations. Chem. Mater., 2008, 20(5), 1798-1807. doi:10.1021/cm702327g\n\n2. S. P. Ong, A. Jain, G. Hautier, B. Kang, G. Ceder, Thermal stabilities of delithiated olivine MPO4 (M=Fe, Mn) cathodes investigated using first principles calculations. Electrochem. Comm., 2010, 12(3), 427-430. doi:10.1016/j.elecom.2010.01.010\n\nStandard constructor for grand potential phase diagram.\n\nParameters\n• entries ([PDEntry]) – A list of PDEntry-like objects having an energy, energy_per_atom and composition.\n\n• {Element (chempots) – float}: Specify the chemical potentials of the open elements.\n\n• elements ([Element]) – Optional list of elements in the phase diagram. If set to None, the elements are determined from the the entries themselves.\n\nas_dict()[source]\nReturns\n\nMSONable dict\n\nclassmethod from_dict(d)[source]\nParameters\n\nd – Dict representation\n\nReturns\n\nGrandPotentialPhaseDiagram\n\nclass PDEntry(composition: pymatgen.core.composition.Composition, energy: float, name: str = None, attribute: object = None)[source]\n\nBases: monty.json.MSONable\n\nAn object encompassing all relevant data for phase diagrams.\n\ncomposition[source]\n\nThe composition associated with the PDEntry.\n\nenergy[source]\n\nThe energy associated with the entry.\n\nname[source]\n\nA name for the entry. This is the string shown in the phase diagrams. By default, this is the reduced formula for the composition, but can be set to some other string for display purposes.\n\nattribute[source]\n\nA arbitrary attribute.\n\nParameters\n• composition (Composition) – Composition\n\n• energy (float) – Energy for composition.\n\n• name (str) – Optional parameter to name the entry. Defaults to the reduced chemical formula.\n\n• attribute – Optional attribute of the entry. This can be used to specify that the entry is a newly found compound, or to specify a particular label for the entry, or else … Used for further analysis and plotting purposes. An attribute can be anything but must be MSONable.\n\nas_dict()[source]\nReturns\n\nMSONable dict.\n\nproperty energy_per_atom[source]\n\nReturns the final energy per atom.\n\nclassmethod from_dict(d)[source]\nParameters\n\nd – Dict representation\n\nReturns\n\nPDEntry\n\nproperty is_element[source]\n\nTrue if the entry is an element.\n\nclass PDPlotter(phasediagram, show_unstable=0, **plotkwargs)[source]\n\nBases: object\n\nA plotter class for phase diagrams.\n\nParameters\n• phasediagram – PhaseDiagram object.\n\n• show_unstable (float) – Whether unstable phases will be plotted as well as red crosses. If a number > 0 is entered, all phases with ehull < show_unstable will be shown.\n\n• **plotkwargs\n\nKeyword args passed to matplotlib.pyplot.plot. Can be used to customize markers etc. If not set, the default is {\n\n”markerfacecolor”: (0.2157, 0.4941, 0.7216), “markersize”: 10, “linewidth”: 3\n\n}\n\nget_chempot_range_map_plot(elements, referenced=True)[source]\n\nReturns a plot of the chemical potential range _map. Currently works only for 3-component PDs.\n\nParameters\n• elements – Sequence of elements to be considered as independent variables. E.g., if you want to show the stability ranges of all Li-Co-O phases wrt to uLi and uO, you will supply [Element(“Li”), Element(“O”)]\n\n• referenced – if True, gives the results with a reference being the energy of the elemental phase. If False, gives absolute values.\n\nReturns\n\nA matplotlib plot object.\n\nget_contour_pd_plot()[source]\n\nPlot a contour phase diagram plot, where phase triangles are colored according to degree of instability by interpolation. Currently only works for 3-component phase diagrams.\n\nReturns\n\nA matplotlib plot object.\n\nget_plot(label_stable=True, label_unstable=True, ordering=None, energy_colormap=None, process_attributes=False, plt=None)[source]\nParameters\n• label_stable – Whether to label stable compounds.\n\n• label_unstable – Whether to label unstable compounds.\n\n• ordering – Ordering of vertices.\n\n• energy_colormap – Colormap for coloring energy.\n\n• process_attributes – Whether to process the attributes.\n\n• plt – Existing plt object if plotting multiple phase diagrams.\n\nReturns\n\nmatplotlib.pyplot.\n\nproperty pd_plot_data[source]\n\nPlot data for phase diagram. 2-comp - Full hull with energies 3/4-comp - Projection into 2D or 3D Gibbs triangle.\n\nReturns\n\n• lines is a list of list of coordinates for lines in the PD.\n\n• stable_entries is a {coordinate : entry} for each stable node\n\nin the phase diagram. (Each coordinate can only have one stable phase) - unstable_entries is a {entry: coordinates} for all unstable nodes in the phase diagram.\n\nReturn type\n\n(lines, stable_entries, unstable_entries)\n\nplot_chempot_range_map(elements, referenced=True)[source]\n\nPlot the chemical potential range _map. Currently works only for 3-component PDs.\n\nParameters\n• elements – Sequence of elements to be considered as independent variables. E.g., if you want to show the stability ranges of all Li-Co-O phases wrt to uLi and uO, you will supply [Element(“Li”), Element(“O”)]\n\n• referenced – if True, gives the results with a reference being the energy of the elemental phase. If False, gives absolute values.\n\nplot_element_profile(element, comp, show_label_index=None, xlim=5)[source]\n\nDraw the element profile plot for a composition varying different chemical potential of an element. X value is the negative value of the chemical potential reference to elemental chemical potential. For example, if choose Element(“Li”), X= -(µLi-µLi0), which corresponds to the voltage versus metal anode. Y values represent for the number of element uptake in this composition (unit: per atom). All reactions are printed to help choosing the profile steps you want to show label in the plot.\n\nParameters\n• element (Element) – An element of which the chemical potential is considered. It also must be in the phase diagram.\n\n• comp (Composition) – A composition.\n\n• show_label_index (list of integers) – The labels for reaction products you want to show in the plot. Default to None (not showing any annotation for reaction products). For the profile steps you want to show the labels, just add it to the show_label_index. The profile step counts from zero. For example, you can set show_label_index=[0, 2, 5] to label profile step 0,2,5.\n\n• xlim (float) – The max x value. x value is from 0 to xlim. Default to 5 eV.\n\nReturns\n\nPlot of element profile evolution by varying the chemical potential of an element.\n\nshow(*args, **kwargs)[source]\n\nDraws the phase diagram using Matplotlib and show it.\n\nParameters\n• *args – Passed to get_plot.\n\n• **kwargs – Passed to get_plot.\n\nwrite_image(stream, image_format='svg', **kwargs)[source]\n\nWrites the phase diagram to an image in a stream.\n\nParameters\n• stream – stream to write to. Can be a file stream or a StringIO stream.\n\n• image_format – format for image. Can be any of matplotlib supported formats. Defaults to svg for best results for vector graphics.\n\n• **kwargs – Pass through to get_plot functino.\n\nclass PhaseDiagram(entries, elements=None)[source]\n\nBases: monty.json.MSONable\n\nSimple phase diagram class taking in elements and entries as inputs. The algorithm is based on the work in the following papers:\n\n1. S. P. Ong, L. Wang, B. Kang, and G. Ceder, Li-Fe-P-O2 Phase Diagram from First Principles Calculations. Chem. Mater., 2008, 20(5), 1798-1807. doi:10.1021/cm702327g\n\n2. S. P. Ong, A. Jain, G. Hautier, B. Kang, G. Ceder, Thermal stabilities of delithiated olivine MPO4 (M=Fe, Mn) cathodes investigated using first principles calculations. Electrochem. Comm., 2010, 12(3), 427-430. doi:10.1016/j.elecom.2010.01.010\n\n..attribute: all_entries\n\nAll entries provided for Phase Diagram construction. Note that this does not mean that all these entries are actually used in the phase diagram. For example, this includes the positive formation energy entries that are filtered out before Phase Diagram construction.\n\nStandard constructor for phase diagram.\n\nParameters\n• entries ([PDEntry]) – A list of PDEntry-like objects having an energy, energy_per_atom and composition.\n\n• elements ([Element]) – Optional list of elements in the phase diagram. If set to None, the elements are determined from the the entries themselves and are sorted alphabetically. If specified, element ordering (e.g. for pd coordinates) is preserved.\n\nproperty all_entries_hulldata[source]\n\nThe actual ndarray used to construct the convex hull.\n\nType\n\nreturn\n\nas_dict()[source]\nReturns\n\nMSONAble dict\n\nformation_energy_tol = 1e-11[source]\nclassmethod from_dict(d)[source]\nParameters\n\nd – Dict representation\n\nReturns\n\nPhaseDiagram\n\nget_all_chempots(comp)[source]\n\nGet chemical potentials at a given compositon.\n\nParameters\n\ncomp – Composition\n\nReturns\n\nChemical potentials.\n\nget_chempot_range_map(elements, referenced=True, joggle=True)[source]\n\nReturns a chemical potential range map for each stable entry.\n\nParameters\n• elements – Sequence of elements to be considered as independent variables. E.g., if you want to show the stability ranges of all Li-Co-O phases wrt to uLi and uO, you will supply [Element(“Li”), Element(“O”)]\n\n• referenced – If True, gives the results with a reference being the energy of the elemental phase. If False, gives absolute values.\n\n• joggle (boolean) – Whether to joggle the input to avoid precision errors.\n\nReturns\n\n[simplices]}. The list of simplices are the sides of the N-1 dim polytope bounding the allowable chemical potential range of each entry.\n\nReturn type\n\nReturns a dict of the form {entry\n\nget_chempot_range_stability_phase(target_comp, open_elt)[source]\n\nreturns a set of chemical potentials corresponding to the max and min chemical potential of the open element for a given composition. It is quite common to have for instance a ternary oxide (e.g., ABO3) for which you want to know what are the A and B chemical potential leading to the highest and lowest oxygen chemical potential (reducing and oxidizing conditions). This is useful for defect computations.\n\nParameters\n• target_comp – A Composition object\n\n• open_elt – Element that you want to constrain to be max or min\n\nReturns\n\n(mu_min,mu_max)}: Chemical potentials are given in “absolute” values (i.e., not referenced to 0)\n\nReturn type\n\n{Element\n\nget_composition_chempots(comp)[source]\n\nGet the chemical potentials for all elements at a given composition.\n\nParameters\n\ncomp – Composition\n\nReturns\n\nDict of chemical potentials.\n\nget_critical_compositions(comp1, comp2)[source]\n\nGet the critical compositions along the tieline between two compositions. I.e. where the decomposition products change. The endpoints are also returned. :param comp1, comp2: compositions that define the tieline :type comp1, comp2: Composition\n\nReturns\n\nlist of critical compositions. All are of\n\nthe form x * comp1 + (1-x) * comp2\n\nReturn type\n\n[(Composition)]\n\nget_decomp_and_e_above_hull(entry, allow_negative=False)[source]\n\nProvides the decomposition and energy above convex hull for an entry. Due to caching, can be much faster if entries with the same composition are processed together.\n\nParameters\n• entry – A PDEntry like object\n\n• allow_negative – Whether to allow negative e_above_hulls. Used to calculate equilibrium reaction energies. Defaults to False.\n\nReturns\n\n(decomp, energy above convex hull) Stable entries should have energy above hull of 0. The decomposition is provided as a dict of {Entry: amount}.\n\nget_decomposition(comp)[source]\n\nProvides the decomposition at a particular composition.\n\nParameters\n\ncomp – A composition\n\nReturns\n\namount}\n\nReturn type\n\nDecomposition as a dict of {Entry\n\nget_e_above_hull(entry)[source]\n\nProvides the energy above convex hull for an entry\n\nParameters\n\nentry – A PDEntry like object\n\nReturns\n\nEnergy above convex hull of entry. Stable entries should have energy above hull of 0.\n\nget_element_profile(element, comp, comp_tol=1e-05)[source]\n\nProvides the element evolution data for a composition. For example, can be used to analyze Li conversion voltages by varying uLi and looking at the phases formed. Also can be used to analyze O2 evolution by varying uO2.\n\nParameters\n• element – An element. Must be in the phase diagram.\n\n• comp – A Composition\n\n• comp_tol – The tolerance to use when calculating decompositions. Phases with amounts less than this tolerance are excluded. Defaults to 1e-5.\n\nReturns\n\n[ {‘chempot’: -10.487582010000001, ‘evolution’: -2.0, ‘reaction’: Reaction Object], …]\n\nReturn type\n\nEvolution data as a list of dictionaries of the following format\n\nget_equilibrium_reaction_energy(entry)[source]\n\nProvides the reaction energy of a stable entry from the neighboring equilibrium stable entries (also known as the inverse distance to hull).\n\nParameters\n\nentry – A PDEntry like object\n\nReturns\n\nEquilibrium reaction energy of entry. Stable entries should have equilibrium reaction energy <= 0.\n\nget_form_energy(entry)[source]\n\nReturns the formation energy for an entry (NOT normalized) from the elemental references.\n\nParameters\n\nentry – A PDEntry-like object.\n\nReturns\n\nFormation energy from the elemental references.\n\nget_form_energy_per_atom(entry)[source]\n\nReturns the formation energy per atom for an entry from the elemental references.\n\nParameters\n\nentry – An PDEntry-like object\n\nReturns\n\nFormation energy per atom from the elemental references.\n\nget_hull_energy(comp)[source]\nParameters\n\ncomp (Composition) – Input composition\n\nReturns\n\nEnergy of lowest energy equilibrium at desired composition. Not normalized by atoms, i.e. E(Li4O2) = 2 * E(Li2O)\n\nget_transition_chempots(element)[source]\n\nGet the critical chemical potentials for an element in the Phase Diagram.\n\nParameters\n\nelement – An element. Has to be in the PD in the first place.\n\nReturns\n\nA sorted sequence of critical chemical potentials, from less negative to more negative.\n\ngetmu_vertices_stability_phase(target_comp, dep_elt, tol_en=0.01)[source]\n\nreturns a set of chemical potentials corresponding to the vertices of the simplex in the chemical potential phase diagram. The simplex is built using all elements in the target_composition except dep_elt. The chemical potential of dep_elt is computed from the target composition energy. This method is useful to get the limiting conditions for defects computations for instance.\n\nParameters\n• target_comp – A Composition object\n\n• dep_elt – the element for which the chemical potential is computed from the energy of\n\n• stable phase at the target composition (the) –\n\n• tol_en – a tolerance on the energy to set\n\nReturns\n\nmu}]: An array of conditions on simplex vertices for which each element has a chemical potential set to a given value. “absolute” values (i.e., not referenced to element energies)\n\nReturn type\n\n[{Element\n\nnumerical_tol = 1e-08[source]\npd_coords(comp)[source]\n\nThe phase diagram is generated in a reduced dimensional space (n_elements - 1). This function returns the coordinates in that space. These coordinates are compatible with the stored simplex objects.\n\nproperty stable_entries[source]\n\nReturns the stable entries in the phase diagram.\n\nproperty unstable_entries[source]\n\nEntries that are unstable in the phase diagram. Includes positive formation energy entries.\n\nexception PhaseDiagramError[source]\n\nBases: Exception\n\nAn exception class for Phase Diagram generation.\n\nclass ReactionDiagram(entry1, entry2, all_entries, tol=0.0001, float_fmt='%.4f')[source]\n\nBases: object\n\nAnalyzes the possible reactions between a pair of compounds, e.g., an electrolyte and an electrode.\n\nParameters\n• entry1 (ComputedEntry) – Entry for 1st component. Note that corrections, if any, must already be pre-applied. This is to give flexibility for different kinds of corrections, e.g., if a particular entry is fitted to an experimental data (such as EC molecule).\n\n• entry2 (ComputedEntry) – Entry for 2nd component. Note that corrections must already be pre-applied. This is to give flexibility for different kinds of corrections, e.g., if a particular entry is fitted to an experimental data (such as EC molecule).\n\n• all_entries ([ComputedEntry]) – All other entries to be considered in the analysis. Note that corrections, if any, must already be pre-applied.\n\n• tol (float) – Tolerance to be used to determine validity of reaction.\n\n• float_fmt (str) – Formatting string to be applied to all floats. Determines number of decimal places in reaction string.\n\nget_compound_pd()[source]\n\nGet the CompoundPhaseDiagram object, which can then be used for plotting.\n\nReturns\n\n(CompoundPhaseDiagram)\n\nclass TransformedPDEntry(comp, original_entry)[source]\n\nThis class repesents a TransformedPDEntry, which allows for a PDEntry to be transformed to a different composition coordinate space. It is used in the construction of phase diagrams that do not have elements as the terminal compositions.\n\nParameters\n• comp (Composition) – Transformed composition as a Composition.\n\n• original_entry (PDEntry) – Original entry that this entry arose from.\n\nas_dict()[source]\nReturns\n\nMSONable dict\n\nclassmethod from_dict(d)[source]\nParameters\n\nd – Dict representation\n\nReturns\n\nTransformedPDEntry\n\nget_facets(qhull_data, joggle=False)[source]\n\nGet the simplex facets for the Convex hull.\n\nParameters\n• qhull_data (np.ndarray) – The data from which to construct the convex hull as a Nxd array (N being number of data points and d being the dimension)\n\n• joggle (boolean) – Whether to joggle the input to avoid precision errors.\n\nReturns\n\nList of simplices of the Convex Hull.\n\norder_phase_diagram(lines, stable_entries, unstable_entries, ordering)[source]\n\nOrders the entries (their coordinates) in a phase diagram plot according to the user specified ordering. Ordering should be given as [‘Up’, ‘Left’, ‘Right’], where Up, Left and Right are the names of the entries in the upper, left and right corners of the triangle respectively.\n\nParameters\n• lines – list of list of coordinates for lines in the PD.\n\n• stable_entries – {coordinate : entry} for each stable node in the phase diagram. (Each coordinate can only have one stable phase)\n\n• unstable_entries – {entry: coordinates} for all unstable nodes in the phase diagram.\n\n• ordering – Ordering of the phase diagram, given as a list [‘Up’, ‘Left’,’Right’]\n\nReturns\n\n• newlines is a list of list of coordinates for lines in the PD.\n\n• newstable_entries is a {coordinate : entry} for each stable node\n\nin the phase diagram. (Each coordinate can only have one stable phase) - newunstable_entries is a {entry: coordinates} for all unstable nodes in the phase diagram.\n\nReturn type\n\n(newlines, newstable_entries, newunstable_entries)\n\ntet_coord(coord)[source]\n\nConvert a 3D coordinate into a tetrahedron based coordinate system for a prettier phase diagram.\n\nParameters\n\ncoordinate – coordinate used in the convex hull computation.\n\nReturns\n\ncoordinates in a tetrahedron-based coordinate system.\n\ntriangular_coord(coord)[source]\n\nConvert a 2D coordinate into a triangle-based coordinate system for a prettier phase diagram.\n\nParameters\n\ncoordinate – coordinate used in the convex hull computation.\n\nReturns\n\ncoordinates in a triangular-based coordinate system.\n\nuniquelines(q)[source]\n\nGiven all the facets, convert it into a set of unique lines. Specifically used for converting convex hull facets into line pairs of coordinates.\n\nParameters\n\nq – A 2-dim sequence, where each row represents a facet. E.g., [[1,2,3],[3,6,7],…]\n\nReturns\n\nA set of tuple of lines. E.g., ((1,2), (1,3), (2,3), ….)\n\nReturn type\n\nsetoflines" ]
[ null ]
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https://cran.rstudio.com/web/packages/dissever/vignettes/dissever-demo.html
[ "# Dissever Tutorial\n\n#### 2018-04-20\n\nlibrary(dissever)\n\nlibrary(raster)\nlibrary(viridis)\nlibrary(dplyr)\nlibrary(magrittr)\n\nHere is the coarse model to dissever:\n\nplot(edgeroi$carbon, col = viridis(100))", null, "and here are the covariates that will be used for the disseveration: plot(edgeroi$predictors, col = viridis(100))", null, "## Example\n\nIn this section, we will dissever the sample dataset with the available environmental covariates, using 4 different regression methods:\n\n• Random Forest (\"rf\")\n• Cubist (\"cubist\")\n• MARS (\"earth\")\n• Linear Model (\"lm\")\n\nIt is simple to switch between regression methods using the method option of dissever.\n\nBut first let’s setup some parameters:\n\nmin_iter <- 5 # Minimum number of iterations\nmax_iter <- 10 # Maximum number of iterations\np_train <- 0.025 # Subsampling of the initial data\n\nWe can then launch the 4 different disseveration procedures:\n\n# Random Forest\nres_rf <- dissever(\ncoarse = edgeroi$carbon, # stack of fine resolution covariates fine = edgeroi$predictors, # coarse resolution raster\nmethod = \"rf\", # regression method used for disseveration\np = p_train, # proportion of pixels sampled for training regression model\nmin_iter = min_iter, # minimum iterations\nmax_iter = max_iter # maximum iterations\n)\n\n# Cubist\nres_cubist <- dissever(\ncoarse = edgeroi$carbon, fine = edgeroi$predictors,\nmethod = \"cubist\",\np = p_train,\nmin_iter = min_iter,\nmax_iter = max_iter\n)\n\n# GAM\nres_gam <- dissever(\ncoarse = edgeroi$carbon, fine = edgeroi$predictors,\nmethod = \"gamSpline\",\np = p_train,\nmin_iter = min_iter,\nmax_iter = max_iter\n)\n\n# Linear model\nres_lm <- dissever(\ncoarse = edgeroi$carbon, fine = edgeroi$predictors,\nmethod = \"lm\",\np = p_train,\nmin_iter = min_iter,\nmax_iter = max_iter\n)\n\n# Analysing the results\n\nThe object returned by dissever is an object of class dissever. It’s basically a list with 3 elements: * fit: a train object storing the regression model used in the final disseveration * map: a RasterLayer object storing the dissevered map * perf: a data.frame object storing the evolution of the RMSE (and confidence intervals) with the disseveration iterations.\n\nThe dissever result has a plot function that can plot either the map or the performance results, depending on the type option.\n\n## Maps\n\nBelow are the dissevered maps for all 4 regression methods:\n\n# Plotting maps\npar(mfrow = c(2, 2))\nplot(res_rf, type = 'map', main = \"Random Forest\")\nplot(res_cubist, type = 'map', main = \"Cubist\")\nplot(res_gam, type = 'map', main = \"GAM\")\nplot(res_lm, type = 'map', main = \"Linear Model\")", null, "## Convergence\n\nWe can also analyse and plot the optimisation of the dissevering model:\n\n# Plot performance\npar(mfrow = c(2, 2))\nplot(res_rf, type = 'perf', main = \"Random Forest\")\nplot(res_cubist, type = 'perf', main = \"Cubist\")\nplot(res_gam, type = 'perf', main = \"GAM\")\nplot(res_lm, type = 'perf', main = \"Linear Model\")", null, "## Performance of the regression\n\nThe tools provided by the caret package can also be leveraged, e.g. to plot the observed vs. predicted values:\n\n# Plot preds vs obs\npreds <- extractPrediction(list(res_rf$fit, res_cubist$fit, res_gam$fit, res_lm$fit))\nplotObsVsPred(preds)", null, "The models can be compared using the preds object that we just derived using the extractPrediction function. In this case I’m computing the R2, the RMSE and the CCC for each model:\n\n# Compare models\nperf <- preds %>%\ngroup_by(model, dataType) %>%\nsummarise(\nrsq = cor(obs, pred)^2,\nrmse = sqrt(mean((pred - obs)^2))\n)\nperf\n## # A tibble: 4 x 4\n## # Groups: model [?]\n## model dataType rsq rmse\n## <fct> <fct> <dbl> <dbl>\n## 1 cubist Training 0.260 5.35\n## 2 gamSpline Training 0.312 4.66\n## 3 lm Training 0.349 4.52\n## 4 rf Training 0.951 1.53\n\n# Ensemble approach\n\nWe can either take the best option (in this case Random Forest – but the results probably show that we should add some kind of validation process), or use a simple ensemble-type approach. For the latter, I am computing weights for each of the maps based on the CCC of the 4 different regression models:\n\n# We can weight results with Rsquared\nw <- perf$rsq / sum(perf$rsq)\n\n# Make stack of weighted predictions and compute sum\nl_maps <- list(res_cubist$map, res_gam$map, res_lm$map, res_rf$map)\nens <- lapply(1:4, function(x) l_maps[[x]] * w[x]) %>%\nstack %>%\nsum\n\nEnsemble modelling seem to work better when the models are not too correlated – i.e. when they capture different facets of the data:\n\ns_res <- stack(l_maps)\nnames(s_res) <- c('Cubist', 'GAM', 'Linear Model', 'Random Forest')\ns_res %>%\nas.data.frame %>%\nna.exclude %>%\ncor\n## Cubist GAM Linear.Model Random.Forest\n## Cubist 1.0000000 0.7725831 0.7027710 0.7421504\n## GAM 0.7725831 1.0000000 0.8880034 0.7831751\n## Linear.Model 0.7027710 0.8880034 1.0000000 0.8094299\n## Random.Forest 0.7421504 0.7831751 0.8094299 1.0000000\n\nHere is the resulting map:\n\n# Plot result\nplot(ens, col = viridis(100), main = \"CCC Weighted Average\")", null, "" ]
[ null, 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", null, 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gFYVN2akNOKbwOoVt2gagEob93T2L3XHozbl6/+2DT2m8zuTJgFQESh/DC9E09qyLaatUOnZ/tmbLJvrYZvW/REsCbjs+mxQrcgaGPjRLdWd5ZM4yL1Jbf0V/UPSHxI/OCktgD66YN6IgganiAAwkKYIwDCnDpQ2PKsYDUAIPqBHt6/veFqX4OIYv70u/8JvvoB7GGLhgDgLfcAnLX65S3/uwaAMwzuqkO8eeoeRcUIwDlr/+hzCqDIfIdEAAqWDyAQ1kiQB7BzokPuP1wpFJwAQBixrlwFQDWya4ENwGKRnIt6BztV4+MWALvDd5wQQGXC4TULAK1RUYgAkAkm2kK5c9f8MoCIEwBdhcrewS4AYX+u7SUKID/I3ZEQQFhQA8LroH6JAAjaUFscAoAlZJsgANB99HDRrQHwQjk+0Lt7nlUMASzrGdyxcwEAWBwTFgAwAQC5CDXVfn6XBYDVwG0A4C6CdnXT5PxPQ5J+o3ELQXsEgITEHaIACvvVe8drI5VlAoDo9uTOlCEasQFQ/asJJgAIh8PhAIodNcdWd2ZkeycAZ4S6Q+pcdkUAcEc5gMghkU0A1LrUs1M+NkREAHhP78KrlQMUgJpCCB0ar5BISQmtBCBBtWgyIwGoXnYRLBGA4jd9Ir6kBKBkh5kLQNTXApCvBaBUB6YvAMlGEgEonLYA5CQCUCgFoGiWBCC9pZUAJJ83YakPERc8klJhxEQEwBFBngQAcjxAvQA04TkAKl4Y1GwAQRg0du+1BwEZ6R+ber9JpQpiWQBEGJKmgkvzBmcuAE0u2Uxzt+kLQNY05K2MANR46mkKQKl/YwFItBKAGj9kBCCrpQDEbYQBARCG6kDuAACJsgJQxZsT4x+UDNYq8LQAVLHkvOfVPABjwfhgpQLALSNSr1R4OS0A0QjAWDDmcwaAC08KQBwegEBYY0EAYMRXP8OQJzz4AMKIEVYBUAmzAtBgTQkcUdUGYOc8V4QAJmohr2oBiEYASJUJ/ZoX/gSAKCIAiDUx6DkAwioPximAwpgWgALVkxqlPggAn6JWDQHAFrJNKQBRvxyQGoCaFoAGqzmLBQBKfnmwVgIAi6OaEoAQoaraL5TrBKAoRGDVC0BBvQBkI7C1ADRBAdTGtQBEyERFABDFWAASUdUBQPWvJiwBQEQcnAPwclVHqDszXHUAOBM0Nw79EwsAOSkAuUoAqupF+3hVCUAIXr3jfzYFIAhYNXWvATBPqHlE3tPUHKR/MCHnHRohsgGA8ER2YX7ScORoiSRKdpBTUggIJQckjSvRx1F7NvZTqjdImNpI6naOhSf5DAsGGhEAFFmpLk1GaCNM9plI8UpQdRpGIXhdB7hD0lviaTcoEN0l4pdUl6yqOool4lqd8CSPTe4Dq1sWA0p2rLteWrdFsOQOcEdAPhgsa+KU00RIVCthxACEgkZR3U0XNocBWp6IoinlD2JZIgyh5aFmTVFER8ZdFRYlIcfkYhCjYnIxLm4tkZCyD2BmS6L+ad5OnegTj/+06KO3NG+BRGrBI/UckaP3t5Md5KQkpqduMxgMrzCzKgDVw1vovQlPZoRYmonlm/T2mFgYit/0hEMJE16i10k+yL1qdU1xu17iqVfnIH651/daTmckUopumroo2duW82O9PS6zUZ3XUl3KSDBxs7Gcx21tBNStMR80yFrlMh+SE+lOJqIPbbGDrf5VJjAmuC3kB9UBqhdtXAk6cjUR6hajiEgFMgDIna3s1c1pJpV+ppB7YtLSj/w8PQFiZkxDVjsoGvrcRPGj9syqalKHZLdkRJ9GO1f62KbSiUgekzrNUAb5MNr14R9RDmFJfysAIJob8SGEEzZop5ZSgoMAICM2gCf3LudHVQGE1XxuEACCYjJ3WaUAQIl5PmUAhv2iTZPJuhy5E6EL4LR5ypi+zVqwc7QTwIqOEbmlYGFxYRzAqJ8b810AHR0V+VVUIgAqVdcPGQDKhNXhAQiYQyb0eKuoD6OjhfjYwYliT+c4gFUrtv/xmAUA9u7uav+DA6C0T3XdrigFvz1BnDELgN8OAFYFQRsA9PV2VuZVAJTHcvIQt6uWd9UrbcWKfgD9YyW/3wEQlSIAzOZ0jzITSm1ivCJlNQhLWR6op76yUgMsLIJVY3UOAJSXwZpQh2SgjEfSCFilALgtSEgAWGUrygkAVTd5e/EcB0AiGrkAICgqSwiA6jADkB8UUiHU9YI6hAhrfDUH4M1ranN5VWDWJgaDwWAwGOYcs6wB4gxgRKpGhNPwlSalCJG6ATK5IJZWkMRKI6X/iEgi2GpTI5f6JGm90ioiHqQ8fOs1MWmlVBOTGSCYUnFzS3veiJQea1L1FeFCO+s0OAmF2Q/xv9JLlQYiVqTJyyECVk19xaRrkS+UtoYSQBkTAUROcr3qKkh2S/Zz7Buk94z1+WCCNJjA0kTaOSlt/2I2B0CMCUwSRUATDVCs75Hqn8zG5kzfBBaGWTegyZU6h0Dlkxi/pMpnOj2Xwz4SU7r+TGLqamqnzhyepqnSuvGRiRvPbCR62hHaPVGaj8PinNCACiqiHh+hVj9MMBX8ERAAtd0la1EVQHTShP9UEQCrIbdf3fDaEtXIIncMQMlSChI/YgD6a6WJ0AZQ0W40PbmyzTiAEc+VaqFdla4uZ0Lus7w0CiDWIc2zKwCKlvfs6BIAz+9bWMh7AIqd43v3dQFAlcWTObMjACfO2wfg1PZd/9/2PwNQsrxzFr8IoNzj7Dm+E8DW7Uvl/tY+p7iLAHBHReQQAMVeALArgvcBAN9plZd2AGAnKN+FUsHLWQEAh3LpGOTtaHNGCQBLukLvt5j2c5CeZEK/VqKc3h7pN0JNfVD9rynPUe4I2QiJ1FF+l5BDlE/oCcGJiMUBSDU/iPIBinKwxwkAUclXCuqUTo0ACEtCqqDsMVAfALz5cpATeYg7qm5laQ8v9BMAfe6h1CI3sGzZsoGBAfl5ZGQkl8tt2rTpK1/5im3bt9566/nnn5/eeVYFIAJug0SI6iO2Wu5eJwZNI06kwc0ZAIkE6l2sBNMjQ4tKsbeyFA4iV7kNpQ/JGOMys17arg9tFFPzXahDxlJBXukLTASjtBin33QZ3+fk7D4AUEZYvWGLBbAqAgALhFWVp1OuVOrqbKJ9zJXBSzSInrFCNW42vg/yd0hcf5hQ3lFUGb8IFZRN69VLqKDg0HPKXCR2+pmU2OV5Bo7PaRliSidoKVelG28his2AaXtAk5AnAlBsrauXgWLhhkQRpCFMPhdNJZKpRJ9J5J5MC42uPxniZVtsYY/bzywwBNFLI6peDNCvK2k7eM1DCOxcGGo/ZQGIIPGvIgGJ9hQA8I7Q+rMxAOKR9vjNvbRnGMA8Z8LjFgCbhIGwADw7uggpQaHTVd67L4zNlwavkDMpJK0q9suvhq3iQncMgKN9JOUOS5xhtysEMBHaO/bPBzDa34aanFWT1Z1jRQBG/TyAP1UWWIQD+MPIotd37QHgkOiN3S8BOL69T+6/65iu3/ctArC/v9j5jAWAeQJAZKPQFwLgDnXGCIDKYF4eMnSKbXd5APrRRv5UBGDXL4ChLV9AXZCKRI4uQdV4Yz7CfPJtWFKRXNQncSPSJksDJYzGIZa8XLB8gnh1HSIsCQBRXsihW9hL4ldzoJxQidwnbl+2GRZRXSwA1BbEl0CtMgDk/vjKLQBqtVpbW9vu3bvjLTt27PjSl7701FNP7du3761vfevLL79spWbCQ+gDZDAcPBdccMHIyAiAY4455q677jrc3TEYXlHM+DfMZWY6/nft2rVs2bL0lnvvvXfdunVdXV1dXV1tbW1btmw588wz429nUwASam2kLD4Zt8FY35PWiKi1lDq6bumWDllPG5Xi7SxI2kkfy3nKcKNkWyWBUuXhS6Q9K15/xAu0xGM6E0FGtDd0KiBfuacRdUVpUxdSWQBIg3Sf9C0SGT0ZiaRwLYiTWU8rvQ4NhFPm8gP1OQCrGoV52VEGIACRqiBuJfrS+EqzRrGM4U9nCohdnkHUegJQHs2UCakKYpQzNoVuQ+05PY1RU37961//v3uWDA5F13x6/wE3cniI9StT6YGmVvzMNOYr02Dm36k0Ui3alFGXMz52suCviLdUXzVYvlS4FiONip/JVT6TZCFK276nbLMx7YWyrccGL505QkdQzsLC9wga/wTCdUIeaQtIz3jVcwAENQuAYCyyBQB7wAr3twNwzh3yAzUypX5ln9deDl0AJcv7w8giAL1DHQAKec+1IgC7x1QeIItF/bUCAItGUkt0wcJtPrcAvK5DZZ0ZD9X0Z1shgHGu9CSdrrdDdtjR6veAwFLPl3RVft5fCOBlp1vGc/QPtg2ViwCOnjfo1xs+F7pj9qIQwEBn6TksBbDg/zEAlqdjnH3OqgKAPaFGVKmXRm4eQFAgQQEAeJxtJAcAUb5JbhcZ/JsOlJZDN8wjSmmASAQio4A5wiIAWBOQmhgSEm1hiLOrqK9k41YNfJAACPMkLABAUErUmdLVmggQmd2nW7iDiYYv0hkNpOlAbvE7AYDtm5Z5pynx+P/I9b3Dw8PprwghnZ2dmf137Nixc+fOtWvXBkHw8Y9//Nprr+3t7V2zZo389oQTTujt7U3vP6t5gARokH2jx8RZcJL9Q50ziqu3e7xD6hfKWoiSkaHlHqly5DpwiYLE1iKkxCzEytiU9UpLFVkbf6xmzGyPjUTxNCe4mhBp0GDzUvkPk0tIHHoiFcBF9LfyaZH/kkgoSYiqqxBUeTgRHjs/CXkHqB8RN+MeUfchbTdsjBSLRR+kHqo6mAAQq4gp44xyyMjl5l5BUcQtAIzyiFO5Z7PdpstJJ7F9fUegF0UmhIqxRskjzvqT/rdZU/qhmmaoV6PNK82MLF8ZU1ej5at1ryaPe0//RyKeDYOvN4FNIsQISjLfZp6pup0btqhnVq+RuIqKJ5kdUsayZH0lzRMy2EdY6h3AHSFkytBYAJo4KBPYETP+CRwnjBdFjIlV8wehHXfKvuv7FoCynZchV7Wn5okTy3LnYwv7APzv8HGBYAAqkbunvwtAFFAAYz7LFXwAcVK+nB0MThTlZykb+TwZ7fJzm1VDCpeEQ1EJQIF5pVIVwOhgSX5ld3lxcGu4qwggcC0AvEu9/O1cKCPInt+38GWnG8C8koq8KvvueDkHoKdz3O2qAehblwOw+NcsnszTczsAezxkNQqAedSuEAChq96AlQUEQNAhvG41Au0xALCqel0dRz2HSvIOS1k/zlgWkSFdfifscXleJWA5WpDg2k9XmrfCvHpZuDqdWZTLBjkKCncYAIIO2GUAKO7nAMaXUmkCi+tBCJcTn8oOHAwnncSe2hru3du7evXq9HbXdR9//PEVK1akN3Z0dHz4wx/+2Mc+tm3btne9611nnXUWAEKSx5nzuofRmMAMr3Z8EQWCm4hFw9zEjH/DXMYXUQjOGBsaGppy55NPPvnUU0+1LOuUU0656KKLtm7dumjRokceeUR+u23btiVLlqT3n+VEiPaEaKrwQIO3r9pB5vLRTtAp9UODbSi2oOmsyupfP4mTUsYmS7CgeZZClUoh5TSttCNMZyDUx2Urb6RsYfHFqo06uIzbBEk2ITCug0GQZHluvAnx4kCuDxpT08qOWVB6LMKT9YRKlthmZxascuUT2UppGbt4x1dEfW3ja6X/Z8rylU7/Ey+SpEbHcULpIWjpNZ9MhAhGWSQAyDXTweMj8hEd8S+AZoandNgXMGkC6FlM8xOrptJKqVZqIWnzaqr4SRqcoYIqRdP8hySKMgmB4mX0TFqecfqf9HzVKr8X9CwRzwnSJzRsj2g+BGDnwlhFKneojXojM+p6PUfK+BcC1ZpdHVH2GJZX80PODgCUHK9QKAMYK1R7+zoB+CERYyrbzYNDJwAoME+6I7w8Ok/qfiDzIJepDBNzOtTzsqe/i72UB+AMo+/YEMB/Yq0XMgBruvtPaOtFSifUxmoA2mh1nOUAjPoLlOnNo7GWrlRQ7tVDbh5Afi8DwAfy8lf2uyJ7fg1AIe/JKP1vTQsAACAASURBVFdLv4EswqWNb+/eeXKLPcwA9J2BRY8wAPaETvvbMCA5I3J6t0PhtyfOyM4wCZV6C36XDMsiygIVvwdDNXtTv778iy4zQria5LkjQAiAXL/OjaffQszXgTLan1o6h4Q5ME93oF19sHRMmXy/FHYTqTeytgsAS/63XFmSBzB8jHowvPkk6IoAhKWD0oD6iAJM1/K+adOmJ5544o477ujv73/44Yevueaa9vb2m2++uVKp9Pf3l8vl008/Pb3/rJrAuHBHEuGiVf6x9DiQmmcOwrQPUNN5p6n/0OQ9SXcjLsHR2GD8r/qWqdktIyigPpaq7nK0mYxzZRwVVEYBqHQAsERkEbSO/AIgGCGpjU3n+riMhvbjSW5jOpstjcBqKrlArL1POp8IjkBKBZpkfmM6abVsPo6PoMJyIgCWFcmSOjkrkCnn47kgpBxALbCl4ljodIhBdFCSkCeEf4TW2U0LPc0kjGl5/0yTdFNha78z2ZOMf9KMmH4oe6tjZwKJOADuNOlnYihvsXhoJTNNkvdZb0+85dJ1dXSzqhGRmliIzds7KgC6ixMyWKmg3yH9o6N7p3WtzTlSxr/Lwres3PbHeSoKqK9SesOC7QBOb9sut/znwCkAfE57uscBjOTyTNfP2fLsUfIDaw8A8AHXLlNogSC/H7VyDsDYfD1hEUhXn9wgJ5EFoA9dyEcAfh+xouUBKOn77+RCAPNp2G2NAzi6ODhYKwCo9hekX6NlRTIuHamiEACcYfhdAGCVaYAcgHIXddwAqboW8/KVhUeNA3hhYL63ow0Ak+HiHeG+P2cAuv5gl/YEaDYsYz/RMK+2uKMAIMqAiuOObbLgmSFqpXxYUxlnqAc7kgtjEbvjSKOt36EGc1xLgESqnEA8vGXOYUHU9N9YNIlyBEW1pzcfAAZPYAAWTtj5/R7iSH4gLLKh4y0AY830EdPHEyKY9vDfsGHD448/vnz58nw+/7d/+7cnn3wygE9+8pNnnnkmY+w73/mOVT/lJv+EYbhly5be3l7O+dKlS0877TRr+kG5BoPBYDAYDIePXC535513ZjZu3Lhx48aNTfdXIs79999/1VVXtbW1nXDCCQC2bds2MTFxxx13vOlNb5r+uQkXzmA10V0zIlSBQ4KU2MstouMpCHcopAeiLitBUjn9oBXRjYqfdGiVVKikDWFyPRfpqmwqOiNlJ6INGrVkPStXdep0DZoS7QSNVEQVzwqK2lal7GiJKkh2u7H0aSNaIUTQSvOUWt2mPxMuCCcAWE0QW8WtSAfq2H9z+svJdPofHfwllGbbCopWAMCuD/IaoW7FcwDwiPKIAODhQWnvj5QVcJZpFPya9PAZ3rRY62NZU7g/NxrjJulqo/GrUffTOgMQJnWFnrr+l06EmDaB0VBgqlJfmJ4HNOp1P41RqIKSTLhA4gHNVPSNXIhHgaoMU7SCZblhACvzg/OtcQA7OycenuI6J+NIGf8cdL/Xbuu59cwFO8qRC+BlrwfaDgWg7OXGqy4Av+w4JeVlzMoMQG4/CUvq95CevPndBIAzLmQpRndY/RjcUkXI7YmobTcAhEWrtpACqNr8hbH5AObnVSkMmRDI55ZDQwBFy1vVPghgbGG+WlUz+3C5ID9IrXl1SQTAKlP5o1tlwmoMgB+6fg8A1HJJpLGs/Ry80GbXCPQIoRXGllYAhC8VszaQxlJFlGh1jlLAJynoGIFM/1YDgDCnsv6EyoEbrJoEaqntsv5QRQ3dsMipr3VOdX7hYEF9/UptAEmXGI/rbKgINR1ZzAjcAcTXW13gdD2yF4DlJ70J80cBIOOY2nmnNYd0/KvRdt111913331xtBiA7du3v+Md7/jd7343g8YEaMVPz3fCUQGQQCIPkYhELgXAdaR3HAxFAxHmKACi39FET0+ZYHIWiEzd5sn6peNXVVNR3Wf5lVT9RU6TyCkA3NHTXEN0omDKgBrnWVYx9hFJQksAABRERb2lriW2fJF6kSiZ7iNlJWxyXfX+Q1DF0ZJIOh0oJ/2TQGN1vW4siQtrGGCiPsKL6n8Zi6TTj0N5wQoASIWzo/Ou2qQ4UisA8HyLH5zxS+IL4jemA3s1MyvJlKef6jBDnPq5VSxYY/cOTc2vKYvANwZ/tawFlhySSEKZ/Be6hcnsX60yH2ZWXNnsoGmjWCpJunxJ6whWeL4FYP9EW4dTBXBScfdSaxhAhzOAg2BG4/+mm2760pe+pK6F8xtvvPHGG29szIQ7SW7cA4ZA2DTsySnDU8nyZTpXmdtwiV39P11/BLC80PPSxHwAu/MdnnYTLKMIgDtqbgxLwh0gAGrdAFBZQvL7AKDWo87lDqmfjDtUOtm07STSalYOc9bCuph5m0QAupwJmWB6V6Vry+5lAIKKveaoXgAFO9jyJx1MVJIF3gRS2e29RZHcIiIiAgqgGpea18vsoCtiey0AMv8yd9TScfR0vzCQJEhUR7kEgFUVsfFLmsNka+lgZwlniQuYXI2zKmoL1LQfp41G5uUi/+aIHKiEExnAlR7e8sUXxglTZGXfXLJDLPHLD85Y4oYrH5ZinwDgt5GBc5cAyA+qV2Px+YF8nw8g8A/OB0iQ4JDN/2pyDIJg0aJF6S96enoyAWMGw2HBF8w/AhbABsMhYUbj/6abbrrpppsACCEuuOCCyy+/vDET7p49eybJjWswvKrwBQvEdJ2gZ4oa99dff/3rX//6devWrVmzhhCybdu2Rx999Prrr59xe0kdcAAgoQ+9EBSOBUeejioldqK6SPQfco9k9VZf5qKRSWxJcbV2bTiLl4bJPpmUOY00KTXP6vaPpfUkm2LSIwKA0HipChWeZomMVzvVMnK8qJU3hDvKG5mmVDSpOvN1dy92BdW+z0KuM2R2SgAchDDdQ522n9RfThOS4C8OgDEhfZ8LdiB1P/OcCoCS1q46JKqUbAD7CZe2sJo71a84KZ6wjjABqFWmwUNaWT1N2gm6sRZYU1oVx5gkCmwqvVQTE1h94fpGE1hSCkOd4kBWfgfs+5xqIas2TlyeWVp/TABEOS53kDkAvZAF3AIwzvMeLABl4QAHXhH+wMb/D37wgzPPPPPYY4/dtGlTJhPuli1bJsmNazC8qvCE5R9qAWjjxo3r16+/9957ZZ7EdevWfeELX8ikGDIYDgueYD4Eph0JaTC8lvAEG6tGAwP9N9xwQ3o7pfT666/v6upqPKRard5yyy2/+tWvADRmwp08N67B8KrCEyxo5Ql70CQrIBn5FUeBZfIFTZfWi0IScSEVFeDSactultujMRm0+rfetB/rOZCEf6fyD0ErWgAwov11xCQp8xtt//Wdz25pXkxUdklqnmztcMMgPfgIhdTEsEBF5jOudGCEC6kVS1qyCADqc+kpNUnPM85D6ZRC8hZFNrT2S8RqMFXZQydWJ7rwhUyjDluokP5m6fxl3HuBeVL3M88uA5jPxl0aAui2xqVmqMPpkjUF9/dNHEwY8JFEWoOS0QPpr2ZQ8RSTalka24mdftIaoHi3TFrqpp2clY4BAIRFpQao7pCpguezPkCpavCt8junU73XbW+dD3o6xGrjyKnfHqmHhWoFEtGeItLl37Ui5RVHgoGwDcC+UAB1WfxnytiI8H0/I+tQSluZrr797W+/853vbGtrU31uyIQ7SW7cA0aABKl4kHLoOCQCMBQVAEyEroyHP6P48kq3H8DjbNXW/sVy56jHB1DtokJOlW4U5WwAPM8BLFw2LP0Ox55XMfbuEPXbCIAwR60aBeCUOY2Uj+lL3QsAxHnLpB66vaA8ZXJW0FaqAShTsaQwCmCeU3l6WGUZliXN/S4OgPrKj5iEjHeEsmNyt2pZ5dupUUdMqBIE3tEeAHe7C8AZJpX2HIDupaMDp3QDmP9Mcp+lp07sP0S4CF0CYPhEALDHSEEXPolDbeQ4JEIlYg7zyk3Tm8/d/uSpYbWsOj/2hqYe7AmVVUh+RYM4vZzshi65XQNtyKShKslbSdCPzDNgVTmAfF9oj/gA2F7t8eaoJ8canzQrx2FlNqPAJE0mPo3UbyNS82/yCKbq/qQd2tEg93CL8PqEYGlJKCZOLwSAabmHc1WdR7BstqHGoLBWpKtJJH2I40TqK5clOnMtCakxxLVzd6C9v0PBqskoEYwq7bpLlYSkU7e1qjSCtEWMa389dffiHhNVKDgisTc00X0DIETqSahvPK4AHzsGOjSySQhgPhsHsMrpb6c1AJ5gPVYZQJtV21frAMAKE8+27PXUeML2BDnyNECZVH76XTVZtkMcXMLDuNkpZazY4BXHhc2eeS62eTVxgp7SapYxgTXfRwCgLQLByFTxlQBopLKnxhGjTf2p9c4AwJE1gcXOoTLvC8CkIDFecPdWOgDMc3qkXXhnrQC8NGWvWuEJO6IRIeTTn/70NA/50Y9+dNttt8nPjZlw9+3bN0lu3ANGOkHPs1XslS/YUFCIv/Upc0kI4ASn9/VuBGCv37W3qLLsjQ4XAbB8GHkMgPCYdEamTgTAC9lpPbsALDpdlc7YumgxXiwCaH+JSP8Bv0TlnOaOiuKzLoCJo9SM4TkRgIE4bkojOJHxYh1OzR7T09oIAFBfhunEv7Ugwzo8Lc8BIKcnYieSBR9oSEgpABAWBYDiECEBAVCt2f78EMC+N6rBX9xJC31yJazkHgBeJwEQLakBoKvCwYoaXnTQAeAMq9LrcQofQWFNUMggr5SLgTOmXjdB6nJVsfcIQZEg9b4TVJeY1O4iMktwHB0maPLGccoA4JdUbiR/foiIAJhYTgE4w+6CLQSAu1XJ+tyrseXzAFQXOXgOB4wn7ENnAlM/iYwC+8Mf/vDjH//4xz/+8bPPPvvggw9+7GMfO0RnNRimjwfmz1AF+uSTT1566aXxv5s2bVq9evWaNWv+53/+p9UWg+HVyUzHf19f386dO+VSFsD69esfffTRSqWyY8cOmQm3ccuh6bjBMAscwPw/fWY1Coxof2eLQrtAAg2FD/2QxJljtFOkipBPLf7q1oKxGlwnhOUNieHjZMrxEpBKpZGt9D3E0is8G1MiHZmTyhhMCdFCew0jVoBrtWGSvCEuvU7q9qShCkdPlPP6IhrMWKr0Dw2FslVFifWq8cLlGii2HkprGom41ACFgKAUgOCgQdYWFl8gpCGMyNOpwPi0wklWNo0LOEOXG5SWrx5WPtoiAByCdqq8CtpoFYDvHpSO3ePWjOIoP/vZz37ve9877bTT5L+HPQpG6XsmNwAdgOInnfjnIHGdbJn32Ou5sfz7bBTlaJUBKKv7Sexf2YB5Eqmnh1ukVV74pGgM09HF0+571gSvU/EGbYjysXEN0OWv46Ix1bLba7cBsGm0tCBrYBy4BzQAj1vBJIU5Gvj5z3/+1re+NTZyrVy5MpMJt3HLwXQvxqXhW+b9If53LMrJAuyyKvsSZ7iNVQH0RyWXBAAmQves7h1yZ4dyAC8NdIdlGwAJSDpuxQ+sR3uPArC4bVzuf/ZRLy48fgzAs6NLtj63AkD7c1asepf1O3P71E2r5WRiErFkyRCA4XJBFlXtyNekNf/loe5YiSJNP3GmA1UVW4eFWxNEzsw81KaJEkiXj9SUGo8xd4ABqNiFU47fCeCZbcqndvx47ndZAPL7iCpb5KC6EABktv28m7KDFAIAZCUvDxYAFF+ynDEACEuQiiXCEbSnDJq2cvlgNV3viIFWVMdk0Hvaz0SW1paj3QqEfkOpfHjcStnCInV/VNR9RFCIoG0ClY5o+3IGoO1ENfG27eZeJwUQ9uNgmOn4nxGzHQU2aZp8EtXLPQDxQnWU25BMMOLxX8GonBlJFPvK6KZiaYNm50GhjDVURUVFcWSHdnBJJ/VpWoIjHS1VnxkIUGVv0+5Bja5Cak/ZeMoSqqfX5hWOBKOZ7TyxFid1yhrm96wzUJIoSBq2QlAtq8WWLznTKPGOxRelniIREYQUQOgzlQrIVmngfc7SFZhdEsnh5BC7jdagTWMAiuygZlhf2NNPhQ7gz/7szwBs3bpV/nvvvfe+wlEwmRrvinjMJ045DW/j2H0n48czCdN5ex2weSuMpqgCNiMiPmPhKeUD1Aoaiqa2sLrsoNkAyWz2VLUbF1QXJUyXfwcQuarqe9AuuKuNIBYH4BQCAKWCZ+nlwsLiOIClhRGZeMaL6yodEL6wwymjYVNcffXVV199dXpLYybcSXLjHjAUfKk1PMaTHDLtrAbAdUIAno64a6c1aQsbCgoyUyKA+bkygCUrRp8tLgbQ199OQrlmIwB8z5arr0peLV73Vjpk4rEOp7rk6AEAOBpjlTyAysvtpR0EQFH7drOaDWDiRCVV9LQrO9qK0rA02N030pFxvZDzodfDIYWbkMoK9lEepL3utyBDjuiUng2Eg0OLQV6XsoVZY2xb3wIAb1j7ojzkiSeP9Zf6APzFKTeQfAhdPy6KWFwkRF44o6LQXQFQzTvefnXTpEMSs3mYT148YdmyyhRAlFfJFVlVCTF+u3IkslLpEJUPqF6BM+WTqr017MTDxKrIdbX2eBtg3GaAzhhXZdIWHCjHMwRFInMCkb6D8gGa6fiXXHnlleedd558EJYtWzYwoDyTRkZGcrlkiJooMMOrHU9YQyP+vn373vKWt6S3E0LuuOOOpUuXZvZfv3694zixAGSiYAxHNJ6wvMnSVBgMr2UOYPzffffdP/nJT8477zwAtVqtra1t9+7dTfec7SiwFIkLZH3yjzqYNpnpfUhL7VEEAD5YxAFQ3VrT/WXpxDDPAFCfx4FjUodhgXAmkM5qT0ns6pg2+giqNEPM10VSI2V7E1FWJ0SihhqrWm8hff7jkKtGRJImm+t/CYDIoVGOAgjzVAWOBaqeRiozkLL9pZT2KoeQXBk3C7VT6qK0NzRShYVpELt8EhHINTGV6xtmq6rvlcgtRznoTK/9UcEhEwB8RONaM+SQAECh1WVPD49blRrlnGecQHO5XMZu24pXJgoGIGnv5iaeztPRf2QcmSfRAynLWiqeq1Wli0YyOqFGO1fjlphJHufsWSaLCUW9Iay54/Ok6p9Yr6OLYwCpp6CxgHyjLYxGIp1jXVja9zOVHkzOElFOWb6EJaTmf8mSIVlBU5Y+hc44bNNQBj8CWOyMABihlUmuYkoOqQlgFmEQPawca4AGwjb5+PvCBnC00+dCqoLUtQzUSkPVQrqFNyzYfs7iFwH4C9gfxxcAeLFvPoCgZskIuz39Kg4un/dP6uwF0Oe1y9ry0Nnql53cG66lSJVnd/Y4ANwdzkCpBIBRvnLeMICAW/u9dgC1isOPVQ+a9FyW1qv8XhqUcwDCIheWNhuN2UiFx7KIYMQGICwhCgAgun0AXheRhT78vjx2FAE8UVspD7EXV/zBHADko3zJA9BVqkj1FWMRgErVLeTrtIaRTqlfLHnlCQtA8UWL7nYhNS4dmSoC8q9gVYKU3zQNVGn3+BmxaioiLDaEyXTVLFC1R0gkWGwc9AUAqyradqp7NXKMA6DUywGwGs/vGQfA8yr4K2jTybIPLgpspuN/z5493/jGN6666ir5765du5YtW9Zq59mPApu6TDRLBKNESJqebpxEkYAUa3wl+kQ8E3QmLEocCwD1LQDcYbEwobIsBkTGH/JIuQdxWxlwWf20Lxjil2Mcjggt7oiMuBPLQ42mMVlbPtIV3XnKCqv7pvelSJVL4w6VWvp4AAiq6mlwJAXFMtp+2VpjeDCNhOqzTg0QJ0Ik2uNHak15EtsCKfIJ5RSEKGAyrHSgWiiwNugUiO06EeKAvnIPlpz7ZiWAixBywQUXHMCBr1gUzIEwpQFrklj3rLsMy35oRWOsfnqLtHm1EoBaP6dNYr6mEpXSnj3Tif/Se9YN+6aCDhoeCqTcBNO2sBan0F4gDd0RTMxbMA5gUbFcCWykSi7Iwg4n9/Rq1x/8qbIAwGiV4mDCYI4QOMgYd91U/LR8/GVBtHZak2kh20ntpaAHQCVMnDFllPtQUFhuDQOYlyvLVAIyTP1/d67yx1wAkY5sL3v5nzz3OgD5vM+rFgASkIgJAP1uqS3vAZBlLgDYqyIAAWe9420Aokh96OiurSr2A3imsLjqq1/a3WtBh8GL+UIKOsSNmM0BRMNOOuYcAHcQLAwBiEgtquxcCKCQ99Z09wN4CkvZ0yUAHlWmK7bSd7prAPy+vG9zAPu9jszNrFTVzjK7ZhyECytyBtScoIqOBdIzSUF9Vb2rtkC9d9JlJKxU0QwAnq4Pz2TFMR9hgSAV6hs54No4WBoOAQRFxnwOwHmxr7xsedyUO+SpNbyvBgANrfHlLgAycrDiO4+EEOLLX/5yeiOldMOGDXGuB7Un53/1V391yy233HXXXXLLjh07du7cuXbt2iAIPv7xj1977bXp/We1FpjBcAjwhBW0Stk7DdavX3/zzTdXKpX+/n4Z87Jo0aLMllnsrcEwuxzk+DcYjmg8YUln0+HhumRalNKwQUF+2223nXnmmWeccUYsAHV0dHz4wx/+2Mc+tm3btne9611nnXVWesKf7Vpgk6h/Gl0gmy0NE0tQi+Uj9WVVUq34qdTUKlan/CeMEdcBIFwLAHGsWCmXKjRBAfCIhHnVPq/P+JfEfMUF1aWNLBVIkqlQm2iA6u8BTVnKmiVUVJqeeDmLlAmM20RFkOnKc5yB6jSPPKmS0dwJNOtJ3SztJI2aHIu4gGuQ6IGUBgjwmAVgtJobsEoApCPhS7RH+jnKyC+J9nw8KA2QL+zgIHwgXrEomCxNfZwljWVKG61XrexZkxQ3nWZWw3i3puqWSWpftGDKoqcHzjScoGNiQ1jaCtZq51allFOmcBWHJBfQqYBNUq64AHaTDlnVvDqWAwBOOnrGAfxxeEHJrQFwKB/zXQATowcfBHAEmMAE4Anb1bEebbQqtcJyEhjjuR4dFfG7itIcLGsflR+CiAJI51GUEaZr8r0AHBr+cawHQO+I0pRUx3LSKFYey9EaBSAcNe3WKo50HA71b3ZUxzAAm/Gi6wPo7etU8RzdKoK19PM2u1ONBFlrvf1PFIAzLixPAIhsNnYUAcDnc5ntEHHNJ06k/zKPiLSOhRYH4FuWVGKdumTP824PgJ584nt8Yuc+AMNLio/9fjWAzkVjVc8B4FdsAMzm0nMcuriU79nyesN9+dIAAPid6m3id4lYWw/AKqtQL3ssKfUdFzeVg9nWHQlKOhpGRj3H9hjt8mynjLfaGYP4HTYAu6sk35JjKxgAa8IB6nKGMp97HQQAbT/Y8c+ZRQiJq/xOwsMPP/zII4/ccccdQ0NDtm2Xy+UNGzaceuqplmWdcsopF1100datW5sIQLMWBdaMTEkg0dTRJyPuTBJHlgkl8zzhyUruygci9r0gqbMDABwV08iI8DmAMM/UDOjomEad94klwYECSKxdsQ+8YFPXKUuJRNJ/PrGFSTiLK8bHzSqvnXiCVraw1AQoP8e15TmyjcQkaSTr31A0SiqXNT02ltUITy45toUF1AJQjuiQFQHY76hsZlJO77bGZZSHS0PpHuTQgwsDFpaPmT1CF1xwQdpe9spEwcyAjBDDWKu00dl/07s1Wq+m7wMUt9AqEWKjGNQqcF0nPp2+GNQqBr4JM0niHMeCZezL6Q9NOiOTWYTqr9BzuIoYjeWe+EEQQppj+muWCCkAMmYBEKVotL8NAHGikZzyAQpqFoBovDz9q2jkAMb/YaHGnR8NnXHJvKflv+2sdtuOcwGEXN3EM7p3ATipuHsidAEsLox3OWpm6PPaAfTXCkAPgOWF4WdHFgN4Q/fLAMqhe1LHPgBx2PyP//R6bzgHgOZDGYUksxECEC6VHjZDZZ2JmHAAJbc2MFaCdhUCUAntB/YfB4AF6NiunhrpHSHjt/02Il1k3FHe9ScBINpORle76av25/EoIACsURZ2RNCh7G3aiafLmXjj4gkAjn4fOCyS2fO39C/P77IAVLscGfou/1aqrh+qRy8K1Ac52JxxKqUZYcGfxwE4Q9QZSfpDhJLhoIu6E66MZcJSgfE8lQhG1ZaXNeHzkNkirTJyg9JJVNjjsUlLAIhcJyhSABNHd0h7mRSDojyT642JRWqsuiNc+g9FrcsYTIcZjf+7775bfvjUpz61Zs2aq6+++utf//oTTzxxxx139Pf3P/zww9dcc016fzVoNm7c+NBDD5199tlhGAZBsG7dugceeCCzq8FwWAiEFc+hBsNcw4x/w1zmIMf/hg0bhBDLly9ft27dRz/60ZNPPjn9bSJYOY5z1VVXua67efPmrVu3joyMHEAYvHCs2Acq45tMQp5VNTTTA6n0P/rY5pqNdOOWpSJK6tqRRjElccsuUe1iSRiRYWI04FZNeUPHhdOVtkauCCG0syTRqcH14nLa5sG0aYwqtUpWMy9oXeI1zpTlK3XeVIMyQ0NzWxgSZdI0xkxsrZPHkojEOdFjt2jVf0HkCjiMvaEBaQKQad8A+IIB8LilEiTyUIWB8INav3rc8o8gH4i0FjOt6pjEdIXWnsutVEGTb2k0pakutdAzHUQdDBLylrqfmWT9mdL9uTFwLIM2gTXxfZ6s2XR2LktHR4JwLsNhYmuaVt8GhJcZAGFR6lHoPCh01JIfhEs86ZbLBGoUQFCuLyc2Q46U8V8L7P964nX/ldMvmIC4+y2kQur+014I4Bf503mOA7BKwetW7Em34FAujX27Kl19lRKAtgXSmBg5LAKwxFFeIBcd/dzTnUsB9A51hKEDGZ3HBADmRtJXWgZYAZAWyZAzqZATnMiv9pQ7Bvd0AOhuI9V5OgFvamJ3xoXUAI0tp1JT0rZT9PwuAhDpEhbjS6nXrUtSVBiAIMoBGNhTeMCdBwA5Lt0HFixU9r7TenaVw3kABp6fL0dG0FuI5jMAjhsAIFQIbWKT7s+hz9igDcAeTexZzhAFkBuAXUleKOWlJMqrC4lyyvIgPRlItviR5wAAIABJREFUpH6LyjJ1kfY4pR4AxAXvZO4igIytpADcUbjDytJhjdYAOHlWWWABoDYJc4DWAAGwyyGAMKfGKi2qLIvhNDIPT8KBjf+vfvWr8kMul7vzzjtb7abavfXWWz/3uc89++yzmzZt+trXvnbeeef93d/93Q033JBxmZ4cQYhgjDCu0htm5BumVeUNstEknkMkThVdP8kKS8sLjqMsX14qbjBThkmdTmWg5o5N/bo3AYko4RQp+SZGyhYEguifQEkqQZMIkVbQelsY6qdddaLUNC20HwNnqeizBpSbTsoWhrrw+CYuDo1d4qpjgLz8AAAoU5UdIzvrtxSnBuUUvm0DGK2qJ1JOXj63pIp7njPRdgS4LswepP6VP8nrfzpyjOSAi5VOfhZVla91CbBGH6D4IZ2+WHMAh8wqab86NJOE4jjKuDSYwhL6naEc7EQ1iYfXLhdEbrHHpduiylYakngJol48rGL0NwbDqxH1Vv/85z//zDPPzJ8///bbb3/ooYdWrly5e/fudevWtRKAvv/973/0ox9Nb/E8r3k2ZYPh4AiEFR4JK2CD4VBgxr9hLnNIx79qt7u72/d9+UFuSWeKa+Syyy5729velt7y3e9+9zM33CQcJqJUWFEmmwjTNcLipWFmh1brXVd5KQuLxqtJpQyPi88zBl+nLJDr2vqMJkTbbqgfcMcGQP1Irg5DnY6rac5A9VXiuay/mvmPklH8xFWpYxotXyqrlS7bG2coiZVJHIktDFoPlG6tSQcslU1RWGD12rdEvxUIANTW9cuEUgWFgAUKICSImAWgwpRXoLTUBjnq65JtMiygIurcBmeKH7GgRajakUFS+2KqFcIs1p1It9mkntdU7tKtYsEadDktS743K3wxiQFr+nmAmh2baD2ptoI1GprTxWGgS16oo+orY5AQDCoMQlm4mCrHLSwiYymCdmFVCKBLI8VqWqHcpVlNZRui/kGN3iNl/JNIlt/STrtW4loukXn5WE0lfeXDbMvYUfKrFav7AFy0WJUS+9GOUxcUytARZMcU+2Rs6WCorO3znIkz5+8EsKvQtTlaASCqWqTMADA76u4sQ1u+ABxVGgbw7OBi6Z7MIyprgZUcb3SMAWA1QesjWvw2AqCyQFeT8NWLYHQ18bsIAGdYDR0awB4DgMJeWusBAGcnA2BXUZ0vyzepGzLc2yM//Ne8LrgcAFtUqxVsAO4+y+ugAKrVPADiRDKZUBp3gACwJ1Qun9gmELkYPSGZxJ0FVWVyrTASyuR2ROXODRC062Se8jK7IrmPO0ABOGPI7ScAwqJqTTDImC/ox0ow9SZigXBHZD5hAoD6XJakjBMnBkVS6o0A1FcZmTGHdPyrqfnmm28+55xz1q9fv2rVqgsvvPDiiy/+5S9/+YlPfKLVYYyxrq6u9JZisQgC7lBa1cVQI64kEqfBBJ6ZXv2GW9SYANeVVUwS6SdTNpVYlMQTusUQh8F7SeNKitL/0qovH0XG3Fahs42BJImRWIfKZ4inUdo6CjemaU2itOUrW5QxeUEoiS4TdR/PO8mWVAsyyIVwIWUj5ikJLNXVOqOACBCpaqwktoXJ5lmVhIwCCKgNIJ3sNpO4049GW1z9tPAFC48g5eLkvj6ttmR3aF05dfJEhY3tN63n1erwWFrKHDKJ4BK762Uyvx8k8omYSRh8I1IG4nbS+YbA+KzDXBwUplYIjpL7aewDpKcTeyypOgkkOaNZjVhlKYHpfNMHlQj3CBv/6STacQb8NNxWXlOsRqiurLxvYAmAby3usUs+gDWL9vfkygDufuk0AOVyntkRgP+z4iW5/xvaXxygbQDsYrjwuDEAmweX793dDaCzWM3ZAYCRmlrX+oUxABXPkbHl1aojKzp3dNT2lwmAgdN5x/N1Izz2WrSrQMqPk3mq8ig9eUw17tm5p/IA8kOC8ESq9tp1IVU9MNxB1Yg1Yckt3AEvcgDe0R4ZtQGIjgCA4MTXfmP59hqAiAlvvkzETJxx5dkzcjwBwI+qOnbyOEeB8haKShFUNmdllOWOEs1TscxCtIcAaiUCQOyypcBnjyOuXydjvqDlV+pzKdJ57dQd4wBqXRSpTC7uqPq9K/Op104BePZBiS+HdPyr3/nCCy98+umn77nnnu3bt69YsWLBggU//elP03kRDYbDhX+ElAIwGA4FZvwb5jKHdPwrAahWq7W3t19xxRUANm/e/OyzzwbBjOuvgiByKM07hDEAFCDIA6mCX3KvkLdU9ceKn8ZFZBgBIIwmWvRYNyPFQwekkJPHioIDrW+XSRHjbqg+aF2RdLKmfsRaLDTjoBIRZVVBTf9Fw4pnEtLao9j4pZsFAG63jAKjiedyyhs6pd1JE9X74RNOmC6wbtXqg/X0EpnqjESyOkwYUX1dSgUKQuTaWhZWC6iVqXhka0frKMjjIPA5C46UMOCmORUziQcnV//E9qOMkibzyFj1Op7GHaaD6zRRBc2WGa6Z0mjKSK74wRQt1nxxCjHBaKsgLxkOhtgW1lArA609ozPaU8LVsp4GwqoSAFFOlRqIjcK6brbaTgMSa4lk6FBjxMOMOFLGPxFgtUQDlKmNyHU4hZyVkcpPA61Fs/5kRzkbwHPbj/6DtvgDoBGJHAHgwd6T5P4jpxXWdb0AYBxYlBsFsKbTXV4aBVAJ7YnQBjBeVsEZf8AiAOWhAizVIR82gD3lDhnSNb6UjR6vvsr3UuhMOVFep4Xz1HVZNchS8xVd9Jwv8SbWBAAqy5mo9yfo/D2TTVnDABDq6K2QKlMUDZQpzdrt+l0AwOdzAJHHRKB+8cpgAQCtUZHnAMorqVTSWGXCHQEgLNuRmwwPpxD4edUN2XisgqKBrtweq0FzHB4FIOPX/C5uTVAA7rCKC+NWYp2wqnWPpNdBaEQBeO0EQLWb2RN5AIU+dfbiPl7rpgDoQaXBOrTjX7Xb2anqyd16662XX3755s2b3/e+9/3Lv/zLITqrwWAwGAwGw2Eku2D9+te//pOf/OTkk0/etWvX2Wef/ZGPfGQmrRHu0KBkMZ8C4HlLRZtH0mYZxQl7dGrhOEo2lbmkIXgeSKesVQ7UBBByDceIkC63EYlkPHwUKfcgWU2iLReXTU06Gm9R7QtWDdFsbUoaFD/pRCNIaYaSLVOpiOKNjVWpRb27FGdKEo9yev0UezRFsboo8YYGQEGSTLj1WaTTsfSZY6X/GrTbRHoNLfckHITX3Qpu64Ih8uemKjN2Rdcutii3Zd4BflB5UAJuRUdoFMxMXXrDaArnnqZMqbPJjOoopYKdjkfRpLRMAtQsBn4S3c9Mq8HHhVQniXJP7dzcsS/1lUoh0ao4BgDkAMAZVW6eNFDFhuVjRSNdSNhXBQcEU14g9OC8QGc6/n/1q1996lOfGhwcvPHGG2W6802bNn3lK1+xbfvWW289//zzm26ZBURdrU0WJDoPAMxDpGMhlLZbJL418h46o+oeshoRKc03DZSnrdBz79NPrA5OpwCOLg7Kiu7by13HtfcDWOhGspJ8UFH6paGarg1ApT+7iDwGYGigNG/AB8BqVuSqnSdWcgDtf6QAxFjiDGTVZE8EcgRAlFcjys6FsghrZHGEFEDHUzYAZ1wU+gIAfoca2KU96omodrNRV06hwh0GgNyQKPQBgLc/D2DsNK97qfKbHNrVAcAeo0rdGEKm+QlLQm5x+yx/afJqC2oW6/IBhGVbJvWhvtIVRTnwjjptpF3yg4EctBbTHaSy8aCofgi/E7rINbwJqRuL34MYW5E8LH6X8ObLn0w948V9XOYBmr5JpCmHdP7Ptus4znHHHQdgwYIF1Wq12SEtEQTcJtxmYVGmGRTUZwBk8VjqM+JHkFpupgu5K/mDIXZVjnwAQtvCiOyhldgR1C1nVB4rmKXLaVl6LtPDXWrI80583kTuqRezSBSpclWMkVRojIgNY4ykylZnRKJU3p1U+EmjV3VcnKt+Oq6LRlGyy+Sp25JEiMm/TYnNZzzrhibiOm+yM/K8zOPxRmUcZLpIGRc6nIGGOWkUUGlOpH6VBESaLQItJ41W/3/23jXIkqM6F/0ys1579+7u6Z6Z1sxoXkg8ZvQYSzYaOMw5gGQhbAWEQ2CIOBDBI8DAhCPwAMLWDxv/cDguDhvLAgHjaweEb+AAfhDc64MNDhAmxDE6GBD4jGwfyWikeWlG8+rp7v2oXVWZeX+szKzX3ru7p3uERtrrR8fu2lVZWVW5s1autb7vi5peCkCsLYCZapGuhNXxeW51xfWiORek4pEs66AM5F0sDm+HmnR4ybqNcKGGK2AMPWS5Y0vtjPYRhxdBD1qrDMlqKa2HkPHzRKmg6EU5VZkCM5BnfpJeXPKimATK1KOuQyazI0s5ssu2VY3/xcXFgwcPfu9734uiaN++fffcc0+/3//kJz/505/+9MyZM3fddddTTz116tSpypZ1kcNjGsGSLk41RiSB8oB2o4jz3H1+LM1pXr7RzCp24PtL+UYAWrAjR7cDuPamS+fiFoAJL90SLgJoy4gk2HK5LtMb8/hkX9Dn4ESoRQyAp6p12nzb28oAJNMAEM4bvydY0jzRAOKN3AhNzOReLXEVKsmIO42KlKNLigaV31aVARldUuppAeDSHhBwTDMWzWtYJ4nJ0LvbFFkTPu64vCaYN78UyrQ6XLAKQGksc2e6grohMluk38snaqY8AHKjqW9RkiNSsGKNWWIRfAKiY+6/413sbDXTPllqq7zJQxIxm3gG7vIBaM/snK1p/Xtl53/T7qZNm/bu3fuGN7why7IHHnggy7L3vOc967YyGNvY1mCp5FKN8gjHNrYXsK1q/H/jG9+4++67Ccjy2GOPzczMfPOb3zxw4MDMzMzevXsnJycfffTR+pYr2v+xjW0tdnnz/zvf+c6//uu/ps+HDx++/vrr9+zZ89BDD1V2M47/yZMn4zg+ceLEsWPHpqensyx71ate9aEPfWh152SQIZM+s0Q18HoctsxWxKbQmCdM26RYHgqiFvqJWTX2redPJcxFBlurAck8SrQFWUMA0ILxdMBSiztRYMmQZKC1SDUCpPIPxUyZLWrTgrs+MFMdzOta0xQcMhEpu6Zy6SQZuBiSrtVvMqE0AAkGQMCsWUUheE7aFJ4NSOaJLc5MaxwAFHJqH7PFZ7QIy6VeE+Y4r4tX4QI/kNqQC9g1Ok8YXYgWPvWqKPEBgGVGK0MrpPAB9LhOJjiANZVAA6kSVyUKZpjQxIhwy7Cv3PZhOhvAMBLqYqjG8FPU2189cH2AAkYl/rQy9ufV0v+MTKINroau5KxrHRgAjNc8J4aQHvFEwKnE1M9cPBbCpoZ5nh1bi7nxf/To0eL2MAyvvfbays5PP/30wsLCgQMHLl68ePDgwQ9/+MOnT592eN69e/eePn26vmVN/SuYSOHQFUrAzLWUxA8LcW4qbc5MrtCZFg78YbcQK0EMhxs3LWTwzvoAzvanKMz8S9MnQlttPhX0AZyfMkhu0hPlQpkIh2KtDT0A3jMhPX3VELFVg/faABDPKQDhPKd4hhJGMFvEpqB+atpAPqQUJFzqcmGkFNG4YO6DiM3jd3QMWrDGBQmAH+HdOQBYepnstTkAnnIAyYxs9Ey+cOFHmwGICZ1OGelTl1El4VKmINr5oFSBJrw6k4ykMLJWLhdvJm37vp2e7nobFIBnT84A0EIH8wxA4zzSCdO4bLiWzQcH7zdV/0R2MG8E5L2emUyyBjdPfG2T92XM/1/96le//vWv33777QCOHTs2It6Zf5qfn9+5c+fLXvayH//4x1/+8pfvuOOOKIoGtD3SNGfKL0CZTIELPY/88dOw4wkzEeQky7EBNCGmNgVGfa3LZUtphDUEoyB2MfRanAqV1L7xNgQ3jtfw6V4qkyagcqUwF5bPASzUkcDeuuIEGlARkiFcdHOr+ZkV1KqNsm6Qz+buKAC6VN9jA+w0a9jKAzeqtDDCZDS4lW9vuDLhaBlYNWBmBqsMlg/Lu+u1ryiP6oSY1CbHZyXr8/AkXYFkBGHQigV8HShhEsVfsGKQw17ny9LwFBJbbtsASp5BNiAXtirRrmWZD1fDf7iM65OzcC3fwxHKX5WquPrSpdgCfbT7V/fhsuoDuaSAXVRYztLEvM5FH2uxRPGkr6SUb3jDG0q9Zey73/1uRbGx0+n86Ec/+ta3vgXgda973Wte8xra0+2glBq4ZV2siDb1+pqcoaTFUSBD4qm5qyLNF1H9aQCQka2achWNKVColcyNGUGSx05v2b/9GIBEedeG8wAClpKGvEOh/vuprQCajX6PBzD0bUABryQjnkzlLcPKm3S2I7oEAFya9zpPGE2qiWUwElwLO8uJUAHobg8BzD6R12KS6yMjcw1KMAoKNM9m4SIH0LjAiXqxPwsAjS0dJyZ/YUIDCOYZXW86ZVgKw3mwRXPTiosazZG1FAAxk8i2D4AtCpr/swnLkmtXv73Yb0QpgHAmBpCkDdETAHqbTGuygWRTqWxItAUl1JIZqTmFHkwP41mGgp/nxTmGbi222vn/1KlTn/70p9/73vfSvy7eOTMzQ/HO/fv3u51Nu5/97GdvvfXWpaWlBx544Dd/8zcffvjhN73pTZ/73OfW1PGxjW09LFMiewHUAI1tbJdlmRLKC4QQT5bt5z//eV2vem5u7k1vetPu3bt37959xx13HDlyZMuWLY8//jh9+/jjj2/btq2+5Tm9nrGNbTWWKZH0lVLqlWW77bbbjh8/XtlZKfWBD3zggQceaDRM5Gp0vPMytcAGmyY3mUvfRv8IFkHlhJYpUuVxEWFrbwXvZQC4VCwLAPDWRLXx2krR8k2bdBJ8EwpyVimKZLagUoshJZGl03EUltSwAX/mlrnJIHIPCk6aTJ/rhoGriL6qFEGLRBl+cVtYTVEWLRgXbjVpPihDjFEKCJkL5KVK6iyijBg3XA5+no/Tmtoy/yobP6M4rRaMfGIGRWohrvpbBZziVVnEayXV1EGzFNC+ZqEE4HkyURyAf5ViuC7bBia/ikGdOiyr2sLlOHwrKkweuf/QKunaPkPjQKvqwLKZL/ubLdL/1BpZ5tfMM10MvoKyxu7DcorxTj2mXkltGLmqusLa/b5sdnh5Rvj1sje+8Y333HPPRz/6UaXUQw899JGPfGR6evpTn/pUt9s9d+5cu93+lV/5lS1btlS2rMupNUc8w5i9VtVhRZVy5RmMmBiEiQvaAJBaufL8BpZhYnnaPTPZsTT2Wp6JMCzKCECi/baMAEwHBsQzPd0F4DG1uOAB0BkXQgJIppgKIpTTmg45BcDrGKBT86yWPgdB21oaQMOVVNt0krRRCuJW7mwJWqeIiJxV2Pa9WLl5nrZ051jvxhjA1rlLADIpzj41azrUUAB6DUw8LQD4iyaW5qZ0EVf0qpmiAHwvMgHZmGVNDUC37H6281kmLp4h3BcDML1jQezWAJbaUTofAoCvJ2dNsq/XCwBIhdRmH7KJfLro7pasz4tn8c57FCvyfoI1Gg88zvlf/uVfFjcGQbBjx47Knp/73Of279//yle+8itf+YrbOCLeeZlaYAONae11JFPg5RcktxUqBpUd5VMYxUiVrzwHtzIZKJt4dKpe9QqD2lQofTPOivmderhbC6EtYL56CQ7XUUiE2XbMebX7d9iMbwFlhWOJxZFVpm8mdQVT5vwhejBKGo/E1RMUjnWXY7Ls5euA5uZHogpxaQPQdc8iMKrvLkFJuTkmmesPhTS1YFnEAaQTjNCtjtLe/dW+BsBCGTRTAI0opRTYGqf/THGpVzoatda/+7u/+7d/+7ee533iE594//vfjysE+h1htkxtpfuv2HVYKfZquZqeFbpKq/WoSscKPiLXvNKinwEEhmrZdFjdp6lQI8LlwpSm4T0CJ0/Tl/RYBd3pTJULfVit4meNKLBVjf89e/Z88IMffPWrX621vu+++/bt2wfgYx/72P79+4UQX/jCFzzP27VrV2XLmvpnTXMkM7kyGk9N7oNe2FobfJBINU3UmiOdqKYa6RA317nSH4OnczdZgPcAwDsRPbFtM4CZjd0pEQNYtPuk1keIvBTAuUuTetEHwKbS6UYM4ORNUDMpAPQ5HJsJSb9d9ABMnNYLL2UAkh6zxZdatkoPWHBNPpAuF+p2tiFYEgCY0l6PJtVq2WVnq3f+v6UA5q65uCWMAWxrLgJ4Yn6uddTcAuMaNhDPAYDXMbSKwZImWFY2kYtsAOB9M0RFz2D1yfsBwDqC5monT5a2vWCuByCNPQD/ZevTppU5PLG4GcCluNnummokA3abyAzKbCaRxNbYEwDEVNpoJADaz7TsZTLeB4B4A9ZibvyvxFP//ve//4Mf/OCLX/zixYsXfd9vt9tbtmz5wQ9+QN/W452XqQU2trE9Z5ZJIeVKnYmHH374W9/61hNPPLGwsHDDDTe89a1vXVxcvBKg37GN7bmxVY1/AIcOHTp06FBxy8GDB4kQaMSWsY3t+WmrGv9f/epX6cO99967Z8+e97///ceOHRsR71xXLTAFv50xpbmNGdBCynn3MmQApM9cTMKEyHpmT54oo2AqgxLBv+CuHtkQIVpJeZZIJj1q3CzOEnipwZ0N7mdeWemhFh8y3+XJrwFRInN4reHRyzQNMSDm5PgVAwFA2MUrLTeZFaBgimUh5e/MMqggOshKkhoi52Eztc8Fcnoql4ZTHPENvSFz8VsbHVUu4RUwAMq2ljYZMWGo0CrVE1FKpJinAAhfNcIEQCvoUx2iWpsWQKZXsQKemprSWmdZlqZpGIZhGI4ugrsithKxi8tvfBDZD8qBn9GnGBGYKerVXF436m2WiBCX5Wxc5kGvpBq6bnUgmCtQHVgQnevG2/LbfAh7mtsf+kBsyoCK3bXZqsb/2Mb2ArM1jv/R8c78n06n89a3vjUMwx//+MdHjhxJ6grtyxnTWrRjJgPZ8ABIV/QTuJcrAyBDltoKH78DUDLFo0oUwXscAEKPFefN0HMlKbyXAEBm4Fo8SYEQBb/KA+OLCoW4t2mkMLcWBMWAYoWBw1Y5wDA5QI6K2vlDogql0V4p9ZCfrJAsG1DK4NKyhe1MatFTAFQgqNuix9mUB4DcEQDKTc0cKDs6jkTVOUDGZ+J5DNmwkymQX2W0rzkn7k4tWNZgIHcnKoWps4alIm1q5/oAYIGkuiXhy9CTAKaDmJig1wYCgJRM9pVS6u1vf3txexAEf/7nfz43N1fceOutt952223btm2L4/jTn/50s9m8cqDfy7TCeFhhFU5pt0oK2La2osq2utX9CTmoxGeE2zHkq5XkqkbYZRw7iGV0sDnvZ9Q++VIEKJNEu8N54VfOVMExov6skxskJbs6eLA0WJbPQjIwK17KfKUTjLKEoq/NbONB2rkltUl8d7ipdPHNX1FeOfLEJBaDeRz76XYAm/9L95eaJwAk2k+kAJDatigF5nkym0oBeIE8fnwzAC+F9hQA3ecss7WVPY6Ccnt0FgDau/TUzxkANcH8mdJ8lmSCYPYy5cQ0TSDz/iYpj3IAXm36SyfE+Vs4gHRX3GgmAGYb3aafAlhIGgAuXGpNl/WzgnaeDfQ7GoDX181nGYB4BlaXDAC8Tn4PCdOeToGYoFWg0CAssR3/iaDMHaH655MJumlN0adk3ISXnsI07Tt/cQKAzjiaEkCjkfSFByDjmi6/uSEBILd0aP9+f9IUY6wNBn954//P/uzP3OcR8U7jAH32s5/9oz/6o8cee+zw4cP333//7bff/od/+If33Xff6oqgxza2K2BSCsV9xtjb3va24nbG2NTUVGXnv/u7v3vyySePHTu2sLBw1113/fqv/zquGOh3bGN7DkxKoa5GHqyxjW097IqO/3VFgQGQihEtFAB4xcizS+uUgiMBQGK/pL4bCdUIQOGQgrKuFtwBuMzSMPRcuIWkNrye1iST29NeTwIQ7T4A1Qh0jU2kBvqwERooW8LMAehCvVj9Sitr3yoLy8h8RKU+VAvuFNNK3Uqk/WAakQ1BJYTMy7mCiGFSWYJ52lV5qKBRCqczH5TPGAdgaK9EylioAUif0eoti4yCj+aGCEsFBiihQuViPwD8KCM+jMDPIj8tni5emxYYADBWd4AG2j/90z+95S1v2bx58+bNm1/72tf+8z//8+giuF+w1RJJBmw4gtGnxn+oTQTIEnXWhla1GHklwZUKtU/NCsowSpcDnMOCN6PyX8tlvga1NviQ+vZ6/muYMoazYhhplFy8V4okuSppQ5m4fkGgq8MYtMjhK9kE/B4A+Jc0gGSSEdUNwElWgmUQubqImW2I+IdLQynkItZeWZbJiWZoYeIcP/zZS/e//ikAm7yl814LwKW+qd7NlAAgFacQtZKcL3gARI/hmRBA1lLBJfOowouA5R9SvgG1aYsBjDfB8yQA95aj8A8A4SuSGHPxFSpSnjoOYllcfIkZSP2X9FtTMYBWkHlMATi9NLlxopNf3fnQvfGp3kBzQ3uohWln4jSjaH24yHhhupWR0abIWuZZMGWZJ7uCtQVgAkIAtr3ibKcfAOj2QgAn2tPEIZlK/oqpswCemJ9bWGiaRxBIAJOzHa/8Omk2+gAmwoSOdZQlsWcoGVXpbfD8svVEgUGDZQpCEURcACwoMFSCiz6lSAy5XxG75DiLs6YA4MEIeBkr4Kd04AHQlqpYC0GQwvBSatmTFfkN9Ql3xKRZwMwX0VvDoV7L2gCtoqGxh/pXphsOOABFXp1DquuckM1g17jJfBkeNunn1Ij5ichJYib3JwFGR1l9Uxe0NC5paLRglG8cIBlpFSoAaEoRSgDClwACTwZBBhtwBtDJfCo2WuivmlGzaEph5VGbffv2/c3f/M273/3upaWlhx566NChQzMzM1cC9Lu8VYZfJl1BW76xns8a2lppOA1SwrKEs4FvUIdDoOPFwWZTrgUnZshJh7s1K9lniOuzAr/xVelLAAAgAElEQVRn5YmtlVsxBTbaGXLFQCjAmMmUYJXaNkNbbBsXyuBS14gCW9X4/wUaU/A6SF2tZmQgrnRbHIV9FoHVeDQcyMvRvdJIJCIVkYCXX6I8NXsmLcNsGJ4X3zv/cgB3bf63ThYCmLATUWpvn+x5ABobemkaUceYwcCyAmsJ4N5HjokxM5NqMqO8TADGDQIQNMwHqVgmFKyilm4aWTEtuHjlAoBrWsbFiVP/moklAL5QqeQAOpl/+tI0AENLeI474TkCyonE0B5qbro0f6NqHeUAonntdQt3RqI3y2AUZIHCrC5i475nBqeFTj8QQgNIFkIApxZC7DoPIPLSfzm/E8BSL5zOOa/NU6P1rWdxj0u9EEDoScriOfdI9JiuwZAvw67o+B+jwMb2fDepuFwxE+i73vWun/3sZzfeeKMQ4r777rvllltQgwFfyc6ObWzrbKsa/2Mb2wvMruj4X1cUGJkrWEoyKz1RCrt5eS2hZfATRsgia3BOui02jlYJqmvBrDSV1MIDAKkpVuQPYJNj9pChizwKjxfKpTkDUdcIwAp0VZbFq5E6KnZ+lATHsPRBoedGtl1qR6Jledg00XaRu625iQyx0EiAscLC1VXTG44Mz0aJiCBR5t+6mjv6IBualGW0p03my1MU+yHMlxDaFBtaYvg48zMpAHTTNaXAtGJ6xUVwQogHHnjggQceKG78xYB+XTbTxT8qiMIRAhHL1SAPLDF2gZZqFNNs5JUPhQOHRnFGD9qVWCn8s7JUV7EPyxIVjvh2tAqYaX8Iu49r2QnF5xs5UAgI5cXRNiDkiD+J52yNejCrGv+/SNPwenmohmkz//SnbfqecCwpI6yrSGGTYmbKEvZYL4YyFHEAwOsqbzb+zTOL58hw5OlrAbx57l9pnwtxs3hI0vUp89VDIzDq6JaGTZu0EWAy/kRH5MWapkR/kaWUgQoVxX4oVAMgSTyXDqMiaPOwuNYbUgCNl7ZftuF8sSepFhv8LoCAZ4nyADSzMJhVAE5e2gAgnM93juYBIJ6xNJIphceAo7yzU7sdnElLe6u5uSieQturo6fjpMG6j80SmSHbkFL/Tx3bBODaXedp6t41O9/NSgEcF/jJlGiFMYBzFyYBzLS6c+EigO1zpkNP7DeV3T/9X2v6AVzR8Z+vhqempt7xjnesvUWWKcKQMzuPa0nIdlMSJFJuJwimfA1ABowyMjytzmUqKAXPZciNwGEgjEMAxUjiNFGVYggdGJFUwy7I2TD0h/KYm3GLPGYum5ADx91EKC1i38F2yvmyZWAszotaDrqsKldhZ2QXnNeCOegWkOPYMwuhV5I5rjaX2HIZdLpyA7Z37pFNeGlu/SqRw90pye0FMvBKb3RygDIlSLolzvwk8QB0umtygJTk+mqEAdcF7NbDdDUXtkx5YMHvWUUhoUuojXCzKnvWdxv21cBODlwALMvyPNCW9XuGTQWj+KALtPLMFtuR1T2hWodGd2cZu7rGfw7jsugnJxDm/BthFL6085Yc1NSlflwNIrXpaoNcm5RTcwLPXhfskg9gSZkqpNi+uQm+xC8EJjnjKWW1CmhZziRzNUZGN7r8W/E66O5QANCQgV9KfAZBRg5Q0nZioTYH6psH7/MMQFeamqTt1mdpyzDgGYCEC/IViG157rySeZZQA5g4g2ie8tqmcb8reMYBXLxZzx7J+5NO5CwzTlmWioH8RUTzGkA8Y8F3W5PGVAxg7zVnAZzvNS+2JwA888wsW/IAnJ2cDlomO7hlwyKAgKvFxFwI7Uz0kt4W1c5CALO+SZndtMHgbf8jrEJVVmVXdPyPI6tje76bkkzJq+YFMLaxra+Nx//YXsx2Rcf/utZDMCs0TVGNTLIyBYLX5aAqXS4AsAwZGADum3hm0e924Q3TttHTYBTf4/YrntSqTXPMF0NBzAE1/o9i3JuaFVKbslBatUltRDNEIcxjzrLyFNjKlsKDMmta8BzCZntbuYo6i78JESmQg6tSrSykgkK+DkORH1X5V+RbqtT+qSGczBJBIV9B8ckUHjPFzt1+gAJDRha/mMpu3Gh03FGrOHZwRPDyuAQNqZVgdbZPs8/wymKnFVMRjRkELHDoMznw2NE2LDG3ktjPwProEvLU6l0sC/sa1njdihyJ9iylHbjUJLqtPayNAfRqM4asUWAj40b2y1GOmVCNjfGwrADyigHDtsoAZNA0y1E0IZk0XK/STUrKZIJYkNPAkoT7//PkfkJUtQLz+pnHBAAttJom0IYy86GFR4XnmesVUdMZGfPUxnIShpkEgB8YkrMi0LUX+wD8ZqlOm3HdapoOHG/PANjaXKJ/AyETCy6mqEnA5ULCYcu0/bbSU/ZnVZ7tZcT7U+4nAwByY7q0Mw+xu4Jopx8iGwjmAWDypOrOcSDnDZre2CZVEELMbW0ubWp0AcxtX/zu0y8HILjqLZpZ/fjiZgDgmkJcwlfqXAjA73AAx5+cOzExC+DWl5yk/Tf43UtpE0Dcf/7W8I8jQGN7vptWDFdFDcTYxnYFbDz+x/ZitlWN/yzL3v3ud2/btm3Hjh1/9Vd/RRu3b98eWYvjuLj/Oi/NdeABWaWzpkpGKErzE5wbgAo4lwwAl7wiKJg1bIlPTrqK4r+FdR5nZiHoKkBtlU5oAk7LYmhds4Vln40DmRrMAcqOVdLeoZS4w8M/9TbLlRBMKl5m5C4ucAfWMeR3LFFUSquECSEqYb4ViQ0SDHHNmcxdY5M37zCemGJ2Uz8U84QoCaiKSOi4GwDgQtPpdMY1qeXFa6OxumpeAGyZkI+3gvswBO5ejaaspDjG7VOJ91S2DzdHjD6gkHmQxvDQf2snqsd7KsXOldAvhodkRhXujCxwNofzUqT5MsyFgoQ5nd2+XuGfq2b8QyS5SjmTBnLh7g+FgrzYcvyoPFxEhECeY7dXFuU+yYqHqML7iiYxL9bSkuNTnCP+6ezRTdOAYagHTFGOSNn0lkUAUrLutQoA+0+jSKD8vAipiNmeOq6yBkcBOzLZiisg8ICrrRsWAGRKtJMQFgfeCmOSgl5MQgqruGripMAtR4qtqfI6mQ8gOE37ZH6nzObFzQ8hbGciFgBkxJUvAPB5v78533nqRyYklkwyKjqSVkiVZ5xuIAnaA4hPTJP8OxVrHn16i99KADQbswRtWTg3Cc80TtVCSd9X50MAUmh6fVMd1cSTHsGSHlVGoX16prMwPwEgWTqDtdhqxv/Xvva1U6dOPfnkk2fPnr3hhhve8Y53CCEmJydPnjw5cP/1dIA0Y6pBshcZ6F1ehL1IU63MAV9SITOXAQfAU12rfeau1Jf+msxXpl1FMx0io9y/cT5TZVIb5gAty4ivRQkUhtWAYkbtudxXhfo3wWwJpfWElg/a0S1iUouYiAq5UbS2cmnCOlVOZL5eZJZP61RsmCuLuZizJWdiAJXaRR4AZdnhGMAzBkB11zZ9K1bB4V01tpwsPPnQGqsRCCv/UlaIMTQHVrOlQ8kMq+calkQbYVKvnOYHQ1yQIg0PmfKYgUEM+rDy0w3bsqwntOwOTIFbnUBl1mbL9mukXS3jX8OLc3005VtRwgLMAii6GnkpOmW+iv4QeQuVhTF3ODth6qOZymt+zSm0UXT3bfXu5g1LAJ7hM8RkE3pygrbMRKSA4YO3d1nsyLQE4F/0AISXONHwKB86EQAiL41TH0C3b5ynqWbPMZ8VGQInvHQ66AGYDuK9k6cBHO/N2q/6xFR0KW1S7ing6lLcBNA4A5AmZvl3wSSSaQGgs9Wje8Ukepvs3ZjOs29ZM0wb5v47Atr0mhTAYkt4bQ4ga9l+RurimSkARJCoGyp6ZAJAd26CML/TRxkpmQCQUQigt09u+V8mBdyfZgDaOwCgt1UTI6U4Z866uOB7PQYAZ9fmZqxm/N944433339/FEWMsbm5Oc/zjh8/vn379mH7v5iKM8Z2dZqWTK8/mmpsY7s6bDz+x/ZiNjf+f/KTnxS3c85vueWWCmPzTTfdBODgwYOHDx/+zGc+E4bhsWPHjh8/fuONN6ZpeujQoYq4xToXQWdN4UuPIj3IpFkBEy+t28suN1kijIZDIChdpXxOyqnSZ/AZHJFGokjvgkkTfcgaXEYchagGU9owTceqFD0aFOZxxD9u1VhRTnWW10Svdg4ayCI9ZJlel9HIn6rRfhcYEkdwK2Bn9l/tQkF0V5VwCrPaIOR95gQ0QKh4Op1tj0mLWZUmgq38KiSVLItA+qkyYo6RyACG1xYBcuWTV5mtpATY8f2MJJfK00k1URfkMYkBWdrizkwqHVQDme7Yys4Vc2HIEXXTVVtN+GfY9tHhFvfjrcR+VlLyvPLAz6ivCreqOETdZxcKWotdReNf+jnWXfmWQiwCiLvZbi+YQ3jY/4mPwzccQrQ9DQyZmaOTdlLQjhlZC2RNAHj57Ucp9PL9I6+gnZ+VHIDum8HvCXl+sQUArUz1BYCkJV2ih7DrqWQAunMiXASIinrBA7A42+gnHix1MgCxxcyDHlcVCSDCvTdFvy0jAC1haqKf7U8FNpZFMh2ZEkvtCMCGJZMI5ql95CkAZBOeSWtwRqGvYElTfMVfYv2ZfIgmLXNnZGQYTPqbJAXDUu6n0xoA2oX3Pl34rATAEkH10TIyL4j+DCbO2Epw8yIwulUTpzPRFwBEzAHEM2zpZRJAeN7cZ/80o0cv15YLZgpIpFLqgx/8YHE75/xrX/vajh076od8/vOfv/feew8cOPDmN795enr6fe973+/8zu88/vjjb3nLW171qlcVxQDW1wFiMhKir3iucCQBIMsAQNjXb6aM1noOrfJdTwx0a8JUBdEj9GsoOC0YZWfTZu5Z+dygn0RPwro+ol+Z66G8PGtGHZUBp0QEk3p0wVCOcQOq8gUWwlNIYJW2Fxtxb74SjZA9NheWr73nlvXYUMgbmkomqaQiVjGmDbqBWXJxQwVm4snW3ZE2HC1SeF0NwOtpGw1mfpe8Uu1QEgCyBiPGsywyrpKMzHSmSmVnqzd51dRAlKyCAisWAC2X8BpQ+rO8nt3gdFgRZuVgU5Yxy/4ibMa5YoUMVNW7Wrla+8DODLOVUBqOTnXVvZ/LcG4uoyRI+swRAg3T4LtMu0rH/9jGti4mGeMe5/zHP/7xsvs++OCDe/bsufPOO6+//vrbbrvtyJEjd95556233up53r59+37t137tyJEjRQdojAIb29jGNrYXjtUxL4cPH77++uv37Nnz0EMP0T71LWMb2wvAgiB48MEHlVJnz5595JFHbr755sOHD7/rXe/q9/snT578/ve/X9GCXG8eIMFkyHngA+ATdtkSBAAQ+kSdrAWvrGsHKDsqzQt1T8pnaYvopLWV7WSu2o5iFczSHHOfCWIN76viIe4Dz3QFclJPk1XWuyzJ8i0VQQMnconlV/Yu3mOqXysZkNpuQAabv3DKHqNPUb6KcmrMBmxkCLq9lfpBJ6OBWuWm9qwwYaq9ngIgYpXHaQsoPBEzJ+BHVZCyDGRbrbGrawXsCKCHiaEOPmok4fKKwj95yf/AQEs9r1RsZAXFvwV+rME7DMYcrCRWtPJRXWTDGpjqKt+HFTe77OXz/DfirEL97P6lzBdTVYqgy7NVjf84jiuYl2PHjn3yk5/86U9/eubMmbvuuuupp546depUZcuVEMjzYgPaImYa5ZsSZiZhNXwKFdOkI2sHTmaDxxVGZllIn7noGmnOpw1zosd+tnvHDWcAMGHxg2ciANzTSeoB6PUD4idjCz4mMwDX7Xz2ktXNaHdDAHxTDKCbNcRRgukgOssAtMOWmEkAbNiyaLokBVFOe0yRgBOVWreTkIiIbtiwSLCvtmWC7mRhByY75vEQwIXORNr1AUSXzFVlE569ZAbk4ipMac8KWRiQXQYSpSZzdeIqQBZpABB66+wCAMzi9MVpAKkbTl3BpiSAzRuXAJw9N9XbkQFgoWQLPoB4d3YR5qZbXVjLP9QQxNbt9TWA1hlNCttLv2Sm+36fewsCgL6Itdiqxv973vOehx9+ePfu3VEU3X///bt27frQhz70wx/+cMeOHY1G4/d///dvvvnm4v7rP+5lJHjL3rJCkkg1QtXwAMiQ58yEtcA7bfF62uAeAwYgazA07A5laCtPtcNy04PJGowXcIZMacoWDUxv0RZeSBsZR8f8K+2/yjglRU/FeULuw8C5foQIfDGhVtxZFBJk1lUyGDqbyMhFqodWLw14z5kUewYduN1KR1WUeyXAQnsiEmpOTHqYSV06dSxtn60Eh29pzdaIB9ZYj1KKK2/MOj3Odyl6PNmKisgKaSyJihs09BDj3xf/XXZ/smHppNElcaPPMoJCsL7PwJ0H9qri7ixb6ONEAAt6XivtavlE1Q+mk8PSZx6ICBHlFdrl22rG/4kTJyqYl29+85sHDhyYmZmZmZmZnJx89NFHH3300cqW/fv3r62LxiopP0PEZ2uACE8ULGrKFWYNHm8w9zCbAACeGICqA6WSS1QEfxVbBjmmidmHPrSe4meWtgEIy9JsyYzKSLNiIeSNDAA0SPDhqX+7dmKHYSlMYw/A7S9/AsBPGtu7nVkAWmh/kQFApGRfAOj5ZgLdMNHzhASQ2ZcOMSX2rUDYjN+dT0uqZOfiplWqN7PtxonO0s9nAIheCiCbyEeM35EAVMD7UwyA39VJy4QA6OaIGHE/3195phYKAPWZpx5RFM7MdmYmuwCWPOOKYQqCdI2EBDC3efHZkzMAdF+ITX0AQZj2rrUPQzIALGPExBgsMiJ6cM5Z64wCwOyrZeHGLNuSAEgW11bDv5rxHwTBl770peKWKIq+/OUvD9v/Mh2gf/iHf7j//vuLW06ePKmvirfU2K42Y5KxsRTA2F6sxiRDXyml3v72t5e2M/YXf/EXW7duLW6sY15Onz7tZK337t17+vTp+pbn5kLGNrbLsCs6/1+mA7R///7f+73fK275+7//+8/931/MGgxglA2pUtQ3vGTaB5BMiUrJrddT3KK9TEgmUZpzwKylssjEEgAj5sAL5bdGz9wBB5pIJgWAYIkDCBcV1USLRJGOOvIMF6+sRAuUQhIA79rkTZHTSJY/CDEQ71MV9K7YykW2qTja7s8Cj6IC9Wpol9cbQCLHS1fHuV2kWqYNhwIz1B1WCoOnjm/DdId5BphQOQuHCQIxqbnkIKQeBdKG12uvxJgqCdo/r80TQyM9K2FBtA+6lCYGMDKRVOHBKg6A4rcDAz/DGLMKyjCDE1uo/WSWDfysBNLlBrODdhb/HdgBFC582IkqW5ZlRh2YuqqHfHR5+sw76ZUJGNeWCGMKXAjG2Nve9rbi9iAINm3aVNm5jnkBUIQKK6UGblkX0xypDS37vVI4OWibHIrfkQRKLRqRnDl+Mp5ZMQoKCFl0ahZVz+hAZ0yZnb1YE0diaph6TAgKQhN0y58X4hkqqED/5TGAiVb/li0mabiQNADcOnkMQMCzh3ohgFfvfPro4kYAaDd77RCA4OameUK62A/xAFE0BcB0EANItdfyEgAXEzNcAntsalOAceb7SwwA3RkRK0cXbPYUjBAnSYs7FBgxKmkBdMuS4TZbEp0FgGRGE4lRuxtummoDmGkZvYzzi63NU4sAiNzoUqfBY3oTQNLD25yyCRNJC56M6KYlMwCQXTBdykL6qZqTOoFbHnMdSvqANdgVnf8v0wHatGnTnXfeWdxy9OhRzZC0uBYgOLohQbKmBUumBIDOHHMBTwIZKsG9ngYQxpIKd/JJ3HA6saRFH0CyvX7HNE7nAiADM+KzlvnhpfMGwNKwEHrakyU2WQNFk5MWzFAyJsomvwgFaB9mnc1Zyjy1k8s/KQBU6pRbjolT1Q/Fl2XxBekg9AXHy2DoCj6Nez0UJ3QmNXEKVBwjFHIBTDCbSeTVwL5hOzTRZhUYIkQvZqQzrzlzgvP00hK2fXp2PLO1VkIP1cdejTG5Ziq558hYKQe6spzX0LaKKTCpDSFnQRuutv8yWZ56XsmxiRZ9JlokmOExiJd5BIB8YOrK3ZGBKbDKISMA7ZVKvmF9GGg1h2ZI9mp4fU++T03hawDujDOgUOCyRgdIgknUHaCBdvPNN1cwL1u2bPnBD35A3z7++OPbtm07c+ZMZcua+pd3tMTUnDbQ36QBhOfpwZkcuox4b6OAJYYmoxdBFplfumOCdvWdTvnLHWL4FZOCYjzl6FPrNtnb7vgAvUWXQgMArwt1LALQi8L/+azBzDc2dwHctRkAfrl17Om5jQAeeeq6IEwB4NEpdo0CYMXjMdnoO/R7pjiADikhpl4rjAFcTJo7GxcBtBoGDdsS/YtpE0BXhkk/BJBJ0d8kATz7SuOZZS1bA9TQAIJ57tO70offptvI6F51d2et/8zvu6MpSSc1XacKNAskgDT2Fr0GAGFdtDT2TpyZBeAFEpQcpJxjaliks0xwW0oVnQcAkWL+BoWy60l3mx5WUpB+J7FIFa3Jw76i8/8YBTa2sY1tbC8Qq2Ne7r777kceeaTb7R47dqzdbg/c8ovu9djG9oux9SZCjAC7eFIeE+XVIXH2pJMmRscD46ozyRyjTJ6mMStRIwJGG4vlhLRI5dLFyZmpTo80UX0TTkzOs1oA3MlWVy8/awrfVj0PvsbREt8rFzRwrZkDRZVVKP/gMm5Ol9sDBiLXLIlWLSnm/i1QBFXW8aUPLgXmgs8ygD1EM0UxT15sX3lMlHMxXBqxmDWyoTA5Ans0wP7xH//x3nvvvXDhwh/8wR8cPHgQwOHDh//0T//U9/3Pfvazv/qrv7qm3ixrjvZpWM7L1RG7JGmBqofZjOdgQkKpCurruvZVCVuwFn0rC1PI77vrzYiQktmhrMHuogK81rHRLWDQJQwu7R90vfmetRs5DJzloj7F3Fal0lNzBiv2Uoz9qBVlOC/HVjX+B2JePvaxj+3fv18I8YUvfMHzvF27dlW2rGNv8zSWhDpP5QoAIAOXHDFJHOXlOxPZmIjR32BKfW1yFgCY0g44RuZiRTLIBxhlCVpLoKJZz05x8WYACM94wSUASCetLn3P6KJPnGD9GdNK3G8B+HLrNgBv3f6zTVEbwM9P7OTnGwCYAqlJpJOm8X4mKNKTKZEVwDeTjf625iKAluj3lQdgG2mVAWf6UwGXAGb9eWAGQLsf2dIOANAcd97xU9r54ObvATgpN/zPpZcD6GThz+avBdD00mMXZwC0uJYnpvP7H5skSXiRmXqGySyIMgCBJ4lhd6pp7vtCMklCafJcCIALTfeMJ0yGCkCz0Zf2ouLNDQBTR3XzJAfQuQatUwqAgIZFq8ElHAE9YSp31oiFXO38vypbVwdIQ6TgqSny15zJBolDkd/j0WjmqZlNWObU8nRdONDSGGoAXtfw9WHBxEK9vjmES5Nn8TsOFstILs7MXMJMhTLkXlcC0IGHcl2Cm4hF37xFdGDujAV/1Wo7XOmPEOZVJ/jgup8R5T5FuNDA3YonzajCRvGEkiOsmi+oljHlHyijLENeCdczZbwZMuVZJuga2qKQzjfpQZaBgC6FN43Jpzji6WKB0WXbqphwFxcXDx48+L3vfS+Kon379t1zzz39fv85AP0CAIP2eFUiFwNyoGac1NkfBojjWmedMEWiqHxX37lU2bZ8dU7Bh3b7EME6/coUeKUqaOCTHFygw/NRURcbdop+Azs20FaIO6v7PQOTWbzsPo7I1eraYHHdrjg9w8b5czn+B2JeDh48SCuBEVvWwTR4Bi+2A8ZnxmvJACDeCFpBpQClV5jM74wMrdNM72w7ZhzLc3eOofBy9ToGZJdMmzmqc1125O7PANj/lx+ZOA1Yfwh2NgvPG8C8m8qUj3De9ITyOwB4ygGcxhyAv1z8r/9151EA/LpOFrcAZBNaxIOHisdlK5QAZhsKQDfzt0RLAFoi3ugtAbjWNw5Q0vT/rb0NQKJFU/QBRH5KqmSUrUtm1I0Tp2jnkEkA28Wl2yaO0pZdjQsA7pz49ye3bwLwv3s7j2+bdd34pyderhd9AMG8yJq2PiQVAOBJwnzFVpZVS0bYLsKLqYCRBJgbb9ON+NyiuY/0lYyY3wEKJVbmvklQq5SzAwCudcZhE2GXbVeUCX2cAhvb890ccchK7Bvf+Mbdd9+9c+fOubm5xx57bGZmxsGA9+7dS6DfK9nZsY1tnW1V439sY3uB2RUd/1eE/8oUrCmjRSUjASBrGHULJk1spnhVRvMr0zYFYFZypGceAKrHAHBpY6EWL8aUpnA9l5zyZSJlsl3oT9fkfVzjTqe6nmWQITdV2AFxNgqepABYfziVTegPW9APjf3UxDGqh9e/tZEA1s+oGpoFAp4JX9GRJmkoVV4y5qIFNiSQNW0CxZKSmcrEct/d4sw9ozyRIc0SKoPR/BLcZl5yNkUGQHvrQwQHDa2U1vq+++4rbo6i6NChQxs2bChufPrppxcWFg4cOHDx4sWDBw9++MMffq5Bv6MCfhwYCQ8syKo4OFh5B72sLBeDKtYMurrpgdQ+9FjrwRWjOO2q5qXOhbuH1Ckvm3FT3vKcVSv5agDIsZL84gCgBBsWvGFKEwqS1+5hKdVVtkrSeUT4Z63EP9U+4WrhwcoaEGkeHqNxaKC+BngELhHNa5TJbG20xki79zYhmmcAVAQAIgHpaDmGG5fG0hzBAgA0j3n7/r8PA/AbaJfFv01htTYVGjw1kaSFGzPeo2kO/qJ5fv4CAATzHIC/U5Js+5YNi6f3MAByPhSxB+TAqwU+0W43AMi+8JspLJNQayo+05oE8NIJU/u8pAw6K2ApNQsPs34XwFG1UYUKQNzSAFgonyGoFfBkuBFAiCzkGYDN3Lzbfth7yS3RCQA/UteZ1gAAOhGIFAAZcYqfqa5AKAF02uHUdBeAk68PZ+Kk6wNQgQeAJ+D28VFqrOmlgW/ffYsMQH/KpNi0wMJLOIDppyihaF7EsqGKLQDwmkxx4AIAACAASURBVCWJtFXblRz/61wDJH3wRPvtDABPFL1uaTIdSOLpZgp6eYtexnsJAC04kShS/9z860icmdQOzEUSj6n0mBW6ou1OG5USQKKXGZXWPKFgpk7NTdZmAJSGXh5FH4jSUp5w7zPnLZmrkyZXZf4tCJ3mEmCV12Q5fcZQAKA5Ix+onzJSUrMgCs2ZSU9QYreECDM9Me9RYdVn/eo72HAb6pyAteJ053FjYTpYIIgzL5Vqf31TlYXVZDrqxpSZwmZmZorbOeeiVo/V6XR+9KMffetb3wLwute97jWveQ1wpUC/g214HVi96MfYAH9X5QzglUaGiOKyvFas/EXgcYMlHuVJ0A9QC1Z8uJrIn2lnWSroQSHjWWmt1jFdyHwN7kDlc/GQlfhGzuMpfestn2KrH2IbHJTkGl5UhEFOj8vjPJcpsF+gaQYt8jtWSEECQLhg/Y/Y1CqIWEtbSUPTCy/MebQzqZ9mEdIWUF4z0yGOSyWch6IXwaQWPQYgtjKlU08QK4o5bxbB/28XALx606l/eWYX7dN70oGXGIDGvosAQk8+enI7gDDIFK0RLSFNeM5cp1oQZk3Okc5yAPA1gCQThKg/401RCuyp/mY65GIysZBEAHyeJVyASBRbGQDONQAutPNp/k+8DcAk723ylgAclZsDlgIIebaoIgCdLNzRnHe35X9v6HUvNGHAUwyA9rXwJQAumBAawLlLk7Rzs9EnPL/YGwOIn5gyuTAfxAR98tKG2VaHdn42AAARm6cwcdqoQ8YbOQCvq9MGAOhpJ4fLmKcA6LXBIK/o+L8yxRBjG9v6GVPg4IyxCvXUQJubm3vTm960e/duAHfcccdAGPAV7e3Yxra+drU4QGMb25WwVY3/LMve9773ffvb3xZCfOITn/it3/otjATBrLMDJENwqUUvA8CSDM0GbIGbYzKEjVVokTv+FKTh7Zh1+gBY6FNAxWDALHyJ4kOgRI8NyVjench+xa2eRjXwYz4MYJlj1D2OEsufDDiFTNx5B6zvXWtugQiCaxXwXKK89HdbijXOFRSYObZYBE2dF3lIyS7BaaFJZ+RJWsmbsH4Gij0EqHBUMlVa4/LUivLYPJeLvkgLu4AN5jEbJbIPMV8fC4tlMD18DivN3vjGN95zzz0f/ehHlVIPPfTQRz7ykenp6U996lPdbvfcuXPPAeg3D/KVq6FLma+y4MngnSuiKDYjxmqUVAOiRKV0qsmaMVlNqNWDKyP0s0YI5w2DXzlwVpWQsyDjNZCJtMLliPIQqs+GLuVaPoTVkVkORuRwGMV/XQ/rB44YwwY4mcd7CuFGmvTWFgG9isxN6aAIhAbs/CAShAuU+XIMQMwz2SFkDXt4AMBQ3QBIDQ8cgkWg8PhQe0aOVchfZPFL+wCE72hvGyCmXB8AOjv0vul5AK/b8PhjF7YCOHdhUs+YodDavARg4UILQHAq0L4G0J6WCClHwU1ez/acpznPkH/RA5DOZgCSxfBxzAFY2BC1CykqALN+96YNJhF/Jp4EML/U1H0BwJ/uA7h+7vyWaIF2OJ+2ACzxqK89AJu9tsmFibNH0zkAuxoX/nn+pa7xyUa/l04A4ClTvgbAUmaKoK3SmatKJtUOADunLwH4+UuZemyKHoQOFID2pUYQmDuTzCgAyQYTWBIxS6clgMn/pACb7UEvfzA8lAAajT6eK/va17526tSpJ5988uzZszfccMM73vGO8+fPjwDBjCNAY3u+G5NYOQxyz549H/zgB1/96ldTzdC+fftQgwFfwb6ObWzrbasa/2Mb2wvMVjX+b7zxxvvvvz+KIsbY3Nyc53l1Lbyi8t06vwyYhAwN+p0LI3paqBFhAESSxxJoBRC0jUhFvg6WiqqP6X8mWKXkUwsOS7js1rWCColyPQ0JF/WhGp3AfKCyoSKSPC9LKpCXMOV04zkFUQaAnKUyi3J7UVX9VFg5i3otl6WKWUY3AzVpcYqBqdo9KdyNemAAdp1dLJ6gRVVFBN5pXzMJR15AVqS3N6Wy5hArkqrWmRNltUyghw4dOnToUHHLFQH9LmcOEj+09AdDK6ZZpsxRhbJoDHmmAw4vFFAzKV3ZkBmogtmvTFxDefXK4tK/g4WEq8OvGrYpflVufGhlTzFOPMwG8PrUKpMAKFHdsx46qtcJDSttdoRYpW+rO7OB29doVw8T+tjGtv7GJJDJOgiGMXbvvfdu3LixuPGmm24CcPDgwcOHD3/mM58Jw3A0CGb9V8NZyEjziyfK8sEAgOZMWMEXgomJFH5HAQgWUpNjKmhEUIbLTNCBTwkmFdjK30ESRa6Qs0S6H+TXSIdrwUgswkkBoDDRF6+FZ5onQ+aegmA7y5LSV6Pl36lX9HpbRVVsXYtDE2CNrgW5cyMK9bD2BWzJjXLpA3tXzNxaI+xhsvaB6qNZrsxCT1ZY6qAKWZnkA9Ill2NXkRZYGd831K+tFcjn2wvjqtTOcuCyug1KjYnyV/bAGiFh/adU4RbimcF4Fjl+BmpyDVTAGG1KMMJnFYuU64gt9y1lslRQyl6N9l3sPqViZ+f3F491e7qN9VRXqc1CITC3y4k12dUy/hlUkAu5V4r1i1MBLaL6M3kiySXTjbCjJSSjV0Y0r12e0TXixxpAMsm6GwEga+noLAPQuSW+bts5AGcXTV3z4qvMUaTqwIV68uIsgD+/+Ku9fgBAd7zWNabUl8qEvbM+AK9tieJ84X5LpjbAJk95aj5z+xIwxRvXdV4xdxZAqsQT83PFWzHb6PpcArgQN0k3I20HJJiVNQSAmzacvi44ZzovIgB97YX2lH0j1Gda2+Qtne/lavMXLrUobScjTSkwNCUXCkBok1lOCsMTMtMcABVlb92wcHSnpVqiNFlPXDxvEHrB1i4AmQpSBZls9En17NneNQCCtlG4Yol7H2klGYBWsDYUmAIJNlVAMEEQRFFNHA4A8PnPf/7ee+89cODAm9/8ZowEweTOQZZljz766OnTp5VS11577S//8i+PkwVjez7YmAdlbC9mG4//sb2YjUkwzVYIgnnwwQf37Nlz5513Xn/99bfddtuyIBjj4nznO99573vfOzk5uXfvXtqv0+l88YtffP3rX7+ankJGSCeY12cAPPCsYTB1KKzD/K6mwI/oSQLMi3bMSHe9n+QS631qEgCY4BS8UQEn1VIXb3c0xzxRjkNImQxXqeDXHSIDrmwjlQh/EW+PsjbqwOSX+UC1zFJW4zQVquhiNTR1yUq7owBZNw1K22bdzGVKZknKS4BkwapAaJsNUYGgu6d8NkReewAHtPm3cPWGrdUrLUy92Kx3XYkrUyajscaMGNNXxwpYU5Gy+7+cvUJt+4ARNeSonIKhFuwZUFvtdrNl1IMphYqNFHpdFEPlPT2Msll5RnFFWmVvJnVd5Xvw6WoQ9wFERCvYYo6t1j4vn4Gqo9wLnA7LHItBd8NsF6ZNx6Gl7Ja12NUy/qHBE2SWINjrGOZlArSnTeZ3NYD+FCMBinRae1bTmooDeGriKDyDq48mo2NTxwPUZHqCAcgaSKc1AH+Bta+TAF513bH/vLQJgMNv9xMPwGQrXmpHABjXhrmn54GgG6FaOmf6TZEYTzIAMjJU0Txh2QRVRdinbMuatTDlAS6aRVTR7U3h9PYegGe6UxQpcUIZZ7smpuLZWfWOm/7ju/++BwC7GAD47jMvu7jJXCrp0jsW6SXV2CSWAEzx/vlsEsAk75HsPNnx+YBn9mcVKgDMU54nAQghN050UIiNnV9stZp9WDX4aybim687CSBV4v88vRUA7wplkf/pgg8AM0nS9wHMZyJLBGBg/4vXMRWUh6kwTNAXnpzFGmxV4z8IggcffPCOO+44f/78I4888uCDD958880jQDBm8vjt3/7tb3/72y5VBuDpp5/+jd/4jX/9139deUc1g2xAuqimFZzKIuMGEYW231HBQgrAW4g5+T3d2JLc2DBiGBjvIZdGouEuiKpfCaaC0jQUWrSXFqIocOGog5zku2yIdMLMc15PoaBn7qwgOCCBIUSI7jXjnJV+AkD3+wAgBAsDAAjtb8XpXYg8J0W+GgDeAwCGzDTlXJ+sfOosozvDkowR/xD3DIkRvbQERyXTYXFqWjDZEABkmANknJIaqBaECGAKblBl9Vl8u9CR5A+JhCmhAbhgcf5SeZGAYBizPncZ5FXXrKhnvupW3OjQgpmsSIwxAMMQZK6dGpuiq4GjkDsKA14YOk37r9QopFmd5XpzhdQGqxbqVdFhlYTa8iruXlWKq2g5hoszlJnGhtloeNdKanfq+wzPry3f2gvJmIbfztFYMjIiGHR/sgZIdSebME9T+dp5S8E8A+B1zKvOsek6X5N0JPtTOW8QYa+yCXhtBiCZ0dfteQbAifY0Ef1lln4me7YBYP7Zhp7MAIhQSoJcPetrQcA0oa2+G01qNOnJhs5iBlKYJ0aiVk4hS5Zn8WS+1AfAF7xnulMA2v2o2w9QSDwJoR0VIWWgXjpx9rFrtgJY+vlmAJ1LG/9Zm9KWH8h9dJbeVg1AbUz27DwD4L9v+xfyigKWvn7TE+4pPJbtDi5xkHKF9V1IASNJvQudCQAO2AUgSTwAXpgAePzsHKXtpoOYKHxUqJhrpMcAZMKXRLToKbQ9WOK9rKWIPTJ/cQkGxQDw5Ll7AbznPe95+OGHd+/eHUXR/fffv2vXLowEwZh/0jTdsmVL8YvNmzdfccq4sY1tBcZkjdxvbGN70dh4/I/txWyrGv9BEHzpS1+qbBwBgjEO0Mc//vFbbrnlwIEDe/bsYYw9/vjjjzzyyMc//vFVd1YDDkhl8yyu9pnCmDyxmK8kM3zH/ZwnQGcZABM7gVUPsHT+WjDH+SEtUY39yi4WbKTH5LkSg5ZSvsl8pROc1hNOCjTn/7YrYDIm1QDcjSWAHpzCGGFF1p/RcB4hUClkLsSBWBiCoggVSVefrtquPCVzBEUUZ8oaQhpWblaJ9AzVcRTVJW99BUxR6ywyoWCWQQflY9eYArhaikABmAAkxYFkKRQ0OotKlq3gh+6IyOstiBJQcVloYT2u42CPlXLmuoRFXg1ttyhvEJH6ymwEsIsCvYW8qq7vYztvmqoI+mJkaKe02yD5ixF00hRPWjbQs8YI6FUz/jVFbux/lg+M7pLfMcEh5SOboDHGKPADEjeFSZkBSBsQplwBAJhmxATtGHe0zTPyFOmUBvD6A0fOxS0Am6NuN/MBHF8wIjlEaaM5kHIAatELljhGhuhIRlTEjEQz3OlYVqKrBiASpydjGaFIeLTLKNMkhOz1AgAytdXBfdHc2AUQ+NniUxsA/L/sl+irZEYDkA3FbBorOssBbPyPTD9BMbDg5NwuAP9XcxcN+O6uzGuV+2TyiaaFiVafQj5L7Yh0LSjqQ0b5QYpOBZ68EDcBNFsLqucB8GYSlwLLhNFYTbZSyTqD0ABkSwLwFgS9CFLDMo3pHQuUalxjHOWKjn9zIw4ePHj33Xd/85vfJJDYgQMH/viP/3jnzp2raospBJfg98yIJ/5D2PQtU9rraQA8VaRikb8PwtC87z3r+giB0AcMyWGuzS41qYZJMA8aAMvMtKsCDpg6IesQmAJ+OlYJ5mqS7EhlxFDFMk7NMmmKHipJsYGQ5jx1RH3OpElO5d6byP9W7lWmQPyK5Me5XAC9LEPfvOFsTlDHfS0zADyK4FJszQCAcGg7cu9q+k0O7KYCnhO+WVRF8QXgJMB0AUJsdmDlf+3+KM0j+W0HIAPb2tpeAFyCX1WxyCpXoSxTPJS3A0P8HlcMVzEaGLVcWKnBgifkRqyrNtOBcMU6xYo3FIrh3L91JFfFip6QXpnsc0kBww6egSU+RUn5yoeh/VEDXmwDXKKR7eQLgwGlSK4F88Hp6InKa2idwPBXy/hnmvJW1mmONdXx0GpTC7OMZxJU+iMjnd/DCAD8nmE+ZNrSc2gA6G7TWYt+RPZxMAQXOYB0Sm+/+TSAV089+a30Zvqy6aUAktROdg0JIGymyQUDGhI9AOhdNwidRH5DnwPgCaMMV7EkwElwkGWNEmANgLSIwvalBoCglch5eqmZX4c3lUrFqYcTxzmAhfnN/OZFABtvOA9gqRdOWvLA+S1NAM/6E5PHNYAsYk4QzUrZezzNHRoZmZGZTmkSBXvJ7IXpoAfgmWgq4ArAYmKqMuLMJweIGBGjRky3zueZaAsAYiYOQjP4EqEBJAj4ggdAbUyMU0jYOutvOQex3W5k7RWkpZezKzr+8xtHyC+HAhsrBozteWJjHpSxvZhtPP7H9mK2Kzr+1xMFxjTCRe3FeZiaPpAoKU+1iCUAryuJ5BAAhXkA3yxeC0XQFPtRAWnV2krh1LGb5/w9bg1qAiFeiZBNhkyaUJAJTmRRMSZh8EqOZaSIqNKC6xoBXU4sZBRGlel8WIrIl1b8dWyXMJqitATSeZ0yB6CbAbPciTBV2CYCpNPMEi1K1yuDbvMZAN2wd6ZQPF1h+s9FKixnyQApR2EOtDEhbUv8XLSAGeKfxCQlKUAtQ1P8uF61z0zpq4IJl2ltBnZFxaLMh5lbPfAzgO3JxoFcvKdYEF0x2mc42ousmNiq0F8NIlos4SVHN1jKT/Ghh9QpEyvK7SwbIkc6yHj5NgzMa4zgVyyOfCWqvKDFBmlPNxcrr0QK6vVMMNdtdzIya04BX874f+c733n77be///3vxyAtpBHqSGu0Iskt3UYaFTIwweasZcRKg3kWzdcO16YRwo459Vwz4dvHSPW2APTm/v5NxwE81tn+axuPAPgfZ006qdc2cQ4/ygC0mv2L7QBA42nPqPcseDSb6VC5p8z7HKX3i72cDgDIyDwKF+eow0QMkM2ODZkKalOFhZeIYgCS1J9uA0A0ry/MtABkWwSAPVuePdWeNu1zDSCd0u1rGQAV5hNyagu0vZ5rGMpHPKfMJcQcwONn5zZNtQEsdhtTzR4AIh8CMN2IlxABuGbCKFm8YuosgEcvXts4zQBkiy1pH4GcobyNmfanHg3p6XSvNbRD0TlWvHW9KGQEQxuEIFq5XdH5fz1RYFAIFrUXK/c+Jq/C0B7G0l9KQaU/dp5VTWImFLzXB8DcnG49D21dHwfHNT5QauL2Do4LN497bupkALKQyciARGQIGE8IQD5wncKti/kTOsYvcrh5lkvQaL9zSuQ54kEtBArTei5AJpUB+UtpslcOmCNDI+reDIwDZL0rc+LAFyadkfFKNkRKh00j14e0ebUYKs/O00KGywJ0jVvjQsu2kIJeSDKyzqWvDVAisl5Xyhj9sH2LGIqpFaat1pvZ80UCh9EltKB2rk/dq6j4LgPJDkYfMsIGwL4UAJ6ktJzgiazShZcxjyjky5id8Ev7F0wLXq8HQk343Wz0V4aTdwVANTbnohn2vEHMh3YLQ83FGXxG+7uoJDi0sJUrgXmxicT8WGQE2QAArw0YNm0AyJqm/6JnlzfPOQryq1/96te//vXbb78dwLFjxypaSKdOnRqhjnTZplnJ0UybrMoVzgHAX2QFIa3SDnU/1bmYVMcTPmtrITL0NykAr9j+7MWkCeCZ7vRTnY0ALsRNjysAs5uMopgBOjHVmIoBZL+SpLEHwI+yRpgA6PWDpGvP1CNELVAYBn47f1lURohIjFI9YrPRiYWxJQ+ABJhnap7MVQuDS88Ar6sBeD3deooDWGyEAB5LthGAPLem1EseANEzo04LxNfYt8R86b7pqQwAPLVt7hKAZ87MPNOeBcCWvG42hYL3ttAyxUbHGxsALJyYPhLtAMDagsqK/KX8EaSTDICIWbYpAxD8u0e/L9qezCqqMKHu0fXytgCALp63NkaBje35bmMiuLG9mG214//UqVOf/vSn3/ve99K/dS2kRx99dIQ60tjG9ryyKzr/rycKjGntdyRPlc2zCOp3nvnqJQBYP48AUcAjnfQDSvR0CnCwYMCihCmj/1AI2g9YXmURob1MXETZ0DSV2ikfFSGIMmAkr+RlUvCeAMAsuY0WwiidJSqXfxcmJmT4eCju5RqUWjjh+r4NBdkUWJHuyJlL+WnB6CzCLb4dV2QQUFBKBoZw0gW63N2q3JZgyTDKK9/wACnfshqWw/tamLiOCnQuYBYpACyQXiABpO2AyCor51G1ureBwYCV21WDgoEuPscB6aRhgZ9iBMiMB1n9txb/G1AfXQGIUTcKsmKUodOWKapYrF1Ip/LiV6QjxqAwJJ/FoArxpHyfAjpsaP2y5nntc0lEvRDUWXkp8YjAj2t2GM2VA/K4pBX9LhzfjLIV/S6x5RrJWgDAE7ND1tLahc/sVazFaPxrrb/zne8Ut3POX/va11aCN0qpD3zgAw888MBXvvIV2lLXQhqtjrRGS20AgGfw4jwUrXyTqVGFymOiiHOWTNkgijJzNYUTsmlJNbnunqeTeuueswCafpooAcDnkmBfiwvNrXOXAGyITOQhIwys4lRZ7AkZzaYAAq6IQjDV4siprWbnWQ3gGoqd/HyzvyCoP4KIebUh/nElz0yaLfWnTLUBWcoxQT9M8xMLg4xQV1kmkkkGwOvpZAMAMColjoNcbqhBdQbob08BaFt44F/0ZEMB0BMylfkYkJFmix5cHAhotPrZ41MA/EVzP4VNmXGrEt//0SwAv4EsYwCis5wQedJH32ptUU9ELKgIGhbeFJ2nTBynxt38L2JGQdO+HRKXZ1cNCgwaPFWib1JgDkFKKSqWyApKRXuc8kRe146dojgoVSeA3B3zPZO6GrS3yo6usED53BJt2XoXescXBqgjs3LBQGmir0IWwrAq4OmGAIDXrc6mWpgCHlZ65w14UKXXTBgA0P2EuWlLGkCczaM5hVcGQHlMTfoAZGPK+FW9zGXcVMMDkE0IGnPS0nDR9RYHDd1Aaacb6XBwltjUvBi4mXe0V/NjmMFHaM5TxUA/xeL0Vbt09/ZaIxyGy2qdx/PXiuCsYUmrorszrOhnhA10m1DAi9XO656SwS1KZfg2UeaMLu8Mk96ioVP1kPJ9IOhH6ghIXV3RCG3UytuimPNCceQUvKLKKGLSXVB1t0qei8u8WefomK/sZ4d2NgUcab6dOH81h5cApFflkGuF34iMjN9TwDCvjwPEJZBIrfWf/MmflLZzvmfPngpa5XOf+9z+/ftf+cpXOgcIGKCFNEIdaS1W5KLMXCpEMSBndvZik1V0zwX2Fok4fxB0b5NNGQBKtcOi0wGEu5Z2tBYApFqkygPQycy59aK/2GoAQC6QBQAeV1OBWWA3fTPvn+5OAji32KKkGICgmTtos7svzf98BoDocUJ3O2bOvNncmSjNpa50lylowgpPmZaTTAjFADCuu9voEE5+dvOEAJC1kE6ah0LM1DpQLBYAdKTEVAogbcjw6RBAlrAijQvckP7/2XvzILmu8v77e865S3dPT88iabRYi5ExyIANZvESYxGT/GIwSyo2Mfk5QEyFBJukKpSBSiqVhBTk/ZEQU8YFAgF5cSUkEDvBkAQSKAyU8ft6tzC2X2I5eJOtxdJIs/X0crfz/vGcc+7t2zOjGUljWZ7n84fdunP79rm3T9/7nGf5PlZ7OvCT9lAKQLUVDZ6K7QGI1Mg3kx8hGbAfGtk+j3G+UYTUq8Cjsq+4JihPa3BvCiA5IideLgDEo7bjWFPB1AXjeFjW+z9XgTEvdESmT0xTVYY5BRGZVkJKKX/wgx8cdec77rjjzjvvvOmmm44cOeL7frPZ7O+FdODAgQW6IzHMC4plvf+f0F5ggOpmrixLRiiLiJCrprA/LStlO8ol46xoSu6uN1nSCXq9KYSGckUWTv+w5GwXVt2cTHJpPSIuf16kRm9Nez2rydiT5EZKK8r1SOoXhXPn0lOtN2dljeehuMjO/UCZ6+OBwurZSfgkAybVVFaV03WkriBR3QxyPkdL7ue3IQCXsFnKG818s95NK9pUe9lzFYmgvXVq9K9EKoxsfGqS49zquVS1OGcfg8UjkuPW0no+SQoemmKUamHHT9JXKTFnXqrrkTKXuFR5DCWxRDWHdOccU3keb9AClH1C1vHTH/zq9wnR3NBSZIUJ6VyV/bEwN5llYYAuo7+0pzlIz9jyTwGQVO17qSxG9+3pmToALY0nQ6Qm69m1jie3RFZLERqBODFFMfE85n48LGn+33zzzfTiox/96LZt2z7wgQ88/fTTpV5I69atW6A7EsO8oFjq/f/jH//41772tSiKrrvuuuuuuw7Axo0bx8fH6a+Tk5PFHvIntApM5wEas6Fwm+63XfI/RUleL2OfH6agJvRANkQpo8KWicFaGD2fRfJu1KNOiZKLV9vIl4rgz5JIo/lT6puEIdfOMwkFABXDa9NjPqOEnjmCcYup5Sk9t9xjL0lFMfciFWRViMxYQjKy3dAGlNPCprG5JKdS5EuL3PIzW2wIwElBltDK3s1txaZIjH9VRsLlDxUr4WGvs4xMpaiM8544JygEpuWxSgw/r+g+y2bhfzr6rZ/SW5wy+AJzrJQ2hEUVjvWbOOXuqvZXpvMXvV+nDT2XK9u9csPdhTueGtOc6hmruUVOs8vZEHnYOiqkGal8H1eFLmMjx1AYQP7C7ByaXDfTvykSsKk/MKVemjItoHQCBcCfEU6PuAdfB/UIQNTyqV4yHtRUF3mcC4DjnP9btmwp9ULq33Jc4ysgsp5rrm0YZT5caCM2is/GbM0CdNflwS8X4slGzLHOWbd/JDC9Tn8+uQ5AMwpJd1j7unmkBmD2GatJTEs5T4+ePgngFaMHXjG4H8D9k6cfmGwAiJr5Nxp4KQAKlo1P1/0ZCSAa0f60AFA5VK7pc6ecBlYK36aImfkWZmQ6KyvnV63E1Aa1m6jpLR0Aql0Z+oWGzapRXd0aM5OVwkzdEZlWNQB/2tPjHgB1ZjPblgBIpsKi0ILrL6u2RNSDLEoU3aiz0GT/0LkASKug6W2W0PVUpwJAd7VpCN6xIgAAIABJREFUtVlcypqC/KFUm5+M114HWKnh0f+OwjUBgI5JpkJaT9FUQPlnuFSWNP/vvvvur3/964888sjk5OSFF154ySWXnHXWWYODg88+++yc+3MVGPPiZGEdFIZ5cXP99de71/29kBbojsQwpy579+695pprarVarVbbvn37k08+Wa/XN27cON/+J7gKTLa7edWJLZ7S8ymzFQJeuYOHFrJRhCBAcYXatesITwHQoQfrMnGJw4SWoJ4bpo+0sovIVFCFgpbGNeLPavIAuciXUwgku1tkQpr0YZDTXcZOO87UxTjHj0izHhmYMA9vld1XQYBWy/6J1EUUKaibQJitgJOJkR90vQuSqnSZhlTmllTz+hQAsjvHipPOIvELdXAuD9T6bwjj+6mlJAYvutKECyPQtyFScxD3ic4P5M/agziff1/6+TEgsiWHwBbWQTmBS95e9FFSmBfw9Djmi3z1b5kvCraY5Og5W4mhHCbLG8v3u3/6ig8cTrLLvmXe+Ff+ljyKbbdYJ2JsJ1ter0ARLl0O4DrBnrwpdwcAhMj9SS7gRYGttKozqm30MwBpV1IDbddyIatmspoAkErrlgIpY2nj13EqWfbiZQCq9W7kZwCSpi/SntqlY+MY5v/JQeQeOwAy6VHTKbrfHEml+H4kVVOm1F1t5io5YADEjQzA0Kpm6TMPdhvNKARw5EAjfMYHENpMaue9oGOKDDOrKwAeE2OPTYwBaFn5Hx1LyjUG0MxqAB49UgMQPmtuZC59wqk7Olb9vENPhKSqkgEFIKpLANGgoCqwNBP10RYK3eA9kVETeKX0yOgsgMlVIf1ewgkBYOBAVjtodladDEDzNL+1VgDwZlGZ0ACm47reNgtA+Fnlufym4frVRx0vVQpAOmFqyjJfUxsN5wECEEwo2Ft0PBzLQAPQ9bg9EQAIDyltowF+kALIRjQ1uPA68KcAoLVBAwgnffMoaUv33ZmE8ePTARIZsiRN03R0dLS4XUq5a9euUqnWFVdcQS8eeuih22+//cYbb9y1a9eePXte+cpXxnH84Q9/+EMf+lBx/xNaBcYwy4BrarZIjqqDwqonzCnEUuc/w7yYEKlWkEqpxx9/vLhdSjk0NNS/f5Ikn/70p7/61a/eeuuto6OjQ0NDv/u7v/tHf/RHu3fvvvzyy88///xi0ltuOR4+fHhsbOzKK690dtYtt9xy5ZVXLmGkpISbpLTu6WkXWvQDFR1C9Lqb9KSOFl9Q3aKn5sv91EqVPEwy1pSwTAY4oCicmUBTh2GhTU2mS45xDcxFZvKHTJf4QhcSs72Q+kO+nzzHudfTI7oJecJEkic25eM3C/15XAI2kdwtmlPf9ArI5lpI9V6QwgtyXwWmDaHTrs0zKrLetaUwa1/dlTb6bgLwIi1/olam8aGRk5dijpRqWot7x3X7prR6rfWXv/zl4nYp5VVXXVWr9VS7LkYH5XgGswQW4+855qN5Xjk9aJEOoZ6DqDnSpQu/pqI3N2cBR47X86cFXD4lZGrmodfRAGQqSGclDcoF6rkgrwfRe3g360weT1B2EWnPZPykFW3WtWHmhSkA5acAdE1kac/5VsK40woApF2l6ykANBWtdNOKpj7Y8DUAVU1IZibRMur6MDcTGupxz/9TwgMEZF6hR0SWi+WgcOPKfHNTTfxCion97ozvR2kR5SrzmY81Lz2MQseGVuKvDVMAcSpTcto1FbULBdBeRZUr9hMDDcBrimi8AuDQc1W6y/kzQg1QlwJBzgwAVFli5Iy1yY6vPSvI76KVSVyrHjFfiWqbH2bQTvymgtXFSaqqMukDCO9ANDQIoLXaTK2JDaDernowUVRbvq6TxBXY504aSlddP7gXAFRX28eZyaka+oVutgcApGM67jUDwiMAgMcqSV0DUAqu1t2LAaAyDncokqIOmhmA9hPhzOkAEA9mivKu5v8FixQjv0gBTEcKQGcEnTHACRcBaSwoB+54iwDs/B8ZGTnqznEcv/Od79y0adOuXbsajQaAs88++9xzz/U875xzznnLW97y8MMPz2EAXX/99Z/73Oe2b9/+4Q9/+NZbb339618P4H3ve9/SDCBocz91icy01bbT6o+FiV4He94LrHS771GKI8kI2zwrMOojaWgOIqPM9CCL7DdhbmqS0uF0lGu0l6JFLinPNcEwWo5x3srejjztMX3Q1+47zUSpBViRwDa9J8Kg58GTpsYVn5qGSjLVGQQAL9Fkz6V2tDLpycsrSvvkyciUYRrmJS3mfGNIkmqwb/dmJQDMSuO+Tgo3KfNcMT0xdJAhkoDpa6M9Kwnv4heesY2O/wegk1Rr/cADDxS3VyqVVqtVMoAWqYOyXCyUzjz/57qvvj/+dVQrql8WaDGSiebgc9lGhZ+k9iR6Sw2AXPazlPtcqvnqD405RGpMZwkzq+FpmodGDybVkrKSUyF7A9nSdonSohDqQv5CpNAu079izJ3CZ9v/R6akMYkl7N1D+RlZQkpmZM3MtEMKUqSpmJ6qAdAd6cLlVPZFuc/DA216PO9tDqWxuWj04MnCOS/DYim2O3zh426hmepZMqVB/gVRNrDI8ognyQBGIxkl2Mq2NEnoVQ1gYNPMy0YOAoitpqovkyNxDcBUVKHvpf6kNNJBdSNNmQzkbXwAyFiEhxQd04wkgdc0q7tkwI5kNANA3crihtmoIuEqE+kEK+PG0EurnikQTtNi1XNaVbSPijJKYBh5zDzdRh81CnlZYJ5i05tU6+JZAKnUAFoTlco+z143k0dMY47q5hfntfNk/yJeE/W9GYDgvxOvnQJIQ9k8zVQ5htMZAG/WypwqQWNT7RRALUPtEAAkVdEepQobRCO9/gWVkSBQa603/IsYwLp9bQDNTbWZM6lO2ar+NlV3LAEg9uJ4WNL8v/nmm0dGRopL5Z07d95777033XTToUOH7rjjjg9+8IPF/c1V/uxnP3vfffetX7/+oYceuvzyy3/6058ODg5ifu67775vfvObxS0PPvjgIofIMEtCZFpBSim/9KUvHXXnxeigLPN4GeZEwjpYzEpmSfP/rrvuuuWWW2699Vb65z/8wz9cc80199xzz6ZNm6rV6p/92Z+dffbZxf2t/GUQUDjtnHPOef/73//Rj3504YdNvV4v+aMGBgbmKAMu6swerUl1meLaVymzivWUaUqqJPVJzQLpki5LskPGdxIbA1xGWhpxnfxqlip1ZaS9grGZx8jSvJU98iRoVyveu7hPbMUyXQ13Ip7nzsJuUXl6qVf0AGWIEgDS+qJUlLnTTKsKgKiKfPfCUth5g1ytr8vWTKuaego6CRNtJVYVdRTRpk7SJf0Vm2MkppWs1lbZnZZrGRSALCp4WWzf+OP0/RwDi9FBWa7P1gu6efp3TxIjCO4CT/P5e3ol1M2ezl1E7+r3Hh3VObQUnCJXvx+33/fj/mvf2/PD7PcMiQTwNAByvLtwiYR2ehDFj8D8IgsyhqQCgwrSas8H5d0o7aJZKyO5q2MKmthC5bpZrK8fnlpTaQE41KlFsQegHalE9xyNGmpubEzVVBfAc2KQ2o+jkhh94en5C8FfTGiobk9UKzNuPKDwNanIbImriHtX2TrMvGkSQjNBovqGJoCrzrzv5zPrAcT2KGv96QcnTgOw57G1lQMKgNDoNgCgs1a79swEBfEL8se2SUVdm1BUYX/KhqY0YacplQbQCQAEM7p6OIVtbwBAtRP6RZAuP6yv1AUi4rpH3QVk4Q5JvpnIdjESGWrVLoChagfAVBhN+cadHo1S5yWRrokA6K5SbQ9AcFDXDmoA3eGe32N3CFGDXPIejpjPqu+NAHSH/TQUADoj5r7cbQjTcqSiAFQPmlt35YiuTJrEBlcQYM5OauVnANob0gNvqABYd18HQDCdiMS0mKU9Yy+g2oLjbIW0JHbs2LFjx47Sxm984xvz7W+G9p73vOfVr371Nddc85GPfOSP//iP3/72t1911VXJ/O73s846iyQTHV/+8pf/89++j243f8zD3rj70gjyXtMk4ePJPJxEH1p6JChljAZlfPI68MisobbtKNRJlTxm7o4pU03R07S/57Cy4aRUU9Y9hbqKmocm1ptqUmic1/pxpCkNXtu4noCLfM1h9PS+14TP3GXxXOP3wWpa9wGI1KPCNK3MsW3ZQC7nZuX8NXmSdWBk1AGkXQVAp07Ehc7R9LWRNvIlMqtNZ934Osz8egQgDJJu5AGI4xDkTaVoWqBtxyX70PKPK+okEy2PYwW8fKoni0Tb35Hrf+K20AvheXOYOHPaUsXd+n+eR7VvStlCxeWK+33RwDwXaDZ2j9luI86wdkzR+lk46UcrUXJliwzSztbUyw0diWLSS/mrL/n8M+RzFYBMbLAsMcJUxR7jJcHPaCSlDneQGoAK02rVximqLQAbalObq0cA+HJNkikAe7t+Yk0f+l+amosz6rfojZ6t95luVQGkQ+2JBa7L0TjO+f98ouJig/eeyeC183477st1X2XHWickSyO7ErUUwCvHDgA40BlaV5kBcCQyF/bZzsieZ1cD8KdUd415iPjTACmWyZ6DUyZKMqBtn3YRDWcAdCOh8KWSWXvSdO6g573rVx+NAEAygFU/TwHUnmlRc6SutSHaL61QAs3A3i6p9cIuADpDPoCp0+XwLzIA7dWevRTmZJOKpJKx2Y04Y3AGwMFWHUCrHVIneQB6KAaQwsjwIDPn1R0SdJygmbVH8+dI0AT1F4sGRWt1AMBvafcTiOpAsT6uYo5GQcOogWDafEeUNlI9ouO6/YFvSQFUK/HEkQEA2tetTRmA57IKgOq49mcE7HoAQLpaSZUBmG0cVyeLZZ3/5ip/4hOfeOtb37pv3z4Anuf9x3/8B8XSlulTGWbxiFTP14lzARbWQWGYU4Vjm/8M8+JgWee/MYA6nc6FF15Ir++///5HHnnkda973Xve855jOWTf+pI0jrPAK2vIWkSSlQNkpbTQMDCyOkpmATUH9cj3k1ZMuq7z60gJ9Pp47IIg96L3t0s0L2JNzkmT1xal1pyX1MoeQFHs5yiYerG0558lx09vN0pzcCWN7pGt09ETk+Q/UN0YaICUdin72zcrHuFOqtfHoRUo8gVfU44nAJenWRTpkZFR7ZSxqeAQmS732fB1GCQAGrX2NKoAYj+wO1DKs8mSdjGC4+QUqoIh9Dyu0/m299Dr+MldRIuhVBdWjL3OuSfmKqu0vh+YTGfyDJW/Sq1ESe+nRN7Oxb63GJte2FeU92zxRamvBWwjbhVZ4R/r8qHtucCV7bXpEkgzz+S6plXjE0UtFV4GwAtSADSxAQxVO9QnfG04/ZLwEIBAJpSB2xn2Z0LjDqU611oYARj2W68aeBbAgNeNtQegmQTNRghgYvrw0wuc7dE4tea/czbIWDvteAAqMu6Hoi6wC5FTPZ1qKnqRVZING44AWBtOAwhUeiSqAZiMTcXDw3vXh3sCAN3V6fmv+QWARw+vie8cBeDNmmBT3mHXBwBvVlAmQDKg9XAMIKjFJN3Uns71iMhvHQ8a0R3ntQonaJKJ7nBPXD9oZt0hCaA7VK0czgAM7OsAiOvmxjr8i8yUrYTmylQmUhu+EJHJ1zZ96R/dsw5A8ExYtYJHrUEBAF1JwmxoJJSaLY+Y9k0i08V7eHfAeK2CCdPoqTUmnE+0dNlFarvc02Ong9rBDIDXyVzYujpuruPE04MA0k2zVPUilEmo6K6SALQUsgsAUxM2nzwTeqICwJ+cxHGwrPPfnNvw8HCn0wGwY8eOG2644S1vecsNN9zwh3/4h7/3e7+3lKMJc6st16GQMZGUdBF7GlyYPCEFe3Mppsvo0CNtQB14KbVAryqqV8yUgK1xdX16i9dLpNqZPsZJHmnR90RQXVflblN8zMB61A6XlORhC9aUeYC5Ey9GzVwPEPNPKv6PrCCkqYxLp6ZUvQ5AhAHF4FTXo9+zik2qjUwFgFTap0VhllNNGappGisAWSqQUGmeKIqVFbEJFibBKKnCRdajRAGYblUpBEbq6ZmvRbn1wYkx20Wa4dQQJdc9Jo4rvyrZJQ4XVzrOgvmSfbOYliy9Ayjmos1HoRWGiXz1mz49oec+u8e9XsD6ccc0PfiCfHFidSjcP20emy3qNH+K8/e6FjH0IqkjHqSyLJO+5oVpEPZE1MiaGQo61Glh0Ots9Q8CWO3NRJkHYMDrzibmHuXLBEDd6wJ4x+iDG9UkgNdUnpnOKgCms0qkfQBPD7d+PN8JL4JTZ/5DpOjYsIE/K0jUwH1lfhsAZKy7DQFA6EJiUFMByGopVRht3nB4dbUFYF1lCsCRuE6mz4FZkxmTPFcNKBPLxvTb3UCSodMyoc/IjoQezN3V5hpm1UxKDWB1o0n90pNExS2reUh30apZwrn+hhTzqtmidzI+AGQKrTEA0B5aYxJAa6wGGEsCQNQQtrFS/kNIKhJAOG2qzWfOjQ91agDUIVMX565M+DQJtNgqsFBGIxmdHdlY3qyICqEakSA8bL6LpAoAccNISHizZpHg2QCfjDW9HjigAXidLJiiFpwirnsA4rp0wx75uQDQ3VunJJ9isimA6rj2uhpAtN/8OiZeoYd3CwD+vd1DOHaWdf6XDYHPfvaz3/rWt84+++xnnnnm4osvXqIBxDDLAIcAmJUMz39mJfM8hMAcQRC87GUvAzA2NtZut+d6y/wIIAjyEienMpKk9EezyvT6HCHO/+Ep93YX8wKQBT7l2KehpHz1pCKdDW6OVrCvKYBFwSyHW3cqQPctkslL1K83UG5xqmT/VzF3HrRL9HZbCr3f893mKxmze5J7QNXr5oA9/WXzugag4PLRdEZO/03ILnnLVNK1oyJ5w0SY9/adleutnZr+8LnjlGpbYnia3EiZOU/j8nEn7DxA2YmJhZ0CLND9dEntLHrpT6POqwTmjI4t7FIqfqjXM4B5s/Lnp/i7WyAcNucWrYwD0vnw+2PTNsFZFzOdzV/N4r8nBKCVEQpKQ9vx1KY8JzVd0uTMUkE6h5VaBECp1OUvO0KRAmigfU51D4CXhIe6tqwllAmAUCQAXhMcXq+Mf+KpZBLAE/HwdAYAa9QUVgBCQ2Ra2VonmTrppp5rHtfMDkkVccPWUp3WArBueKaT+ABWV1sbK3ni+JGoFqcSwJH/xzSsVHVb2JHIn+47DUD2xEB1AgD8lu6MCMB4+2Dja3lJbywqqyIASaqoJYXnpbG0SceeBpCEND9lOE4OIRx5uQLgz/jhZAwgHjT7t8bU6H9nAGY2SnJx0fSLB4TxiAyaCFShU5DwZ1MAfjPRqymOK554dAOAoCMAyG4hOFjVAOKRdNVpUwCiyGu3AwBZKrpJCHJZFS5wWs0zuH3rCaPfTjgNCtJ5HXMtkoqkkVBITqS6szoAoDoZ/ULjmiBVSQDVwxpA42lNb8980W1IWGFGf9YcszLeNVdmbUh1edXpJRoSzyPmW1y9evVZZ521cePGJEluvPHG66677uqrr15620iB0NdeoZ2Qe7ojv92LdP6bvpIuBYFyfUq17smAR3WDrm07XNf3zAqgFZJhzFEjKsYTWd5AulQfayNfrtqWxBuRadCYUyfn2B8smLvsoWcEc9XdoMfuMcVivckZIgyEsmJhFBwMg1IdskiAXqU1070LphcS8vpkScXGIhGugdfCmTpa2fZhQd4inmLAyITpFxZRnLx8/lpCkA00h9G4BESaiVMkBFBCx7khIvz5m3wdW3W6MaP7bJ3+gjJHMGcf8/xd7gukL6zwTyVg4tdGXcJWtxYrJdNgjrlUrMp0iQXl9mFKUA5fqW2cjHO7p6iwZ47Wu7PLOCGTPR7Mn6/5ASMrmUHDbgcYjQCQGRQpn0q6PJkNBeZH9WwyDGAmM1VC3cwLbTLFoGwDaMgOgK7W+9MmgJkMFAJ7IlqzLx4BcLhTBw73X5lFcurOf4Y5fpZ1/pub8rPPPtvpdJ555pmnn356aGgoSZLzzz//mmuuWaZPZZjFI5ymNsOsPHj+MyuZZZ3/+ap0YmJi8+bNZ5555v333/+Nb3zjzW9+c6VSWeCdcyBM3Mo4S7qJaW3R7QJAmqFW7dnfhQBc2MtK72eB73w/AJKqsh13RRJSyq2gGhCZmuiV6mpKs9eeeVdqnTqqmwFQdhnq/ED96ZnzoZWiWNjc3TxsJZdp/lXaY85uTc4r5rSC0hRA1jFOG0kX3/PyVbvNB59reD2vySXmxAwB09EGwvh7VEfM6fhxb3EVNFpYHaCKprxRITWsB4h8P6Z9mC0KyI8Wpka7Iji+6ZtmOBV0ULSGjhPhe+T4Kbl8FvIG9XR6sXnTpQRqOsicsbASSpY3OqXE0jx0vcDQ+xsskHfAIFcoMtifj+r9yWhlkpFNyme/V3WuAJmpsrFn4yJiJiRtHT/9B8l859fMw7X0T5LXixu2GjExPYlUOz8+uaCikQxHAtjAR1pPUAWAmhdTavNqNfNkNAZgPK673OdApQC2hIfIA0T+nge768aTQQAzWfU0fwLAY531T8yuBjA1UwF6urgsjVNl/gtkvnDqO8GMpu/FzQrbZhHRiADQ3Ry57u5KaQDTrersnkEAExj5qQCsCg6AsTXTANqbzPwPD3rp1jYAtL3oYBXA2COojscAZtd7puyrZaZKba8HIB60PcjqunW4BiCq+yRUk6WSikIAOJVXAImvTE8WGEf44VeGa+9roTAPBw6YZ0dlwsS8OiMSQDhp9H4yD8OPJ+gtC4gHzNMtqUoAY2uPHJ6sA0i6FQB+Klz8LtwyA2Dz8BQFB5utMG17AGr/YyIgwTQ6hbq0LNCme6M2cbRgwsTCghlN8bvgsIlJtTYP0rPSOVNpPP5M4s/EAFpjnvtCk4oA4Ld01FAA/NmMNCEpb1o1uzNnNAAM7Df92mrPhe3VAJBVj68XzBLn/8c//vGvfe1rURRdd9111113HYCdO3f+7d/+re/7O3bsKMW1zI1nx44dn/zkJx955JGdO3fecMMNl1xyycc//vE/+ZM/KfWOXwxaybK9Np8SdEHesBT5gm0k5GTW7Pdk51CmpemWVagToRLuVFNnE8oBKlo21l2fIQZ678hGgS0p3dMlef6R6lINv8sNys/XPnjmMIN6My2QFJI/bJ2zptaqyj4KShk/oV/QpitHTEyYQOavy1ByTiL6K7PmrAJzdcjOtHJFN8WEnuLRdJBRayRITXYPlRYDiI6vHOzUWgE7Q6do8cy5z0JBMRxHdKxUWYm+n96cZWK5JVTYuRDwNQsAGwsrTpgsoDCxVoUir1Jj1CKuTVgxhqXiwlwq/Mxdaafuu1pG59M3aWpuxpoSngyqSRLwpizI9ebMPGMkBZOmgVQ8lAIIajFVgfn2nrIvHtnTHgUwGZs0lKGgvU7NAJjJqvfNjgB4rtsAEMikmYQA4swb8DYAmE1CqlqabbfmuxSL4dSa/8UGqMXvN1PIKiRDLLprEwD14XZeMm3tD69jirCoG5d3iERWMfnMGgBW7BZxI9PTPgBvStFaLhqEiq2xQlbsPrMzLZW9WTNhZCwGd3sAkprnzwBANJx7AmitSE3c0nqa1VJQlD8WAJIqDr62hkJjL9VOnZZsc510n94dFu3VJNRiRVXsUzwZ8Ka3mDOh6ferY0892xgBEJ9mtsc20DsdhQCeeGodFdsKPwuf8QFUxxHbi1c7mF9nsV+EkxkAfzYl6UVXfh/XROdlIQAtbRljS9vLbt4uo557tYpBXWAB1A4mAMJDne6aCoC0IqmnGMk/yvHp+JwhAFSvTQdv0a2gcuwC9Fji/L/77ru//vWvP/LII5OTkxdeeOEll1wyOjr613/91z/96U8PHDjwa7/2a08++WRRC9dc7r/6q7966KGHVq9e/cUvfvH222+/6aab7rzzzr/5m785nnEzzImhKJfAMCuNpcz/JEl+53d+Z8OGDZs2bfrKV75CG3fu3HnGGWds27bthz/84XxbGOYFylLm/969e6+55pparbZhw4bt27c/+eST//Vf/3XRRReNjIycddZZg4ODu3btKu5vTKFVq1ZFUUQvaEuxgfaSxirSTJS0bVzkywW8FlDct8KDc4qFyMik2mYZrIMdzrPqxaYJi99MAKhmxx7KiLmRHIJInXupcOSkpwqs1L2oSLkurKhsVNwIs5iet1cGQanNaSpckjWKXaLsZ3VN8ngxBOYaxYuCV0bFeUQgs22xaWQiA+3pRAtFKkrFNa6/Esk8uDWc6gjyBjsNFaE0tRHQto0AqSwGXhpYQbk0FQC6/pxeqUWTpKeQAaRTG6VSczl4TtSnFOq85pVJPGr3vbnkEIvT1YXDiiswioUBuTrinE2+nDM175XhHD9KFMq+qBqxZ1zFshaqIcr6lRhl3gJPFoRJMiCYcFp8AKC6+fSmRbML9WoPyUAGgBovKJlRWdBUVAGGARzsNowXpxsMhBGAmhc/0xoB8Ei0nlbns90AQOiZi9lNFHV0SjI50awBaM3WcDwsZf5/85vf3Lt37+OPP37w4MFXvOIVV1111fj4eGkFvHfv3gXWxMeM0JBx3nUhsQkU1O0hHsDsJg1AbppFywfQ3FdX7b6CEgUAwRGznRp4aU/TjAgmzfbgiBSpBPJGhzNbMfkGp/RHaRImMmRSAhJTHhWOG/+f9tBdDQAixchuO11tsxQAgKIaqMymIYgU3REAaK21B0+R2q7sVCcVTgNAtyFap2kAA3sEVeE4ug1J8z+pg5xhA153LJwGUPciAL5IdjdNvdvuhzYBEAJiJALgV5K06gOo7026I7b7WG+EyLPdnKhHR8c3F81vaSo1mHqp/TUdEtUjGra5vddO01ACkIlur6u6q2EOSxLB7a7X9gFkgeys9gGYDJMw8Gc1gGSo4kblNwWATq905JJJUqSZ1vpf/uVfipuDIHjrW98a9BZ2XHHFFfTioYceuv3222+88cYbb7xx27YHgSwpAAAgAElEQVRttPGss87av39/cX9zBT/zmc9s3779sssu27p166WXXvq2t73tu9/9LsXPloC2QsZJ743VBYDIyrGJPrCmg7N7ClvKVVq0RcW6/4YojVahJk+jijJBLWPKhS3Gew9Iq3a4aCNPibIi4pwXoPDIEYWNTjzaPFFcoZySpng9zVCoAhNh4UstfWLo2TEU/HgpAGRZj8pcsVukk9N1pXNGHRuaXLtznYs9EYqRJSamnkBmVCocZtQVj+LoYZA0am0AqyotX2UA4lRORRUAs8dpAJ0yaGf9nDCO1sd0IZFoF5nNE4bmVmLMyX+5dib3xtHylKAeOYaeAjHHfIKHWpYNGnk0nQ+Z6rQ3piYyTeESken5yu/dnrRDan9V8aAJqJUK46OunyQKQNvzm5UQQLMVRiSRl4lWLYZt7wWgG3lJpABkbQ+ArCYU881SSaVkaSbSTMLKRjw/vPKVr7zhhhsqlYoQYmxszPM8twIeGRmhFfCuXbtKW84777wT8ukizTPDRGaCL7PrAaCzNSLR7bTjkYHiVl9w0cxqVl03C0A/2KDt1F5KK1Hqb6o69lamTa9TNQ35XACgvV5XDgoA7fV2rg7HALwDQTAtAHgdIxQi0lwi3BXnmy0KAOIBY82oTv7prTEBYHad2X/0sTToXQDMrlMAuquN4aUV0kACoGU5gKCZyb0SQHtUdDdqABNxLSgElR+Z2vDQ7s3mTFMBINwyE/gJgIEw2r/BAzC7PqQAVhIKr5tfmdQXySr6bap4wITtjLkvxejPWwAaT5nBR0M+STJ2Rz0AHemT2ep1zBVQsXYtFugsks1D0joahK8AkGSiVwtqz3VRWA5VxmOv7QE4bEN1x4ySSilVMoCEEOedd9769etLOydJ8ulPf/qrX/3qrbfeOjo6il5vTtZbUGZ+mZdeeumDDz74ne9856mnntq8efPY2Ni3v/1tZzcxzMkkTU8VJVyGOfGkKdIky7IzzjijuDkMw+9973ubN28ubnzVq14F4Nprr925c+fnPve5MAz3799fWgH3b3leToNhjok09XSwdu3aW2655aj7xnH8zne+c9OmTbt27Wo0GgDWrVt355130l937969YcOG4v750mR2dvaKK64Iw/D+++9/+OGHKSK2RHS+gjSHNznO6K3wynfoC3iVFPRpPZGGzmdjrEupRGnPYqchc1jqntFTe2W9OOa9/Q7Y/o7WJHWzsONnjtW5KxwTtjoMNr6gPZnVAvpT7qaqkXxbBpDTryChBKDbpWCZSDIdmNN0sT/bCkAAEBLadgBwjWzskApahRogzaQOHQ0odNLO/Dyl1LRQtt4jD6JbB4CgknheCsAtTTbVpwBsHThEQinNtEJVMIeO0wPk1JJWFMUqsLlYbIMwFKrASgd39NVjlr2nniyVMog0zWNhtAWZ1coqR8Sch8aEnu12WfAWzIebvRQm07Y5hqScbJR7IaGg4ZkrA/k9n6I9c1jVESKTALJEAEg9lfhUbZq0myEA3VUkGQql4ywAEKWhOU4qqP7RiwWArC3jkCLCaHbndtcdI2kaitrY2NgPfvCD4mYhRMn6cXzxi1/86Ec/etFFF73jHe/AXCvgBdbEx4wWiAeEK0lJKpg5IwPgr28BEB2jm4qWuTiqnWu5kcZYOK6wrwGqQqW7TRMA/FlMvxQA0ood6ojpb6gasXyqCkCkpveFE4ANx8206IQKgNc0DqdcR8oG+tMKWjZgZ/ahW6hnywYbecug2kENq/4HQLVTF+EiXwh5vNKtbX2AkoVNBU9mU7jDiZgc/9UjslXvec4e6AwC+MX4an/CKtae3gIwWO2SRKcns4F6F8D4eZ43pQD40z0lvc5z7zdzl2d3FQDMnJk2N9UAKCtMGEz3FLvEdRPsE4lpCz/8eArb1CytKgBJVQAKQOqb77o14AFonjZKu7nGU91hQZe38uDx1TDS/X9xdztq4v7lL3/Zbbnssss+85nPtFqtQ4cONZvN173udcX9zbnt2LHj3HPPnZmZufHGG9/1rnf95Cc/efvb3/6FL3zhuMbNMCeEJFmJBhDDEEmCJPF9f2svL3nJS/r3/fznP3/bbbcBOOOMM97whjc8/PDD69at2717N/2VVsD9W563U2GYJZMkR5G2L3DXXXfdcsstFcstt9yyZcuWj3zkI+edd9473/nOr371q6V0N/OPUhXYli1bnn322YsuumhpZfB67gWrEQdy3eCVKKnpOL+LSDWlTJbK0R0UfQSgU+EMaqK47jTHNx4gW6ZuPUMiSszitW+d1q9R65IenDunMOzeheccHbOpV6jOXUFmT2m8UzBOKRnFZoVNedNKwoV1S3XRfTWBItW0EhV9qWZ5DlBZM9e8BWYQfW8UdingJAZSYyzreRa3nsyoN2Qok4CyUlNQ5XCne3w5EKeIDgq0yV5fZPpzf518T2H80Wy+hRrFHzX9eYmIJCslRPcLYi38J7uDBvWiIcmGDPPpb+X+Xfrtuh7jke6vhy/qDxWOYJRLkqppeZ35pkg7a+f6Q2Y+04rf18LPAOhMiEkfgEzzZh3OByBt2pzJ3abka19k5ArytXauJjpNcZwr4CXM/yAIPv/5z7/5zW8eHx+/6667Pv/5z5999tmlFfC6desWWBMfOwJJ1ejlAMBrp18yPAXgyX1rAHhBmkwEANydJxlKUXVKZQJA9TlF/VOd007bXBzyTFOHCgBQmkTI0q5K10cAotWSOqrK2CiAkxoCgPA5D0DlsGkO6rXNbS0N8wbp7kZHH5T2SuCpyCb0SFBiTdsW9sQ142YRmaZEou66BMCGVVPJcBPA1L1raDKTfwiASLWibhJKxBMhgMem1xyeHQDQaocA4onQP91IJ9SqXQCJlhUZA/BkSkoNswNh1lIgbaRq4V6RicoTAYCkasv+rQyEVtI9EYjuiO2T2gaAwLZsyTxzQaKGSl2HpQQA/GZGaUPwbdOPmgAQDaG7SqMgvyQS8xU0ZyXuxrGzlPm/Y8eOHTt2lDZee+2111577Zz7n+gqMMzVYrov09lRsja0En1KPD1xrpIvvUgWmDBZ5jmXYE+qtc2Annsk7t4tCxn7Is1c1KzQH96aRIWD2zGUtII0fW6hcMZeCvteGlUW+NTj3RxN2bKu7hwPwgUeML272YleOFe6d2t7W5eRrQKjLDnbN9tFvtBnRWnP9BGLOx4Kt4mmCvc0RwCMd0xHpOkoHJ+uA+hMHVnMgOc9kSQ53n7pzyPzWT86TY69LmyuGOuSi7+SpJwNPWcSdFGzqr/xS78yUN7mxS4w+swg0Xf/KhjWR7m10S/dBcsyJUTfXDA9cGzkK60IAKlvHngiM5U7blZrz8zztKJJ6IUeIZ6fZakAoGc9U3BkR+cSZiHymjXXYgxAVktBibpeT3EAgMFoNu9rtXR0kuhssfP/6quv/slPfnL66adXKpUbbrhhy5YtAGgFrJSiFbBbE7stxzG6nExhdktGAS8AVT9pdisApNIAslRS0Eore3+2VRQAgjAGMPumOG4GANSEGRIpWPpToJ5c/rQNn3VMJVekPd1IQEnoBz0Ama+pDDCxdiqViTW3mOexags6GoCoAQDd1ZmLItEnmu5d0winACANzN3Pb5mEeid3pLpmilTHk8kzfADVNS0Aie34JFJjvrvflZvzwXSy8fsKwKFHN9HpkOyiGMkovx5AWwYAAi9FUEh1BvxKEnsBgA0vGXeJ+QDajzcG95Aeo4iGgYIBFEyJcKr8cyO1RmowFQ0KMkBljO6QuSBk8ME9CDxJFk/mC8oNHziQAVCxjBv51TZvMSK6OB6WNP+XygmtAmOYFwBLUgJlmBcTQRD84z/+Y2lj/wp4gTUxw6wcTmgVmLDizr1Zz/lakCzfuYpjXXdo+mfmiTmXscVc6ZKYrMtwzHpTm2Wi7cFNP43+yJcbZDm6FCU2fGa9PkWVFHvStAh2qdxO+IS8WTKyn5iK/itgXT49hcE6NafVc6WUVc02HycWrv7tJ3fzRtYD1HUttWkw5qQyvxzqcimlWppsa53ILJUAUqkBtDt+u+MDSBLlyoNlWwIIx4+vG3aaQmdH3w3A0pVATySi7P4pVsUvxv1DnTTMPxbv9Sk5aUr7OOfZAknQ8+lNL8LXKNJ0niIAUWib2uPHxfyOn7LH1x4EMNJB/QXzuU/I9H4XUR0AkprRfYkHTTxXK23Tok31u/a1CFMApF2edpWY8QCoSKjeDtbOA1T0jJJKTTYSA6g2OtWK+S15IgNQ8WNPpgD89vQTc57tIklT6FMhB05qjESplWNuxtVpulHYzjnmpiZtU52uTGIzwUhCbP3oVLMeAkjXmGlAIaFOKo1nbtrEY6r7FN0cdZgF9QhA8sxA9QAAzGw17j33DcouySUg7wBN6QZtq9wzIadfZhOZ1yYARFMBaDwhXB696Wwfl2egjEx39PZqr3m6BvDqtQcBjLdrex4fA9CYNnu6R1U8oEj3XKSaRJK0MknH9CnBpIzHnZoOADRfGr1szSHaQj0xopbvr20D8GSWFnTgBp8Q9b1dAP6s32nTQ80oPqe+8fcUVdft70sCSENBMk5+K1MUz1XwOj3nG9fMcyeuIq4KN0KvpQeeofdaZ60vyCkb7cc4joPlnP/5PbHRaFx11VUn4JBKuo5gLunH/ImudapLnaULtzmQEBN6pfS1LEioWbuHLAbtWY+0gjTaNiDVcJec3x8vO6rjXUQJilVayRxilCYE5gapRFrI9hep1rYLuozmfn4Xi84oFpvnQsGcSz501wvMXoqFT0HLvnYWaV7LQONWnVysAkUrR/Ucx2zJi4Lm+Lg0k6R3oqd9f0qh4HqNjysCBh0nOlvsD8ApgdZqNVICveeee5ZJ9WTeAR+rGlB/c4yyxVMU9SGKwUGv13iiOJfnzVHzlR9wwXql/hCYG1ia6f5YWMG+d+l0wlrzTne0PyKGvgyeOT5xHhtYQvcsHgonlNTNFip+FKmpfhSu1UYqNAVKzB1DeLMCgNfMFwa53WN/KUkNALIQFD6rNjoA1jSaNS8G4MuUXgCgrDhZsc/AY0LHiT4lDCBARyp1umLVtNg2BwDlV+UbwyyomNl77oa9AEaC2YPdBoDxdm3voRHYMGKWCr+SAEhtU5123XTvqo+2ztvwNIB9q4ceHVlPx++MaACUCgOnh9lx91g0z0wAiEh6TQlAtVF7xkzmZEDC5vFMb/UaT5iQUDBDyUkgdUHXX8IZE+1VonrGFIBdj28CgLai3KPiCpPwZ9O0IgFMne5RcLZ60MTUqG5r4KBObdCULJLkHHOUOJVkAKHp1UZmARxp9sjszG7E0JOSBhZOZQCSUFQPRgDaY0F1PEIhG0lGWdTwAEQNQZ8urWIQ7eBOE7a8qzKZUbysdkhPb1KwDwivq1c/0gUQ7DezvbNpiI7TPnIMFeU5yzr/nz+FLoY5NnSaaJ1oram8xSGE2L59u+/35H4vVQmUYV7g0Pw/2aNgmJPDss7/E2sACYS+Dr3+vhYAtTRzDUQ92uKyhm3ipPln5lvhH6tuTKtJk39O+wTGRydNRYlOSHDTylo49xI5k7Q0kuRzlXrpQo6zduNxCs5z0I1Aes22OsYNkmz24sLZfpzsF5J2VW9GK8ITIHHxQAHIAGkUWXzyq2WBn1Y9AGkgda8rKOurAis0uKB1jE15tqelIlsQ0asZrede9gOAjCADAcCdiZIZgDST5Ov2p1QwYQ5OPfbU9HFVwUwn423MSiVLzemCIHjFK15xnEqgzyfkGSrGwpzLp1wRppTx/ZCXJc3MZFtkMvicOc5K5dvnc/x4CzqEeiklO+exsL5As4uFlSh6ea2olal10H1upP7uNGZLBpmHo2mdag+rAYrz2iAI/SnzAdHzq8nlzm3b1DzUZT/QacZQ7nO0Pg4aXQCDVKeTySPtGoCKH88mtlO3zACMpMdVlDedjMfoHn0/hnkxsqzz/4QaQALak8XI17z1StZV7myU/j2LT3etBJk+ZPSg0K4csO0tIJxrfU4fu9tYjLgtjHY9K/oJg1J0QKQm2Uja+O4cn1KwCIlS1Rv1VXEG2Rx9xwJFj43MGkCpL9xlQbH4Kx+Y8fm7yFeeL+WZB4GLc5VMn2LcoRBKAwDE5nNJ7x82kSIZyGQki3smPd1alsYv//IvT05OBsAVL73in//5n4+6/1KVQE8488W/Fq4CK6X+CM/rmV2uNcoxZC8VbZ1ihSb6ar4WybzNMco/4QV+Zaa2K9GlpvH9gbBSlLyodpGvcEylGABkvqnplUnxIPQWK3PniuEqsP0BAcrwSMyLvgHnawNqy+DXo3qtC6CbKACTs1VKf8lsPVGlFq1pNAHMtEbnuw5Hhea/BC566UXHfJDnCQ3EAsWeFdTygjqEtD1Kt/JrcRgkAMYa03+99Vu0Y1crADcdupj+eaQ5kDR92KiZX4tpcUXFYgDWrGm+YvgAgLoXUWu21ZXm/z73XgDPtEf2tRoAnvTWmGEcCQBoT1PrsWBCUNGfDrNEewDi0SwfdiwAyJYCkPmY3mpCosEMQDMk1ii2WB+Qpm/GIJLHGgBqEwKA6iCcNtY8hcmKOUAzGyW9ZcD6o5ubACv8WN+feTaBqb1KARgZbJGkyOFOjVItATSbVQDimUqyLo8xqdPbzwYVOs1kAAAqB+F1fQBxTVDwy/VrC6aMiqOKfQCz6xSdXbJg3dbA3i4A78hseGQAwMHXVgH4e3VrXQBANU1JWuWZqea2VQsdaBEs9/znEBjzgqYU9joqS1UCZZgXMkud/wzzYmK55/+JNoBMTVMpwGR1COchDx555comCgw5J0fqu3WYsP0f7KdkmiQZSuvOQg7mvNVnxfiXzegk6aBCvq83jzcrDwFoE2Kzribn3SkUr5UX3KW6GHet+nUX3aEyX4K0wkIT2jOiYdLEBMtou6LVPcKGIP+/b1/0+nhMC+VCzYu2inAkJiS6UvsKgA5SAGGQqFoGoAN0Qw9AOqXSpgCQTsxx5ZcJUgK99dZb6Z//8A//cOWVVy6H6slSmdP9Q5Gv/tznnKOOdjGn0+/mcd6afh/tPI3HXReX8p5KLiCKSLgWGf1FXv1N40s7FP9ZPEhPkrUEgMyEwOCb97pDlcfm/pRE9odphRll78552wQ7OpEZqZhux2t7PoC8aQbF0bqSQnDtTOxPFIBostV/fV6MCKTCifIpP4OfAUhjCUBWE+rh8MqxA68eegbAxbXd22yTnNvawwAOdeoueig7EgClqMdSB7UYwFlrD9Jfrxy7j14cSuq7p8cAzCa1/z12D4DugEeteP6v5DLaZ/+RMQDa14mfApCRRwnUVOoFQERSwz0CBIBsKAGQDQFeBqCbie5qH0AwIZqneQAqNknZ1VgBoDIogqL/AFRXdxt0xzZb2qsEde2oPme2TL5c114yDSC7ZwiA6mRO5pecMWuqrdjOxfZ0BYC/umOa7A6l6lDuY/dmBTk106qR5ImGRTxNkQfQ4GMrG9Qaq3qtvC5MdTRpaInUzvy+KrCkKrxQAlCBJ9sJgHBSAwimE/MQr1oNp/G4eqANIFpcvOWkcIIfBnn8yxR5zXMzNUaGN5/dAxf8kgCQVM3D3glSAaA6PQlNbVlE4qRa9XxC0iWZ6R5TKXetq8II5eJFdUWaqTYJoM2tc52GsjSw4m2d2o2RHCKAvPqMDuJJ6qGWhtIYhaEgfa05Un8o0SezL2xtl0hzNVs7Nvt2Yf5ZUkR1cYTMM6WI7uHhSRlTJ+06ADRq7QZJdY3iYKsO4Ei1nh0OAGSDR7l0J5ClKoE+D8wX+VrI7jkGFpPWU9Yut+lrhV51lGo2b+R3vkMtyFEVoud/Y/mHPGd0G75wf1KZXQnYM5DpHO+ifWSsS5WStF2rXFbRfK62eUY2joy2anVrAEjrwesIszCwBfMx/LitAMSTxxEDPpXQ2teusCuJVGOoBWCo2gHQif2KHwNYG04PyjaANapVl0Y0daM3CaDmxVNRBUC7HRh1e5KN7gaq3gXw8voB2n/Q1rgPqvbrRvYA+NZT5/ysvRkAHRxAwyoH7mskAIStPotWJ6JDBq9pKCa6UtiovflyZxWArJLJgPLINJXQK2vWuCBRGqC9WgBob0ooO5Psj4H9ef5AsZYKQDhtorR+S89sEQDEuk5zsgpgeBoAuiOe019urwOAVuInmQQw2w0osOh56Zp1MwCeOzyURfkvKwGG9tkaLqogq6J5mlkbmO128FqhuUkAiFanACp7Pa8FADIxBlzqIxp0ixCg0ARNB157XRX2txM1PJIDyIPUAyHtMJsE+G+8MDmu7DyGYRiGYZhTkRO5BtVCFEM8WgnTSt3m85bzJa0TO/PlnL5uAGndOA/J4s68wlpNAYBvtT1k0ZtSyJcstqS2UbO5FpG0m7NeA5cnWZYuLOOO5jrVRxGK0a5AJVVb3WaPSq6gQmpnJttd9K+808x1UiPXYuZLkmFIQuGigT3nEZkrk4Y2tRMmeuUCW3AxL2nbCPhG5YLc+yoxvh9/1h7NRxoCFCaIzYu0UJS3bqBJ67NBr3MkrgO40zt9X7IKc/moViD9SdA9soeLZGHZntJfPaOcmX/ifGHcPvI9XRla/iklB2eh5UWxOYb7XRR+O6VG8XPUY/Z29TpqNYPdAiCvbRS0ig8KVRHUSd5ebC1FycHjthdcQUDhB+u2qw7SKgCopjJrYmqeENl86syssLWU8ZAGUJLDedEiIJTObMmbF6RKaQDNKAQwXGltqE0DiLQ6nAwC+MHstkOVPbTztK4DOGtw/5NTowCy1BTpufsVldo5/u/9289pPAsgkMkqbwZAs1n9+v+8AcDL1hya7IawJXgAxtZOATi4Z8S4eQZSynTWgc19LurUGF+4BiA7Uvs0D0RSzwDgoPTbQDH1IkVcBwChdHxaFwDaCkBaVU53kXDCjGkF1K1CS9HdHAHYunZ8wIsB7K6PAWj/f3U3nGiTqTE0F2qqJmYVgLQhnzs8BIowDuYJ/3rCp2dlGoACbfHaeGjNDIDWI6N0Xu6GnNSRkYvL10DeIiYeBCYAoHKk/AOMBkU4QQVJikJ75CtqjcnaQQDI1oa0Z7ah0h2WACgA98LkhOcACaR6qb7uoh5gcSOcE68i6OnrFIrd/EsD+L0RdpHp3swe6bbP12gMMBaYjFJbw19OVugftmv1ZYeii0VbRYXcvLhX5r56AJknVMkac3kV9ATyTNvUrBqQFZUFMn88WFUB16gPhTwG1z9SK5PBIAo5QO5Pc5KHzzJTVCxUT1kNAHTMrd+1raHQ+6BsU15RI+g+V00AxNW5LM4Vw3x1YT3Wj5sqxep3zKPjPCdF66dg+rhKRqfMXirjKm7J91kGitqJJcoJQH12z5ypQqUCMTp/17W0qNhrRFOdvFshlZC2GMHfQhWkOUhibziJ+RHJxJhTXlNQQMSYQbZyXivKMEE8lCIXYHzxI4SuDrc7LRfvk1HkAdg4PAnAlykVZ3US/+BAA8DWgfGZzGSj3D95OoA4lRsbUwA8le6LVgEQ1QRAvd5+7ZpnAAzazJpLRv/7NH8CwKPdDVvDQwCufMUD/7r7XAC7Ht8kZO99ftYDEB7wkroGkA5as7grddWoW7rvSJe+shb9lHRWyQC01wt9MM/NIEgQvD5qnkMz3QGYVqwagFzdpcLA4PG8toraacV1Y5wNeEY64VXrDwD4aWejOGTMCDqXTuJPTdVoS+W0JoBqJT68dwhAMO4lA/n6JK2nzS0KgFjXefXmvQDGwunHptcAmK4P03upOBHAnsfHak+ZdTUAkZnYXFpFa4O5Di7Dia59MGMer9GQb+ouFYA8ec6bzZ8x8YAPwJ994d7/T6wBpIeGa8i0yY0tuDcAiLjsAdJKZgM+gHjA61/z0RYKQEZ1QVatLhhAIgYATyHMNADP10aT20tUkGcQ5x0qAimtFHVp3G4leiwGkHucZLqU82QO5au0qoCedS2NJFOCRKJllEpfAUaBuphYagygip8MeADSiqLudMW1ackAoutQqS9kAJHkaFYxq1XjAfKgpADgAZSe6CvT/C/1y46cTCGqAUASSgANvz7gDQGoKpWKCoAhvz4a1gBMeVPH0wzyFGJoTWOBvwrZY2/ObQCRl6h/vhnDaH4PUPHgZD3bX1megnM0A6hnY5HFeYDm3lLwUOaz2p0g/TaPJmtebIaaH83k6zh1ePNkcv3bHXSPzkU0vD4DSJrdSgaQ00YHcgMoGjB/UoXFmAxyAygeAIBONYPUAJqetyLmv8ZoWOukVn9Z6UroAxjyEwC+TH3hA+hIr+EDQN2LanY+N/w6gERKT2UAOsFAp1IDoMIEwEAgB71BADVl7l9VGYYKAGpqKFAjAAa8Bt1tYnhC9BpAqQcgrKmkqgGkFfMUEQl0xQcgql7JAMqVpGiAUtM62qvJkJqDFmZXt6YBhKEZW1CpAbn2mAyVMYBqoXtLSN1aBjAQDAAY8jVdnIbvAxgNa6JqLqMOFYDhACqsAshSUQk9AJUgQaUGwK+ppFooOKhomUoAIpR0VQc9PezXAYxWq5UwAzAcmOvTrNRqA6bgH2QAAQCimkmgrtWFb9W3lbVsK7EPIAtkNChRyNMN4wxAUFhkB4MeANl84YYATqQBFMXNf/mvj5zAAzKnNB+2L26Obn7/yRzI80Sq4n/Z+6WTPQrmBcfNN6+I+Y+Z9v972cdO1of/L+DPXnGyPvxE84blOewb+7ZcvDwf1MvNN9/8/u8+Hx90DByjAbRnz57vfe97xS133HHHiRgPwzAMwzDMsnOMBtBTTz31wAMPFLfs2bNH6xduqI9hGIZhGMZxjAbQ9u3bt2/fXtzy5S9/mZ1ADMMwDMOcErAOEMMwDMMwKw42gBiGYRiGWXGwAcQwDMMwzIqDDSCGYRiGYVYcbAAxDMMwDLPiYAOIYRiGYZgVBxtADMMwDMOsONgAYhiGYRhmxQlOdyUAACAASURBVMEGEMMwDMMwKw42gBiGYRiGWXGwAcQwDMMwzIoj7wWWJMmuXbv279+fZdlpp5322te+1vOOsVMYwzAMwzDMCxlj4tx2223vf//7BwcHzzrrLAC7d++enZ296aabfvmXf/lkjo5hGIZhGGYZMAbQH/zBH/zgBz/Ytm2b+8NTTz3167/+6z/72c9O0sAYhmEYhmGWC5MDFMfxunXrin9Ys2ZNlmUnY0gMwzAMwzDLi/EAfexjH3vNa15z0UUXbdu2TQixe/fuu+6662Mf+9jJHRzDMAzDMMxyYDxA11577e23337xxRcnSRLH8UUXXfSjH/3ogx/84MkdHMMwDMMwzHKQ13lR5ZerAtuwYcNJHBbDMAzDMMzywVVgDMMwDMOsOLgKjGEYhmGYFQdXgTEMwzAMs+LgKjCGYRiGYVYcXAXGMAzDMMyKg6vAGIZhGIZZcXAVGMMwDMMwKw6uAmMYhmEYZsXBVWAMwzAMw6w4uAqMYRiGYZgVB1eBMQzDMAyz4sirwBqNxvve975arfaLX/zizjvvPHLkyObNm0/iyBiGYRiGYZYJ4wH6yle+cvrpp59++umf+9znfu3Xfu1HP/rRO97xji984Qsnd3AMwzAMwzDLgfEAfeITn/j5z38ex/HWrVv/53/+54wzztizZ88b3/jGD33oQ3O+bXZ29tFHHy1uefrpp5d9sAzDMAzDMCcCYwAlSTI8PBxFUaVSaTQaAAYHB9M0ne9t3//+9//P//k/xS0TExPLOlCGYRiGYZgThTGArrrqqgsuuCDLsiuvvPKKK664/PLLv/3tb//mb/7mfG+7/PLLL7/88uKW//zP//yN3/iN5R0swzAMwzDMicAYQNdff/1PfvKTRqNx7rnn/vu///uPf/zjq6+++r3vfe/JHRzDMAzDMMxyYAwgIcSb3vQmev3Od77ziSeeuPrqq0/aoBiGYRiGYZYTYwD93d/9XXHrJz/5yXq9DuADH/jASRgUwzAMwzDMcmIMoB//+Mff+ta33v/+91erVQBxHJeKvBiGYRiGYV40GAPon/7pn26++ebPfe5zn/3sZ1//+tf/67/+6/XXX39yR8YwDMMwDLNM5ErQ7373u9/4xjf+/u///vnnn79AATzDMAzDMMypjiz+47TTTvuP//iP0dHRX/qlXzpZA2IYhmEYhllucgNo//793W5XSnnBBRe85S1veeihh07isBiGYRiGYZYPYwDt2LHj3HPPnZmZufHGG9/1rnf95Cc/efvb3869wBiGYRiGeVFicoD+6q/+6qGHHlq9evUXv/jF22+/fcuWLc8+++xFF100Xy8whmEYhmGYUxfjAVq1alUURfSCtgghTtqgGIZhGIZhlhPjAfrMZz6zffv2yy67bOvWrZdeeunb3va27373u9ddd93JHRzDMAzDMMxyYAygSy+99MEHH/zOd77z1FNPbd68eWxs7Nvf/va2bdtO7uAYhmEYhmGWg1wHaHZ29oorrgjD8P7773/44YcpIrZ4qtVqFEVBEJzoETKnPFmWVSqVkz2K5YXnPzMfPP+ZlcwLef4LrTWAHTt2fPKTn3zkkUf+6Z/+6YYbbrjkkkt++MMf/smf/MmSkqDvvPPOOI6XbajMKcyGDRvOPPPMkz2K5YXnPzMfPP+ZlcwLdv4bA2j9+vU/+9nPxsbGtm3b9v3vf99VgT399NMne4QMwzAMwzAnGK4CYxiGYRhmxcFVYAzDMAzDrDhMCAzA9PQ0VYHNzs6OjY1deumlXAXGMAzDMMyLktwAYhiGYRiGWSHIo+/CMAzDMAzz4oINIIZhGIZhVhxsADEMwzAMs+JgA4hhGIZhmBUHG0AMwzAMw6w42ABiGIZhGGbFwQYQwzAMwzArDjaAGIZhGIZZcbABxDAMwzDMioMNIIZhGIZhVhxsADEMwzAMs+JgA4hhGIZhmBUHG0AMwzAMw6w42ABiGIZhGGbFwQYQwzAMwzArDjaAGIZhGIZZcbABxDAMwzDMioMNIIZhGIZhVhxsADEMwzAMs+JgA4hhGIZhmBUHG0AMwzAMw6w42ABiGIZhGGbFwQYQwzAMwzArDjaAGIZhGIZZcbABxDAMwzDMioMNIIZhGIZhVhxsADEMwzAMs+JgA2ix/PCHP3zTm940MjIyODj4+te//h//8R8BPProo0KIq6+++mSPjmGeP171qleJPv7wD//wN37jN4QQ3//+9wFMTEwIIZRSzWYTwL/9278JId71rnfdf//9Qoi3v/3tJ/skGIZZ6XgnewCnBo899tjb3vY2z/Pe8Y53aK1vu+229773vY1G42Uve9nJHhrDPN9ceeWV+/bty7LsK1/5Sr1e/+3f/m0Ab3zjG2dmZr797W/fc889l1566b333gsgy7L77rvvkksuuf/++wG89a1vPclDZxiGsbAHaFHccccd3W73wx/+8De+8Y1//ud//uEPf/jyl7+c7ulFHnjggTe/+c1DQ0ObNm269tprJycnAdx2221CiGuvvfZXfuVXhoaG3vrWtz777LO0/6233nr22WfX6/ULL7yQHhgM88LnL/7iL3bu3PmFL3wBwKpVq3bu3Llz587f+q3fIvuGZvK99967cePGjRs33nXXXQDox/KWt7zlpA6cYRgmhw2gRXHmmWcCuOmmmz71qU/dfffdW7duffTRRz/xiU8U9zl48OCv/uqv3nvvvR/60IcuvPDCnTt3XnPNNe6vX/rSl8bGxt72trd973vfe/e736213rVr17ve9S6t9Z/+6Z/u27fvzW9+86FDh57vE2OYE8fGjRvPOeece+65R2t9zz33XHDBBRdeeOFdd92ltb7//vvPOeec00477WSPkWEYxsAG0KLYvn371772tU2bNv35n//5hRdeODw8fPHFFz/wwAPFfb75zW9OTk5+6lOf+tSnPnXzzTdfcMEFN998MyVAAHjta1/7jW984+tf//p555135513PvHEE3//93+vtf785z//p3/6p3/5l385Ozv7ta997WScHMOcMC677LLx8fEnn3zynnvuOf/88y+44IK777776f+fvXOPk6Os8v6v6qlLV1/mlsxkcg8DhAQIm3CNDiCXhMCARjEbkfUWUEkCvqAsq6L7+vEVdlGXVVbD1SWiKyAbFXaRLMtFQS5RAwkElQQJuWcyM5npnunu6ro8Ve8fp7rSmckkk2SGZJjz/YNPT3V11VM1lenD+Z3zO5s3d3R0sP7FMMxRBQdAA+UTn/jEqlWr8vn8yy+//MUvfvGFF1644oorKnfYsmULgBkzZgBQFOWUU06JNwI488wzK19s27aN3jr//PMVRbnqqqsArF+//t27HoYZAi699FIAP//5zzs6OigA6ujoePjhh8EFQAzDHGVwADQgbrvttpqamuXLlycSidmzZ3/3u98dN25ca2trGIbxPpMmTQKwbt06AGEYvv766wAmTJhA78YlPr///e8BTJ48eezYsQAefPDBNWvWrF69+ne/+92NN9747l4Wwwwys2fPrqmpufPOO4UQp5122qmnnqrr+p133llVVfX+97//SK+OYRhmDxwADYiLL764VCotXrx47ty5S5YsOeOMM3bs2DF//nxFUeJ9Lr/88urq6ptvvvnmm2/+2Mc+tmrVqoULF1ZVVdG7r7zyypVXXnnllVf+8Y9/PO+88yZPnkwJpLvuuuvFF1+8+eabzznnnA0bNhyZy2OYQULTtHnz5m3btm3GjBnJZDKRSMyaNWvr1q1z5szRdf1Ir45hGGYPHAANiJkzZz711FMf+MAHXnvtteXLl2ez2a9+9av33HNP5T5jxox5+umnTzvttB/+8IcvvfTSkiVL7r333vjdT3/60xs3bnz88ccvu+yyBx98UFGUc88994EHHti1a9eNN964bdu2Bx54gM1RmPcALS0tAM466yz6cfbs2WD9i2GYow+lUsRhhoKnn3567ty5X/va12655ZYjvRaGYRiGYQDOADEMwzAMMwLhAIhhGIZhmBEHS2AMwzAMw4w49swC833/1Vdf3blzZxAE48ePP/XUUzWNJ4UxDMMwDPMeJApxnn766UWLFmUymenTpwNYv359oVBYvnz5eeeddyRXxzAMwzAMMwREEtgJJ5zw2GOPTZs2LX5j06ZN8+fPf+21147c2hiGYRiGYYaEKAPkeV5jY2PlG/X19UEQHNSxXnrpJc/zBm1pzHuIcePG0UDZ9zD8/DP9MRKef4YZdkQB0E033TRz5szm5uZp06YpirJ+/fqXX375pptuGviBfvOb31xwwQVs9sr0JQiCRCIRz4V9T8LPP9MfI+H5Z5jhSBQALVmypKWlZeXKlTt37gTQ3Nx866230nCrAWLbtmEYjuMMyTKZ4czPf/7zRYsWHelVDC38/DP9MRKef4YZjuzp86LOr7gLbNy4cUdwWQzDMAzDMEMHd4ExDMMwDDPiiAKga6+99qmnnuIuMIZhGIZhRgLRKIxB6QJjGIZhGIYZFgxaFxjDMAzDMMxwIcoALVmy5LnnnjvnnHN83/c8r7m5+dlnn73mmmuO7OIYhmEYhmGGAu4CYxiGYRhmxMFdYAzDMAzDjDi4C4xhGIZhmBEHd4ExDMMwDDPi4C4whmEYhmFGHNwFxjAMwzDMiIO7wBiGYRiGGXFwFxjDMAzDMCOOQ+wCa29v7/XWmjVruGiaYRiGYZhhQRQAHWwX2OrVq//1X/+1csv27dt93x+KJTIMwzAMwwwuh9gFdskll1xyySWVW+69997FixcP7WIZhmEYhmEGA+4CYxiGYRhmxLGnC8wwjEWLFpmmuXr16nXr1mWz2UmTJh3BlTEMwzAMwwwRUQZo2bJls2bN6unpueOOOxYsWPD8889fdtlld95555FdHMMwDMMwzFAQZYBuueWW119/ffTo0Xfddddzzz03efLkbdu2NTc3L1269Miuj2EYhmEYZtCJMkCjRo1yXZde0BZFUY7YohiGYRiGYYaSKAN0++23n3vuuS0tLU1NTfPmzbv00kt//etff+lLXzqyi2MYhmEYhhkKogBo3rx5a9euffzxxzdt2jRp0qSGhoZHH3200heRYRiGYRjmPcOeLrBCofDRj3407gIjRYxhGIZhGOa9B3eBMQzDMAwz4uAuMIZhGIZhRhzcBcYwDMMwzIiDu8AYhmEYhhlxcBcYwzAMwzAjDu4CYxiGYRhmxMFdYAzDMAzDjDi4C4xhGIZhmBEHd4ExDMMwDDPi4C4whmEYhmFGHNwFxjAMwzDMiGNPF1hVVdWVV155BJfCMAzDMAzz7qAe6QUwDMMwDMO823AAxDAMwzDMiIMDIIZhGIZhRhwcADEMwzAMM+LgAIhhGIZhmBEHB0AMwzAMw4w4OABiGIZhGGbEwQEQwzAMwzAjDg6AGIZhGIYZcXAAxDAMwzDMiIMDIIZhGIZhRhzagXfZF1LK7u7uyi2FQmEw1sMwDMMwDDPkHGIA9Mgjj1x77bWVWxzHCcNwMJbEMAzDMAwztBxiAPTxj3/84x//eOWWe++99xv/eG3Q9j4AZzzzdwBua/7PB3Y0A/hgw2sAvvPHi/94/oP9HfAH2SYAX6jZGG+55I0PAlh58n/395GL1n0IwP/O+K8DvvWR9RcD+I/jH02piQFeIJ09l7demv0IbaGLOuuEt9fsmAjgxTP/c873PgNg8uXvvP7XCQD+eOHPaM+PnXISvfj563/q7+C3Tf0lgC+8foUMVDpafys583dXAPjDOQ8PcOVHIU113QfeafijCusjC/8t1FWtIAHIhKp3uQC8ah1AYAolCAHo3X6p3gBgbbfpLbdaT7Y6AHxLNbpKAIKEQceM9wwNASAUSmGcCSC1w3FrdAB6txcYKgBRCugjigzzExMA0ltLABQZBIag9ciEACCKvmYHABRX0kdCQ4RCARCqCDQFgJ/WAGjFaAfVDWg7gItufRHAb5eeFuoaAJkQXpUOwMh6ouAAkCkTgFOn08fpblRenTvKCnQVgBKEoarQC2FLANISAIwOR/U8AIUpVX5CBZDocKEqdAeiy/SCUFcBeElR+VsQXih1BYCXjvbU7Oh/zKSupLc7dBZp0gKgegEA+lH1Qq3g0w60bEWGvqXSDbFaSwAUz3cakgCsDR2wbQAwDABIJuB4AJAvwEoA8CaNloYCoKtt8/6fHIZhjgiHGADtE6ECwW4Au0tFAK7szHk9AEqyK9oY7O7vswW/DkDlDl1uvteWXnS6hf526PUWHSoMdgMDDYDoI11OEB+ELqrb69ntRAfv7CkCqPF66K14z2xbLjpKP4vvcvOe3A1gt1OgAGg/l9nr4MMRoTpHegnvBgqUbLYY6Kqe9wH4ljC6HABeaACQCaHIEICR82zDB+B0FektB7rbVQLgO8LotAEElkfHjPeMA6B8WgLwukqOYtDRpKEC0OwozlBk2FMdAPC7bFQEQL4lKLzQCj6FJvsIgIRCgY4nNVTELqIiACr6WQDZzkJoaACkpbmhDsDsckXeASBdH0BJGPRxuhuVV+eIkII2RYZ0XkWGtH7fEQDMrpLqegDytZrvqgCsrBvuHQCpXkBRlOftOwByw2hPvbgnAPKzDp1FJsoBkBsAoB9VL4x+d46gF4oMaUme1By6n65fMgDA2Z1HsQgApgkAth8FQD15JH0AXsaiuMouevt9cBiGOTIMZgAUs/GSHwH4Ua7xfaM2Ani5+1gAG+f9e6/djn1m0dsXLqfXX6l7i17MG/c3ADIvNKyauQLA6WsWAlg9K0rDnL5mYfx6SnVXfwuI9yF+e9JjAG7rnPH5mrUA6tRU/NbS7WcBuHP873sdoa29CsDZU//aa3udXnyz+af0+tWv3xVtbepvIQAw7cVPNo3eDeCJE56gLfed+NOvb/4wgF+dfs9UPb2/DwPxLWKGBWanE4ooIvFqDABeRgOQ6HBVVwIIhZra1APgov9Y9YtvXATAzHqlehNAckuPTJsAKFSKCSzNqTMA+JaS2RSFNWanC0C1fdUQAJw6Q5QkAKdGp338pABgtpWklQSg531KQXkZLQqApKQgJhTKwnv/B8BDX2ihMypROgn0kZhQVZ686mwACnyUF0kxhCJDe3waQPckDUDtBkfv8QCotmuPz9CdKU7KlO9StHgK7OiKAAjbByDTutru0E3rnpIAIJyA7klgqBTwCSeg4wMmhVPlFSLUAED1EOgAIHXF7A4AuGmV8meJDo8uUHWjw1KsFh9Hz/v0y1JcX5dRMsxutABkjxHW7hAApjckX9kEAE45vpcSADJpCoz0t1u10dUASr4PhmGOPoYkACL+adWlnz/jeQB/aJsMAOUgo+mpqzbOvR/7+mr/1OZzT1/bBeCNXPSXqFco05DMx6+3dVf3+vj0+5YAcCa5fYMtAPetOfsrF77VayOFPk0rP0tBWwytcC+0AMALu5owbnXfg/flyR2v0XouaHk1DrCm3b8EwH998rt3HLMCwAXP3LDPpTLDFOEEXkan1zIhAl0ByTeAl9bMTgnAqTMUqQP4r7+/MN1ZpJ31rAug1JgiRSZUFSPnAkjusAHkJybTmwoA3DqTUiBe2vjg954F8Pj155OwZeQ8CpK8lNIzxQJgdvkAAitS07y0Rhmg9IYur57CbqN8NI1CHz+lkQZEglR+gk7pk2Srq/ohgJZlv3ni2vMAqELtPDEJQC+GRjeFU0GivQRAdQ0Aqh9ShOQ0pLyUAJBo9a3tRQBOfZSIpQCRLp9SPoGhAxC2n59aC8BNq4muSIqiCEl1o1utulJaGl24l9YA+CnKb0lrlw8gd6xldIcAnJroj4mZDdwqBYDZXnTqkwCUIKS7R/dBdQO3WgegFfwoBhVCtV0AoVDNTgVArYx+v15K5N/XBCDR7gBQbVft6AaAnjxMyhG5yvZ2AGpyRGRAGWbYwW3wDMMwDMOMOIYwAxTnNmJ5K9reJ7ly3p/mN9dvBNCY6KEt6/46Ecfv45ixigTgw5Ne6/Xu1PM2Anjs+Cfpx17y2cmTdvS71L3TP/veZ+79ABZsnHvAPZ/c8RqA+W/Nu+5v/xvAbzqnx2+9edVdAF4sJaNjzvv3r7XNAHBrw7oDHpY5+gmFEqqKcAMAIueRjPLB5b8BsOLGiyk5pMiQ0jzCKetMZS1Js2Wx0QCQbHUrD6vKkKSixT/8xb9/Zj7t+fj156Osr9FhSVcycgplL6gU2qnVqBo6MNTUOzkAsjpJKpKX1oycB8DIeZQCCfSgrI4FAGpsWRhvguqZch6Ax68/P7BUAIqh1v25CCA/KUF1ynajldzSA0BaFoDiGL1mgw9Az7p0paGh0R0IhUKnM3bb7igLgFOfsLZ7AAJLi66li+StcrolrVFRTiiUWB8UeQ8AhEI6HalacS2UKhEYCgC9GJZqVADJNt9LaQB6jq3KvN0NQKZNKi0i8SsuMHJq9LgAnATNUERSneoGdLrkO1l7UjUAe4wJQJR0wzIAaLvz6OgC9mhh6N6Tt2YY5uhhCAOggTB77QIAxWfqdy3sAPDsG9MpFrn1kgMEBI/ka1ZsnoWK6Grai5+Mq3OIXvJZHBj15ac9oz+Z6ajcct6f5qNcPFTJq+sn77/iJ2b975rWn9AAoHJVL5YCAN2h9c31HwQwoSq3oukpeqtp5WcxsFCMOToJVcUebRjdPoUXpGFVQnGAn9LoS1p1JQUEMiFIPBJ5L9GhANByJYoM6Os5tamHymvuWXq5hkhHo8oba5dDX8BxiBBXFuuFAECi3aFiIFGS9F0u8qXCuBoAVke0wsBQqcbZrRZmewkAyqFAekuJDk76WqlW1PwlD0CRksqVzE4/uhzbz02vRll6q9rkdp6UApDa6VvbewCUGtMUGuqt9t/97H8ALLtlQWqnC8BsL5Ua0yiXHMUVP3qPT9IbyjEKFQkBkJZGdyAUCu0TltPZFL1ZbW4c3JRqBYDCWC3RFQAo1apdJ1cDqNlQEOUrBeCnBPV8qW6kuEEogWHs9Uss14MHlpnc2AUgSBoAZNqk++wnqzGxGhT57ZIAwAoYwxyVHOEAiGH2z5w5c7LZLIDjjjvu4YeHsRcAwxwC/PwzzNAx+AFQ34Li/fDJKasALL/g/c//dgaAjZ+8e9/HfPLqXsXCC9PZhbMeATDtxU+63SaApimte/Z/6ipUaG3HPrMI+22nuvU///aTV93V37uVxJdGuSsA1K3WlwvmvdqruWz22gUJ3QPwiQm//9JxT9NVxO8aVfz/ifvgt7/97YuPj9vdKa/58q4jvZYDoARhcpcTCkUae5XWPbp0LgBY6DrBAjD6lSw1QyXcINZZIhVMKMZuG4BMm5VSlDvKouyOyHsol+vSlsBQpakA0AqgWmDNlpQ+iSuOr/r+owB+cs0HS40pALcsu/fL/7AEgCJDqvm1R0X6Ts1bkeFQlP8AqARYE4oSKVCmIiWAi/5j1aM3R3Kw0ekAUKSk7rO4l6ruTwUA+YlJtSEFQFqCsmLzHnjx7m98FIBA6Kc0AHpP5GZEmTCUhSc969LpQiGiC8+XFJ/WlnTqKAXlqPkSAKe2FoA0Va2zACCoMyOpsSSNvALAqVIDOogHP6kAaDstXb+2iHLbHRWJAwgMpWtaCkDV5uhfpbB9bXcRQKipsjpJ1wuqy+4qAFA7uvX4V05F0EINq5IAIK1DTgINo+efYYYdgx8ANYzd86VOPe1UE7NPfp9rAtCTT9TN2EuB+lrbjGd2nAAg98d6ABs/F0Unp69ZqCkBgFUzV5BK5Xab/cVbcdxzwE5yd2Lvv099xa9l2QkArq3ZRj/2F/egHBtV7kBb2nbWXHzKOgA9gfXPqy8BsLBiYb30Oybm5JNFa9vBmYy/8sor//zP/7xiRe/f0YQJEzo6oictm80mEgP1hRoQIRQZkvULgFCo9KVOSo0uQzMrALijLBJrFBnQ1zyA4sQkgOTWIkUeigw/9KNnADx2zRwAqh9SvYtbZ5JIZLaXqIUqVJXMO0UApfoEKV+i3NpNOyy5Y8V9n/8IAJH3aCXf+vinq+wsgOKkKuqcT2+XpBY5dQYVEv3bI3cBuPbTX1BckpxMCpXMTrcwJQPg8evPN3wPgLB9mdYBiHxUQxNbNVJUZ3T7cZ+aW20A+MU3LgoNBUDV24VSfQJA97EpEuzoR1oDAAgFsvwCABBYUQTm1Jll6S3amTrmnDqzeEwNSBrzIs1R9UIAZndAdpHprQ51kAWa0npmEoCRBwDhhNQwr7oBXUvXCYmqd1wAIh+GmgpAcXytrRuArEnBcQGgaAMIK3rdFU0DAKEqySQAlEoDen764RCef4ZhBgJ3gTFHO24ovTA48H5lvvnNb/7t3/5t3+2lUimTyZTKDHL0wzBDw8E+/wzDDJChrQHKPXE8gKaVZwCAFjTUd2Pv1Ai1fdVmimNSPZUf3GrXtkz4E4D/O/Mvey1XCeKPR0mak3qf9NhnFilqiArN64TffQrA+nN+0t86N869f4OXB3BAW8K+VCalaMvHJr8C4FObz/3J5Odpix+qABrGZv/n9RkA2k7YzPaGA8eFdCEHHqyfccYZANat611Hv3Xr1gkTJgzy4ioI1ciNMLI5dqVSUWDr1Blk0CcTghIS0tJItNLzfnJrEUBoCPqis8eYUe7HlQCK4yzLDUDVyjrNrIh6zaShUKIl0RqpV6V607cUAEZOArhn6eWX3/m/AB75agtlgBKtBdJuku9kSc2hZRBkD/2Fj18LwK8WwdjIupAUN9X20xsKAJyxGaoFbrn/BUPx6PjkIURNZ6FQKDOk531K0hSmZPQeH0BqRyk/KQHArY7MG62SpApxyjP5SUHGSKEhQstAReOYIkPfMmlJdDkxIlsEkMwWO2bXA6h5y6aqZNUNKBUU6Bo5PgeGKJs3Ko1/KNJvp/KYJOoBCEXSqdMAiPK5hBNlegJLEyTPOQ6A0KtwO9TLrtz7eEwOmoN9/hmGGSCDHwDF86gFjAAAIABJREFUccDpaxYuOuYlAL+2TgHQaSf7ykbfGbMGwILCaGqGmr12Ae2zJV8bRw/x0bB3Y1dfpYk0rzBQKjvtZ/3TktqWdgCf3dr8o4kvHtS1xOuJWbr9rItq3gDw/U1zSp4OQFOCtp01ADAz2me83gXgBxvOR/kSKEJq21mz4NRXALw/vaHvuWjxtXUFAD35xH7CtZGGE4Y9pbCzs/Pb3/525XZFURYvXlxVVdVr/5aWFsMw+gZAmzdv3rJly0knneR53g033LB06dKhWK2eddW0DsCpTyy5YwWAH355IYBEh2u5EoBbbcRtU9TTFAqVYhc/KUqTEgCq1neTRzNNsUht6vn6L34G4B8Xfy7R7gLwMrpTqwMQpSCq2nElfd8bOc/sDFEOnryM/tD/vRQAdJidPgC16JKaE6QT5Y+4JE4pMiw1WijXxASGGvechxUiFIBQVegqDMVbcePFAGRKQYpMk2muWTRew8x7sRkjeTdLSyPZrueYZGp7FGqQFfXyb84HUGjUUq3RtUT9+ZpS9n2GKFdBxfecwjhCkUGyzQfgpbV4vofIk72kjK8irpeiLVR7FAqVJMjA0qI6qlabKo2kodJ5w6ShOD7d3rA2AwCFIgClIgbaEwwVbTrb/p6YA+GEoctzphlmCNgTAPm+/+qrr+7cuTMIgvHjx5966qmaxj1izFHB7t1BqVTq6tpr+IlpmkFwENJAdXX11Vdfff31169fv/7yyy8/66yzTjvttMFeKcMwDDM8iEKcp59+etGiRZlMZvr06QDWr19fKBSWL19+3nnnHfKh42wNzUr8bcfU/vaMvXBib8NeNciz1y7oZeqD/suQ60bvZTv2vk+/aigSwPfLIyxOevnv/vS+n/X6VC/xq1d6Kc5mnZre/MuO0wDk3SgPn9C8fVZhk95HUIpoxnFbW0sZAP9ReP+Hy5ccUz+qB4DzRD2A9TcPqCVthOCEYSBCRVFuu+22wznOjBkzZs2apWnaKaeccvHFF69bt25wAyAlhChJ0n0AmO2l7V4tAGuXA6BUb8a1vST0qJZY/MNfAFh200LKZzi1WtXbBQCU/kF5Svn8e373fz//WQCaI6lMWJQkTdgQeWfRz1cCuO/zH6Ecybz7X1i5+ANA1Fm2Z6K7H2o5G0CxqZZcDWPm3f/Cf/39hQDMToesiag5y+x0VdsH4NUY9mgDQNr2KSMSCqVrkgHgl//nIt3x6bOURiIFMD9Bz2xxAUAoUWV3EPV22aONzNslAIkOj4wW9Xzwsy9dBiCVdwCI0QaZK4qSWvb4Ueizigx6KV9OQypODtFVJ1oLqLAu9GoM3xIA9LxPGS8vrcV+iZQBoppoYft0+aofFbOH6p49y8cva2HZYmhqAJTGegCR+SEQer6ia/QiKJUABKENHYcMZ4AYZoiI/s5ee+21Tz311LRp0+I3Nm3aNH/+/Nde67eBa+B8sfYd+m9fGasXX6l7i/wArRq7MkbZT8tVJRRDYG9Twb6DTvtGP33pdUZNCUzFB/BPL1129okbUFGNNOcvl8W7PWsLAOO1TgBpc0/rx23nrACQEfbXbr8KQPH8fC83xdlrF1AV1GM3D+hKRxRuqHjhoVdT+L7/17/+9YQTTrj77rv/8Ic/LF++vL29/Xe/+90111wziIsEEKqKU6MLLyTDZb/aigIRAQBSV77y458C+MevfZbcBUOh3LP0cgBWDwklMHIefRMXGw09H7WDAXh06VwhI9O/OHYpjjEBJAEqwZGGWhiXAvD49edffs//otx+L2w/VDUAqisjs0EZFsYlAKR2lCi8ePz68ymI8TK63WCgbGYoTVWRAoBMiPTWIoB5978QD3Ct+7MLoGeKZbW5tDO1kVOfWu2bNkVCgSFIjJN6NKRMdUOyefRTkRbWeVKKoiWKVMwuT8uVABQnZeh6NVtSmU7c/6/IIPIOSJY9mvNk4RjVyiiuH6QTAMy2gl9Nul5AtyJW1lQ3MockRUyRgmKpwBA+BaluQKYGmi1jw2505QBA0xRpAYjCoNpqpWgDUByXqoKUhKnABKB6RRxGEbMbKu5hPP8Mw/RH9MfC87zGxsbKN+rr6w9KX2CYIcINhRceegVoNpudPn26lHLx4sVhGE6cOLG5ufm6666bMWPGIC6SYYYINxRuKI70KhjmPUiUAbrppptmzpzZ3Nw8bdo0RVHWr1//8ssv33TTTYd59F4OhFQLvE9IcvJDldI2TU9efQijIajZqrMtU+lFNBD6mjd+r+sYlHNXAFbNXNH05NUA6hq7/9zZiIo81tPTH48/NUHLAegOTADbX5jYtCm6BDI8XGmbC5c+jT7D0YgNv20CsM8JaCMcJ9TcUB54vwrmzJkzZ84cej169OgwDAFomvbQQw8N/vrKKEFoZj2ZEJRoMXJu97EpAImOKGfzlVs/B0BHGHddUcpEz7rxXPT8eAOA8PYUHVeiugHJSV5Gj+fDf/+LVwJI5EqUeglVhUTnqEraEtGEeaGUO7lct6oKFdMz3Goz0AMARs6j0e7lYR1BnCuyGy0Av/r6XL0kac3kzZPa4VDaRvUC6gIj0c2t1t1qAcDs9MO0BqA0ShWlEEBmUyl7vAUgkQ1INUu2ydJoahkLQOMmLAOAU6XSODCt4MfKV7kdLBocFugqlYqr5dwP5XviPUOh0gu32ojvKkl7oSGiCRvlqRpiVw5AMLGOrkX1o1+WJxRSsUJDaAUHALQoKFG6iwAgBOKhGWVPoMgQ6LBqoOn5P6wjMAyzT6I/GUuWLHnuuefOOecc3/c9z2tubn722WcHXSNgmEPACYUH/j9gZoTihMLl559hhoA9fV7U+RV3gY0bN+7wjx76eykX/ZXyNK38LPWHP7/z2E9tPhcVk+SJynZ02qFXkzzt09laBaCuMao+PuAEDFRMtCDiVvmfbToDFRkgAFMeAoDiDUF/VzF77YKHT14O4Fe5UwGccdGf4uH2xG+6T0yL3p6wtICptW0bztjPMpnhQAitKFU/pIxIfmJSdUMAxTE6gNRO17cMAHo+IGuZZKtLCZj8lFQ0t7wQ1P4pD8Ap2zpTe/YHl//mFzfMA6AEoUwYABKtNuU/jE6HMjF2o0UFQ6IkqaLZr1UBaAVJKRk/KeJiYcoeeTUG+U0DoFZ2xZWJVprFoQPoPDFZtSlqU6cKbr88zgJCoSn3jy6dS1chTZXMe+izZqdTbEgBMIRCA1bN9hL12It8KdmmAzByXqneBGBtLxqWBqDzRAtAYrcqvBCAkQ8k+R5lNK0gAQg3oIqiGNULVLvCg0cGVOsdWEZU0eyi7PoTpXMCQ6U/TH5yr8BC9cPi9AYA9mjNoFxUKUo7yYTqpUwAoQYxphGA6oV04caGnQAgJYQAEBaKYckBoKZT5eOqh1MDxDDMEDGEXWDoE8cQLetbnjjhicotZ5+44b/+ejL2NQ6ib930i389FgAqAiAKibIFi5SvAVZME9HOZQuf2Ciob6X2hG++BaAozXhLr0Efq2au2OQDwDiji/77g19+EMB3rlpDO2wsjG5K7TXxA0DbrmoAfqgumLxm4MseUTihfrAS2JFCkYGwo7JZM+vRfInkrsj1J5EQAOxRguYtOLW6m1YBSFNJtksAiXbHHp8EYHa6FADNu/8FAL+4YR79WDlhPooDRNQeZXa6FHgJJ6DSZoqH4iamuB0sNLRo0laP99+fOg9A99R0VWcBgFOfoKLjyAVndzQiA+V+tI9+/8lf/p+L6LMktElDdas0ul7ak8yNvIxOwVznKWnVMwAYu21rex5A9uRaqptWbdfsVADY45PFegHA6CH/IYUCIFEKNBkC8FMiHjFGddkoV0wbnY5qOyi3zsXCoVNn0lWEQhF5B0BgRQ5MviVgCXqLjCXJmtLTFZoGr9khTVgLhFBlCEAJoHlBdJ+TAkCgq7QA94xJAFQ3MDsdAMI0lO4eAJBB5XyMQ8YJdSdUgOHxT4BhhhHvRhcYwxwODlgCYEYuDoQLLgJimMEnCoDezS6wXukfkJ41ed8798rE7HPUPMlhS7Wz+na8Y19uzvukr6/0Ps9CI1GJvkNep2gZAD/dNBtAtmCdeeGfKt99Y2fjiube9j9QQwCdrVVfmbWPymgGgBNoXjBMAiAZyrROgxTs8UnKpsQCTeyqTFi7HCUwAUhdEbYEEBhqot2p3Pnh78wDoIxBZqsDwKkzzfKUhuzUFIDkLo9OF1qaLLvd0BnJubhUn6BDxbNINVvGSxI9NoDqv8iO02oAWLtlYKsAqAvdFApZFoVCoYM88tUWatr3MvpjX54DIEgppN8JJ6BSbvIQ0go+iXR6MXRqdABaUdKcjaq3C1S2LNMmJVFKNaqZDQAkdzkAVFfmJyYBSF0Y3T4AUQooA+SnIoNp1Qui5JZQvPp0fMekqdLs1XjNsCV5AoVCoeRcXArtJ1RavCqiXw3NZDVyHvkeeSklkY0socXWdgBhoaiVZ52iwio2HF1NhdvuhBp9dRsAxTSVVBJA6Zg0Xjnws9MfTqC5rKAxzBAwtF1glfRVvg6Ks9d9BEDD2GzTU1cBqBx2Qewz+sG+prL3jXLiIKnpqavIwPDcsW+jPKmjkrmpN4EDzAsjR59PTlkVj47/WtsMAB89fi39ePqahSfWtQL4yeTn4wu5rfN49NMgNsJxQ90/zEaadwcFMq1LQ6VgLZaxiNCIurGs3dJLk0GOam0vAuiemqYgJrA0peyzR64zNNVBJlT65v7QvzzzkczrAD72jzfVvlmg3aIxGpag73t7jPmRW54C8ORVZwNwqwSZ+oRC8VNRHIB02Q5Hi3Sluj8XUXZoBCDTJh2TVmiPT0ZDsnIeFdagPB0MgNkFAIXxpmbvifC0YjRlomp9Nw2Qzx1rURgXz1oPNIVEvcJYneaXkbkRAJqbpvhRsFIxlEMJysY8JAKW6hM0UMyr1QEEQrE6XADGtqw3thpk9mOIyjsQV/YAoK43+o0oflQt5FtCKwUAUjtcmv2Ooh3Nfu8z/CuUPoBwx86o5+vsU7zTp9LVkYCYWH0Y4Q/ghrp3MAmgu++++7vf/a6u68uWLbvwwgsP59QM894mCoCWLFnS0tKycuXKnTt3Amhubr711lsnTZp0RNfGMADghJrDPijMSMUJNWfATtCbN2++7bbb1qxZ09raetFFF73zzjs80Yhh+mNou8CIA6pLA+GFGb86/GX0WkO8ZdXMFVN/uhhAw4yoSHmf80oHSLVhA4jTPzfsOD2lOZU77NMLm3M//TFsJLAg1HIlJW1SvkHL2U5DCkDulDSA6o0O1SYHZSHMrdYt2wdQ/Zdcbno1vSAZRZGRnBQVMheibMrPb5v3n3IegKodTmR8DCDykU7GFkEkThlGlDaztvcAuPThF6l+2dzZQ3bJTkNKKU90ifuhKAVC3VKhUKjFzLeUTKsDoDjOCmjEadajafBxpkc4YeUR4uyXTJvUwOVbatlwOYxUuU6H+sJCAUpodZ6UApDoCqQWnddLaQD0QkjV0KEKsytyvvbSCVCKS4YoFzKbXR5VYQeZBNU+O/VJEgcBxKXNpHwpQViqFQCo5lovSJLVFBlSekm13Sjx4/txRTPlfgKnRCkfNZUCoDTWy7c3AdBXb6Ad1HSK7rMnD6uCxwk0d8DVCCtXrmxubq6tra2trc1kMq+++uqZZ555OGdnmPcwg9kF1u5Zs9cu8EO11xf8YYY+Q0fbzpoWqwXAEyc8seGTdwNoWvnZG9/3PwD+WGgCcNfxaq9Cn14jwwCcvmZhV2cKwNsXLicZq1eL/ss/OP33/3w3gNlrF9zaEI0o70/IGwqWbt93dRQzyKiKO8q6/N/+97Fr5gAILINqX5JtEoCWK5GuZHY6Tm0KQKiGpHMpMnAzCgC/OkE1MYoMydWQvo9DoYg8NWeZZBhIP4JaugwNgGq7dHzVD/X2EsqT5I3uaALGihsvNrNRzERdYIGuunUmAKPTiTvYKRKKnAOrRKBbANJbIiPEREfUaxabN7rVupcSoNZ6oQCgYWFeWosMGFWF4g+rzaXyIJTnhXWcllEkAOjFsGtaCkD1RgeA3lnMnlwLQJVR/3hY/j+15NZifkqKtlCHvJEPKJyKbB7dPTMrqPSnc7qhegCglUI/odALOm8oFL0YomxWGehquWE+UNxyA5dpAICU0aD4fIE0L23UqCBfABAUCgAE6sWE8QDgujQfPnScSCYTe3r3Dplisfj0009XblFV9dxzz+2V4Nm5c2fcyzJ9+nTK6DMMs0+4C4w52nFCzQs5jc+MUJxQa91R7Orq+va3v125XVXVadOm9U3VK8qeyjMeZ8Qw+2Ewu8Dqdbsy2dP05NX79AE6HJqevBqBgoMckUFTNYwqp9d2xZBvbhwHYLYdaWEbL/kRDTf99IRVAG7d0du2J+b0NQsp0bV61iPkuIiyjPVIvgYAjb8AQOkf7J0Je3dyP8T2Ys27dq6hwA11b5jUAAkneOSrLZZdBODWmdTBRPmP0NDIoM+vtqjVSJEhCUDJLR7NiBC2L8uTGYyd3QDcsVV0ZOqoKo3WqWg3Oz1dsyEaY653FgEEhk6qjZfR6WbFzV+l0dFYCfLjEZZGXWAf+pdnaJDqihsvplSTyHuiPDUCgNXmCidARXuaIgNy0HHrTMoSme0lPb9XePqhf3kGwIpvXWR2RokZKvEuNVpWa9RBRo1aigT5Dfpm5MdDOA2pUo0CwOgJyTNJkSHt4NaZ2eNUAFZHpHn5lkp2Sma3AKAVfLONysOD0BIAAg16AQC8ZJTvMbpDci2K81jl9YTRZAw7GjmiOD586jUTpGcpCRMlAJC5nCL2XLh8e1P8I02Dj3YGAAO9//YcBG6oh0JXVfWpp/r0kPahsbHxpZdeotfr168fxEoGhnnvMSRdYDQ2a9KEfqOHgz5gufv90CKqvtHS0u1nAXj7wuUUu5AbIVE52wt93A5RLmmqnGsWm03TNPg49DlKeOz4J4/0Eg4LJ9RcDIMMkBKEWs7WcnbuxBoAmXeKpfoEKrrfSXjScjYNNk9u6SZxyq+2qjY7AKSllaeUB/6oNABqxlZlSI1LiY5ojHmiS5ImZW0v0mEVKUNERojUIU9UbSolOlwAiQ50T0kAMLsDpyoB4Ilrz/vYXSsByIRaGKsBMLoNvSABkHql90Sd80oQirxE2eUZFS1gXo1BtU1ejVEYawB49Oa5ANLtpajix5UkjZGXNBD5ZQPIbInawVJ5v+sEC8DuExMAjJ5wzMtZAIUpGSVSCcMgoQLIHmeMXVUC0D3ZFB4A6IWA7Aaohc2p0e2GWlozBUaZ7UEUIeWicCrR7mi78/H6UZb84sY91XaVIpX+VNgPansZLaJcgkU1QAAU0wAQlpvFFE1D0gKAUuFwAqCDev5bWlpuv/32YrHY3t6ez+dPO+20Qz8xw7zX4S4w5mjHCzU/OPRp8AwzrDmo53/y5Mk33njjmWeeKYS4//77uQWMYfbDnn8ehmEsWrTINM3Vq1evW7cum80ecgC0/zzNvHF/09dC8AAHPBjB64DMf2seJUVozgb2XjClr/ZzCaRk9RoiRlxg7fn/xdlrF5w8aicqxmtUvkU5p0GXCN+TOIHmDocaoFAo9viM6gWp7Q6AjpnpqndclLMLXkZXfQ3Ap+757+VfmE8fSWzvBtD+vtGj1uUBhEI1qAi3nDWhfEwolLigmF6oZccd0WOHJnVsRd+RuaZEIhsAoHnmIu/41QkAIu+RDU9hnEkvWpb91lR9AKoX1r4Z9ZLR+HeyJQyF+sHvPQsaAk9V0oZKYtm/PHj39Z+/DoCRc8m0MLnLqdpUQjnj5dQZlPJx60z6iDRVrQh6i86l5/24ZYyGjlGVtLBlqTFKq9ijBAC9EBYbVABWZ1BsNADUvGVTykf1AnoRTQ2reFJI8FJ8WLslAFGKckWKK+mmQQZ0RnIh2uOdGLsxaSJKAkkZDXs3DGr+CksOSV3kdgjDoPnwStGOpsFrWliVBACpH+DR2S8H+/wvWbJkyZIlh3NGhhkhRP+uli1b9q1vfeuNN964++67v/e9751//vnf+MY3vvKVryxdunTQT3mw0c+gsz0fCV6rZz3SK4751OZzz562Vzt6f6uNC3ricKq/HfrStrPmEEI6Kk7qpdAxRxEhufNF5SPVbzv05Urf8cKJ5J77b/iwkfcA+NUWiUQU/QBQbTcaaCWlYvsAlOo9zfAA9LxP0UMgQ7KElhmL3lJkbPcXLYdkplBEBomk9QBIdHiFcSaAx68/n1boVamBbgJIdLjkxUyTv9xqnfQsBaByJUWGVD/0pc8sNWwXgLQ0aimPo4co4EuroTABhGo0wkyaqmq7AOZ/+/nHrz8/vjMAVNunCV/U46a6UZxn5Dzfii6QxoRJXaGyIUUGuWN0AFZnQB341MoeStC8PsWHgqi5nY4WW1GrrhcYOgCU1ywcAHDqDFqS6ZpROCnUSAtzAdcFEIVBlbNOkxaAIJNQac9MCo4HAFLSbzOsstC53yeHYZgjQRQA3XLLLa+//vro0aPvuuuu5557bvLkydu2bWtubu4vAHrwwQevu+66yi2O49RUDflymRGIF2r+cMgAMcxQwM8/wwwR0b+rUaNGua5LL2hLZS9lXz72sY9dcskllVt+/OMf3/6dfxiaRQ4ylTZFcZ7m0UIKwE8mP0+JlgNy7DOLqPb5oEqMqR/t82c9F2+hFFTl3Iz+GLG5H1cKT+7vaTxaUEA9XNKI/llFs8BoukJS0Dx20/bJqMatT7jVAoDZHlbOMwegFl0aUkG5E6fOJFsgxZWJVhuAW2dSeXLPJGPU2h4ApcYU5YQUiVAFymaGsetgjHCDB2/7LoArvnZTaqcLINEuqfupMN50qlUAJN4lWgsknwWaEug0c96hfjQANBNDOAE1pqE8oJ62m50+FUqHQiFHIq0o3VEWgBXfuijpR5XCZDskhEKrjf14KDUV6KpmBwACoSR3eQASrfnCMdUAeo5JUqF05ynVJH6pktYQ0kQO1Q2cWg0ACohn2hOxXEgLA0AtDYl2h5bh1Rha+a2opS4WtgwDopxkEyqAMGlEv7vt7QBgmkgmAEAKsrUMgsOSwIbN888ww43ob9ntt99+7rnntrS0NDU1zZs379JLL/31r3/9pS99qb+PCSFqa2srt6RSqf52HhZ8OFWgFwOMM+LOr33OZ63k9DULqWVs1cwVtOfstQt6+T4vf+f91856BMC0+5cAePOquw76At67uKHwh8U0+AB63ldcGdQYAAI9Mj6mkEU11Kiz2vXpezEUCmk3qutR6ONXJ6inXdYkyeg5MjPMRbaHStmOz+hEHIh0T00DSO1wKPJIZAMKgEiK6p6SoNIcCr8AKK684ms3AUju8uyGqN1d7/EAZN7x/WkplJu83FEWhQ563g+MkNYTt2X1TLQAaHZIs7dUN6DVUrWQU5+g4EYmBB1NkSG9teeGGSrFVYWxRqJLAnBSOgCj20+9kwPQPbWGDi7yHjWgBZbhpVQARre0x6cBaE4oK1rojW6fgjmnVktvLaFCm1NkEKmEiCaqxnbVNPJMtR3V1gDkpldTKGZ0OlE9kONSuAPXjVSw8jBUmU7QXaX+LwUIa9MAAiNylVS6D8sJetg8/wwz3Ij+hs6bN2/t2rWPP/74pk2bJk2a1NDQ8Oijj1b6IjLMkcIdLqMwGGYI4OefYYaIKAAqlUpVVVVXXnklgNWrV7/xxhueN4Tzt0kJUgwZ51GOLLGrYUwv+584i9N30Ae0A9hFakrQY5u9NpLi9uFUgTS4uB/NnXgYhiHvUdxAeMOkDZ7SM2QeCIBm2BcnJgEEQsm8XQLgVydoipY9StCw91Jj2mwvAjB2dgdJA4DYnZc1KQCF8TQ9w49mYhiab2kA9M4iZYCqNjlk4ody1bOXUslokaS31E6flCnF9Wk0hEzrlG6JvXzsBiNSuNpLJAZlj7cAWLtlop2SKGrLst8COCe54cufuwZAYaxB8ll+vKEXBADFUItjdACRrNZaoNEcpdE6FTgrhiotE4BWiPwenTpNz0f3inwOqZBZWsKrS9KPdBUyrUcvLI1EsVAolAqKYwPaLi1BCaHMJpsSPHHhdmgIysm5VRqdSJFhNEDDdgAofhDQKJIgLGetpOJHK4wSPDKIMkBVGWolozQPlYRH12IZAJw6M7rDweFlgIbP888ww4vo31VNTWQWvGzZsiuuuGL16tWf+MQn7rvvviO3MIZhGIZhmKGid3PB97///V/96lczZszYunXrOeec87nPfe5gjxg3lu+nD7xv0Uzf4aCUFOnsSAOAr8bVMxOqcgBWNB3YFX7g9B3PHud+evk+993zgEMtVs1cEc/KiLf0XQCdqL+jxTXXIxAv0OSw6IJREBhi/j1PP/j/LgWQ6PAoJWPtcgD4SVGYkgGNK3cCADVv2VStAmDlrx8CcOGnrqIqGW9sdXGMCYAsjIVTrtU11Y6TTQDjny1GnsV+GJbntyffyQJIGKpTpwFIt3sgDyFKTshAEQEAuzopbAnAqTOiafN2EOUqhEIFu5SPSW7pzh9bDaDYIP7z1nkAHm87n1ZYXZTkvlO9sUSd+aobONVUjGwACFWFlpHa7tCelbXYdDo9H9XrmJ0uHSSuFooMr9ujhKhTq9MUeq0U0ER34YRUfG2PEtT5T/9Gpa6QqU98xlAoZAHg1OheityV9qyEsnERMhA9NoDMOwoVSodCoFgCAKEq9NdSqOT3I0elqeiKCIVQqzIAwto0jYMFQJmnw2TYPP8MM9zo/e/KMIypU6cCaGhosG37EI64auaKfZoE7p/4i79lfQuApO41JPMAVs/tPVh+wca52JdoNUTEtodtO2sAYOaet+a/NQ+DN2iiv3jx3Zwbf3TihcILh4MEoMBLaytuvDjheQCM3bZTn0TFF7/ZFTWFkRuN6LFJ8Aos4/RvLgFQDYdKfTtOTlRv8gGI9hCAPUqt6XCnyl4xAAAgAElEQVRRnvYAoNSYpr4wY7cdjLJQUc+r2TLMKShLM3qPF5XxCpVeCFvSZ1U3siYSpUDrLAAILHP06i4Au2fVAggM/SO3PAXgV1+fS7M4nBqd+rO0gh856OQd+rZXZFi7IQTQNdUAEAid+rbiMKs4RicLn1izE04gKESQIbkmkoa4+D9++W/XXgFAGuqiHzwG4CfXfJAksJ4pllJWlChKK4xV0ttDAKUaFYBeCEngC4USOy5GPoeqUp6eIenC9byv5aL4BkCYNBQnWs+esmPT2Ou3LESQSQAojrO0wh4lMbC0cOJo+h3F0+mp5lrJSxwGw+b5Z5jhRvTvavTo0dOnT587d67v+3fccYfv+5/5zGcuvPDCI7s4hgHgSVUG3AbMjFD4+WeYISLKAG3btq1UKm3dunXz5s3V1dW+75911lmLFy8+tIP2TZYMnCdOeGL/Owyu+NWLpqeuaqjvRjkf87W2Gbc2rKMf56fmVe7ZnwH0PumlXvVNX61z7RmGtc/PDiT3Qym3/WiOwxovEMOjCyaE6gXGbpvcbpz6pJ8SAETZ79i3BADTjhID+WmjqNlbtV1FJmkfp1YHkGoNKL1Bsk56256OhHRrAKAwVq97PQdAkQH1t8uE8OtSANxqnSqXUc48BZYJwKsxjN1RTpea3slJCIBMqKXxVXRYe7QCILM9ANA9Nf3j+y4GYKVDjcaFZiP9rjTaSG4tAnBHWZFsV2PQ1HczF6WplL2Lf+te3e2MzQAojDWsjhCk31FvuYhyP7Tm7/3936kiAKB6wc8+dQkAPZ+nJE3V2wEJTPGA+nEdSvb4BACjmya9RwXjTp3hVNGU+IBKrQNdoTWHhihPfY8kKr86yqKJvAcA5XRaaAi7qQ5lQyYAXkb3MtGfTTpRdA9NlSwDFBnG2ynVd5gMm+efYYYbeySwrq6uSZMmHX/88atXr37ooYcuuOCCRCJxaAelep1/2DXrO2PWDM4yB4MFG+ceMHjaOPd+6lCj6I2iHyIOd0ike+KEJ3pNDVuwcW7R07HfGK7vJPlDpumpq+LYaJ+hzwENioYLbqAOj2GoQWjstkNDoy9CI+cKl+ZMCVQYEnoZnWKIRLtDAxkUKckQyE9Fj4Zekr3cC8s1MaVAt0BzHmQAIDB0pTy4igQyI+dR0U/USJX3KN4KdJW6k4yc23NMEmXXQVBZku0DEG7gZhIAkq0ugEBTqCZIOCGV4OhZl+ppzC6PutvMLo/60UgaQ9zJVfbmMXIe9V7J6uT/u/dHAG74p2sj6a3sCenUJ+zR1FFFklyY3u7TMSm6UvxgziOrAaxc/AGZUAFoBUkKl9npqhUdq0oQ0n0o1guaBRYjSoEiJQDFlrtn1ACo+7MtMzrKqpwoSaR1WhgJiCjPayuNr+o+xgCgFfeMlKcd4j0p0o2FxcBQxWAEQMPm+WeY4Ub072rZsmWzZs3q6em54447FixY8Pzzz1922WV33nnnkV0cwwDwA+FzDQQzUuHnn2GGiEOcBTYQjp70z9LtZ2HA2tn+syaV9d1x7idKGmnB/uWq2WsX0B+yvuXbffWv/lSt09cs7OpMYQDSWF1j9/53YAaXUFOLkzKKDEUp+v9+0lNinYWahgJdpe4w1Y3Gl0ojqhf2U4JanNLtXtxaBUC4AaWRRN7Te3wATo1uj88AsLbkyEXayHkiH83ToNxPz0QTQPXbQdxgRZkhd5RldvoAtKKM29BiAg0AssclABj5SDzS85FzT+cpaUUCQLLNp6UGmvLxu1YC+PE/zjf8EEB6SwlA7lirMNYAULMh8lgvjEvc9PWlAEw3KNUKAInWkO6A2enQ2ApK/Bg575cP3Q3gon+4QU5JAUju0p686mwAhWNMyi1phcijSHH9mg0BABpK76c0q9UGUKpN0RR2vZw/U2RIOTA/KWi0qlNnUGhBibd4YK1TZ3opAcDqcEkcLI7RE7sDAHpB0siRUETW3l7GBCBKAUCpOJU6y1Q/urrAPKxRGAzDDBGHOAtsqJm9dsHAK1oOWAFz5/jf0wuKVA5HGOp7lqYnr1YMiT6FPpVQS//A29YWbJwbn6jXZ/d5kNhYEkDzcW//ZPLzAO4+8WdA9Jd3+n1LAPzlc8NywoYfqDIcHkWgvqUYuYAkMLfaoFqQuBeaKm+8jE5fkHFZh+oGenseQGl8FW3uPDGZavUBuFUagFCDkYvGmJttpPeknBodgF6XIsUn0V6iSEjNl6SVBmB17NWDLfIeFSf5KY0mP0AobrUJ6guT0XJ0GwBIkkNFCxvpO9bugLaoXpDoCADkxxs/uflDAMwer1K2S+7yssfRxA+VgqfkLoeGzGtFWao3AXSdlKZKpsAyqjbkgWi+R3GM+ZFPLAGQcW3ak6p8aAF0e4UbkHwWGhoVM1Grl9XhUpyX2qnToA8vpdp1CoCqrVFRju7K7ikmgNSOSPuT5bki9KPeWQyOqQbgW4IUN7M7unCzvUQ6mioDUjBTm3oAOPVJWphvqbSnb6mwBAA7aWL9/h6b/TOMnn+GGV5E//9Hs8Cuu+46mgV24403XnjhhfuZBcYw7xq+FFIeXBHoK6+8smDBPrwY7r777mOPPXbatGnPPPPMIK2OYYaWQ3j+GYYZCEfdLDAy18GAO5tOX7Owsy0z0KOrIYCmlZ9tGJsdyMH3T6x8HdCi8IC5n6Ynr7745DdQTlZVqnX9fXb6fUvijE6vnNaztgBQL+w4A3REcj9xGu+Lm98PPHbIx/HDg/s/4G9+85sPPPDAqaee2mv75s2bb7vttjVr1rS2tl500UXvvPOOpg2yv5ziAxUjJkhPoaph4QRazgagCZWEp1CocZeQrE4CUIKo1hhlkxsz6wHQezzSdxJl2SWxNScTdQByTYnqjSUAqu3SmHRre0h6mbUlByA/tTb9do6O6dSkAHgpxR6VBqBIaE4IING+14JjvKSSbJUo13EDELbs1WMlPNCaZUJQcTclYJSkSLYFANpOTZq5EEDtG0XABOClI5XKHpXa9b4aAPVri3SXSBxM7SjRnQksjeZdZLa4lM4xcp6RA4DCODO9NRpnQWur+UsegCJl9uRauplU5a3n/fTWaPRpWJ7xTgm2uAo7uj91Bi3Mr7a0QlSFrXph5Z1RpFRcMo1UyTUxP20UqBbblQC8jE6F23/3s//56WcvAyCr+nteBsTBPv8MwwyQPV8AhULhox/9qGmaq1evXrduHSliR4q29ir4KnDgXvrOtkxci3NABr7ngI62Xynt2GcWNR/3NoAXNhzXt16nVwdZw5hcrNPtk76d8/3FNHGl0Xem/QKQvd6KY77DVwMPyKqZK6j66nuTnz/7MI4jpXJQPihnnHEGgHXr1vXavnLlyubm5tra2tra2kwm8+qrr5555pmHsa7eKEFodbiBpsQOhH5SR7k9SvU9qtpRZEg91artQsYd8ilUDBGTBkq1KgC9BwC8jK6VaCSWGQ02NyRVGukFVd+ZAwChJrf0AKAZ6QAKx9UCSG/o6p5eB+oPLwUAtBLiHnuaM6/abjSO3tIzW6hDXgDwkyoVEmW2OiRjKUEUXYVqJLGpXkDLdqv1aMS6ETWFUTtY3ZsOhTW73ldDlTfVb9s0N94epVS/EwDYdn4yuQsA6v5cBBAYKqWmVVdmNtkAnDojtcMB0HVCYtS6IoDMJrswLgEgtaNEk9SIKx9+6of/tACAXoj68EOhxKFJoNHio/nw0tKoTovcB6SpkBYWaErs1hiHPhTXhoZGI9VQzp/TPQyFQjVeqh9SF/3DH/qAnKiijxZ5sBzs888wzADhLjDmaEdKIUthEARz9+ayyy7bsWNH3/1bWlqam5v7bt+5c2ec1Jw+ffrOnTuHdt0MMxhIKQL2AWKYIWAIu8AOjchu5/iB7j+4SZ1BpH5UDxUjg/5bQcv6loYxkSrRXybmvD/NB+AH6gszfoWDKaAGsLjpeQB/sJsusN6q3F4p+Z16wuZeS8IAXCgPFkprrc0e7nEUXVMU5ctf/vJeGxWlvr7+4I5TUdofBIPgxrT30SENNbY9lFbkYUP5D0WGqhcb9hgAEvmobFmRkTrmV1uUpLE6o0NSHiLRXqKDSFMlM8PAMmiLXpAhzdMwdCrOTbSXKL8SudFYZnorpVUETQ3zLSFktCRKhJQaU1TqqwSRvQ39qHqhZocAhO2rLsl2Cg0pM7r9XrY3bpWIRkB0FgEkt/jUcmWPMalzrX5tkfrRssdbiWwAwOxGaRTVR6PmryWUp9DXvZ6jKSLxsDC3SlBDXHq7nzvWAlDzlzxlmPKTEokOAYDuzA++vSCz3QWg93h0nxUZ0otQKInWAgB3lEVCXigUytYUGwSAVKuk+nSZEG6VAKDZAUlgqhvEHonRgAsZkIsjfcRPaZEYV5IaaWQySGzNAShmDmsa/OEwYcKEjo4Oep3NZg/Z2o1h3pMcpV1gg8iPco2frW5998/bt8AodoasjDP2KUJNv2+JM8XBvnrdK/0P98nU2rbns1MBbOhq+ErdW/vZs5JBD30GkSBAEEJRlDlz5hzOcRobG1966SV6vX79+nHjxg3G6vYQRt53AX1Vh0KhniZqLCqOsxIdNO4qJGPAIJ2gcpnAMuhFKJREqw3AnZrWCwEAahd3q1IkAFGfESJZJwCgakrn39QCyGx1RB4A1HxJFSqA4qQqACLvkawTRyqqt6eRKozKd1Qa9aXIkLqu6Fu/eqPTcTJ9ZSaTuyLfPypLUv2QAoI9VTU7HFLH6LxX3/4rMnGOXRYV1zdoSFlCpfohUsQAuBmFPpve7gJoP7OGUh6j10kKp1IA3bR49GnbmVHlX8Mfetw6E2XtL7Uz0pukpUlLADByLllUezUG9cHpWTcot31RcRWtxEupoaoBcKpUmhqmFaKaJy1nk1u0NCMXA5GXpIVRcZLZ5ZMWpriSzrJnhJjMD+Dx6ZcgwKHF6qVSKZPJbNu27XDOzjDvYbgLjDnakYEqD8MJ1/f9N998MwzDlpaWl19+uVgsbt68OZ/Pn3baaYO4SIYZIg75+d+6deuECRMGfT0M855haLvAepX6DoRBH2v1LqR//mHXLOzX+PFg58bvp2nrgP6HP4kVt8l7Nh77zCJ6EfoqgI3z/n1IR6oNLmGghIdRBJrNZqdPn+553uTJk2+88cYzzzxTCHH//fcPegsYVMUeJURJqi4ASFPNHUsWeSEA4YFccBCX0wo1moT1/9l78yi5rvre97uHM9XQ1d3qljVYspFHYeQRbFh68XXAYKNwn7McL27iS3wDThaW4T374rDIWuHdPHJhhYTwDCuxMc66ckhylx9gMtwADs+EG/CNmTwF4QSBB81qq+fuqjp1hr33++O3z6lSyxKSutvqsvbnr+qqU+fsc/p01a9/w/dbIOKc3ODDiYxyM5TP0J5tRq4eSqk2pCJB+QbZVlQJAqyDlfElTYqRv3p7Q4XSOeVsWtlqzVNFC5At6w+vQrtbKutkNRlNGQDaZ5SAKXeSNryoaZt/qfQzfll01vfmUUy9/dnv3FxBTLuijBR8SScVTaTxCCn0MLKVqO9O9v9iBcCqf1UAKocV1aR4nFM+KRyLiy5sUTmcA2DKkM4QU4qaoKniVq4nq0kq5/E4TVZX0ZM/QzE7ltUkqQdRpc9I23seTutgOgOQR4JOnKmwOwrXTOlqU6lRxjZ5RpNryWhItc758wa8lgKQtxYlSUr3vzHmy1/+cu/zQRDceOONvu8f64179uzZu3fvJZdckmXZ3Xff/er3MzgcK5zud8DAwMCtt966mH2NJZVN37i9N9w5hQadfnT0PFboQ/EfNKOp++Pwcwtbi6H3l0JLKotxF+/Y/pP3/ZwJ+b9tVQH8crV1sse97rmb/umSU59+L9GKm5McA77++uvLetnIyIgxNkTYvn379u3bF7+kV8QwqJA11/uDP4sBeDMpUwEA+sIOx1qzmxsAosOpHRObsYOWLLXtMizNpy+vAVi1s00jTtGEAiCSnISJS6lifzalwpYRjMSas5rtQZFxSgJ9tGXlYExj2+mqqKx8lTWpbFUEQMaqNCyzQ15ULEt1MG0ApA1Bc2HBVGJV/qqSAh0UY25e2ySjIW0DQIVCFR5hUxcHAOoHVOUgjXQF9sSLys7U6yvRRPeZPGIUNb785vrgCxkAHcnWWg8ANQ8B0D4f2RkDOPDWwfXfminXrAJOgpNeM6eIJF5fp0Yi2crpCsyfX60/3wLQXh3RQBwNannNnDqcUGhwB3Eer4kA5BXrn+rPZhRopg2fpvmospkM+501EYDKXhvuxKuHEhqIyxZlZKEV16k6OgBijF199dVr1qzpffL+++/fsWMHgCeffLLRaNx+++133XXXrl27br755muuucZlPR2OXpb6n2CHY6nRimn1GulIczhOFq2Y4R7n/Etf+vmTEHfeeWeZ6dmyZcsVV1whpbz00ktvvPHGnTt3ugDI4ehlKQOgNUH7+CmfV0F7ZuVwUnKLy5T+odLbK+bkLv7nXweQbkiO9V7a4Cdb/5JyP5+cumAqq+FkLN6WJP3TR4hUr/7uVOt1jflzIwD13fHA7gTFFFgyWiFrquZ6n9IY3kxqjdyVpgwQfNl4IQEQnxX4c13xGCNY+eMCl3imDJWlqGgFQEc+lWZI/IY3O7oWAsirknyvek0kKCOiAl4amFPZiLIdeSSomhNMmfZZHoBkOKAamT+blQNTIlYAokmQnxe9V3lMdMjBPmHK5oqo49hrKRp2ExkjncPStj1eZStQZEef1eT0hR6AwRdYNGln3DqjIQCeWo8zkWD+vAEAAz+dAcBqIWW8VCNkYmHcTN3QeVXsu6EOQLZQG9MA6DSzmtUuCqZslq61NuIKAKYuDKJJqppxclIDQAVEsiJhylRemgGQjdYoezTw0+bEVXUA4uDpmQJ74IEHfvCDHzz00EPj4+OPP/74+9///tOyDIdjxeJMhh0rHaMZnBCc40zllO//O+64wxizYcOGrVu3fvCDH9yyZcuSr83h6Gte1RLYq5P7ueXFt6+EDt/Tnui65Lv/8bm3/PdjvfqTrX95/Lcv2ODBH15Ln8J/9E6bAVrQ77WM9FUAVH1+OhutAZg9LyrNGQDka6rVQxkA7dt0SzochGNZ73tLF4VShlj5R/RNZzVJ6jvat6I7LFVeswOgvXFAtq3esVUPGrPKxbSH9qgIZgodoCYNbOfhWAogXl+3FqfFYLxV9GnmlEbqjIbUJkxHBADfToOrwrE1mMno84RMJJK1vuwIALJtbdtpPzhSEqm1JgAw8tT89CU1ANGk1RYid1gt69WXOYDOkBj+l2kAUFrUPbpE8+sFgPoBFa+iviUOYOaCaOg5BSBteJSaAkAGF6XrRXX3fHPtIACvZcj2la4YTxeOmycNJjsAUDlsrHx2buY32oRWMGOtagGIxMQbG+iROegMiaFdHQATcnF376ne/2EYPvzww4s6tMPxmuY12AP0yKbHNj32PixbXalfOE70cxyOdel6Yx3yln+xGFWznmjAkjisvQKaAX0TABlfUtQSzOnmuVUApYJOONZEIZMDQEWis6YGwJ9NrUu50jQFloe8OpUCoEKM9jiVe4Ipu2U26FOrL1N2ksufzeKigTePOACeBgD8qYQsGkRiRGlrRfNiQlJEwJQhtZs8EtQETT8yZWjnPNWw0ohaF6pC9DVvBKNZp6xubbOyugQQTeTlpBU1CxvBKRJqr4tkS9GJh5MegEP/W33t/5oH0N5QAZBVRXLZKgBaoPJyBmDmfJ/kjgZ/2qL9V3fPx6saAERHe20OoHVuHYDXMiQLVEY/PLOKhQya+rKnL6pTYSuaVNYTI+QA8lByGwja54NZKwWZDHK/SaEnoweVsbQsAgK48//5cl3EAD7+u79BlnDBnLYbBKdyI3Xpq/vf4egjXAnMsdIxihn18zdzOF6TuPvf4VgmXoMZIKy83M/Sihv92ktvBfD9n77uZCtQJ1K0OpFLt0CmaEGxb8lH+pnuzkuvZLTHZ94wVD2YkKaObOXJWh9Aa30AoOycRVFqYcqQVDGmzNyFNQBaIJxWAKIJ2x8tEgZAthWlW0oo/QOAKU2OqjyV5DihPU6XqzPiAfCnrBdpOK1oQlv7HqWmavvaKEpddm/alCpBIGHr2L5EXdjefEZvyQZ9Ok0Rq9L9w5bPtH1Mu02G/QOX1QCE06BmaHKJB7VUz+UAqoe9g/+uDqB+QAPwZ5VS1IXNafrdaxkVMABZ3SOJoPbqQRqVTxuiuOCqXAORV8mVNqer11rrlTdSMKsBaI+RKwip/sQjvra5MU6ZNso/ARCZaI+SEoH1Ou3annQUgM/ddQvV9cxqxmB1pZkSAPgRdc6Tpl/uf4ej71iWAOiMmvY6EY4V+pxau9LDr/sWALzupJdxUgHTbXuuBXB+dfy/jPzbyR3l7TvoBhheM3dSFmbHRPVHD5BhyCqsvcafPZcD8JogOwXTAYAAIC+FcCyO11cAiFhRb8rEVfXqmAIQTKX0VS3iXFvDqbLRB/SArCd4XEyQATqyJRbqAdK+0RkFWAJANujTqBdPbSUoG/SrBzsgdzDBAMhZ60omC1d1+vov/SL8qYQ0fnic0sCaSDQVy8roR8aqtyRUerAHU2nlcAhAhazxku2CopAlGZZUYJKxDqc5Cq3CYLxDIZo/Z03vy7abZNCrHKZqHS+Oa5RHUQtJGiplBXtSr8lpzeRNAYCKgKlgdNxgKqXwlGIX2dHlNBx8DmDy9f7gS7YaSKNqMtYUiumiPYvOhWearn/1YDJzfgigM4ThFgNQ3d05oRvoWPTJ/e9w9B2uBOZwOBwOh+OMY1kyQC73c4KshGm1Y/EXR5nYnzhLewOwPvkPmClTHcsBDOxlAGr7OqQQQzNK2uetYQlAxj4lfpobKlSjWbWzbbVzAk4qO0ZwHtMMlyh2rgFAMHqgI7/QEDI0ZQZlG2WNCGSqUSSEOqMBVdxkrFQtAClQ21EvOzlVurFC2MOVxy1cWjnlSJrnNajSJGPrEpo2PErSlEcsHSdUkUAi3aNkgMcjEkBeYUO7MtrScAMgjzgNW/lzCsDEVXUqb2VVEc4wAF7b5AFtkFPdUAtQMzIA7TMAqbTt25SSyepeWSikImA0aefR0lpt9lwBIBwIbWuzZ/8VpF9NZzSc2ygBRJM2vcS5zfSAqmD0SymeQc/gnkh0fW8KwG9an43O6gDPH32/nCj9cv87HH3HaegBum3PtYv5cnWccRjg9CjJnRxMI5hK04ZH34sLFAvnNso1/2sKQN6IZi6sAvCbmlwUSvsqr5lR1SlteNRAY6fBo8DOMaU21GDQFJqoWogUAHiaUYmNKSNm2wAgOIB8Y1idsuZZNFPGlChd6GmHPE5oY6ZsmcygkFJUGoBq2BJSMsCpXab0EeOppvBCS+sXJooOJ1tOkozEFQ0PKBaUbUPFsnAiK6Mo6uypHswBjDwVU8UtbRTT/jkLEg1g7nU+ObeXDmiGg6zjhQZ6BCFFosu597KTiVw4mDbBDADkFUZua1ascsijQX0A0ZQGwHI75c4y6xdG8RD9uq1mQc0DgI4qSo2KPlXZhCGjeCqZnTp9cv87HH3HKQZAX//61++9997eZ/bv3+/+SB3LAVOMOSsMx5mKu/8djmXiFAOgq6+++iMf+UjvM1/72te+/P/+6Ym816V/HCcF02D9EFwzY0SzE8YpUKVnqODizwoAacObvGKInvdadmrJWpBq40/GAJLRCmkFUe0MgGpUQC3PMXUl28oXb3ao91k0bYOtEZzc5v3JmOUaRdbAa2o5GwNgSQ7UAGif8xgAWKp4nNiXCl96UyFbVgUgHQ5Y3QMg24qSGeU4Uulj3zVS1VZMyNhBKkalNxHb91QOxu3VNQAiM6TlIzrFS3vnjGgAoPbhVTvzYLwDIBmq5SEHEMxkrbU+AJ4Zr0Vyjoxkh+JVglZVShpaUcfcUG6GKVn2evPUOsZTLmrkqfn919cBjPw4p52T2qHoWC+OtOFRaTGPbN905eWEDFOzKg/9XvlErnxqjrat5YYznhoAanF59n65/x2OvuMU/zRHRkZKt23ixRdfXIr1OBwLYQqsD3VQWuvCUgIRgD+b0Xe5yAy3as6c6lw81dSdE441s+EKbUzlJC4ZAO7buoxoZmI+BmAktyNagvFmB4DxParjsDQ3gQRA41o81SwpptxTBUCkyk5yzbbtS2LhMAT1FfmzaVl6o+6cdKBoEiqGvABOcU9Wk+G+WQDp2gEAWjJp9Q8LVeuaR7WqylhKV6CM8/JG1BnsmoK110UUG1EAASCrS2rWSQZ4WYTKakXQxgGA4qFSZjoZ8qhah6IExpSmKxCOd/KwAmDq0hq50NN5+XOqjPDoLcLneSQBiMRQXCWaid5AZmSmMxoAoAKfaGZqOEBP+ZJpQxKRYnFD7H16/zscKx83BeZwOBwOh+OM41Vtgnb6QI5TgCmG/hGCY0qHYy0A7UsbVJOi3lgZK8oHMGWC8TYAI4S1lYhTkuHRkU/lJJ7pYCpBUWnSPrfuXapIBRRjYhCMzN6zuldqGFJeh5OUYiSNJBd4TrNdeUV01Q6p5Vlyqpqh3eGqe611PSznwiirkYecuoy9OLctxqKwnc84ZZ5Ihsdr5mXuB0U3tPZAD6gu5jVzukQAagdSAMmg13sxuTKUkmHKUL4nmNOdIQ7AnzPUnuy1TDDTlRrUHqezk+2ESlFlv7b2PVoJj9Nogmy8/KwCADLWdHZkhSFjVdb46NenAiuWaISgZBiKPnea4GOF8GNeEXQFjGCUG/P0om7f/rr/HY4+YkWYod6w7rJvHPyXV3Mljj6i75Rw5y4aAKA9Rp0uNDfeGfFJqVm2FUtzAAw5BTTv/eKjO3793wPgcZpVKwCCGU1CiL3WpKDyluQAVC0shRALq6+ea0Sj8vUIgJy1TUIsyWXSBMBj34YmgtuveaV1hUSaff7yNGDn4XnREh5P2hIAACAASURBVASlKXiSHU0T42nDF7bFx0ZC3kyqfQ8AOX+VE1hMKSMKQcV5gx4Za54qCp60L2wUlRsArXVW2pHprkEptfgkA5zKZCXRRErXhwpqXVXrVDG6emlubDUwg1UT4MVwGajph2QVS5HDZMgr+5OqBxNaUjziA4iAYMq2B5lCEhqFexqdgqbiZKopbDW1RbUw993973D0C64E5ljpMOW+ABxnLu7+dziWidPsBXbDussAuPSP43j0iw6KMaydti9YReNCIrEpASqRBNNZmcygohVL83f81fcA7Lj1XXSGzfMa/Ej1oAViQhCcyltM6bThgwwoChE/q0PoS6pnUXqJz3fK99o0T+/+26l9kGsAuuKjXgVsDglJynIFQA9VSTqIp7J0+PKnEgA8zSjxw9PMaggJid5qXYE3n1UOCwDtdVHlYIyeUTIe5zztlrH8OVleKxJVMpxRSkb2aOpQN3SZ4lp4boJRps34khZfNoMj11R6y6pMUVVOHPFWFTD65zCYzuhXUD2YtNf4AJgy1EnNlFzw2yltyCiPhUIiSEmnA+RwrEROZwDkKl+OE6FfSgBG8njTsPZ5dKANIF5foW9oqnzxVFMkJOKcvpjf8Vff+//e82YAKL59y9NUobAjXcoAMIJRBUoLhsgHoH1BFSgjGE2Md9ZYrUJPyTzqjrKbQHa/+GmdvrSGpsMVTx3RDFSW2BBIAKj4bC5Gj0Ci18yTYR9AOBbbebRAlrELVdbo7FCoV+vI746SzWYAOiN+6XRWSjsWbToCQCktzXMrmah9XoZEVmlaGhr+MkLQML93OAWQr6p1NbKPXAm1KNGSyClWeyyaMijCrGSAy8SWxlghq0gxmpbMn1UAvMPz2eo6ABUJWkBlXxuAKabfRZyXgZ21sF3kFFif3P8OR9/hSmCOlY77AnCcybj73+FYJk5nBsilf/qUTY+9DwBy7gb6jka2cthMgKLcDmUsWKrov43OaEiJkG/8p608TQCYmmyviwAwbSVtRKxLrSD0FsKU6bp0FRmRbNAHoD3GUwYgq3t0RH9Wg/I9QO8DFKUZpox1kheMfLtEMxMzLaBHGUhSL3b3PyVaPFPK5ooKdOSTIpGdLBOc1IagyFcDOpKUPcoj3hnxAXjzuXWNSJUVeIwpW8ZKHzFbTiqMJrympnGwPGCCEk9F4YnWw1Kl7blYEaYyfcXbKW3TXhelNQ6SoFygb8QZAKE02XiF48qKKKY6qzEAzYtXUWIvGbTt2HT9/cmYPOd5nOPIgprIXQXL4ViJuAyQY6XD1GKLCA5H/+Luf4djmTjNTdCOfuTFt+94NQ/XN0q4BiLVeSQoe8G0kS079w6AKZXWAgDRgSalCuRUUmZlyBU1bXhk0RBpaylKHTCi7JURzHb2FAmSvCLmzrUGnz7J7fgsOmwt3AGwouc6bfiF/hAntaFwrJWMVkAD24VdKDXKsFYCAFIU6RxhesbyQaYcdpbe9hqXakbUCWR8YXuemllhKS86gyGAcEZToisZ9KiD22syaiSibp5kbZ0umu2hAZg2tDeeaq8JAMoT1LiTNvyAmp2L49oRd6UX5KJYmpcXnGSjvZaxprPNHEA84lv/9iEeTmu7E/DiAQCIWDHFAXgHVFYVKLSL/MnYKhEIZluOBI/2zACYXX/Ct9Arscj7/6mnnvqDP/iDRx55hH584IEHPvWpT3med999973tbW9b1Mocjj7HBUCnyKZHf9MVgF4l+sULyUDEuZbWAyur+ZW9cygCEVUL6FvW+DI4NA9A18KyO3h2UwjAa5nGiwkAEedkS071Jp4qWIMtTqJ4PFUk/5NX5erHDwPobGiQoRiAvBGiKJ/FZ9XpSdlSFO7Q8wCS0Qo9Dsea1CitK75VRLRbpGrdMD20NhpxQlWzuQtrJJDDlJFx2nsZdBGckQoOBNO+deAitUOSRyIohsiqwrcxWRMAzw2FPumA9OdsZMaLpm9rMZZ1PTHofGkcjDfLjmxOIRE1awNQjQqZV3SGuD9HAZA1MqNGct/nXAn0+IvRqB2KLmlaAAVYXjMnzw1ySWudW6fRtjLMYqnqbGgA8GcOYjEs4v7/2Mc+9oUvfOHKK6+kH/fs2fPJT37ymWeeGRsbe8c73vHSSy9J6b4CHGcu3bs/z/Onn3760KFDWuv169dfeeWV7m/DsRJwOiiOM5nF3P9vetObAOzcuZN+fPTRR7du3To0NDQ0NFSv159++umrr756qdbpcPQdNsT55je/+d73vrder2/evBnArl27Wq3WQw89dN11153O1a1gXPrnVYOZ/sgAMWN4nPppTgUXfzZLVlfLV/3JuEgMdAsxeUUAEN02XlBCAkVRhuRqmDILXB3yiqA8SjiRkmZP+PyEqQYA8uFqqaQMgGljbdKLsW2mbWLJmyrMUJVWg1VQBYpqPYEHwMiAqlcoykkoqlQDLzDKjgTjbRTlIToNMp/XkV92B8OeLycNaN7TFEzyzYYjHZAAZBwBEHGufJt6oVJg2Qae1ay1e9LgVMYyglH9jreLpQIA9GDVahEpTUW6fJVVCvDnjCSz1UxT13M6HNC5aL8GoDKu5jaQ8rWgqycyQ/JO/mxGdcnSxMNW4mq8Up6VrcEpW/3MFmeFYcC0McY8+OCDvc/7vv+rv/qrYRge573btm3zfb8MgA4dOnTxxRfT482bNx86dGgxC3M4+h37QfyBD3zgscceK/82AOzevfumm276l3/p40GtTd+4HcCLN/y3070Qx5mBMaydsp5+EWYFDxUAVQtoLqnrkFWEAmnDG3quCWDiqjrLAfpS73StIfKKyKsSQDCVUoSUDkiSTOSpsvI2gcxGawDkbCer0EyZAeC1bf5AeYze4s9mVC1i000EPgC1qma/s5OcvC/yho0V5FTLrlVpu0Eg0WOFUcLyokpk7TVMcLgFW4riALKaLFUNS+MIapMCQCdIY2LRmC1aBTNWPbKc5GLKqIi0gqxNmAq5jdKSDIAaGbC6RILR+JkJJJXttMeLvXUvbzIkAZDKYt4ISwmioZ8qAPMbfYoa84BZ3cUWo5iplCaiXxk/ap6k/EVTmLsYjNbGmKeeeqr3ScbYtm3bFgRA999//44dOwA8+eSTr7grxrqqjHpxJmUOR79jA6Asy9asWdP7wujoqPvzcKwEmAL6ogna4VgGmAKD4Jx//vOf/7kb33nnnXfeeeexXl2zZs0TTzxBj3ft2rVu3bolW6XD0YfYAOjDH/7w5ZdfvnXr1osvvpgxtmvXru9+97sf/vCHT+/ietn8Z9sB/Ntvfe50L8TxasNOsgn0OHMuZ5999sTEBD2emZk5fvngZDGcq1U13uzYZEmuUQOKpmAe56oWAMgjQfkPnipmszi6vaGCwisUgBFMhQKASTUAFYmsygG0RyOqyMjYlH0hpRs8/djeWKdtdGGsTokKnoKaduVshxxPzVDd+sbHKSk+l1APshFMNMnXolBhLsSU86qwpqeFwhDL7Y9d+Z+u86gGIGNF8j+iY50oRKKLETltc11FBZAuUVn5UpEsRbEpaVRrYX6jLZM1z2sAiF62+bZyAcloCICpov28aKCWsSqn3mTh3A4gHvGp59qfTWmUrzqW03tb6wKeGgCttb7f1HQWNFXnNX0A8+dGCdXRpmwJrJyD01hUBuhk7//jsG3btk9/+tPtdnt8fLzZbF511VVLs1+Hoz+xH2fbt2/ftm3bo48+SlXhrVu3fuITn9i4ceNpXdsRnELo44pfrw24Aj/hXORx5lw6nU69Xt+/f/8yrZNpLSabyJUVDwykmG2jDFAGffqO92dT6p7xU0W6f6YmdU8bEABkyEOOoj0omEqjAxSpJM0Lh+zheoID0Ei5z9Azr8QzAAim7Fc4SxXVhthcDKqRtRJaaukIhsAjYy/701QR0/Q8ST1AsqXo+55nnjeT0vnSZmRnweO8q6aoDIDOiE9dO0wZqiKpgNM1EbE1TqcAqFd30cYQhSVFWTvTktEklwoYdec0N4YAvKamDqdyhL58HEylVCzTkV8KP5KjGQ3ZMeVTfS0tjMVER1G5MIhE2hDoCT3DsRafbqEI+KLDKV2Hrud8yvPVVQBmcZn0k7r/j88555xzzz33XH311UKIHTt2uDEXxxlO9w+AJr/KKTCXHXWsEE5KB+U4cy779u07++yzl2uVDsfysEgdoOuvv/76668vf9y+ffv27duXYFkOR//jpsAcKx2mjc6VUmp4eLj3ec75008/vSBPeZw5lz179uzdu/eSSy7Jsuzuu+8+TqvEKa/UKu+RlmCu6QFlRAxnymcAlG/bh7O6RwUgFImfrMKiSQ0gq/I8BIDBnyUA5FRLNSoAksF67YVZADNvGPIzBUBFMhnyAOQRC6dJPJBT3660xTJljdzbdl4MpU974JVVqnLlvYKHPC6LXNbpkymjha0bUm7Gn83oLapnGwAQrGhb1tQOrAWTLQVApFoVWkR24yKbRT+mDY+qdd58JmINAJH1h+86XShT290CMHl5nVJcwZSilVMayWvmpTupmGmDvO4BOi8jAjovK9IIq0KUDVcAKJ9TKigaiynNU5nv6EtG6VdDZTL+8jR8H4CcbAJgaSRenraXN88BYKDuT3IAas2i3OCZNk4J2uFYDl7LU2CO1wycCyHECy+8cOSTvNFoHL3xseZcGo3G7bffftddd+3atevmm2++5pprlrYHwnCm6hGoCAIsaNvo/daniozoKN3TgALAb2ryqPKbmoy97EuC04Pg0DxFKlmFRYcVAOVzeovhNnpgRemJCkPonTvLi9BHCgBQRYgWBbRm7Xs0l94VU6bFz7ap0SdvhEzZhVGYpX1OY+HdYI7CoNQU0sxy6pIqANJWtsePFQAV8LKQR5U1fwrokVIsJQPKlh2mFF0ZKEOOZl7bqjkXGxieKnovCSTyZodCH6a0HfsvLOvz4ar1ICtG6IXvAVDDAS1MzLTRbtNbogNVANmFte74G72kAgA8kGjHAExeHGJungUSgHKFJodjReKmwBwrnVIIbmho6OdufJw5ly1btlxxxRVSyksvvfTGG2/cuXOnawJ1rHycEKjDsUz0zRSY44zlpKZgjp5zyfP8+eefv+iiix544IEf/OAHDz300Pj4+OOPP/7+979/qRcKHUkjmFbWjbzwxrKFIXrgz2aUAVKhMIW9g9ck9wwezNkSGM0cUR5CRz691/jSplWElQhqr+m2J1vvrcx4re4IVWmjoerFhFWZqgmklWQUjDp54zUR71H3MYJTpoTl2vigfVKBSftWhzCPRFm3oneRsk5JVmG1A9aegnInZTqn1HWEsNXDUsIH3cyQ9TUr81jlM4AHIJi2exOFCQYranzUvzxz2aravg4KhUYAUJq1OwCyjQ05pQGrIQSlxAwAJOdXB3bNAUC7A+oUFoJ2G07YoyDPbQExSQCwOVHmfsqj0EktMnxZwikwh8PRS99MgTnOWLgCP+Em0KPnXCYmJjZv3pxl2R133PH9739/w4YNURR99KMf3bJlyxIvlCGrSX82o2Alb4T0lUwhRV6x0+/ldBJPNYUsNOIOQMaazDi1QDRTuIDRS7MdAEaI5rlVAP68md1EQ1j24CIDKfVpnwU9QYwqumcgbBMMk/ZwuhbagW3BSYEQRRRVzJwLGofSkaB6U6/GtPIAoHI4F3bMXvcq/qV1JjoGgN/U5RR62fFDwYTxJT/SR4xCCjHTNpKjp4+KpTlPOugJ2owvqfTGM+vkamfckpzeq2shdV9pYS9jWf8CACEARAfmCy3sI+4wf1b16lUCQOCXBUFquvKlBHIACAIAmG/Sq0xKGwnVayQFLpI2FsFJ3f8Oh+PEcVNgjpUO06Yc7T4RFsy5jIyMGGMASCkffvjhpV+fw7GcnOz973A4TpAVOgXmvNYdJSxHX0zBGMa0z8uOZhTNvOSAgUpETdBeM6dqkfY5afpJj3WGOIB42JqQc1UYZhWuUlSKStZXkkGSEDTUU0wd0AD8ORWvEgCqhzL0wFPd4yMm0NPhC4Ak+oxgJDvEi+ejsQ4AMR+rwQqArO6Rcg8Aqs0B4EXupuyY5jkHEB1OAdT22ePmkShlD8sBMSvtrQx1HxvJWSsBikyMUoXPe84qFQBIUxqtYgPW3L7M0IikcMmgRuZcQQYgdceUA6jvY1aiUBlqtUYgKfHDJmYpFWSP6/uUcAqmEltHE4IqXCXhWHPuwkEA+qwhPjEH2BKYKTYzxSJNNQh3TwPAuVgM/XL/Oxx9x0qZArvpZzcA+LsLvkE/uujHUcKVKb+YVzLMGJ7qZNgXsQIQjLdpCqm0PhVFLazsCuqM2L4ZCi9EhoGXbFjBek6ZpXaya36jH00qAJV9bRKP5go0MO8186wIhmiEm6KrckqLxzk1AxnBKCIpTUnzSJCIomgZWjwVj1jFp9hCJJo0G/2phKI6I1g5/GULeYUUdblbK7tcnIUKrBlq95ooYytcSW5DEAojlO7OUikNwOQ5o16cdszaAMABT1DJT4hmBwCS4tLNtQEg8BFYtUMqIALWp4zNxWXFauEvkbbKXyHisAFWknLVAKBqATAAmoeHrakBYFLSubDxaXsd9KIEx/vl/nc4+o5iLtdNgTkcDofD4ThjWClTYGXux+FYANP9UQIwhdsUJWCMb+2rKDUi26o02OJHDn/NbZQjO2N6xvbzNjud9QMAPJoCQ0D5HpGY0jTDm88B8ExQHWt+QyAyAyAca5I3Fvmri9I7IpJleU579J+PFokGEI9Iem9ZLyNa59Zp1CuYSlE8XxS8DAkClRkm7fHSp6LYwFqv0+BYKZ/D0rzbYmy1GTV6mo67+R7BUakAYIGHdgcAhCD1HTbXtv+9RcER3c1JYue2csVyBUC0krKyVmyTmiMLWyajYbecURop9e162rFVVWp3vdKoTOntm7JySvUqALTa5eJRpq+qFfSkxE6Nfrn/HY6+w36GbN++/dvf/vYv/MIv5HmeZdnWrVu/9a1vLf2csMNx8jDlmkAdZy7u/nc4lonuFNjk5OTq1avf/e53l4YDX/rSl9797nefpoU5HBamTH8IwTGmPVbaeHZGwzLTA0D7Xad3eqB9TradtUOsq9kDAMiHq73qxulwoAJyD7XGn6rmWRvR2ay5XgIIZnVWYQDi9bZNuFT0yauiPCJ6TdHbigxEtYfOMPlaKFre1OsjALJtyF6Dx2kyWgEgUl3ultZczs9Ty1F5XKZsbzJPFaJyAQLUam3VonsyN5RNCQIUjTgAoLSZnrGHo7xO4FNOCIFHfdPdfh1K8JQGn+02pZdMkmDBTLtSZTO1zdaMDgFgY5M239OTxSl20i4XQBLYSFPMp7377PZTCwGADQ1mG4YB8ORlLIK+uf8djn7Dflj88R//8Z/8yZ9ce+21d99991//9V+/8Y1vBHDbbbedaQHQpsfe9+Lbd5zuVTiOgCnD+qQJlL6oaLV5yBFyACRLmNVsRUx0VDLoAYgmUm+qDSAZathqUVEbEs2k8JGwqoPltBfVqtKGRwFHMNVmKgKQNLg/bwCokNMyKJRRIRcd+/3ZXi0AhNOajM2TIUlaPkM/iSk2Onx5WN+vAduLbQSjncxdNEDVOlHUyLpRVBH3ePMZehu3leJKA9CRT47rnTURtWlXxlghTSSY0Cjc0wAwij8qYaExmLKi9mTWj9ptCtsKpFSuSm3k4fv2RypjVSLbUi2EjV1GCiXxiWkzN08v2Wf2vwwAgQ8KjJLUznblebdwVigiUlkQvm9abQCmkxSLF/Zwa0ZBypPNBIA/18Ii6KP73+HoL+znzmc+85kf/vCHa9eu/dGPfnTzzTc/88wz9Xr9OG/74Q9/+JWvfKX3mWeffdb9jTqWA6eD4jiTcfe/w7FM2ADI933ylbz00kvf+973/vZv//bnP//547ytVqstMGaqVqvLt8qlYtuubQC+ftHXj7WBS/84Fkn5z7rIDEkzE1mN+7MKQDLoWe/3mlR+DUAwnfW8/QjRX9JWJpEeAKt2NknSxghG5qPU7wwgnNSUapKxIsEh+tbsDPlhZgAkQ9Kfs2ujOlpnkNFQPUtV3vAAhNPWYr2E5JWT1VU6XKmGXKo5cz8sfNpzVnY0ww6cA+DNDj2ODqj8vAH09EermqdfySm0LAXyZsemVaQgsw7ydQe6XclmyP6rxqbnAZSlKzM3X+ZmDBIArKiFscCPf2EzraSUsabrIOa7dhnAQoVoe6nHYgD5uiGZpigyQMwrpt+L4po4OGGTUq1FZYAcDscyYT993vOe91x22WV33HHHPffc85GPfORd73rXrbfemi+wtulh8+bNJJlY8uCDD37/if+xvIs9JXo1FReEPm9+9pbvXf7Iq7mYX3vprQAeft23Xs2D9js8N7xP/gNWHksGpN/UAJiG7GgUnTfKs40+td2tuQtrAPKQB53CtKu0njgGIjEA5s6rUlhTPZBQKaozxIMZDaB6sCNm2wCStfXwwByA9usGARhuK1/RpKbmFdEpBAkHeTogAPizMhjvAAimGHulr/zgcPcr3BSRTdenvYj5aBrLFFYbtnvGl+mqCIA3k/7uH/45gE9tf49udC3MQNJEHgNAoSHLbaWPqVB7tvnJmnOh8LQvrLi6jTsUsowM2efbMQt8ACZJqQSmN57VOrcOoP7kgcq/7Lc7ocJWWT6jka5XuggkTcSUDZKM5GakAYC12iAHDKq45TmmZ+166CM0PeYH6YnQR/e/w9Ff2ADo93//99/5zncePHgQgJTy7//+77/4xS+eiPm2w7HclPGBw3EG4u5/h2OZsAFQp9N5y1veQo+ffPLJH//4x1ddddV73vOe07ewJeNoUekyJ/Qqp3/gcj+nRB9NwRgJGVupHq+jCi8IBiCYs+3DyWjozykA2mMkAG0EI3nlsjYEWBMM0vJJB5jsAD1+F0yZ8csrAAafT4PxNsh7VXBQtkZwFIUz7XX1e0SsAcy9zieb0tI0wwhG3dZMacpCdfNART2rTPx0/eHTHICOeuxR6xEAspswglvZZaW9GTst9Yd33QYgH+AkbawCxnJ73SjFJecUAH82taWu6dly5oucXI3kTAkAqFRsE3SS2ixOIACowcrklhoAntnbRmSGjuLP5fV/fvGIX5jSUGSgkQOAlJhv0Y9WiloIygaZLC/dOSjBw1C0RUsJwCQJiQmhHdsH5V2hYxwztffz6aP73+HoL2wANDg42Ol0ANx333333nvvjTfeeO+9937wgx/8rd/6rdO6vBNi06O/iZNxz3A+G/0FUxp9IkpOvTXk7q4zbktOiVUOVCEHkAzwYE6DSlHaAFA+F3Z03JgiaKCIhObkDfeaa6kZSJAF2PTF0eizthuGmmN4qsl73J+MqThFgZfysepfO+gZJgonZTSRApCznbLoVtqzW7sM2DDIWq8LQc/zZseadgWetbMQjB1Z4qGQiCnVWVMFEIx3qJEIQLyqBsBr2RhReUzA0CWiRijRzACImZZt8alU7Hh8785r1llCvDxrn61XAUy8eRQA0xj97gSoHpcXYVy7DcAk1saMVSsU8Zg8J61CGwAdOfoO9Ay3Z/mC+IZ58gjxxiw3Kgegkw5V3Jiwn65G54sLgPrm/nc4+gu+4OfPfOYzf/M3f/Onf/qnX/3qVz/xiU+cljU5HEfgSgCOM5nF3f9PPfXULbfcUv549tlnhwX0T6/DccaycATD9/0LL7wQwOrVq+M4fqW3nDpvftb+HS5t7enMzOj0dnBf99xNAP7pkr87rStywHDIlopXcQAyBgnGWKP1zNCP2mMkzFPOi2mfF3POvJQZnD83QmG9nkdMewBQfSlvrZUAKoeVnGwC0BWfMkBMadkGesSEOsMMQDhlyF6jnNJq7GySxzt6Ez9FrsSmoEASjrK0o8eCtmClrZF7mpdur5S1osk1fzKmxmrjCzql9oaKTAwAkRlKksnYULNzNBZzMjSlQpvo+ceMUkH1ankUFUkAH/izL/3J9v8AYPa8gOxgh36aAYj2zloz1HZsuhkda+3ezfcsGPIqPecJacUYjVI2nVOTtLdysqx8e1nwEg07kaebLQAstMVBjjqOMN549fjYxz72hS984corr6QfO51OvV7fv3//6VmNw7HCsJ8pIyMjmzdvPvvss/M8/+xnP/uhD33oN37jN972trct7cFOIe6hmOnVb9ZZ+fRek9d26MOUZn1RAmBIa1wL26/TGeLU4kNTWkwZCgjCMXTWRAC0b2tkAJgie3ZF0QPPefVgAuDQm0MA/hxqBzSA+Y1e7QDpH6bWR11plioAOpJk2J4PV0nHeWCvAlDdPU9xj/Y9Pt8BoOsh2ZOJRNDAufYFK0pvtB4KMkRhIM9SDatqGAgy3iqrS4WGoRGCFk+W73y6ZeODgQr5mnWGOCNLLo9REdBwVF+aBWkbFoEOAChtH8y3aD5L1SOKzOgQAB78lXcFah7A6kPz9hqSJHS7Q7vSzRbVpHgYmgs2AmAvHiCNRNMz30qKiKwSATCjQ3YnSUYihywIFriGlZUvNjRoXckKvel8cpK24UEIAEqxIACAOMUiWMz9/6Y3vQnAzp076cd9+/adffbZi1mMw/Fawn547d+/v9Pp7Nu3b8+ePY1GI8/za6655o477ji9i3M4QF8Aqh8CIIdjGWBKQyljzIMPPnjE84zdeuutxxdg27Ztm+/7ZQC0Z8+evXv3XnLJJVmW3X333XfeeecyrtvhWPF0S2DT09MbN2684IILnnzyyYcffvitb31rGIbLeuzfPbzlE6t3HutVyv3kZmGX0onwxmfeDeDJK750ymtzrCCURj/ooDBlqofS1lrrjbXqGduiO371IIBgJmueWwWgfSZjKxREnb/b7vun//HbbwOgilpYVpPT50sAXtPunMamhv817ozY/ataCIDHqap5APJI8IAD8OazeAQAGi/YPIetkaU5lZZ4O5X2GUVFq9KeLK8crFHVQAAAIABJREFUIc+j6x7ZxbOU0xY8zWzmSfBS74eKUyqSNvdDCY+ieTkbrc2c7wMQqa36VV7OqOlbNLPS8qIw0tIAkCubEBLCVAMAquYlQx4AnpnoQBMAm4vtIZIieyQ4qNO5UCbkq0cAmOkZ9rO9AFgQ2ME0yHLIq7StAM2vtTv0FnsJZJHvKS3GgsIofr5JpS7KM6FI/DBP6k6HHqASAUDCF2XnrrQH3/O8p556qvfpIAjiOF4QAN1///07duwA8OSTTx69p0ajcfvtt9911127du26+eabr7nmmquuumoRK3M4+hv7V33ffff91//6X3/84x8/8MAD99577y/+4i/+3u/93u/8zu8syb8I5ZTWgnrW0dFP2dfS+wAnr1hIoY8Lg14b9EsGiGkTHJoPDvOpy4YAtDfWC+FBA2B+o/+l//tTAP7T/3EPPS9bOQ09lSTDsjKWAnj5DXJgrwEQHU4BdEa8POIAmhtCr2U1iyl2SUYrMlYAgqmERKJfflPt7P/ZBtBaFwJorveHnmsCML5U1qyKUdWMp5m2g/oez+wVppF1Cqq0ZFRWM74kNT+mNMUQ2pc0/GUETxs+etzBrP5hxZ95wxCAtM7CGQMgmM7DsSM0kY0QtrNnoGKHy7rdPz4ABF68sQFAhZyWGr2ccOsFpmzLzlF6rbb5Ril9eAIA8ySVosz6URLOrn/neYp70rUD1tHs4DQo7pFHtEXqZsvuTXAMNezZTc+iaPRBMe1VHgW9oyWBj0XDlJZGjo6OHl+dn7jzzjuP86G9ZcuWK664Qkp56aWX3njjjTt37nQBkONMxv6pfvzjH//Rj340MjLyuc997tvf/vZDDz30xBNP/OEf/uHpXZzDAZBYSx8EQA7HsrB09/8DDzxw2223JUmyf//+xx9/3EU/jjMc++/OqlWr0jSlB/QMY+yYbzphKH8zvGaOHh8+NAjgOu+mYzXtfu/yRxakbegttIefC71XMk3pIpf7eY2Qq74IgLTkrfOHDAdNbLVHBdWzqCf64//lz/5m/lIAWZWTECIVjAA89mtXJ2+QALyWvu3zfw/gr977S2W3L4B4mA8+nwLwZ9PmhgoAHcn2WQEA7bPosAFAqRo6XHNjCICSSf4cj9dXAEQH2lbjR3Dj27/u9roIgApYOKFB6R/BAGjJ6EcaE1NRwI+axCa9n2zQJjmOUHEEpi4bSusMgD9vwokMQDjWtCYVSWHXVfGpkCeUplJX+bztLBY8q9rrEMyQUFAHSQYA7djmV6QkMUOT2MxQOZZFyRsW+Op1awF0Rm1Nv/WW8yjxEx6YY+PT3ff20N0J5YSGGjazNT5pPb+8o6pjlL4KgvKj01R8APA9LMYMI1fdlvPFcccdd3z/+9/fsGFDFEUf/ehHt2zZsiS7dTj6FPun++lPf/raa6/dtm3bpk2bbrjhhl/6pV/62te+9qEPfWiRe+8NX2Z/OLr6TeMA9h5chUvsBr97eAuOrIVNHT7Chf7ER9zf+My76b1bNrkhT8fpwBimzOy5ksavwol07twQRRnrk7/x6+984NsAvJYOpuzXLVWa5tdUKUTwmvmff+B/B6AbNjVLQoj1A4piKZbm5HgKgFxLk9GQAqn2hmKyveiXIkvU8MDc+FtGALRH61kVAHgGehBNmtr+DEDlYDr/ugqArC5pVt9rHtE/pAKrv2wgqMVH1QIVcAB5VVJnj+jYhc1tHgaQ1lntEMV5uT8Zg+Ieil2UMgN2teRfZnzZO/quIxsAtddF2mcA/DnV3Ymdaec00oVSclqUoVjhxlqpABh/67rh51oAKo/vshtU7dFxVNxTzOEXXVFCoF4DYALJpm1DFsVGvFa1LT52V0khSO2DBseU7qypAcjFWfi3hcd51bj++uuvv/56ehyG4cMPP3zaluJwrDBsAHTDDTc8++yzX/3qV3fv3r1x48bVq1f/7d/+7cUXX3x6F+dwAIBSTgnXceZC9/8SZOQdDscRdDv+Wq3Wr/zKrwRB8OSTT+7cuTNNF6VdQVD+5uJ//nUAtTdOzv5wFMCLv/W5coOj+6BfvOG/AfhSc9BnGYBfrh7RNXnlx7fPXJXRnm958e0Ant51Dh3lySu+tOmx9wH4uwu+QRsv6Lne9Ohvbtw4jh7VnE2Pve/Ft+9Y/Gk6lhelXtGde6VhBJvbKP15E72cAGBKD/60e/dqXzx6x78DwBqFd3qac8EBhBOZbJMeD6c8R7oqIg2hzmgAII9YNJYBML5MhiQAGSuyD0sbIh6pAogmcrKdD6c1ZXGSYRrOGlq1swnACE72YVxh5McZgMnXe3noAxjYy0sTD09rFNkjFklK82iPpw0OwJ/NktEKLbX0aWelTVZVAmit4QC8tr0OPE5tu7Tk7Gg9QBrdEoJOp6QzamtzNDEXjsW2KCY5ebx3XboGKiTeQ1NprfOHyAMkqzBetJjPXFgFMPxcz13k+wDMSMOII+ZM2cQc/e5sOqcSmYEizUMFr8BnZaan0jMnK0TXtaPohqbxurLB/BSh+3+hZq3D4Vgs9o//vvvuu+KKK+bn5z/72c/ecsst3/nOd971rnfdf//9p3dxDgdAur19EAA5HMtCnh896eZwOBaP/bdiwRTYOeecs3///q1bty7JGPxPtv4lPbhz9TUn+JZ316wOxwKj06c/+rmbfnYDPX5k02MAsKn7rjKd0/uu656zPde97US37bm2d3vHiqZfdIAMwhkz8ELLujoAutbNEPA4p44fADSFXrbRqNBmDkSi4/U1AOFYTM3F//mP/zuAP/q9X6feZ9nR1FEEIBn2UdivAjCCUcMQTzUNwPuzCj0GqzxOGy95APzZjLIpwaxdT1bj5NgaTOeUrtAeB9BaH1AiSnmoHM4B5BXRPNsDEE3aPBMAGtHPwalfR2QAMPSTmJcKyJRlURqBBwCJVW02gmvfA2B8QckSm3nShrI4XlOT6g8A2pLHCXUWG8FphD4ZDmjNc+cG9N7KYQWg/lKHEj+jj+2jppzWda8vnUbocF4zl7MxSIoawNx8d8GUxQl8U4gn2QRPxfYPmWowcc0qAJRnEsXVYDmMtA8G/m0KQH5oHIuhT+5/h6PvWN4psF6u/Ph2/13jAN54+JxyPovmtqbGBhY0Oz8aB++MErxSE3RZ4ToOve8aidpHb9BWwdFPOlYmJs9NP/wHzJSp7euIyaYatNp0FAnRtBTZXwAQHUXBDc/Nuz77PwGMyPkdd/8ygOCwLZm9/OZ6NGUAfOY/3wogTHuUAwWVxkLZygFkdRlM5QBE8dXO47S2TwMgv4tk0Ju+0AfgtSOvbb9H5zd6AGTbkCJR0uC297nNDJcA8iJyY0XqLW0IAMqTZEefVTkVpwDQg+ZaIVIAGP7XGGRoL6ylvI1dUhsjMHhUrjKCk5oRFe8ApAMSheojeuzSjBA0j6ZrYVm0onfJWHlTbQCr980CwHyLWpvV+etX/eNuAKbVpgxi9bsv2JMR3I50FclFTX3Na88yE5MgZ4xKCMAURh+64lMhjwH0+52+pDb6D8X+0fWNZ71KQkuhA2Ty3Og+uP8djr5jeafAHA6Hw+FwOFYgr+oU2H845ykAjx3eXD5DqaA3P3vLglIXpX+WBFsp62HTo795ZhrI9ytKwZxEG+kDDzzwqU99yvO8++67b4Gh73FeWjxMae/QrK6HPLXNt6pRARCfFQDgmaFBccMZaTfzVH31rl+kLbNBAUCd1/DmcwBnfW++zBIB4KnOahKAKIwmqj9pZmsbAJJBRnPvZXGHEhUA/MkcgArFyI9TAMrnlCWa3RQEsxqA19T0rpnzfdEBgDxg1NpMBq6yo+NVhaNFhQEIpzXTAODPKdqy3CCcMVSeE80EgKoF5LQKZT3nS4zkZXGQsjjK53lVAMiqDID2bEnOCJY3Qnt2KQAYwUvzV6qX+bOplYkiF4tWm3Iw4vkDNnGoFBsoxDUSqxhkPd6ltEmaJAWgD71cWrhT7odyVwCMb/NOxpdzF9YAjHz7oN1bJwFgVE6S0KZwfmeetPPwenGfZkrBuB44h2Pp6WZrBwYGbr311qXde29Y8/RHP0djWYcPDW568Yhw53uXP/Jm3LK0hz4OLvrpL0yWG32iXwB79uz55Cc/+cwzz4yNjb3jHe946aWXZFGSOM5LS7NOxnQ9VLWgLNyQICF9l4fjnXhNBMBw+62fDoS1fR0AzQ0hhRe1A5m100ozkZDZuwFNh82mAJhSVkVQcGpeqQCt9QGA6gFtAw6Aak9UXQrHbUMSU4Lahry2oaqZioSKBIDaIRVOpACmXh+FkxqAP5fTcVXIAMi2oR4gpgwtvozJ8tAqPWoBMg6zRxfMFJo63UtUdPwU62QUxHRGPArjyCWeaWRVDiCYSqldSUWS0URVqmDtO4RdSbfTqNht4d9uvSmqlVLvp6ylLvB470r7UDzk+ySAZASnBeQVMX9xAwDPsOobz/fujbzAmJC8UYRZdF/5PtnFo70oLzCT5cYFQA7HMnAqVqMOx6uJUSfRA/Hoo49u3bp1aGho8+bN9Xr96aefPpGXHI4Vi1F56bfqcDiWkGUUlzjvH9+74JkrR/cBeLpHm6fkpLxOj0+fVricdeuxmMsn2pgHxwI3bN/33/CGNyzo1j906FBZut28efOhQ4dO5KUlgRUaxJSTmLq0IRMDgKpaacMv25YpKxMdyGn7wdmY/FO9Zq6tPXtICR7CNCLqp85Ga57SALTvUaFNBdwOagWc3DCStTYPQZJCAFStMOlMNYDqVE65ohS+7a2OczI0HXgppWcoMdNeLapjCkB0oE1K0ypgNHfWGfEoa8W0TXFxhbThwbqYQhTWHChElY2Qxqr+MMoeqZCrgAFI6ywZYACqYwaAjA15vhrBqAtbNDMSCjKC28xTVciWQk+SZiFC2HxPnpeNyfTA5PmChmWbK+rpfaZfRPusgJJh0xf6jd05gMrjuwzpDxVeGbzwYzftmJ6neEU0GnYBi5PxnMsnMixZS4DD4ShZlgDo0dh+4C7w8Hp6fAN6Yp2bfnbDW1a9COA74xd8/aKvn+DOaYL9L875zrE22HL+vpNf8kJIU/HoOfmbfnbDiYyhnQLra7MArnvuJvRINTquu+66mZkZnmVyl3z/+9/f+xJj7Ctf+crGjRsXvKU3JNJHfvcc56XFYzjLhiveVDsbrvQ+TyPlwXjn3//FPwH46//zHVAGPRbrs5sbVPrhqUJ37qmbneVxTqbo/mxGO0+GvLTGAYjMaFEcRTAAk5cEq56zSozl2wGkw0HZe0RHkbEq2nSMP5UA0JG04+hRUU7ioOcpjAMkFac6g4xTaJLabbw5TYFdz5SWAEVmuUHhLwYgq0uydjfFx8/oD2Za59YB0EkZiWhfDDsnT6Nkhs5CR5IEHkVi6HR05IvU9vqAbC6oNaeodjEpS5cuu43gtkqV5yh9MwAA+aoagKwmaR6ttYa31vgAhn6aRj8dBwApbQCkcjE8hCLuAQqlRCF4UNTCFp24sfc/sPX8rYvdl8PhOBInL+pY0Xzzm988qe3XrFnzxBNP0ONdu3atW7fuRF5yOFYmJ3v/OxyOE2cpA6DD89UrP7796Y9ap4vRVfNnVefLV9/87C0L6lw7f3zOTrERwC3XPHniRzlO7odYkgzNsTQS/+6CbywYWFsqlimxdKaxbdu2T3/60+12e3x8vNlsXnXVVXmeP//88xdddNHRLy3HAsr0D9OgXmNKrtzwhX/+6n/8BQDZuZJyQpOv92QMAF7L6AHKQETRgSNkqyiLoyM/oAyNL6jMFExngAeAZ4bmlIxgKpIAVj2XJIMk8xOC7NMB9AgFQRkqnxlfWG0bpctxJypdBeRvGttG46wmSWxQtlR7tQAQr4Y/AwDRpKm8nAHwZ1N1hJ0Fp5SP9nhetX3TlF7SgpHSTxpZC472xjoJEdldTSU0OGYin3JURtj8VmfEZ9QF3jkqgUdN0EKQzUV39CzwbRN0JbT5nlxZVcN23PsRaIZq5BaiPSuA5LXN4M86AORsbFUc2zZXxITUs/OgaS8qopV5psIM1ZbY1KKaoB0OxzKxlAHQ6nqLoh8aYv+/DO/9Uv/e5Y8saHOJDoq8CgCP/OiKP3r7M0u4kuWjTxuMTpDXwNmdc84599xzz9VXXy2E2LFjh5RyYmJi8+bNWZYd/dKSH11LxnNDX/zVQymNdNE38WO/dvXE1YMAhnbF1N8zGDaoi2X6Qp/Uk8Np0zy3CqB6sMObWblbliqanOJxHkwBAFOG5rbShkfj6N58TnqAOvKp+4daf1QxcF5WkVDMZ4lmZ0EBiClTDFX5AMKiD6mzpubNpADS4aAzBADnPNqknWQ1aSfU0jwbDVE4ySufUxXJSHhNDYBnOgslgHSAhdMGQH1fMndOACA4YN3QaMTd+EILCYCnikpgPFWk65jWeDhtFa67191GHh7ILCzXAKBsFU8NVnksAegooE4mpu3beapp+oyOfnBrJZgDAK9lvJYBUNttpSmN4N3qKZW6ijYgVmhG2wisdIMXHDR+325j6hXvF4fDcTpxJTDHa43t27dv3769/HFkZMQY84ovORwOh+OMZRkDoKMHmhY889wHrLFXH1V/lipBsjJPvN/TPyuBPBKttRJAbX9GSQtvHgCmLq4OPm+rUfH6OgAVsDzyAAzsK/V7bG2oMxpElJuhPIdgwrpq+OxImwivmdNUlPa47T4+cgOWWt94poyYjwGowQpJ9fB2mq2uA5CzMRXFuoUa2onSlE2RsbXvAHD2N+fRo+UTjLcp1ZSOhpT7oQRYMiypVlXKLQJIBjiAymHVWiPpCoQzGoA3k9qaly9pzSYiHcJSMYhTXU9kJquRRJC2WZxCB6iULqTTLOtcM5trMq4C4MpQys1r2vk7KEOVNdrJhq+3KZmkfU9MzAGAUgs8MRAE1pcesDkhuuy+TymofFVNVI7QEDIychkgh2MFsiwB0C0vvh3AI5seo0n4F9720LG2POUIYPmmsV6R0pvsOJzUklZa6ONYAgy8mVRH8tfu+UcAX/7EDQMvtAAkwwGA6qEsGfIAyJaifpr6S0lnNAQgOooKTFSgAaA8NndeFUA4kQEwgkUHUgBQxvgMQHNDGEznALxmTuGFESwZtW8Pxtsoykk8zYrymQ0UeLOTD1cBiLJDrzsvllAIYhFcRQGAPLJmpbRyANrndFxSagYwt1FGUxxAHtjAIIw1nR25vWY1PvyjWXqpM9QAIBJT2TsPgKV5EfrkAIwQ1PqjIklRTtrwyB5VeyBHMxUJmgIzPUKLAJhSqh4B4JJ31g8AqB5KqSbI0txWx3qhc6cmIaXId11UKnqoCoC/PI3pWQBMSrVuBIBod7rHqkRAIXsYePE5gwCin45jvgmaNaPNzBHDsA6HY4WwlAGQ0gAfBjDg1QCADw8HFXqwhEchGl5tOXZ7LHzhg6fH3+ZVXlIfofQcsDhD7P7ANIYqOpSRaAAYHIjqg/TlHQBgyuQVAUBKZftORBY2QgAiUJJJAP6AjWC0ADmrh5kHwAgWtkn+R+pQApADQaAVAClzCi+MYGVyyM8ZinF0nuaqGgDgocdD2hvPBysAvFxngxUAsqedhgKR8r3alwCyRlAGQLRUXfUYBV6Fj6muBWFOGkI2AAroNIsVZlVWHyoak+sRAI+bypBGTwBk1yA4OAOgI0m5qLwqw7oAoD1IaQBID76WAHiYL9ABsosPZdigjh/jaU5HeQXFIHom9YFuAISoogcrAHie2WekVEMVACLPQIpEKmfUOU4BUK0SNCoAwuEa6AoUAkhZp415OByOlcZSBkAvjyu++nsA/ny1feYp629x1xIehfir1T9/myXk7Sewzau8pD7ixakvAgtVMV97KB1/+Ru/DQC4G8Cd95/e5ThWCl/84hefeK8TOHU4VhynGADt3bv3H/7hH3qfefzxx5diPQ6Hw+FwOBzLzikGQLt3717gS7B3795y1sbhcDgcDodjJXOKAdC111577bXX9j7z4IMPuiSQw+FwOByOvsC5wTscDofD4TjjcAGQw+FwOByOMw4XADkcDofD4TjjcAGQw+FwOByOMw4XADkcDofD4TjjcAGQw+FwOByOMw4XADkcDofD4TjjcAGQw+FwOByOMw4XADkcDofD4TjjcAGQw+FwOByOMw4XADkcDofD4Tjj6HqB5Xn+9NNPHzp06P9v795CoujfAI7PquWBdsvMklU8LZJSkUZtoqbVhXYOtQNoiUIo1V0h1J1kBIFRZmqgKRGChZDYwaTUtLKbULOS7MSahnmzESWVqzPvxe5fJf5pr+/OztR8P1frb2f5PQ/zgA+z8+yIohgYGLhq1SoPj1k+KQwAAEDNHC3OvXv3cnJy9Hp9VFSUIAh9fX0jIyPV1dXr169XMjoAAAAZOBqgw4cP3717NzIycuINi8Wyc+fOp0+fKhQYAACAXBz3ANlstoCAgKlv+Pv7i6KoREgAAADyclwBys/Pj46Ojo+Pj4yM1Ol0fX19jx8/zs/PVzY4AAAAOTiuAB08eLCtrW3dunVjY2M2my0+Pr6lpSUvL0/Z4AAAAOQwOedln/yamAIzGo0KhgUAACAfpsAAAIDmMAUGAAA0hykwAACgOUyBAQAAzWEKDAAAaA5TYAAAQHOYAgMAAJrDFBgAANAcpsAAAIDmMAUGAAA0hykwAACgOZNTYAaDISsry8fH582bNx0dHVarNTg4WMHIAAAAZOK4AlRRUREaGhoaGlpSUpKcnNzS0rJ9+/aysjJlgwMAAJCD4wrQiRMnent7bTZbeHj469evTSbT+/fvExISDh069H8/NjIy8vLly6kr/f39sgcLAADgDI4GaGxsbMGCBaOjo15eXgaDQRAEvV4/Pj7+q481NTWdOnVq6sqnT59kDRQAAMBZHA1QRkZGbGysKIp79uxJT09PS0urr6/fvXv3rz6WlpaWlpY2deX27dupqanyBgsAAOAMjgaoqKiovb3dYDDExMQ0NDS0trZmZ2fv379f2eAAAADk4GiAdDpdUlKS/fWOHTvevXuXnZ2tWFAAAABycjRAlZWVU1cLCwvnzZsnCMKBAwcUCAoAAEBOjgaotbX1+vXrOTk53t7egiDYbLafhrwAAAD+Go4GqKam5urVqyUlJefOnVu9enVdXV1RUZGykQEAAMhk8peg9+7dm5CQkJubu3bt2mkG4AEAAP50blP/CAwMvHHjxsKFC+Pi4pQKCAAAQG6TDdDQ0NCPHz/c3NxiY2M3bdrU09OjYFgAAADycTRApaWlMTExX758KS4u3rVrV3t7+7Zt23gWGAAA+Cs57gE6efJkT0/PokWLysvL29raQkJCBgcH4+Pjf/UsMAAAgD+X4wqQn5/f6Oio/YV9RafTKRYUAACAnBxXgM6cOZOYmLhly5bw8PCUlJStW7feunXryJEjygYHAAAgB0cDlJKS0t3dffPmTYvFEhwcvHjx4vr6+sjISGWDAwAAkMPk7wCNjIykp6d7eno+efLk2bNn9m/Efp+3t/fo6OjcuXOdG58oiuPj4y74Pk6SJHb5t7u4u7u7ubnNeKQoil5eXnLHoyzqX4O7UP/AH00nSZIgCKWlpYWFhc+fP6+pqTl79uyGDRuam5uPHTv2r26C7ujosNlszo3vzp07Dx8+lPte7IGBgQsXLpw+fVrWXQRByMzMrKmpkXuX48eP5+XlhYaGyrpLeXl5XFzc5s2bf+dgo9EYEREhazyKo/5nRP0DUBFJkiRJCggIGB4eliRp6dKlFotFkqSBgYHg4GBJaVeuXNm3b5/cu/T09KxYsULuXSRJ0ul0oijKvUt0dHRXV5fcu2RlZV2+fFnuXTSO+p8F6h/A72AKDAAAaA5TYAAAQHOYAgMAAJozOQVmMBgyMjIUDAUAAMA13AsKCpSOYTq+vr5hYWFyD3To9fqgoKCoqChZdxEEwWQyrVy5Uu5dlixZYjabnT6S/RM/P7/o6Oj58+fLuovGUf+zQP0D+B2OMXgAAADtmPlXvAAAAP4yNEAAAEBzaIAAAIDm0AABAADNoQECAACaQwMEAAA0x6UNUEFBgdf/zJ07t7CwUJKk/Px8o9EYHBxcWVlpP+zixYsmkykyMrK5ufm/rKgkHbvMzMz/mKDiuTjxZGkT9a/adKh/QIsUeQSrKIobN2589erV/fv3ly9f/uXLl8HBQYPBYLVaLRZLSEiI1Wrt7e0NCgqy2WyzW1FJOvYDamtrvb29KyoqJElSeTrT5OKsk+WyXFSL+ldtOtQ/oB0eM7dIMrh27ZrZbI6IiPj69askSWNjYzabzdPT09PTs7GxMT4+3tfX19fXV6/Xd3Z2dnZ2zmLFbDarIR1BED58+HD+/PmcnBz7wbNL0GXpTJOLwWBwysly5alRJ+pftelQ/4B2KNAAffv2rbi4uKmpSRCEmJiYNWvWGI3G79+/nz9/3sfHZ2hoaOIhrFFRUUNDQ7NbUUk6oijm5uYWFxfX1tbaj1dzOtPn4qyT5ZpcVIv6V2061D+gKQo0QJcuXUpNTdXr9YIgNDQ0vH37tr+///Pnz8nJyZs3bxYEQafTTRwsiuKsV1xj+nQaGxvNZvPq1asn/gH8ZvCKpDN9Li9evHDWydIy6l+16VD/gKYo0ADV1dWVlZXZX7e2tqalpfn7+/v7+ycmJj569CggIKCjo8P+bl9fn9Fo/Pjx4yxWVJLOgwcPOjo6qqurrVbrnDlzvn79OrsE1ZBLV1eXU06Wa3JRLepftelQ/4C2uPieo+Hh4bCwMFEU7X9WVVUlJSVZrdb+/v6goKCuri6LxWIymUZGRuw3D9rvIpzFikrSmTjy6NGjEzeBqjOdGXNx1slyQS6qRf2rNh3qH9AaV18BamhoSE5OnrgmnJWV1d3dvWzZMnd392PHjkVHRwuCcPToUbPZ7O7uXlVV5eHhERISMosV9aTzE9WmM2MuK1ascMrJckEuqkX9qzbCmuimAAAAIklEQVQd6h/QGp0kSUrHAAAA4FL8EjQAANAcGiAAAKA5/wB9URXyM1eEOQAAAABJRU5ErkJggg==", null, 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", null, 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", null, 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", null, 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null ]
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https://www.nagwa.com/en/videos/169163426941/
[ "# Lesson Video: NOT Gates Physics\n\nIn this video, we will learn how to determine the input and output of NOT gates in logic circuits and complete truth tables for NOT gates.\n\n15:55\n\n### Video Transcript\n\nIn this video, we’re going to be looking at a type of logic gate known as a NOT gate. A logic gate is a component with one or more inputs and one output, each of which can take one of two values, zero or one. A logic gate will determine the value of its output based on the input values it receives. Now, before we look at the specific properties of a NOT gate, let’s first discuss some of the terminology that we use when we’re talking about logic gates.\n\nAs we’ve already mentioned, the inputs and output of a logic gate can each take one of two values. And these two values are often represented as either zero or one. So the input can take a value of zero or one and so can the output. However, there are many different ways of representing the two values that an input or output can take. For example, instead of saying that an output is set to zero, we may say that it’s set to false. And conversely, instead of saying that an input or output is set to one, we could say that it’s set to true. Alternatively, instead of using zero and one, or false and true, we could use off and on.\n\nFor example, let’s say that our input is set to zero and our output is set to one. It would then be equivalent to say that the input was set to false and the output was set to true or to say that the input was off and the output was on. It doesn’t matter which set of terminology we use as they’re all just different ways of representing the two possible states of an input or an output. But we do need to be aware of the different words we can use to describe them.\n\nIt’s worth noting that we use the off and on terminology most commonly when we’re talking about electrical circuits. For example, let’s consider a logic gate in an electrical circuit. So here’s our logic gate, specifically a NOT gate, and we have an input on the left and an output on the right. These dotted lines just show us that the circuit extends in this direction and this direction. In this context, the value of an input describes whether or not a voltage is being applied to it. So if there were no voltage being applied to the input, then we could say that it’s off. And this is equivalent to saying that it has a value of zero or false. If we were to then apply a voltage to the input, then its value would change to on. Or equivalently, we could say that its value has now changed to one or true.\n\nSimilarly, the value of our output describes whether or not the logic gate is supplying a voltage to it. So if the logic gate is providing a voltage to the output, we can say that its value is on or one or true. Or if the logic gate is not providing a voltage to the output, then we can say that its value is off or zero or false. So now that we started looking at a NOT gate, let’s consider it in a bit more detail. The first thing to know is that this is the symbol that we use to represent a NOT gate.\n\nIn this diagram, the input is on the left and the output is on the right. We can see that the NOT gate has only one input. And like all logic gates, it has one output. As we mentioned earlier, logic gates will give a certain output depending on the inputs that are provided to it. In the case of a NOT gate, the relationship between the input and the output is pretty simple. If the input is zero, then the output will be one or if the input is one, then the output will be zero. And that’s basically all there is to it.\n\nOne useful way of representing how the output of a logic eight depends on its inputs is by using a truth table. In a truth table, we have one column showing the possible values of our output and another column for each input. So in the case of our NOT gate, because there’s only one input, we only have one input column in our truth table. We also have an output column that shows us the corresponding output for each of the inputs shown in the input column. In the input column, we can write down the two possible inputs to a NOT gate, zero or one. Now, in the output column, we can write down the output values that a NOT gate will give us for each of the possible inputs. When the input of a NOT gate is zero, we find that the output is one. And when the input to a NOT gate is one, we find that we get an output of zero.\n\nAnd that’s it. We now have the completed truth table for a NOT gate. This truth table shows us why we call the NOT gate a NOT gate. The output that the gate produces is always the opposite of the input. In other words, the output value is not the input value. The symbol that we use to represent a NOT gate is actually related to the way that it behaves. This part of the symbol represents an arrow pointing from the input to the output, which on its own would suggest that whatever value we put into the input would then be passed to the output.\n\nHowever, the symbol for a NOT gate also includes this circle. This is also known as an inverting circle. And it’s used in logic gate symbols to represent inverting a value, which means if it’s a zero, changing it to a one and if it’s a one, changing it to a zero. So the symbol for a NOT gate actually tells us what it does. It takes a value from the input, passes it in the direction of the arrow, and then inverts it so that the output value will be the inverse or opposite of the input value.\n\nSo now that we’ve looked at what a NOT gate does, let’s solidify our understanding by looking at a NOT gate in action.\n\nLet’s consider a simple situation where the output of a NOT gate is connected to a lamp. Once again, we’re using dotted lines to show that the circuit extends in this direction and in this direction. And really, we just do this so that we don’t have to draw in the rest of the circuit. Let’s start by thinking about what happens when the input of our NOT gate is set to zero. Because we’re dealing with an electrical circuit, it would also make sense to say that our input is set to off. But just to keep things simple in this explanation, we’ll stick to zeros and ones. A truth table tells us that when the input of a NOT gate is set to zero, then the output will take a value of one.\n\nIn a circuit context, an output value of one means that charge will flow through the output. Hence, there is a current through the lamp, causing it to light up. Conversely, if we set the input to one, then we can see from the bottom row of our truth table that the output will take a value of zero. In a circuit context, this means that no current is flowing through the output, which means no current is flowing through the lamp. So it won’t light up. Now, this isn’t actually a very useful application for a NOT gate as changing our input state will just switch the light on and off, which would still be true if we didn’t have a logic gate at all.\n\nHowever, this doesn’t mean that NOT gates aren’t useful in real life. In fact, we need them for building most digital circuits. And any smart phone or computer relies on millions or billions of NOT gates in order to work properly. Now, let’s take a look at what happens when we connect the output of one NOT gate to the input of another. Let’s call these two NOT gates A and B. We can see that the output of NOT gate A is connected directly to the input of NOT gate B. This means that whatever value is output from NOT gate A will become the input of NOT gate B.\n\nLet’s see what happens if, for example, the input value of NOT gate A is zero. Our truth table for a NOT gate shows us that, with an input value of zero, a NOT gate will produce an output value of one. So the output value of NOT gate A is one. And because this is connected to NOT gate B, that means that one is also the input value for NOT gate B. Once again, the truth table shows us what happens at this NOT gate. With an input value of one, the output value will be zero. So the output value of NOT gate B will be zero. So we can see that, in this case, the final output value is the same as the initial input value.\n\nWhen we have several NOT gates connected together like this, we can think of the series of input and output values as being like a signal passing from left to right. The signal is changed or inverted every time it goes through a NOT gate, such that if it were initially a zero, it becomes a one. And if it were initially a one, it becomes a zero. Now, let’s see what these two connected NOT gates do when our input to NOT gate A is a one. Well, we know that each NOT gate inverts the signal. So NOT gate A will change its input of one into an output of zero. This then becomes the input for NOT gate B. So NOT gate B will invert its input of zero into an output of one.\n\nThis result confirms the fact that when we connect two NOT gates together like this, the final output will always be the same as the initial input. We can keep using the same method for larger numbers of NOT gates connected together. For example, let’s imagine we had three NOT gates connected together, called A, B, and C. If we have an initial input signal of zero going into NOT gate A, then it will produce an output signal of one. This then becomes the input signal for NOT gate B. So B produces an output value of zero. And then this zero becomes the input value for C. So C has an output of one. What we find is that when we have three NOT gates connected together, the final output value will be the inverse or opposite of the initial input value.\n\nMore generally, we find that if we have an odd number of NOT gates connected in series, like we have in our diagram, then the output will be the inverse of the initial input. But for any even number of NOT gates connected together in series, the output will be the same as the initial input. Okay, so now that we’ve looked at NOT gates in some detail, let’s have a look at some example questions.\n\nWhich of the following symbols represents a NOT gate?\n\nSo in this question, we’ve been given four fairly similar-looking symbols. And we need to figure out which one of them is used to represent a NOT gate. We can actually work out the answer to this question by recalling how a NOT gate works. The NOT gate is a logic gate that gets its name from the fact that its output value is not the same as the input value. The inputs and outputs of logic gates can only take the values zero or one. This means that if the input value of a NOT gate is zero, then its output value must be one. Conversely, if the input value of a NOT gate is one, then the output value must be zero.\n\nWe can represent this information in a truth table, which shows us the outputs that are produced as a result of all of the possible inputs. This statement and our truth table both tell us something important about NOT gates, that is that they only have one input. And like all other logic gates, they also have one output. We can use this information to help us decide which of our answer options is correct. When we draw a logic gate symbol, we usually draw the inputs on the left and the outputs on the right. If we look at option A, we can see that it has one output, and it has two inputs represented by the two horizontal lines on the left. This means that the symbol shown in option A can’t possibly be a NOT gate because it has two inputs and a NOT gate only has one input.\n\nIf we look at the other available options, we can also see that options B and C have two inputs each, which means that neither B nor C can be the correct answer either. So by process of elimination, we’re just left with option D as it’s the only option we’ve been given that just has one input as well as one output. To help us recall the symbol that we use to represent a NOT gate, we should recall that the symbol we use actually represents the function of a NOT gate. This small circle in the symbol for a NOT gate is actually used in many different logic gate symbols, and it represents an inversion. In other words, it represents a zero being changed to a one or a one being changed to a zero.\n\nThe other part of the symbol for a NOT gate is just an arrow pointing from the input to the output. So the symbol for a NOT gate represents the fact that it takes a value from the input, passes it towards the output, and inverts it along the way. Meaning that the output value will be the opposite or inverse of the input value. Just as we’ve shown in our truth table for a NOT gate. So this helps us confirm that the correct symbol that represents a NOT gate is indeed option D.\n\nNow that we’ve answered that question, let’s take a look at another one.\n\nThe diagram shows three NOT gates connected as part of a logic circuit. The truth table shows the two different possible inputs. What is the value of 𝑝 in the table? What is the value of 𝑞 in the table?\n\nSo in this question, we’ve been given a diagram showing a logic circuit consisting of three NOT gates. A logic circuit is made by connecting logic gates together such that the output of a logic gate becomes one of the inputs of another logic gate. For example, if we give the NOT gates in our diagram the names A, B, and C, then we could say that the output of NOT gate A is the input of NOT gate B. And similarly, the output of NOT gate B is the input of NOT gate C. We’ve also been given a truth table, although a couple of things about this truth table might seem slightly unusual.\n\nA truth table is used to show how different inputs or combinations of inputs produce certain outputs. And we often use them to show how a single logic gate behaves. However, in this case, we can see that the input and output referred to in the table are not just the input and output of a single logic gate. Instead, they’re the input and output of a logic circuit which contains three NOT gates. In addition to this, we can see that instead of our outputs being given as zeros and ones, which would be normal for a truth table, the possible outputs are given as 𝑝 and 𝑞. The questions we’ve been asked are, what is the value of 𝑝 and what is the value of 𝑞?\n\nSince 𝑝 and 𝑞 are in the output row of our table, these questions are essentially asking us, what are the possible outputs of our logic circuit? Specifically, 𝑝 refers to the output when the input to our circuit is zero. And 𝑞 refers to the output when the input to our circuit is one. So to find 𝑝, we need to figure out what the output of our circuit would be when the input is zero. Well, if our initial input to our circuit is zero, that means that NOT gate A has a zero as its input. Let’s recall that the output of a NOT gate will always be the inverse of its input. In other words, if we input a zero into a NOT gate, then it will output a one. And if we input a one into a NOT gate, then it will output a zero.\n\nSo if our input into NOT gate A is a zero, then its output will be a one. And our logic circuit diagram shows us that the output of A becomes the input of gate B. Since B is a NOT gate as well, inputting a one will mean that it outputs a zero. And this then becomes the input to gate C. Once again, gate C is a NOT gate, too. So inputting a zero will mean that it outputs a one. And we’ve now reached the end of our diagram. So we’ve shown that when we input a zero into our circuit diagram, then the output labeled in the diagram will be one. And since 𝑝 represents the output of the circuit when the input is zero, that means that the value of 𝑝 in the table is one.\n\nThe value of 𝑞 in the table represents the output of the circuit when the input to the circuit is one. So let’s see what happens when we input one into our logic circuit. As before, each of the NOT gates will invert the input, meaning a one is changed into a zero or a zero would be changed into a one. Since NOT gate A has an input of one, that means it has an output of zero. This means that NOT gate B has an input of zero, so it has an output of one. And finally, if gate C has an input of one, then it has an output of zero, which means that the overall output of the circuit is zero. And so the value of 𝑞 in the table is zero.\n\nOkay, so now we’ve looked at a couple of example questions. Let’s summarize what we’ve talked about in this lesson. Firstly, we’ve seen that a NOT gate is a logic gate with one binary input and one binary output, where the word binary simply means that it can take one of two values. So the input of a NOT gate can take a value of either zero or one and so can the output. Secondly, we saw that the output of a NOT gate is the inverse of the input, meaning that if the input is a zero, then the output will be a one. And if the input is a one, then the output will be a zero. And finally, we saw that NOT gates, along with other logic gates, are commonly used in the circuitry found in computers." ]
[ null ]
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https://istopdeath.com/write-in-ymxb-form-9-2y2x5x-y/
[ "# Write in y=mx+b Form 9-(2y+2x)=5(x-y)", null, "The slope-intercept form is , where is the slope and is the y-intercept.\nRewrite in slope-intercept form.\nSimplify each term.\nApply the distributive property.\nMultiply by .\nMultiply by .\nSimplify .\nApply the distributive property.\nMultiply by .\nMove all terms containing to the left side of the equation.\nAdd to both sides of the equation.\nMove .\nMove all terms not containing to the right side of the equation.\nAdd to both sides of the equation.\nSubtract from both sides of the equation.\nDivide each term by and simplify.\nDivide each term in by .\nCancel the common factor of .\nCancel the common factor.\nDivide by .\nDivide by .\nRewrite in slope-intercept form.\nWrite in y=mx+b Form 9-(2y+2x)=5(x-y)", null, "", null, "", null, "", null, "", null, "" ]
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https://www.learnwithesa.com/curriculum/program/3/24
[ "", null, "Program Outline", null, "# Number Concepts 4\n\nUnderstanding place value, rounding, skip counting, recognizing large numbers, working with decimals, fractions and problem solving are among the skills covered in this Level 4 math program. Rules and examples are provided to introduce new concepts.\n\n## Number Concepts\n\n### Unit 1: Number Sense\n\nThis Level 4 unit focuses on understanding, comparing and writing numbers to 100,000.\n16 Lessons\n\n### Unit 2: Fractions\n\nLevel 4- Understanding, comparing and writing basic fractions, adding and subtracting fractions with like denominators.\n13 Lessons\n\n### Unit 3: Decimals\n\nLevel 4- Understanding, comparing, writing, adding and subtracting decimals to hundredths.\n13 Lessons\n\n### Unit 4: Mixed Operations\n\nLevel 4- Activities that help students practice converting between simple fractions and decimals to hundredths.\n6 Lessons" ]
[ null, "https://www.facebook.com/tr", null, "https://www.learnwithesa.com/assets/img/butterfly.png", null ]
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https://sciencing.com/calculate-average-current-7163114.html
[ "# How to Calculate Average Current", null, "••• AndreyPopov/iStock/GettyImages\n\nCurrent is the rate of “flow” of electrons in an electrical circuit. In other words, it is the amount of electricity traveling past a specific point in a certain time period. Average current refers to the average of every instantaneous current value from zero to the peak and back again on a sine wave; alternating or AC current is represented by a sine wave.\n\nAccording to Integrated Publishing: Electrical Engineering Training Series, you would use the following formula to determine average current: I avg = 0.636 X I max. I avg is the average current from zero to peak and back to zero (one alteration) and I max is the “peak” current. The unit of measurement for current is the ampere or amp.\n\nWrite, on a piece of paper, the formula for finding average current: I avg = 0.636 X I max.\n\nList all the known information using units; since you are determining average current, you should be given the maximum current by your teacher.\n\nList your unknown or what it is you are being asked to find. In this case you are being asked to find the average current.\n\nPlug in your values and then follow through; multiply the given maximum voltage by the constant, 0.636, to obtain the average current.\n\n#### Tips\n\n• Always include units as you complete your problems." ]
[ null, "https://img-aws.ehowcdn.com/360x267p/s3-us-west-1.amazonaws.com/contentlab.studiod/getty/ec02f5429a2348f383432ee4597277d0", null ]
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https://www.physicsforums.com/threads/work-required-to-move-charge.314902/
[ "# Work required to move charge\n\n## Homework Statement\n\nsituation:\nthere are two charges (+q) one at one corner of an equilateral triangle the other at another corner. the triangle has sides length a.\n\nwhat is the work required to bring another charge (+q) in from infinity to the other corner on the equilateral triangle.\n\n## The Attempt at a Solution\n\nok so i know dW = -dU = F.dl\n\ni thought that maybe finding (F) at the corner that we are bringing the charge to may help...this is:\nFc [at corner] = q2 / 2*pi*epsilon*a2\n\nthen i could just integrate this over the distance i am moving it with respect to a...however i know that the one limit will be $$\\infty$$ however i dont know what the other will be\n\nthanks for any help\n\nLast edited:\n\nLowlyPion\nHomework Helper\nConsider the Voltage at the point from each of the 2 other charges.\n\nV = k*q / r\n\nSince work = q*ΔV\n\nand V = 0\n\nThen\n\nWork = q*ΣV\n\nok so\nthe E at the point is 2q / 4*pi*epsilon*a2\nthe V at the point is 2q / 4*pi*epsilon*a\n\nso work to bring in point is = q(2q / 4*pi*epsilon*a) = q2 / 2*pi*epsilon*a\n\nLowlyPion\nHomework Helper\nok so\nthe E at the point is 2q / 4*pi*epsilon*a2\nthe V at the point is 2q / 4*pi*epsilon*a\n\nso work to bring in point is = q(2q / 4*pi*epsilon*a) = q2 / 2*pi*epsilon*a\n\nLooks like it.\n\nThough E is a vector, don't forget, and V is a scalar here. In your first equation then the E would need to be added as vectors. Whereas for V you are adding scalars.\n\nhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/mulpoi.html#c1\n\nok thanks...", null, "" ]
[ null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null ]
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https://socratic.org/questions/circle-a-has-a-center-at-4-1-and-a-radius-of-3-circle-b-has-a-center-at-1-3-and-
[ "# Circle A has a center at (-4 ,-1 ) and a radius of 3 . Circle B has a center at (1 ,3 ) and a radius of 2 . Do the circles overlap? If not what is the smallest distance between them?\n\nsmallest distance = $1.40312$\nCircle $A$ center is located at ${c}_{A} = \\left(- 4 , - 1\\right)$\nCircle $B$ center is located at ${c}_{B} = \\left(1 , 3\\right)$\nTheir distance is ${d}_{A B} = \\left\\lVert {c}_{A} - {c}_{B} \\right\\rVert = 6.40312$. If they were tangents their center distance will be ${r}_{A} + {r}_{B}$. Where ${r}_{A} , {r}_{B}$ are their respective radius. In the present case we have\n${d}_{A B} > {r}_{A} + {r}_{B}$ so their smallest distance is given by ${d}_{A B} - \\left({r}_{A} + {r}_{B}\\right) = 1.40312$" ]
[ null ]
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https://mathematica.stackexchange.com/questions/73103/nsolve-precisiongoal
[ "# NSolve & PrecisionGoal\n\nI am using NSolve to find numerical solutions of a particular equation. I do not need the solutions to as high of a precision as the other numbers in my notebook. To improve run time (I am iterating this within a Table), I would like to decrease the precision, i.e., something like:\n\nNSolve[ x^5 - 3x^4 + 3x^3 -4x^2 + 15x == 7, PrecisionGoal->3]\n\n\nHowever, NSolve does not accept the PrecisionGoal option (nor AccuracyGoal). The similar FindRoot does; however, I would like the complete set of solutions, whereas FindRoot returns only a single solution.\n\nNSolve does accept the somewhat related option WorkingPrecision, which determines the number of digits used in the internal calculation. Obviously, by decreasing WorkingPrecision, the resulting solutions are less precise, although there's no obvious relation between WorkingPrecision and the precision of the resulting roots (i.e., if I wanted my solutions to have a precision of 3, it's not clear what I should set the WorkingPrecision to be).\n\nA few notes:\n\n1) Although the example equation in the above is relatively simple, my actual equation to solve is not this simple, and so is not amenable to using Solve, although this example may be.\n\n2) Note that I am talking specifically about NSolve; NDSolve does accept PrecisionGoal and AccuracyGoal, but I'm not solving a differential equation.\n\n• It's inexplicable to me that NSolve and FindRoot are designed this way and that information as commonly needed as this isn't made MUCH easier to find the Wolfram \"documentation\". – Jerry Guern Oct 29 '15 at 3:27\n\nPerhaps someone who knows how NSolve works will comment on my speculations or even answer. But since this question has languished, I'll share how it appears to me.\n\nIt appears to me that increasing the precision of the approximations of the roots is a minor expense relative to finding the roots. It is perhaps so minor that a PrecisionGoal option seemed pointless to the developers. There is a jump in timing when the precision reaches machine precision, but that may be because arithmetic becomes more expensive.\n\nIndeed, the computed solutions at precisions below machine precision are identical, except that the returned solutions have different precisions. The underlying numbers appear to be the same. We can examine them by setting the precision of the solutions to infinity.\n\nThe following converts a set of approximate solutions to the (exact) rational numbers computed.\n\nsolbits[wp_: MachinePrecision] := x /. SetPrecision[\nNSolve[x^5 - 3 x^4 + 3 x^3 - 4 x^2 + 15 x == 7, x,\nWorkingPrecision -> wp],\nInfinity]\n\n\nBelow I compare the numbers computed for increasing settings for WorkingPrecision. The second set of differences show the lengths of the runs of the settings for which the numbers computed for the approximate solutions are the same. The initial 15 shows that the numbers computed at working precisions below machine precision are identical.\n\nsolpos = SparseArray[\nMax /@ Abs@Differences@Table[solbits[wp], {wp, 1, 100}]\n][\"NonzeroPositions\"]\nDifferences@Flatten[{0, solpos}]\n(*\n{{15}, {16}, {19}, {20}, {21}, {22}, {31}, {32}, {33}, {38}, {39}, {41}, \\\n{42}, {43}, {45}, {46}, {54}, {55}, {56}, {57}, {58}, {63}, {64}, {65}, {66}, \\\n{67}, {77}, {85}, {94}, {95}, {96}}\n\n{15, 1, 3, 1, 1, 1, 9, 1, 1, 5, 1, 2, 1, 1, 2, 1, 8, 1, 1, 1, 1, 5, 1, 1, 1, \\\n1, 10, 8, 9, 1, 1}\n*)\n\n\nThe plot below shows that the time spent by NSolve is roughly the same for working precisions below machine precision, after which the timing rises. The timing continues to rise as working precision is increased beyond machine precision, although the rate is slow.\n\nNeeds[\"GeneralUtilities\"]\n\ng[n_] := NSolve[x^15 - 3 x^4 + 3 x^3 - 4 x^2 + 15 x == 7, x, WorkingPrecision -> n];\nBenchmarkPlot[{g[#] &},\n# &,\nRange[4, 24, 2],\nPlotRange -> {{3, 31}, All}]", null, "Conclusion\n\nI do not think you can compute all solutions faster than with MachinePrecision. The setting of WorkingPrecision seems to have an palpable effect only for settings above machine precision, something I did not appreciate before. I suspect that having a separate PrecisionGoal would not meaningfully speed up the computation, mainly because I assume once you're close to the root, a couple of iterations of Newton's method yields results accurate to machine precision. For polynomials this would not be a time-consuming calculation. But it's only a guess.\n\nCaveat: In this exploration I looked only at univariate polynomial equations. Different types of systems probably use different algorithms, which probably have different behaviors.\n\nNote: There is a SystemOptions[] option \"NSolveOptions\" -> {\"Tolerance\" -> 0}, but changing the setting made no difference. I do not know what the option is for.\n\n• All accurate, I think. For multivariate I'd say the situation is even more tilted toward lowering precision not allowing for substantial speed gain. – Daniel Lichtblau Apr 4 '15 at 17:36\n• Some explanation of that mysterious Tolerance option can be found here – Daniel Lichtblau Apr 4 '15 at 19:48\n\nGive this a try:\n\neq1 = x^2 + y^3 + 10 y^2 - 40 x == 1;\neq2 = 2 x + 3 y - 20 y^2 == -10;\nDo[a1 = NSolve[{eq1, eq2}, {x, y}, Reals], {100}] // Timing\n\neq1 = SetPrecision[eq1, 4];\neq2 = SetPrecision[eq2, 4];\nDo[a2 = NSolve[{eq1, eq2}, {x, y}, Reals], {100}] // Timing\n\n{Sort@a1,Sort@a2}\n\n(*\n\n{1.326008, Null}\n{0.826805, Null}\n\n{{{x -> 0.0712826, y -> -0.641068}, {x -> 0.146691, y -> 0.796314},\n{x -> 38.5495, y -> 2.1632}, {x -> 39.1885, y -> -2.02844}},\n{{x -> 0.07, y -> -0.6411}, {x -> 0.15, y -> 0.7963},\n{x -> 38.55, y -> 2.163}, {x -> 39.19, y -> -2.028}}}\n\n*)\n\n\nSpeed difference depends on equations, but I've used this to speed things where high precision is not needed...\n\nBecause WorkingPrecision determines the minimum number of digits used in the calculations, you can reduce it, if you hope to reduce time by reducing accuracy. However, WorkingPrecision less than MachinePrecision, the default value, is unlikely to have a large effect on timing, as you can see from,\n\nTable[First@Timing[Do[NSolve[x^5 - 3 x^4 + 3 x^3 - 4 x^2 + 15 x == 7,\nWorkingPrecision -> wp], {i, 1000}]], {wp, 3, 15, 3}]\n(* {0.984375, 0.984375, 0.968750, 0.984375, 1.031250} *)\n\n• The problem with decreasing WorkingPrecision is that then it isn't clear what precision the output of NSolve has. I'd rather adjust that, similar to how PrecisionGoal works for other functions. – Lauren Pearce Feb 4 '15 at 6:22\n• You can query the precision of the output with Precision, as described here. The thrust of my Answer, though, is that you will not save much time with WorkingPrecison set less than MachinePrecision`. – bbgodfrey Feb 4 '15 at 13:13" ]
[ null, "https://i.stack.imgur.com/OOnHP.png", null ]
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https://www.gradesaver.com/textbooks/math/other-math/CLONE-547b8018-14a8-4d02-afd6-6bc35a0864ed/chapter-6-percent-6-4-using-proportions-to-solve-percent-problems-6-4-exercises-page-419/46
[ "## Basic College Mathematics (10th Edition)\n\nPercent= 39;whole= 3020. $\\frac{x}{3020}=\\frac{39}{100}$ Cross products: $100x=117780$ Solve for x. Round to the nearest number: $x=1178$" ]
[ null ]
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https://jacksimpson.co/r-multiple-plots/
[ "Home » Multiple plots in figures with R\n\n# Multiple plots in figures with R\n\nThe other day I was working with R in a Jupyter Notebook when I discovered that I needed to include multiple figures in the same plot.\n\nSurprisingly, R doesn’t include this capability out of the box, so I went searching and found this function that does the job. I’ve included the code below for my own future reference in case the linked site ever disappears.\n\n```multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {\nlibrary(grid)\n\n# Make a list from the ... arguments and plotlist\nplots <- c(list(...), plotlist)\n\nnumPlots = length(plots)\n\n# If layout is NULL, then use 'cols' to determine layout\nif (is.null(layout)) {\n# Make the panel\n# ncol: Number of columns of plots\n# nrow: Number of rows needed, calculated from # of cols\nlayout <- matrix(seq(1, cols * ceiling(numPlots/cols)),\nncol = cols, nrow = ceiling(numPlots/cols))\n}\n\nif (numPlots==1) {\nprint(plots[])\n\n} else {\n# Set up the page\ngrid.newpage()\npushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))\n\n# Make each plot, in the correct location\nfor (i in 1:numPlots) {\n# Get the i,j matrix positions of the regions that contain this subplot\nmatchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))\n\nprint(plots[[i]], vp = viewport(layout.pos.row = matchidx\\$row,\nlayout.pos.col = matchidx\\$col))\n}\n}\n}\n```\n\nThen to call the function, you just have to pass it the plots:\n\n```multiplot(p1, p2, p3, p4, cols=2)\n```" ]
[ null ]
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https://sage.math.clemson.edu:34567/home/pub/737/
[ "# Math Club 2015-09-11\n\n## 2273 days ago by calkin\n\nA=plot(x^2-2, (x,0,3)) show(A)\nB=plot(2*x-3,(x,0,3),color='red') show(A+B)\ndef newton_iterate(x): a=x/2+1/x return(a)\nx0=1 xlist=[x0] N=10 for j in range(N): current_x = xlist[-1] new_x = current_x/2 + 1/current_x xlist.append(new_x) for appr in xlist: print appr\nprint sqrt(2.) for appr in xlist: print appr.n(),(appr -sqrt(2)).n(digits=14)\nN = 20 a_list=[2,3] b_list=[1,2] for i in range(1,N): a=a_list[i] b=b_list[i] a_list.append(a^2 + 2*b^2) #b_list.append(2*a*b) #b_list = b_list + [2*a*b] b_list += [2*a*b]\nfor j in range(len(b_list)): print exp((log(b_list[j])/2^j).n())\nfor j in range(len(b_list)): print (b_list[j]/(1+sqrt(2))^(2^j)).n()\nfor i in range(10): print b_list[i], floor(sqrt(2)/4*(1+sqrt(2))^(2^i))\nN = 15 a_list= b_list= for i in range(N): a=a_list[i] b=b_list[i] a_list.append(a^2 + 4*b^2) #b_list.append(2*a*b) #b_list = b_list + [2*a*b] b_list += [2*a*b]\nfor j in range(5): print j, a_list[j],b_list[j]\n\n## Continuing our investigations into the approximations using Newton's method of $\\sqrt{4}$.\n\nStarting with $x_0=1$, $x_1=5/2$, and\n\n$x_{n+1} = \\frac{x_n}{2} + \\frac{2}{x_n}$\n\nwe can write\n\n$x_n = \\frac{a_n}{b_n}$\n\nin which $a_n, b_n$ are integers with no common factors.  Then\n\n$\\frac{a_{n+1}}{b_{n+1}} = \\frac{a_n}{2b_n} + \\frac{2b_n}{a_n} = \\frac{a_n^2 + 4 b_n^2}{2a_nb_n}$\n\nNow, for $n\\geq 1$, we have $a_n$ is odd  and $b_n$ is even, so $a_n^2+ 4b_n^2$ is odd.  Furthermore, any odd prime divisor of $2a_nb_n$ must {\\em fail} to divide $a_n^2 + 4b_n^2$, since $a_n$ and $b_n$ have no common factors.\n\nHence\n\n$a_{n+1} = a_n^2 + 4b_n^2 \\mbox{ and } b_{n+1} = 2a_nb_n .$\n\n## Proving that $an-2b_n =1$.\n\nWe'll prove this by induction.  Suppose that $a_n - 2b_n=1$.  Then\n\n$a_{n+1} - 2 b_{n+1} = (a_n^2 + 4 b_n^2) -2 (2a_nb_n)$\n\n$= (a_n^2 + 4 b_n^2) - 2(4 a_n b_n)$\n\n$= a_n^2- 4 a_nb_n + 4 b_n^2 = (a_n-2b_n)^2 = 1^2 = 1$\n\n## How big is $x_n - 2$?\n\n$x_n-2 = \\frac{a_n}{b_n} - 2 = \\frac{a_n -2b_n }{b_n} = \\frac{1}{b_n}.$" ]
[ null ]
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https://boeingconsult.com/Environment/thermal-calculations-a.html
[ "## General thermal requirements\n\n Heat flow Thermal conductance Thermal conductivity Thermal resistance\n\nThe First Law of Thermodynamics is the low of conservation of energy. The second law states that heat flows form hotter body to a cooler body. The easiest way to conserve energy would be to accept a lower temperature inside in winter and a higher temperature in summer. People should be encouraged to wear warmer clothes in winter to safe on heating costs. Cooling costs in summer could be reduce by accepting an inside temperature adjusted to the outside temperature. If we accept a temperature range from 22°C to 26°C related to the outside temperature the cooling cost would be much less.\n\n### Conductivity and thermal resistance\n\nAs show in Figure 1 heat will flow through a building material until equilibrium is reached (Law of Thermodynamics). The heat travels trough the material by conductivity. The thermal conductance (C) is measured in W/m²×°C.", null, "Figure 1\n\n[top]\n\n### Thermal conductance\n\nThe thermal conductance is the time rate of heat flow through a material of a given thickness per unit temperature gradient across the material. Also known as Heat Transfer Coefficient.", null, "Figure 2 Consider a building material where the temperature difference between to parallel faces one metre apart is 1°C. If the heat flows at a rate of 1 Watt per square metre through this one metre thickness, the material has a thermal conductivity of 1 W/m²×°C (1 Watt per metre thickness per 1°C) (This is useful for comparing materials.)\n\n[top]\n\n### Thermal conductivity\n\nVery similar to, and often confused with, Conductance as described above. The difference to be noted is that Conductance involves area while Conductivity involves length.\n\nFor most building materials you will find standard figures that enables you to calculate an R value for a given thickness.\n\nThe thermal conductivity is also known as the k-value (or as SI unit", null, ")\n\nApproximate k-values in W / m °C of the thermal conductivity's of some substances are shown in Table 1\n\nTable 1*\n\n Concrete 1.44 Plaster (cement) 0.65 Clay brick 1.1 Polystyrene 0.036 Glass 0.7 Polyurethane foam 0.025 Glass fibre (batts) 0.042 Softwood 0.11 Hardwood 0.19 Steel 50 Motionless dry air 0.023 Water 0.6\n(*Be aware that some of the above figures can have a range\nand vary; depending on the source.)\n\nThe SI units for the figures in Table 1 are:\n\nwatt / metre degree kelvin [W / m °K]\n\nIt makes no difference whether we use degree celsius or degree kelvin, because the temperature difference between 1 °C is the same as 1 °K\n\n[top]\n\n### Thermal resistance\n\nThermal resistance (R) is the reciprocal of thermal conductance. It is a measure of the resistance to heat transmission across a material, or a structure.\n\nThe \"R value\" of a wall or an insulating material is its resistance to the flow of heat energy. The higher the R-value, the higher the energy efficiency. The R-value is the reciprocal of the U-value", null, "&", null, "Thermal conductivity figures refer always to one metre thickness of a specific building material. To calculate the R-value of a particular material we must divide the thickness of the material by the k-value.\n\nThe thermal resistance (R) of single layer is calculated by dividing the layer thickness (s) by the k-value:", null, "s = thickness in metres\nk = thermal conductivity\n The total thermal resistance (R) of a given building element can be calculated by adding each single element (material) together as shown in the formula below: Standard Formula", null, "fo = external surface resistance  fi = internal surface resistance  k = conductivity of material  s = material thickness in metres\nThe fo and fi in the above equation stand for external and internal surface resistance. This air film accounts for the effects of the convective and radiative components of the heat exchange at the surface. The inside air film layer (fi) is considered to be still air and the outside layer (fo)is considered to be moving air. Typical normal figures are:\n\nfo = 0.4 to 0.6\nfi = 0.12 to 0.15\n\nPlease note that the American publication give R-values in imperial units. To convert the American units in metric unit you must multiply them by 0.176 or divide our R-values by 0.176 to compare them with the American figures. (e.g. American R 8 is R 1.4 in metric units)\n\nAn example calculation of the R-value is outlined below for:\n\n a) Wall 1 200 mm concrete wall b) Wall 2 200 mm concrete wall  with a 100 mm polystyrene insulation.\n\nUsing the above formula and the figure from Table 1 the R-value is:\n\n a)", null, "b)", null, "Remember that the unit for the material thickness must be in metre.\n\nThe figure below shows the relevance of the R-values graphically.", null, "(a)                                               (b)\nFigure 3\n\nThe diagrams above are vertical slices through exterior walls. Figure 3 (b) shows how the position of the external insulation helps to keep the wall structure and interior surfaces warm. The range of the outdoor air temperature in (a) and (b) is 45°C (-5°C Winter and +40°C Summer) and the indoor air temperature is kept constant at 20°C (Summer and Winter). The thick solid diagonal lines show the temperature within the wall at various points. Note the warmth of the wall structure in (b); it's the external insulation at work.\n\nThe inside surface of the wall is nearer to the temperature of the inside air. Thus, the building's occupants do not gain or lose heat as readily by being near surfaces that are hotter or colder than the indoor air. (Keeping the wall warm also has the advantage of keeping water pipes in the wall from freezing in the winter.)\n\nFigure 3 also indicates that with an external yearly temperature range of 45° (-5°C Winter and 40°C Summer) the thermal stress in the material (a) is extreme compared to (b) and of course for (a) much more energy is needed to maintain a comfortable internal surface temperature throughout the year.\n\n[top]" ]
[ null, "https://boeingconsult.com/Environment/conductivity.gif", null, "https://boeingconsult.com/Environment/conductance.jpg", null, "https://boeingconsult.com/Environment/lambda.lc.gif", null, "https://boeingconsult.com/Environment/Ru.gif", null, "https://boeingconsult.com/Environment/Ur.gif", null, "https://boeingconsult.com/Environment/eqa2tr.gif", null, "https://boeingconsult.com/Environment/eqa3tr.gif", null, "https://boeingconsult.com/Environment/eqa4tr-a.gif", null, "https://boeingconsult.com/Environment/eqa4tr-b.gif", null, "https://boeingconsult.com/Environment/temp-gradient.gif", null ]
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https://www.numbers.education/8786.html
[ "Is 8786 a prime number? What are the divisors of 8786?\n\n## Parity of 8 786\n\n8 786 is an even number, because it is evenly divisible by 2: 8 786 / 2 = 4 393.\n\nFind out more:\n\n## Is 8 786 a perfect square number?\n\nA number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 8 786 is about 93.734.\n\nThus, the square root of 8 786 is not an integer, and therefore 8 786 is not a square number.\n\n## What is the square number of 8 786?\n\nThe square of a number (here 8 786) is the result of the product of this number (8 786) by itself (i.e., 8 786 × 8 786); the square of 8 786 is sometimes called \"raising 8 786 to the power 2\", or \"8 786 squared\".\n\nThe square of 8 786 is 77 193 796 because 8 786 × 8 786 = 8 7862 = 77 193 796.\n\nAs a consequence, 8 786 is the square root of 77 193 796.\n\n## Number of digits of 8 786\n\n8 786 is a number with 4 digits.\n\n## What are the multiples of 8 786?\n\nThe multiples of 8 786 are all integers evenly divisible by 8 786, that is all numbers such that the remainder of the division by 8 786 is zero. There are infinitely many multiples of 8 786. The smallest multiples of 8 786 are:\n\n## Numbers near 8 786\n\n### Nearest numbers from 8 786\n\nFind out whether some integer is a prime number" ]
[ null ]
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https://crypto.stackexchange.com/questions/24155/exponentiation-with-fully-homomorphic-encryption?noredirect=1
[ "# Exponentiation with fully homomorphic encryption [duplicate]\n\nI have often heard that because a fully homomorphic encryption scheme allows for both additions and multiplications on encrypted data, most other operations can be simulated. I don't understand how exponentiation can be done, i.e., how to build $E(x^y)=E(x)^{E(y)}$ ?\n\nIf it can't be done, is there a FHE that support $E(x) . E(y) = E(x^y)$ where the operation on encrypted data is not necessarily exponentiation?\n\n• If you know the maximum number of bits in $y$, you can get the binary expansion of $y$ and then do the traditional square-and-multiply. – mikeazo Feb 27 '15 at 2:58\n• – Thomas Feb 27 '15 at 5:12\n• Calculating $y-1$ times the product $E(x)E(x)$ gives us $E(x)^{E(y)}$. And it decrypts to $x^y$, since $E(x) \\cdot E(x) \\cdot .. \\cdot E(x) = E(x \\cdot x \\cdot .. \\cdot x) = E(x^y)$. – Hilder Vitor Lima Pereira Feb 27 '15 at 16:14\n• @VitorLima, the problem with \"y-1 times the product E(x)E(x)\" is that you don't know when you reach zero, i.e., you don't know when to stop. This question is very related to this discussion. – mikeazo Feb 27 '15 at 20:36\n• @VitorLima I don't think you need to know $y$ to do what you suggested, if encryption is FHE, you can do $E(y-1)$. I think the point mikeazo was making is that at some point, you will get E(0), however, due to semantic security, you wouldn't be able to tell E(0) from E(something else). – nullgraph Feb 27 '15 at 21:35" ]
[ null ]
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https://www.radiomuseum.org/tubes/tube_41.html
[ "", null, "", null, "# 41\n\nID = 2968\nCountry:\nUnited States of America (USA)\nBrand:\n##### Common type USA tube/semicond.\nTube type:  Vacuum Pentode   Power/Output\nIdentical to 41 = ER41 = VT-48 = PH41 = NU-41 = PA\nSimilar Tubes\nOther shape (e.g. bulb type):\n41S\nNormally replaceable-slightly different:\n38041 ; 41E\nOther class quality (otherwise equal):\nCV608\nOther base:\n6AR5 ; 6K6G ; 6K6GT ; 7B5 ; EL1\nOther base and other heater:\nEL2\nFirst year Sep.1932 -- Collector info (Sammler) Backed up by >20 models.\nFirst Source (s)\n1933 : The AWA Journal Vol. #7\nPredecessor Tubes 38   89   PA\nSuccessor Tubes 6K6G   6AR5   6K6GT   7B5   EL2   EL1\n\nBase 6-Pin-Base U6A, old, USA (Codex=Kdo)\nFilament Vf 6.3 Volts / If 0.4 Ampere / Indirect / Specified voltage AC/DC\nDescription\n\n* RMA/JEDEC register record available by courtesy of TCA* - This tube was already listed by several manufacturers when RMA started its standardization in 1934. In order to characterize popular receiving types, manufacturers were asked to supply average characteristics as measured on production lots. Here are the filled answer forms supplied by Radio Valve Co., Raytheon, Sparton, Triad, Tung Sol, Ken Rad, Hytron and Arcturus. Full record is downloadable here.\n\nDimensions (WHD)\nincl. pins / tip\nx 106 x 39 mm / x 4.17 x 1.54 inch\nWeight 42 g / 1.48 oz\nTube prices 2 Tube prices (visible for members only)\nInformation source Essential Characteristics, GE 1973\nTaschenbuch zum Röhren-Codex 1948/49", null, "41: Courtesy Bureau Belper (De Muiderkring, Bussum) Anonymous 10 Collector", null, "41: Telefunken Werkstattbuch Wolfgang Bauer More ...", null, "Just Qvigstad", null, "41: Sylvania Technical Manual Peter Hoddow More ...\n Usage in Models 1= 1932?? ; 5= 1932? ; 27= 1932 ; 19= 1933?? ; 55= 1933? ; 91= 1933 ; 28= 1934?? ; 45= 1934? ; 174= 1934 ; 31= 1935?? ; 51= 1935? ; 170= 1935 ; 32= 1936?? ; 60= 1936? ; 153= 1936 ; 41= 1937?? ; 44= 1937? ; 266= 1937 ; 49= 1938?? ; 41= 1938? ; 201= 1938 ; 55= 1939?? ; 43= 1939? ; 87= 1939 ; 43= 1940?? ; 22= 1940? ; 52= 1940 ; 28= 1941?? ; 7= 1941? ; 13= 1941 ; 20= 1942?? ; 9= 1942? ; 2= 1942 ; 1= 1944? ; 1= 1945 ; 1= 1946?? ; 8= 1947?? ; 2= 1948?? ; 1= 1949?? ; 1= 1950?? ; 1= 1951 ; 1= 1954 ; 5= 9999\n\nQuantity of Models at Radiomuseum.org with this tube (valve, valves, valvola, valvole, válvula, lampe):1987\n\n### Collection of", null, "", null, "41" ]
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https://wikiwaves.org/wiki/index.php?title=Fundamental_Solution_for_thin_plates&diff=next&oldid=11911
[ "# Difference between revisions of \"Fundamental Solution for thin plates\"\n\n## Introduction\n\nOn this page, we aim to derive the Green's function for a thin uniform plate. This derivation relies heavily on concepts discussed in Boyling 1996. We seek the fundamental solution for the Biharmonic equation in $\\displaystyle{ \\mathbb{R}^2 \\, }$, which is taken to be of the form\n\n$\\displaystyle{ \\left(\\Delta^2 - k^2\\right) u =0, }$\n\nwhere $\\displaystyle{ u \\, }$ is the displacement, $\\displaystyle{ k \\, }$ is the wavenumber, and $\\displaystyle{ \\Delta = \\partial_r^2 + \\frac{1}{r}\\partial_r, }$ in polar coordinates.\n\n## Linear Operators\n\nWe consider the operator $\\displaystyle{ P(\\Delta) = \\left(\\Delta^2 - k^4\\right) = \\left(\\Delta - (ik)^2\\right) \\left(\\Delta -k^2\\right) }$, whereas Boyling considers more general linear operators of the form\n\n$\\displaystyle{ P(\\lambda) = c(\\lambda - \\lambda_1)^{m_1}(\\lambda - \\lambda_2)^{m_2} \\ldots (\\lambda - \\lambda_p)^{m_p}, }$\n\nwhich for our case, is identical when $\\displaystyle{ c=1 \\, }$, $\\displaystyle{ \\lambda_1 = (ik)^2 \\, }$, $\\displaystyle{ \\lambda_2 = k^2 \\, }$, $\\displaystyle{ m_1 = m_2 = 1 \\, }$, and $\\displaystyle{ m_3=m_4=\\ldots =0 \\, }$.\n\nThe reciprocal of $\\displaystyle{ P(\\lambda) \\, }$ is taken to be of the form\n\n$\\displaystyle{ \\frac{1}{P(\\lambda)} = \\sum_{q=1}^{p} \\sum_{n=1}^{m_q} \\frac{c_{qn}}{(\\lambda - \\lambda_q)^n}. }$\n\nwhere\n\n$\\displaystyle{ c_{qn} = \\lim_{\\lambda \\rightarrow \\lambda_q} \\frac{1}{(m_q - n)!} \\frac{\\partial^{m_q - n}}{\\partial \\lambda^{m_q-n}} \\left[\\frac{(\\lambda - \\lambda_q)^{m_q}}{P(\\lambda)}\\right]. }$\n\nIt is straightforward to compute the $\\displaystyle{ c_{qn} \\, }$ coefficients\n\n\\displaystyle{ \\begin{align} c_{11} &= \\lim_{\\lambda \\rightarrow \\lambda_q} \\frac{1}{(0)!} \\frac{\\partial^{0}}{\\partial \\lambda^{0}} \\left[\\frac{(\\lambda - \\lambda_1)}{P(\\lambda)}\\right] = \\lim_{\\lambda \\rightarrow (ik)^2} \\frac{1}{\\lambda - \\lambda_2} = - \\frac{1}{2 k^2}, \\\\ c_{21} &= \\frac{1}{2 k^2}, \\end{align} }\n\nas well as determining a corresponding quantity $\\displaystyle{ P_{qn} \\, }$ such that $\\displaystyle{ \\sum_{q=1}^{p} \\sum_{n=1}^{m_q} c_{qn}P_{qn} = 1 }$, where\n\n$\\displaystyle{ P_{qn}(\\lambda) \\left[\\lambda - \\lambda_q\\right]^n = P(\\lambda), \\quad \\mbox{for all q,n}. }$\n\nThat is, $\\displaystyle{ P_{11} = (\\lambda - k^2) \\, }$ and $\\displaystyle{ P_{21} = (\\lambda - (ik)^2) \\, }$.\n\n## Determining the Green's function\n\nIn order to compute the Green's function for polynomials in the Laplacian, we express our unknown Green's function in terms of the fundamental solution of Helmholtz's equation:\n\n$\\displaystyle{ G(r) = \\sum_{q=1}^{p} \\sum_{n=1}^{m_q} c_{qn} G_{n,\\lambda_q}(r) = c_{11} G_{1,\\lambda_1}+ c_{21} G_{1,\\lambda_2}. }$\n\nUsing the Green's function for the Helmholtz Equation\n\n$\\displaystyle{ G_{1,\\beta} = \\frac{i}{4} H_0^{(1)} (\\beta r), }$\n\n(where $\\displaystyle{ H_0^{(1)} \\, }$ denotes Hankel functions of the first kind) which incorporates the Sommerfeld radiation condition\n\n$\\displaystyle{ \\lim_{r \\rightarrow \\infty} r^{1/2} \\left(\\frac{\\partial}{\\partial r} - ik \\right)G = 0, }$\n\nwe obtain the final expression\n\n\\displaystyle{ \\begin{align} G(r) &= \\left(-\\frac{1}{2 k^2}\\right)\\left(\\frac{i}{4}H_0^{(1)}(ikr)\\right) + \\left(\\frac{1}{2 k^2}\\right)\\left(\\frac{i}{4}H_0^{(1)}(kr)\\right) \\\\ &= \\frac{i}{8 k^2} \\left[H_0^{(1)}(kr) - H_0^{(1)}(ikr) \\right]. \\end{align} }\n\nThis is the fundamental solution for our governing equation above.\n\n## Behaviour at $\\displaystyle{ r=0 }$\n\nTo determine the solution at $\\displaystyle{ r \\rightarrow 0 }$ (where the above expression is singular), the following identities from Abramowitz and Stegun 1964 are used\n\n\\displaystyle{ \\begin{align} H_0^{(1)}(z) &= J_0(z) + i Y_0(z), \\\\ K_0(z) &= \\frac{\\pi i}{2} H_0^{(1)}(iz), \\quad -\\pi \\lt arg(z) \\leq \\pi/2, \\\\ K_0(z) &= \\int_{0}^{\\infty} \\cos \\left[z\\sinh \\theta \\right]d \\theta, \\\\ Y_0(z) &= \\frac{1}{\\pi}\\int_0^\\pi \\sin \\left[z \\sin \\theta \\right] d \\theta - \\frac{1}{\\pi} \\int_0^\\infty 2 e^{-z \\sinh \\theta} d \\theta, \\ | arg(z) | \\lt \\frac{\\pi}{2} \\end{align} }\n\nfrom pages 358, 375, 376, and 360 respectively.\n\nLet us consider\n\n\\displaystyle{ \\begin{align} &H_0^{(1)}(kr) - H_0^{(1)}(ikr) \\\\ =& J_0(kr) + i Y_0(kr) + \\frac{2i}{\\pi} K_0(kr) \\\\ =& J_0(kr) + \\frac{i}{\\pi}\\int_0^\\pi \\sin \\left(kr \\sin \\theta \\right) d \\theta - \\frac{i}{\\pi} \\int_0^\\infty 2 e^{-kr \\sinh \\theta} d \\theta + \\frac{2i}{\\pi} \\int_{0}^{\\infty} \\cos \\left( kr \\sinh \\theta \\right)d \\theta \\end{align} }\n\nwhere introducing the limit yields\n\n\\displaystyle{ \\begin{align} \\lim_{r \\rightarrow 0}& J_0(kr) = 1, \\\\ \\lim_{r \\rightarrow 0}& \\sin \\left(kr \\sin \\theta \\right) = 0, \\\\ \\lim_{r \\rightarrow 0}& e^{-kr \\sinh \\theta} =1, \\\\ \\lim_{r \\rightarrow 0}& \\cos \\left( kr \\sinh \\theta \\right) = 1. \\end{align} }\n\nConsequently\n\n$\\displaystyle{ \\lim_{r \\rightarrow 0} \\left( H_0^{(1)}(kr) - H_0^{(1)}(ikr) \\right) = \\lim_{r \\rightarrow 0} J_0(kr) -\\frac{2i}{\\pi}\\int_{0}^{\\infty} 1 d\\theta + \\frac{2i}{\\pi}\\int_{0}^{\\infty} 1 d\\theta = 1, }$\n\nwhich then allows us to determine that\n\n$\\displaystyle{ \\lim_{r \\rightarrow 0} G(r) = \\frac{i}{8 k^2}. }$\n\n## Solution\n\nThe fundamental solution for a thin uniform plate in $\\displaystyle{ \\mathbb{R}^2 \\, }$ governed by\n\n$\\displaystyle{ \\left(\\Delta^2 - k^2\\right) u =0, }$\n\nis defined as follows\n\n\\displaystyle{ G(r) = \\left\\{ \\begin{align} &\\frac{i}{8 k^2} \\left[H_0^{(1)}(kr) - H_0^{(1)}(ikr) \\right] &\\mbox{for} \\ r\\gt 0, \\\\ &\\frac{i}{8 k^2} &\\mbox{for } \\ r=0. \\end{align} \\right. }" ]
[ null ]
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https://answers.everydaycalculation.com/lcm/24-6
[ "Solutions by everydaycalculation.com\n\n## What is the LCM of 24 and 6?\n\nThe lcm of 24 and 6 is 24.\n\n#### Steps to find LCM\n\n1. Find the prime factorization of 24\n24 = 2 × 2 × 2 × 3\n2. Find the prime factorization of 6\n6 = 2 × 3\n3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:\n\nLCM = 2 × 2 × 2 × 3\n4. LCM = 24\n\nMathStep (Works offline)", null, "Download our mobile app and learn how to find LCM of upto four numbers in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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https://www.dsprelated.com/freebooks/pasp/Torque.html
[ "### Torque", null, "", null, "When twisting things, the rotational force we apply about the center is called a torque (or moment, or moment of force). Informally, we think of the torque as the tangential applied force", null, "times the moment arm (length of the lever arm)", null, "", null, "(B.26)\n\nas depicted in Fig.B.7. The moment arm is the distance from the applied force to the point being twisted. For example, in the case of a wrench turning a bolt,", null, "is the force applied at the end of the wrench by one's hand, orthogonal to the wrench, while the moment arm", null, "is the length of the wrench. Doubling the length of the wrench doubles the torque. This is an example of leverage. When", null, "is increased, a given twisting angle", null, "is spread out over a larger arc length", null, ", thereby reducing the tangential force", null, "required to assert a given torque", null, ". For more general applied forces", null, ", we may compute the tangential component", null, "by projecting", null, "onto the tangent direction. More precisely, the torque", null, "about the origin", null, "applied at a point", null, "may be defined by", null, "(B.27)\n\nwhere", null, "is the applied force (at", null, ") and", null, "denotes the cross product, introduced above in §B.4.12. Note that the torque vector", null, "is orthogonal to both the lever arm and the tangential-force direction. It thus points in the direction of the angular velocity vector (along the axis of rotation). The torque magnitude is", null, "where", null, "denotes the angle from", null, "to", null, ". We can interpret", null, "as the length of the projection of", null, "onto the tangent direction (the line orthogonal to", null, "in the direction of the force), so that we can write", null, "where", null, ", thus getting back to Eq.", null, "(B.26).\nNext Section:\nNewton's Second Law for Rotations\nPrevious Section:\nRotational Kinetic Energy Revisited" ]
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http://blog.ivank.net/quadtree-visualization.html
[ "", null, "### Hot to use it\n\nClick on the first or second bitmap (A or B) to edit it. Quadtrees of bitmaps are drawn on the right side. Then you can rebuild the last bitmap (C) depending on A and B by clicking the right button.\n\nQuadtree is a data strucutre, which is used to representa bitmap as a tree. Conversion from a bitmap to the tree can be described as follows:\n\n• a tree for a constatn-colored bitmap is a leaf of this color\n• otherwise it is an inner node, it's for children are trees for it's for quadrants\n\n## The code\n\nA qadtree node has a method for copying the tree, QNode.Copy(bool p). When \"p\" is true, it inverts it's colors (\"negation\").\n\n### Logic operations on trees\n\nfunction GetLogic(a, b, op) // tree a, tree b, operation, returns tree\n{\nif(a.leaf)\n{\nif(op==\"and\") return (a.black ? b.Copy(false) : a.Copy(false));\nif(op==\"or\" ) return (a.black ? a.Copy(false) : b.Copy(false));\nif(op==\"xor\") return (a.black ? b.Copy(true ) : b.Copy(false));\nif(op==\"min\") return (a.black ? b.Copy(true ) : a.Copy(false));\n}\nelse if(b.leaf)\n{\nif(op==\"and\") return (b.black ? a.Copy(false) : b.Copy(false));\nif(op==\"or\" ) return (b.black ? b.Copy(false) : a.Copy(false));\nif(op==\"xor\") return (b.black ? a.Copy(true ) : a.Copy(false));\nif(op==\"min\") return (b.black ? b.Copy(true ) : a.Copy(false));\n}\nelse\n{\nvar t = new QNode();\nt.c1 = GetLogic(a.c1, b.c1, op);\nt.c2 = GetLogic(a.c2, b.c2, op);\nt.c3 = GetLogic(a.c3, b.c3, op);\nt.c4 = GetLogic(a.c4, b.c4, op);\nreturn t;\n}\n}" ]
[ null, "http://www.ivank.net/blogspot/thumbs/qtree.jpg", null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.6368251,"math_prob":0.86135757,"size":1635,"snap":"2020-10-2020-16","text_gpt3_token_len":475,"char_repetition_ratio":0.18270999,"word_repetition_ratio":0.03816794,"special_character_ratio":0.31743118,"punctuation_ratio":0.23762377,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9948014,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-06T19:24:41Z\",\"WARC-Record-ID\":\"<urn:uuid:39d78076-19ca-4d90-84f7-b561847ffa16>\",\"Content-Length\":\"9196\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:17bb8eeb-1bda-4404-b080-8d8e7830f362>\",\"WARC-Concurrent-To\":\"<urn:uuid:d8c7bf4a-033c-4972-ae17-f76af08b5587>\",\"WARC-IP-Address\":\"176.227.168.27\",\"WARC-Target-URI\":\"http://blog.ivank.net/quadtree-visualization.html\",\"WARC-Payload-Digest\":\"sha1:WW6ZMRRVNSM2LWZAE42ZCL2SIWL5EYMN\",\"WARC-Block-Digest\":\"sha1:MTFZVCSBL7EHFTGDEKSQ43PF4SJOGTM3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371656216.67_warc_CC-MAIN-20200406164846-20200406195346-00451.warc.gz\"}"}
http://www.numbersaplenty.com/141140
[ "Search a number\nBaseRepresentation\nbin100010011101010100\n321011121102\n4202131110\n514004030\n63005232\n71125326\noct423524\n9234542\n10141140\n119704a\n1269818\n134c31c\n1439616\n152bc45\nhex22754\n\n141140 has 12 divisors (see below), whose sum is σ = 296436. Its totient is φ = 56448.\n\nThe previous prime is 141131. The next prime is 141157. The reversal of 141140 is 41141.\n\nAdding to 141140 its reverse (41141), we get a palindrome (182281).\n\nSubtracting from 141140 its reverse (41141), we obtain a palindrome (99999).\n\nIt can be written as a sum of positive squares in 2 ways, for example, as 111556 + 29584 = 334^2 + 172^2 .\n\nIt is a congruent number.\n\nIt is an unprimeable number.\n\nIt is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 3509 + ... + 3548.\n\nIt is an arithmetic number, because the mean of its divisors is an integer number (24703).\n\n2141140 is an apocalyptic number.\n\n141140 is a gapful number since it is divisible by the number (10) formed by its first and last digit.\n\nIt is an amenable number.\n\n141140 is an abundant number, since it is smaller than the sum of its proper divisors (155296).\n\nIt is a pseudoperfect number, because it is the sum of a subset of its proper divisors.\n\n141140 is a wasteful number, since it uses less digits than its factorization.\n\n141140 is an evil number, because the sum of its binary digits is even.\n\nThe sum of its prime factors is 7066 (or 7064 counting only the distinct ones).\n\nThe product of its (nonzero) digits is 16, while the sum is 11.\n\nThe square root of 141140 is about 375.6860391337. The cubic root of 141140 is about 52.0654993163.\n\nThe spelling of 141140 in words is \"one hundred forty-one thousand, one hundred forty\", and thus it is an iban number." ]
[ null ]
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https://programs.programmingoneonone.com/2021/07/c-program-to-assign-return-value-of-function-to-variable.html
[ "In this tutorial, we are going to write a C program to assign the return value of a function to another variable in C Programming with practical program code and step-by-step full complete explanation.\n\n## C program to assign the return value of the function to a variable.\n\n```\n#include<stdio.h>\n#include<conio.h>\n\nvoid main()\n{\nint input(int);\nint x;\n\nclrscr();\n\nx=input(x);\n\nprintf(\"X=%d\",x);\n}\n\nint input(int k)\n{\nprintf(\"Enter value of x=\");\nscanf(\"%d\",&k);\n\nreturn(k);\n}\n```\n\n### Output\n\n```\nEnter value of x=5\nx=5\n```" ]
[ null ]
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https://math.stackexchange.com/questions/734773/fracdydx-3y2-3-general-solution
[ "# $\\frac{dy}{dx} = 3y^{2/3}$ general solution? [closed]\n\nWhat's the general solution of $\\frac{dy}{dx} = 3y^{2/3}$ ? Im pretty sure this is a separable equation, but I'm not sure how to go forward? Just multiply by $dx$ and $\\frac{1}{3y^{2/3}}$ well then I get $y^{1/3} =x+ C$, correct?\n\n• You are almost correct. It should be $3y^{1/3}=x+c$ – Guy Apr 1 '14 at 4:38\n• Note that the special solution $y$ identically $0$ is not picked up by the \"general\" solution. – André Nicolas Apr 1 '14 at 6:44\n• Also note that the solution to the initial value problem with $y(0)=0$ is non-unique, since (for any $k>0$) you can take $y(x)=0$ for $x<k$ and then $y(x)=(x-k)^3$. – Hans Lundmark Apr 1 '14 at 6:53\n\nOn the left hand side you get , $3y^{\\frac{1}{3}}$ and on the right hand side you get, $x+C$ $\\Rightarrow 3y^{\\frac{1}{3}}=x+C \\Rightarrow y = (x+C)^3/27$.\n• \"On the left hand side you get, $y^{\\frac{1}{3}}$\" Sorry but I do not, unless $y\\ne0$. – Did Apr 10 '14 at 6:39\n\\begin{align}\\frac{dy}{dx}=3y^{\\frac{2}{3}}\\\\\\frac{dy}{y^{\\frac{2}{3}}}=3dx\\\\\\int\\frac{dy}{y^{\\frac{2}{3}}}=\\int 3dx\\\\3y^{\\frac{1}{3}}=3x+C\\\\y^{\\frac{1}{3}}=x+C\\end{align}" ]
[ null ]
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https://www.datamining365.com/2021/01/best-data-science-courses-udemy.html
[ "# Best Data Science/Machine Learning Courses On Udemy In 2021\n\nHere are some of the must try list of Data Science/Machine Learning courses on Udemy this 2021.\n\n# Machine Learning A-Z™: Hands-On Python & R In Data Science:\n\nThis is one of the best and popular courses out there to learn and understand Machine Learning from front to back, it is evident that with over 700k+ students enrolled and with over 130k+ ratings it is the highest rated course with rating of 4.5/5 as of end 2020.\n\nDefinitely, this course would be the good choice to look out for in 2021.\n\n# What's In For You:\n\n1. Machine Learning in Python & R.\n\n2. Making accurate predictions.\n\n3. Making robust Machine Learning models.\n\n4. Using Machine Learning for personal purpose.\n\n5. Handling advanced techniques like Dimensionality Reduction.\n\n6. Building an army of powerful Machine Learning models and know how to combine them to solve any problem.\n\n7. Having a great intuition of many Machine Learning models.\n\n8. Making Powerful analysis.\n\n10. Handling specific topics like Reinforcement Learning, NLP and Deep Learning.\n\n11. Knowing which Machine Learning Model to choose for each type of problem.\n\n# The Data Science Course 2020: Complete Data Science Bootcamp:\n\nThis is one of the biggest courses on Data Science, from \"Why Data Science\" to \"Advanced Case Studies\". Along with the practical approach, this course is packed with lots and lots of math required to understand the intuition behind the algorithms.\n\nWith over 300k+ students enrolled and 83k ratings it has a rating of 4.5/5 in the platform.\n\n# What's in for you:\n\n1. This course provides the entire toolkit you need to become a data scientist.\n\n2. It's your turn to impress interviewers by showing an understanding of the data science field after this course.\n\n3. Understanding the mathematics behind Machine Learning (an absolute must which other courses don’t teach!).\n\n4. Learning how to pre-process data.\n\n5. Start coding in Python and learn how to use it for statistical analysis.\n\n4. Performing linear and logistic regressions in Python.\n\n5. Performing cluster and factor analysis.\n\n6. Being able to create Machine Learning algorithms in Python, using NumPy, statsmodels and scikit-learn.\n\n7. Unfolding  the power of deep neural networks.\n\n8. Using state-of-the-art Deep Learning frameworks such as Google’s TensorFlow and Develop a business intuition while coding and solving tasks with big data.\n\n9. Improving Machine Learning algorithms by studying underfitting, overfitting, training, validation, n-fold cross validation, testing, and how hyperparameters could improve performance.\n\n# Complete Machine Learning & Data Science Bootcamp 2021:\n\nThis is the new course on Machine Learning and Data Science which is taught by one of the most popular udemy instructors Andrie Neagoie, his other courses are quite popular in software development domain mainly in web development.\n\nWith over 30k+ students and 5k + ratings this course is rated at 4.6/5 with some great reviews.\n\n# What's In For You:\n\n1. Understanding the Deep Learning, Transfer Learning and Neural Networks using the latest Tensorflow 2.0.\n\n2. Use modern tools that big tech companies like Google, Apple, Amazon and Facebook use.\n\n3. Learning which Machine Learning model to choose for each type of problem.\n\n4. Real life case studies and projects to understand how things are done in the real world.\n\n5. Learning best practices when it comes to Data Science Workflow.\n\n6. Implementing Machine Learning algorithms.\n\n7. Knowing to improve your Machine Learning Models.\n\n8. Supervised and Unsupervised Learning.\n\n9. Exploring large datasets using data visualization tools like Matplotlib and Seaborn.\n\n10. Learning NumPy and how it is used in Machine Learning.\n\n11. Exploring large datasets and wrangle data using Pandas.\n\n12. Learning to perform Classification and Regression modelling.\n\n13. Learning about Data Engineering and how tools like Hadoop, Spark and Kafka are used in the industry and much more....\n\n# Python For Data Science And Machine Learning Bootcamp:\n\nThis is the second most enrolled course on Data Science Bootcamp. Along with the practical approach, this course is more inclined to practical approach on Machine Learning techniques with a python crash course.\n\nWith over 400k+ students enrolled and 90k+ ratings it has a rating of 4.6/5 in the platform. And, the instructor Jose Portilla is famous for his python courses.\n\n# What's In For You:\n\n1. Using Python for Data Science and Machine Learning.\n\n2. Using Spark for Big Data Analysis.\n\n3. Implementing Machine Learning Algorithms.\n\n4. Learning to use NumPy for Numerical Data.\n\n5. Learning to use Pandas for Data Analysis.\n\n6. Learning to use Matplotlib for Python Plotting.\n\n7. Learning to use Seaborn for statistical plots.\n\n8. Using Plotly for interactive dynamic visualizations.\n\n9. Using SciKit-Learn for Machine Learning Tasks.\n\n10. K-Means Clustering and Support Vector Machines.\n\n11. Linear and Logistic Regression.\n\n12. Natural Language Processing and Spam Filters.\n\n13. Neural Networks.\n\n# Machine Learning, Data Science and Deep Learning with Python:\n\nThis course is a complete hands-on machine learning tutorial with Data Science, Tensorflow, Artificial Intelligence, and Neural Networks with one major captone project. Instructor starts with installing and some refreshers in statistics, probability and python to machine learning real world models.\n\nThis course is rated at 4.5/5 with 140k+ students enrolled.\n\n# What's In For You:\n\n1. Building artificial neural networks with Tensorflow and Keras.\n\n2. Classifying images, data, and sentiments using deep learning.\n\n3. Making predictions using linear regression, polynomial regression, and multivariate regression.\n\n4. Data Visualization Techniques with MatPlotLib and Seaborn.\n\n5. Implementing machine learning at massive scale with Apache Spark's MLLib.\n\n6. Understanding reinforcement learning - and how to build a Pac-Man bot.\n\n7. Classifying data using K-Means clustering, Support Vector Machines (SVM), KNN, Decision Trees, Naive Bayes, and PCA.\n\n8. Using train/test and K-Fold cross validation to choose and tune your models.\n\n9. Building a movie recommender system using item-based and user-based collaborative filtering.\n\n10. Cleaning your input data to remove outliers.\n\n11. Designing and evaluating A/B tests using T-Tests and P-Values.\n\n1.", null, "2.", null, "" ]
[ null, "https://www.blogger.com/img/blogger_logo_round_35.png", null, "https://4.bp.blogspot.com/-AjOSeUSTqoQ/X1ojbJdHB1I/AAAAAAAALJo/ZDi26k1W4qkxgLMkPzTQ12F2EHquikBegCK4BGAYYCw/s35/20191120_133638%25252B-%25252BCopy.jpg", null ]
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http://7167508.ru/support-vector-regression-pdf.html
[ "# Support Vector Regression Pdf", null, "If so, what can I do to get rid of it. Thank you for your excellent description.\n\n## Understanding Support Vector Machine Regression - MATLAB & Simulink\n\nHi Alexandre, very nice explanation, thank you very much! Each of these solver algorithms iteratively computes until the specified convergence criterion is met.\n\nDoes this auto correlation imply that my model is not good. In this way, the sum of kernels above can be used to measure the relative nearness of each test point to the data points originating in one or the other of the sets to be discriminated. If you wish to have a more detailled answer, posting a question on stackoverflow might help. You can try to increase the range of the trained hyper parameters and see if it find a better model. Yes it is possible, that means that tuning did not improve the model.", null, "Thank you for the tutorial. Hope to hear from you soon.\n\nThere are many hyperplanes that might classify the data. An overview of Support Vector Machines. If there must be scale, I didn't find parameter to set it in R.\n\nThe final model, which is used for testing and for classifying new data, is then trained on the whole training set using the selected parameters. This is not the same as doing a grid search. You just need to add the gamma parameter in the tune function.", null, "Dropping b drops the sum constraint. Hi Alexandre, Thank you very much for your post. Maybe this paper can help you get better results. The standard way of doing it is by doing a grid search. The optimization problem previously described is computationally simpler to solve in its Lagrange dual formulation.\n\nThat was what made me think this function was poorly coded or it might use sofisticated techniques I am not aware of. Mathematics Stack Exchange. With a normalized or standardized dataset, these hyperplanes can be described by the equations.\n\n## Support-vector machine\n\nAlso, if your data set is small, examples picked to be in one set can make the result change considerably. How would this behave if for example, I wanted to predict some more X variables that are not in the training set? Vapnik suggested a way to create nonlinear classifiers by applying the kernel trick to maximum-margin hyperplanes.\n\nYou can give a vector as input to perform multivariate support vector regression if you wish. In order to improve the performance of the support vector regression we will need to select the best parameters for the model. Seen this way, support vector machines belong to a natural class of algorithms for statistical inference, and many of its unique features are due to the behavior of the hinge loss. After that we have applied Multiple regression to find the relation among dependent variable and independent variables. You can go on this site to post such questions, define marketing strategy pdf but don't forget to do your own research before.\n\nBut how about using predict to predict future values n. Thank you so much for all the information, I have a few questions. The minimization problem can be expressed in standard quadratic programming form and solved using common quadratic programming techniques. For data on the wrong side of the margin, the function's value is proportional to the distance from the margin. Maybe you can find a dedicated forum or a teacher to help you with this matter.", null, "But I also came across in an article that there is another option of finding this optimal combination by implementing some performance metrics. How can I encode this input information? Artificial neural networks. From Wikipedia, the free encyclopedia. How do we perform evaluation on test data.\n\nIt is considered a fundamental method in data science. You will understand how epsilon and C affect the model by reading this article.\n\n## Select a Web Site\n\nThat was making the confusion. How can I perform grid search setting the cost parameter of the function and the kernel?\n\n## Step 1 Simple linear regression in R\n\nThank you for this valuable post. If you wish you can add me to linkedin, I like to connect with my readers.\n\nThe particular value of the parameters differ greatly between problems so you just have to do a grid search first and then try to narrow the range until you find values which give you satisfaction. The parameters of the maximum-margin hyperplane are derived by solving the optimization. There is some information about how to do it in Python on this on this page.\n\nThis is machine translation Translated by. Currently we are working on a research paper in which we have conducted psychological experiment to get data-set. My input is the day of the week and the output is the correspondent energy consumption value.\n\nYou can specify a tunecontrol parameter to specify the behavior of the tune method. Machine learning and data mining Problems." ]
[ null, "https://i1.rgstatic.net/publication/255995594_Predicting_Stock_Market_Price_Using_Support_Vector_Regression/links/00b7d5215cdd42ff82000000/largepreview.png", null, "https://www.saedsayad.com/images/SVR_1.png", null, "https://image.slidesharecdn.com/4-supportvectorregression-171230051802/95/support-vector-regression-8-638.jpg", null, "https://www.saedsayad.com/images/SVR_5.png", null ]
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http://emilydolson.github.io/D3-visualising-data/08-d3enter.html
[ "# D3 - Into the data\n\n## Learning Objectives\n\n• Making axes\n• Actually plotting data (d3.enter)\n\nWe design our axes based on our data. This means we have to know the minimum and maximum values of our data and have to decide whether we want linear or logarithmic axes.\n\n``````// Create a logarithmic scale for the income\nvar xScale = d3.scale.log(); // income\nxScale.domain([250, 1e5]); // set minimum and maximum value\nxScale.range([0, canvas_width]); // set minimum and maximum range on the page``````\n\nD3's scale object provides a number of functions to create the scaling we want for our data. For example, we can choose between a logarithmic scale (`log`), a linear scale (`linear`), a square root scale (`sqrt`), or a categorical scale (e.g. `category20` can represent 20 different colours).\n\nThe domain consists of the data values that will get mapped to the minimum and maximum positions on the page specified by the range. Often, the domain will be set to the minimum and maximum values of the data and the range to the edges of the plotting area.\n\nInstead of spreading this code over three lines, we often find another notation online that achieves the same thing:\n\n``var xScale = d3.scale.log().domain([300, 1e5]).range([0, canvas_width]); ``\n\nThese two notations are interchangeable and it is entirely up to you to use the one that seems more intuitive to you. In the same way that we could switch setting up the domain and range in the more verbose notation, we can swap these two in the shorter notation without it making any difference.\n\nThe next step is to create the actual axis and linking it to the scale we just created:\n\n``````// Creating the x axis.\nvar xAxis = d3.svg.axis().orient(\"bottom\").scale(xScale);``````\n\n`orient()` influences the orientation of the axis and the position of the ticks. We will still need to position it inside the canvas.\n\nSo far, the xAxis exists, but it's not actually showing up anywhere on the page. To push the axis to our canvas, we create a new group element (using `.append`).\n\n``````// Add the x-axis.\ncanvas.append(\"g\")\n.attr(\"class\", \"x axis\")\n.attr(\"transform\", \"translate(0,\" + canvas_height + \")\")\n.call(xAxis);``````\n\n`.call()` calls the axis we just created and pushes it to the element. We add a transform attribute to move the axis to the bottom of the plotting area (instead of having it across the top). There are a number of transform options, but here we are just using `translate` and pass in the amount to shift the axis in the x and y directions, respectively. Here we shift it only in the y direction (i.e. down) by an amount given by height of the canvas.\nWe also give it a class, just in case we might want to select the axis later in our code.\n\n# We might need a y-axis, too\n\nCreate a linear scale for the y-axis, with 10 being the minimum and 85 being the maximum value. Then, add the axis to the canvas.\n\nHint #1: You probably want to orient the axis \"left\" Hint #2: Remember that SVG coordinates are flipped from what you might expect - (0,0) is the upper left corner.\n\nWe're slowly getting there. Having our two axes, we can now finally add our data.\n\n``````var data_canvas = canvas.append(\"g\")\n.attr(\"class\", \"data_canvas\");\n\nvar circles = data_canvas.selectAll(\"circle\")\n.data(nations, function(d){return d.country});\n\ncircles.enter().append(\"circle\").attr(\"class\",\"data_point\")\n.attr(\"cx\", function(d) { return xScale(d.gdpPercap); })\n.attr(\"cy\", function(d) { return yScale(d.lifeExp); })\n.attr(\"r\", 5);``````\n\nWe're starting this bit by adding a `g` element to our canvas. This group is going to be our data canvas, so that's the class name we give it. We then select all circles. This is an empty set at the moment, since we haven't created any circles, yet. We are then telling our page where to find the data, using `.data(nations)`.\n\nWe are also inserting what is called a key function `.data(nations, function(d){return d.country});`. This function will help D3 keep track of the data when we start changing it (and the order of the objects). It's important to keep the identifier unique, which is why we return only the country of the current element.\n\nNow comes the interesting part: The function `enter()` takes each element in the dataset and does everything that follows afterwards for each of these elements we're adding in. These new circles need to be added with the class 'data_point', so that next time we call `data_canvas.selectAll(\".data_point\")` we get the circles that have already been added to our plot.\n\nWhat we want to do is to create one circle for each data point. That's what the last four lines of code do. They are creating the circle, and then setting the attributes `cx`, `cy`, and `r`. The attributes `cx` and `cy` define the position of the centre of the circle and are based on the income (we are looking at the most recent data point: `[nation.income.length-1]`.) and life expectancy of the data point (that is temporarily called `d`). The radius is set to an arbitrary number... for now.\n\nRight now, we're displaying data from a semi-random year. We can use the `filter()` function to just look at the most recent data (2007):\n\n``var filtered_nations = nations.filter(function(nation){return nation.year==2007})``\n\nSimilar to previous functions, this function iterates over each of the elements in the array `nations`, temporarily calling it `nation`. It only includes elements in the new array `filtered_nations` if the function evaluates to 'true' for that element. Here this will be the case for data points whose year is 2007.\n\n# Filtering by region\n\nYou might have noticed that our data contains information about the continent in which a country is.\n\nCreate a filter so that you only display data points from \"Africa\".\n\n# A new dimension\n\nChange the code so that the radius of the circles represents the population. First, create a 'sqrt' scale (`d3.scale.sqrt()`) with a minimum of 0 and a maximum of 5e8. The range should be between 0 and 40." ]
[ null ]
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https://riptutorial.com/go/example/4039/basic-test
[ "# Go Testing Basic Test\n\n30% OFF - 9th Anniversary discount on Entity Framework Extensions until December 15 with code: ZZZANNIVERSARY9\n\n## Example\n\n`main.go`:\n\n``````package main\n\nimport (\n\"fmt\"\n)\n\nfunc main() {\nfmt.Println(Sum(4,5))\n}\n\nfunc Sum(a, b int) int {\nreturn a + b\n}\n``````\n\n`main_test.go`:\n\n``````package main\n\nimport (\n\"testing\"\n)\n\nfunc TestSum(t *testing.T) {\ngot := Sum(1, 2)\nwant := 3\nif got != want {\nt.Errorf(\"Sum(1, 2) == %d, want %d\", got, want)\n}\n}\n``````\n\nTo run the test just use the `go test` command:\n\n``````\\$ go test\nok test_app 0.005s\n``````\n\nUse the `-v` flag to see the results of each test:\n\n``````\\$ go test -v\n=== RUN TestSum\n--- PASS: TestSum (0.00s)\nPASS\nok _/tmp 0.000s\n``````\n\nUse the path `./...` to test subdirectories recursively:\n\n``````\\$ go test -v ./...\nok github.com/me/project/dir1 0.008s\n=== RUN TestSum\n--- PASS: TestSum (0.00s)\nPASS\nok github.com/me/project/dir2 0.008s\n=== RUN TestDiff\n--- PASS: TestDiff (0.00s)\nPASS\n``````\n\nRun a Particular Test:\nIf there are multiple tests and you want to run a specific test, it can be done like this:\n\n``````go test -v -run=<TestName> // will execute only test with this name\n``````\n\nExample:\n\n``````go test -v run=TestSum\n``````\n\n### Got any Go Question?", null, "PDF - Download Go for free" ]
[ null, "https://riptutorial.com/Images/icon-pdf-2.png", null ]
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https://docs.hashstack.finance/developers/permissible-cdr
[ "Comment on page\n\n# Permissible CDR\n\nThe following documentation outlines a code implementation for a function that calculates the creditworthiness and loan-to-value (LTV) ratio of a borrower based on several input parameters. The code also includes a function to calculate the overall market risk based on three input parameters.\nThe code implementation consists of two functions: `calculate_creditworthiness()` and `calculate_market_risk()`. The `calculate_creditworthiness()` function assesses the borrower's creditworthiness by considering the user's repayment history, collateral to debt correlation, and the overall market risk. The function returns both the creditworthiness score and the LTV ratio. The `calculate_market_risk()` function estimates the general market risk based on the effective asset flow rate, volatility, and price variation, and returns the assessed risk.\nThe documentation provides additional information about the input parameters used in both functions and their relationship to market risk.\n\n### Parameters:\n\n1. 1.\n`collateral_debt_correlation`: This parameter represents the correlation between the value of the collateral and the borrower's debt. In other words, it assesses the likelihood that the value of the collateral will decrease below the borrower's debt level. The lower the correlation, the riskier the loan.\n2. 2.\n`effective_asset_flow_rate`: This parameter represents the effective flow rate of assets, which is the rate at which assets can be converted to cash in the market. It evaluates the liquidity of assets and their ability to be sold quickly at a reasonable price. A low effective asset flow rate indicates a riskier market, which is represented as a boolean as of this version.\n3. 3.\n`volatility`: This parameter represents the degree of variation of an asset's price over time. It measures the risk of the asset's price fluctuating in the market. Higher volatility indicates a riskier market.\n4. 4.\n`price_variation`: This parameter represents an asset's price variation in a given time period. It measures the magnitude of the change in the asset's price. A higher price variation indicates a riskier market.\n5. 5.\n`wallet_history`: This parameter represents the user's repayment history. It tracks the status of the borrower's previous loans, indicating their consistency in repaying loans. A good repayment history indicates a lower credit risk for the borrower.\nAll of these parameters, except for `wallet_history`, are market-associated and evaluate the market risk at the time of loan request. Understanding the relationships between these parameters and market risk is critical to assessing the borrower's creditworthiness.\ndef calculate_creditworthiness(collateral_debt_correlation, effective_asset_flow_rate, volatility, price_variation):\n//Step 1: User repayment history\nwallet_history = \"A track of loan's status as in success or failed loans\"\n//Consistency of the user's loan repayment justifies the trust in lending the funds\n// A score from this can be taken with a discounting factor to older status. (Rn + delta*Rn-1 + delta^2*Rn-2 +...)\n// Step 2: Calculate credit risk\ncredit_score= score*[collateral_debt_correlation + calculate_market_risk(effective_asset_flow_rate, volatility, price_variation)]/2\n// Step 3: Calculate loan-to-value (LTV) ratio\nltv_ratio = 3 * credit_score\n// Step 4: Return creditworthiness score and LTV ratio\nreturn credit_score, ltv_ratio\ndef calculate_market_risk(effective_asset_flow_rate, volatility, price_variation):\n// Calculate overall market risk using a weighted average of effective asset flow rate, volatility, and price variation\nweights = [0.4, 0.3, 0.3] // Adjust weights as desired\nmarket_risk = np.average([effective_asset_flow_rate, volatility, price_variation], weights=weights)\nreturn market_risk" ]
[ null ]
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https://studysoup.com/tsg/1897/physics-principles-with-applications-6-edition-chapter-8-problem-54p
[ "×\n\n# (II) A diver (such as the one shown in Fig. 8-28) can", null, "## Problem 54P Chapter 8\n\nPhysics: Principles with Applications | 6th Edition\n\n• 2901 Step-by-step solutions solved by professors and subject experts\n• Get 24/7 help from StudySoup virtual teaching assistants", null, "Physics: Principles with Applications | 6th Edition\n\n4 5 0 382 Reviews\n16\n3\nProblem 54P\n\n(II) A diver (such as the one shown in Fig. 8-28) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations 1.5 s when in the tuck position, what is her angular speed (rev s) when in the straight position?", null, "Step-by-Step Solution:\n\nStep-by-step solution\n\nStep 1 of 3</p>\n\nCONCEPT\n\nConsider the diver and platform as a system. There is no external torque acting on the system to change the angular velocity. So the angular momentum is conserved.\n\nTherefore, by applying the conservation of angular momentum to the diver and platform system, we can calculate the final angular speed of the person.\n\nStep 2 of 3 </p>\n\nLet", null, "be the moment of inertia of diver in the straight position.\n\nLet", null, "be the moment of inertia of diver in the tuck position.\n\nAs the person initially makes 2.0 rotations in 1.5 s, initial angular velocity of the diver is given by the following expression", null, "As the moment of inertia in tuck position is reduced by a factor of 3.5", null, "Step 3 of 3\n\n##### ISBN: 9780130606204\n\nUnlock Textbook Solution\n\n(II) A diver (such as the one shown in Fig. 8-28) can\n\n×\nGet Full Access to Physics: Principles With Applications - 6 Edition - Chapter 8 - Problem 54p\n\nGet Full Access to Physics: Principles With Applications - 6 Edition - Chapter 8 - Problem 54p" ]
[ null, "https://studysoup.com/cdn/62cover_2418946", null, "https://studysoup.com/cdn/62cover_2418946", null, "https://lh3.googleusercontent.com/_STa0mrvsC5b1YUQSi3DEzkANHYjZdJgIfN2lXg4IBnep5IKKbgU5hoU8hMEYt296FluWwoZMrfWIB6OCD-3YCUq0rfEx2GOzyhio_9bHQoJUNoHt_Wles3GtfgqXMG-5kvAWcHn", null, "https://lh4.googleusercontent.com/e05DfCsQ29PZPk6tAq1Yq_t2Q0x2rDE-Kd9vE9BQlxrUpl6WvPvfhFazH86YWSBGsMcBr9xpL3lY4zNFGqP7GYHJytiur1oswgweoajvoDKRKO4uI-D8cXufoZ1zSpCzEoXPw2sc", null, "https://lh4.googleusercontent.com/3ZCO_a_q4Nt_5jpmoPr51D-lBJOT4WOgMXK-m6hUM_qQQ2kckmdHrwv57_5EoWhpZ4pZ3QfQQCRO5bpt3QaY1XceufbM7ukP2T_PCnjb81t9L1oIVL3bXwO9sLKpn6_2SWqSGKkV", null, "https://lh3.googleusercontent.com/0aPorMVNvkzR-pc1g2J3aboSs_EnHOaxUFilXOpOKpwm0W8ZHKnZEnAWsXnpiBo8cZYKDsKPoHH-c08QYVk6qXyyIwayzw2_3gGVHkP2le-d4_8eNzXTP08gYNpRXuESwDP_HmJ1", null, "https://lh6.googleusercontent.com/WvKGG7orcebPhSoQehtiQ13G-PezYIwJzGiAlEpYHR1VunaK2Nzj1WC1UwRnNaII8a0XXNTtBgkMj7-MGrBCRu1T4AFDRkEuUAn_PYjtfnyzkiLtvCS_XZLyRJ7pqlgVlwGgROZ0", null ]
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https://dealii.org/developer/doxygen/deal.II/step_52.html
[ "", null, "Reference documentation for deal.II version Git 28ce845196 2019-06-26 10:31:03 +0200\nThe step-52 tutorial program\n\nThis tutorial depends on step-26.\n\n1. Introduction\n2. The commented program\n\nThis program was contributed by Bruno Turcksin and Damien Lebrun-Grandie.\n\nNote\nIn order to run this program, deal.II must be configured to use the UMFPACK sparse direct solver. Refer to the ReadMe for instructions how to do this.\n\nIntroduction\n\nThis program shows how to use Runge-Kutta methods to solve a time-dependent problem. It solves a small variation of the heat equation discussed first in step-26 but, since the purpose of this program is only to demonstrate using more advanced ways to interface with deal.II's time stepping algorithms, only solves a simple problem on a uniformly refined mesh.\n\nProblem statement\n\nIn this example, we solve the one-group time-dependent diffusion approximation of the neutron transport equation (see step-28 for the time-independent multigroup diffusion). This is a model for how neutrons move around highly scattering media, and consequently it is a variant of the time-dependent diffusion equation – which is just a different name for the heat equation discussed in step-26, plus some extra terms. We assume that the medium is not fissible and therefore, the neutron flux satisfies the following equation:\n\n\\begin{eqnarray*} \\frac{1}{v}\\frac{\\partial \\phi(x,t)}{\\partial t} = \\nabla \\cdot D(x) \\nabla \\phi(x,t) - \\Sigma_a(x) \\phi(x,t) + S(x,t) \\end{eqnarray*}\n\naugmented by appropriate boundary conditions. Here, $$v$$ is the velocity of neutrons (for simplicity we assume it is equal to 1 which can be achieved by simply scaling the time variable), $$D$$ is the diffusion coefficient, $$\\Sigma_a$$ is the absorption cross section, and $$S$$ is a source. Because we are only interested in the time dependence, we assume that $$D$$ and $$\\Sigma_a$$ are constant.\n\nSince this program only intends to demonstrate how to use advanced time stepping algorithms, we will only look for the solutions of relatively simple problems. Specifically, we are looking for a solution on a square domain $$[0,b]\\times[0,b]$$ of the form\n\n\\begin{eqnarray*} \\phi(x,t) = A\\sin(\\omega t)(bx-x^2). \\end{eqnarray*}\n\nBy using quadratic finite elements, we can represent this function exactly at any particular time, and all the error will be due to the time discretization. We do this because it is then easy to observe the order of convergence of the various time stepping schemes we will consider, without having to separate spatial and temporal errors.\n\nWe impose the following boundary conditions: homogeneous Dirichlet for $$x=0$$ and $$x=b$$ and homogeneous Neumann conditions for $$y=0$$ and $$y=b$$. We choose the source term so that the corresponding solution is in fact of the form stated above:\n\n\\begin{eqnarray*} S=A\\left(\\frac{1}{v}\\omega \\cos(\\omega t)(bx -x^2) + \\sin(\\omega t) \\left(\\Sigma_a (bx-x^2)+2D\\right) \\right). \\end{eqnarray*}\n\nBecause the solution is a sine in time, we know that the exact solution satisfies $$\\phi\\left(x,\\pi\\right) = 0$$. Therefore, the error at time $$t=\\pi$$ is simply the norm of the numerical solution, i.e., $$\\|e(\\cdot,t=\\pi)\\|_{L_2} = \\|\\phi_h(\\cdot,t=\\pi)\\|_{L_2}$$, and is particularly easily evaluated. In the code, we evaluate the $$l_2$$ norm of the vector of nodal values of $$\\phi_h$$ instead of the $$L_2$$ norm of the associated spatial function, since the former is simpler to compute; however, on uniform meshes, the two are just related by a constant and we can consequently observe the temporal convergence order with either.\n\nRunge-Kutta methods\n\nThe Runge-Kutta methods implemented in deal.II assume that the equation to be solved can be written as:\n\n\\begin{eqnarray*} \\frac{dy}{dt} = g(t,y). \\end{eqnarray*}\n\nOn the other hand, when using finite elements, discretized time derivatives always result in the presence of a mass matrix on the left hand side. This can easily be seen by considering that if the solution vector $$y(t)$$ in the equation above is in fact the vector of nodal coefficients $$U(t)$$ for a variable of the form\n\n\\begin{eqnarray*} u_h(x,t) = \\sum_j U_j(t) \\varphi_j(x) \\end{eqnarray*}\n\nwith spatial shape functions $$\\varphi_j(x)$$, then multiplying an equation of the form\n\n\\begin{eqnarray*} \\frac{\\partial u(x,t)}{\\partial t} = q(t,u(x,t)) \\end{eqnarray*}\n\nby test functions, integrating over $$\\Omega$$, substituting $$u\\rightarrow u_h$$ and restricting the test functions to the $$\\varphi_i(x)$$ from above, then this spatially discretized equation has the form\n\n\\begin{eqnarray*} M\\frac{dU}{dt} = f(t,U), \\end{eqnarray*}\n\nwhere $$M$$ is the mass matrix and $$f(t,U)$$ is the spatially discretized version of $$q(t,u(x,t))$$ (where $$q$$ is typically the place where spatial derivatives appear, but this is not of much concern for the moment given that we only consider time derivatives). In other words, this form fits the general scheme above if we write\n\n\\begin{eqnarray*} \\frac{dy}{dt} = g(t,y) = M^{-1}f(t,y). \\end{eqnarray*}\n\nRunke-Kutta methods are time stepping schemes that approximate $$y(t_n)\\approx y_{n}$$ through a particular one-step approach. They are typically written in the form\n\n\\begin{eqnarray*} y_{n+1} = y_n + \\sum_{i=1}^s b_i k_i \\end{eqnarray*}\n\nwhere for the form of the right hand side above\n\n\\begin{eqnarray*} k_i = h M^{-1} f\\left(t_n+c_ih,y_n+\\sum_{j=1}^sa_{ij}k_j\\right). \\end{eqnarray*}\n\nHere $$a_{ij}$$, $$b_i$$, and $$c_i$$ are known coefficients that identify which particular Runge-Kutta scheme you want to use, and $$h=t_{n+1}-t_n$$ is the time step used. Different time stepping methods of the Runge-Kutta class differ in the number of stages $$s$$ and the values they use for the coefficients $$a_{ij}$$, $$b_i$$, and $$c_i$$ but are otherwise easy to implement since one can look up tabulated values for these coefficients. (These tables are often called Butcher tableaus.)\n\nAt the time of the writing of this tutorial, the methods implemented in deal.II can be divided in three categories:\n\n1. Explicit Runge-Kutta; in order for a method to be explicit, it is necessary that in the formula above defining $$k_i$$, $$k_i$$ does not appear on the right hand side. In other words, these methods have to satisfy $$a_{ii}=0, i=1,\\ldots,s$$.\n2. Embedded (or adaptive) Runge-Kutta; we will discuss their properties below.\n3. Implicit Runge-Kutta; this class of methods require the solution of a possibly nonlinear system the stages $$k_i$$ above, i.e., they have $$a_{ii}\\neq 0$$ for at least one of the stages $$i=1,\\ldots,s$$.\n\nMany well known time stepping schemes that one does not typically associate with the names Runge or Kutta can in fact be written in a way so that they, too, can be expressed in these categories. They oftentimes represent the lowest-order members of these families.\n\nExplicit Runge-Kutta methods\n\nThese methods, only require a function to evaluate $$M^{-1}f(t,y)$$ but not (as implicit methods) to solve an equation that involves $$f(t,y)$$ for $$y$$. As all explicit time stepping methods, they become unstable when the time step chosen is too large.\n\nWell known methods in this class include forward Euler, third order Runge-Kutta, and fourth order Runge-Kutta (often abbreviated as RK4).\n\nEmbedded Runge-Kutta methods\n\nThese methods use both a lower and a higher order method to estimate the error and decide if the time step needs to be shortened or can be increased. The term \"embedded\" refers to the fact that the lower-order method does not require additional evaluates of the function $$M^{-1}f(\\cdot,\\cdot)$$ but reuses data that has to be computed for the high order method anyway. It is, in other words, essentially free, and we get the error estimate as a side product of using the higher order method.\n\nThis class of methods include Heun-Euler, Bogacki-Shampine, Dormand-Prince (ode45 in Matlab and often abbreviated as RK45 to indicate that the lower and higher order methods used here are 4th and 5th order Runge-Kutta methods, respectively), Fehlberg, and Cash-Karp.\n\nAt the time of the writing, only embedded explicit methods have been implemented.\n\nImplicit Runge-Kutta methods\n\nImplicit methods require the solution of (possibly nonlinear) systems of the form $$\\alpha y = f(t,y)$$ for $$y$$ in each (sub-)timestep. Internally, this is done using a Newton-type method and, consequently, they require that the user provide functions that can evaluate $$M^{-1}f(t,y)$$ and $$\\left(I-\\tau M^{-1} \\frac{\\partial f}{\\partial y}\\right)^{-1}$$ or equivalently $$\\left(M - \\tau \\frac{\\partial f}{\\partial y}\\right)^{-1} M$$.\n\nThe particular form of this operator results from the fact that each Newton step requires the solution of an equation of the form\n\n\\begin{align*} \\left(M - \\tau \\frac{\\partial f}{\\partial y}\\right) \\Delta y = -M h(t,y) \\end{align*}\n\nfor some (given) $$h(t,y)$$. Implicit methods are always stable, regardless of the time step size, but too large time steps of course affect the accuracy of the solution, even if the numerical solution remains stable and bounded.\n\nMethods in this class include backward Euler, implicit midpoint, Crank-Nicolson, and the two stage SDIRK method (short for \"singly diagonally implicit Runge-Kutta\", a term coined to indicate that the diagonal elements $$a_{ii}$$ defining the time stepping method are all equal; this property allows for the Newton matrix $$I-\\tau M^{-1}\\frac{\\partial f}{\\partial y}$$ to be re-used between stages because $$\\tau$$ is the same every time).\n\nSpatially discrete formulation\n\nBy expanding the solution of our model problem as always using shape functions $$\\psi_j$$ and writing\n\n\\begin{eqnarray*} \\phi_h(x,t) = \\sum_j U_j(t) \\psi_j(x), \\end{eqnarray*}\n\nwe immediately get the spatially discretized version of the diffusion equation as\n\n\\begin{eqnarray*} M \\frac{dU(t)}{dt} = -{\\cal D} U(t) - {\\cal A} U(t) + {\\cal S}(t) \\end{eqnarray*}\n\nwhere\n\n\\begin{eqnarray*} M_{ij} &=& (\\psi_i,\\psi_j), \\\\ {\\cal D}_{ij} &=& (D\\nabla\\psi_i,\\nabla\\psi_j)_\\Omega, \\\\ {\\cal A}_{ij} &=& (\\Sigma_a\\psi_i,\\psi_j)_\\Omega, \\\\ {\\cal S}_{i}(t) &=& (\\psi_i,S(x,t))_\\Omega. \\end{eqnarray*}\n\nSee also step-24 and step-26 to understand how we arrive here. Boundary terms are not necessary due to the chosen boundary conditions for the current problem. To use the Runge-Kutta methods, we recast this as follows:\n\n\\begin{eqnarray*} f(y) = -{\\cal D}y - {\\cal A}y + {\\cal S}. \\end{eqnarray*}\n\nIn the code, we will need to be able to evaluate this function $$f(U)$$ along with its derivative,\n\n\\begin{eqnarray*} \\frac{\\partial f}{\\partial y} = -{\\cal D} - {\\cal A}. \\end{eqnarray*}\n\nNotes on the testcase\n\nTo simplify the problem, the domain is two dimensional and the mesh is uniformly refined (there is no need to adapt the mesh since we use quadratic finite elements and the exact solution is quadratic). Going from a two dimensional domain to a three dimensional domain is not very challenging. However if you intend to solve more complex problems where the mesh must be adapted (as is done, for example, in step-26), then it is important to remember the following issues:\n\n1. You will need to project the solution to the new mesh when the mesh is changed. Of course, the mesh used should be the same from the beginning to the end of each time step, a question that arises because Runge-Kutta methods use multiple evaluations of the equations within each time step.\n2. You will need to update the mass matrix and its inverse every time the mesh is changed.\n\nThe techniques for these steps are readily available by looking at step-26.\n\nThe commented program\n\nInclude files\n\nThe first task as usual is to include the functionality of these well-known deal.II library files and some C++ header files.\n\n#include <deal.II/base/function.h>\n#include <deal.II/grid/grid_generator.h>\n#include <deal.II/grid/tria_accessor.h>\n#include <deal.II/grid/tria_iterator.h>\n#include <deal.II/grid/tria.h>\n#include <deal.II/grid/grid_out.h>\n#include <deal.II/dofs/dof_handler.h>\n#include <deal.II/dofs/dof_accessor.h>\n#include <deal.II/dofs/dof_tools.h>\n#include <deal.II/fe/fe_q.h>\n#include <deal.II/fe/fe_values.h>\n#include <deal.II/lac/affine_constraints.h>\n#include <deal.II/lac/sparse_direct.h>\n#include <deal.II/numerics/vector_tools.h>\n#include <deal.II/numerics/data_out.h>\n#include <fstream>\n#include <iostream>\n#include <cmath>\n#include <map>\n\nThis is the only include file that is new: It includes all the Runge-Kutta methods.\n\n#include <deal.II/base/time_stepping.h>\n\nThe next step is like in all previous tutorial programs: We put everything into a namespace of its own and then import the deal.II classes and functions into it.\n\nnamespace Step52\n{\nusing namespace dealii;\n\nThe Diffusion class\n\nThe next piece is the declaration of the main class. Most of the functions in this class are not new and have been explained in previous tutorials. The only interesting functions are evaluate_diffusion() and id_minus_tau_J_inverse(). evaluate_diffusion() evaluates the diffusion equation, $$M^{-1}(f(t,y))$$, at a given time and a given $$y$$. id_minus_tau_J_inverse() evaluates $$\\left(I-\\tau M^{-1} \\frac{\\partial f(t,y)}{\\partial y}\\right)^{-1}$$ or equivalently $$\\left(M-\\tau \\frac{\\partial f}{\\partial y}\\right)^{-1} M$$ at a given time, for a given $$\\tau$$ and $$y$$. This function is needed when an implicit method is used.\n\nclass Diffusion\n{\npublic:\nDiffusion();\nvoid run();\nprivate:\nvoid setup_system();\nvoid assemble_system();\ndouble get_source(const double time, const Point<2> &point) const;\nVector<double> evaluate_diffusion(const double time,\nconst Vector<double> &y) const;\nVector<double> id_minus_tau_J_inverse(const double time,\nconst double tau,\nconst Vector<double> &y);\nvoid output_results(const unsigned int time_step,\n\nThe next three functions are the drivers for the explicit methods, the implicit methods, and the embedded explicit methods respectively. The driver function for embedded explicit methods returns the number of steps executed given that it only takes the number of time steps passed as an argument as a hint, but internally computed the optimal time step itself.\n\nvoid explicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time);\nvoid implicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time);\nunsigned int\nembedded_explicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time);\nconst unsigned int fe_degree;\nconst double diffusion_coefficient;\nconst double absorption_cross_section;\nTriangulation<2> triangulation;\nconst FE_Q<2> fe;\nDoFHandler<2> dof_handler;\nAffineConstraints<double> constraint_matrix;\nSparsityPattern sparsity_pattern;\nSparseMatrix<double> system_matrix;\nSparseMatrix<double> mass_matrix;\nSparseMatrix<double> mass_minus_tau_Jacobian;\nSparseDirectUMFPACK inverse_mass_matrix;\nVector<double> solution;\n};\n\nWe choose quadratic finite elements and we initialize the parameters.\n\nDiffusion::Diffusion()\n: fe_degree(2)\n, diffusion_coefficient(1. / 30.)\n, absorption_cross_section(1.)\n, fe(fe_degree)\n, dof_handler(triangulation)\n{}\n\nDiffusion::setup_system\n\nNow, we create the constraint matrix and the sparsity pattern. Then, we initialize the matrices and the solution vector.\n\nvoid Diffusion::setup_system()\n{\ndof_handler.distribute_dofs(fe);\n1,\nconstraint_matrix);\nconstraint_matrix.close();\nDynamicSparsityPattern dsp(dof_handler.n_dofs());\nDoFTools::make_sparsity_pattern(dof_handler, dsp, constraint_matrix);\nsparsity_pattern.copy_from(dsp);\nsystem_matrix.reinit(sparsity_pattern);\nmass_matrix.reinit(sparsity_pattern);\nmass_minus_tau_Jacobian.reinit(sparsity_pattern);\nsolution.reinit(dof_handler.n_dofs());\n}\n\nDiffusion::assemble_system\n\nIn this function, we compute $$-\\int D \\nabla b_i \\cdot \\nabla b_j d\\boldsymbol{r} - \\int \\Sigma_a b_i b_j d\\boldsymbol{r}$$ and the mass matrix $$\\int b_i b_j d\\boldsymbol{r}$$. The mass matrix is then inverted using a direct solver; the inverse_mass_matrix variable will then store the inverse of the mass matrix so that $$M^{-1}$$ can be applied to a vector using the vmult() function of that object. (Internally, UMFPACK does not really store the inverse of the matrix, but its LU factors; applying the inverse matrix is then equivalent to doing one forward and one backward solves with these two factors, which has the same complexity as applying an explicit inverse of the matrix).\n\nvoid Diffusion::assemble_system()\n{\nsystem_matrix = 0.;\nmass_matrix = 0.;\nFEValues<2> fe_values(fe,\nconst unsigned int dofs_per_cell = fe.dofs_per_cell;\nconst unsigned int n_q_points = quadrature_formula.size();\nFullMatrix<double> cell_matrix(dofs_per_cell, dofs_per_cell);\nFullMatrix<double> cell_mass_matrix(dofs_per_cell, dofs_per_cell);\nstd::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);\nfor (const auto &cell : dof_handler.active_cell_iterators())\n{\ncell_matrix = 0.;\ncell_mass_matrix = 0.;\nfe_values.reinit(cell);\nfor (unsigned int q_point = 0; q_point < n_q_points; ++q_point)\nfor (unsigned int i = 0; i < dofs_per_cell; ++i)\nfor (unsigned int j = 0; j < dofs_per_cell; ++j)\n{\ncell_matrix(i, j) +=\n((-diffusion_coefficient * // (-D\n- absorption_cross_section * // -Sigma\nfe_values.shape_value(i, q_point) * // * phi_i\nfe_values.shape_value(j, q_point)) // * phi_j)\n* fe_values.JxW(q_point)); // * dx\ncell_mass_matrix(i, j) += fe_values.shape_value(i, q_point) *\nfe_values.shape_value(j, q_point) *\nfe_values.JxW(q_point);\n}\ncell->get_dof_indices(local_dof_indices);\nconstraint_matrix.distribute_local_to_global(cell_matrix,\nlocal_dof_indices,\nsystem_matrix);\nconstraint_matrix.distribute_local_to_global(cell_mass_matrix,\nlocal_dof_indices,\nmass_matrix);\n}\ninverse_mass_matrix.initialize(mass_matrix);\n}\n\nDiffusion::get_source\n\nIn this function, the source term of the equation for a given time and a given point is computed.\n\ndouble Diffusion::get_source(const double time, const Point<2> &point) const\n{\nconst double intensity = 10.;\nconst double frequency = numbers::PI / 10.;\nconst double b = 5.;\nconst double x = point(0);\nreturn intensity *\n(frequency * std::cos(frequency * time) * (b * x - x * x) +\nstd::sin(frequency * time) *\n(absorption_cross_section * (b * x - x * x) +\n2. * diffusion_coefficient));\n}\n\nDiffusion::evaluate_diffusion\n\nNext, we evaluate the weak form of the diffusion equation at a given time $$t$$ and for a given vector $$y$$. In other words, as outlined in the introduction, we evaluate $$M^{-1}(-{\\cal D}y - {\\cal A}y + {\\cal S})$$. For this, we have to apply the matrix $$-{\\cal D} - {\\cal A}$$ (previously computed and stored in the variable system_matrix) to $$y$$ and then add the source term which we integrate as we usually do. (Integrating up the solution could be done using VectorTools::create_right_hand_side() if you wanted to save a few lines of code, or wanted to take advantage of doing the integration in parallel.) The result is then multiplied by $$M^{-1}$$.\n\nVector<double> Diffusion::evaluate_diffusion(const double time,\nconst Vector<double> &y) const\n{\nVector<double> tmp(dof_handler.n_dofs());\ntmp = 0.;\nsystem_matrix.vmult(tmp, y);\nFEValues<2> fe_values(fe,\nconst unsigned int dofs_per_cell = fe.dofs_per_cell;\nconst unsigned int n_q_points = quadrature_formula.size();\nVector<double> cell_source(dofs_per_cell);\nstd::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);\nfor (const auto &cell : dof_handler.active_cell_iterators())\n{\ncell_source = 0.;\nfe_values.reinit(cell);\nfor (unsigned int q_point = 0; q_point < n_q_points; ++q_point)\n{\nconst double source =\nfor (unsigned int i = 0; i < dofs_per_cell; ++i)\ncell_source(i) += fe_values.shape_value(i, q_point) * // phi_i(x)\nsource * // * S(x)\nfe_values.JxW(q_point); // * dx\n}\ncell->get_dof_indices(local_dof_indices);\nconstraint_matrix.distribute_local_to_global(cell_source,\nlocal_dof_indices,\ntmp);\n}\nVector<double> value(dof_handler.n_dofs());\ninverse_mass_matrix.vmult(value, tmp);\nreturn value;\n}\n\nDiffusion::id_minus_tau_J_inverse\n\nWe compute $$\\left(M-\\tau \\frac{\\partial f}{\\partial y}\\right)^{-1} M$$. This is done in several steps:\n\n• compute $$M-\\tau \\frac{\\partial f}{\\partial y}$$\n• invert the matrix to get $$\\left(M-\\tau \\frac{\\partial f} {\\partial y}\\right)^{-1}$$\n• compute $$tmp=My$$\n• compute $$z=\\left(M-\\tau \\frac{\\partial f}{\\partial y}\\right)^{-1} tmp = \\left(M-\\tau \\frac{\\partial f}{\\partial y}\\right)^{-1} My$$\n• return z.\nVector<double> Diffusion::id_minus_tau_J_inverse(const double / *time* /,\nconst double tau,\nconst Vector<double> &y)\n{\nSparseDirectUMFPACK inverse_mass_minus_tau_Jacobian;\nmass_minus_tau_Jacobian.copy_from(mass_matrix);\ninverse_mass_minus_tau_Jacobian.initialize(mass_minus_tau_Jacobian);\nVector<double> tmp(dof_handler.n_dofs());\nmass_matrix.vmult(tmp, y);\nVector<double> result(y);\ninverse_mass_minus_tau_Jacobian.vmult(result, tmp);\nreturn result;\n}\n\nDiffusion::output_results\n\nThe following function then outputs the solution in vtu files indexed by the number of the time step and the name of the time stepping method. Of course, the (exact) result should really be the same for all time stepping method, but the output here at least allows us to compare them.\n\nvoid Diffusion::output_results(const unsigned int time_step,\n{\nstd::string method_name;\nswitch (method)\n{\ncase TimeStepping::FORWARD_EULER:\n{\nmethod_name = \"forward_euler\";\nbreak;\n}\ncase TimeStepping::RK_THIRD_ORDER:\n{\nmethod_name = \"rk3\";\nbreak;\n}\ncase TimeStepping::RK_CLASSIC_FOURTH_ORDER:\n{\nmethod_name = \"rk4\";\nbreak;\n}\ncase TimeStepping::BACKWARD_EULER:\n{\nmethod_name = \"backward_euler\";\nbreak;\n}\ncase TimeStepping::IMPLICIT_MIDPOINT:\n{\nmethod_name = \"implicit_midpoint\";\nbreak;\n}\ncase TimeStepping::SDIRK_TWO_STAGES:\n{\nmethod_name = \"sdirk\";\nbreak;\n}\ncase TimeStepping::HEUN_EULER:\n{\nmethod_name = \"heun_euler\";\nbreak;\n}\ncase TimeStepping::BOGACKI_SHAMPINE:\n{\nmethod_name = \"bocacki_shampine\";\nbreak;\n}\ncase TimeStepping::DOPRI:\n{\nmethod_name = \"dopri\";\nbreak;\n}\ncase TimeStepping::FEHLBERG:\n{\nmethod_name = \"fehlberg\";\nbreak;\n}\ncase TimeStepping::CASH_KARP:\n{\nmethod_name = \"cash_karp\";\nbreak;\n}\ndefault:\n{\nbreak;\n}\n}\nDataOut<2> data_out;\ndata_out.attach_dof_handler(dof_handler);\ndata_out.build_patches();\nconst std::string filename = \"solution-\" + method_name + \"-\" +\nUtilities::int_to_string(time_step, 3) +\n\".vtu\";\nstd::ofstream output(filename);\ndata_out.write_vtu(output);\n}\n\nDiffusion::explicit_method\n\nThis function is the driver for all the explicit methods. At the top it initializes the time stepping and the solution (by setting it to zero and then ensuring that boundary value and hanging node constraints are respected; of course, with the mesh we use here, hanging node constraints are not in fact an issue). It then calls evolve_one_time_step which performs one time step.\n\nFor explicit methods, evolve_one_time_step needs to evaluate $$M^{-1}(f(t,y))$$, i.e, it needs evaluate_diffusion. Because evaluate_diffusion is a member function, it needs to be bound to this. After each evolution step, we again apply the correct boundary values and hanging node constraints.\n\nFinally, the solution is output every 10 time steps.\n\nvoid Diffusion::explicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time)\n{\nconst double time_step =\n(final_time - initial_time) / static_cast<double>(n_time_steps);\ndouble time = initial_time;\nsolution = 0.;\nconstraint_matrix.distribute(solution);\nmethod);\noutput_results(0, method);\nfor (unsigned int i = 0; i < n_time_steps; ++i)\n{\ntime = explicit_runge_kutta.evolve_one_time_step(\n[this](const double time, const Vector<double> &y) {\nreturn this->evaluate_diffusion(time, y);\n},\ntime,\ntime_step,\nsolution);\nconstraint_matrix.distribute(solution);\nif ((i + 1) % 10 == 0)\noutput_results(i + 1, method);\n}\n}\n\nDiffusion::implicit_method\n\nThis function is equivalent to explicit_method but for implicit methods. When using implicit methods, we need to evaluate $$M^{-1}(f(t,y))$$ and $$\\left(I-\\tau M^{-1} \\frac{\\partial f(t,y)}{\\partial y}\\right)^{-1}$$ for which we use the two member functions previously introduced.\n\nvoid Diffusion::implicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time)\n{\nconst double time_step =\n(final_time - initial_time) / static_cast<double>(n_time_steps);\ndouble time = initial_time;\nsolution = 0.;\nconstraint_matrix.distribute(solution);\nmethod);\noutput_results(0, method);\nfor (unsigned int i = 0; i < n_time_steps; ++i)\n{\ntime = implicit_runge_kutta.evolve_one_time_step(\n[this](const double time, const Vector<double> &y) {\nreturn this->evaluate_diffusion(time, y);\n},\n[this](const double time, const double tau, const Vector<double> &y) {\nreturn this->id_minus_tau_J_inverse(time, tau, y);\n},\ntime,\ntime_step,\nsolution);\nconstraint_matrix.distribute(solution);\nif ((i + 1) % 10 == 0)\noutput_results(i + 1, method);\n}\n}\n\nDiffusion::embedded_explicit_method\n\nThis function is the driver for the embedded explicit methods. It requires more parameters:\n\n• coarsen_param: factor multiplying the current time step when the error is below the threshold.\n• refine_param: factor multiplying the current time step when the error is above the threshold.\n• min_delta: smallest time step acceptable.\n• max_delta: largest time step acceptable.\n• refine_tol: threshold above which the time step is refined.\n• coarsen_tol: threshold below which the time step is coarsen. Embedded methods use a guessed time step. If the error using this time step is too large, the time step will be reduced. If the error is below the threshold, a larger time step will be tried for the next time step. delta_t_guess is the guessed time step produced by the embedded method.\nunsigned int Diffusion::embedded_explicit_method(\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time)\n{\ndouble time_step =\n(final_time - initial_time) / static_cast<double>(n_time_steps);\ndouble time = initial_time;\nconst double coarsen_param = 1.2;\nconst double refine_param = 0.8;\nconst double min_delta = 1e-8;\nconst double max_delta = 10 * time_step;\nconst double refine_tol = 1e-1;\nconst double coarsen_tol = 1e-5;\nsolution = 0.;\nconstraint_matrix.distribute(solution);\nembedded_explicit_runge_kutta(method,\ncoarsen_param,\nrefine_param,\nmin_delta,\nmax_delta,\nrefine_tol,\ncoarsen_tol);\noutput_results(0, method);\n\nNow for the time loop. The last time step is chosen such that the final time is exactly reached.\n\nunsigned int n_steps = 0;\nwhile (time < final_time)\n{\nif (time + time_step > final_time)\ntime_step = final_time - time;\ntime = embedded_explicit_runge_kutta.evolve_one_time_step(\n[this](const double time, const Vector<double> &y) {\nreturn this->evaluate_diffusion(time, y);\n},\ntime,\ntime_step,\nsolution);\nconstraint_matrix.distribute(solution);\nif ((n_steps + 1) % 10 == 0)\noutput_results(n_steps + 1, method);\ntime_step = embedded_explicit_runge_kutta.get_status().delta_t_guess;\n++n_steps;\n}\nreturn n_steps;\n}\n\nDiffusion::run\n\nThe following is the main function of the program. At the top, we create the grid (a [0,5]x[0,5] square) and refine it four times to get a mesh that has 16 by 16 cells, for a total of 256. We then set the boundary indicator to 1 for those parts of the boundary where $$x=0$$ and $$x=5$$.\n\nvoid Diffusion::run()\n{\nGridGenerator::hyper_cube(triangulation, 0., 5.);\ntriangulation.refine_global(4);\nfor (const auto &cell : triangulation.active_cell_iterators())\nfor (unsigned int f = 0; f < GeometryInfo<2>::faces_per_cell; ++f)\nif (cell->face(f)->at_boundary())\n{\nif ((cell->face(f)->center() == 0.) ||\n(cell->face(f)->center() == 5.))\ncell->face(f)->set_boundary_id(1);\nelse\ncell->face(f)->set_boundary_id(0);\n}\n\nNext, we set up the linear systems and fill them with content so that they can be used throughout the time stepping process:\n\nsetup_system();\nassemble_system();\n\nFinally, we solve the diffusion problem using several of the Runge-Kutta methods implemented in namespace TimeStepping, each time outputting the error at the end time. (As explained in the introduction, since the exact solution is zero at the final time, the error equals the numerical solution and can be computed by just taking the $$l_2$$ norm of the solution vector.)\n\nunsigned int n_steps = 0;\nconst unsigned int n_time_steps = 200;\nconst double initial_time = 0.;\nconst double final_time = 10.;\nstd::cout << \"Explicit methods:\" << std::endl;\nexplicit_method(TimeStepping::FORWARD_EULER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Forward Euler: error=\" << solution.l2_norm()\n<< std::endl;\nexplicit_method(TimeStepping::RK_THIRD_ORDER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Third order Runge-Kutta: error=\" << solution.l2_norm()\n<< std::endl;\nexplicit_method(TimeStepping::RK_CLASSIC_FOURTH_ORDER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Fourth order Runge-Kutta: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << std::endl;\nstd::cout << \"Implicit methods:\" << std::endl;\nimplicit_method(TimeStepping::BACKWARD_EULER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Backward Euler: error=\" << solution.l2_norm()\n<< std::endl;\nimplicit_method(TimeStepping::IMPLICIT_MIDPOINT,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Implicit Midpoint: error=\" << solution.l2_norm()\n<< std::endl;\nimplicit_method(TimeStepping::CRANK_NICOLSON,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Crank-Nicolson: error=\" << solution.l2_norm()\n<< std::endl;\nimplicit_method(TimeStepping::SDIRK_TWO_STAGES,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"SDIRK: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << std::endl;\nstd::cout << \"Embedded explicit methods:\" << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::HEUN_EULER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Heun-Euler: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::BOGACKI_SHAMPINE,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Bogacki-Shampine: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::DOPRI,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Dopri: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::FEHLBERG,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Fehlberg: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::CASH_KARP,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Cash-Karp: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\n}\n} // namespace Step52\n\nThe main() function\n\nThe following main function is similar to previous examples and need not be commented on.\n\nint main()\n{\ntry\n{\nStep52::Diffusion diffusion;\ndiffusion.run();\n}\ncatch (std::exception &exc)\n{\nstd::cerr << std::endl\n<< std::endl\n<< \"----------------------------------------------------\"\n<< std::endl;\nstd::cerr << \"Exception on processing: \" << std::endl\n<< exc.what() << std::endl\n<< \"Aborting!\" << std::endl\n<< \"----------------------------------------------------\"\n<< std::endl;\nreturn 1;\n}\ncatch (...)\n{\nstd::cerr << std::endl\n<< std::endl\n<< \"----------------------------------------------------\"\n<< std::endl;\nstd::cerr << \"Unknown exception!\" << std::endl\n<< \"Aborting!\" << std::endl\n<< \"----------------------------------------------------\"\n<< std::endl;\nreturn 1;\n};\nreturn 0;\n}\n\nResults\n\nThe point of this program is less to show particular results, but instead to show how it is done. This we have already demonstrated simply by discussing the code above. Consequently, the output the program yields is relatively sparse and consists only of the console output and the solutions given in VTU format for visualization.\n\nThe console output contains both errors and, for some of the methods, the number of steps they performed:\n\nExplicit methods:\nForward Euler: error=1.00883\nThird order Runge-Kutta: error=0.000227982\nFourth order Runge-Kutta: error=1.90541e-06\nImplicit methods:\nBackward Euler: error=1.03428\nImplicit Midpoint: error=0.00862702\nCrank-Nicolson: error=0.00862675\nSDIRK: error=0.0042349\nEmbedded %explicit methods:\nHeun-Euler: error=0.0073012\nsteps performed=284\nBogacki-Shampine: error=0.000403281\nsteps performed=181\nDopri: error=0.0165485\nsteps performed=119\nFehlberg: error=0.00104926\nsteps performed=106\nCash-Karp: error=8.59366e-07\nsteps performed=107\n\nAs expected the higher order methods give (much) more accurate solutions. We also see that the (rather inaccurate) Heun-Euler method increased the number of time steps in order to satisfy the tolerance. On the other hand, the other embedded methods used a lot less time steps than what was prescribed.\n\nThe plain program\n\n/* ---------------------------------------------------------------------\n*\n* Copyright (C) 2014 - 2019 by the deal.II authors\n*\n* This file is part of the deal.II library.\n*\n* The deal.II library is free software; you can use it, redistribute\n* it, and/or modify it under the terms of the GNU Lesser General\n* version 2.1 of the License, or (at your option) any later version.\n* The full text of the license can be found in the file LICENSE.md at\n* the top level directory of deal.II.\n*\n* ---------------------------------------------------------------------\n*\n* Authors: Damien Lebrun-Grandie, Bruno Turcksin, 2014\n*/\n#include <deal.II/base/function.h>\n#include <deal.II/grid/grid_generator.h>\n#include <deal.II/grid/tria_accessor.h>\n#include <deal.II/grid/tria_iterator.h>\n#include <deal.II/grid/tria.h>\n#include <deal.II/grid/grid_out.h>\n#include <deal.II/dofs/dof_handler.h>\n#include <deal.II/dofs/dof_accessor.h>\n#include <deal.II/dofs/dof_tools.h>\n#include <deal.II/fe/fe_q.h>\n#include <deal.II/fe/fe_values.h>\n#include <deal.II/lac/affine_constraints.h>\n#include <deal.II/lac/sparse_direct.h>\n#include <deal.II/numerics/vector_tools.h>\n#include <deal.II/numerics/data_out.h>\n#include <fstream>\n#include <iostream>\n#include <cmath>\n#include <map>\n#include <deal.II/base/time_stepping.h>\nnamespace Step52\n{\nusing namespace dealii;\nclass Diffusion\n{\npublic:\nDiffusion();\nvoid run();\nprivate:\nvoid setup_system();\nvoid assemble_system();\ndouble get_source(const double time, const Point<2> &point) const;\nVector<double> evaluate_diffusion(const double time,\nconst Vector<double> &y) const;\nVector<double> id_minus_tau_J_inverse(const double time,\nconst double tau,\nconst Vector<double> &y);\nvoid output_results(const unsigned int time_step,\nvoid explicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time);\nvoid implicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time);\nunsigned int\nembedded_explicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time);\nconst unsigned int fe_degree;\nconst double diffusion_coefficient;\nconst double absorption_cross_section;\nTriangulation<2> triangulation;\nconst FE_Q<2> fe;\nDoFHandler<2> dof_handler;\nAffineConstraints<double> constraint_matrix;\nSparsityPattern sparsity_pattern;\nSparseMatrix<double> system_matrix;\nSparseMatrix<double> mass_matrix;\nSparseMatrix<double> mass_minus_tau_Jacobian;\nSparseDirectUMFPACK inverse_mass_matrix;\nVector<double> solution;\n};\nDiffusion::Diffusion()\n: fe_degree(2)\n, diffusion_coefficient(1. / 30.)\n, absorption_cross_section(1.)\n, fe(fe_degree)\n, dof_handler(triangulation)\n{}\nvoid Diffusion::setup_system()\n{\ndof_handler.distribute_dofs(fe);\n1,\nconstraint_matrix);\nconstraint_matrix.close();\nDynamicSparsityPattern dsp(dof_handler.n_dofs());\nDoFTools::make_sparsity_pattern(dof_handler, dsp, constraint_matrix);\nsparsity_pattern.copy_from(dsp);\nsystem_matrix.reinit(sparsity_pattern);\nmass_matrix.reinit(sparsity_pattern);\nmass_minus_tau_Jacobian.reinit(sparsity_pattern);\nsolution.reinit(dof_handler.n_dofs());\n}\nvoid Diffusion::assemble_system()\n{\nsystem_matrix = 0.;\nmass_matrix = 0.;\nFEValues<2> fe_values(fe,\nconst unsigned int dofs_per_cell = fe.dofs_per_cell;\nconst unsigned int n_q_points = quadrature_formula.size();\nFullMatrix<double> cell_matrix(dofs_per_cell, dofs_per_cell);\nFullMatrix<double> cell_mass_matrix(dofs_per_cell, dofs_per_cell);\nstd::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);\nfor (const auto &cell : dof_handler.active_cell_iterators())\n{\ncell_matrix = 0.;\ncell_mass_matrix = 0.;\nfe_values.reinit(cell);\nfor (unsigned int q_point = 0; q_point < n_q_points; ++q_point)\nfor (unsigned int i = 0; i < dofs_per_cell; ++i)\nfor (unsigned int j = 0; j < dofs_per_cell; ++j)\n{\ncell_matrix(i, j) +=\n((-diffusion_coefficient * // (-D\n- absorption_cross_section * // -Sigma\nfe_values.shape_value(i, q_point) * // * phi_i\nfe_values.shape_value(j, q_point)) // * phi_j)\n* fe_values.JxW(q_point)); // * dx\ncell_mass_matrix(i, j) += fe_values.shape_value(i, q_point) *\nfe_values.shape_value(j, q_point) *\nfe_values.JxW(q_point);\n}\ncell->get_dof_indices(local_dof_indices);\nconstraint_matrix.distribute_local_to_global(cell_matrix,\nlocal_dof_indices,\nsystem_matrix);\nconstraint_matrix.distribute_local_to_global(cell_mass_matrix,\nlocal_dof_indices,\nmass_matrix);\n}\ninverse_mass_matrix.initialize(mass_matrix);\n}\ndouble Diffusion::get_source(const double time, const Point<2> &point) const\n{\nconst double intensity = 10.;\nconst double frequency = numbers::PI / 10.;\nconst double b = 5.;\nconst double x = point(0);\nreturn intensity *\n(frequency * std::cos(frequency * time) * (b * x - x * x) +\nstd::sin(frequency * time) *\n(absorption_cross_section * (b * x - x * x) +\n2. * diffusion_coefficient));\n}\nVector<double> Diffusion::evaluate_diffusion(const double time,\nconst Vector<double> &y) const\n{\nVector<double> tmp(dof_handler.n_dofs());\ntmp = 0.;\nsystem_matrix.vmult(tmp, y);\nFEValues<2> fe_values(fe,\nconst unsigned int dofs_per_cell = fe.dofs_per_cell;\nconst unsigned int n_q_points = quadrature_formula.size();\nVector<double> cell_source(dofs_per_cell);\nstd::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);\nfor (const auto &cell : dof_handler.active_cell_iterators())\n{\ncell_source = 0.;\nfe_values.reinit(cell);\nfor (unsigned int q_point = 0; q_point < n_q_points; ++q_point)\n{\nconst double source =\nfor (unsigned int i = 0; i < dofs_per_cell; ++i)\ncell_source(i) += fe_values.shape_value(i, q_point) * // phi_i(x)\nsource * // * S(x)\nfe_values.JxW(q_point); // * dx\n}\ncell->get_dof_indices(local_dof_indices);\nconstraint_matrix.distribute_local_to_global(cell_source,\nlocal_dof_indices,\ntmp);\n}\nVector<double> value(dof_handler.n_dofs());\ninverse_mass_matrix.vmult(value, tmp);\nreturn value;\n}\nVector<double> Diffusion::id_minus_tau_J_inverse(const double /*time*/,\nconst double tau,\nconst Vector<double> &y)\n{\nSparseDirectUMFPACK inverse_mass_minus_tau_Jacobian;\nmass_minus_tau_Jacobian.copy_from(mass_matrix);\ninverse_mass_minus_tau_Jacobian.initialize(mass_minus_tau_Jacobian);\nVector<double> tmp(dof_handler.n_dofs());\nmass_matrix.vmult(tmp, y);\nVector<double> result(y);\ninverse_mass_minus_tau_Jacobian.vmult(result, tmp);\nreturn result;\n}\nvoid Diffusion::output_results(const unsigned int time_step,\n{\nstd::string method_name;\nswitch (method)\n{\ncase TimeStepping::FORWARD_EULER:\n{\nmethod_name = \"forward_euler\";\nbreak;\n}\ncase TimeStepping::RK_THIRD_ORDER:\n{\nmethod_name = \"rk3\";\nbreak;\n}\ncase TimeStepping::RK_CLASSIC_FOURTH_ORDER:\n{\nmethod_name = \"rk4\";\nbreak;\n}\ncase TimeStepping::BACKWARD_EULER:\n{\nmethod_name = \"backward_euler\";\nbreak;\n}\ncase TimeStepping::IMPLICIT_MIDPOINT:\n{\nmethod_name = \"implicit_midpoint\";\nbreak;\n}\ncase TimeStepping::SDIRK_TWO_STAGES:\n{\nmethod_name = \"sdirk\";\nbreak;\n}\ncase TimeStepping::HEUN_EULER:\n{\nmethod_name = \"heun_euler\";\nbreak;\n}\ncase TimeStepping::BOGACKI_SHAMPINE:\n{\nmethod_name = \"bocacki_shampine\";\nbreak;\n}\ncase TimeStepping::DOPRI:\n{\nmethod_name = \"dopri\";\nbreak;\n}\ncase TimeStepping::FEHLBERG:\n{\nmethod_name = \"fehlberg\";\nbreak;\n}\ncase TimeStepping::CASH_KARP:\n{\nmethod_name = \"cash_karp\";\nbreak;\n}\ndefault:\n{\nbreak;\n}\n}\nDataOut<2> data_out;\ndata_out.attach_dof_handler(dof_handler);\ndata_out.build_patches();\nconst std::string filename = \"solution-\" + method_name + \"-\" +\nUtilities::int_to_string(time_step, 3) +\n\".vtu\";\nstd::ofstream output(filename);\ndata_out.write_vtu(output);\n}\nvoid Diffusion::explicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time)\n{\nconst double time_step =\n(final_time - initial_time) / static_cast<double>(n_time_steps);\ndouble time = initial_time;\nsolution = 0.;\nconstraint_matrix.distribute(solution);\nmethod);\noutput_results(0, method);\nfor (unsigned int i = 0; i < n_time_steps; ++i)\n{\ntime = explicit_runge_kutta.evolve_one_time_step(\n[this](const double time, const Vector<double> &y) {\nreturn this->evaluate_diffusion(time, y);\n},\ntime,\ntime_step,\nconstraint_matrix.distribute(solution);\nif ((i + 1) % 10 == 0)\noutput_results(i + 1, method);\n}\n}\nvoid Diffusion::implicit_method(const TimeStepping::runge_kutta_method method,\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time)\n{\nconst double time_step =\n(final_time - initial_time) / static_cast<double>(n_time_steps);\ndouble time = initial_time;\nsolution = 0.;\nconstraint_matrix.distribute(solution);\nmethod);\noutput_results(0, method);\nfor (unsigned int i = 0; i < n_time_steps; ++i)\n{\ntime = implicit_runge_kutta.evolve_one_time_step(\n[this](const double time, const Vector<double> &y) {\nreturn this->evaluate_diffusion(time, y);\n},\n[this](const double time, const double tau, const Vector<double> &y) {\nreturn this->id_minus_tau_J_inverse(time, tau, y);\n},\ntime,\ntime_step,\nconstraint_matrix.distribute(solution);\nif ((i + 1) % 10 == 0)\noutput_results(i + 1, method);\n}\n}\nunsigned int Diffusion::embedded_explicit_method(\nconst unsigned int n_time_steps,\nconst double initial_time,\nconst double final_time)\n{\ndouble time_step =\n(final_time - initial_time) / static_cast<double>(n_time_steps);\ndouble time = initial_time;\nconst double coarsen_param = 1.2;\nconst double refine_param = 0.8;\nconst double min_delta = 1e-8;\nconst double max_delta = 10 * time_step;\nconst double refine_tol = 1e-1;\nconst double coarsen_tol = 1e-5;\nsolution = 0.;\nconstraint_matrix.distribute(solution);\nembedded_explicit_runge_kutta(method,\ncoarsen_param,\nrefine_param,\nmin_delta,\nmax_delta,\nrefine_tol,\ncoarsen_tol);\noutput_results(0, method);\nunsigned int n_steps = 0;\nwhile (time < final_time)\n{\nif (time + time_step > final_time)\ntime_step = final_time - time;\ntime = embedded_explicit_runge_kutta.evolve_one_time_step(\n[this](const double time, const Vector<double> &y) {\nreturn this->evaluate_diffusion(time, y);\n},\ntime,\ntime_step,\nconstraint_matrix.distribute(solution);\nif ((n_steps + 1) % 10 == 0)\noutput_results(n_steps + 1, method);\ntime_step = embedded_explicit_runge_kutta.get_status().delta_t_guess;\n++n_steps;\n}\nreturn n_steps;\n}\nvoid Diffusion::run()\n{\nGridGenerator::hyper_cube(triangulation, 0., 5.);\ntriangulation.refine_global(4);\nfor (const auto &cell : triangulation.active_cell_iterators())\nfor (unsigned int f = 0; f < GeometryInfo<2>::faces_per_cell; ++f)\nif (cell->face(f)->at_boundary())\n{\nif ((cell->face(f)->center() == 0.) ||\n(cell->face(f)->center() == 5.))\ncell->face(f)->set_boundary_id(1);\nelse\ncell->face(f)->set_boundary_id(0);\n}\nsetup_system();\nassemble_system();\nunsigned int n_steps = 0;\nconst unsigned int n_time_steps = 200;\nconst double initial_time = 0.;\nconst double final_time = 10.;\nstd::cout << \"Explicit methods:\" << std::endl;\nexplicit_method(TimeStepping::FORWARD_EULER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Forward Euler: error=\" << solution.l2_norm()\n<< std::endl;\nexplicit_method(TimeStepping::RK_THIRD_ORDER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Third order Runge-Kutta: error=\" << solution.l2_norm()\n<< std::endl;\nexplicit_method(TimeStepping::RK_CLASSIC_FOURTH_ORDER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Fourth order Runge-Kutta: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << std::endl;\nstd::cout << \"Implicit methods:\" << std::endl;\nimplicit_method(TimeStepping::BACKWARD_EULER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Backward Euler: error=\" << solution.l2_norm()\n<< std::endl;\nimplicit_method(TimeStepping::IMPLICIT_MIDPOINT,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Implicit Midpoint: error=\" << solution.l2_norm()\n<< std::endl;\nimplicit_method(TimeStepping::CRANK_NICOLSON,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Crank-Nicolson: error=\" << solution.l2_norm()\n<< std::endl;\nimplicit_method(TimeStepping::SDIRK_TWO_STAGES,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"SDIRK: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << std::endl;\nstd::cout << \"Embedded explicit methods:\" << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::HEUN_EULER,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Heun-Euler: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::BOGACKI_SHAMPINE,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Bogacki-Shampine: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::DOPRI,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Dopri: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::FEHLBERG,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Fehlberg: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\nn_steps = embedded_explicit_method(TimeStepping::CASH_KARP,\nn_time_steps,\ninitial_time,\nfinal_time);\nstd::cout << \"Cash-Karp: error=\" << solution.l2_norm()\n<< std::endl;\nstd::cout << \" steps performed=\" << n_steps << std::endl;\n}\n} // namespace Step52\nint main()\n{\ntry\n{\nStep52::Diffusion diffusion;\ndiffusion.run();\n}\ncatch (std::exception &exc)\n{\nstd::cerr << std::endl\n<< std::endl\n<< \"----------------------------------------------------\"\n<< std::endl;\nstd::cerr << \"Exception on processing: \" << std::endl\n<< exc.what() << std::endl\n<< \"Aborting!\" << std::endl\n<< \"----------------------------------------------------\"\n<< std::endl;\nreturn 1;\n}\ncatch (...)\n{\nstd::cerr << std::endl\n<< std::endl\n<< \"----------------------------------------------------\"\n<< std::endl;\nstd::cerr << \"Unknown exception!\" << std::endl\n<< \"Aborting!\" << std::endl\n<< \"----------------------------------------------------\"\n<< std::endl;\nreturn 1;\n};\nreturn 0;\n}" ]
[ null, "https://dealii.org/developer/doxygen/deal.II/logo200.png", null ]
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https://stats.stackexchange.com/questions/124489/how-to-calculate-the-hr-and-95ci-using-the-log-rank-test-in-r
[ "How to calculate the HR and 95%CI using the log-rank test in R?\n\nThe R survival package is very useful to do survival analysis. And I know the survdiff function can be used to compare the difference of survival time in two or more groups. And the p-value number can also be calculated as below. However, how can I calculate the HR and 95% CI using the log-rank test.\n\nAnd I also know I can use the coxph() function to calculate the HR and 95% CI using the Cox regression. However, as the assumption of both the Cox model and log-rank test are that the hazard ratio stay constant over time, so I think I can also calculate the HR and 95% CI using the log-rank test.\n\nAccording to the book Survival Analysis: A Practical Approach, I got two formulas on Page 62 and 66 to do this (as shown below). So I wrote the R code as below, is there anybody know whether I'm right?", null, "", null, "Input codes:\n\nlibrary(survival)\ndata.survdiff <- survdiff(Surv(time, status) ~ group)\np.val = 1 - pchisq(data.survdiff$chisq, length(data.survdiff$n) - 1)\nHR = (data.survdiff$obs/data.survdiff$exp)/(data.survdiff$obs/data.survdiff$exp)\nup95 = exp(log(HR) + qnorm(0.975)*sqrt(1/data.survdiff$exp+1/data.survdiff$exp))\nlow95 = exp(log(HR) - qnorm(0.975)*sqrt(1/data.survdiff$exp+1/data.survdiff$exp))\n\nOutput results:\n\n> data.survdiff\nCall:\nsurvdiff(formula = Surv(data[, \"os_whw\"], data[, \"status_whw\"] ==\n1) ~ data[, \"pcascore\"] >= median(data[, \"pcascore\"]))\n\nN Observed Expected (O-E)^2/E (O-E)^2/V\ndata[, \"pcascore\"] >= median(data[, \"pcascore\"])=FALSE 4 3 4.33 0.411 0.974\ndata[, \"pcascore\"] >= median(data[, \"pcascore\"])=TRUE 5 5 3.67 0.486 0.974\n\nChisq= 1 on 1 degrees of freedom, p= 0.324\n> p.val\n 0.3235935\n> HR\n 1.970484\n> up95\n 7.917248\n> low95\n 0.4904239\n\nIf your research question is whether groups differ in survival, regardless of other characteristics, you could use the ordinary Kaplan-Meier estimation and obtain p values. That p value is derived from the log rank test. It will merely tell you if groups differ in survival time. That is appropriate if (1) groups are randomized, or (2) you only want to know if groups differ in survivalor (3) you'd like to inspect survival curves.\n\nHowever, if groups are not randomized and they differ in baseline charactersitics (e.g age, sex etc) then crude survival differences are of little use (e.g differences in survival might be due to age differences); thats when Cox regression comes in. You can use Cox regression to compare survival and adjust for confounders. If your Cox regression does not contain any other predictor than 'group', it will yied same p value as the log rank test from the Kaplan-Meier estimation. But the Cox regession allows you to obtain hazard ratios with confidence intervals for each predictor, along with p values.\n\nUse the coxph function from survival package or the cph function from rms package.\n\nIn general there is no reason to tweak this in any other way. I think you'll be fine using the functions from the Rms package, which is accompanied by an excellent book with the same name as the package (Springer; FE Harrell). The package comes with functions that let you visualize and tabulate your results easily.\n\nThere might be theoretical reasons for your approach which is beyond me, but in that case one of the experts might guide us. In other scenarios, you'll be fine with this approach.\n\n(Btw: you can obtain Cox adjusted survival curves; google it or check out RMS package documentation).\n\nPosting here as I do not have enough rep. to comment. Your implementation seems correct, and you are right in thinking that the log-rank can be used to find the HR and 95%-Interval, I do have a couple of questions thought:\n\n1. Is there any particular reason why you are recalculating the p-value? (as the survdiff()-function already provides it, it just seems like extra work).\n2. Is the HR and accompanying 95% interval, found using your functions, in accordance with that found using the coxph()-function? That is use the coxph()-function to validate your own implementation.\n\nNote: Why use the log-rank test to calculate the HR and 95%CI, when the coxph()-function does it for you? In order to practise, to see if your understood the material or just for the lulz?\n\n• 1. It's ture that the survdiff() function already provides the p-value, but you want to extract the p-value when you deal with many data. For example, you want to compare the difference between age>= 60 or not, sex, race, cohort, treatment protocol and so on. You can put them into a \"for\" cycle and only output the p-value every time. 2. Both the Cox and log-rank test can give HR and 95% CI. I just want to use the two methods to select more robust predictors. I used both the two methods at the same time. – zjuwhw Nov 18 '14 at 12:09\n• I could be wrong - but it seems to me that log-rank test is primarily used as a hypothesis test for the null hypothesis \"two groups having identical survival and hazard functions\" (en.wikipedia.org/wiki/Log-rank_test), it is probably not able to give HR estimate. BTW, what do you mean by \"more robust predictor\"? Variable selection is in general a bad idea, see for example 4.3 in: biostat.mc.vanderbilt.edu/wiki/pub/Main/RmS/rms.pdf See Sec 4.10 for general modeling strategy and Sec 18 of the same for a tutorial in Cox Regression. Hope this helps. – Clark Chong Nov 19 '14 at 5:50\n• Hi, Clark. Thank you for your kind and helpful comments. I agree with your idea that log-rank test is used to compare the survival of two groups. However, I think it can be used to give HR, the reason has been included in the question. And I'm a bioinformatic to deal with gene expression data. Your material is useful and I realize the Harrell's package \"rms\" is popular after I begin to use CrossValidated. To select more robust predictor from many predictors means that I want use both log-rank test and Cox to calculate the p-value of a predictor. And I'm also going to use cross validation. – zjuwhw Nov 20 '14 at 6:53" ]
[ null, "https://i.stack.imgur.com/vyOPa.png", null, "https://i.stack.imgur.com/NuJw1.png", null ]
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https://encyclopedia2.thefreedictionary.com/topological+soliton
[ "topological soliton\n\ntopological soliton\n\n[¦täp·ə¦läj·ə·kəl ′säl·ə‚tän]\n(physics)\nA soliton whose confinement can be related to the existence of multiple states of minimum energy whose arrangement around the wave has special geometrical properties.\nReferences in periodicals archive ?\nThe ambitious aim of this project is to provide the missing link between fundamental theory and nuclear physics.At the heart of the methodology for this audacious proposal is a concept known as a topological soliton -- a particle-like solution of a nonlinear wave equation, where stability is due to a topological twisting or winding.\nThis section will focus on extracting the shock wave solutions to the KGZ equation (1) and (2) that are also known as topological soliton solution.\nFinally, the numerical simulation that was conducted using finite difference scheme leads to the simulations for the topological soliton solutions.\nIn [5, 6], the ansatz method is applied to obtain the topological soliton solution of the generalized Rosenau-KdV equation.\nBiswas, \"Topological solitons and other solutions of the Rosenau-KdV equation with power law nonlinearity,\" Romanian Journal of Physics, vol.\nIn this model, there appear particle-like excitations as topological solitons. Their mass is field energy only.\nThe investigations seem to support the conjecture that the particles we find in experiments are topological solitons characterised by topological quantum numbers.\nof Kent, UK) provide discussion of the state of research concerning topological solitons. Chapters contain discussion of solitons in classical field theories and the forces that exist between solitons, a survey of static and dynamic multi-soliton solutions, and discussion of kinks in one dimension, lumps and vortices in two dimensions, monopoles and Skyrmions in three dimensions, and instantons in four dimensions.\nThe thesis of the project is: that by careful control of the constituent nanostructure properties, a 3-dimensional medium can be created in which a large number of topological solitons can exist.\nSite: Follow: Share:\nOpen / Close" ]
[ null ]
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https://tristansweeney.com/leetcode/algorithms/2020/04/29/leetcode-subsum-k.html
[ "# Intro and Context\n\nI’ve spent arguably too long trying to intuit the best soution to leetcode’s recent daily challenge, Subsum Equals K. It’s been a year since I’ve done anything algorithmically difficult, since firmware is mostly a game of data structures and synchronization, so this wiped the floor with me like the intro boss of a From Software game.\n\nFrom Software created the games Demon’s Souls, Dark Souls 1 thru 3, Bloodborne, and Sekiro. These games are famous for being unforgivingly difficult. There’s no leinency and a steep learning curve, so newcomers will die repeatedly until finally developing the skills needed to play the game.\n\nMy first of the bunch was Dark Souls 2, and I still remember the joy of finally defeating the first boss, ‘The Last Giant’. I think that’s the same joy felt when finally understanding something difficult. That “a-ha!” moment when you accheve the impossible is worth all the blood, sweat, and tears shed along the way. And I was lucky enough to have two of those moments, as I found a good solution on my own, then got to sort out the magic of the optimal solution.\n\nI started this aside just to give context since I love the games From Software makes, but look at that, it ties in. Life finds a way?\n\nThe problem is this: given an array of integers, find the number of continuous subarrays equal to `k`. Not too hard to solve (I thought), and I quickly whipped something that crushed it (I thought). My strategy was simple and O(n) time, O(1) space: inchworm along the array, advancing the ending index when the sum was greater than `k` and advancing the starting index when the subsum was less than `k`. This woked… for positive integers. It immediately failed when the array had negative numbers in it.", null, "This was hard enough to merit hours of time sunk, so I might as well write a reflection on it, since it’ll help it stick and be potentially useful to anyone who finds this.\n\n# Simple Solution\n\nIt took a while to envision a solution that handled negatives; I stared into the void over the course of two nights while working on this (and admittedly watching Netflix w/ my SO). I felt there was a memoization solution, but couldn’t intuit what I had to memoize since I was stuck thinking I needed a 2d array. This wasn’t shaking out as I put down code. A hint stuck in my mind, `sum(i, j) = sum(0, j) - sum(0, i)`, and I used a spreadsheet to work out what data I needed to memoize.", null, "Clearly I only needed a 1d array of cumulative sums. I calculated that array, and walked all the valid `start, end` pairs, pulling values from that array find if the subarray sum was `k`. I came up with the below (I’m doing these in rust to build some muscle-memory), and felt confident in it. I submitted it, it worked, big horrah and… I was only in the 14th percentile of runtime? What am I missing?\n\n``````impl Solution {\nfn gen_sum_array(nums: &Vec<i32>) -> Vec<i32> {\nlet mut sum_array = vec![0; nums.len()];\nsum_array = nums;\nfor i in 1..nums.len() {\nsum_array[i] = nums[i] + sum_array[i - 1];\n}\nsum_array\n}\n\npub fn subarray_sum(nums: Vec<i32>, k: i32) -> i32 {\nlet sum_array = Self::gen_sum_array(&nums);\nlet mut matches = 0;\nfor i in 0..nums.len() {\nlet basis = if i == 0 { 0 } else { sum_array[i - 1]};\nfor j in i..nums.len() {\nif (sum_array[j] - basis) == k {\nmatches += 1;\n}\n}\n}\nmatches\n}\n}\n``````\n\n## Slight Opimization\n\nThere’s a slight optimization to this approach I missed. The solution I found is O(n^2) time and O(n) space, but it’s O(n^2) time and O(1) space to accumulate the rows of that table on the fly. That makes sense, Since you don’t iterate over more than you did before, you just do marginally more math during that iteration. The solutions leetcode presents are in Java, don’t mind the language change.\n\n``````public class Solution {\npublic int subarraySum(int[] nums, int k) {\nint count = 0;\nfor (int start = 0; start < nums.length; start++) {\nint sum=0;\nfor (int end = start; end < nums.length; end++) {\nsum+=nums[end];\nif (sum == k)\ncount++;\n}\n}\nreturn count;\n}\n}\n``````\n\n# Optimal Solution\n\nThere’s an optimal solution, and I busted my brain for half an hour trying to get why the magic worked. It builds a frequency map as you iterate down the array, and is O(n) time and O(n) space. It’s below, and without meditation on why it worked it seems some eldritch black magic. I’m comment adverse, they often just describe in english what the code clearly is doing, but this is something that I’d expect comments on. I’ll show further down how some careful naming makes this solution more intuitive.\n\n``````public class Solution {\npublic int subarraySum(int[] nums, int k) {\nint count = 0, sum = 0;\nHashMap < Integer, Integer > map = new HashMap < > ();\nmap.put(0, 1);\nfor (int i = 0; i < nums.length; i++) {\nsum += nums[i];\nif (map.containsKey(sum - k))\ncount += map.get(sum - k);\nmap.put(sum, map.getOrDefault(sum, 0) + 1);\n}\nreturn count;\n}\n}\n``````\n\nThe magic works like this: A subarray sums to `k` when `sum(i, j) = k` (obviously). Taking the hint `sum(i, j) = sum(0, j) - sum(0, i)`, we can decompose what condition we’re seeking to `sum(0, j) - sum(0, i) = k`. Rearranging, this condition is `sum(0, j) - k = sum(0, i)`. Let’s define that term `sum(0, j) - k` as the complementary sum.\n\nThe index `j` can be end to all subarrays that have a starting index `i` in the range `0..j`. Assuming we know `sum(0, j)`, we can derive the complementary sum for `j`. The number of subarrays summing to `k` that end at `j` is equal to the number of previous occurances where `sum(0, i)` was that complementary sum.\n\nAssume we have a frequency map `{sum(0, i): num_occurances}` and knowing the complementary sum, the number of subarrays summing to `k` is stored in this map. We may not know where those `i` are, but we only needed to know that they occured.\n\nOf course that map is initalized to to `{0: 1}`, as our sum begins at `0` and we begin exactly once.\n\nHopefully that clarified the philosophy behind the optimal solution. It iterates `0..j`, calculating `sum(0, j)` and it’s complementary sum, incrementing the number of subarrays summing to `k` by the number of times the complentary sum was seen, then stashing `sum(0, j)` into the map as it moves to `j + 1`.\n\n# Conclusion\n\nI think the code is easier to mentally model with variable names slightly massaged, I provided that below. I provided it in rust since I think it’s cleaner, the use of `Option` returns and the hashmap `.entry` function reduces the amount of fumbling with the map object needed to accomplish the needed task. It has some comments explaining the semantics for the uninitiated.\n\nThis solution was difficult to internalize at first, but I’m glad I took the time for it. It turned out to be a good intuition builder, hopefully later algorithm challenges won’t require some deep reflection up on a mountainside.\n\nIt’s 2:51 AM, Elvis left the building and stumbled home a while ago, I’m running on fumes. Hope you’ve enjoyed this. Bye.\n\n``````use std::collections::HashMap;\n\nimpl Solution {\npub fn subarray_sum(nums: Vec<i32>, k: i32) -> i32 {\n/* Map of prior_sum: num_occurences */\nlet mut sum_map = HashMap::new();\nsum_map.insert(0,1); /* Start having seen a sum of zero one time */\n\nlet mut sum = 0;\nlet mut count = 0;\n\nfor v in nums.iter() {\nsum += v;\n\n/* complemtary sum, such that `sum - comp_sum == k` */\nlet comp_sum = sum - k;\n/* rust-iom, `get` returns an Option, unwrap_or returns the\n* value if it's `Some(value)`, or the value passed in if\n* it's `None`.\n*/\ncount += sum_map.get(&comp_sum).unwrap_or(&0);\n/* rust-iom, get the `Entry` object for the key `sum`, if that\n* key doesn't exist insert it with the value 0.\n*\n* The `Entry` is a reference into the map, and `*entry += 1` is\n* the same as `map[i] + 1`.\n*/\n*sum_map.entry(sum).or_insert(0) += 1;\n}\n\ncount\n}\n}\n``````" ]
[ null, "https://tristansweeney.com/images/leetcode_subsum/you_died.jpg", null, "https://tristansweeney.com/images/leetcode_subsum/memo.PNG", null ]
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https://math.stackexchange.com/questions/4261599/2d-convolution-in-analytic-form
[ "# 2d convolution in analytic form\n\nI have an image of a 2D-sinusoidal pattern $$f(x, y)$$ with wavelength $$\\lambda$$ which I would like to convolve with a 2D circular pill-box function $$h(x,y)$$ of radius $$r$$.\n\nThe image is given by $$f(x,y) = \\dfrac{1}{2}\\bigg[1 + \\sin\\bigg(\\dfrac{2\\pi x}{\\lambda}\\bigg)\\bigg].$$ Similarly the circular pill-box function is given by $$h(x,y)= \\dfrac{1}{\\pi r^2} \\begin{cases} 1& \\text{if } x^2 + y^2 \\leq r^2\\\\ 0 & \\text{otherwise} \\end{cases}$$ $$\\qquad$$ where the scaling constant $$\\dfrac{1}{\\pi r^2}$$ ensures that the area of the filter is one.\n\nThe 2D convolution integral may be expressed as $$g(x,y) = \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} f(\\tau_u, \\tau_v)\\, h(x - \\tau_u, y-\\tau_v) \\, \\mathrm{d}\\tau_u \\, \\mathrm{d}\\tau_v$$\n\n$$\\qquad$$ where $$\\tau$$ is a dummy variable to represent the shift of one function with respect to the other.\n\nHow do I evaluate the convolution integral so that I can express the convolved image $$g(x,y)$$ in analytic form.\n\n• What do you mean by simplifying in to a special form; could you please be more explict : ) If i plug in the equations of $f(x,y)$ and $h(x,y)$ in the convolution integral, shouldn't I get an expression for the convolved image? Sep 27, 2021 at 11:04\n• If I plug in the expressions for $f(x,y)$ and $g(x,y)$ and evaluate the integral, shouldn't I obtain an expression for $g(x,y)$. For eg $g(x,y) = \\mathrm{sinc\\bigg(\\dfrac{A}{B}\\bigg)} \\dfrac{1}{2}\\bigg[1 + \\sin\\bigg(\\dfrac{2\\pi x}{\\lambda}\\bigg)\\bigg]$, where $A$ and $B$ are some constants. Sep 27, 2021 at 11:14" ]
[ null ]
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https://old.robowiki.net/cgi-bin/robowiki?WritingFastCode/Distance
[ "#", null, "WritingFastCode/Distance\n\nRobo Home | WritingFastCode | Changes | Preferences | AllPages\n\nCalculating the distance between two points is a slow operation due to the call to Math.sqrt(). However you can often use the square of the distance.\n\nFor example, if you're finding which of two enemies is closer:\n\n```\nPoint2D enemyOne;\nPoint2D enemyTwo;\nPoint2D me;\n\n//Slow\nif(me.distance(enemyOne) < me.distance(enemyTwo)){\n...\n}\n\n//Fast\nif(me.distanceSq(enemyOne) < me.distanceSq(enemyTwo)){\n...\n}\n\n```\n\nThe two pieces of code work exactly the same. You can also use this trick for comparing to a constant, like so:\n\n```\nPoint2D enemyOne;\nPoint2D me;\n\n//Slow\nif(me.distance(enemyOne) < 100){\n...\n}\n\n//Fast\nif(me.distanceSq(enemyOne) < 10000){ // distance is less than 100\n...\n}\n\n```\n\nThis optimization is only worth doing inside loops that get called a lot, Math.sqrt() a few times is fine but once you start doing thousands of calls it can really slow your bot down.\n\nDiscussion\n\nRobo Home | WritingFastCode | Changes | Preferences | AllPages" ]
[ null, "https://old.robowiki.net/images/RoboWiki.png", null ]
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https://www.freepatentsonline.com/y2010/0046414.html
[ "Title:\nSYSTEMS AND METHODS FOR LEVERAGING SPATIAL REUSE IN OFDMA RELAY NETWORKS\nKind Code:\nA1\n\nAbstract:\nSystems and methods for scheduling transmission that leverages both diversity and spatial reuse gains in the presence of finite user buffers in a two-hop wireless relay setting are disclosed. The system includes partitioning a set of relays to enable spatial reuse while accounting for half-duplex nature of relays, and assigning and reusing of channels to the relays (and associated users) in the two partitions to maximize the aggregate system throughput while ensuring proportional fairness.\n\nInventors:\nSundaresan, Karthikeyan (Howell, NJ, US)\nApplication Number:\n12/388398\nPublication Date:\n02/25/2010\nFiling Date:\n02/18/2009\nExport Citation:\nAssignee:\nNEC LABORATORIES AMERICA, INC. (Princeton, NJ, US)\nPrimary Class:\nOther Classes:\n370/329\nInternational Classes:\nH04B7/14; H04W72/04\nView Patent Images:\nRelated US Applications:\n 20150215806 Congestion Control Method and Device July, 2015 Xu 20040105385 Device for accessing a telecommunication network for the selective degradation of data flows June, 2004 Galand et al. 20130265921 METHOD AND SYSTEM FOR SIGNALING BY BIT MANIPULATION IN COMMUNICATION PROTOCOLS October, 2013 Naim et al. 20100284265 SEQUENCE NUMBER ESTABLISHING METHOD, WIRELESS COMMUNICATION TERMINAL APPARATUS AND WIRELESS COMMUNICATION BASE STATION APPARATUS November, 2010 Ogawa et al. 20160249353 SYSTEM AND METHOD FOR NETWORK CONTROL August, 2016 Nakata et al. 20080259821 DYNAMIC PACKET TRAINING October, 2008 Funk et al. 20120163294 PACKET DATA TRANSFER APPARATUS AND PACKET DATA TRANSFER METHOD IN MOBILE COMMUNICATION SYSTEM June, 2012 Kim et al. 20140177615 METHOD FOR SCANNING A WIRELESS FIDELITY (WI-FI) DIRECT DEVICE AND TERMINAL DEVICE FOR THE SAME June, 2014 Kim et al. 20060126551 Device and method for distributing broadcast services on a local network June, 2006 Delaunay et al. 20070280208 PARTITIONED VOICE COMMUNICATION COMPONENTS OF A COMPUTING PLATFORM December, 2007 Smith et al. 20070091879 Method and apparatus for providing internet protocol connectivity without consulting a domain name system server April, 2007 Croak et al.\n\nPrimary Examiner:\nCHOUDHURY, FAISAL\nAttorney, Agent or Firm:\nNEC LABORATORIES AMERICA, INC. (PRINCETON, NJ, US)\nClaims:\nWhat is claimed is:\n\n1. A method for scheduling transmissions in a relay-enabled two-hop wireless network, comprising: (i) partitioning a set of relays to enable spatial reuse while accounting for half-duplex nature of relays, and (ii) assigning and reusing of channels across the relays (and associated users) in the two partitions to maximize the aggregate system throughput while ensuring proportional fairness.\n\n2. The method of claim 1, comprising grouping wireless sub-carriers to form one or more sub-channels.\n\n3. The method of claim 2, wherein the grouping comprises a distributed model.\n\n4. The method of claim 3, comprising applying a 5/12-approximation for a finite buffer model.\n\n5. The method of claim 2, wherein the grouping comprises a contiguous permutation model.\n\n6. The method of claim 5, comprising applying a ¾-approximation for a back-logged buffer model or a ⅜-approximation for the finite buffer model.\n\n7. The method of claim 2, wherein the grouping comprises a Partially Used Subchannelization (PUSC) model.\n\n8. The method of claim 7, comprising: a. arranging relays in circular geometry while considering contiguous partitions of a relay set; b. for each contiguous partition, determining a schedule of maximum utility; and c. determining a partition that provides the schedule of maximum utility.\n\n9. The method of claim 8, further comprising: a. determining a user under each relay in every pair of relays that provides a maximum utility in the presence of finite buffer and interference for a considered channel; b. selecting a user pair that provides the maximum utility for the considered channel and adding the user pair to the schedule; and c. updating buffers of scheduled users.\n\n10. The method of claim 2, wherein the grouping comprises an Adaptive Modulation and Coding (AMC) model.\n\n11. The method of claim 10, wherein the AMC model includes backlogged buffering, further comprising: a. determining a user pair for each channel that provides a highest marginal utility, where V is a set of chosen pairs and initial empty partitions include L and R; b. determining a mapping from the user pair chosen for each channel to corresponding relay pairs c. determining a relay pair (s1,s2) in V of maximum utility weight and checking a partition feasibility for (s1,s2) and (s2,s1) with current {L,R} d. determining conflicting pairs of (s1,s2) and (s2,s1) as T1 and T2 respectively; e. determining a better fit among {(s1,s2), T2} and {(s2,s1), T1} as A and the other as C; f. adding pairs in A to an existing schedule given by partitions of L and R and adding non-chosen pairs in C to a blocked set B and removing A and C from V. g. adding the relay (user) from each of the pairs in B that provides the higher utility transmission in isolation to its corresponding partition in {L,R}.\n\n12. The method of claim 1, comprising communicating with IEEE 802.16j transceivers.\n\n13. The method of claim 10, wherein the AMC model includes finite buffering, comprising: a. for a given channel, determining a user pair that provides maximum utility with finite buffer and interference; b. processing a scheduling method from the AMC model with backlogged buffering to restore partition feasibility; and c. generating a feasible transmission schedule.\n\n14. A method for scheduling transmission in a relay-enabled two-hop wireless network, comprising: a. receiving a finite user buffer model; b. receiving a two-hop model with interference data for spatial reuse; c. receiving a PUSC and AMC model with user and channel data; and d. performing a scheduling of unicast user data flows with spatial reuse gain and diversity.\n\n15. The method of claim 14, comprising grouping wireless sub-carriers to form one or more sub-channels.\n\n16. The method of claim 15, wherein the grouping comprises a distributed model.\n\n17. The method of claim 16, comprising applying a 5/12-approximation.\n\n18. The method of claim 15, wherein the grouping comprises a contiguous permutation models.\n\n19. The method of claim 18, comprising applying a ¾-approximation for a back-logged buffer or a ⅜-approximation for a finite buffer.\n\n20. A base station in a relay-enabled two-hop wireless network, comprising: a. a finite user buffer model; b. a two-hop model with spatial and reuse data; c. a PUSC and AMC model with users and the channels; and d. a scheduler of unicast user data flows with spatial reuse gain and diversity.\n\nDescription:\n\nThis application claims priority to U.S. Provisional Application Ser. No. 61/090,698 filed Aug. 21, 2008, the content of which is incorporated by reference.\n\n# BACKGROUND\n\nThe last decade has seen a significant amount of research in multi-hop wireless networks (MWNs). While their completely decentralized nature has contributed to scalable solutions, they have also faced significant challenges in moving towards commercial adoption. However, with the next generation wireless networks moving towards smaller (micro, pico) cells for providing higher data rates, there is a revived interest in MWNs from the perspective of integrating them with infrastructure wireless networks. With a decrease in cell size, relays are now needed to provide extended coverage, resulting in a multi-hop network.\n\nUser and channel diversity gains, available in conventional one-hop cellular networks, have been effectively leveraged to improve system performance through several channel-dependent scheduling schemes. However, they do not provide spatial reuse. MWNs on the other hand, provide spatial reuse although their large scale makes it difficult to provide hard performance guarantees. Further, since diversity gains require channel state feedback from relay stations and mobile users and must be exploited at fine time scales (order of frames), they cannot be effectively leveraged in a large multi-hop setting. Relay-enabled networks with a two-hop structure, provide a unique middle-ground between these two networks, providing us access to a multitude of diversity and spatial reuse gains. While this provides potential for significant performance improvement, it also calls for more sophisticated, tailored scheduling solutions that take into account the two-hop nature of the system.\n\nRelay-enabled wireless networks have been used to provide improved coverage and capacity. These networks have gained attention both in the standards community (IEEE 802.16j) and in the industry. Scheduling, being a key component in these networks, has received higher emphasis. These systems are typically the TDMA variants where the scheduling decision reduces mainly to deciding whether to employ a relay or not and for which particular user. They focus on link level performance and do not exploit (i) multiple OFDM channels, and (ii) spatial reuse and diversity across the relay and access hops that is available at a network level.\n\nScheduling forms a crucial component in the efficient exploitation of the spatial reuse and diversity gains delivered by the two-hop relay-assisted cellular networks. Conventional systems leverage only the multi-user and channel diversity gains available in one hop cellular networks. On the other hand, conventional systems that consider scheduling in relay networks do not leverage spatial reuse across hops. Further, conventional relay scheduling solutions do not incorporate finite data in user buffers and instead assume backlogged data. In fact, data in user buffers is limited in practice and incorporation of this aspect along with spatial reuse changes the problem completely, making it more difficult.\n\n# BRIEF DESCRIPTION OF THE DRAWINGS\n\nFIG. 1 is an exemplary block diagram showing a multi hop wireless relay network, associated gains and transmission frame structure.\n\nFIG. 2 shows an exemplary block diagram of a base station with spatial reuse and diversity scheduling operating under PUSC and AMC models, while incorporating finite data in user buffers.\n\nFIG. 3 shows an exemplary flow-chart describing the scheduling operations in the PUSC model with finite buffering.\n\nFIG. 4 shows an exemplary flow-chart describing the scheduling operations in the AMC model with backlogged buffering.\n\nFIG. 5 shows an exemplary flow-chart describing the scheduling operations in the AMC model with finite buffering.\n\n# SUMMARY\n\nSystems and methods for scheduling transmission that leverages both diversity and spatial reuse gains in the presence of finite user buffers in a two-hop wireless relay setting are disclosed.\n\nIn one aspect, the system includes partitioning a set of relays to enable spatial reuse while accounting for half-duplex nature of relays, and assigning and reusing of channels to the relays (and associated users) in the two partitions to maximize the aggregate system throughput while ensuring proportional fairness.\n\nIn another aspect, a method for scheduling transmissions in a relay-enabled two-hop wireless network includes: partitioning a set of relays to enable spatial reuse while accounting for half-duplex nature of relays, and assigning and reusing of channels across the relays (and associated users) in the two partitions to maximize the aggregate system throughput while ensuring proportional fairness.\n\nImplementations of the above aspect may include one or more of the following. The method includes grouping wireless sub-carriers to form one or more sub-channels. The grouping can be a distributed model. The method can apply a 5/12-approximation for the finite buffer model and such the grouping can be a contiguous permutation models. The method can include applying a ¾-approximation for the back-logged buffer model or a ⅜-approximation for the finite buffer model. The grouping can be a Partially Used Subchannelization (PUSC) model. The method can include arranging relays in circular geometry while considering all contiguous partitions of the relay set; for each contiguous partition, determining the schedule of maximum utility; and determining the partition that provides the schedule of maximum utility. The method can also include determining a user under each relay in ever pair of relays that provides maximum utility in the presence of finite buffer and interference for a considered channel; selecting the user pair that provides the maximum utility for the considered channel and adding it to the schedule; and updating buffers of scheduled users. The grouping can be an Adaptive Modulation and Coding (AMC) model. The AMC model includes backlogged buffering with determining a user pair for each channel that provides the highest marginal utility, where V is the set of chosen pairs and initial empty partitions include L and R; determining the mapping from the user pair chosen for each channel to their corresponding relay pairs; determining a relay pair (s1,s2) in V of maximum utility weight and checking a partition feasibility for (s1,s2) and (s2,s1) with current {L,R}; determining conflicting pairs of (s1,s2) and (s2,s1) as T1 and T2 respectively; determining a better fit among {(s1,s2), T2} and {(s2,s1), T1} as A and the other as C; adding pairs in A to an existing schedule given by partitions of L and R and adding non-chosen pairs in C to a blocked set B and removing A and C from V; adding the relay (user) from each of the pairs in B that provides the higher utility transmission in isolation to its corresponding partition in {L,R}. The system can include IEEE 802.16j transceivers. The AMC model can include finite buffering by for a given channel, determining a user pair that provides maximum utility with finite buffer and interference; processing the scheduling method from AMC model with backlogged buffering to restore partition feasibility; and generating a feasible transmission schedule.\n\nAdvantages of the system may include one or more of the following. The system is efficient with performance guarantees for leveraging spatial reuse in addition to diversity gains. To work with the IEEE 802.16j and 802.16m standards, two sub-carrier grouping embodiments can be used, namely distributed grouping such as Partially Used Subchannelization (PUSC) and contiguous grouping such as Adaptive Modulation and Coding (AMC) permutation models. These models define how the sub-carriers are grouped to form a sub-channel. Under distributed permutation, the hardness of the scheduling problem for the finite buffer case is solved with a 5/12-approximation process. Under contiguous permutation, the hardness of the scheduling problem under both back-logged and finite buffer cases is solved through a ¾-approximation and ⅜-approximation processes, respectively.\n\nThe scheduler provides three solutions that provide high performance and run in polynomial time, making it conducive for real-time implementation at BS at the granularity of frames. The three solutions are for the following cases: (i) PUSC with finite user buffers, (ii) AMC with backlogged user buffers, and (iii) AMC with finite user buffers. The three embodiments provide theoretical guarantees of achieving a worst-case performance within a factor of the optimal. In one implementation, the performance guarantees of the three solutions are within about 10% of practical optimum. The running time complexity of each of these solutions is also low, making them conducive for real-time implementation at BS. The solutions are simple greedy algorithms, whose simplicity makes them conducive for implementation at the base station. The solutions involve two main components: (i) partitioning of set of relays to enable spatial reuse while accounting for half-duplex nature of relays, and (ii) assignment and reuse of channels to the relays (and associated users) in the two partitions to maximize the aggregate system throughput while ensuring proportional fairness. Efficient yet simple solutions are devised for each of these components under the PUSC and AMC models and approximation guarantees established with respect to each of these components. The embodiments provide approximate solutions with good worst-case performance guarantees and superior average-case performance. This is achieved even though the determination of the optimal spatial reuse + diversity schedule across two hops in the presence of finite user buffers is an NP-hard problem for both PUSC and AMC models.\n\n# Description\n\nFIG. 1A shows an exemplary block diagram representing a spatial reuse and diversity scheduler at a base station (BS). In this embodiment, the base station is part of a downlink OFDMA-based, relay-enabled, two-hop wireless network. A set of K mobile stations (MS) are uniformly located within an extended cell radius. A small set of R relay stations (RS) are added to the mid-way belt of the network. MS that are closer to the BS directly communicate with it. However, MS farther from the BS connect with the RS that is closest to them. The one-hop links between BS and RS are referred to as relay links, RS and MS as access links, and BS and MS as direct links. The BS, RS and MS are allowed to operate on multiple channels from a set of NT total OFDM sub-channels. Data flows are considered and assumed to originate in the Internet and destined towards the MS. All stations are assumed to be half-duplex. Hence, an RS can be active on only its relay or access link in any slot but not both. Let PS, PR denote the maximum power used by the BS,RS for their transmission (PR≦PB), which is split equally across all sub-channels and no power adaptation across channels is assumed, given the marginal gains resulting from it.\n\nA sub-channel corresponds to a group of sub-carriers. There are two models defined in IEEE 802.16j for sub-carrier grouping, namely distributed and contiguous permutations. In distributed permutation, also referred to as partial usage of sub-carriers (PUSC), the sub-carriers constituting a sub-channel are chosen randomly from the entire frequency spectrum. In contiguous permutation, also referred to as band adaptive modulation and coding (AMC), adjacent sub-carriers are chosen. In PUSC, a single channel quality value (averaged over entire spectrum) is fed back by a RS/MS, which is common to all its sub-channels, thereby eliminating channel diversity and providing only MUD. The random choice of sub-carriers in a channel however helps average out interference. In AMC, the high correlation in channel gains across adjacent sub-carriers helps leverage channel diversity in addition to multi-user diversity through scheduling (eg. channels 3, 2 and 1 assigned to MS 1, 2 and 3 respectively in FIG. 1B). However, a RS/MS now has to feed back channel quality on all its sub-channels to BS.\n\nWhile the addition of relays improves the individual links on the relay and access hops, the packets now take two hops to reach the MS. Spatial reuse forms the key in addressing this loss factor of half arising from multi-hop burden. With comparable values of PR and PB, the spatial separation of RS allows relay (eg. BS-RS3 in FIG. 1A) and access (RS1-MS1) links to operate in tandem, spatially reusing the same set of channels across hops without causing mutual interference (interference from RS1 on RS3 and from BS on MS1 are weaker than the received signal strength from BS and RS3 respectively). Spatial reuse is possible with both PUSC and AMC. MS (RS) provide feedback on interference, i.e. received power from BS (other RS). This embodiment does not reuse channels within the access hop, since it does not lead to benefits unless the access hop becomes the network bottleneck, which is not common. Further, it comes at the cost of spatial reuse across hops, which is a more important feature to be leveraged.\n\nIn the two-hop relay-enabled wireless network, the relay stations (RS) are connected to the wireless infrastructure (base station, BS) and provide improved coverage and capacity to several applications including serving mobile users (MS) in business hot-spots, office buildings, transportation vehicles, coverage holes, among others. The two-hop network model coupled with OFDM provides two key benefits, namely diversity and spatial reuse gains. Two kinds of diversity gains can be exploited through scheduling: (i) multi-user diversity (MUD): for a given sub-channel, different users experience different fading statistics, allowing us to pick a user with a larger gain; and (ii) channel diversity: sub-channels experiencing high gain could vary from one user to another, allowing for multiple users to be assigned their best channels in tandem. In addition to the diversity gain, the two-hop network model also provides room for spatial reuse, whereby simultaneous transmissions on the relay hop (BS-RS) and access hop (RS-MS) can be leveraged on the same channel as long as there is no mutual interference. While diversity improves performance to a certain extent, spatial reuse is the key in delivering high throughputs in a multi-hop model, as detailed below.\n\nThe system can be a synchronized, time-slotted system similar to a WiMAX relay, with BS and RS transmitting data in frames. Every frame consists of several time slots and has to be populated with user assignments across both time slots and channels (FIG. 1C). It is sufficient to consider the problem with one time slot per frame since channels in other time slots can be considered as additional channels available to the considered time slot. The RS assignments to relay channels and the MS assignments to access channels for the current frame are indicated to RS and MS through a MAP that follows the preamble in the frame (eg. 802.16j), which is transmitted at the lowest modulation and coding. In every slot of a frame, a set of RS and MS on the relay and access hops respectively are activated based on the assignments provided by the BS.\n\nThe scheduling processeso maximize the end-to-end system throughput subject to the popular proportional fairness model. The system converges to the optimum if the scheduler's decisions at each epoch (interval) are made to maximize the aggregate marginal (incremental) utility,\n\n$Smax=argmaxS{∑kεSΔUk}.$\n\nΔUk denotes the marginal flow (two-hop) utility received by user k in a feasible schedule S and is given by\n\n$βkrkeffr_k$\n\nfor proportional fairness, where βk captures the priority weight of user's QoS class and Fk its average throughput. rkeff corresponds to the user's two-hop flow rate, which in turn is determined by the instantaneous effective rate on the relay and access hops combined.\n\nThe system can work with the popular model in 802.16j standard, where the RS are assumed to be transparent. Here the RS pass the frame, received from BS on the relay hop, unchanged to the MS on the access hop. The MAP that carries the schedule information is not changed and hence a sub-channel that gets assigned to a MS on the relay hop is retained on the access hop as well. Under this model, let rk,nrel and rk,nace if be the bit-rates obtained for a user (flow) k on the relay (BS-R(k)) and access (R(k)-k) hops respectively on channel n, and Bk be the available data in user k's buffer at the BS. R(k) is the relay to whom user k is associated. No per-user buffer is assumed at the simplistic RS. Then\n\n$rkeff=12·min{∑nεAkmin{rk,nrel,rk,nacc},Bkd},$\n\nwhere d is the frame duration and Ak is the set of channels assigned to user k.\n\nFIG. 2 shows an exemplary base station of FIG. 1A. The base station has a scheduler 22 that incorporates spatial reuse and diversity gains. The scheduler 22 receives a finite user buffer model 20 and a two-hop wireless relay model 24 with spatial reuse (interference) information. The scheduler 22 also receives channel and user information from the PUSC and AMC model. The scheduler 22 generates a transmission schedule for both unicast and multicast data.\n\nIn one embodiment, the scheduler determines (i) how to allocate channels to RS and MS to leverage diversity, and (ii) how to spatially reuse the channels across relay and access hops, such that the aggregate marginal utility of all the MS (flows) is maximized. Since the RS are half-duplex, leveraging spatial reuse now requires that the set of RS be partitioned into two: one set comprising of RS operating on the relay hop, while the other operating on the access hop using the same set of channels during the frame. Hence, the equivalent spatial reuse and diversity scheduling (SDS) problem is: Given a set of RS and MS with active flows, find a partition of the RS (operating on relay and access hops) and an assignment of the channels to relay/user pairs (one from each partition operating on the same channel) such that aggregate marginal utility is maximized. The solution to the problem gives us a schedule that leverages diversity and spatial reuse gains. Since the flows occur over two hops, the resulting flow schedule is executed over two frames. The problem can be formulated as follows.\n\n$Maximize∑c=1N∑k2:Y(k2)=1∑k2:Y(k2)=0w(k1,k2,c)X(k1,k2,c)$\n\nsubject to\n\n$Y(k1)⊕Y(k2)=1,∀(k1,k2);R(k1)=R(k2)$ $∑k1∑k2X(k1,k2,c)≤1,∀c$ $∑c∑k2;k2≠k2w(k1,k2,c)X(k1,k2,c)≤Bk1r_k2d,∀k1$ $Y(k1),Y(k2),X(k1,k2,c)∈{0,1};k1,k2∈[1,K]⋃∅$\n\nY(k) indicates the assignment of MS k and its associated RS, R(k) to the relay set that will operate on the relay hop (Y(k)=1) or access hop (Y(k)=0). X(k1,k2,c) indicates the assignment of channel c to R(k1) that will operate (receiving) on the relay hop in tandem with R(k2) that will operate (transmitting) on the access hop, while the weight w (k1,k2,c) represents the net marginal utility that will result from the schedule of the two flows taking interference into account. The first constraint captures the half duplex nature of RS, assigning all MS associated with the same RS to belong to only one of the two partitions, represented by the xor operation. The second constraint captures channel feasibility in assigning a channel to atmost one user on a hop. The last constraint captures buffer feasibility for users (βk=1 for simplicity). In leveraging spatial reuse, the interference between the relay and access links operating on the same channel is taken into account. The weight function can be simplified as follows.\n\n$w(k1,k2,c)=min{rk1,crel,rk2,cacc}2r_k2+min{rk2,crel,rk2,cacc}2r_k2rk1,crel=log(1+sR(k1),crel1R(k2),R(k3),c+nc);ForSINR>>1, wehaverk1,crel≈log(SR(k3),crel)-log(IR(k3),R(k2),c+nc)=S^k2,crel-I^R(k2),R(k2),crk2,cacc=log(1+sk2,cacc1k2,BS,c+nc)=S^k2,cacc  Hence,w(k1,k2,c)=r~(k1,k2,c)2r_k1+r^(k2,k2,c)2r_k2wherer^(k1,k2,c)=min{S~k2,crel-I~R(k2),R(k2),cS~k2,cacc},r^(k2,k1,c)=min{S^k2,crel-I^R(k2),R(k2),cS~k2,cacc}(1)$\n\nwhere Sx,c and Ix,y,c indicate the received signal and interference power (from y) respectively at x on channel c. We assume an interference model with large scale fading, where if the distance (D) between R(k1) and R(k3) is greater than that between R(k1) and R(k2), then ÎR(k1),R(k2),c≦ÎR(k1),R(k2),c. Further, by definition, w(k1,k2,c.)=w(k2,k1,c). Also,\n\n$w(k1,c)=r^(k2,c)2r_k1,$\n\ncorresponds to the case with no interference (IR(k1),R(k2),c=0,Ik1,BS,c=0) and hence no reuse on channel c.\n\nFIG. 3 shows an exemplary flow-chart describing the scheduling operations in the PUSC model with finite buffering. In 101, the process arranges relays in circular geometry with consideration to all contiguous partitions of the relay set. In 102, for each contiguous partition the process determines a schedule of maximum utility. In 103, the process determines the partition that provides the schedule of maximum utility.\n\nOperation 102 can be expanded to include operations 104-107. For a given channel: For every relay pair, find a user under each relay in the pair that provides maximum utility in presence of finite buffer and interference. In 104, across all relay pairs, the process finds relay (user) pair providing maximum utility for given channel. In one embodiment, for a given channel, c, for every relay pair, the process finds a user under each relay in the pair that provides maximum utility in presence of finite buffer and interference. This is accomplished in the following set of equations below.\n\n for all (R1, R2) : R1 ∈ Pl ∪ , R2 ∈ Pr ∪  do $kR1=argmaxk1∈R1{min{r^(k1,R2,c),Qk1}2r_k1}$ $kR2=argmaxk2∈R2{min{r^(k2,R1,c),Qk2}2r_k2}$ end for\n\nwhere R and k denotes relay and user respectively; {circumflex over (r)}(k1, R2, c) denotes instantaneous rate for user k1 in both relay and access hops combined when operating on channel c and receiving interference from relay R2 which also operates on the same channel; rk denotes the average throughput received by user k thus far; Qk denotes the data left in user k's buffer.\n\nIn 105, the process selects a user pair for given channel added to schedule and then updates buffers of scheduled users in 106. In 105, across all relay pairs, the determination of the relay (user) pair providing maximum utility for given channel can be done with the equation below, where the best user pair is chosen.\n\n$(k1*,k2*)=argmax(R1,R2):R1∈Pl⋃∅,R2∈Pr⋃∅$ ${min{r^(kR1,kR2,c),QkR1}2r…kR1+min{r^(kR2,kR1,c),QkR2}2r¨kR2}$\n\nwhere P1 and Pr are the L and R partitions respectively considered in the flow chart.\n\nIn 106, the selected user pair for the given channel is added to schedule ‘S’ and the buffers of scheduled users are updated. This is accomplished using the equations:\n\nS←S∪(k1*,k2*,c)\n\nQk1*=Qk1*−min{{circumflex over (r)}(k1*,k2*,c), Qk1*}\n\nQk2*=Qk2*−min{{circumflex over (r)}(k2*,k1*,c), Qk2*}\n\nIn 107, the process repeats operations 104,105,106 for each of the remaining channels, thereby coming up with a schedule for all the channels that leverages spatial reuse across the two partitions formed.\n\nFIG. 4 shows an exemplary flow-chart describing the scheduling operations in the AMC model with backlogged buffering. In 201, the process determines a user pair for each channel that provides the highest marginal utility. V is the set of chosen pairs. Initial empty partitions are L and R. In one embodiment, this is accomplished for each channel ‘c’ as follows:\n\n(k1c,k2c)=arg maxk1,k2:R(k1)≠R(k2){ω(k1,k2,c)}\n\nThe process map the user pair to corresponding relay pairs and store their respective weights as follows:\n\n(R1c, R2c)=(R(k1c), R(k2c)) ω(c)=ω(k1c, k2c, c)\n\nV is the set of chosen pairs. Initial empty partitions are L and R.\n\nV←{(R1c, R2c, c)}, ∀c\n\nIn 202, the process finds a relay pair (s1,s2) in V of maximum utility weight and checks a partition feasibility for (s1,s2) and (s2,s1) with current {L,R}. In one embodiment, the system finds the relay pair (R1c*,R2c*) in V of maximum utility weight. Check partition feasibility for (R1c*, R2c*) and (R2c*, R1c*) with current {L,R}. This is accomplished in the equation below.\n\n Choose (R1c* , R2c* , c*) = arg max(R1c,R2c ,c)∈V{wc} if {{R1c* ∉ }&{R2c* ∉ }} then a1 = (R1c* , R2c* , c*) if {{R2c* ∉ }&{R1c* ∉ }} then a2 = (R2c* , R1c* , c*)\n\nIn 203, the process determines conflicting pairs of (s1,s2) and (s2,s1), namely T1 and T2, amongst other outstanding pairs in V. In one embodiment, the system finds conflicting pairs of (R1c*, R2c*) and (R2c*, R1c*), namely T1 and T2 amongst other outstanding pairs in V. The set of conflicting pairs for a given pair is obtained using the following equations by using the given pair as input.\n\n for all (R1ĉ, R2ĉ, ĉ) ∈ V : (R1ĉ, R2ĉ) ≠ (R1c* , R2c*) do if {R1ĉ&R2ĉ} ∈ {(  ∪ {R1c*}) || (  ∪ {R2c*})} then wl = wl + w(R1ĉ, R2ĉ, ĉ) ←  ∪ {(R1ĉ, R2ĉ)} end if end for\n\nIn 204, the process determines a better fit among {(s1,s2), T2} and {(s2,s1), T1} in terms of aggregate weight. The process denotes one of the set as A and other as C. In one embodiment, the process finds the better of (R1c*, R2c*)∪T2 and (R2c*, R1c*)∪T1 in terms of aggregate weight. Denote chosen one as Ta and other as Tb. This is accomplished using the equations below.\n\n if (w(a1) + (wl2) ≧ (w(a2) + wl1) then (R1c′ , R2c′ , c′) = a1;  =  ;  = else (R1c′ , R2c′ , c′) = a2;  =  ;  = end if\n\nIn 205, the process adds the pairs in A to the existing schedule given by partitions of L and R. The process also adds the non-chosen C to a blocked set B and removes A and C from V.: In one embodiment, the process adds the pairs in Ta along with the partition under consideration to the existing schedule, given by partitions of L and R. Add the eliminated pairs Tb to a blocked set B. Remove the considered pair, Ta and Tb from V. This is accomplished in the following equations.\n\n∪{R1c1∪ĉεR1ĉ}\n\n∪{R2c1∪ĉεR2ĉ}\n\n∪ĉε{(R1ĉ, R2ĉ, ĉ)}\n\nV←V\\{(R1c1, R2c1, c1)∪ĉε{(R1ĉ, R2ĉ, ĉ)}∪ĉε{(RR1ĉ, R2ĉ, ĉ)}:\n\nIn 206, the process repeats operations 201-205 until V is empty.\n\nIn 207, from the pairs in B, the process adds the relay (user) from each pair that provides the higher utility transmission in isolation to corresponding partition in {L,R}. From the pairs in B, add the relay (user) from each pair that provides the higher utility transmission in isolation to corresponding partition in {L,R}. Finally, {L,R} provides the desired schedule. The pseudo-code for this embodiment is as follows:\n\n for all (R1ĉ, R2ĉ, c) ∈  do if w(R1ĉ, ĉ) ≧ w(R2ĉ, ĉ) then Add R1ĉto the partition (  or ) that already contains R1c′ , c′ ≠ ĉ. else Add R2ĉto the partition (  or ) that already contains R1c′ , c′ ≠ ĉ. end if end for\n\nFIG. 5 shows an exemplary flow-chart to process the AMCmodel with finite buffering. In 301, for a given channel, the process finds a user pair that provides maximum utility in presence of finite buffer and interference. The process updates the buffer of users in chosen pair and this operation is epeated for remaining channels. In one embodiment, this is accomplished in the following equations:\n\n for c = 1 to N do (k1c, k2c, c) = arg max(k1, k2):R(k1)≠R(k2); k1, k2∈[1, K]∪ ${min{r^(k1,k2,c),Qk1}2r_k1+min{r^(k2,k1,c),Qk2}2r_k2}$ Qk1c = Qk1c − min{{circumflex over (r)}(k1c, k2c, c), Qk1c} Qk2c = Qk2c − min{{circumflex over (r)}(k2c, k1c, c), Qk2c} (R1c, R2c) = (R(k1c), R(k2c)) w(c) = w(k1c, k2c, c) end for\n\nNext, in 302, given the set of chosen user pairs for all channels as V, the process of FIG. 5 runs the process of FIG. 4 to process the AMC model with backlogged buffering. After operation 302 is done to restore partition feasibility, the process generates a feasible transmission schedule.\n\nNext, factors involved in scheduling under PUSC are discussed. Under the PUSC model, the sub-carriers constituting a channel are picked randomly and a user sends only one channel quality value that is common to all his sub-channels. This makes the problem simpler than the case where different sub-channels have different values (AMC). However, even for this model, the problem is hard to solve (NP-hard) if the users have finite buffers; unlike the backlogged cases where the problem is optimally solvable. Given the hardness of the problem, one embodiment uses an approximation process SDSPUSC(B) with good running time complexity. The process consists of two components: (i) it considers only contiguous partitioning of the relay stations; and (ii) given a feasible contiguous partition, it uses a greedy algorithm in choosing a pair of users from the two partitions who will maximize the aggregate marginal utility of the two flows combined for a given channel, subject to interference and their finite buffer size.\n\nIn PUSC, the interference and instantaneous rate depend only on the interfering relay station and not on the specific channel being used. Thus, every relay can determine its best user for a channel (subject to buffer constraint), independent of the other user operating on the channel as long as the other interfering relay station is known. Thus, scheduling decisions can be made only with respect to relays (R1, R2) by choosing the relay pair with highest marginal utility; and the users already selected within the chosen relays provide the users to be scheduled for the channel. After the scheduling decision is made on each channel, the buffer size for each scheduled user is updated. Finally, the contiguous partition providing the maximum aggregate marginal utility is selected to be the schedule. Pseudo-code for the PUSC scheduler with finite user buffering is as follows:\n\n 1: ← { } % set of partitions considered 2: for i = to 0 to R − 1 do 3: for j = 1 to R do 4: P ← Two contiguous partitions formed by two lines drawn at i and j in a circular arrangement of relays. 5: P = {Pl|Pr} 6: if P ∉  then 7: ←  ∪ P 8: SP ← { } % Schedule with partition P 9: Qk ← Bk % initialize user buffers 10: % For given partition P, determine user pair assignments to channels 11: for c = 1 to N do 12: for all (R1, R2) : R1 ∈ Pl ∪ , R2 ∈ Pr ∪  do 13: $kR1=argmaxk1∈R1{min{r^(k1,R2,c),Qk1}2r_k1}$ 14: $kR2=argmaxk2∈R2{min{r^(k2,R1,c),Qk2}2r_k2}$ 15: end for 16: (k1*, k2*) = arg max(R1, R2): R1 ∈ Pl ∪ , R2 ∈ Pr ∪  17: ${min{r^(kR1,kR2,c),QkR1}2r_kR1+min{r^(kR2,kR1,c),QkR2}2r_kR2}$ 18: Qk1* = Qk1* − min{{circumflex over (r)}(k1*, k2*, c), Qk1*} 19: Qk2* = Qk2* − min{{circumflex over (r)}(k2*, k1*, c), Qk2*} 20: S ← S ∪ (k1*, k2*, c) 21: end for 22: if |SP| > |Smax| then 23: Smax ← SP 24: Pmax ← P 25: end if 26: end if 27: end for 28: end for 29: Output Pmax and Smax\n\n# PUSC Scheduler for Finite User Buffer: SDSPUSC(B)\n\nWhile the simplicity of the algorithm is conducive for real-time implementation at BS, establishing its approximation guarantee is non-trivial. Here, the loss in performance can be bounded due to the two components, namely (i) contiguous partitioning and, (ii) greedy scheduling.\n\nIn the embodiment with Contiguous Partitioning, the placement of relays around BS induces a circular ordering in them and a feasible schedule under PUSC can be represented as a bipartite graph. The two partitions of relays forming the two vertex sets, with an edge between a pair of relays indicates that both the relays operate on the same channel (c). In PUSC the edges are important and not the specific channels that are assigned to them. Also, an edge could be assigned multiple channels. In bounding the performance loss, a construction from a non-contiguous partition to a contiguous partition. A non-contiguous partition can be converted to a contiguous partition losing atmost one transmission from the schedule. Further, the lost transmission can be made the weakest transmission from the weakest edge of the bipartite schedule graph. The updated set of edges in the contiguous partition after the transformation have equivalent or weaker interference. Under PUSC, any non-contiguous partition can be converted to a contiguous partition with a performance within ⅚ that of the optimal.\n\nIn the embodiment with Greedy Scheduling, the sub-optimality of greedy scheduling can be bounded within ½ that of the optimal. The greedy scheduler tries to find an assignment of a pair of users from the two partitions for each channel such that the aggregate marginal utility is maximized, thereby maximizing a sub-modular function. The greedy scheduling part of SDSPUSC provides an approximation guarantee of ½. SDSPUSC(B) is a 5/12-approx with respect to the optimal solution. It has a running time complexity of O(R3KN)\n\nNext, factors involved in scheduling under the AMC model are discussed. Under the band AMC model, since contiguous carriers constitute a sub-channel, there exists a notion of channel quality specific to a sub-channel. This allows exploitation of channel diversity in addition to MUD. However, it also makes the problem harder compared to PUSC model, since channel index forms an additional decision parameter. The SDS problem is NP-hard under the AMC model, even with backlogged user buffers. Given the hardness of the problem, a simple greedy process, SDSAMC can be used with an efficient approximation guarantee. The SDSAMC first identifies the user pair that delivers the highest aggregate marginal utility for each channel. However, the corresponding set of relay pairs chosen (V) might not result in a feasible partitioning of relays, causing partition violations. Partition feasibility is then restored amongst the relay pairs using a greedy algorithm. Sets and eventually store a feasible partition of the set of relays along with their channel assignment. The chosen pairs are added to the partitions in the decreasing order of their weights, while satisfying partition feasibility. Given a feasible set of partitioned pairs at an intermediate step, the addition of a new pair is decided as follows. The pair with the largest utility weight, say (s1,s2) on channel c* is considered. Since w(s1,s2,c*)=w(s2,s1,c*), both (s1,s2) and its inverted version (s2,s1) are first checked for feasibility to see if they can be added to the current partitions without causing any partition conflicts. The outstanding pairs that will be eliminated due to the addition of this pair and its inverted version to the existing partitions are determined as and respectively. A pair is eliminated if both its elements belong to the same partition. Note that the conflicting pairs of (s1, s2) in can be scheduled along with (s2,s1) and vice versa. If the considered pair and the conflicting pairs of together provide a higher weight than the inverted pair and the conflicting pairs of then (s1,s2)∪ is chosen for schedule by adding them to the appropriate partitions. Otherwise, (s2, s1)∪, is chosen for schedule. When (s1,s2)∪ is chosen, the pairs conflicting with the chosen set, namely are removed from V by adding them to a blocked set and vice versa. The set of remaining pairs, V is updated by removing the set of scheduled and blocked pairs from it. After all elements in V have been appropriately assigned to partitions, the blocked set containing pairs conflicting with {} is examined. The stronger (higher weight) relay in each of the blocked pairs is alone retained and added to the appropriate partition ( or ) already containing it, which can be done without any partition violations. The relays in and on specific channels are then mapped back to their respective users initially chosen.\n\n 1: for all c ∈ [1, N] do 2: (k1c, k2c) = arg maxk1,k2:R(k1)≠R(k2){w(k1 , k2, c)} 3: (R1c, R2c) = (R(k1c), R(k2c)) % Store the user-relay mapping 4: w(c) = w(k1c, k2c, c) 5: end for 6: Let V ← {(R1c, R2c, c)}, ∀c be set of chosen relay pair elements. 7: % Generate a feasible partition from chosen pairs. 8: Initialize  = { },  = { },  = { } 9: Arrange the N vertices of V in decreasing order of wc. 10: while V ≠  do 11:  =  =  =  =  = { }, wl = wl1 = wl2 = 0, a1 = a2 = { } 12: Choose (R1c* , R2c* , c*) = arg max(R1c,R2c,c)∈V{wc} 13: if {{R1c* ∉  }&{R2c* ∉  }} then 14: a1 = (R1c* , R2c* , c*) 15: if {{R2c* ∉  }&{R1c* ∉  }} then 16: a2 = (R2c* , R1c* , c*) 17: { , wl1} = Get_Conflicts(R1c* , R2c* , c*) 18: { , wl2} = Get_Conflicts(R2c* , R1c* , c*) 19: if (w(a1) + wl2) ≧ (w(a2) + wl1 ) then 20: (R1c′ , R2c′ , c′) = a1;  = ;  = 21: else 22: (R1c′ , R2c′ , c′) = a2;  = ;  = 23: end if 24:  ←  ∪ {R1c′  R1ĉ} 25:  ←  ∪ {R2c′  R2ĉ} 26:  ←    {(R1ĉ, R2ĉ, ĉ)} 27: V ← V\\ {(R1c′ , R2c′ , c′)  {(R1ĉ, R2ĉ, ĉ)}  {(R1ĉ, R2ĉ, ĉ)}} 28: end while 29: % Restore stronger transmissions from eliminated pairs 30: for all (R1ĉ, R2ĉ, ĉ) ∈  do 31: if w(R1ĉ, ĉ) ≧ w(R2ĉ, ĉ) then 32: Add R1ĉto the partition (  or ) that already contains R1c′ , c′ ≠ ĉ. 33: else 34: Add R2ĉto the partition (  or ) that already contains R1c′ , c′ ≠ ĉ. 35: end if 36: end for 37: Output { }. 38: 39: Get_Conflicts(R1ĉ, R2ĉ, ĉ) 40: for all (R1ĉ, R2ĉ, ĉ) ∈ V : (R1ĉ, R2ĉ) ≠ (R1c* , R2c*) do 41: if {R1ĉ&R2ĉ} ∈ {(  ∪ {R1c*}) || (  ∪ {R2c*})} then 42: wl = wl + w(R1ĉ, R2ĉ, ĉ) 43:  ← ∪ {(R1ĉ, R2ĉ)} 44: end if 45: end for\n\n# AMC Scheduler for Finite User Buffer: SDSAMC(A)\n\nSDSAMC is a ¾-approximation algorithm to the SDS problem under AMC with backlogged buffers. It has a time complexity of O(N(N+K2)). The initial selection of relay pairs for each channel runs in O(K2N). The greedy algorithm to restore partition feasibility runs in O(N2), resulting in a net time complexity of O(N(N+K2)).\n\nNext, factors involved in scheduling under the AMC model with Finite User Buffers are discussed. Given that the backlogged buffer version is hard, the finite buffer version is strongly NP-hard. Hence, one embodiment uses an approximation solution, SDSAMC(B).\n\n 1: ∀k ∈ [1, K], Qk ← Bk % initialize user buffers 2: for c = 1 to N do 3: (k1c, k2c, c) = arg max(k1, k2):R(k1)≠R(k2); k1, k2∈[1, K]∪ 4: ${min{r^(k1,k2,c),Qk1}2r_k1+min{r^(k2,k1,c),Qk2}2r_k2}$ 5: Qk1c = Qk1c − min{{circumflex over (r)}(k1c, k2c, c), Qk1c} 6: Qk2c = Qk2c − min{{circumflex over (r)}(k2c, k1c, c), Qk2c} 7: (R1c, R2c) = (R(k1c), R(k2c)) 8: w(c) = w(k1c, k2c, c) 9: end for 10: Run the greedy algorithm from SRSAMC for restoring feasible partitions. 11: Output { }.\n\n# AMC Scheduler for Finite User Buffer: SDSAMC(B)\n\nSDSAMC(B) provides an approximation guarantee of 3/8 z,93 with a time complexity of O(N(N+R2)). The performance guarantee of the channel assignment part due to the greedy approach is once again ½. Further, after the greedy channel assignment, the greedy solution to restore partitioning feasibility ensures ¾ of the value carried over from the assignment phase, resulting in a net guarantee of ⅜. Also, the time complexity of SDSAMC(B) is the larger of the two components (SDSAMC), namely O(N(N+K2)). Extensions of PUSC and AMC solutions to incorporate relay cooperation with performance guarantees are also contemplated by the inventors.\n\nPerformance Evaluation\n\nAn event-driven packet level simulator written in C++, named QNS, is used for evaluation of the various embodiments. A single cell relay-enabled OFDMA downlink system is modeled. The extended radius of the cell is assumed to be 600 m. RS are distributed uniformly within a region of 250 m≦r≦350 m, with\n\n$PRPB=0.75.$\n\nThe wireless links incorporate path loss (exponent=4) and Rayleigh fading as well as interference from other links operating on the same channel. Each user's Rayleigh channel has a Doppler fading equivalent to a velocity of 3-10 Km/hour. We consider constant bit rate (CBR) applications as the generators of traffic. A time slot is considered to be of 5 ms duration, and carrier frequency is assumed to be 2 GHz. The peak rate of the individual sub-channels is 250 Kbps. The number of users, relays, sub-channels and buffer sizes are the parameters of variation. The data flows are sent at 125 Kbps. The metrics of evaluation are average user throughput and aggregate system utility. The simulated tests show that, for a given network capacity, when the number of users (channels) is small (large), the injected traffic load can be sustained using diversity gains alone. However, when the number of users (channels) increases (decreases), spatial reuse must be exploited to sustain a larger fraction of the injected traffic load. This in turn results in the throughput gain of spatial reuse increasing to 50% over diversity. The gain then stabilizes with increasing load once the available spatial reuse has been exploited. The utility results clearly indicate the need for spatial reuse in improving both throughput and fairness in the system. In addition to the significant gains over DIV, SDSAMC also performs reasonably close to the (loose) upper bound with a maximum deviation of about 20%. This is especially noteworthy, given that the optimal is going to be lower than the upper bound. Further, it also indicates that the additional gain that can result from a further degree of spatial reuse exploitation within access links is not appreciable and hence reuse across hops is the key.\n\nThe PUSC and AMC embodiments were also evaluated as a function of relays, sub-channels and users. When not varied, the number of relays is fixed at five, sub-channels at eight and users at thirty. For PUSC, the buffer sizes of users are uniformly distributed between [0,1000] bits. Three schemes are considered: SDSPUSC(B) is the proposed scheme. UBPUSC is a scheme that provides a loose (possibly unachievable) upper bound by considering backlogged user buffers. DPUSC is a (default) variant that computes a schedule assuming backlogged user buffers but executes it in the presence of finite user buffers. This scheme helps capture the degradation in performance when finite user buffers are not accounted for in scheduling SDSPUSC(B) provides a performance better than the guarantee of 5/12 even with respect to the loose upper bound. While the absolute performance gap increases with increasing channels, the approximation ratio itself does not increase and the performance gap narrows with increasing users. This is because, when the number of user is less than the number of channels, the performance is dependent on how efficiently the available buffer data are used. However, when there are more users than channels, the performance is dependent on the availability of channels, reducing the burden on efficient buffer usage. This in turn results in closer performance to the upper bound when users outnumber the channels. Further, DPUSC suffers in performance, indicating that finite user buffers should be accounted for when making scheduling decisions. Also, since there is no channel diversity in PUSC, this makes the entire performance closely tied to how well the user buffers are utilized, especially when the number of users is small compared to channels.\n\nIn the case of AMC, this burden from user buffer utilization is shared by channel diversity. To isolate the impact of two components, we first consider backlogged buffers and evaluate SDSAMC against an optimal scheme, OPTAMC. OPTAMC considers all possible relay set partitions in determining the best pair of relays to be assigned to each AMC sub-channel. SDSAMC performs very close to optimal under all network conditions—much better than its guarantee of ¾. Its ability to leverage channel diversity effectively is also evident with increasing channels where SDSAMC stays very close to OPTAMC.\n\nThe impact of varying buffer sizes on the performance of SDSPUSC(B) and SDSAMC(B) is discussed next. When the finite buffer constraint is relaxed by increasing the user data availability, the performance of the solutions converges to the upper bound of their respective backlogged versions. The tests indicate that the finite buffer constraint is the single most performance-determining factor in PUSC, while it is both channel diversity and finite buffer constraints that determine performance in AMC and stringent buffer constraints can reduce performance.\n\nIn sum, the system provides efficient scheduling of user transmissions with backlogged and finite buffers on the multiple OFDM carriers (channels) over the two hops of the relay-enabled wireless network. The system supports the IEEE 802.16j and 802.16m standards and can work with the two sub-carrier grouping models (PUSC, AMC). While the extent of diversity gain varies depending on the model, spatial reuse is common to both the models and is crucial in delivering the promised throughput benefits of relays. The system leverages spatial reuse with diversity gains being leveraged when available. The embodiments are simple to implement at the base station, while also providing worst case guarantees. The proposed solutions are evaluated to highlight their benefits in a variety of network conditions. These solutions have also been extended with guarantees to incorporate relay cooperation. The system is simple to implement at the base station, thereby enabling their easy adoption.\n\nThe system may be implemented in hardware, firmware or software, or a combination of the three. Preferably the invention is implemented in a computer program executed on a programmable computer having a processor, a data storage system, volatile and non-volatile memory and/or storage elements, at least one input device and at least one output device.\n\nEach computer program is tangibly stored in a machine-readable storage media or device (e.g., program memory or magnetic disk) readable by a general or special purpose programmable computer, for configuring and controlling operation of a computer when the storage media or device is read by the computer to perform the procedures described herein. The inventive system may also be considered to be embodied in a computer-readable storage medium, configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner to perform the functions described herein.\n\nThe invention has been described herein in considerable detail in order to comply with the patent Statutes and to provide those skilled in the art with the information needed to apply the novel principles and to construct and use such specialized components as are required. However, it is to be understood that the invention can be carried out by specifically different equipment and devices, and that various modifications, both as to the equipment details and operating procedures, can be accomplished without departing from the scope of the invention itself." ]
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https://blog.floydhub.com/attention-mechanism/
[ "# Attention Mechanism\n\nWhat is Attention, and why is it used in state-of-the-art models? This article discusses the types of Attention and walks you through their implementations.\n\nCan I have your Attention please! The introduction of the Attention Mechanism in deep learning has improved the success of various models in recent years, and continues to be an omnipresent component in state-of-the-art models. Therefore, it is vital that we pay Attention to Attention and how it goes about achieving its effectiveness.\n\nIn this article, I will be covering the main concepts behind Attention, including an implementation of a sequence-to-sequence Attention model, followed by the application of Attention in Transformers and how they can be used for state-of-the-art results. It is advised that you have some knowledge of Recurrent Neural Networks (RNNs) and their variants, or an understanding of how sequence-to-sequence models work.\n\n## What is Attention?\n\nWhen we think about the English word “Attention”, we know that it means directing your focus at something and taking greater notice. The Attention mechanism in Deep Learning is based off this concept of directing your focus, and it pays greater attention to certain factors when processing the data.\n\nIn broad terms, Attention is one component of a network’s architecture, and is in charge of managing and quantifying the interdependence:\n\n1. Between the input and output elements (General Attention)\n2. Within the input elements (Self-Attention)\n\nLet me give you an example of how Attention works in a translation task. Say we have the sentence “How was your day”, which we would like to translate to the French version - “Comment se passe ta journée”. What the Attention component of the network will do for each word in the output sentence is map the important and relevant words from the input sentence and assign higher weights to these words, enhancing the accuracy of the output prediction.", null, "Weights are assigned to input words at each step of the translation\n\nThe above explanation of Attention is very broad and vague due to the various types of Attention mechanisms available. But fret not, you’ll gain a clearer picture of how Attention works and achieves its objectives further in the article. As the Attention mechanism has undergone multiple adaptations over the years to suit various tasks, there are many different versions of Attention that are applied. We will only cover the more popular adaptations here, which are its usage in sequence-to-sequence models and the more recent Self-Attention.\n\nWhile Attention does have its application in other fields of deep learning such as Computer Vision, its main breakthrough and success comes from its application in Natural Language Processing (NLP) tasks. This is due to the fact that Attention was introduced to address the problem of long sequences in Machine Translation, which is also a problem for most other NLP tasks as well.\n\n## Attention in Sequence-to-Sequence Models\n\nMost articles on the Attention Mechanism will use the example of sequence-to-sequence (seq2seq) models to explain how it works. This is because Attention was originally introduced as a solution to address the main issue surrounding seq2seq models, and to great success. If you are unfamiliar with seq2seq models, also known as the Encoder-Decoder model, I recommend having a read through this article to get you up to speed.\n\nThe standard seq2seq model is generally unable to accurately process long input sequences, since only the last hidden state of the encoder RNN is used as the context vector for the decoder. On the other hand, the Attention Mechanism directly addresses this issue as it retains and utilises all the hidden states of the input sequence during the decoding process. It does this by creating a unique mapping between each time step of the decoder output to all the encoder hidden states. This means that for each output that the decoder makes, it has access to the entire input sequence and can selectively pick out specific elements from that sequence to produce the output.\n\nTherefore, the mechanism allows the model to focus and place more “Attention” on the relevant parts of the input sequence as needed.\n\n## Types of Attention\n\nBefore we delve into the specific mechanics behind Attention, we must note that there are 2 different major types of Attention:\n\nWhile the underlying principles of Attention are the same in these 2 types, their differences lie mainly in their architectures and computations.\n\n## Bahdanau Attention\n\nThe first type of Attention, commonly referred to as Additive Attention, came from a paper by Dzmitry Bahdanau, which explains the less-descriptive original name. The paper aimed to improve the sequence-to-sequence model in machine translation by aligning the decoder with the relevant input sentences and implementing Attention. The entire step-by-step process of applying Attention in Bahdanau’s paper is as follows:\n\n1. Producing the Encoder Hidden States - Encoder produces hidden states of each element in the input sequence\n2. Calculating Alignment Scores between the previous decoder hidden state and each of the encoder’s hidden states are calculated (Note: The last encoder hidden state can be used as the first hidden state in the decoder)\n3. Softmaxing the Alignment Scores - the alignment scores for each encoder hidden state are combined and represented in a single vector and subsequently softmaxed\n4. Calculating the Context Vector - the encoder hidden states and their respective alignment scores are multiplied to form the context vector\n5. Decoding the Output - the context vector is concatenated with the previous decoder output and fed into the Decoder RNN for that time step along with the previous decoder hidden state to produce a new output\n6. The process (steps 2-5) repeats itself for each time step of the decoder until an token is produced or output is past the specified maximum length\n\nNow that we have a high-level understanding of the flow of the Attention mechanism for Bahdanau, let’s take a look at the inner workings and computations involved, together with some code implementation of a language seq2seq model with Attention in PyTorch.\n\n### 1. Producing the Encoder Hidden States\n\nFor our first step, we’ll be using an RNN or any of its variants (e.g. LSTM, GRU) to encode the input sequence. After passing the input sequence through the encoder RNN, a hidden state/output will be produced for each input passed in. Instead of using only the hidden state at the final time step, we’ll be carrying forward all the hidden states produced by the encoder to the next step.\n\nclass EncoderLSTM(nn.Module):\ndef __init__(self, input_size, hidden_size, n_layers=1, drop_prob=0):\nsuper(EncoderLSTM, self).__init__()\nself.hidden_size = hidden_size\nself.n_layers = n_layers\n\nself.embedding = nn.Embedding(input_size, hidden_size)\nself.lstm = nn.LSTM(hidden_size, hidden_size, n_layers, dropout=drop_prob, batch_first=True)\n\ndef forward(self, inputs, hidden):\n# Embed input words\nembedded = self.embedding(inputs)\n# Pass the embedded word vectors into LSTM and return all outputs\noutput, hidden = self.lstm(embedded, hidden)\nreturn output, hidden\n\ndef init_hidden(self, batch_size=1):\nreturn (torch.zeros(self.n_layers, batch_size, self.hidden_size, device=device),\ntorch.zeros(self.n_layers, batch_size, self.hidden_size, device=device))\n\n\nIn the code implementation of the encoder above, we’re first embedding the input words into word vectors (assuming that it’s a language task) and then passing it through an LSTM. The encoder over here is exactly the same as a normal encoder-decoder structure without Attention.\n\n### 2. Calculating Alignment Scores\n\nFor these next 3 steps, we will be going through the processes that happen in the Attention Decoder and discuss how the Attention mechanism is utilised. The class BahdanauDecoderLSTM defined below encompasses these 3 steps in the forward function.\n\nclass BahdanauDecoder(nn.Module):\ndef __init__(self, hidden_size, output_size, n_layers=1, drop_prob=0.1):\nsuper(BahdanauDecoder, self).__init__()\nself.hidden_size = hidden_size\nself.output_size = output_size\nself.n_layers = n_layers\nself.drop_prob = drop_prob\n\nself.embedding = nn.Embedding(self.output_size, self.hidden_size)\n\nself.fc_hidden = nn.Linear(self.hidden_size, self.hidden_size, bias=False)\nself.fc_encoder = nn.Linear(self.hidden_size, self.hidden_size, bias=False)\nself.weight = nn.Parameter(torch.FloatTensor(1, hidden_size))\nself.attn_combine = nn.Linear(self.hidden_size * 2, self.hidden_size)\nself.dropout = nn.Dropout(self.drop_prob)\nself.lstm = nn.LSTM(self.hidden_size*2, self.hidden_size, batch_first=True)\nself.classifier = nn.Linear(self.hidden_size, self.output_size)\n\ndef forward(self, inputs, hidden, encoder_outputs):\nencoder_outputs = encoder_outputs.squeeze()\n# Embed input words\nembedded = self.embedding(inputs).view(1, -1)\nembedded = self.dropout(embedded)\n\n# Calculating Alignment Scores\nx = torch.tanh(self.fc_hidden(hidden)+self.fc_encoder(encoder_outputs))\nalignment_scores = x.bmm(self.weight.unsqueeze(2))\n\n# Softmaxing alignment scores to get Attention weights\nattn_weights = F.softmax(alignment_scores.view(1,-1), dim=1)\n\n# Multiplying the Attention weights with encoder outputs to get the context vector\ncontext_vector = torch.bmm(attn_weights.unsqueeze(0),\nencoder_outputs.unsqueeze(0))\n\n# Concatenating context vector with embedded input word\noutput = torch.cat((embedded, context_vector), 1).unsqueeze(0)\n# Passing the concatenated vector as input to the LSTM cell\noutput, hidden = self.lstm(output, hidden)\n# Passing the LSTM output through a Linear layer acting as a classifier\noutput = F.log_softmax(self.classifier(output), dim=1)\nreturn output, hidden, attn_weights\n\n\nAfter obtaining all of our encoder outputs, we can start using the decoder to produce outputs. At each time step of the decoder, we have to calculate the alignment score of each encoder output with respect to the decoder input and hidden state at that time step. The alignment score is the essence of the Attention mechanism, as it quantifies the amount of “Attention” the decoder will place on each of the encoder outputs when producing the next output.\n\nThe alignment scores for Bahdanau Attention are calculated using the hidden state produced by the decoder in the previous time step and the encoder outputs with the following equation:\n\nscore_{alignment} = W_{combined} \\cdot tanh(W_{decoder} \\cdot H_{decoder} + W_{encoder} \\cdot H_{encoder})\n\nThe decoder hidden state and encoder outputs will be passed through their individual Linear layer and have their own individual trainable weights.\n\nIn the illustration above, the hidden size is 3 and the number of encoder outputs is 2.\n\nThereafter, they will be added together before being passed through a tanh activation function. The decoder hidden state is added to each encoder output in this case.\n\nLastly, the resultant vector from the previous few steps will undergo matrix multiplication with a trainable vector, obtaining a final alignment score vector which holds a score for each encoder output.\n\nNote: As there is no previous hidden state or output for the first decoder step, the last encoder hidden state and a Start Of String (<SOS>) token can be used to replace these two, respectively.\n\n### 3. Softmaxing the Alignment Scores\n\nAfter generating the alignment scores vector in the previous step, we can then apply a softmax on this vector to obtain the attention weights. The softmax function will cause the values in the vector to sum up to 1 and each individual value will lie between 0 and 1, therefore representing the weightage each input holds at that time step.\n\n### 4. Calculating the Context Vector\n\nAfter computing the attention weights in the previous step, we can now generate the context vector by doing an element-wise multiplication of the attention weights with the encoder outputs.\n\nDue to the softmax function in the previous step, if the score of a specific input element is closer to 1 its effect and influence on the decoder output is amplified, whereas if the score is close to 0, its influence is drowned out and nullified.\n\n### 5. Decoding the Output\n\nThe context vector we produced will then be concatenated with the previous decoder output. It is then fed into the decoder RNN cell to produce a new hidden state and the process repeats itself from step 2. The final output for the time step is obtained by passing the new hidden state through a Linear layer, which acts as a classifier to give the probability scores of the next predicted word.", null, "Context vector and previous output will give new decoder hidden state\n\nSteps 2 to 4 are repeated until the decoder generates an End Of Sentence token or the output length exceeds a specified maximum length.\n\n## Luong Attention\n\nThe second type of Attention was proposed by Thang Luong in this paper. It is often referred to as Multiplicative Attention and was built on top of the Attention mechanism proposed by Bahdanau. The two main differences between Luong Attention and Bahdanau Attention are:\n\n1. The way that the alignment score is calculated\n2. The position at which the Attention mechanism is being introduced in the decoder\n\nThere are three types of alignment scoring functions proposed in Luong’s paper compared to Bahdanau’s one type. Also, the general structure of the Attention Decoder is different for Luong Attention, as the context vector is only utilised after the RNN produced the output for that time step. We will explore these differences in greater detail as we go through the Luong Attention process, which is:\n\n1. Producing the Encoder Hidden States - Encoder produces hidden states of each element in the input sequence\n2. Decoder RNN - the previous decoder hidden state and decoder output is passed through the Decoder RNN to generate a new hidden state for that time step\n3. Calculating Alignment Scores - using the new decoder hidden state and the encoder hidden states, alignment scores are calculated\n4. Softmaxing the Alignment Scores - the alignment scores for each encoder hidden state are combined and represented in a single vector and subsequently softmaxed\n5. Calculating the Context Vector - the encoder hidden states and their respective alignment scores are multiplied to form the context vector\n6. Producing the Final Output - the context vector is concatenated with the decoder hidden state generated in step 2 as passed through a fully connected layer to produce a new output\n7. The process (steps 2-6) repeats itself for each time step of the decoder until an token is produced or output is past the specified maximum length\n\nAs we can already see above, the order of steps in Luong Attention is different from Bahdanau Attention. The code implementation and some calculations in this process is different as well, which we will go through now.\n\n### 1. Producing the Encoder Hidden States\n\nJust as in Bahdanau Attention, the encoder produces a hidden state for each element in the input sequence.\n\n### 2. Decoder RNN\n\nUnlike in Bahdanau Attention, the decoder in Luong Attention uses the RNN in the first step of the decoding process rather than the last. The RNN will take the hidden state produced in the previous time step and the word embedding of the final output from the previous time step to produce a new hidden state which will be used in the subsequent steps\n\nclass LuongDecoder(nn.Module):\ndef __init__(self, hidden_size, output_size, attention, n_layers=1, drop_prob=0.1):\nsuper(LuongDecoder, self).__init__()\nself.hidden_size = hidden_size\nself.output_size = output_size\nself.n_layers = n_layers\nself.drop_prob = drop_prob\n\n# The Attention Mechanism is defined in a separate class\nself.attention = attention\n\nself.embedding = nn.Embedding(self.output_size, self.hidden_size)\nself.dropout = nn.Dropout(self.drop_prob)\nself.lstm = nn.LSTM(self.hidden_size, self.hidden_size)\nself.classifier = nn.Linear(self.hidden_size*2, self.output_size)\n\ndef forward(self, inputs, hidden, encoder_outputs):\n# Embed input words\nembedded = self.embedding(inputs).view(1,1,-1)\nembedded = self.dropout(embedded)\n\n# Passing previous output word (embedded) and hidden state into LSTM cell\nlstm_out, hidden = self.lstm(embedded, hidden)\n\n# Calculating Alignment Scores - see Attention class for the forward pass function\nalignment_scores = self.attention(lstm_out,encoder_outputs)\n# Softmaxing alignment scores to obtain Attention weights\nattn_weights = F.softmax(alignment_scores.view(1,-1), dim=1)\n\n# Multiplying Attention weights with encoder outputs to get context vector\ncontext_vector = torch.bmm(attn_weights.unsqueeze(0),encoder_outputs)\n\n# Concatenating output from LSTM with context vector\noutput = torch.cat((lstm_out, context_vector),-1)\n# Pass concatenated vector through Linear layer acting as a Classifier\noutput = F.log_softmax(self.classifier(output), dim=1)\nreturn output, hidden, attn_weights\n\nclass Attention(nn.Module):\ndef __init__(self, hidden_size, method=\"dot\"):\nsuper(Attention, self).__init__()\nself.method = method\nself.hidden_size = hidden_size\n\n# Defining the layers/weights required depending on alignment scoring method\nif method == \"general\":\nself.fc = nn.Linear(hidden_size, hidden_size, bias=False)\n\nelif method == \"concat\":\nself.fc = nn.Linear(hidden_size, hidden_size, bias=False)\nself.weight = nn.Parameter(torch.FloatTensor(1, hidden_size))\n\ndef forward(self, decoder_hidden, encoder_outputs):\nif self.method == \"dot\":\n# For the dot scoring method, no weights or linear layers are involved\nreturn encoder_outputs.bmm(decoder_hidden.view(1,-1,1)).squeeze(-1)\n\nelif self.method == \"general\":\n# For general scoring, decoder hidden state is passed through linear layers to introduce a weight matrix\nout = self.fc(decoder_hidden)\nreturn encoder_outputs.bmm(out.view(1,-1,1)).squeeze(-1)\n\nelif self.method == \"concat\":\n# For concat scoring, decoder hidden state and encoder outputs are concatenated first\nout = torch.tanh(self.fc(decoder_hidden+encoder_outputs))\nreturn out.bmm(self.weight.unsqueeze(-1)).squeeze(-1)\n\n\n### 3. Calculating Alignment Scores\n\nIn Luong Attention, there are three different ways that the alignment scoring function is defined- dot, general and concat. These scoring functions make use of the encoder outputs and the decoder hidden state produced in the previous step to calculate the alignment scores.\n\n• Dot\nThe first one is the dot scoring function. This is the simplest of the functions; to produce the alignment score we only need to take the hidden states of the encoder and multiply them by the hidden state of the decoder.\n\nscore_{alignment} = H_{encoder} \\cdot H_{decoder}\n\n• General\nThe second type is called general and is similar to the dot function, except that a weight matrix is added into the equation as well.\n\nscore_{alignment} = W(H_{encoder} \\cdot H_{decoder})\n\n• Concat\nThe last function is slightly similar to the way that alignment scores are calculated in Bahdanau Attention, whereby the decoder hidden state is added to the encoder hidden states.\n\nscore_{alignment} = W \\cdot tanh(W_{combined}(H_{encoder} + H_{decoder}))\n\nHowever, the difference lies in the fact that the decoder hidden state and encoder hidden states are added together first before being passed through a Linear layer. This means that the decoder hidden state and encoder hidden state will not have their individual weight matrix, but a shared one instead, unlike in Bahdanau Attention.After being passed through the Linear layer, a tanh activation function will be applied on the output before being multiplied by a weight matrix to produce the alignment score.\n\n### 4. Softmaxing the Alignment Scores\n\nSimilar to Bahdanau Attention, the alignment scores are softmaxed so that the weights will be between 0 to 1.\n\n### 5. Calculating the Context Vector\n\nAgain, this step is the same as the one in Bahdanau Attention where the attention weights are multiplied with the encoder outputs.\n\n### 6. Producing the Final Output\n\nIn the last step, the context vector we just produced is concatenated with the decoder hidden state we generated in step 2. This combined vector is then passed through a Linear layer which acts as a classifier for us to obtain the probability scores of the next predicted word.\n\n## Testing The Model\n\nSince we’ve defined the structure of the Attention encoder-decoder model and understood how it works, let’s see how we can use it for an NLP task - Machine Translation.\n\n### Ready to build, train, and deploy AI?\n\nWe will be using English to German sentence pairs obtained from the Tatoeba Project, and the compiled sentences pairs can be found at this link. You can run the code implementation in this article on FloydHub using their GPUs on the cloud by clicking the following link and using the main.ipynb notebook.", null, "This will speed up the training process significantly. Alternatively, the link to the GitHub repository can be found here.\n\nThe goal of this implementation is not to develop a complete English to German translator, but rather just as a sanity check to ensure that our model is able to learn and fit to a set of training data. I will briefly go through the data preprocessing steps before running through the training procedure.\n\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport torch.optim as optim\nimport numpy as np\nimport pandas\nimport spacy\nfrom spacy.lang.en import English\nfrom spacy.lang.de import German\nimport matplotlib.pyplot as plt\nimport matplotlib.ticker as ticker\nfrom tqdm import tqdm_notebook\nimport random\nfrom collections import Counter\n\nif torch.cuda.is_available:\ndevice = torch.device(\"cuda\")\nelse:\ndevice = torch.device(\"cpu\")\n\n\nWe start by importing the relevant libraries and defining the device we are running our training on (GPU/CPU). If you’re using FloydHub with GPU to run this code, the training time will be significantly reduced. In the next code block, we’ll be doing our data preprocessing steps:\n\n1. Tokenizing the sentences and creating our vocabulary dictionaries\n2. Assigning each word in our vocabulary to integer indexes\n3. Converting our sentences into their word token indexes\n# Reading the English-German sentences pairs from the file\nwith open(\"deu.txt\",\"r+\") as file:\ndeu = [x[:-1] for x in file.readlines()]\nen = []\nde = []\nfor line in deu:\nen.append(line.split(\"\\t\"))\nde.append(line.split(\"\\t\"))\n\n# Setting the number of training sentences we'll use\ntraining_examples = 10000\n# We'll be using the spaCy's English and German tokenizers\nspacy_en = English()\nspacy_de = German()\n\nen_words = Counter()\nde_words = Counter()\nen_inputs = []\nde_inputs = []\n\n# Tokenizing the English and German sentences and creating our word banks for both languages\nfor i in tqdm_notebook(range(training_examples)):\nen_tokens = spacy_en(en[i])\nde_tokens = spacy_de(de[i])\nif len(en_tokens)==0 or len(de_tokens)==0:\ncontinue\nfor token in en_tokens:\nen_words.update([token.text.lower()])\nen_inputs.append([token.text.lower() for token in en_tokens] + ['_EOS'])\nfor token in de_tokens:\nde_words.update([token.text.lower()])\nde_inputs.append([token.text.lower() for token in de_tokens] + ['_EOS'])\n\n# Assigning an index to each word token, including the Start Of String(SOS), End Of String(EOS) and Unknown(UNK) tokens\nen_words = ['_SOS','_EOS','_UNK'] + sorted(en_words,key=en_words.get,reverse=True)\nen_w2i = {o:i for i,o in enumerate(en_words)}\nen_i2w = {i:o for i,o in enumerate(en_words)}\nde_words = ['_SOS','_EOS','_UNK'] + sorted(de_words,key=de_words.get,reverse=True)\nde_w2i = {o:i for i,o in enumerate(de_words)}\nde_i2w = {i:o for i,o in enumerate(de_words)}\n\n# Converting our English and German sentences to their token indexes\nfor i in range(len(en_inputs)):\nen_sentence = en_inputs[i]\nde_sentence = de_inputs[i]\nen_inputs[i] = [en_w2i[word] for word in en_sentence]\nde_inputs[i] = [de_w2i[word] for word in de_sentence]\n\n\nSince we’ve already defined our Encoder and Attention Decoder model classes earlier, we can now instantiate the models.\n\nhidden_size = 256\nencoder = EncoderLSTM(len(en_words), hidden_size).to(device)\nattn = Attention(hidden_size,\"concat\")\ndecoder = LuongDecoder(hidden_size,len(de_words),attn).to(device)\n\nlr = 0.001\n\n\nWe’ll be testing the LuongDecoder model with the scoring function set as concat. During our training cycle, we’ll be using a method called teacher forcing for 50% of the training inputs, which uses the real target outputs as the input to the next step of the decoder instead of our decoder output for the previous time step. This allows the model to converge faster, although there are some drawbacks involved (e.g. instability of trained model).\n\nEPOCHS = 10\nteacher_forcing_prob = 0.5\nencoder.train()\ndecoder.train()\ntk0 = tqdm_notebook(range(1,EPOCHS+1),total=EPOCHS)\nfor epoch in tk0:\navg_loss = 0.\ntk1 = tqdm_notebook(enumerate(en_inputs),total=len(en_inputs),leave=False)\nfor i, sentence in tk1:\nloss = 0.\nh = encoder.init_hidden()\ninp = torch.tensor(sentence).unsqueeze(0).to(device)\nencoder_outputs, h = encoder(inp,h)\n\n#First decoder input will be the SOS token\ndecoder_input = torch.tensor([en_w2i['_SOS']],device=device)\n#First decoder hidden state will be last encoder hidden state\ndecoder_hidden = h\noutput = []\nteacher_forcing = True if random.random() < teacher_forcing_prob else False\n\nfor ii in range(len(de_inputs[i])):\ndecoder_output, decoder_hidden, attn_weights = decoder(decoder_input, decoder_hidden, encoder_outputs)\n# Get the index value of the word with the highest score from the decoder output\ntop_value, top_index = decoder_output.topk(1)\nif teacher_forcing:\ndecoder_input = torch.tensor([de_inputs[i][ii]],device=device)\nelse:\ndecoder_input = torch.tensor([top_index.item()],device=device)\noutput.append(top_index.item())\n# Calculate the loss of the prediction against the actual word\nloss += F.nll_loss(decoder_output.view(1,-1), torch.tensor([de_inputs[i][ii]],device=device))\nloss.backward()\nencoder_optimizer.step()\ndecoder_optimizer.step()\navg_loss += loss.item()/len(en_inputs)\ntk0.set_postfix(loss=avg_loss)\n# Save model after every epoch (Optional)\ntorch.save({\"encoder\":encoder.state_dict(),\"decoder\":decoder.state_dict(),\"e_optimizer\":encoder_optimizer.state_dict(),\"d_optimizer\":decoder_optimizer},\"./model.pt\")\n\n\nUsing our trained model, let’s visualise some of the outputs that the model produces and the attention weights the model assigns to each input element.\n\nencoder.eval()\ndecoder.eval()\n# Choose a random sentences\ni = random.randint(0,len(en_inputs)-1)\nh = encoder.init_hidden()\ninp = torch.tensor(en_inputs[i]).unsqueeze(0).to(device)\nencoder_outputs, h = encoder(inp,h)\n\ndecoder_input = torch.tensor([en_w2i['_SOS']],device=device)\ndecoder_hidden = h\noutput = []\nattentions = []\nwhile True:\ndecoder_output, decoder_hidden, attn_weights = decoder(decoder_input, decoder_hidden, encoder_outputs)\n_, top_index = decoder_output.topk(1)\ndecoder_input = torch.tensor([top_index.item()],device=device)\n# If the decoder output is the End Of Sentence token, stop decoding process\nif top_index.item() == de_w2i[\"_EOS\"]:\nbreak\noutput.append(top_index.item())\nattentions.append(attn_weights.squeeze().cpu().detach().numpy())\nprint(\"English: \"+ \" \".join([en_i2w[x] for x in en_inputs[i]]))\nprint(\"Predicted: \" + \" \".join([de_i2w[x] for x in output]))\nprint(\"Actual: \" + \" \".join([de_i2w[x] for x in de_inputs[i]]))\n\n# Plotting the heatmap for the Attention weights\nfig = plt.figure(figsize=(12,9))\ncax = ax.matshow(np.array(attentions))\nfig.colorbar(cax)\nax.set_xticklabels(['']+[en_i2w[x] for x in en_inputs[i]])\nax.set_yticklabels(['']+[de_i2w[x] for x in output])\nax.xaxis.set_major_locator(ticker.MultipleLocator(1))\nax.yaxis.set_major_locator(ticker.MultipleLocator(1))\nplt.show()\n\n[Out]: English: she kissed him . _EOS\nPredicted: sie küsste ihn .\nActual: sie küsste ihn . _EOS", null, "Plot showing the weights assigned to each input word for each output\n\nFrom the example above, we can see that for each output word from the decoder, the weights assigned to the input words are different and we can see the relationship between the inputs and outputs that the model is able to draw. You can try this on a few more examples to test the results of the translator.\n\nIn our training, we have clearly overfitted our model to the training sentences. If we were to test the trained model on sentences it has never seen before, it is unlikely to produce decent results. Nevertheless, this process acts as a sanity check to ensure that our model works and is able to function end-to-end and learn.\n\nThe challenge of training an effective model can be attributed largely to the lack of training data and training time. Due to the complex nature of the different languages involved and a large number of vocabulary and grammatical permutations, an effective model will require tons of data and training time before any results can be seen on evaluation data.\n\n## Conclusion\n\nThe Attention mechanism has revolutionised the way we create NLP models and is currently a standard fixture in most state-of-the-art NLP models. This is because it enables the model to “remember” all the words in the input and focus on specific words when formulating a response.\n\nWe covered the early implementations of Attention in seq2seq models with RNNs in this article. However, the more recent adaptations of Attention has seen models move beyond RNNs to Self-Attention and the realm of Transformer models. Google’s BERT, OpenAI’s GPT and the more recent XLNet are the more popular NLP models today and are largely based on self-attention and the Transformer architecture.\n\nI’ll be covering the workings of these models and how you can implement and fine-tune them for your own downstream tasks in my next article. Stay tuned!" ]
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https://www.askiitians.com/rd-sharma-solutions/class-9/chapter-1-number-system/exercise-1-2/
[ "", null, "×", null, "", null, "", null, "", null, "", null, "#### Thank you for registering.\n\nOne of our academic counsellors will contact you within 1 working day.\n\nClick to Chat\n\n1800-1023-196\n\n+91-120-4616500\n\nCART 0\n\n• 0\n\nMY CART (5)\n\nUse Coupon: CART20 and get 20% off on all online Study Material\n\nITEM\nDETAILS\nMRP\nDISCOUNT\nFINAL PRICE\nTotal Price: Rs.\n\nThere are no items in this cart.\nContinue Shopping", null, "• Complete JEE Main/Advanced Course and Test Series\n• OFFERED PRICE: Rs. 15,900\n• View Details\n\n```Chapter 1: Number System Exercise – 1.2\n\nQuestion: 1\n\nExpress the following rational numbers as decimals:\n\n(i) 42/100\n\n(ii) 327/500\n\n(iii) 15/4\n\nSolution:\n\n(i) By long division method", null, "Therefore, 42/100 = 0.42\n\n(ii) By long division method", null, "Therefore, 327/500 = 0.654\n\n(iii) By long division method", null, "Therefore, 15/4 = 3.75\n\nQuestion: 2\n\nExpress the following rational numbers as decimals:\n\n(i)  2/3\n\n(ii) – (4/9)\n\n(iii) – (2/15)\n\n(iv) – (22/13)\n\n(v)   437/999\n\nSolution:\n\n(i) By long division method", null, "Therefore, 2/3 = 0.66\n\n(ii) By long division method", null, "Therefore, - 4/9 = - 0.444\n\n(iii) By long division method", null, "Therefore, 2/15 = -1.333\n\n(iv) By long division method", null, "Therefore, - 22/13 = - 1.69230769\n\n(v) By long division method", null, "Therefore, 437/999 = 0.43743\n\nQuestion: 3\n\nLook at several examples of rational numbers in the form of p/q (q ≠ 0), where p and q are integers with no common factor other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?\n\nSolution:\n\nA rational number p/q is a terminating decimal\n\nonly, when prime factors of q are q and 5 only. Therefore,\n\np/q is a terminating decimal only, when prime\n\nfactorization of q must have only powers of 2 or 5 or both.\n```", null, "", null, "### Course Features\n\n• 728 Video Lectures\n• Revision Notes\n• Previous Year Papers\n• Mind Map\n• Study Planner\n• NCERT Solutions\n• Discussion Forum\n• Test paper with Video Solution", null, "" ]
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https://cpt.hitbullseye.com/Snapdeal/Snapdeal-Aptitude-Test.php
[ "# Sample Aptitude Questions of Snapdeal\n\n1. The difference of two numbers is 11 and one fifth of their sum is 9. The numbers are :\n1. 31,20\n2. 30,19\n3. 29,18\n4. 28,17\n\nx − y = 11, x + y = 5 × 9 x − y = 11, x + y = 45, y = 17, x = 28\n2. How many numbers between 1 and 100 are divisible by 7 ?\n1. 9\n2. 11\n3. 17\n4. 14\n\nNo. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d\n98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7\n98/7= N = 14\n1. Three cubes of edges 6 cms, 8 cms and 10 cms are meted without loss of metal into a single cube. The edge of the new cube will be:\n1. 8 cms\n2. 12 cms\n3. 14 cms\n4. 16 cms\n\nVolume of new cube = Volume of cube 1 + cube 2 + cube 3 = 63 + 83 + 103, = 216 + 512 + 1000 a3 = 1728, a = (1728)1/3 = 12\n2. If 378 coins consist of rupee, 50 paise and 25 paise coins, whose values are proportional to 13 :11 : 7, the number of 50 paise coins will be :\n1. 128\n2. 132\n3. 133\n4. 136\n\nIf values are proportional to 13 : 11 : 7, then the number of coins will be proportional to 13/1 : 11/0.50 : 7/0.25 ⇒ 13 : 22 : 28. Now from this the number of coins of 50 paise will be 378 × 22/63 = 132.\n3. In how many ways can 3 integers be selected from the set {1, 2, 3, …….., 37} such that sum of the three integers is an odd number?\n1. 3876\n2. 7638\n3. 6378\n4. 1938\n5. 969\n\nThere are 18 even and 19 odd numbers in the given set. For sum to be odd either all 3 numbers should be odd or 2 of them even and one odd. This is possible in 19C3 + (18C2 × 19C1) = 3876 ways\n4. The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 275, then the mean profit for the last 15 days would be\n1. Rs. 200\n2. Rs. 350\n3. Rs. 275\n4. Rs. 425\n\nAverage would be : 350 = (275 + x)/2 On solving, x = 425.\n5. There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs. 42 per day while the average expenditure per head diminishes by Re 1. Find the original expenditure of the mess.\n1. Rs. 480\n2. Rs. 520\n3. Rs. 420\n4. Rs. 460\n\nLet d be the average daily expenditure\nOriginal expenditure = 35 × d\nNew expenditure = 35 × d + 42\nNew average expenditure will be :\n(35 × d + 42)/42 = d - 1\nOn solving, we get d = 12\nTherefore original expenditure = 35 × 12 = 420\n6. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's present age?\n1. 16 years\n2. 18 years\n3. 20 years\n4. 22 years\n5. 25 years\n\nLet the ages of Kunal and Sagar be K and S respectively.\nGiven : (K-6)/(S-6) = 6/5 => 5K – 6S = -6 ……(i)\nAnd: (K+4)/(S+4) = 11/10 => 10K – 11 S = 4 …..(ii)\nSolving (i) & (ii) we get: S = 16 years.\n7. A number X is 150 more than a second number, Y. If the sum of X and Y is 5 times Y, what is the value of Y?\n1. 50\n2. 40\n3. 80\n4. 60\n5. 70" ]
[ null ]
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https://answers.everydaycalculation.com/multiply-fractions/4-70-times-30-49
[ "Solutions by everydaycalculation.com\n\n## Multiply 4/70 with 30/49\n\nThis multiplication involving fractions can also be rephrased as \"What is 4/70 of 30/49?\"\n\n4/70 × 30/49 is 12/343.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 4/70 × 30/49 = 4 × 30/70 × 49 = 120/3430\n3. After reducing the fraction, the answer is 12/343\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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http://www.jaac-online.com/article/doi/10.11948/20220197
[ "", null, "2023 Volume 13 Issue 4\nArticle Contents\n\nLorand Gabriel Parajdi, Flavius Pătrulescu, Radu Precup, Ioan Ştefan Haplea. TWO NUMERICAL METHODS FOR SOLVING A NONLINEAR SYSTEM OF INTEGRAL EQUATIONS OF MIXED VOLTERRA-FREDHOLM TYPE ARISING FROM A CONTROL PROBLEM RELATED TO LEUKEMIA[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1797-1812. doi: 10.11948/20220197\n Citation: Lorand Gabriel Parajdi, Flavius Pătrulescu, Radu Precup, Ioan Ştefan Haplea. TWO NUMERICAL METHODS FOR SOLVING A NONLINEAR SYSTEM OF INTEGRAL EQUATIONS OF MIXED VOLTERRA-FREDHOLM TYPE ARISING FROM A CONTROL PROBLEM RELATED TO LEUKEMIA[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1797-1812.", null, "# TWO NUMERICAL METHODS FOR SOLVING A NONLINEAR SYSTEM OF INTEGRAL EQUATIONS OF MIXED VOLTERRA-FREDHOLM TYPE ARISING FROM A CONTROL PROBLEM RELATED TO LEUKEMIA\n\n• The aim of this paper is to present two algorithms for numerical solving of a fixed final state control problem in connection with the leukemia treatment strategy. In the absence of the controllability condition, our model leads to a nonlinear integral system of Volterra type to whom explicit iterative techniques apply and converge. Once using the controllability condition, the control variable is expressed in terms of the state variables and the integral system changes to a mixed Volterra-Fredholm type one making direct iterative techniques inoperative. However, two paths can be followed. One consists in an iterative procedure where at each step the control variable is calculated using the approximate values of the state variables from the previous step. The other looks for the numerical value of the control variable by using the bisection method. Numerical simulations, error analysis and biological interpretation are given.\n\nMSC: 45G15, 34H05, 65R20, 92C50, 93B05\n•", null, "## Article Metrics", null, "", null, "DownLoad:  Full-Size Img  PowerPoint" ]
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https://www.geeksforgeeks.org/design-a-chess-game/?ref=lbp
[ "# Design a Chess Game\n\n• Difficulty Level : Hard\n• Last Updated : 30 Sep, 2020\n\nProblem Statement: The problem is to design a Chess Game using Object Oriented Principles.\n\nSolution:\nThese type of questions are asked in interviews to Judge the Object-Oriented Design skill of a candidate. So, first of all we should think about the classes.\n\nThe main classes will be:\n\n1. Spot: A spot represents one block of the 8×8 grid and an optional piece.\n2. Piece: The basic building block of the system, every piece will be placed on a spot. Piece class is an abstract class. The extended classes (Pawn, King, Queen, Rook, Knight, Bishop) implements the abstracted operations.\n3. Board: Board is an 8×8 set of boxes containing all active chess pieces.\n4. Player: Player class represents one of the participants playing the game.\n5. Move: Represents a game move, containing the starting and ending spot. The Move class will also keep track of the player who made the move.\n6. Game: This class controls the flow of a game. It keeps track of all the game moves, which player has the current turn, and the final result of the game.\n7. Let’s look at the details. These codes are self-explanatory. You can have a look at the properties/variables and methods of different classes.\n\nSpot: To represent a cell on the chess board:\n\n `public` `class` `Spot {``    ``private` `Piece piece;``    ``private` `int` `x;``    ``private` `int` `y;`` ` `    ``public` `Spot(``int` `x, ``int` `y, Piece piece)``    ``{``        ``this``.setPiece(piece);``        ``this``.setX(x);``        ``this``.setY(y);``    ``}`` ` `    ``public` `Piece getPiece()``    ``{``        ``return` `this``.piece;``    ``}`` ` `    ``public` `void` `setPiece(Piece p)``    ``{``        ``this``.piece = p;``    ``}`` ` `    ``public` `int` `getX()``    ``{``        ``return` `this``.x;``    ``}`` ` `    ``public` `void` `setX(``int` `x)``    ``{``        ``this``.x = x;``    ``}`` ` `    ``public` `int` `getY()``    ``{``        ``return` `this``.y;``    ``}`` ` `    ``public` `void` `setY(``int` `y)``    ``{``        ``this``.y = y;``    ``}``}`\n\nPiece: An abstract class to represent common functionality of all chess pieces:\n\n `public` `abstract` `class` `Piece {`` ` `    ``private` `boolean` `killed = ``false``;``    ``private` `boolean` `white = ``false``;`` ` `    ``public` `Piece(``boolean` `white)``    ``{``        ``this``.setWhite(white);``    ``}`` ` `    ``public` `boolean` `isWhite()``    ``{``        ``return` `this``.white;``    ``}`` ` `    ``public` `void` `setWhite(``boolean` `white)``    ``{``        ``this``.white = white;``    ``}`` ` `    ``public` `boolean` `isKilled()``    ``{``        ``return` `this``.killed;``    ``}`` ` `    ``public` `void` `setKilled(``boolean` `killed)``    ``{``        ``this``.killed = killed;``    ``}`` ` `    ``public` `abstract` `boolean` `canMove(Board board, ``                                 ``Spot start, Spot end);``}`\n\nKing: To represent King as a chess piece:\n\n `public` `class` `King ``extends` `Piece {``    ``private` `boolean` `castlingDone = ``false``;`` ` `    ``public` `King(``boolean` `white)``    ``{``        ``super``(white);``    ``}`` ` `    ``public` `boolean` `isCastlingDone()``    ``{``        ``return` `this``.castlingDone;``    ``}`` ` `    ``public` `void` `setCastlingDone(``boolean` `castlingDone)``    ``{``        ``this``.castlingDone = castlingDone;``    ``}`` ` `    ``@Override``    ``public` `boolean` `canMove(Board board, Spot start, Spot end)``    ``{``        ``// we can't move the piece to a Spot that ``        ``// has a piece of the same color``        ``if` `(end.getPiece().isWhite() == ``this``.isWhite()) {``            ``return` `false``;``        ``}`` ` `        ``int` `x = Math.abs(start.getX() - end.getX());``        ``int` `y = Math.abs(start.getY() - end.getY());``        ``if` `(x + y == ``1``) {``            ``// check if this move will not result in the king``            ``// being attacked if so return true``            ``return` `true``;``        ``}`` ` `        ``return` `this``.isValidCastling(board, start, end);``    ``}`` ` `    ``private` `boolean` `isValidCastling(Board board, ``                                     ``Spot start, Spot end)``    ``{`` ` `        ``if` `(``this``.isCastlingDone()) {``            ``return` `false``;``        ``}`` ` `        ``// Logic for returning true or false``    ``}`` ` `    ``public` `boolean` `isCastlingMove(Spot start, Spot end)``    ``{``        ``// check if the starting and ``        ``// ending position are correct``    ``}``}`\n\nKnight: To represent Knight as a chess piece\n\n `public` `class` `Knight ``extends` `Piece {``    ``public` `Knight(``boolean` `white)``    ``{``        ``super``(white);``    ``}`` ` `    ``@Override``    ``public` `boolean` `canMove(Board board, Spot start, ``                                            ``Spot end)``    ``{``        ``// we can't move the piece to a spot that has``        ``// a piece of the same colour``        ``if` `(end.getPiece().isWhite() == ``this``.isWhite()) {``            ``return` `false``;``        ``}`` ` `        ``int` `x = Math.abs(start.getX() - end.getX());``        ``int` `y = Math.abs(start.getY() - end.getY());``        ``return` `x * y == ``2``;``    ``}``}`\n\nSimilarly, we can create classes for other pieces like Queen, Pawns, Rooks, Bishops etc.\n\nBoard: To represent a chess board:\n\n `public` `class` `Board {``    ``Spot[][] boxes;`` ` `    ``public` `Board()``    ``{``        ``this``.resetBoard();``    ``}`` ` `    ``public` `Spot getBox(``int` `x, ``int` `y)``    ``{`` ` `        ``if` `(x < ``0` `|| x > ``7` `|| y < ``0` `|| y > ``7``) {``            ``throw` `new` `Exception(``\"Index out of bound\"``);``        ``}`` ` `        ``return` `boxes[x][y];``    ``}`` ` `    ``public` `void` `resetBoard()``    ``{``        ``// initialize white pieces``        ``boxes[``0``][``0``] = ``new` `Spot(``0``, ``0``, ``new` `Rook(``true``));``        ``boxes[``0``][``1``] = ``new` `Spot(``0``, ``1``, ``new` `Knight(``true``));``        ``boxes[``0``][``2``] = ``new` `Spot(``0``, ``2``, ``new` `Bishop(``true``));``        ``//...``        ``boxes[``1``][``0``] = ``new` `Spot(``1``, ``0``, ``new` `Pawn(``true``));``        ``boxes[``1``][``1``] = ``new` `Spot(``1``, ``1``, ``new` `Pawn(``true``));``        ``//...`` ` `        ``// initialize black pieces``        ``boxes[``7``][``0``] = ``new` `Spot(``7``, ``0``, ``new` `Rook(``false``));``        ``boxes[``7``][``1``] = ``new` `Spot(``7``, ``1``, ``new` `Knight(``false``));``        ``boxes[``7``][``2``] = ``new` `Spot(``7``, ``2``, ``new` `Bishop(``false``));``        ``//...``        ``boxes[``6``][``0``] = ``new` `Spot(``6``, ``0``, ``new` `Pawn(``false``));``        ``boxes[``6``][``1``] = ``new` `Spot(``6``, ``1``, ``new` `Pawn(``false``));``        ``//...`` ` `        ``// initialize remaining boxes without any piece``        ``for` `(``int` `i = ``2``; i < ``6``; i++) {``            ``for` `(``int` `j = ``0``; j < ``8``; j++) {``                ``boxes[i][j] = ``new` `Spot(i, j, ``null``);``            ``}``        ``}``    ``}``}`\n\nPlayer: An abstract class for player, it can be a human or a computer.\n\n `public` `abstract` `class` `Player {``    ``public` `boolean` `whiteSide;``    ``public` `boolean` `humanPlayer;`` ` `    ``public` `boolean` `isWhiteSide()``    ``{``        ``return` `this``.whiteSide;``    ``}``    ``public` `boolean` `isHumanPlayer()``    ``{``        ``return` `this``.humanPlayer;``    ``}``}`` ` `public` `class` `HumanPlayer ``extends` `Player {`` ` `    ``public` `HumanPlayer(``boolean` `whiteSide)``    ``{``        ``this``.whiteSide = whiteSide;``        ``this``.humanPlayer = ``true``;``    ``}``}`` ` `public` `class` `ComputerPlayer ``extends` `Player {`` ` `    ``public` `ComputerPlayer(``boolean` `whiteSide)``    ``{``        ``this``.whiteSide = whiteSide;``        ``this``.humanPlayer = ``false``;``    ``}``}`\n\nMove: To represent a chess move:\n\n `public` `class` `Move {``    ``private` `Player player;``    ``private` `Spot start;``    ``private` `Spot end;``    ``private` `Piece pieceMoved;``    ``private` `Piece pieceKilled;``    ``private` `boolean` `castlingMove = ``false``;`` ` `    ``public` `Move(Player player, Spot start, Spot end)``    ``{``        ``this``.player = player;``        ``this``.start = start;``        ``this``.end = end;``        ``this``.pieceMoved = start.getPiece();``    ``}`` ` `    ``public` `boolean` `isCastlingMove()``    ``{``        ``return` `this``.castlingMove;``    ``}`` ` `    ``public` `void` `setCastlingMove(``boolean` `castlingMove)``    ``{``        ``this``.castlingMove = castlingMove;``    ``}``}`\n\n `public` `enum` `GameStatus {``    ``ACTIVE,``    ``BLACK_WIN,``    ``WHITE_WIN,``    ``FORFEIT,``    ``STALEMATE,``    ``RESIGNATION``}`\n\nGame: To represent a chess game:\n\n `public` `class` `Game {``    ``private` `Player[] players;``    ``private` `Board board;``    ``private` `Player currentTurn;``    ``private` `GameStatus status;``    ``private` `List movesPlayed;`` ` `    ``private` `void` `initialize(Player p1, Player p2)``    ``{``        ``players[``0``] = p1;``        ``players[``1``] = p2;`` ` `        ``board.resetBoard();`` ` `        ``if` `(p1.isWhiteSide()) {``            ``this``.currentTurn = p1;``        ``}``        ``else` `{``            ``this``.currentTurn = p2;``        ``}`` ` `        ``movesPlayed.clear();``    ``}`` ` `    ``public` `boolean` `isEnd()``    ``{``        ``return` `this``.getStatus() != GameStatus.ACTIVE;``    ``}`` ` `    ``public` `boolean` `getStatus()``    ``{``        ``return` `this``.status;``    ``}`` ` `    ``public` `void` `setStatus(GameStatus status)``    ``{``        ``this``.status = status;``    ``}`` ` `    ``public` `boolean` `playerMove(Player player, ``int` `startX, ``                                ``int` `startY, ``int` `endX, ``int` `endY)``    ``{``        ``Spot startBox = board.getBox(startX, startY);``        ``Spot endBox = board.getBox(startY, endY);``        ``Move move = ``new` `Move(player, startBox, endBox);``        ``return` `this``.makeMove(move, player);``    ``}`` ` `    ``private` `boolean` `makeMove(Move move, Player player)``    ``{``        ``Piece sourcePiece = move.getStart().getPiece();``        ``if` `(sourcePiece == ``null``) {``            ``return` `false``;``        ``}`` ` `        ``// valid player``        ``if` `(player != currentTurn) {``            ``return` `false``;``        ``}`` ` `        ``if` `(sourcePiece.isWhite() != player.isWhiteSide()) {``            ``return` `false``;``        ``}`` ` `        ``// valid move?``        ``if` `(!sourcePiece.canMove(board, move.getStart(), ``                                            ``move.getEnd())) {``            ``return` `false``;``        ``}`` ` `        ``// kill?``        ``Piece destPiece = move.getStart().getPiece();``        ``if` `(destPiece != ``null``) {``            ``destPiece.setKilled(``true``);``            ``move.setPieceKilled(destPiece);``        ``}`` ` `        ``// castling?``        ``if` `(sourcePiece != ``null` `&& sourcePiece ``instanceof` `King``            ``&& sourcePiece.isCastlingMove()) {``            ``move.setCastlingMove(``true``);``        ``}`` ` `        ``// store the move``        ``movesPlayed.add(move);`` ` `        ``// move piece from the stat box to end box``        ``move.getEnd().setPiece(move.getStart().getPiece());``        ``move.getStart.setPiece(``null``);`` ` `        ``if` `(destPiece != ``null` `&& destPiece ``instanceof` `King) {``            ``if` `(player.isWhiteSide()) {``                ``this``.setStatus(GameStatus.WHITE_WIN);``            ``}``            ``else` `{``                ``this``.setStatus(GameStatus.BLACK_WIN);``            ``}``        ``}`` ` `        ``// set the current turn to the other player``        ``if` `(``this``.currentTurn == players[``0``]) {``            ``this``.currentTurn = players[``1``];``        ``}``        ``else` `{``            ``this``.currentTurn = players[``0``];``        ``}`` ` `        ``return` `true``;``    ``}``}`\n\nReference: http://massivetechinterview.blogspot.com/2015/07/design-chess-game-using-oo-principles.html\n\nMy Personal Notes arrow_drop_up" ]
[ null ]
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https://brebru.com/webquests/math/equations/equations.html
[ "Solving Equations Review!\n\nIntroduction:\nJust as with solving one-step or two-step or any equation, one goal in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign. The other goal is to have the number in front of the variable equal to one. Keep in mind that the variable does not always have to be x. These equations can make use of any letter as a variable.\n\nThe strategy for getting the variable by itself with a coefficient of 1 involves using opposite operations. For example, to move something that is added to the other side of the equation, you should subtract. The most important thing to remember in solving a linear equation is that whatever you do to one side of the equation, you MUST do to the other side. So if you subtract a number from one side, you MUST subtract the same value from the other side.\n\nThink of a strategy you can use to help you remember the steps needed to solve equations with multiple steps.\n(include 4 different examples of different types of equations requiring differ\nent operations)\n\ndefine these vocabulary terms:\n\nEquation\n\nVariable\n\nSolve(solving for a variable)\n\ninverse\n\nsimplify\n\nProcess:\nWrite out the process for solving an equation with one variable ( in your own words).\n\nWrite out the process for solving an equation with 2 variables on different sides of the equal sign.\n\nResources:\n\nWatch This!\n\nhttp://www.algebralab.org/lessons/lesson.aspx?file=algebra_onevariablemultistep.xml\n\nhttp://www.onlinemathlearning.com/multi-step-equations.html\n\nEvaluation:\nPut your steps and definitions into a powerpoint presentation including all of your definitions and sample problems!\n\nConclusion:\nHow confident do you feel about solving equations?\n\nReflect on where you have the most difficulty or where you feel you are strongest in solving equations." ]
[ null ]
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https://sampleprograms.io/projects/quick-sort/kotlin/
[ "# Quick Sort in Kotlin\n\nPublished on 28 April 2022 (Updated: 18 September 2022)", null, "Welcome to the Quick Sort in Kotlin page! Here, you'll find the source code for this program as well as a description of how the program works.\n\n## Current Solution\n\n``````fun main(args: Array<String>)\n{\nvar arr: IntArray\ntry\n{\narr = args.split(\", \").map{ it.toInt() }.toIntArray()\nif (arr.size < 2) {\nthrow Exception()\n}\n}\ncatch(e: Exception)\n{\nprintln(\"Usage: please provide a list of at least two integers to sort in the format \\\"1, 2, 3, 4, 5\\\"\")\nreturn\n}\n\nvar ans:IntArray = quickSort(arr)\nfor(i in 0 until ans.count())\n{\nif (i==ans.count() - 1)\n{\nprintln(\"\\${ans[i]}\")\nreturn\n}\nprint(\"\\${ans[i]}, \")\n}\n}\n\nfun quickSort(arr: IntArray):IntArray\n{\nif (arr.count() == 1)\n{\nreturn(arr.sliceArray(0..0))\n}\nvar pivot:Int = (arr.count() - 1) / 2\narr[pivot] = arr[arr.count() - 1].also {arr[arr.count() - 1] = arr[pivot]}\npivot = arr.count()-1\n\nvar ans = intArrayOf()\nvar left = intArrayOf()\nfor(i in 0 until arr.count())\n{\nif(arr[i] > arr[pivot] || i == pivot)\n{\nfor(j in arr.count() - 2 downTo 0)\n{\nif(i>j || j == 0)\n{\narr[pivot] = arr[i].also {arr[i] = arr[pivot]}\npivot = i\n\nif(pivot!=0){\nleft = arr.sliceArray(0..pivot-1)\nans = quickSort(arr.sliceArray(0..pivot - 1))\nans = ans + arr.sliceArray(pivot..pivot)\n}\nelse\n{\nans = arr.sliceArray(pivot..pivot)\n}\nif(pivot!=arr.count()-1){\nans = ans + quickSort(arr.sliceArray(pivot + 1..arr.count() - 1))\n}\n\nreturn (ans)\n}\nif(arr[j]<arr[pivot])\n{\narr[i] = arr[j].also {arr[j] = arr[i]}\nbreak\n}\n}\n}\n}\nreturn (intArrayOf())\n}\n``````\n\nQuick Sort in Kotlin was written by:\n\n• Blake.Ke\n• Jeremy Grifski\n• mikenmo\n\nIf you see anything you'd like to change or update, please consider contributing.\n\nNote: The solution shown above is the current solution in the Sample Programs repository as of Oct 09 2020 22:39:08. The solution was first committed on Oct 01 2020 21:55:29. As a result, documentation below may be outdated.\n\n## How to Implement the Solution\n\nNo 'How to Implement the Solution' section available. Please consider contributing.\n\n## How to Run the Solution\n\nNo 'How to Run the Solution' section available. Please consider contributing." ]
[ null, "https://sampleprograms.io/assets/images/sample-programs-in-every-language.jpg", null ]
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https://laneas.com/publication/performance-analysis-spectral-community-detection-realistic-graph-models
[ "# Performance Analysis of Spectral Community Detection in Realistic Graph Models\n\nConference Paper\n\n### Authors:\n\nHafiz Tiomoko Ali; Romain Couillet\n\n### Source:\n\n41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016), Shanghai, China (2016)\n\n### Abstract:\n\nThis article proposes a spectral analysis of dense random graphs generated by (a modified version of) the degree-corrected stochastic block model, for a setting where the inter block probabilities differ by $\\mathcal{O}(n^{-\\frac{1}{2}})$ with n the number of nodes. We study a normalized ver- sion of the graph modularity matrix which is shown to be asymptoti- cally well approximated by an analytically tractable (spiked) random matrix. The analysis of the latter allows for the precise evaluation of (i) the transition phase where clustering becomes asymptotically fea- sible and (ii) the alignment between the dominant eigenvectors and the block-wise canonical basis, thus enabling the estimation of mis- classification rates (prior to post-processing) in simple scenarios.\n\nFull Text:", null, "Tiomoko2016Performance.pdf" ]
[ null, "https://laneas.com/modules/file/icons/application-pdf.png", null ]
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https://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/High_Temperatures_in_Active_Regions
[ "# High Temperatures in Active Regions\n\nNugget\nNumber: 97\n1st Author: Jim McTiernan\n2nd Author:\nPublished: 16 March 2009\nNext Nugget: Chree Analysis for Flares\nPrevious Nugget: The Jakimiec Track\nList all\n\n## Introduction\n\nSince RHESSI was launched in February 2002, it has observed thousands of solar flares (more than 46,000(!) in the latest reprocessing of the RHESSI flare list). It was immediately noticed in 2002 that RHESSI was observing solar emission even when there are no flares present (Ref. 1). The minimum temperature required for detectability would be about 5 MK, a temperature range that is not often considered for solar active regions. Most of the instruments previously used for temperature measurements of solar active regions, such as Yohkoh SXT, SOHO EIT or CDS, didn't have much response to higher temperatures. This Nugget describes measurements of the temperature for approximately 7000 time intervals from Feb 2002 through August 2006 (Ref. 2).\n\n## Background Subtraction and Interval Selection", null, "Figure 1:This is the RHESSI 3 to 6 keV count rate for one orbit. The black dashed lines show an interval which was chosen for a temperature measurement. The red line is the expected background level.\n\nFigure 1 shows the RHESSI count rate for a typical orbit for 8 April 2006. (Nothing special about April 2006, it was just a convenient option when the original SPD poster with this calculation was created.) The plot shows a jump at each day-night transition (terminator). This immediately tells us that the Sun is emitting detectable X-rays. Two things then need to be accomplished before we can get a temperature measurement of a steady-state component that could be related to active regions:\n\n1) Avoid microflares, the SAA, particle events, etc: For each orbit, an interval of between 1 and 5 minutes was chosen based on the following criteria: no flares or particle events, no attenuators, no data gaps, and at least 5 minutes from the SAA. The intervals chosen have the minimum (daylight) count rate for the orbit, subject to a flatness test that insures that there are no microflares in the intervals; the interval in Figure 1 is followed by a microflare.\n\n2) Find the background level: You cannot assume that the background can be given by the nighttime values before and after spacecraft day. The background depends on the cosmic ray flux and local particle flux, and it varies with the position of the spacecraft. Figure 2 shows background data, which is calculated from the 5 minute periods before and after daylight for each orbit in the mission.", null, "Figure 2:This is the RHESSI 3 to 6 keV background level, plotted versus the longitude of the ascending node of the orbit, and orbital phase. The longitude of the ascending node is the longitude at which the spacecraft passes over the equator, moving from south to north; the combination of this quantity and the orbital phase gives complete information about the latitude and longitude of the spacecraft. On orbit, a spacecraft follows a series of vertical lines on this plot, going up.\n\nFor the low-latitude regions where most of the temperature measurements were taken, the uncertainty in the background is approximately 1/2 the background rate. For the 3 to 6 keV energy band shown in Figures 1 and 2, this is approximately 1 count per second per detector. The uncertainty is higher for higher latitude regions; e.g., regions which are red in Figure 2.\n\n## Measurements\n\nGiven a way to choose time intervals and calculate background, we calculate the temperature and emission measure. A total of 8747 time intervals were analyzed, from 14 February 2002 to 2 August 2006. Of these intervals, 6961 had enough counts above the background for a spectrum to be fitted. (The spectra for the fits were accumulated in 1/3 keV energy channels in the energy range from 3 to 30 keV. To be included in the fit, the background-subtracted count rate for a channel was required to be greater than 3 times its uncertainty. Detectors 1,3,4,6,9 were used.) We also obtained temperature and emission measure (EM) from the standard soft X-ray photometry from GOES for each of the intervals. GOES 10 data were used prior to 16 March 2003, and GOES 12 data were used after.\n\nThe RHESSI temperature is between 6 and 11 MK, and the GOES temperature is usually between 3 and 6 MK. The GOES EM is typically a factor of 50 to 100 times the RHESSI EM. This is consistent with a differential emission measure that decreases with increasing temperature.", null, "Figure 3:RHESSI temperature versus GOES temperature for time intervals before 14 September 2002. The blue dashed line is a linear fit with slope of 0.89. The red dashed line indicates where the two temperatures are equal.", null, "Figure 4:RHESSI temperature versus GOES temperature for all time intervals. The red dashed line indicates where the two temperatures are equal.\n\nThere is a small problem here, though. From Figure 3, it looks as if the two measurements have some correlation. This is not wildly unexpected; GOES should always measure a temperature lower than RHESSI, since it observes lower energy photons, so there should be some correlation due to that. We don't expect the correlation to be perfect; this would require the distribution of emission measure (DEM) to be a constant for all intervals.\n\nIn Figure 4, which shows all of the measurements, the rough correlation is gone, and often the GOES T is higher than the RHESSI T. Probably this is due to particles affecting the GOES measurements; we don't have a background subtraction method available for GOES to deal with this sort of problem. This erodes confidence in the GOES measurements -- below an EM (for GOES) of 3x1048 cm − 3, the GOES temperature is often higher than RHESSI's, and the results are suspect. (This is the C level in the GOES long wavelength channel -- which is typically only seen when the Sun is at its most active.)", null, "Figure 5:Top: 28-day averages of GOES (red stars) and RHESSI (black diamonds) temperatures. Middle: 28-day averages of GOES and RHESSI EM. Bottom: The black line is the fraction of time intervals that resulted in zero value for RHESSI temperature. The red line is a normalized value of sunspot number.\n\nHere in Figure 5 is the overall time variation of the RHESSI and GOES temperatures and EMs. The average RHESSI temperature is relatively constant for the mission, with a drop from the 7 to 8 MK range to the 6.5 to 7.5 MK range. The RHESSI EM bounces up and down, but the bounces are superposed on a steady decrease of about one order of magnitude. Some of the bounces are pretty well correlated with the monthly sunspot number, particularly in 2002; the correlation coefficient between RHESSI EM and sunspot number is 0.61. The GOES values start relatively constant, and then become erratic at the start of 2003. (The average GOES temperature does remain lower than the average RHESSI temperature, even though the presence of GOES temperatures higher than RHESSI temperatures for individual intervals makes us distrust the GOES values.) The GOES EM decreases steadily by about 2 orders of magnitude.\n\n## Heating?\n\nThe proven coronal heating process is the heating by flares that results in hot post-flare loops. Is it possible that all we are seeing is post-flare loops, with no need for nanoflare or wave heating or anything fancy? Maybe. The radiative cooling time for a loop of 8 MK and density of 109cm − 3 is about 200 minutes. The conductive cooling time (for a loop length of 105 km) is about 13 minutes. Using the approximation of total cooling time of", null, "$\\tau_{mix}=(5/3)\\tau_r^{7/12}*\\tau_c^{5/12}$ (Ref. 3), we find a cooling time of approximately an hour. If there are flares/microflares occurring more frequently than this, then it's conceivable that all of this is residual heating from those events. We know that there are anywhere from 5 to 90 microflares per day (Ref. 4) so there should be events often enough. Whether a single small microflare can result in enough heat to result in a persistent EM as large as observed is an issue that needs to be addressed by solar heating experts in the future." ]
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https://www.gradesaver.com/textbooks/science/physics/college-physics-4th-edition/chapter-17-problems-page-651/1
[ "## College Physics (4th Edition)\n\nWe can rank the situations in order of electric potential energy, from highest to lowest: $a = d \\gt b = e \\gt c$\nWe can write a general equation for the electric potential energy: $U = \\frac{k~Q_1~Q_2}{d}$ Let $q_1 = 1~\\mu C$ Let $q_2 = 1~\\mu C$ Let $r = 1~m$ Let $U_0 = \\frac{k~q_1~q_2}{r}$ We can find an expression for the electric potential energy in each case. (a) $U = \\frac{k~(q_1)~(2q_2)}{r} = 2~U_0$ (b) $U = \\frac{k~(2q_1)~(-q_2)}{r} = -2~U_0$ (c) $U = \\frac{k~(2q_1)~(-4q_2)}{2r} = -4~U_0$ (d) $U = \\frac{k~(-2q_1)~(-2q_2)}{2r} = 2~U_0$ (e) $U = \\frac{k~(4q_1)~(-2q_2)}{4r} = -2~U_0$ We can rank the situations in order of electric potential energy, from highest to lowest: $a = d \\gt b = e \\gt c$" ]
[ null ]
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http://theoakpine.co.uk/990815-help-with-optimization.shtml
[ "2411 Shares\n\nHelp with optimization problem?", null, "Topic: Time and work problem solving methods\nJune 20, 2019 / By Devan\nQuestion: So I have this optimization problem to do. I tried to get some help from school tutors, they did not know how to do it. \"Must be solved by a calculus method\" You are at the southernmost point of a circular lake of radius 1 mile. Your plan is to swim a straight course to another point on the shore of the lake, then jog to the northernmost point. You can jog twice as fast as you can swim. Find the route you must take to minimize the time this trip will take and find the time in minutes. I have never seen an optimization like this and I am having a hard time just to set it up. I need to solve this by a CALCULUS method. Please, I need some help.", null, "Best Answers: Help with optimization problem?", null, "Candi | 6 days ago\nSwim to a point on the circle angle 2A (to avoid fractions) round from the southern end. Then jog round the arc (pi - 2A) that remains. (We must work in radians due to differentiation of trig function.) A diagram will show that the straight part = 2*cosA. The time for the whole exercise is T = 2*cosA + (1/2)*(pi - 2A) = 2*cosA + pi/2 - A (The 1/2 at the front of the second term is due to speed being twice as fast.) dT/dA = -2*sinA - 1 For minimum we need dT/dA = 0 ----> sinA = -1/2 ----> A = -30 degrees. 2A = -60 degrees or 60 degrees round the other way. This is where you swim to and then jog the rest.\n👍 120 | 👎 6\nDid you like the answer? Help with optimization problem? Share with your friends\n\nWe found more questions related to the topic: Time and work problem solving methods", null, "Originally Answered: Optimization Problem-?\n1. Okay if cost per square cm = 2 on the top, and 1 for the sides There are one top, one bottom and 4 sides... if X = size of side of square.. and Y = height Cost = 2*2X^2 + 4XY Then you know that 2X^2 + 4XY = 2000 Take the derivative of the cost function with regard to X and set to zero and solve for x... sub into other equation. 2. Define functions for the cost... as it's set.. and then for the area.. then derivative of area function set to zero and sub.", null, "Originally Answered: Optimization Problem-?\nThe equation of a line is y = mx + b which ability at (6, 10), the equation is 10 = m(6) + b, or 10 = 6m + b or b = 10 - 6m The x-intercept of this line represents the backside of the triangle. The x-intercept is stumbled on by utilising making y = 0, so y = mx + b 0 = mx + b -b = mx x = -b/m <==== the backside. The y-intercept represents the top of the triangle, stumbled on by utilising making x = 0. y = mx + b y = b <====== the top The formula of the area of the triangle is (a million/2)(base)(top). for this reason, A = (a million/2)(-b/m)(b) A = (a million/2)(-b^2 / m) A = (-a million/2)(b^2/m) yet all of us know that b = 10 - 6m, so A = (-a million/2)( [10 - 6m]^2 / m ) So this would be our area formula, A(m) A(m) = (-a million/2)( [10 - 6m]^2 / m ) we would choose to shrink the area, so we take the spinoff as frequent. A'(m) = (-a million/2) [ 2(10 - 6m)(-6)m - (10 - 6m)^2 (a million) ] / [ m^2 ] A'(m) = (-a million/2) [ (-12m)(10 - 6m) - (10 - 6m)^2 ] / [ m^2 ] A'(m) = (-a million/2) [ (10 - 6m)(-12m - (10 - 6m)) ] / [ m^2 ] A'(m) = (-a million/2) [ (10 - 6m)(-12m - 10 + 6m) ] / [ m^2 ] A'(m) = (-a million/2) [ (10 - 6m)(-6m - 10) ] / [ m^2 ] Now, we make A'(m) = 0. 0 = (-a million/2) [ (10 - 6m)(-6m - 10) ] / [ m^2 ] serious values: 5/3, -5/3 we are able to reject 5/3 by way of fact it incredibly is a favorable slope (the only thank you to form triangles from the 1st quadrant is that if the slope is detrimental). That leaves -5/3, so this tells us the minimum area happens while the slope m = -5/3. to discover the equation of the line, all we would desire to do is discover extreme college the thank you to discover the equation of the line with slope m = = -5/3 and by way of (6, 10). (y2 - y1)/(x2 - x1) = -5/3 (y - 10)/(x - 6) = -5/3 y - 10 = (-5/3)(x - 6) y - 10 = (-5/3)x + 10 y = (-5/3)x + 20", null, "Amanda\nThe distance that you will swim will be the third leg of an isosceles triangle. Splitting this triangle down the middle gives two congruent triangles with hypotenuse of 1 mile. Let's call the base of each of these triangles 'x'. When you draw it, you'll notice that: x/1 = cosΘ ==> 2x = 2cosΘ. Therefore, the distance that you will swim is 2cosΘ, since there are two triangles. The rate that you'll travel this distance is 'r'. This distance that you'll jog is pi minus the arc-length subtended by the angle pi - 2Θ. (pi - (pi - 2Θ)) = 2Θ The rate that you'll jog this distance is 2r. Now let's use: time = distance / rate. t = 2cosΘ/r + 2Θ/2r. Differentiating yields: t ' = -2sinΘ/r + 1/r. Now let's set our numerator equal to 0. -2sinΘ + 1 = 0 sinΘ = 1/2 Θ = pi/6 t(pi/6) = 2cos(pi/6)/r + 2(pi/6)/2r t(pi/6) = (sqrt3)/r + pi/6r. Since you didn't give the rate, I can't find the exact time in minutes. But notice that the rate at which he swims must be slow. Let's say that it is 1/10 mi/min. Then we'd have: t(pi/6) = (sqrt3)/(1/10) + pi(6/10) t(pi/6) = 17.3 + 5.23 = 22.5. Therefore, the time is reasonable. Essentially, you'll swim a distance of sqrt3 miles to the point on the circle that makes an angle of 2pi/3 with the point that you started from. Then you'll jog a distance of pi/3 around the edge of the lake. Note that the straight-line distance is 2 miles, since radius is 1. The distance that you'll travel, however is pi/3 + sqrt3 = 2.77 miles, which makes sense. Hope this helped.\n👍 40 | 👎 -3", null, "Wallace\ny-10 = m(x-6) is the equation of all strains via (6,10) the are reduce off is a triangle to grasp the peak and base of this triangle we need to calculate the intersections with x-axis and y-axis. x=zero => y=10-6m y=zero => x=6-10/m so the field is (10-6m)(6-10/m)/two = (60+60-36m-one hundred/m)/two = 60 - 18m - 50/m We need to take the by-product and placed it 0 to discover a minimal = -18 + 50/m² = zero => 50/m² = 18 => m² = 50/18 = 25/nine => m = +- five/three to look if it is a minimal, derive once more -one hundred/m³ > zero if m\n👍 35 | 👎 -12", null, "Originally Answered: Please help with hellish calculus optimization problem?\nYou find the extrema of the function as you normally would: take the derivative with respect to I, set the derivative equal to zero, solve for the values of I that make that equation true, then check to see if those extrema are maxima or minima. P(I) = (100*I)/(I^2 + I + 4) dP(I)/dI = 100/((I^2 + I + 4) - (100*I)*(2*I + 1)/(I^2 + I + 4)^2 dP/dI = 100*(4 - I^2)/(I^2 + I + 4)^2 Set this equal to zero and solve for I: 0 = 100*(4 - I^2)/(I^2 + I + 4)^2 0 = 4 - I^2 I = +2, I = -2 Because I is the light intensity, the negative root has no physical meaning. Now check to see if this is a maximum. The easiest way is simply to plot the P(I) vs I, but you can also take the second derivative and determine its sign at I = 2. If the second derivative is negative, the extremum at I=2 is a maximum. If it's positive, then the extremum is a minimum. P'' = 200*(I^3 - 12I - 4)/(I^2 + I + 4)^3 P''(2) = -4 so this is, in fact, a maximum. (The extremum at I=-2 is a miminum.)\n\nIf you have your own answer to the question time and work problem solving methods, then you can write your own version, using the form below for an extended answer." ]
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https://www.51cto.com/article/250777.html
[ "# Web前端研发工程师编程能力飞升之路\n\nWEB前端研发工程师，在国内是一个朝阳职业，自07-08年正式有这个职业以来，也不过三四年的时间。这个领域没有学校的正规教育，没有行内成体系的理论指引，几乎所有从事这个职业的人都是靠自己自学成才。自学成才，一条艰辛的坎坷路，我也是这样一路走来。从2002年开始接触WEB前端研发至今已然有了9个年头，如今再回首，期间的走了很多弯路。推已及人，如果能让那些后来者少走些弯路，辛甚辛甚!\n\n[]\n\n【前言】\n\n`var str=\"www.baidu.com/?page\";  strstr=str.replace('?page',\"\");  alert(str);  strstr=str.substring(0,str.indexOf(\"/\"));  alert(str); `\n\n`// 计算系统当前是星期几  var str = \"\";  var week = new Date().getDay();  if (week == 0) {          str = \"今天是星期日\";  } else if (week == 1) {          str = \"今天是星期一\";  } else if (week == 2) {          str = \"今天是星期二\";   } else if (week == 3) {          str = \"今天是星期三\";   } else if (week == 4) {          str = \"今天是星期四\";   } else if (week == 5) {          str = \"今天是星期五\";   } else if (week == 6) {          str = \"今天是星期六\";   }  // 或者更好一些  var str1 = \"今天是星期\";  var week = new Date().getDay();  switch (week) {          case 0 :                  str1 += \"日\";                  break;          case 1 :                  str1 += \"一\";                  break;          case 2 :                  str1 += \"二\";                  break;          case 3 :                  str1 += \"三\";                  break;          case 4 :                  str1 += \"四\";                  break;          case 5 :                  str1 += \"五\";                  break;          case 6 :                  str1 += \"六\";                  break;  }  alert(str);  alert(str1); `\n\n【进阶之路】\n\nJavaScriptHTMLCSS之类的编码帮助手册里的每个方法/属性都通读几遍!只有将基础打好，以后的路才能走的顺畅。参考这些帮助文档，力争写出无瑕疵的代码。\n\n#p#\n\n`var str=\"www.baidu.com/?page\";  strstr=str.replace(/?page/,\"\");  alert(str); `\n\n`var a = new Array(\"日\", \"一\", \"二\", \"三\", \"四\", \"五\", \"六\");  var week = new Date().getDay();  var str = \"今天是星期\"+ a[week];  alert(str); `\n\n【进阶之路】\n\n#p#\n\n`var str=\"www.baidu.com/?page\";  // 1、字符串剪裁  str.substring(0, str.indexOf(\"?page\"));  // 2、正则表达式  str.replace(/?page/, \"\");  // 3、字符串分拆、合并  str.split(\"?page\").join(\"\"); `\n\n“入室”阶段，程序员应该能够肯定的回答：对于这个需求而言，我的代码就是最优秀的代码。\n\n`// 计算系统当前是星期几  var str = \"今天是星期\" + \"日一二三四五六\".charAt(new Date().getDay()); `\n\n【进阶之路】\n\n#p#\n\n`var str = \"http://www.xxx.com/?pn=0\";   // 删除指定字符 pn=0 // 我将这个字符串里所可能想到的各种情况都列举出来  var a = [           \"http://www.xxx.com/VMpn=?pn=0\"// pn= 可能出现在 ? 前          , \"http://www.xxx.com/VMpn=?pn=\"// URL里允许pn 值为空          , \"http://www.xxx.com/VMpn=?pn=0&a=1\"// URL 里可有多个字段          , \"http://www.xxx.com/VMpn=?a=1&pn=0\"// 可能排在最后          , \"http://www.xxx.com/VMpn=?a=1&pn=0&pn=1\"// 可能有多个 pn 字段          , \"http://www.xxx.com/VMpn=?a=1&pn=0&b=2\"// 可能在中间          , \"http://www.xxx.com/VMpn=?a=1&pn=0&pn=1&b=1\"  // 可能在中间成组          , \"http://www.xxx.com/VMpn=?a=1&pn=0&b=1&pn=1\"  // 可能零星分布  ];  /* 需求的不言之秘：  ? 若出现在字符串最尾则要去之  ? & 两个符号不可重叠  */  var reg = /((\\?)(pn=[^&]*&)+(?!pn=))|(((\\?|&)pn=[^&]*)+\\$)|(&pn=[^&]*)/g;   for (var i = 0; i < a.length; i++) {      alert(a[i] + \"\\n\" + a[i].replace(reg, \"\\$2\"));  } `\n\n【进阶之路】\n\n#p#\n\n`/**   * 在拼接正则表达式字符串时，消除原字符串中特殊字符对正则表达式的干扰   * @author:meizz   * @version: 2010/12/16   * @param               {String}        str     被正则表达式字符串保护编码的字符串   * @return              {String}                被保护处理过后的字符串  */  function escapeReg(str) {          return str.replace(new RegExp(\"([.*+?^=!:\\x24{}()|[\\\\]\\/\\\\\\\\])\", \"g\"), \"\\\\\\x241\");  }   /**   * 删除URL字符串中指定的 Query   * @author:meizz   * @version:2010/12/16   * @param               {String}        url     URL字符串   * @param               {String}        key     被删除的Query名   * @return              {String}                被删除指定 query 后的URL字符串  */   function delUrlQuery(url, key) {          key = escapeReg(key);          var reg = new RegExp(\"((\\\\?)(\"+ key +\"=[^&]*&)+(?!\"+ key +    \"=))|(((\\\\?|&)\"+ key +\"=[^&]*)+\\$)|(&\"+ key +\"=[^&]*)\", \"g\");          return url.replace(reg, \"\\x241\")  }   // 应用实例  var str = \"http://www.xxx.com/?pn=0\";   // 删除指定字符 pn=0 delUrlQuery(str, \"pn\"); `\n\n【进阶之路】\n\n#p#\n\n`// 库文件 /mz/string/escapeReg.js  /**   * 在拼接正则表达式字符串时，消除原字符串中特殊字符对正则表达式的干扰   * @author:meizz   * @version: 2010/12/16   * @param               {String}        str     被正则表达式字符串保护编码的字符串   * @return              {String}                被保护处理过后的字符串  */  mz.string.escapeReg = function (str) {          return str.replace(new RegExp(\"([.*+?^=!:\\x24{}()|[\\\\]\\/\\\\\\\\])\", \"g\"), \"\\\\\\x241\");  }   // 库文件 /mz/url/delQuery.js  /// include mz.string.escapeReg;  /**   * 删除URL字符串中指定的 Query   * @author:meizz   * @version:2010/12/16   * @param               {String}        url     URL字符串   * @param               {String}        key     被删除的Query名   * @return              {String}                被删除指定 query 后的URL字符串  */  mz.url.delQuery = function (url, key) {          key = mz.string.escapeReg(key);          var reg = new RegExp(\"((\\\\?)(\"+ key +\"=[^&]*&)+(?!\"+ key +    \"=))|(((\\\\?|&)\"+ key +\"=[^&]*)+\\$)|(&\"+ key +\"=[^&]*)\", \"g\");          return url.replace(reg, \"\\x241\")  }   // 应用实例  /// include mz.url.delQuery;  var str = \"http://www.xxx.com/?pn=0\";   // 删除指定字符 pn=0 mz.url.delQuery(str, \"pn\"); `\n\n`// 库文件 /mz/url/delQuery.js  /// include mz.string.escapeReg;  /**   * 删除URL字符串中指定的 Query   * @author:meizz   * @version:2010/12/16   * @param               {String}        url     URL字符串   * @param               {String}        key     被删除的Query名   * @return              {String}                被删除指定 query 后的URL字符串  */  String.prototype.delQuery = function ( key) {          key = mz.string.escapeReg(key);          var reg = new RegExp(\"((\\\\?)(\"+ key +\"=[^&]*&)+(?!\"+ key +    \"=))|(((\\\\?|&)\"+ key +\"=[^&]*)+\\$)|(&\"+ key +\"=[^&]*)\", \"g\");          return this.replace(reg, \"\\x241\")  }   // 应用实例  /// include mz.url.delQuery;  var str = \"http://www.xxx.com/?pn=0\";   // 删除指定字符 pn=0 str.delQuery(\"pn\"); `\n\n【进阶出路】\n\n#p#\n\n【进阶出路】\n\n#p#\n\n【编辑推荐】", null, "", null, "", null, "", null, "", null, "", null, "51CTO技术栈公众号", null, "" ]
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https://www.kymat.io/gallery_2d/mnist_keras.html
[ "# Classification of MNIST with scattering¶\n\nHere we demonstrate a simple application of scattering on the MNIST dataset. We use 10000 images to train a linear classifier. Features are normalized by batch normalization.\n\n## Preliminaries¶\n\nSince we’re using TensorFlow and Keras to train the model, import the relevant modules.\n\n```import tensorflow as tf\nfrom tensorflow.keras.models import Model\nfrom tensorflow.keras.layers import Input, Flatten, Dense\n```\n\nFinally, we import the Scattering2D class from the kymatio.keras package.\n\n```from kymatio.keras import Scattering2D\n```\n\n## Training and testing the model¶\n\nFirst, we load in the data and normalize it.\n\n```(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()\n\nx_train, x_test = x_train / 255., x_test / 255.\n```\n\nWe then create a Keras model using the scattering transform followed by a dense layer and a softmax activation.\n\n```inputs = Input(shape=(28, 28))\nx = Scattering2D(J=3, L=8)(inputs)\nx = Flatten()(x)\nx_out = Dense(10, activation='softmax')(x)\nmodel = Model(inputs, x_out)\n```\n\nDisplay the created model.\n\n```model.summary()\n```\n\nOnce the model is created, we couple it with an Adam optimizer and a cross-entropy loss function.\n\n```model.compile(optimizer='adam',\nloss='sparse_categorical_crossentropy',\nmetrics=['accuracy'])\n```\n\nWe then train the model using model.fit on a subset of the MNIST data.\n\n```model.fit(x_train[:10000], y_train[:10000], epochs=15,\nbatch_size=64, validation_split=0.2)\n```\n\nFinally, we evaluate the model on the held-out test data.\n\n```model.evaluate(x_test, y_test)\n```\n\nTotal running time of the script: ( 0 minutes 0.000 seconds)\n\nGallery generated by Sphinx-Gallery" ]
[ null ]
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https://www.seminarsonly.com/IT/Planar%20Separators.php
[ "", null, "", null, "", null, "## Planar Separators\n\nPublished on Sep 21, 2019\n\n### Abstract\n\nI/O-efficient graph algorithms have received considerable attention lately because massive graphs arise naturally in many applications. Recent web crawls, for example, produce graphs of on the order of 200 million nodes and 2 billion edges.\n\nRecent work in web modeling uses depth-first search, breadth-first search, shortest paths, and connected components as primitive operations for investigating the structure of the web.\n\nMassive graphs are also often manipulated in Geographic Information Systems (GIS), where many fundamental problems can be formulated as basic graph problems. The graphs arising in GIS applications are often planar. Yet another example of massive graphs is AT&T's 20TB phone call graph . When working with such large data sets, the transfer of data between internal and external memory, and not the internal memory computation, is often the bottleneck. Thus, I/O-efficient algorithms can lead to considerable run-time improvements.\n\nBreadth-first search (BFS) and depth-first search (DFS) are the two most fundamental graph-searching strategies. They are extensively used in internal memory algorithms, as they are easy to perform in linear time; yet they provide valuable information about the structure of the given graph. Unfortunately, no I/O-efficient algorithms for BFS and DFS in arbitrary sparse graphs are known, while existing algorithms perform reasonably well on dense graphs. Together with recent results on single-source shortest paths (SSSP) and DFS, our algorithm leads to I/O-efficient algorithms for SSSP, BFS, and DFS on undirected embedded planar graphs.\n\n### Model of Computation\n\nThe algorithms in this paper are designed and analyzed in the Parallel Disk Model (PDM). In thismodel, D identical disks of unlimited size are attached to a machine with an internal memory capable of holding M data items. These disks constitute the external memory of the machine. Initially, all data is stored on disk. Each disk is partitioned into blocks of B data items each. An I/O-operation is the transfer of up to D blocks, at most one per disk, to or from internal memory from or to external memory.\n\nThe complexity of an algorithm in the PDM is the number of I/O-operations it performs. Sorting, permuting, and scanning an array of N consecutive data items are primitive operations often used in external memory algorithms. Their I/O-complexities are sort(N) = Q((N=DB) logM=B(N=B)),\nperm(N) = Q(min(N; sort(N))), and scan(N) = O(N=DB), respectively.\n\n Are you interested in this topic.Then mail to us immediately to get the full report. email :- [email protected]" ]
[ null, "https://www.seminarsonly.com/IT/chem.jpg", null, "https://www.seminarsonly.com/IT/www.seminarsonly.com.png", null, "https://www.seminarsonly.com/IT/top image.gif", null ]
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https://stats.stackexchange.com/questions/340462/what-is-predicted-and-controlled-in-reinforcement-learning
[ "# What is predicted and controlled in reinforcement Learning?\n\nIn reinforcement learning, I saw many notions with respect to control and prediction, like Monte Carlo prediction and Monte Carlo control.\n\nBut what are we actually predicting and controlling?\n\nThe difference between prediction and control is to do with goals regarding the policy. The policy describes the way of acting depending on current state, and in the literature is often noted as $\\pi(a|s)$, the probability of taking action $a$ when in state $s$.\n\nSo, my question is for prediction, predict what?\n\nA prediction task in RL is where the policy is supplied, and the goal is to measure how well it performs. That is, to predict the expected total reward from any given state assuming the function $\\pi(a|s)$ is fixed.\n\nfor control, control what？\n\nA control task in RL is where the policy is not fixed, and the goal is to find the optimal policy. That is, to find the policy $\\pi(a|s)$ that maximises the expected total reward from any given state.\n\nA control algorithm based on value functions (of which Monte Carlo Control is one example) usually works by also solving the prediction problem, i.e. it predicts the values of acting in different ways, and adjusts the policy to choose the best actions at each step. As a result, the output of the value-based algorithms is usually an approximately optimal policy and the expected future rewards for following that policy.\n\n• Just keep in mind \"RL\" is pretty ill-defined. Usually people mean \"model-free full RL\" where there is no model for the rewards, no model for the dynamics, assumption that actions affect both reward state and observations. But in reality there is usually a model for the rewards, some sort of assumption on the state dynamics, in some case observations are not affected by actions. Apr 16 '20 at 10:13\n\nThe term control comes from dynamical systems theory, specifically, optimal control. As Richard Sutton writes in the 1.7 Early History of Reinforcement Learning section of his book \n\nConnections between optimal control and dynamic programming, on the one hand, and learning, on the other, were slow to be recognized. We cannot be sure about what accounted for this separation, but its main cause was likely the separation between the disciplines involved and their different goals.\n\nHe even goes on to write\n\nWe consider all of the work in optimal control also to be, in a sense, work in reinforcement learning. We define a reinforcement learning method as any effective way of solving reinforcement learning problems, and it is now clear that these problems are closely related to optimal control problems, particularly stochastic optimal control problems such as those formulated as MDPs. Accordingly, we must consider the solution methods of optimal control, such as dynamic programming, also to be reinforcement learning methods.\n\nPrediction is described as the computation of $$v_\\pi(s)$$ and $$q_\\pi(s, a)$$ for a fixed arbitrary policy $$\\pi$$, where\n\n• $$v_\\pi(s)$$ is the value of a state $$s$$ under policy $$\\pi$$, given a set of episodes obtained by following $$\\pi$$ and passing through $$s$$.\n• $$q_\\pi(s, a)$$ is the action-value for a state-action pair $$(s, a)$$. It's the expected return when starting in state $$s$$, taking action $$a$$, and thereafter following policy $$\\pi$$.\n\nControl is described as approximating optimal policies. When doing control, one maintains both an approximate policy and an approximate value function. The value function is repeatedly altered to more closely approximate the value function for the current policy, and the policy is repeatedly improved with respect to the current value function. This is the idea of generalised policy iteration (GPI). See 5.1 Monte Carlo Control in .\n\n Reinforcement Learning: An Introduction, by Richard S. Sutton and Andrew G. Barto" ]
[ null ]
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https://alanchattaway.blogspot.com/2012/08/how-many-squares.html
[ "## Sunday, August 26, 2012\n\n### How many squares?\n\nI keep seeing this puzzle on Facebook, so I'm posting my systematic solution here.", null, "There's a pattern of 16 basic squares in a regular 4  x  4 grid, plus two more superimposed on that grid to create 8 small squares.\n\nFirst consider the basic squares.  There are 4 x 4 = 16 of them.\n\nNow group them into 2 x 2 squares. There are 3 of those across:", null, "and there are obviously 3 of them down also, so there are 3 x 3 = 9 of them.\n\nIf you do the same using 3 x 3 squares, there are 2 across and 2 down, so there are 2 x 2 = 4 of them.\n\nAnd of course if you group them into a 4 x 4 square, there's just 1 of those.\n\nNow if you do the same with the two superimposed squares, there are 8 small squares and 2 large squares:", null, "So the total number of squares is:\n\n16 + 9 + 4 + 1 + 8 + 2 = 40" ]
[ null, "https://1.bp.blogspot.com/-d2Zp6LH2fko/UDpdX5XLe7I/AAAAAAAAAl0/cVUH9De7s6g/s400/40+squares.png", null, "https://4.bp.blogspot.com/-gTD4xqbRwGw/UDpjHxNY1-I/AAAAAAAAAmE/Ys2m3Th9gV0/s400/40+squares+basic+2x2.png", null, "https://3.bp.blogspot.com/-0zYWKU9U2kQ/UDpmMFwxucI/AAAAAAAAAmc/xLN-IKPB7pg/s200/40+squares+last.png", null ]
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