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[ "# Charge Compensation and Optimal Stoichiometry in Superconducting (CaxLa1–x)(Ba1.75–xLa0.25+x)Cu3Oy\n\nCharge Compensation and Optimal Stoichiometry in Superconducting (CaxLa1–x)(Ba1.75–xLa0.25+x)Cu3Oy, D. R. Harshman and A. T. Fiory [arXiv]\nThe superconductive and magnetic properties of charge-compensated (CaxLa1–x)(Ba1.75–xLa0.25+x)Cu3Oy (normally denoted as CLBLCO) are considered through quantitative examination of data for electrical resistivity, magnetic susceptibility, transition width, muon-spin rotation, x-ray absorption, and crystal structure. A derivative of LaBa2Cu3Oy, cation doping of this unique tetragonal cuprate is constrained by compensating La substitution for Ba with Ca substitution for La, where for 0 ≤ x ≤ 0.5 local maxima in TC occur for y near 7.15. It is shown that optimum superconductivity occurs for 0.4 ≤ x ≤ 0.5, that the superconductivity and magnetism observed are nonsymbiotic phenomena, and that charge-compensated doping leaves the carrier density in the cuprate planes nearly invariant with x, implying that only a small fraction of superconducting condensate resides therein. Applying a model of electronic interactions between physically separated charges in adjacent layers, the mean in-plane spacing between interacting charges, ℓ = 7.1206 Å, and the distance between interacting layers, ζ = 2.1297 Å, are determined for x = 0.45. The theoretical optimal TC0 ∝ ℓ–1ζ–1 of 82.3 K is in excellent agreement with experiment (≈ 80.5 K), bringing the number of compounds for which TC0 is accurately predicted to 37 from six different superconductor families (overall accuracy of ±1.35 K).", null, "Transition temperature measured by μ+SR plotted against the μ+SR Gaussian relaxation parameter divided by the muon gyromagnetic ratio, σμ/γμ, for polycryst. samples of CLBLCO with depleted oxygen at x = 0.4 (filled circles), excess oxygen at x = 0.4 (filled triangles), and optimum oxygen at x = 0.1 and x = 0.4 (filled squares). Similarly obtained μ+SR data for ceramic samples of YBa2Cu3O7–δ for various δ are presented for comparison. The dashed line represents a non-existent proportional behavior.", null, "Experimental TC0 versus (ℓζ)–1, where ℓ is intra-layer mean spacing of interacting charges and ζ is inter-layer interaction distance, for CLBLCO (x = 0.45, star symbol), compared to other cuprates (open circles), Fe-based pnictides and chalcogenides (open triangles), a ruthenate (filled circle) and an organic (filled triangle). The solid line through the data points represents theory. Inset: transition temperatures of CLBLCO (filled symbols) and pair-breaking theory (open symbols) as function of doping x.", null, "Transition temperatures TC for CLBLCO, maximized by oxygen content y, extracted from resistivity (filled circles after Ref. 1, open circles after Ref. 4) and magnetic susceptibility (filled triangles after Ref. 1, open triangles after Ref. 2) as function of x. Star symbol denotes theoretical TC0 averaged over x = 0.4 – 0.5. Inset represents dTC/dP versus TC after Ref. 2; curve denotes trend.", null, "Resistivity measurements ρ(TC+) and ρ(0), left scale, and the percentage transition widths ΔTC/TC, right scale, plotted as functions of x for (CaxLa1–x)(Ba1.75–xLa0.25+x)Cu3Oy, with y set to maximize TC (after Ref. 1). Inset shows ħt–1(0)/kBTC plotted against doping x. Horizontal dashed line denotes unity.\n\nD. R. Harshman and A. T. Fiory, Phys. Rev. B 86, 144533 (2012)." ]

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[ "# ALJABAR LINEAR ELEMENTER VERSI APLIKASI PDF\n\nALJABAR LINEAR ELEMENTER – Ebook written by VERSI APLIKASI. Read this book using Google Play Books app on your PC, android, iOS devices. Sistem Informasi. Aljabar Linear Elementer Versi Aplikasi Jilid 2 Edisi 8. Share to: Facebook; Twitter; Google; Digg; Reddit; LinkedIn; StumbleUpon. Anton. Buy Aljabar Linear Elementer Versi Aplikasi Ed 8 Jl 1 in Bandung,Indonesia. Get great deals on Books & Stationery Chat to Buy.", null, "Author: Arashizil Dazilkree Country: Peru Language: English (Spanish) Genre: Politics Published (Last): 1 July 2008 Pages: 217 PDF File Size: 7.87 Mb ePub File Size: 9.6 Mb ISBN: 764-9-40235-800-9 Downloads: 19247 Price: Free* [*Free Regsitration Required] Uploader: Faejas", null, "If there are any rows that consist entirely of zeros, then they are grouped together at the bottom of the matrix. In any two successive rows that do not consist entirely of zeros, the leading 1 in the lower row occurs farther slementer the right than the leading 1 aljzbar the higher row.\n\nMultiply the corresponding entries from the row and column together, and then add up the resulting products. Jika terbukti melakukan kecurangan akademik berupa mencontek atau bekerja sama pada saat kuis, UTS dan UAS, maka akan mendapatkan sanksi nilai 0.\n\nTo be of reduced row-echelon form, a matrix must have the following properties: Vectors in Coordinate Systems If equivalent vectors, v and w, are located so aplkkasi their initial points fall a;likasi the origin, then it is obvious that their terminal points must coincide since the vectors have the same length and direction ; thus the vectors have the same components.\n\nHelp Center Find new research papers in: A matrix that has the first three properties is said to be in versl form. Special case In the special case of a homogeneous linear system of two equations in two unknowns, say: Remember me on this computer.\n\nAdjoint of Matrix If A is any n x n matrix and Cij is the cofactor of aijthen the matrix Is called the matrix of cofactor from A. In addition, we define the zero vector space to have dimension zero.\n\nHERODIAS FLAUBERT PDF\n\n### Aljabar Linier Elementer (Anton and Rorres) | Muhammad Nufail –\n\nMore generally, we elemdnter the determinant of an n x n matrix to be This method of evaluating det A is called cofactor expansion along the first row of A. The trace of A is undefined if A is not a square matrix. Conversely, vectors with the same components are equivalent since they have the same length and the same direction. If no such matrix B can be found, then A is said to be singular.\n\nPoint Penilaian Nilai akhir akan ditentukan dengan komponen sebagai berikut: We aplikask this a leading 1.\n\n### ALJABAR LINEAR | Reny Rian Marliana –\n\nTo see that T is linear, observe that: The dimension of a finite-dimensional vector space V, denoted by dim Vis defined to be the number of vectors in a basis for V.\n\nElementary Linear Algebra, 9th Edition. Matrices of different sizes cannot be added or subtracted. To find the entry in row i and column j of ABsingle out row i from the matrix A and column j from the matrix B. Tidak meninggalkan sampah di ruangan kelas 6.\n\n## Print Version", null, "Augmented Matrices A system of m linear equations in n unknowns can be abbreviated by writing only the rectangular array of numbers This is called the augmented matrix for the system. If, as shown in Aljanar 3.\n\nAdd a multiple of one equation to another.", null, "The set of all ordered n- tuples is called n-space and is denoted by Rn. Solution Consider a general system of two linear equations in the unknowns x and y: Method for Solving a System of Linear Equations Since the rows horizontal lines of an augmented matrix correspond to the equations in the associated system, these three operations correspond to the following operations on the rows of the augmented matrix: Tidak ada ujian susulan untuk kuis.\n\nDISDETTA CONTRATTO TELETU PDF\n\nThe various costs in whole dollars involved in producing a single item of a product are given in the table: Adjoin the identity matrix to the right side of A, thereby producing a matrix of the form [A I], apply row operations to this matrix until the left side is reduced to I; these operations will convert the right side to A-1, so the final matrix will have the form [I A-1].", null, "Solution Howard Anton Multiply a row through by a nonzero constant. Each column that contains a leading 1 has zeros everywhere else in that column. Add a multiple of one row to another row. Essential Linear Algebra with Applications. A homogeneous system of linear equations with more unknowns than equations has infinitely many solutions. If A is an m x r matrix and B is an r x n matrix, then the product AB is the m x n matrix whose entries are determined as follows.\n\nIf A is any matrix and c is any scalar, then the product cA is the matrix obtained by multiplying each entry of the matrix A by c. The numbers in the array aljabra called the entries in the matrix.\n\nTwo matrices are defined to be equal if they have the same size and their corresponding entries are equal. Thus, a matrix in reduced row-echelon form is of necessity in row-echelon form, but not conversely.\n\nGaussian Elimination Howard Anton" ]

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[ "For the past several years, I have had a spreadsheet. There is, however, one problem: it’s not a great spreadsheet. It doesn’t have the flexibility to allow for change in your daily life. This is why I created the Newton's Second Law of Motion Worksheet app. It’s a full-featured, customizable, and adaptable online sheet using a simple formula. It’s like a spreadsheet but much more efficient. When you’re on your phone, you’ll either not have access to your phone or you’ll have to type in the formula. This is because\n\nNewton’s second law only applies to a change in displacement for the entire object. But with the Newton’s second law app, you can do a change in displacement for an entire object.\n\nThe formula for the sheet is: (m x a)^2 + (m x b)^2. The formula means to apply the Newton’s second law to m and a and to the square of the displacement of m and a, the displacement of m x a and the displacement of m x b. If you use this formula, you’ll notice that the formula only needs to be entered once.\n\nThe top 10 Newton’s Second Law of Motion Worksheet Apps are the only one that contains the formula for moving a mouse around in a circle.\n\nThe formula is: (m x a)^2 + (m x b)^2. The formula is: (m x b)^2 + (m x a)^2. The formula is: (m x b)^2 + (m x a)^2.The first two terms in the formula are the displacement of the mouse. The last term is the displacement of the mouse, which you can make use of as you move the mouse. Newton’s Second Law of Motion is basically a rule that says that every object has a certain amount of inertia. This means that its movement is going to be proportional to its velocity so that if you hold an object in your hand, you can still move it in a straight line. You can also make use of this to solve problems such as trying to move a ball around a fixed circle using only your right hand.\n\nThe formula, if you’re not familiar with it, was invented by Isaac Newton in 1727. It is actually the “top 10 Newton’s Second Law of Motion Worksheets” that you will be using in your classroom. The first two terms are just the displacement of the mouse, the last term is the displacement of the mouse, which you can make use of as you move the mouse.\n\nThe formula itself is amazing.\n\nThe first part is the general concept of what you’re trying to achieve, and then the second part is more specific. This section is also really useful if you’re a beginner programmer. If you have to make a change to a code file, the second part will help you figure out exactly what you should be changing.\n\nWhile the formula is awesome, I’ve found it to be one of the most challenging to memorize, and I think it’s because the idea of the displacement is not intuitive for many people. You basically have to think about what you want to achieve and just move the mouse in the right direction at the right time. In my opinion, this formula is a great way to start learning something new, and it will make sense when you start applying it to problems in your life." ]

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[ "# numpy.random.rand¶\n\n`numpy.random.``rand`(d0, d1, ..., dn)\n\nRandom values in a given shape.\n\nCreate an array of the given shape and populate it with random samples from a uniform distribution over `[0, 1)`.\n\nParameters: d0, d1, …, dn : int, optional The dimensions of the returned array, should all be positive. If no argument is given a single Python float is returned. out : ndarray, shape `(d0, d1, ..., dn)` Random values.\n\nNotes\n\nThis is a convenience function. If you want an interface that takes a shape-tuple as the first argument, refer to np.random.random_sample .\n\nExamples\n\n```>>> np.random.rand(3,2)\narray([[ 0.14022471, 0.96360618], #random\n[ 0.37601032, 0.25528411], #random\n[ 0.49313049, 0.94909878]]) #random\n```\n\n#### Previous topic\n\nRandom sampling (`numpy.random`)\n\n#### Next topic\n\nnumpy.random.randn" ]

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[ "Discover a lot of information on the number 29680: properties, mathematical operations, how to write it, symbolism, numerology, representations and many other interesting things!\n\nMathematical properties of 29680\n\nIs 29680 a prime number? No\nIs 29680 a perfect number? No\nNumber of divisors 40\nList of dividers 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 53, 56, 70, 80, 106, 112, 140, 212, 265, 280, 371, 424, 530, 560, 742, 848, 1060, 1484, 1855, 2120, 2968, 3710, 4240, 5936, 7420, 14840, 29680\nSum of divisors 80352\nPrime factorization 24 x 5 x 7 x 53\nPrime factors 2, 5, 7, 53\n\nHow to write / spell 29680 in letters?\n\nIn letters, the number 29680 is written as: Twenty-nine thousand six hundred and eighty. And in other languages? how does it spell?\n\n29680 in other languages\nWrite 29680 in english Twenty-nine thousand six hundred and eighty\nWrite 29680 in french Vingt-neuf mille six cent quatre-vingts\nWrite 29680 in spanish Veintinueve mil seiscientos ochenta\nWrite 29680 in portuguese Vinte e nove mil seiscentos oitenta\n\nDecomposition of the number 29680\n\nThe number 29680 is composed of:\n\n1 iteration of the number 2 : The number 2 (two) represents double, association, cooperation, union, complementarity. It is the symbol of duality.... Find out more about the number 2\n\n1 iteration of the number 9 : The number 9 (nine) represents humanity, altruism. It symbolizes generosity, idealism and humanitarian vocations.... Find out more about the number 9\n\n1 iteration of the number 6 : The number 6 (six) is the symbol of harmony. It represents balance, understanding, happiness.... Find out more about the number 6\n\n1 iteration of the number 8 : The number 8 (eight) represents power, ambition. It symbolizes balance, realization.... Find out more about the number 8\n\n1 iteration of the number 0 : ... Find out more about the number 0\n\nOther ways to write 29680\nIn letter Twenty-nine thousand six hundred and eighty\nIn roman numeral\nIn binary 111001111110000\nIn octal 71760\nIn US dollars USD 29,680.00 (\\$)\nIn euros 29 680,00 EUR (€)\nSome related numbers\nPrevious number 29679\nNext number 29681\nNext prime number 29683\n\nMathematical operations\n\nOperations and solutions\n29680*2 = 59360 The double of 29680 is 59360\n29680*3 = 89040 The triple of 29680 is 89040\n29680/2 = 14840 The half of 29680 is 14840.000000\n29680/3 = 9893.3333333333 The third of 29680 is 9893.333333\n296802 = 880902400 The square of 29680 is 880902400.000000\n296803 = 26145183232000 The cube of 29680 is 26145183232000.000000\n√29680 = 172.27884373886 The square root of 29680 is 172.278844\nlog(29680) = 10.298228697281 The natural (Neperian) logarithm of 29680 is 10.298229\nlog10(29680) = 4.472463896607 The decimal logarithm (base 10) of 29680 is 4.472464\nsin(29680) = -0.9807374052559 The sine of 29680 is -0.980737\ncos(29680) = -0.1953308524835 The cosine of 29680 is -0.195331\ntan(29680) = 5.0209037271197 The tangent of 29680 is 5.020904" ]

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[ "# Measures of central tendency example problems\n\n##### 2020-02-20 18:58\n\nFinding the Mean, Median, Mode Practice Problems Now you get a chance to work out some problems. You may use a calculator if you would like. Study each of these problems carefully; you will see similar problems on the lesson knowledge check. You will need paper and a pencil to complete the following exercises. You will be able toA measure of central tendency (also referred to as measures of centre or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution. measures of central tendency example problems\n\nAs such, measures of central tendency are sometimes called measures of central location. They are also classed as summary statistics. However, one of the problems with the mode is that it is not unique, so it leaves us with problems when we have two or more values that share the highest frequency, such as below: An example of a normally\n\nCentral Tendency Word Problems. For example: On the video game, Erin's scores were 1245, 1150, 1450, 950, and 950. Find the mean, median, and mode. Which is the best representation of Erin's scores? We help you determine the exact lessons you need. Measures of central tendency are used to describe what is normal for a set of data. Mean, median, and mode are the three measures of central tendency. The mean and median can only be used formeasures of central tendency example problems Measures of central tendency are a key way to discuss and communicate with graphs. The term central tendency refers to the middle, or typical, value of a set of data, which is most commonly measured by using the three m's: mean, median, and mode.\n\n## Measures of central tendency example problems free\n\nPractice Problems: Measures of Central Tendency Answer A high school teacher at a small private school assigns trigonometry practice problems to be worked via the net. Students must use a password to access the problems and the time of login and logoff are automatically recorded for the teacher. measures of central tendency example problems Measures of central tendency are numbers that describe what is average or typical within a distribution of data. There are three main measures of central tendency: mean, median, and mode. While they are all measures of central tendency, each is calculated differently and Sep 01, 2014 Central Tendency Example Problems Statistics (PSY 210 and ECON 261) at Nevada State College Understanding and Calculating Measures of Central Tendency Duration: 6: 19. NurseKillam 129, 667 views. Measures of Central Tendency: Mean, Median, and Mode Example A football team had offensive drives of 43, 42, 45, 44, 45, and 48 yards. Find the mean offensive drive for the team. 7. Example The heights of players on Central High Schools basketball team 3. It should seem clear how the mean and the median are measures of the the central tendency of the data since the mean is a familiar average and the median is the middle. However, explain why the mode is also considered a measure of central tendency.\n\nRating: 4.91 / Views: 926" ]

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[ "# Modernization Hub\n\n##### Modernization and Improvement", null, "## Lecture 8: Recurrent Neural Networks and Language Models\n\n[MUSIC] Stanford University.>>All right, hello everybody. Welcome to Lecture seven or\nmaybe it’s eight. Definitely today is the beginning of where we talk about models that\nreally matter in practice. We’ll talk today about the simplest\nrecurrent neural network model one can think of. But in general, this model family is what most people\nnow use in real production settings. So it’s really exciting. We only have a little bit\nof math in between and a lot of it is quite applied and\nshould be quite fun. Just one organizational\nitem before we get started. I’ll have an extra office\nhour today right after class. I’ll be again on Queuestatus 68 or so. Last week we had to end at 8:30. And there’s still a lot of\npeople who had a question, so I’ll be here after class for\nprobably another two hours or so. Try to get through everybody’s questions. Are there any questions around projects?>>[LAUGH]\n>>And organizational stuff? All right, then let’s take a look\nat the overview for today. So to really appreciate the power of\nrecurrent neural networks it makes sense to get a little bit of background\non traditional language models. Which will have huge RAM requirements and\nwon’t be quite feasible in their best kinds of settings where\nthey obtain the highest accuracies. And then we’ll motivate recurrent\nneural networks with language modeling. It’s a very important\nkind of fundamental task in NLP that tries to\npredict the next word. Something that sounds quite simple but\nis really powerful. And then we’ll dive a little bit into\nthe problems that you can actually quite easily understand once\nyou have figured out how to take gradients and you actually\nunderstand what backpropagation does. And then we can go and\nsee how to extend these models and apply them to real sequence tasks\nthat people really run in practice. All right, so let’s dive right in. Language models. So basically, we want to just compute the probability\nof an entire sequence of words. And you might say,\nwell why is that useful? Why should we be able to compute\nhow likely a sequence is? And actually comes up for\na lot of different kinds of problems. So one, for instance,\nin machine translation, you might have a bunch of potential\ntranslations that a system gives you. And then you might wanna understand\nwhich order of words is the best. So “the cat is small” should get a higher\nprobability than “small the is cat”. But based on another language\nthat you translate from, it might not be as obvious. And the other language might have\na reversed word order and whatnot. Another one is when you do speech\nrecognition, for instance. It also comes up in the machine\ntranslation a little bit, where you might have, well this particular example is clearly\nmore a machine translation example. But comes up also in speech\nrecognition where you might wanna understand which word might be the better\nchoice given the rest of the sequence. So “walking home after school” sounds\na lot more natural than “walking house after school”. But home and\nhouse have the same translation or same word in German which is haus,\nH A U S. And you want to know which one is\nthe better one for that translation. So comes up in a lot of\ndifferent kinds of areas. Now basically it’s hard to compute\nthe perfect probabilities for all potential sequences ’cause\nthere are a lot of them. And so what we usually end up doing is\nwe basically condition on just a window, we try to predict the next word based\non the just the previous n words before the one that\nwe’re trying to predict. So this is, of course,\nan incorrect assumption. The next word that I will utter will\ndepend on many words in the past. But it’s something that had to be done to use traditional count based\nmachine learning models. So basically we’ll approximate this\noverall sequence probability here with just a simpler version. In the perfect sense this would basically\nbe the product here of each word, given all preceding words\nfrom the first one all the way to the one just\nbefore the i_th one. But in practice, this probability with\ntraditional machine learning models we couldn’t really compute so we actually approximate that with some\nnumber of n words just before each word. So this is a simple Markov assumption\njust assuming the next action or next word that is uttered just\ndepends on n previous words. And now if we wanted to use traditional\nmethods that are just basically based on the counts of words and not\nusing our fancy word vectors and so on. Then the way we would compute and estimate\nthese probabilities is essentially just by counting how often does, if you want to\nget the probability for the second word, given the first word. We would just basically count up how often\ndo these two words co-occur in this order, divided by how often the first\nword appears in the whole corpus. Let’s say we have a very large corpus and\nwe just collect all these counts. And now if we wanted to condition not just\non the first and the previous word but on the two previous words, then we’d\nhave to compute all these counts. And now you can kind of sense that well, if we want to ideally condition on as\nmany n-grams as possible before but we have a large vocabulary of say 100,000\nwords, then we’ll have a lot of counts. Essentially 100,000 cubed, many numbers we would have to store\nto estimate all these probabilities. Does that make sense? Are there any questions for\nthese traditional methods? All right, now, the problem with\nthat is that the performance usually improves as we have more and\nmore of these counts. But, also,\nyou now increase your RAM requirements. And so,\none of the best models of this traditional type actually required 140 gigs of RAM for\njust computing all these counts when they wanted to compute them for\n126 billion token corpus. So it’s very,\nvery inefficient in terms of RAM. And you would never be able\nto put a model that basically stores all these different n-gram counts. You could never store it in a phone or\nany small machine. And now, of course, once computer\nscientists struggle with a problem like that, they’ll find ways to deal with it,\nand so, there are a lot of different\nways you can back off. You say, well, if I don’t find the 4-gram,\nor I didn’t store it, because it was not frequent enough,\nthen maybe I’ll try the 3-gram. And if I can’t find that or I don’t have\nmany counts for that, then I can back off and estimate my probabilities with fewer\nand fewer words in the context size. But in general you want\nto have at least tri or 4-grams that you store and the RAM\nrequirements for those are very large. So that is actually something\nthat you’ll observe in a lot of comparisons between deep\nlearning models and traditional NLP models that are based on\njust counting words for specific classes. The more powerful your models are, sometimes the RAM requirements can\nget very large very quickly, and there are a lot of different ways\npeople tried to combat these issues. Now our way will be to use\nrecurrent neural networks. Where basically, they’re similar to\nthe normal neural networks that we’ve seen already, but they will actually tie\nthe weights between different time steps. And as you go over it, you keep using, re-using essentially the same\nlinear plus non-linearity layer. And that will at least in theory,\nallow us to actually condition what we’re trying to predict\non all the previous words. And now here the RAM requirements will\nonly scale with the number of words not with the length of the sequence\nthat we might want to condition on. So now how’s this really defined? Again, they’re you’ll see different\nkinds of visualizations and I’m introducing you to a couple. I like sort of this unfolded one where we\nhave here a abstract hidden time step t and we basically, it’s conditioned on\nH_t-1, and then here you compute H_t+1. But in general,\nthe equations here are quite intuitive. We assume we have a list of word vectors. For now,\nlet’s assume the word vectors are fixed. Later on we can actually loosen\nthat assumption and get rid of it. And now, at each time step\nto compute the hidden state. At that time step will essentially\njust have these two matrices, these two linear layers,\nmatrix vector products and we sum them up. And that’s essentially similar to\nsaying we concatenate h_t-1 and the word vector at time step t, and\nwe also concatenate these two matrices. And then we apply\nan element-wise non-linearity. So this is essentially just a standard\nsingle layer neural network. And then on top of that we can\nuse this as a feature vector, or as our input to our standard\nsoftmax classification layer. To get an output probability for\ninstance over all the words. So now the way we would write\nthis out in this formulation is basically the probability that\nthe next word is of this specific, at this specific index j conditioned\non all the previous words is essentially the j_th element\nof this large output vector. Yes? What is s? So here you can have different\nways to define your matrices. Some people just use u, v,\nand w or something like that. But here we basically use the superscript\njust identify which matrix we have. And these are all different matrices, so\nW_(hh), the reason we call it hh is it’s the W that computes the hidden\nlayer h given the input h t- 1. And then you have an h_x here,\nwhich essentially maps x into the same vector space that we have. Our hidden states in and\nthen s is just our softmax w. The weights of the softmax classifier. And so let’s look at the dimensions here. It’s again very important. You have another question? So why do we concatenate and\nnot add is the question. So they’re the same. So when you write W_(h) using same notation plus W_(hx) times x then this is actually the same thing. And so this will now basically be\na vector, and we are feed in linearity but it doesn’t really change things, so\nlet’s just look at this inside part here. Now if we concatenated h and\nx together we’re now have, and let’s say, x here has a certain\ndimensionality which we’ll call d. So x is in R_d and\nour h will define to be in for having the dimensionality R_(Dh). Now, what would the dimensionality be\nif we concatenated these two matrices? So we have here the output has to be,\nagain a Dh matrix. And now this vector here is a, what dimensionality does this factor\nhave when we concatenate the two? That’s right. So this is a d plus Dh times one and here we have Dh times our matrix. It has to be the same dimensionality, so d plus Dh and\nthat’s why we could essentially concatenate here W_h in this way,\nand W_hx here. And now we could basically multiply these. And if you, again if this is confusing,\nyou can write out all the indices. And you realize that these\ntwo are exactly the same. Does that make sense? Right, so as you sum up all the values\nhere, It’ll essentially just get summed up also, it doesn’t matter\nif you do it in one go or not. Just a single layer and that worked\nwhere you compact in two inputs but it’s in many cases for recurrent\nneutral networks is written this way. All right. So now, here are two other ways\nyou’ll often see these visualized. This is kind of a not unrolled version of\na hidden, of a recurrent neural network. And sometimes you’ll also see\nsort of this self loop here. I actually find these kinds of\nunrolled versions the most intuitive. All right. Now when you start and you. Yup? Good question. So what is x[t]? It’s essentially the word vector for the word that appears\nat the t_th time step. As opposed to x_t and intuitively here\nx_t you could define it in any way. It’s really just like as you go through\nthe lectures you’ll actually observe different versions but intuitively\nhere x_t is just a vector at xt but here xt is already an input, and\nwhat it means in practice is you actually have to now go at that t time\nstep, find the word identity and pull that word vector from your glove or word\nto vec vectors, and get that in there. So x_t we used in previous\nlectures as the t_th element for instance in the whole embedding matrix,\nall our word vectors. So this is just to make it very explicit\nthat we look up the identity of the word at the tth time step and then get\nthe word vector for that identity, like the vector in all our word vectors. Yep. So I’m showing here a single layer\nneural network at each time step, and then the question is whether that\nis standard or just for simplicity? It is actually the simplest and\nstill somewhat useful. Variant of a recurrent neural network,\nthough we’ll see a lot of extensions even in this class, and then in the lecture\nnext week we’ll go to even better versions of these kinds of\nrecurrent neural networks. But this is actually a somewhat\npractical neural network, though we can improve it in many ways. Now, you might be curious when\nyou just start your sequence, and this is age 0 here and\nthere isn’t any previous words. What you would do and the simplest thing\nis you just initialize the vector for the first hidden layer at the first or the\n0 time step as just a vector of all 0s. Right and this is the X[t] definition\nyou had just describe through the column vector of L which is our embedding matrix\nat index [t] which the time step t. All right so it’s very important to keep\ntrack properly of all our dimensionality. Here, W(S) to Softmax actually goes\nover the size of our vocabulary, V times the hidden state. So the output here is the same\nas the vector of the length of the number of words that we\nmight wanna to be able to predict. All right, any questions for the feed forward definition of\na recurrent neural network? All right, so how do we train this? Well fortunately, we can use all the same machinery we’ve\nalready introduced and carefully derived. So basically here we have probability\ndistribution over the vocabulary and we’re going to use the same exact cross\nentropy loss function that we had before, but now the classes are essentially\njust the next word. So this actually sometimes\ncreates a little confusion on the nomenclature that we have\n’cause now technically this is unsupervised in the sense that\nyou just give it raw text. But this is the same kind of objective\nfunction we use when we have supervised training where we have a specific\nclass that we’re trying to predict. So the class at each time step is\njust a word index of the next word. And you’re already familiar with that, here we’re just summing over the entire\nvocabulary for each of the elements of Y. And now, in theory, you could just. To evaluate how well you can predict\nthe next word over many different words in longer sequences, you could in theory just\ntake this negative of the average log probability is over this entire dataset. But for maybe historical reasons, and also\nreasons like information theory and so on that we don’t need to get into, what’s\nmore common is actually to use perplexity. So that’s just 2 to\nthe power of this value and, hence, we want to basically\nbe less perplexed. So the lower our perplexity is,\nthe less the model is perplexed or confused about what the next word is. And we essentially, ideally we’ll assign\na higher probability to the word that actually appears in the longer\nsequence at each time step. Yes? Any reason why 2 to the J? Yes, but it’s sort of a rat hole\nwe can go down, maybe after class. Information theory bits and\nso on, it’s not necessary. All right.>>[LAUGH]\n>>All right, so now you would think, well this is pretty\nsimple, we have a single set of W matrices, and training should\nbe relatively straightforward. Sadly, and this is really the main\ndrawback of this and a reason of why we introduce all these other more powerful\nrecurrent neural network models, training these kinds of models\nis actually incredibly hard. And we can now analyze, using the tools of back propagation and\nchain rule and all of that. Now we can analyze and\nunderstand why that is. So basically we’re multiplying here,\nthe same matrix at each time step, right? So you can kind of think of\nthis matrix multiplication as amplifying certain patterns over and\nover again at every single time step. And so, in a perfect world, we would want the inputs from many time\nsteps ago to actually be able to still modify what we’re trying to predict\nat a later, much later, time step. And so, one thing I would like\nto encourage you to do is to try to take the derivatives\nwith respect to these Ws, if you just had a two or\nthree word sequence. It’s a great exercise,\ngreat preparation for the midterm. And it’ll give you some\ninteresting insights. Now, as we multiply the same matrix\nat each time step during foreprop, we have to do the same thing during\nback propagation We have, remember, our deltas, our air signals and sort of\nthe global elements of the gradients. They will essentially at each time step\nflow through this network backwards. So when we take our cross-entropy\nloss here, we take derivatives, we back propagate we compute our deltas. Now the first time step here that just\nhappened close to that output would make a very good update and\nwill probably also make a good update to the word vector here if\nwe wanted to update those. We’ll talk about that later. But then as you go backwards in\ntime what actually will happen is your signal might get either too weak,\nor too strong. And that is essentially called\nthe vanishing gradient problem. As you go backwards through time, and you\ntry to send the air signal at time step t, many time steps into the past, you’ll\nhave the vanishing gradient problem. So, what does that mean and\nhow does it happen? Let’s define here a simpler, but\nsimilar recurrent neural network that will allow us to give you an intuition and\nsimplify the math downstream. So here we essentially just say, all\nright, instead of our original definition where we had some kind of f\nsome kind of non-linearity, here we use the sigma function,\nyou could use other one. First introduce the rectified linear units\nand so on instead of applying it here, we’ll apply it in the definition\njust right in here. So it’s the same thing. And then let’s assume, for now,\nwe don’t have the softmax. We just have here, a standard,\na bunch of un-normalized scores. Which really doesn’t matter for\nthe math, but it’ll simplify the math. Now if you want to compute the total\nerror with respect to an entire sequence, with respect to your W then\nyou basically have to sum up all the errors at all the time steps. At each time step, we have an error of how incorrect we\nwere about predicting the next word. And that’s basically the sum here and now we’re going to look at the element\nat the t timestamp of that sum. So let’s just look at a single time step,\na single error at a single time step. And now even computing that will\nrequire us to have a very large chain rule application,\nbecause essentially this error at time step t will depend on all\nthe previous time steps too. So you have here the delta or\ndE_t over dy_t, so the t, the hidden state. Sorry, the soft max output or\nhere these unnormalized square output Yt. But then you have to multiply that\nwith the partial derivative of yt with respect to the hidden state. So that’s just That’s just this guy\nright here, or this guy for ht. But now, that one depends on,\nof course, the previous one, right? This one here, but it also depends\non that one, and that one, and the one before that, and so on. And so that’s why you have to sum over\nall the time step from the first one, all the way to the current one, where\nyou’re trying to predict the next word. And now, each of these was\nalso computed with a W, so you have to multiply partial of that,\nas well. Now, let’s dig into\nthis a little bit more. And you don’t have to worry too\nmuch if this is a little fast. You won’t have to really\ngo through all of this, but it’s very similar to a lot of\nthe math that we’ve done before. So you can kind of feel comfortable for\nthe most part going over it at this speed. So now, remember here,\nour definition of h_t. We basically have all these partials\nof all the h_t’s with respect to the previous time steps,\nthe h’s of the previous time steps. Now, to compute each of these,\nwe’ll have to use the chain rule again. And now, what this means is essentially a partial derivative of a vector\nwith respect to another vector. Something that if we’re clever with\nour backprop definitions before, we never actually have to do in practice,\nright? ’cause this is a very large matrix, and we’re combining the computation with the\nflow graph, and our delta messages before such that we don’t actually have to\ncompute explicitly, these Jacobians. But for the analysis of the math here, we’ll basically look at\nall the derivatives. So just because we haven’t defined it,\nwhat’s the partial for each of these is essentially called the Jacobian,\nwhere you have all the partial derivatives with respect to each element of the top\nhere ht with respect to the bottom. And so in general, if you have\na vector valued function output and a vector valued input, and you take\nthe partials here, you get this large matrix of all the partial derivatives\nwith respect to all outputs. Any questions? All right, so basically here,\na lot of chain rule. And now, we got this beast\nwhich is essentially a matrix. And we multiply, for each partial here, we actually have to multiply all of these,\nright? So this is a large product\nof a lot of these Jacobians. Now, we can try to simplify this,\nand just say, all right. Let’s say, there is an upper bound. And we also,\nthe derivative of h with respect to h_j. Actually, with this simple definition of\neach h actually can be computed this way. And now,\nwe can essentially upper bound the norm of this matrix with\nthe multiplication of basically these equation right here,\nwhere we have W_t. And if you remember our\nbackprop equations, you’ll see some common terms here, but we’ll actually write this out as\nnot just an element wise product. But we can write the same thing as\na diagonal where we have instead of the element wise. Elements we basically just put them into\nthe diagonal of a larger matrix, and with zero path,\neverything that is off diagonal. Now, we multiply these two norms here. And now, we just define beta, W and\nbeta h, as essentially the upper bounds. Some number, single scalar for each as like how large they\ncould maximally be, right? We have W, we could compute easily\nany kind of norm for our W, right? It’s just a matrix, computed matrix norm,\nwe get a single number out. And now, basically, when we write\nthis all, we put all this together, then we see that an upper bound for\nthis Jacobians is essentially for each one of these\nelements as this product. And if we define each of the elements\nhere, in terms of their upper bounds beta, then we basically have this product\nbeta here taken to the t- k power. And so as the sequence gets longer and\nlonger, and t gets larger and larger, it really depends on the value\nof beta to have this either blow up or get very, very small, right? If now the norms of this matrix,\nfor instance, that norm, and then you have\ncontrol over that norm, right? You initialize your wait matrix W with some small random values initially\nbefore you start training. If you initialize this to a matrix that\nhas a norm that is larger than one, then at each back propagation step and\nthe longer the time sequence goes. You basically will get a gradient\nthat is going to explode, cuz you take some value that’s larger\nthan one to a large power here. Say, you have 100 or something,\nand your norm is just two, then you have two to the 100th as an upper\nbound for that gradient and vice-versa. If you initialize your matrix W in\nthe beginning to a bunch of small random values such that the norm of\nyour W is actually smaller than one, then the final gradient that will be\nsent from ht to hk could become a very, very small number, right,\nhalf to the power of 100th. Basically, none of the errors will arrive. None of the error signal, we got small and\nsmaller as you go further and further backwards in time. Yeah. So if the gradient here is exploding, does\nthat mean a word that is further away has a bigger impact on a word that’s closer? And the answer is when\nit’s exploding like that, you’ll get to not a number in no time. And that doesn’t even become a practical\nissue because the numbers will literally become not a number,\ncuz it’s too large a value to compute. And we’ll have to think\nof ways to come back. It turns out the exploding gradient\nproblem has some really great hacks that make them easier to deal with than\nthe vanishing gradient problem. And we’ll get to those in a second. All right, so now,\nyou might say this could be a problem. Now, why is the vanishing gradient\nproblem, an actual common practice? And again, it basically prevents\nus from allowing a word that appears very much in the past\nto have any influence on what we’re trying to break in\nterms of the next word. And so here a couple of examples from just\nlanguage modeling where that is a real problem. So let’s say, for instance,\nyou have Jane walked into the room. John walked in too. It was late in the day. Jane said hi to. Now, you can put an almost\nprobability mass of one, that the next word in this blank is John,\nright? But if now,\neach of these words have the word vector, you type it in to the hidden state,\nyou compute this. And now, you want the model to pick up\nthe pattern that if somebody met somebody else, and your all this complex stuff. And then they said hi too, and\nthe next thing is the name. You wanna put a very high probability\non it, but you can’t get your model to actually send that error signal way\nback over here, to now modify the hidden state in a way that would allow you\nto give John a high probability. And really, this is a large problem in\nany kind of time sequence that you have. And many people might\nintuitively say well, language is mostly a Sequence problem,\nright? You have words that appear\nfrom left to right or in some temporal order as we speak. And so this is a huge problem. And now we’ll have a little bit\nof code that we can look into. But before that we’ll have\nthe awesome Shayne give us a little bit of an intercession,\nintermission.>>Hi, so let’s take a short break\nfrom recurrent neural networks to talk about transition-based\ndependency parsing, which is exactly what you guys saw\nthis time last week in lecture. So just as a recap, a transition-based\ndependency parser is a method of taking a sentence and\nturning it into dependence parse tree. And you do this by looking at\nthe state of the sentence and then predicting a transition. And you do this over and over again in a greedy fashion until\nyou have a full transition sequence which itself encodes, the dependency\nparse tree for that sentence. So I wanna show you how to get from\nthe model that you’ll be implementing in your assignment two question two, which you’re hopefully working\non right now, to SyntaxNet. So what is SyntaxNet? SyntaxNet is a model that Google came out with and they claim\nit’s the world’s most accurate parser. And it’s new,\nfast performant TensorFlow framework for syntactic parsing is available for\nover 40 languages. The one in English is called\nthe Parse McParseface.>>[LAUGH]\n>>So my slide seemed to have been jumbled a little bit here, but\nhopefully you can read through it. So basically the baseline we’re\ngonna begin with is the Chen and Manning model which came out in 2014. And Chen and Manning are respectively\nin just two stages of improvements, those directly modified Chen and Manning’s model, which is exactly what\nyou guys will be doing in assignment two. And so we’re going to focus today\non the main bulk of these changes, modifications which were\nintroduced in 2015 by Weiss et al. So without further ado, I’m gonna look\nat their three main contributions. So the first one is they leverage\nunlabeled data using something called Tri-Training. The second is that they tuned\ntheir neural network and made some slight modifications. And the last and probably most important\nis that they added a final layer on top of the model involving a structured\nperceptron with beam search. So each of these seeks to solve a problem. So the first one is tri-training. So as you know, in most supervised models, they perform better the more\ndata that they have. And this is especially the case for\ndependency parsing, where as you can imagine there are an\ninfinite number of possible sentences with a ton of complexity and\nyou’re never gonna see all of them, and you’re gonna see even some\nof them very, very rarely. So the more data you have, the better. So what they did is they took\na ton of unlabeled data and two highly performing dependency parsers\nthat were very different from each other. And when they agreed, independently\nagreed on a dependency parse tree for a given sentence, then that would\nbe added to the labeled data set. And so now you have ten\nmillion new tokens of data that you can use in addition\nto what you already have. And this by itself improved\na highly performing network’s performance by 1% using\nthe unlabeled attachment score. So the problem here was not having\nenough data for the task and they improved it using this. The second augmentation they made\nwas by taking the existing model, which is the one you\nguys are implementing, which has an input layer\nconsisting of the word vectors. The vectors for the part of speech tags\nand the arc labels with one hidden layer and one soft max layer predicting which\ntransition and they changed it to this. Now this is actually pretty much the same\nthing, except for three small changes. The first is that they added, there are two hidden layers\ninstead of one hidden layer. The second is that they used\na RELU nonlinearity function instead of the cube nonlinearity function. And the third and most important is\nthat they added a perceptron layer on top of the soft max layer. And notice that the arrows,\nthat it takes in as input the outputs from all\nthe previous layers in the network. So this perceptron layer wants\nto solve one particular problem, and this problem is that greedy algorithms\naren’t able to really look ahead. They make short term decisions and as a result they can’t really\nrecover from one incorrect decision. So what they said is, let’s allow\nthe network then to look ahead and so we’re going to have a tree\nwhich we can search over and this tree is the tree of all the possible\npartial transition sequences. So each edge is a possible transition\nform the state that you’re at. As you can imagine, even with three transitions your tree\nis gonna blossom very, very quickly and you can’t look that far ahead and\nexplore all of the possible branches. So what you have to do\nis prune some branches. And for that they use beam search. Now beam search is only\ngonna keep track of the top K partial transition\nsequences up to a depth of M. Now how do you decide which K? You’re going to use a score computed\nusing the perceptron weights. You guys probably have a decent idea\nat this point of how perceptron works. The exact function they used\nis shown here, and I’m gonna leave up the annotations so you can take\na look at it later if you’re interested. But basically those are the three\nthings that they did solve, the problems with the previous\nChen & Manning model. So in summary, Chen & Manning had\nan unlabeled attachment score of 92%, already phenomenal performance. And with those three changes,\nthey boosted it to 94%, and then there’s only 0.6%\nleft to get you to SyntaxNet, which is Google’s 2016\nstate of the art model. And if you’re curious what the did to get\nthat 0.6%, take a look at Andrew All’s paper Which uses global normalization\ninstead of local normalization. So the main takeaway, and\nit’s pretty straight forward but I can’t stress it enough, is when you’re\ntrying to improve upon an existing model, you need to identify the specific\nflaws that are in this model. In this case the greedy algorithm and\nsolved those problems specifically. In this case they did that\nusing semi-supervised method using unlabeled data. They tune the model better and they use the structured\nperception with beam search. Thank you very much.>>[APPLAUSE]\n>>Kind of awesome. You can now look at these\nkinds of pictures and you totally know what’s going on. And in like state of the art stuff\nthat the largest companies in the world publishes. Exciting times. All right, so we’ll gonna through a little bit of\nlike a practical Python notebook sort of implementation that shows you a simple\nversion of the vanishing gradient problem. Where we don’t even have a full recurrent\nreal network we just have a simple two layer neural network and even in\nthose kinds of networks you will see that the error that you start at\nthe top and the norm of the gradients as you go down through your network,\nthe norm is already getting smaller. And if you remember these were the two\nequations where I said if you get to the end of those two equations you know\nall the things that you need to know, and you’ll actually see these three\nequations in the code as well. So let’s jump into this. I don’t see it. Let me get out of the presentation All right, better, all right. Now, zoom in. So here, we’re going to define\na super simple problem. This is a code that we started,\nand 231N (with Andrej), and we just modified it to\nmake it even simpler. So let’s say our data set,\nto keep it also very simple, is just this kind of\nclassification data set. Where we have basically three classes,\nthe blue, yellow, and red. And they’re basically in\nthe spiral clusterform. We’re going to define our\nsimple nonlinearities. You can kind of see it as a solution\nalmost to parts of the problem set, which is why we’re only showing it now. And we’ll put this on the website too,\nso no worries. You can visit later. But basically, you could define here f,\nour different nonlinearities, element-wise, and the gradients for them. So this is f and\nf prime if f is a sigmoid function. We’ll also look at the relu, the other\nnonlinearity that’s very popular. And here, we just have the maximum between\n0 and x, and very simple function. Now, this is a relatively\nstraight forward definition and implementation of this simple\nthree layer neural network. Has this input, here our nonlinearity,\nour data x, just these points in two dimensional space, the class,\nit’s one of those three classes. We’ll have this model here,\nwe have our step size for SDG, and our regularization value. Now, these are all our parameters,\nw1, w2 and w3 for all the outputs, and\nvariables of the hidden states. Two sets is bigger, all right.>>[LAUGH]\n>>All right, now, if our nonlinearity is the relu, then we have here relu,\nand we just input x, multiply it. And in this case,\nyour x can be the entirety of the dataset, cuz the dataset’s so small, each\nmini-batch, we can essentially do a batch. Again, if you have realistic datasets,\nyou wouldn’t wanna do full batch training, but we can get away with it here. It’s a very tiny dataset. We multiply w1 times x\nplus our bias terms, and then we have our element-wise\nrectified linear units or relu. Then we’ve computed in layer two,\nsame idea. But now, it’s input instead of\nx is the previous hidden layer. And then we compute our scores this way. And then here, we’ll normalize\nour scores with the softmax. Just exponentiate our scores,\nsome of them. So very similar to the equations\nthat we walk through. And now,\nit’s just basically an if statement. Either we have used relu\nas our activations, or we use a sigmoid, but\nthe math inside is the same. All right, now,\nwe’re going to compute our loss. Our good friend, the simple average cross\nentropy loss plus the regularization. So here,\nwe have negative log of the probabilities, we summed them up overall the elements. And then here, we have our regularization\nas the L2, standard L2 regularization. And we just basically sum up the squares\nof all the elements in all our parameters, and I guess it does cut off a little bit. Let me zoom in. All three have the same of\namount of regularization, and we add that to our final loss. And now, every 1,000 iterations,\nwe’ll just print our loss and see what’s happening. And this is something you\nalways want to do too. You always wanna visualize,\nsee what’s going on. And hopefully,\na lot of this now looks very familiar. Maybe if implemented it not quite as\nefficiently, as efficiently in problem set one, but maybe you have, and\nthen it’s very, very straightforward. Now, that was the forward propagation,\nwe can compute our error. Now, we’re going to go backwards, and we’re computing our delta\nmessages first from the scores. Then we have here, back propagation. And now,\nwe have the hidden layer activations, transposed times delta\nmessages to compute w. Again, remember, we have always for\neach w here, we have this outer product. And that’s the outer\nproduct we see right here. And now, the softmax was the same\nregardless of whether we used a value or a sigmoid. Let’s walk through the sigmoid here. We now, basically, have our delta scores,\nand have here the product. So this is exactly computing delta for\nthe next layer. And that’s exactly this equation here,\nand just Python code. And then again,\nwe’ll have our updates dw, which is, again, this outer product right there. So it’s a very nice\nsort of equations code, almost a nice one to one\nmapping between the two. All right, now, we’re going to go through the network\nfrom the top down to the first layer. Again, here, our outer product. And now, we add the derivatives for\nour regularization. In this case, it’s very simple, just matrices themselves\ntimes the regularization. And we combine all our gradients\nin this data structure. And then we update all our parameters\nwith our step_size and SGD. All right, then we can evaluate how\nwell we do on the training set, so that we can basically print out\nthe training accuracy as we train us. All right, now, we’re going to\ninitialize all the dimensionality. So we have there just our two\ndimensional inputs, three classes. We compute our hidden sizes\nof the hidden vectors. Let’s say, they’re 50, it’s pretty large. And now, we can run this. All right, we’ll train it with both\nsigmoids and rectify linear units. And now,\nonce we wanna analyze what’s going on, we can essentially now plot some of\nthe magnitudes of the gradients. So those are essentially the updates as we\ndo back propagation through the snap work. And what we’ll see here is\nthe some of the gradients for the first and the second layer when\nwe use sigmoid non-linearities. And basically here, the main takeaway\nmessages that blue is the first layer, and green is the second layer. So the second layer is\ncloser to the softmax, closer to what we’re trying to predict. And hence, it’s gradient is\nusually had larger in magnitude than the one that arrives\nat the first layer. And now, imagine you do this 100 times. And you have intuitively your vanishing\ngradient problem in recurrent neural networks. They’ll essentially be zero. They’re already almost half in size over the iterations when\nyou just had two layers. And the problem is a little less strong\nwhen you use rectified linear units. But even there, you’re going to have\nsome decrease as you continue to train. All right,\nany questions around this code snippet and vanishing creating problems? No, sure. [LAUGH] That’s a good question. The question is why\nare the gradings flatlining. And it’s essentially\nbecause the dataset is so simple that you actually just\nperfectly fitted your training data. And then there’s not much else to do\nyou’re basically in a local optimum and then not much else is happening. So yeah, so these are the outputs where\nif you visualize the decision boundaries, here at the relue and the relue you\nsee a little bit more sort of edges, because you have sort of linear\nparts of your decision boundary and the sigmoid is a little smoother,\nlittle rounder. All right, so now you can implement a very\nquick versions to get an intuition for the vanishing gradient problem. Now the exploding gradient problem is,\nin theory, just as bad. But in practice,\nit turns out we can actually have a hack, that was first introduced by\nThomas Mikolov, and it’s very unmathematical in some ways ’cause say,\nall you have is a large gradient of 100. Let’s just cap it to five. That’s it,\nyou just define the threshold and you say whenever the value is larger\nthan a certain value, just cut it. Totally not the right\nmathematical direction anymore. But turns out to work very\nwell in practice, yep. So vanishing creating problems,\nhow would you cap it? It’s like it gets smaller and\nsmaller, and you just multiply it? But then it’s like, it might overshoot. It might go in the completely\nwrong direction. And you don’t want to have the hundredth\nword unless it really matters. You can’t just make all\nthe hundred words or thousand words of the past\nall matter the same amount. Right?\nIntuitively. That doesn’t make that much sense either. So this gradient clipping solution\nis actually really powerful. And then a couple years after it\nwas introduced, Yoshua Bengio and one of his students Actually gained\na little bit of intuition and it’s something I encourage\nyou always to do too. Not just in the equations, where you\ncan write out recurrent neural network, where everything’s one dimensional,\nand the math comes out easy and you gain intuition about it. But you can also, and this is what\nthey did here, implement a very simple recurrent neural network which\njust had a single hidden unit. Not very useful for anything in practice\nbut now, with the single unit W. And you know, at still the bias term, they can actually visualize exactly\nwhat the air surface looks like. So and oftentimes we call the air\nsurface or the energy landscape or so that the landscape of\nour objective function. This error surface and basically. You can see here the size of\nthe z axis here is the error that you have when you trained\nus on a very simple problem. I forgot what the problem here was but it’s something very simple\nlike keep around this unit and remember the value and then just\nreturn that value 50 times later. Something simple like that. And what they essentially observe\nis that in this air surface or air landscape you have\nthese high curvature walls. And so as you do an update each little line here you can interpret as\nwhat happens at an sg update step. You update your parameters. And you say, in order to minimize\nmy objective function right now, I’m going to change the value\nof my one hidden unit and my bias term just like by this amount\nto go over here, go over here. And all of a sudden you hit\nand it moves you somewhere way different. And so intuitively what happens here is, if you rescale to the thick size with\nthe special method, then essentially you’re not going to jump to some crazy,\nfaraway place, but you’re just going to stay in this general area that seemed\nuseful before you hit that curvature wall. Yeah? So the question is, intuitively,\nwhy wouldn’t such a trick work for the vanishing grading problem but it does\nwork for the exploding grading problem. Why does the reason for the vanishing does not apply to\nthe exploding grading problem. So intuitively,\nthis is exactly the issue here. So the exploding,\nas you move way too far away, you basically jump out of the area\nwhere you, in this case here for instance, we’re getting closer and\ncloser to a local optimum, but the local optimum was very\nclose to high curvature wall. And without the gradient problem,\nwithout the clipping trick, you would go way far away. Right, now, on the vanishing grading\nproblem, it get’s smaller and smaller. So in general clipping doesn’t make sense,\nbut let’s say, so that’s the obvious answer. You can’t, something gets smaller and\nsmaller, it doesn’t help to have a maximum and then make it, you know cut it to that\nmaximum ’cause that’s not the problem. It goes in the opposite direction. And so. That’s kind of most\nobvious intuitive answers. Now, you could say. Why couldn’t you, if it gets below\na certain threshold, blow it up? But then that would mean that. Let’s say you had. You wanted to predict the word. And now you’re 50 time steps away. And really,\nthe 51st doesn’t actually impact the word you’re trying to\npredict at time step T, right? So you’re 50 times to 54 and\nit doesn’t really modify that word. And now you’re artificially going to\nblow up and make it more important. So that’s less intuitive than saying, I don’t wanna jump into some completely\ndifferent part of my error surface. The wall just comes from this is what\nthe error surface looks like for a very very simple recurrent node network\nwith a very simple kind of problem that it tries to solve. And you can actually use most\nof the networks that you have, you can try to make them\nhave just two parameters and then you can visualize\nsomething like this too. In fact it’s very intuitive\nsometimes to do that. When you try different optimizers,\nwe’ll get to those in a later lecture like Adam or SGD or achieve momentum,\nwe’ll talk about those soon. You can actually always try to visualise\nthat in some simple kind of landscape. This just happens to be the landscape that\nthis particular recurrent neural network problem has with one-hidden unit and\njust a bias term. So the question is, how could we know for sure that this happens with non-linear\nactions and multiple weight. So you also have some\nnon-linearity here in this. So that intuitively wouldn’t prevent\nus from transferring that knowledge. Now, in general, it’s very hard. We can’t really visualize\na very high dimensional spaces. There is actually now an interesting\nnew idea that was introduced, I think by Ian Goodfellow\nwhere you can actually try to, let’s say you have your parameter space,\ninside your parameter space, you have some kind of cross function. So you say my w matrices are at this value\nand so on, and I have some error when all my values are here, and then I start\nto optimize and I end up somewhere here. Now the problem is, we can’t\nvisualize it because it’s usually in realistic settings,\nyou have the 100 million. Workflow. At least a million or so\nparameters, sometimes 100 million. And so, something crazy might be going\non as you optimize between this. And so, because we can’t visualize it and we can’t even sub-sample it because\nit’s such a high-dimensional space. What they do is they actually\ndraw a line between the point from where they started with their random\ninitialization before optimization. And end the line all the way to the point where you actually\nfinished the optimization. And then you can evaluate along\nthis line at a certain intervals, you can evaluate how big your area is. And if that area changes between\ntwo such intervals a lot, then that means we have very\nhigh curvature in that area. So that’s one trick of how\nyou might use this idea and gain some intuition of\nthe curvature of the space. But yeah, only in two dimensions can we\nget such nice intuitive visualizations. Yeah. So the question is why don’t\nwe just have less dependence? And the question of course,\nit’s a legit question, but ideally we’ll let\nthe model figure this out. Ideally we’re better at\noptimizing the model, and the model has in theory these\nlong range dependencies. In practice, they rarely ever do. In fact when you implement these, and\nyou can start playing around with this and this is something I\nencourage you all to do too. As you implement your models you can try\nto make it a little bit more interactive. Have some IPython Notebook,\ngive it a sequence and look at the probability of the next word. And then give it a different sequence\nwhere you change words like ten time steps away, and\nlook again at the probabilities. And what you’ll often observe is that\nafter seven words or so, the words before actually don’t matter, especially not for\nthese simple recurrent neural networks. But because this is a big problem, there are actually a lot of\ndifferent kinds of solutions. And so the biggest and\nbest one is one we’ll introduce next week. But a simpler one is to use\nrectified linear units and to also initialize both of your w’s\nto ones from hidden to hidden and the ones from the input to the hidden\nstate with the identity matrix. And this is a trick that I\nintroduced a couple years ago and then it was sort of combined\nwith rectified linear units. And applied to recurrent\nneural networks by Quoc Le. And so the main idea here is if\nyou move around in your space. Let’s say you have your h, and usually we have here our whh times h,\nplus whx plus x. And let’s assume for now that h and\nx have the same dimensionality. So then all these\nare essentially square matrices. And we have here our different vectors. Now, in the standard initialization,\nwhat you would do is you’d just have a bunch of small random values\nand all the different elements of w. And what that means is\nas you start optimizing, whatever x is you have some random\nprojection into the hidden space. Instead, the idea here is we actually\nhave identity initialization. Maybe you can scale it, so instead\nyou have a half times the identity, and what does that do? Intuitively when you combine\nthe hidden state and the word vector? That’s exactly right. If this is an identity initialized matrix. So it’s just, 1, 1, 1,\n1, 1, 1 on the diagonal. And you multiply all of these by one half. Same as just having a half,\na half, a half, and so on. And you multiply this with this vector and\nyou do the same thing here. What essentially that means is that\nyou have a half, times that vector, plus half times that other vector. And intuitively that means in\nthe beginning, if you don’t know anything. Let’s not do a crazy random projection\ninto the middle of nowhere in our parameter space, but just average. And say, well as I move through the space\nmy hidden state is just a moving average of the word vectors. And then I start making some updates. And it turns out when you look here and you apply this to the very\ntight problem of MNIST. Which we don’t really have to go into,\nbut its a bunch of small digits. And they’re trying to basically predict what digit it is by going over\nall the pixels in a sequence. Instead of using other kinds of neural networks like\nconvolutional neural networks. And basically we look\nat the test accuracy. These are very long time sequences. And the test accuracy for\nthese is much, much higher. When you use this identity initialization\ninstead of random initialization, and also using rectified linear units. Now more importantly for\nreal language modeling, we can compare recurrent neural\nnetworks in this simple form. So we had the question before like,\ndo these actually matter or did I just kind of describe single\nlayer recurrent neural networks for the class to describe the concept. And here we actually have these\nsimple recurrent neural networks, and we basically compare. This one is called Kneser-Ney with 5\ngrams, so a lot of counts, and some clever back off and smoothing techniques which\nwe won’t need to get into for the class. And we compare these on\ntwo different corpora and we basically look at the perplexity. So these are all perplexity numbers,\nand we look at the neural network or the neural network that’s\ncombined with Kneser-Ney, assuming probability estimates. And of course when you combine the two\nthen you don’t really get the advantage of having less RAM. So ideally this by itself would do best,\nbut in general combining the two\nused to still work better. These are results from five years ago,\nand they failed most very quickly. I think the best results now are pure\nneural network language models. But basically we can see\nthat compared to Kneser-Ney, even back then, the neural\nnetwork actually works very well. And has much lower perplexity than just\nthe Kneser-Ney or just account based. Now one problem that you’ll\nobserve in a lot of cases, is that the softmax is really,\nreally large. So your word vectors are one\nset of parameters, but your softmax is another set of parameters. And if your hidden state is 1000, and let’s say you have\n100,000 different words. Then that’s 100,000 times 1000 dimensional\nmatrix that you’d have to multiply with the hidden state at\nevery single time step. So that’s not very efficient, and so one way to improve this is with\na class-based word prediction. Where we first try to predict some\nclass that we can come up, and there are different kinds\nof things we can do. In many cases you can sort,\njust the words by how frequent they are. And say the thousand most frequent\nwords are in the first class, the next thousand most frequent\nwords in the second class and so on. And so you first basically classify, try\nto predict the class based on the history. And then you predict the word inside\nthat class, based on that class. And so this one is only\na thousand dimensional, and so you can basically do this. And now the more classes\nthe better the perplexity, but also the slower the speed\nthe less you gain from this. And especially at training time\nwhich is what we see here, this makes a huge difference. So if you have just very few classes,\nyou can actually reduce the number here of seconds\nthat each eproc takes. By almost 10x compared to\nhaving more classes or even more than 10x if you\nhave the full softmax. And even the test time, is faster cuz now\nyou only essentially evaluate the word probabilities for the classes that\nhave a very high probability here. All right, one last trick and\nthis is maybe obvious to some but it wasn’t obvious to others even in\nthe past when people published on this. But you essentially only need\nto do a single backward’s pass through the sequence. Once you accumulate all the deltas\nfrom each error at each time set. So looking at this figure,\nreally quick again. Here, essentially you have\none forward pass where you compute all the hidden states and\nall your errors, and then you only have a single\nbackwards pass, and as you go backwards in time you keep accumulating\nall the deltas of each time step. And so originally people said, for this\ntime step I’m gonna go all the way back, and then I go to the next time step,\nand then I go all the way back, and then the next step, and all the way back,\nwhich is really inefficient. And is essentially same as combining all the deltas in one clean\nback propagation step. And again, it’s kind of is intuitive. An intuitive sort of\nimplementation trick but people gave that the term back\npropagation through time. All right, now that we have these\nsimple recurrent neural networks, we can use them for\na lot of fun applications. In fact, the name entity recognition\nthat we’re gonna use in example with the Window. In the Window model, you could only\ncondition the probability of this being a location, a person, or an organization\nbased on the words in that Window. The recurrent neural network\nyou can in theory take and condition these probabilities\non a lot larger context sizes. And so\nyou can do Named Entity Recognition (NER), you can do entity level sentiment in\ncontext, so for instance you can say. I liked the acting, but\nthe plot was a little thin. And you can say I want to now for\nacting say positive, and predict the positive class for that word. Predict the null class, and\nall sentiment for all the other words, and then plot should get\nnegative class label. Or you can classify opinionated\nexpressions, and this is what researchers at Cornell where they\nessentially used RNNs for opinion mining and essentially wanted\nto classify whether each word in a relatively smaller purpose here is\neither the direct subjective expression or the expressive subjective expression,\nso either direct or expressive. So basically this is direct\nsubjective expressions, explicitly mention some private state or\nspeech event, whereas the ESEs just indicate the sentiment or emotion without\nexplicitly stating or conveying them. So here’s an example, like the committee as usual has\nrefused to make any statements. And so you want to classify\nas usual as an ESE, and basically give each of these\nwords here a certain label. And this is something you’ll actually\nobserve a lot in sequence tagging paths. Again, all the same models\nthe recurrent neural network. You have the soft max at every time step. But now the soft max actually\nhas a set of classes that indicate whether a certain\nexpression begins or ends. And so here you would basically\nhave this BIO notation scheme where you have the beginning or\nthe end, or a null token. It’s not any of the expressions\nthat I care about. So here you would say for instance,\nas usual is an overall ESE expression, so it begins here, and\nit’s in the middle right here. And then these are neither ESEs or DSEs. All right, now they started with\nthe standard recurrent neural network, and I want you to at some point be able\nto glance over these equations, and just say I’ve seen this before. It doesn’t have to be W superscript HH,\nand so on. But whenever you see, the summation\norder of course, doesn’t matter either. But here, they use W, V, and\nU, but then they defined, instead of writing out softmax,\nthey write g here. But once you look at these equations,\nI hope that eventually you’re just like it’s just a recurrent neural network,\nright? You have here,\nare your hidden to hidden matrix. You have your input to hidden matrix, and\nhere you have your softmax waits you. So same idea, but these are the actual\nequations from this real paper that you can now kind of read and immediately sort\nof have the intuition of what happens. All right, you need directional\nrecurrent neural network where we, if we try to make the prediction here,\nof whether this is an ESE or whatever name entity recognition,\nany kind of sequence labelling task, what’s the problem with\nthis kind of model? What do you think as we go\nfrom left to right only? What do you think could be a problem for\nmaking the most accurate predictions? That’s right. Words that come after\nthe current word can’t be helping us to make accurate\npredictions at that time step, right? Cuz we only went from left to right. And so one of the most common\nextensions of recurrent neural networks is actually to do bidirectional\nrecurrent neural networks where instead of just going from left to\nright, we also go from right to left. And it’s essentially the exact same model. In fact, you could implement it by\nchanging your input and just reversing all the words of your input, and\nthen it’s exactly the same thing. And now, here’s the reason why they\ndon’t have superscripts with WHH, cuz now they have these\narrows that indicate whether you’re going from left to right,\nor from right to left. And now, they basically have\nthis concatenation here, and in order to make a prediction at a certain\ntime step t they essentially concatenate the hidden states from both the left\ndirection and the right direction. And those are now the feature vectors. And this vector ht coming from the left,\nhas all the context ordinal, again seven plus words,\ndepending on how well you train your RNN. From all the words on the left, ht from the right has all the contacts\nfrom the words on the right, and that is now your feature vector to make an\naccurate prediction at a certain time set. Any questions around bidirectional\nrecurrent neural networks? You’ll see these a lot in all\nthe recent papers you’ll be learning, in various modifications. Yeah. Have people tried\nConvolutional Neural Networks? They have, and we have a special lecture\nalso we will talk a little bit about Convolutional Neural Networks. So you don’t necessarily have a cycle,\nright? You just go, basically as you implement\nthis, you go once all the way for your the left, and you don’t have any interactions with\nthe step that goes from the right. You can compute your\nfeet forward HTs here for that direction,\nare only coming from the left. And the HT from the other direction,\nyou can compete, in fact you could paralyze this if\nyou want to be super efficient and. Have one core,\nimplement the left direction, and one core implement the right direction. So in that sense it doesn’t make\nthe vanishing create any problem worse. But, of course,\njust like any recurring neural network, it does have the vanishing\ncreating problem, and the exploding creating problems and it has\nto be clever about flipping it and so, yeah We call them standard feedforward neural networks or\nWindow based feedforward neural networks. And now we have recurrent neural networks. And this is really one of\nthe most powerful family and we’ll see lots of extensions. In fact, if there’s no other\nquestion we can go even deeper. It is after all deep learning. And so, now you’ll observe [LAUGH] we\ndefinitely had to skip that superscript. And we have different, Characters here for each of our matrices, because,\ninstead of just going from left to right, you can also have a deep neural\nnetwork at each time step. And so now, to compute the ith\nlayer at a given time step, you essentially again, have only the things\ncoming from the left that modify it but, you just don’t take in the vector from the\nleft, you also take the vector from below. So, in the simplest definition that is\njust your x, your input vector right? But as you go deeper you now also have\nthe previous hidden layers input. Instead of why are the, So the question is, why do we feed the hidden layer into\nanother hidden layer instead of the y? In fact, you can actually have so\ncalled short circuit connections, too, where each of these h’s can\ngo directly to the y as well. And so here in this figure you see\nthat only the top ones go into the y. But you can actually have short circuit\nconnections where y here has as input not just ht from the top layer,\nnoted here as capital L, but the concatenation of all the h’s. It’s just another way to make\nthis monster even more monstrous. And in fact there a lot of modifications,\nin fact, Shayne has a paper, an ArXiv right now on a search based\nodyssey type thing where you have so many different kinds of knobs that you can\ntune for even more sophisticated recurrent neural networks of the type that we’ll\nintroduce next week that, it gets a little unwieldy and it turns out a lot of\nthe things don’t matter that much, but each can kind of give you a little\nbit of a boost in many cases. So if you have three layers,\nyou have four layers, what’s the dimensionality\nof all the layers and the various different kinds of connections\nand short circuit connections. We’ll introduce some of these, but\nin general this like a pretty decent model and will eventually extract away from\nhow we compute that hidden state, and that will be a more complex kind of cell\ntype that we’ll introduce next Tuesday. Do we have one more question? So now how do we evaluate this? It’s very important to evaluate\nwhere some of the classes appear very frequently and others are not very\nfrequent, you don’t wanna use accuracy. In fact, in these kinds of sentences,\nyou often observe, this is an extreme one where you have a lot of ESEs and\nDSEs but in many cases, just content. Standard sort of non-sentiment context and words, and so a lot of these\nare actually O, have no label. And so it’s very important to use F1 and we basically had this question also after\nclass, but it’s important for all of you to know because the F1 metric is really\none of the most commonly used metrics. And it’s essentially just the harmonic\nmean of precision and recall. Precision is just the true\npositives divided by true positives plus false positives and recall is just true positives divided\nby true positives plus false negatives. And then you have here the harmonic\nmean of these two numbers. So intuitively, you can be very\naccurate by always saying something or have a very high recall for\na certain class but if you always miss another class\nThat would hurt you a lot. And now here’s an evaluation\nthat you should also be familiar with where basically this is something\nI would like to see in a lot of your project reports too as you analyze the\nvarious hyper parameters that you have. And so one thing they found here is they\nhave two different data set sizes that they train on,\nin many cases if you train with more data, you basically do better but then also it’s\nnot always the case that more layers. So this is the depth that we had here, the\nnumber l for all these different layers. It’s not always the case\nthat more layers are better. In fact here, the highest performance\nthey get is with three layers, instead of four or five. All right, so let’s recap. Recurring neural networks, best deep learning model family that\nyou’ll learn about in this class. Training them can be very hard. Fortunately, you understand\nback propagation now. You can gain an intuition of\nwhy that might be the case. We’ll in the next lecture extend\nthem some much more powerful models the Gated Recurring Units or LSTMs,\nand those are the models you’ll see all over the place in all the state\nof the art models these days. All right. Thank you." ]

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[ "# ICSE Class 10 Geometric Progression Previous Years Questions Solution\n\nThis page consists of the solution to previous years questions from the chapter Geometric Progression (G.P.). Geometric Progression is a comparatively new addition to the ICSE Class 10 Maths syllabus. ICSE Class 10 Geometric Progression Previous Years Questions Solution is going to be very beneficial for the students appearing for ICSE class 10 Board exam. The page contains solution to G.P. PYQs which came in ICSE Board exams till the year 2023. You can also download the PDF of the questions from the chapter.\n\n## Download PDF of ICSE Class 10 Geometric Progression Previous Years Questions Solution\n\n1. The 4th, 6th and the last term of a geometric progression are 10, 40 and 640 respectively. If the common ratio is positive, find the first term, common ratio and the number of terms of the series. \n\nSolution: first term = 1.25, common ratio = 2, no. of terms = 10\n\nStep-by-step Explanation:\n\n$\\style{font-size:12px}{4th\\;term\\;=\\;ar^3\\;=\\;10\\;….(i)\\\\6th\\;term\\;=\\;ar^5\\;=\\;40\\;….(2)\\\\last\\;term\\;=\\;640\\\\Dividing\\;(2)\\;by\\;(1),\\;we\\;get\\\\\\frac{ar^5}{ar^3}=\\frac{40}{10}\\\\r^2\\;=\\;4\\\\r=\\pm2\\\\as\\;common\\;ratio\\;is\\;positive,\\;\\\\therefore\\;r\\;=\\;2\\\\Putting\\;r=\\;2\\;in\\;(1)\\\\a\\times2^3\\;=\\;10\\\\a=\\frac{10}8\\\\a=1.25\\\\\\\\let\\;nth\\;term\\;be\\;the\\;last\\;term.\\\\\\therefore ar^{n-1}\\;=\\;640\\\\1.25\\times2^{n-1}=640\\\\2^{n-1}=\\frac{640}{1.25}\\\\2^{n-1}=512\\\\2^{n-1}=2^9\\\\n-1=9\\\\n=10}$\n\nICSE Class 10 Maths PYQ Solution Chapter-wise\n\nWatch video solution of Geometric Progression [G.P.] PYQs here.\n\n2. The first and last trem of a Geometric Progression (G.P.) are 3 and 96 respectively. If the common ratio is 2, find:\n\n(i) ‘n’ the number of terms of the G.P. (ii) sum of n terms \n\nSolution: (i) 6 (ii) 189\n\nStep-by-step Explanation:\n\n$\\style{font-size:12px}{1st\\;term\\;=\\;a\\;=\\;3\\;\\\\common\\;ratio=r=2\\\\last\\;term\\;=\\;96\\\\(i)\\;Let\\;the\\;nth\\;term\\;be\\;the\\;last\\;term.\\\\\\therefore ar^{n-1}=96\\\\3\\times2^{n-1}=96\\\\2^{n-1}=32\\\\2^{n-1}=2^5\\\\n-1=5\\\\n=6\\\\\\\\(ii)\\;S_n=\\frac{a(r^n-1)}{r-1}\\\\=\\frac{3\\;(2^6-1)}{2-1}\\\\=3\\times63\\\\=189}$\n\n3. The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series. \n\nSolution: first term = 2, common ratio = 2\n\nStep-by-step Explanation:\n\n$\\style{font-size:12px}{4th\\;term\\;=\\;ar^3=16\\;…(1)\\\\7th\\;term\\;=\\;ar^6=128\\;…(2)\\\\Dividing\\;(2)\\;by\\;(1),\\;we\\;get,\\\\\\frac{ar^6}{ar^3}=\\frac{128}{16}\\\\r^3\\;=\\;8\\\\r=\\sqrt8\\\\r=2\\\\Putting\\;r=2\\;in\\;(1)\\\\a\\times2^3=16\\\\a=\\frac{16}8\\\\a=2}$\n\nSubscribe to my YouTube channel for more such educational content.\n\n#### Sample Papers\n\nSample Papers for Class 6\n\nSample Papers for Class 7\n\nSample Papers for Class 8\n\nSample Papers for Class 9\n\nSample Papers for Class 10\n\n#### Board Papers\n\nICSE Class 9 Board Exam Papers\n\nICSE Class 10 Board Exam Papers\n\n#### Chapter wise Quiz/MCQ/Test\n\nCBSE Chapter-wise Quiz for Class 6\n\nCBSE Chapter-wise Quiz for Class 7\n\nCBSE Chapter-wise Quiz for Class 8\n\nCBSE Chapter-wise Quiz for Class 9\n\nCBSE Chapter-wise Quiz for Class 10\n\n#### Sample Papers\n\nSample Papers for Class 6\n\nSample Papers for Class 7\n\nSample Papers for Class 8\n\nSample Papers for Class 9\n\nSample Papers for Class 10\n\n#### Board Papers\n\nCBSE Class 10 Previous years’ Board Papers\n\nSharing is caring!" ]

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[ "## Conversion formula\n\nThe conversion factor from hours to seconds is 3600, which means that 1 hour is equal to 3600 seconds:\n\n1 hr = 3600 s\n\nTo convert 10 hours into seconds we have to multiply 10 by the conversion factor in order to get the time amount from hours to seconds. We can also form a simple proportion to calculate the result:\n\n1 hr → 3600 s\n\n10 hr → T(s)\n\nSolve the above proportion to obtain the time T in seconds:\n\nT(s) = 10 hr × 3600 s\n\nT(s) = 36000 s\n\nThe final result is:\n\n10 hr → 36000 s\n\nWe conclude that 10 hours is equivalent to 36000 seconds:\n\n10 hours = 36000 seconds\n\n## Alternative conversion\n\nWe can also convert by utilizing the inverse value of the conversion factor. In this case 1 second is equal to 2.7777777777778E-5 × 10 hours.\n\nAnother way is saying that 10 hours is equal to 1 ÷ 2.7777777777778E-5 seconds.\n\n## Approximate result\n\nFor practical purposes we can round our final result to an approximate numerical value. We can say that ten hours is approximately thirty-six thousand seconds:\n\n10 hr ≅ 36000 s\n\nAn alternative is also that one second is approximately zero times ten hours.\n\n## Conversion table\n\n### hours to seconds chart\n\nFor quick reference purposes, below is the conversion table you can use to convert from hours to seconds\n\nhours (hr) seconds (s)\n11 hours 39600 seconds\n12 hours 43200 seconds\n13 hours 46800 seconds\n14 hours 50400 seconds\n15 hours 54000 seconds\n16 hours 57600 seconds\n17 hours 61200 seconds\n18 hours 64800 seconds\n19 hours 68400 seconds\n20 hours 72000 seconds" ]

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[ "PDA\n\nView Full Version : Fold Equity\n\nbruce\n09-15-2005, 09:04 PM\nIs this mathematically sound?\n\nLet's assume we're playing NLHE in a nine handed game. I'm UTG and I decide to raise. Let's also assume that my opponents will only call with QQ-AA and AK. We have a total of 1225 two card starting hands. We have six combos\nof a pocket pair so that's 18 combos and 16 more combos for\nAK. That's 34 combos of hands. 34 divided by 1225 is 0.028 or 2.8%. So that means each subsequent player has\na 2.8% chance of having a playable hand. I have 8 players\nyet to act so there is a roughly 22% chance I will be called based on my ranges.\n\nIs my math flawed or am I accurate.\n\nThanks.\n\nBruce\n\nTom1975\n09-16-2005, 12:42 PM\nYou're wrong for two reasons. First there are 1326 starting hands, not 1225. So the odds of one opponent having a playable hand is 34/1326. Secondly, to figure this out for 8 opponents, you can't just multiply 34/1326\n\nTom1975\n09-16-2005, 12:42 PM\nYou're wrong for two reasons. First there are 1326 starting hands, not 1225. So the odds of one opponent having a playable hand is 34/1326. Secondly, to figure this out for 8 opponents, you can't just multiply 34/1326 by 8 (although this will give you a decent approximation).\n\nbruce\n09-16-2005, 12:55 PM\nThx for the reply. How do you account for eight players? Why\ncan't you multiply by eight? Sorry for asking a basic question, but it's been 25 years since I received my degree.\nWhat I'm really trying to find out is what's the statistical likelyhood if I raise UTG and put my opponents on the above calling range that I will pick up the blinds if they only will call with my assigned range of hands?\n\nBruce\n\nLetYouDown\n09-16-2005, 01:19 PM\n[ QUOTE ]\nWhy can't you multiply by eight?\n\n[/ QUOTE ]\nBecause of this (http://archiveserver.twoplustwo.com/showthreaded.php?Cat=&Board=&Number=417383&page=&v iew=&sb=5&o=&fpart=)" ]

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[ "1\n\n## Mental Math and Money\n\nPublished on Sunday, March 01, 2009 in , , ,", null, "With the economy in the condition it's in, knowing about money will come in handy more and more. Here are a few quick mental math tricks that can help you get a better overall idea of some financial questions.\n\nFirst, let's look a pay. It's common to know how much you make per hour, but when you try to figure it with hours per week, and account for vacations, it all seems to complicated to work out. The shortcut, however, is startlingly simple. Double your hourly pay, and then just multiply by 1,000 (just adding 3 zeroes will work in many cases), and you'll get your yearly pay! Do you make \\$9/hour? \\$9 doubled is \\$18, and multiplying by 1,000 gives us \\$18,000/year! \\$21.75 per hour? That's \\$43,500/year.\n\nIt's not hard to do this mentally, with a little practice. That same calculation also works backwards, as long as you work it backwards. If someone is making \\$250,000/year, get rid of the 3 zeroes at the end first, giving us \\$250, and the divide by 2, giving us \\$125/hour as the equivalent. These calculations assume that you work 40 hours a week, and take 2 weeks for vacation.\n\nIf you want to take these calculations to extreme, just for fun, Salary Money can take this all the way down to how much you make per second!\n\nThere is a similar quick mental math trick you can do for weekly expenditures. In this case, you simply halve your weekly amount, and then multiply by 100. \\$20/week? Half of \\$20 is \\$10, and multiplying by 100 gives \\$1,000/year. I usually spend about \\$75 on groceries each week, so I can easily see that \\$3,750 is what I can expect spend on groceries this year. As above, this assumes that normal expenditures don't apply during a two-week vacation period.\n\nProbably one of the toughest things to calculate is interest. First, you have to determine if the interest involved is simple, continuous or compound, and you must understand the differences.\n\nHowever, there is one well-known rule that makes it easy to calculate how long it will take you to double your money at a given interest rate. It's called the Rule of 72 (although there are those who believe it should be updated to the Rule of 76). All you have to do is divide 72 by the interest rate in question, and you'll get the approximate time required to double your money. Since 72 is so easily divisible by so many numbers (such as 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 and 36), this calculation usually isn't difficult.\n\nDividing 72 by 5 might seem hard, but you consider that all you have to do is double the number and then divide by 10. 72 doubled is 144, and dividing by 10 gives us about 14.4 years to double at 5% annual interest. So, at 4% interest, your money would take roughly 18 years (72/4) to double. At 3%, though, it would take roughly 24 years (72/3) to double! If you've ever wondered why there's so much talk over seemingly small interest rate changes, now you know.\n\nNote that, due to the complex nature of money, these calculations are all approximate. However, they're also time tested, so you can quickly get a general picture of your economic situations with these handy monetary mental math tricks." ]

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[ "# Electromagnetic Waves – Check Properties & Related FAQs\n\n0\n\nSave\n\nPreparation for Engineering Entrance Exams like JEE Main, BITSAT, VITEEE is incomplete unless you learn important Physics concepts. In order to crack these exams, read this article carefully to understand the concept of Electromagnetic waves, its properties, and Electromagnetic Spectrum. Also, check related FAQs to gain familiarity with the question types.\n\n## What is an Electromagnetic Wave?\n\nAs the name suggests, electromagnetic waves are those waves that consist of both the vibrating particles of the electric field (E) as well as a magnetic field (B). Both fields E and B oscillate at right angles to each other and perpendicular to the direction of propagation. Electromagnetic waves are often used in communication to transmit radio-waves of various wavelengths.", null, "In the diagram given above the direction of propagation is along the z-axis and the electric field, as well as magnetic field, propagate perpendicular to the z-axis.\n\nYou can practice with – Chemistry Sample Paper and Maths Sample Paper\n\n## Properties of Electromagnetic Waves\n\n1) The nature of electromagnetic waves is transversal which, means the oscillations of the wave are perpendicular to the direction of the wave.\n\n2) Electromagnetic waves propagate in a vacuum i.e. through free space with a uniform velocity which is given by", null, "From the above equation, it can be clearly seen that the velocity of an electromagnetic wave through free space is equal to the velocity of the light ‘c’.\n\n## Electromagnetic Spectrum\n\nBased on the various methods of generating electromagnetic waves, they are classified and named accordingly. This classification ranging from lowest frequency to highest frequency is known as the Electromagnetic spectrum.\n\nElectromagnetic waves are classified into the following types. Check the below points and make short notes for revision.\n\nGenerated from: Alternating Current (A.C) circuits\n\nFrequency (ϑ) = 60Hz to 50Hz.\n\nWavelength(λ) = 5 × 106 m to 6 × 106 m\n\nThey are extensively used in communication systems such as transmitting radio waves.\n\nGenerated from: LC Oscillators\n\nFrequency (ϑ) = 109 Hz to 300Hz.\n\nWavelength(λ) = 0.3 m to 106 m\n\n### Microwaves\n\nThis category of waves is extensively used for their shorter wavelength in navigation, T.V Communication, studying the properties of matter, microwave ovens, etc\n\nGenerated from: Oscillating Currents in special vacuum tubes.\n\nFrequency (ϑ) = 1011 Hz to 109 Hz.\n\nWavelength(λ) = 10-3 m to 0.3m\n\n### Infrared waves\n\nThese waves are easily absorbed by most of the materials. They are extensively used in physical therapy, infrared photography, etc.\n\nGenerated from: Hot bodies and molecules.\n\nFrequency (ϑ) = 4.3 × 1014 HZ to 3× 1011 Hz.\n\nWavelength(λ) = 7 ×10-7 m to 10-3m\n\n### Visible light\n\nThese waves are easily detected by a human eye.\n\nGenerated from: Rearrangement of electrons in atoms and molecules.\n\nFrequency (ϑ) = 7.5 × 1014 HZ to 4.3× 1014 Hz.\n\nWavelength(λ) = 4 ×10-7 m to 7×10-7m\n\n### Ultraviolet rays\n\nThe most important source of ultraviolet rays is Sun. The uppermost layer of the atmosphere i.e. the stratosphere absorbs most of the light from the sun. This layer then radiates the absorbed energy as heat radiation.\n\nGenerated from: Sun\n\nFrequency (ϑ) = 3 × 10-9 HZ to 4 × 10-7 Hz.\n\nWavelength(λ) = 10-17 m to 7.5 × 1014m\n\n### X- Rays\n\nExtensively used in medical diagnostics.\n\nGenerated when high energy electrons bombard a metal with a high melting point.\n\nFrequency (ϑ) = 7.5 × 1020 HZ to 7.5× 1015 Hz.\n\nWavelength(λ) = 4 ×10-13 m to 4 × 10-8m\n\n### Gamma Rays\n\nUsed to detect metal flaws in metal casting\n\nGenerated from: Radioactive nuclei radiates gamma rays. They can also be found in some nuclear reactions in nuclear reactors.\n\nFrequency (ϑ) = 5 × 1024 HZ to 3× 1018 Hz.\n\nWavelength(λ) = 6 × 10-7 m to 10-10m\n\nGamma rays are highly penetrating and cause serious effects on living tissues.\n\nCheck the FAQs related to Electromagnetic Wave. Read the question and answer properly and familiarise yourself with the underlying concept.\n\nQ.1 What is the definition of electromagnetic waves?\nAns.1\n\nElectromagnetic wave are a transversal wave that consists of oscillations of both an electric field and magnetic field.\n\nQ.2 What is the example of electromagnetic waves?\nAns.2\n\nElectromagnetic waves are classified into various electromagnetic spectrums based on their frequency and wavelength. Some examples of electromagnetic waves are Infrared rays, X-Rays, gamma rays, etc.\n\nQ.3 What produces an electromagnetic field?\nAns.3\n\nWhen an electron is accelerated by an electric field, it tends to move. This movement causes both oscillating electric and magnetic fields.\n\nHope this article on Electromagnetic Waves has helped you in preparing for the upcoming competitive exams. You must also check related articles – Magnetic Flux, JEE Main Sample paper for Numerical Questions and JEE Main Physics Sample Paper\n\nAll the Best for your Exam Preparations!\n\nAs we all know, practice is the key to success. Therefore, boost your preparation by starting your practice now." ]

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[ "Cody\n\n# Problem 12. Fibonacci sequence\n\nSolution 1903429\n\nSubmitted on 17 Aug 2019 by David Kuckuk\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\nf = 1\n\n2   Pass\nn = 6; f = 8; assert(isequal(fib(n),f))\n\nf = 8\n\n3   Pass\nn = 10; f = 55; assert(isequal(fib(n),f))\n\nf = 55\n\n4   Pass\nn = 20; f = 6765; assert(isequal(fib(n),f))\n\nf = 6765" ]

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[ "# Satellite orbit around the earth\n\nThe CNES has been a great user of Scilab, and a long-term partner of us. Upon their advice, we presented one of their use case at the the 6th International Conference on Astrodynamics Tools and Techniques (ICATT).\n\nThe question is a classical problem of space mechanics solved step-by-step, to demonstrate the capacities of Scilab in this field:\n\n### 1.   Express the physics problem\n\nThe problem is based on the universal law of gravitation:\n\nWe write down Newton’s second law of motion in an earth-centred referential:\n\n(1)\n\n(2)\n\nPosition of the satellite is at a distance r [x; y]\n\nEarth mass centre is at O [0; 0]\n\nGravitational constant:\n\nMass of the earth:\n\n1. ### Translate your problem into Scilab\n\nScilab is a matrix-based language. Instead of expressing the system as set of 4 independent equations (along the x and y axis, for position and speed), we describe it as a single matrix equation, of dimension 4×4:\n\nThis method is a classical trick to switch from a second order scalar differential equation to a first order matrix differential equation.\n\nwith\n\nTo simplify the equation, we define the variable:\n\nOpen scinotes with edit myEarthRotation.sci\n\nDefine the skeleton of the function:\n\n```function udot=f(t, u)\nG = 6.67D-11; //Gravitational constant\nM = 5.98D24; //Mass of the Earth\nc = -G * M;\nr_earth = 6.378E6; //radius of the Earth\nr = sqrt(u(1)^2 + u(2)^2);\n​\n// Write the relationhsip between udot and u\nif r < r_earth then\nudot = [0 0 0 0]';\nelse\nA = [[0 0 1 0];\n[0 0 0 1];\n[c/r^3 0 0 0];\n[0 c/r^3 0 0]];\nudot = A*u;\nend\nendfunction\n​\n```\n\nThe condition defined by the distance r of the satellite with the centre of earth stops the simulation if it’s colliding with earth’s surface.\n\nTry out the final script with the following initial conditions in speed and altitude:\n\n```--> geo_alt = 35784; // in kms\n--> geo_speed = 1074; // in m/s\n--> simulation_time = 24; // in hours\n--> U = earthrotation(geo_alt, geo_speed, simulation_time);\n```\n\n### 3.   Compute the results and create a visual animation\n\nWith this function, we go to the core of the problem:\n\n```function U=earthrotation(altitude, v_init, hours)\n// altitude given in km\n// v_init is a vector [vx; vy] given in m/s\n// hours is the number of hours for the simulation\nr_earth = 6.378E6;\naltitude = altitude * 1000;\nU0 = [r_earth + altitude; 0; 0; v_init];\nt = 0:10:(3600*hours); // simulation time, one point every 10 seconds\nU = ode(U0, 0, t, f);\n\n// Draw the earth in blue\nangle = 0:0.01:2*%pi;\nx_earth = 6378 * cos(angle);\ny_earth = 6378 * sin(angle);\nfig = scf();\na = gca();\na.isoview = \"on\";\nplot(x_earth, y_earth, 'b--');\nplot(0, 0, 'b+');\n\n// Draw the trajectory computed\ncomet(U(1,:)/1000, U(2,:)/1000, \"colors\", 3);\nendfunction\n```\n\nThe resolution of the ordinary differential equation (ODE) is computed with the Scilab function ode.\n\node solves Ordinary Different Equations defined by:\n\nwhere y is a real vector or matrix\n\nThe simplest call of ode is: y = ode(y0,t0,t,f) where y0 is the vector of initial conditions, t0 is the initial time, t is the vector of times at which the solution y is computed and y is matrix of solution vectors y=[y(t(1)),y(t(2)),…].\n\n### Go further\n\nTo go further in numerical analysis, find out more about the solvers:" ]

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[ "# Tipping\n\n## Materials:\n\n• writing utensil\n• calculator\n• digital device with spreadsheet program\n• digital device with internet access\n\n## Observation\n\nAccording to unit 5, weight, static friction, and normal force must be balanced in all directions in order for a body to remain in static equilibrium. The following video shows how to predict the maximum slope for which an object will not tip. The result depends only on the center of mass height (", null, ") and horizontal distance (", null, ")from the center of mass to the edge of the support base:\n\n•", null, ", or in terms of the slope angle,", null, "## Questions\n\nThe above model assume that only gravity, friction, and normal force act on the object and that the center of gravity is the same as the center of mass. Are these assumptions reasonable? Can the models correctly predict the slope beyond which tipping occurs for an object such as the human body?\n\n## Search Existing Knowledge\n\n1) Can you find any existing information that helps to answer our question? Explain below, and cite your sources.\n\n## Hypothesis Generation:\n\n2) We need to turn our question into a set of  testable statements such that the results of testing the statements will provide evidence that helps us to answer the question. Choosing a % difference that is very large might ensure that your hypothesis is supported by the data, but that result would not provide evidence that the model is valid. Such a hypothesis would not be very useful. Instead, choose a % difference that would give strong evidence the values are the same if you hypothesis is confirmed.\n\n• If the assumptions are reasonable and the tipping model is valid, then the experimentally determined maximum slope before ___________ occurs will be less than _________% different from", null, ".\n\n## Experimental Hypothesis Testing\n\n### General Overview of Experimental Procedure\n\n1. Find the center of mass height (", null, ") and distance from center of mass to support base edge (", null, ").\n2. Calculate the predicted max slope before tipping as", null, ".\n3. Measure the slope angle at which each object begins to tip.\n4. Find the slope by calculating the tangent of the slope angle (slope =", null, ")\n5. Compare the values of the measured and predicted max slope and see if they match to within % difference you chose in your hypothesis.\n\n4) Calculate the center of mass height according to the method described in the video below. Record your results of the calculation here:\n\n5) Record the value of the horizontal distance from center of mass to edge of support base, as discussed in the video above.\n\n6) According to the video on tipping, the maximum slope before tipping is equal to", null, ". Use your values above to predict the slope at which the object will tip.\n\n15) Watch the following video and record the maximum tipping angle.\n\n7) Calculate the tangent of the tipping angle to get the slope.\n\n8) Compare the measured slope to the experimentally determined slope by calculating a percent difference. Cite any sources you used to find information on calculating percent difference.\n\n## Conclusions\n\n9) Do the results support or refute your second hypothesis?\n\n10) With regard to our original question, do our data and conclusions provide evidence that the tipping model derived in the first video is valid?", null, "" ]

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[ "The problem of sharing variables between threads in Python multi-process programming\n\nSource: Internet\nAuthor: User\n\nThis article is mainly about exploring the sharing of variables between Python's multiple-process programming threads, and multi-process programming is an important knowledge in Python's advanced learning, and friends who need it can refer to\n\n1, Questions:\n\nSome students in the group posted the following code, asked why the list last printed is null value?\n\n?\n\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27-28 From multiprocessing import Process, manager import OS Manager = Manager () vip_list = [] #vip_list = Manager.list () de F TestFunc (cc): Vip_list.append (cc) print ' Process ID: ', os.getpid () if __name__ = = ' __main__ ': threads = [] for LL in Range: t = Process (Target=testfunc, args= (ll,)) T.daemon = True threads.append (t) for I in range (len (threads)): THR Eads[i].start () for J in Range (len (threads)): Threads[j].join () print \"------------------------\" print ' Process ID: ', Os.getpid () Print vip_list\n\nIn fact, if you understand Python's multithreaded model, the GIL problem, and then understand the multithreading, the principle of multiple processes, the above questions are not difficult to answer, but if you do not know it does not matter, run the above code you know what is the problem.\n\n?\n\n 1 2 3 4 5 6 7 8 9 10 11 12 13-14 Python aa.py process id:632 process id:635 process id:637 process id:633 process id:636 process id:634 process Id:6 Process id:638 Process id:641 process id:640------------------------process id:619 []\n\nOpen the 6th line comment and you will see the following results:\n\n?\n\n 1 2 3 4 5 6 7 8 9 10 11 12-13 Process id:32074 Process id:32073 process id:32072 process id:32078 process id:32076 process id:32071 process id:32 077 process id:32079 Process id:32075 process id:32080------------------------process id:32066 [3, 2, 1, 7, 5, 0, 6, 8, 4, 9]\n\n2, Python multi-process sharing variables in several ways:\n\n(1) Shared Memory:\n\nData can be stored in a shared memory map using Value or Array. For example, the following code\n\nHttp://docs.python.org/2/library/multiprocessing.html#sharing-state-between-processes\n\n?\n\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16-17 From multiprocessing import Process, Value, Array def f (N, a): N.value = 3.1415927 to I in range (Len (a)): a[i] =-a[i] if __name__ = = ' __main__ ': num = Value (' d ', 0.0) arr = Array (' i ', range) P = Process (target=f, args= (num, arr)) p. Start () p.join () Print num.value print arr[:]\n\nResults:\n\n?\n\n 1 2 3.1415927 [0,-1,-2,-3,-4,-5,-6,-7,-8,-9]\n\n(2) Server Process:\n\nA manager object returned by manager () controls a server process which holds Python objects and allows the other processes to manipulate them using proxies.\n\nA Manager returned by manager () would support types list, dict, Namespace, Lock, Rlock, Semaphore, Boundedsemaphore, Condit Ion, Event, Queue, Value and Array.\n\nCode see the example at the beginning.\n\nHttp://docs.python.org/2/library/multiprocessing.html#managers\n\n3, the problem of multiple processes is far more than that: Data synchronization\n\nRead a simple piece of code: a simple counter:\n\n?\n\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 The 25 26 From multiprocessing import Process, manager import OS Manager = Manager () sum = Manager. Value (' tmp ', 0) def testfunc (cc): Sum.value + = cc if __name__ = ' __main__ ': threads = [] for ll in range (m): t =   Process (Target=testfunc, args= (1,)) T.daemon = True threads.append (t) for I in range (len (threads)): Threads[i].start () For j in Range (len (threads)): Threads[j].join () print \"------------------------\" print ' Process ID: ', os.getpid () print Sum.value\n\nResults:\n\n?\n\n 1 2 3 ------------------------Process id:17378 97\n\nPerhaps you would ask: WTF? In fact, this problem in the multi-threaded era exists, but in the era of multiple processes and a repeat of the Cup: lock!\n\n?\n\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 From multiprocessing import Process, manager, lock import OS lock = Lock () Manager = Manager () sum = Manager. Value (' tmp ', 0) def testfunc (CC, lock): with Lock:sum.value + = cc if __name__ = ' __main__ ': threads = [] for L L in range (m): T = Process (Target=testfunc, args= (1, lock)) T.daemon = True threads.append (t) for I in Range (Len (threa DS): Threads[i].start () for J in Range (len (threads)): Threads[j].join () print \"------------------------\" print \"Proce SS ID: ', os.getpid () print Sum.value\n\nWhat is the performance of this code? Run and watch, or increase the number of cycles try ...\n\n4, the final proposal:\n\nNote this usually sharing data between processes May is the best choice, because of all synchronization issues; An approach involving actors exchanging messages is usually seen as a better choice. Also Python Documentation:as mentioned above, when doing concurrent the IT is programming the best to usually using Sha Red state as far as possible. This is particularly true when using multiple processes. However, if you really did need to use some shared data then multiprocessing provides a couple of ways of doing.\n\n5, refer:\n\nHttp://stackoverflow.com/questions/14124588/python-multiprocessing-shared-memory\n\nhttp://eli.thegreenplace.net/2012/01/04/shared-counter-with-pythons-multiprocessing/\n\nHttp://docs.python.org/2/library/multiprocessing.html#multiprocessing.sharedctypes.synchronized\n\nRelated Keywords:\nRelated Article", null, "E-Commerce Solutions\n\nLeverage the same tools powering the Alibaba Ecosystem", null, "Apsara Conference 2019\n\nThe Rise of Data Intelligence, September 25th - 27th, Hangzhou, China", null, "Alibaba Cloud Free Trial\n\nLearn and experience the power of Alibaba Cloud with a free trial worth \\$300-1200 USD" ]

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[ "# Can TI-89 do double integrals?\n\n## Can TI-89 do double integrals?\n\nTo calculate a double integral using the TI-89 family, Voyage 200, TI-Nspire CAS, or TI-Nspire CX CAS, please follow the example below. Texas Instruments recommends all users update the handhelds to the latest version of the operating system.\n\n## What calculator can do integrals?\n\nSummary: Your TI-83/84 can compute any definite integral by using a numerical process….Definite Integrals on the Home Screen.\n\nOn the home screen, select fnint . [ MATH ] [ 9 ]\nSecond argument: the variable of integration x [ , ] [ x,T,θ,n ]\n\nWhich is better ti 84 or 89?\n\nTI-89 vs TI-84: Functionality The biggest factor when choosing between these two calculators should probably center around what tasks you classes you plan on taking. If you are trying to knock out your high school requirements for math and never touch the subject again, the TI-84 is best.\n\n### Can a TI 84 integrate?\n\nSummary: Your TI-83/84 can compute any definite integral by using a numerical process. That can be a big help to you in checking your work. This page shows you two ways to compute a definite integral with numeric limits, and how to plot an accumulation function.\n\n### How do you solve the system in the TI calculator?\n\nThe TI calculator solves the system, and displays the system and the solution as follows: The answer is therefore, x=1, y=2, and z=3. solve (3x+3y-4z=-3 and -x+2y+5z=18 and 8x+4y-7z=-5, {x,y,z}) and press [ENTER]\n\nWhat is the correct syntax for the integral function?\n\nThe syntax for the integral function is (integrand, variable of integration) for indefinite integrals and (integrand, variable of integration, lower limit, upper limit) for definite integrals. Thank you. I couldn’t remember the correct syntax before an exam.\n\n#### How do you evaluate an indefinite integral on a calculator?\n\nTo evaluate an indefinite integral (one without definite limits), from the home screen press F3 to access the calculus menu, and then navigate to 2: Integrate. Press ENTER to paste the integral symbol." ]

[ null ]

[ "+ 7\n\n# Loan Calculator Problem\n\nI need some help. According to this question my input and output have a difference of 1 number in months 5 here is 1313 I have 1312 and rest of the program is okay That is why output is (10629) not as expected. You take a loan from a friend and need to calculate how much you will owe him after 6 months. You are going to pay him back 10% of the remaining loan amount each month. Create a program that takes the loan amount as input, calculates and outputs the remaining amount after 6 months. Sample Input: 20000 Sample Output: 10628 Here is the monthly payment schedule: Month 1 Payment: 10% of 20000 = 2000 Remaining amount: 18000 Month 2 Payment: 10% of 18000 = 1800 Remaining amount: 16200 Month 3: Payment: 10% of 16200 = 1620 Remaining amount: 14580 Month 4: Payment: 10% of 14580 = 1458 Remaining amount: 13122 Month 5: Payment: 10% of 13122 = 1313 Remaining amount: 11809 Month 6: Payment: 10% of 11809 = 1181 Remaining amount: 10628 https://code.sololearn.com/cQCKlK9H1NGe/?ref=a\n\n12th Dec 2020, 11:35 AM", null, "+ 31\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); //your code goes here for (int x = 1; x <= 6; x++){ amount = amount * 9 / 10; } System.out.println(amount); } }\n12th Dec 2020, 11:46 AM\nИван Чикyнов", null, "+ 64\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); for (int x = 0; x <3; x++){ int actual_amount = (amount * 10)/100; amount = amount - actual_amount; } System.out.println(amount); } }\n31st Mar 2021, 2:51 PM\nPrãbîñ Pãñtã", null, "+ 8\nfor(int x =0;x<3;x++){ amount = amount - (amount * 10/100); } System.out.println(amount); 👍, it was quite easy but took long to revise the concept of logic 😅\n15th Dec 2021, 1:44 AM\nNitin Singh", null, "+ 6\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); int total = 0; int tenP; //Please Subscribe to My Youtube Channel //Channel Name: Fazal Tuts4U for(int i=0; i<3; i++){ tenP = (amount*10)/100; total = amount - tenP; amount = total; } System.out.println(total); } }\n3rd Sep 2021, 5:10 PM\nFazal Haroon", null, "+ 4\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); for (int x = 0; x <3; x++){ int actual_amount = (amount * 10)/100; amount = amount - actual_amount; } System.out.println(amount); //your code goes here } }\n22nd Mar 2021, 8:19 AM\nLalitha E", null, "+ 2\nThank You guys I find it very useful to multiply the amount by 9/10 which is almost equal to 0.10 And Maths.ceil() also does the same thing Most interesting part is that dividing the amount by Double or Float 10.0 does the exact same job but not with Int 10?\n12th Dec 2020, 12:22 PM", null, "+ 2\npublic static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); //your code goes here int numOfMonths=1; int payment; int remainingAmount; while(numOfMonths<=3){ payment=(10*amount)/100; remainingAmount=(amount-payment); amount=remainingAmount; numOfMonths++; } System.out.println(amount);\n8th Apr 2021, 10:39 AM\nRomina\n+ 2\nI am getting this loan calculator problem. Can anyone copy that code plzzz.\n30th Nov 2021, 6:49 AM\nVenkata Hyndavi Nanduri", null, "+ 1\nYou calculate the amount for 10% with an integer, which is not so fine. Please analize yourself why? This is important to understand it if you will code in the future for industry. The solution is: for(int x = 0; x < 6; x++) { amount -= amount / 10.0; } System.out.println(amount);\n12th Dec 2020, 12:03 PM\nJaScript", null, "13th Dec 2020, 5:14 AM\nCoder", null, "+ 1\nwhenever I code different code for this question. I got \"No output\". can you explain the reason for that?\n2nd Mar 2021, 5:01 AM\nH.A.R.U. Hettiarachchi", null, "+ 1\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); //your code goes h for(int i=1 ; i<= 3 ; i++){ amount = amount - (amount/ 10); } System.out.println(amount); } } // this is for after 3 month\n15th Apr 2021, 11:12 AM\nRai Prashant Ramkishor", null, "+ 1\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); for (int x = 0; x <3; x++){ int actual_amount = (amount * 10)/100; amount = amount - actual_amount; } System.out.println(amount); } }\n21st May 2021, 11:36 AM\nYasiru Dahanayaka", null, "+ 1\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); // your code goes here int x = 0; do{ x++; int y = (amount * 10)/100; amount -= y; } while(x < 3); System.out.println(amount); } }\n8th Aug 2021, 4:48 PM", null, "+ 1\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); int total=0; for (int i = 1; i <= 3; i++){ total = amount * 10 / 100; amount=amount-total; } System.out.println(amount); } }\n14th Aug 2021, 10:57 AM\nKiran Vellanki", null, "+ 1\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); //your code goes here int b=0; for(int a=1;a<=3;a++){ b=amount/10; amount=amount-b; } System.out.print(amount); } }\n19th Aug 2021, 5:17 AM", null, "+ 1\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); //your code goes here for (int i = 1; i <=3 ; ++i){ amount = (90 * amount) / 100; } System.out.println(amount); } }\n22nd Aug 2021, 8:56 PM\nMwaniki Grace Waigumo", null, "+ 1\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); int one = (amount * 10)/ 100; amount = amount - one; int two = (amount * 10)/ 100; amount = amount - two; int three = (amount * 10)/ 100; amount = amount - three; System.out.println(amount); (this is the Logic)\n5th Sep 2021, 2:55 PM\nAjay Prakash N", null, "+ 1\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); for (int x = 0; x <3; x++){ int actual_amount = (amount * 10)/100; amount = amount - actual_amount; } System.out.println(amount); } }\n17th Dec 2021, 9:23 AM\nMirmahmud Ilyosov", null, "+ 1\nimport java.util.Scanner; public class Program { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int amount = scanner.nextInt(); for (int x = 0; x <3; x++){ int actual_amount = (amount * 10)/100; amount = amount - actual_amount; } System.out.println(amount); //your code goes here } } Good Luck\n19th Dec 2021, 2:16 PM", null, "" ]

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[ "", null, "", null, "", null, "", null, "", null, "", null, "IEVref: 103-07-14", null, "ID: Language: en", null, "Status: Standard", null, "", null, "", null, "", null, "Term: phasor Synonym1: complex RMS value [Preferred]", null, "", null, "Synonym2:", null, "", null, "Synonym3:", null, "", null, "Symbol: Definition: representation of a sinusoidal integral quantity by a complex quantity whose argument is equal to the initial phase and whose modulus is equal to the RMS value Note 1 to entry: For a quantity $a\\left(t\\right)=\\stackrel{^}{A}\\text{cos}\\left(\\omega \\text{ }t+{\\vartheta }_{0}\\right)$ the phasor is $\\underset{_}{A}=A\\text{exp}\\left(\\mathrm{j}{\\vartheta }_{0}\\right)$, where $A=\\frac{\\stackrel{^}{A}}{\\sqrt{2}}$ is the RMS value and ${\\vartheta }_{0}$ is the initial phase. A phasor can also be represented graphically. Note 2 to entry: Electric current phasor $\\underset{_}{I}$ and voltage phasor $\\underset{_}{U}$ are often used. Note 3 to entry: The similar representation with the modulus equal to the amplitude is sometimes also called \"phasor\". Publication date: 2017-07 Source: Replaces: 103-07-14:2009-12 Internal notes: 2017-08-25: Corrected tag; missing quotation mark. LMO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5:" ]

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[ "# Biot Number Calculator\n\nCreated by Miłosz Panfil, PhD\nReviewed by Dominik Czernia, PhD candidate\nLast updated: Apr 03, 2020\n\nThis Biot number calculator helps you compute the Biot number. What is the Biot number? The Biot number determines how quick is the heat transfer from the surface of the body to its interior. The text below explains the physics behind the heat transfer and gives the Biot number formula.\n\n## What is the Biot number?\n\nThe Biot number helps us answer the following question: How greatly the temperature inside a body will vary if we heat up a part of its surface? If the Biot number is small (much less than 1) then the temperature on the surface and in the interior will be very similar. On the other hand if the Biot number is large (much larger than 1) then there will be a large temperature gradient inside the body.\n\n## Heat transfer\n\nIf we warm the surface of a material, two things happen. First, we warm the surface. Efficiency of this process depends on the heat transfer coefficient. Secondly, the heat from the surface starts to flow through the rest of the material heating the interior. How quickly this happens depends on the thermal conductivity of a material. Check the thermal conductivity calculator to learn more about this phenomenon.\n\nThe Biot number compares the efficiency of these two processes.\n\n1. If the heat transfer is more efficient than the thermal conductivity then the surface will warm up quicker then the rest of the body - Biot number is larger than 1.\n\n2. On the opposite, if the material conducts heat well then beside warming it up only in one place, its temperature will be pretty uniform - Biot number is smaller than 1.\n\n## Biot number formula\n\nThe Biot number formula is\n\nBi = Lc * h / k,\n\nwhere\n\n• Lc [m] is the characteristic length of a material,\n• h [W/(m² * K)] is the heat transfer coefficient at the material's surface,\n• k [W/(m * K)] is the thermal conductivity of the material.\n• Bi is the resulting Biot number.\n\nWe can compute the characteristic length Lc knowing the volume V and the area A of a surface through which the material is heated up (or cooled down):\n\nLc = V / A.\n\nFor example for a copper pan of water with characteristic length Lc = 15 cm, the Biot number is Bi = 2.807. This means that when we heat the pan, there will be a significant difference in temperatures between the water at the bottom and at the top of the pot. If we decrease the amount of water (decrease the characteristic length), the Biot number drops signaling a more uniform temperature inside the pot.\n\nIn the computations with the Biot number calculator we took the water thermal conductivity k = 0.7 [W/(m * K)] and the heat transfer coefficient between copper and water h = 13.1 [W/(m² * K)].\n\nMiłosz Panfil, PhD\nCharacteristic length\nSurface area\nVolume\nBiot number\nCharacteristic length\nm\nHeat transfer coefficient\nW/(m² * K)\nThermal conductivity\nW/(m⋅K)\nBiot number\nPeople also viewed…\n\n### Grams to cups\n\nThe grams to cups calculator converts between cups and grams. You can choose between 20 different popular kitchen ingredients or directly type in the product density.\n\n### Korean age\n\nIf you're wondering what would your age be from a Korean perspective, use this Korean age calculator to find out.\n\n### Mean free path\n\nThe mean free path calculator lets you find the mean free path of any particle in an ideal gas.\n\n### Wave speed\n\nCalculate the speed of waves using the wave speed calculator.", null, "" ]

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[ "### Diff for /gforth/test/ttester.fs between versions 1.11 and 1.16\n\nversion 1.11, 2008/03/06 19:24:30 version 1.16, 2009/09/21 15:32:56\nLine 1 Line 1\n\\ for the original tester  \\ This file contains the code for ttester, a utility for testing Forth words,\n\\ as developed by several authors (see below), together with some explanations\n\\ of its use.\n\n\\ ttester is based on the original tester suite by Hayes:\n\\ From: John Hayes S1I  \\ From: John Hayes S1I\n\\ Subject: tester.fr  \\ Subject: tester.fr\n\\ Date: Mon, 27 Nov 95 13:10:09 PST    \\ Date: Mon, 27 Nov 95 13:10:09 PST\n\\ (C) 1995 JOHNS HOPKINS UNIVERSITY / APPLIED PHYSICS LABORATORY  \\ (C) 1995 JOHNS HOPKINS UNIVERSITY / APPLIED PHYSICS LABORATORY\n\\ MAY BE DISTRIBUTED FREELY AS LONG AS THIS COPYRIGHT NOTICE REMAINS.  \\ MAY BE DISTRIBUTED FREELY AS LONG AS THIS COPYRIGHT NOTICE REMAINS.\n\\ VERSION 1.1  \\ VERSION 1.1\n\\ All the subsequent changes have been placed in the public domain.\n\\ for the FNEARLY= stuff:  \\ The primary changes from the original are the replacement of \"{\" by \"T{\"\n\\ and \"}\" by \"}T\" (to avoid conflicts with the uses of { for locals and }\n\\ for FSL arrays), modifications so that the stack is allowed to be non-empty\n\\ before T{, and extensions for the handling of floating point tests.\n\\ Code for testing equality of floating point values comes\n\\ from ftester.fs written by David N. Williams, based on the idea of  \\ from ftester.fs written by David N. Williams, based on the idea of\n\\ approximate equality in Dirk Zoller's float.4th  \\ approximate equality in Dirk Zoller's float.4th.\n\\ public domain  \\ Further revisions were provided by Anton Ertl, including the ability\n\\ to handle either integrated or separate floating point stacks.\n\\ for the rest:  \\ Revision history and possibly newer versions can be found at\n\\ revised by Anton Ertl 2007-08-12, 2007-08-19, 2007-08-28  \\ http://www.complang.tuwien.ac.at/cvsweb/cgi-bin/cvsweb/gforth/test/ttester.fs\n\\ public domain  \\ Explanatory material and minor reformatting (no code changes) by\n\\ C. G. Montgomery March 2009, with helpful comments from David Williams\n\\ The original has the following shortcomings:  \\ and Krishna Myneni.\n\n\\ - It does not work as expected if the stack is non-empty before the {.  \\ Usage:\n\n\\ - It does not check FP results if the system has a separate FP stack.  \\ The basic usage takes the form  T{ <code> -> <expected stack> }T .\n\\ This executes  <code>  and compares the resulting stack contents with\n\\ - There is a conflict with the use of } for FSL arrays and { for locals.  \\ the  <expected stack>  values, and reports any discrepancy between the\n\\ two sets of values.\n\\ I have revised it to address these shortcomings.  You can find the  \\ For example:\n\\ result at  \\ T{ 1 2 3 swap -> 1 3 2 }T  ok\n\\ T{ 1 2 3 swap -> 1 2 2 }T INCORRECT RESULT: T{ 1 2 3 swap -> 1 2 2 }T ok\n\\ http://www.forth200x.org/tests/tester.fs  \\ T{ 1 2 3 swap -> 1 2 }T WRONG NUMBER OF RESULTS: T{ 1 2 3 swap -> 1 2 }T ok\n\\ http://www.forth200x.org/tests/ttester.fs\n\\ Floating point testing can involve further complications.  The code\n\\ attempts to determine whether floating-point support is present, and\n\\ if so, whether there is a separate floating-point stack, and behave\n\\ accordingly.  The CONSTANTs HAS-FLOATING and HAS-FLOATING-STACK\n\\ contain the results of its efforts, so the behavior of the code can\n\\ be modified by the user if necessary.\n\n\\ Then there are the perennial issues of floating point value\n\\ comparisons.  Exact equality is specified by SET-EXACT (the\n\\ default).  If approximate equality tests are desired, execute\n\\ SET-NEAR .  Then the FVARIABLEs REL-NEAR (default 1E-12) and\n\\ ABS-NEAR (default 0E) contain the values to be used in comparisons\n\\ by the (internal) word FNEARLY= .\n\n\\ When there is not a separate floating point stack and you want to\n\\ use approximate equality for FP values, it is necessary to identify\n\\ which stack items are floating point quantities.  This can be done\n\\ by replacing the closing }T with a version that specifies this, such\n\\ as RRXR}T which identifies the stack picture ( r r x r ).  The code\n\\ provides such words for all combinations of R and X with up to four\n\\ stack items.  They can be used with either an integrated or separate\n\\ floating point stacks. Adding more if you need them is\n\\ straightforward; see the examples in the source.  Here is an example\n\\ which also illustrates controlling the precision of comparisons:\n\n\\   SET-NEAR\n\\   1E-6 REL-NEAR F!\n\\   T{ S\" 3.14159E\" >FLOAT -> -1E FACOS TRUE RX}T\n\n\\ The word ERROR is now vectored, so that its action can be changed by\n\\ the user (for example, to add a counter for the number of errors).\n\\ The default action ERROR1 can be used as a factor in the display of\n\\ error reports.\n\n\\ tester.fs is intended to be a drop-in replacement of the original.  \\ Loading ttester.fs does not change BASE.  Remember that floating point input\n\\ is ambiguous if the base is not decimal.\n\n\\ ttester.fs is a version that uses T{ and }T instead of { and } and  \\ The file defines some 70 words in all, but in most cases only the\n\\ keeps the BASE as it was before loading ttester.fs  \\ ones mentioned above will be needed for successful testing.\n\n\\ In spirit of the original, I have strived to avoid any potential\n\\ non-portabilities and stayed as much within the CORE words as\n\\ possible; e.g., FLOATING words are used only if the FLOATING wordset\n\\ is present\n\n\\ There are a few things to be noted:\n\n\\ changes BASE to HEX (like the original tester).  Floating-point\n\\ input is ambiguous when the base is not decimal, so you have to set\n\\ it to decimal yourself when you want to deal with decimal numbers.\n\n\\ - For FP it is often useful to use approximate equality for checking\n\\ the results.  You can turn on approximate matching with SET-NEAR\n\\ (and turn it off (default) with SET-EXACT, and you can tune it by\n\\ setting the variables REL-NEAR and ABS-NEAR.  If you want your tests\n\\ to work with a shared stack, you have to specify the types of the\n\\ elements on the stack by using one of the closing words that specify\n\\ types, e.g. RRRX}T for checking the stack picture ( r r r x ).\n\\ There are such words for all combination of R and X with up to 4\n\\ stack items, and defining more if you need them is straightforward\n\\ (see source).  If your tests are only intended for a separate-stack\n\\ system or if you need only exact matching, you can use the plain }T\n\nBASE @  BASE @\nHEX  DECIMAL\n\n\\ SET THE FOLLOWING FLAG TO TRUE FOR MORE VERBOSE OUTPUT; THIS MAY  VARIABLE ACTUAL-DEPTH                   \\ stack record\n\\ ALLOW YOU TO TELL WHICH TEST CAUSED YOUR SYSTEM TO HANG.  CREATE ACTUAL-RESULTS 32 CELLS ALLOT\nVARIABLE VERBOSE\nFALSE VERBOSE !\n\nVARIABLE ACTUAL-DEPTH                   \\ STACK RECORD\nCREATE ACTUAL-RESULTS 20 CELLS ALLOT\nVARIABLE START-DEPTH  VARIABLE START-DEPTH\nVARIABLE XCURSOR \\ FOR ...}T  VARIABLE XCURSOR      \\ for ...}T\nVARIABLE ERROR-XT  VARIABLE ERROR-XT\n\n: ERROR ERROR-XT @ EXECUTE ;  : ERROR ERROR-XT @ EXECUTE ;   \\ for vectoring of error reporting\n\n: \"FLOATING\" S\" FLOATING\" ; \\ ONLY COMPILED S\" IN CORE  : \"FLOATING\" S\" FLOATING\" ;    \\ only compiled S\" in CORE\n: \"FLOATING-STACK\" S\" FLOATING-STACK\" ;  : \"FLOATING-STACK\" S\" FLOATING-STACK\" ;\n\"FLOATING\" ENVIRONMENT? [IF]  \"FLOATING\" ENVIRONMENT? [IF]\n[IF]      [IF]\nLine 92  VARIABLE ERROR-XT Line 104  VARIABLE ERROR-XT\n[ELSE]      [ELSE]\nFALSE          FALSE\n[THEN]      [THEN]\n[ELSE] \\ WE DON'T KNOW WHETHER THE FP STACK IS SEPARATE  [ELSE]            \\ We don't know whether the FP stack is separate.\nHAS-FLOATING \\ IF WE HAVE FLOATING, WE ASSUME IT IS      HAS-FLOATING  \\ If we have FLOATING, we assume it is.\n[THEN] CONSTANT HAS-FLOATING-STACK  [THEN] CONSTANT HAS-FLOATING-STACK\n\nHAS-FLOATING [IF]  HAS-FLOATING [IF]\n\\ SET THE FOLLOWING TO THE RELATIVE AND ABSOLUTE TOLERANCES YOU      \\ Set the following to the relative and absolute tolerances you\n\\ WANT FOR APPROXIMATE FLOAT EQUALITY, TO BE USED WITH F~ IN      \\ want for approximate float equality, to be used with F~ in\n\\ FNEARLY=.  KEEP THE SIGNS, BECAUSE F~ NEEDS THEM.      \\ FNEARLY=.  Keep the signs, because F~ needs them.\nFVARIABLE REL-NEAR DECIMAL 1E-12 HEX REL-NEAR F!      FVARIABLE REL-NEAR 1E-12 REL-NEAR F!\nFVARIABLE ABS-NEAR    DECIMAL 0E HEX ABS-NEAR F!      FVARIABLE ABS-NEAR 0E    ABS-NEAR F!\n\n\\ WHEN EXACT? IS TRUE, }F USES FEXACTLY=, OTHERWISE FNEARLY=.      \\ When EXACT? is TRUE, }F uses FEXACTLY=, otherwise FNEARLY=.\n\nTRUE VALUE EXACT?      TRUE VALUE EXACT?\n: SET-EXACT  ( -- )   TRUE TO EXACT? ;      : SET-EXACT  ( -- )   TRUE TO EXACT? ;\n: SET-NEAR   ( -- )  FALSE TO EXACT? ;      : SET-NEAR   ( -- )  FALSE TO EXACT? ;\n\nDECIMAL\n: FEXACTLY=  ( F: X Y -- S: FLAG )      : FEXACTLY=  ( F: X Y -- S: FLAG )\n(          (\nLEAVE TRUE IF THE TWO FLOATS ARE IDENTICAL.          Leave TRUE if the two floats are identical.\n)          )\n0E F~ ;          0E F~ ;\nHEX\n\n: FABS=  ( F: X Y -- S: FLAG )      : FABS=  ( F: X Y -- S: FLAG )\n(          (\nLEAVE TRUE IF THE TWO FLOATS ARE EQUAL WITHIN THE TOLERANCE          Leave TRUE if the two floats are equal within the tolerance\nSTORED IN ABS-NEAR.          stored in ABS-NEAR.\n)          )\nABS-NEAR F@ F~ ;          ABS-NEAR F@ F~ ;\n\n: FREL=  ( F: X Y -- S: FLAG )      : FREL=  ( F: X Y -- S: FLAG )\n(          (\nLEAVE TRUE IF THE TWO FLOATS ARE RELATIVELY EQUAL BASED ON THE          Leave TRUE if the two floats are relatively equal based on the\nTOLERANCE STORED IN ABS-NEAR.          tolerance stored in ABS-NEAR.\n)          )\nREL-NEAR F@ FNEGATE F~ ;          REL-NEAR F@ FNEGATE F~ ;\n\nLine 136  HAS-FLOATING [IF] Line 146  HAS-FLOATING [IF]\n\n: FNEARLY=  ( F: X Y -- S: FLAG )      : FNEARLY=  ( F: X Y -- S: FLAG )\n(          (\nLEAVE TRUE IF THE TWO FLOATS ARE NEARLY EQUAL.  THIS IS A          Leave TRUE if the two floats are nearly equal.  This is a\nREFINEMENT OF DIRK ZOLLER'S FEQ TO ALSO ALLOW X = Y, INCLUDING          refinement of Dirk Zoller's FEQ to also allow X = Y, including\nBOTH ZERO, OR TO ALLOW APPROXIMATE EQUALITY WHEN X AND Y ARE TOO          both zero, or to allow approximately equality when X and Y are too\nSMALL TO SATISFY THE RELATIVE APPROXIMATION MODE IN THE F~          small to satisfy the relative approximation mode in the F~\nSPECIFICATION.          specification.\n)          )\nF2DUP FEXACTLY= IF F2DROP TRUE EXIT THEN          F2DUP FEXACTLY= IF F2DROP TRUE EXIT THEN\nF2DUP FREL=     IF F2DROP TRUE EXIT THEN          F2DUP FREL=     IF F2DROP TRUE EXIT THEN\nLine 156  HAS-FLOATING [IF] Line 166  HAS-FLOATING [IF]\n\nHAS-FLOATING-STACK [IF]  HAS-FLOATING-STACK [IF]\nVARIABLE ACTUAL-FDEPTH      VARIABLE ACTUAL-FDEPTH\nCREATE ACTUAL-FRESULTS 20 FLOATS ALLOT      CREATE ACTUAL-FRESULTS 32 FLOATS ALLOT\nVARIABLE START-FDEPTH      VARIABLE START-FDEPTH\nVARIABLE FCURSOR      VARIABLE FCURSOR\n\nLine 167  HAS-FLOATING-STACK [IF] Line 177  HAS-FLOATING-STACK [IF]\nFDEPTH START-FDEPTH @ > IF          FDEPTH START-FDEPTH @ > IF\nFDEPTH START-FDEPTH @ DO FDROP LOOP              FDEPTH START-FDEPTH @ DO FDROP LOOP\nTHEN ;          THEN ;\n\n: F{ ( -- )      : F{ ( -- )\nFDEPTH START-FDEPTH ! 0 FCURSOR ! ;          FDEPTH START-FDEPTH ! 0 FCURSOR ! ;\n\nLine 213  HAS-FLOATING-STACK [IF] Line 223  HAS-FLOATING-STACK [IF]\n: F} ;      : F} ;\n: F...}T ;      : F...}T ;\n\nDECIMAL      HAS-FLOATING [IF]\n: COMPUTE-CELLS-PER-FP ( -- U )      : COMPUTE-CELLS-PER-FP ( -- U )\nDEPTH 0E DEPTH 1- >R FDROP R> SWAP - ;          DEPTH 0E DEPTH 1- >R FDROP R> SWAP - ;\nHEX\n\nCOMPUTE-CELLS-PER-FP CONSTANT CELLS-PER-FP      COMPUTE-CELLS-PER-FP CONSTANT CELLS-PER-FP\n\n: FTESTER ( R -- )      : FTESTER ( R -- )\nDEPTH CELLS-PER-FP < ACTUAL-DEPTH @ XCURSOR @ START-DEPTH @ + CELLS-PER-FP + < OR IF          DEPTH CELLS-PER-FP < ACTUAL-DEPTH @ XCURSOR @ START-DEPTH @ + CELLS-PER-FP + < OR IF\nS\" NUMBER OF RESULTS AFTER '->' BELOW ...}T SPECIFICATION: \" ERROR EXIT              S\" NUMBER OF RESULTS AFTER '->' BELOW ...}T SPECIFICATION: \" ERROR EXIT\nLine 227  HAS-FLOATING-STACK [IF] Line 236  HAS-FLOATING-STACK [IF]\nS\" INCORRECT FP RESULT: \" ERROR              S\" INCORRECT FP RESULT: \" ERROR\nTHEN THEN          THEN THEN\nCELLS-PER-FP XCURSOR +! ;          CELLS-PER-FP XCURSOR +! ;\n[THEN]          [THEN]\n[THEN]\n\n: EMPTY-STACK   \\ ( ... -- ) EMPTY STACK: HANDLES UNDERFLOWED STACK TOO.  : EMPTY-STACK   \\ ( ... -- ) empty stack; handles underflowed stack too.\nDEPTH START-DEPTH @ < IF      DEPTH START-DEPTH @ < IF\nDEPTH START-DEPTH @ SWAP DO 0 LOOP          DEPTH START-DEPTH @ SWAP DO 0 LOOP\nTHEN      THEN\nLine 238  HAS-FLOATING-STACK [IF] Line 248  HAS-FLOATING-STACK [IF]\nTHEN      THEN\nEMPTY-FSTACK ;      EMPTY-FSTACK ;\n\n: ERROR1        \\ ( C-ADDR U -- ) DISPLAY AN ERROR MESSAGE FOLLOWED BY  : ERROR1        \\ ( C-ADDR U -- ) display an error message\n\\ THE LINE THAT HAD THE ERROR.                  \\ followed by the line that had the error.\nTYPE SOURCE TYPE CR                  \\ DISPLAY LINE CORRESPONDING TO ERROR     TYPE SOURCE TYPE CR                  \\ display line corresponding to error\nEMPTY-STACK                          \\ THROW AWAY EVERY THING ELSE     EMPTY-STACK                          \\ throw away everything else\n;  ;\n\n' ERROR1 ERROR-XT !  ' ERROR1 ERROR-XT !\n\n: T{            \\ ( -- ) SYNTACTIC SUGAR.  : T{            \\ ( -- ) syntactic sugar.\nDEPTH START-DEPTH ! 0 XCURSOR ! F{ ;     DEPTH START-DEPTH ! 0 XCURSOR ! F{ ;\n\n: ->            \\ ( ... -- ) RECORD DEPTH AND CONTENT OF STACK.  : ->            \\ ( ... -- ) record depth and contents of stack.\nDEPTH DUP ACTUAL-DEPTH !             \\ RECORD DEPTH     DEPTH DUP ACTUAL-DEPTH !             \\ record depth\nSTART-DEPTH @ > IF           \\ IF THERE IS SOMETHING ON STACK     START-DEPTH @ > IF           \\ if there is something on the stack\nDEPTH START-DEPTH @ - 0 DO ACTUAL-RESULTS I CELLS + ! LOOP \\ SAVE THEM         DEPTH START-DEPTH @ - 0 DO ACTUAL-RESULTS I CELLS + ! LOOP \\ save them\nTHEN     THEN\nF-> ;     F-> ;\n\n: }T            \\ ( ... -- ) COMPARE STACK (EXPECTED) CONTENTS WITH SAVED  : }T            \\ ( ... -- ) COMPARE STACK (EXPECTED) CONTENTS WITH SAVED\n\\ (ACTUAL) CONTENTS.                  \\ (ACTUAL) CONTENTS.\nDEPTH ACTUAL-DEPTH @ = IF            \\ IF DEPTHS MATCH     DEPTH ACTUAL-DEPTH @ = IF            \\ if depths match\nDEPTH START-DEPTH @ > IF          \\ IF THERE IS SOMETHING ON THE STACK        DEPTH START-DEPTH @ > IF          \\ if there is something on the stack\nDEPTH START-DEPTH @ - 0 DO     \\ FOR EACH STACK ITEM           DEPTH START-DEPTH @ - 0 DO     \\ for each stack item\nACTUAL-RESULTS I CELLS + @  \\ COMPARE ACTUAL WITH EXPECTED              ACTUAL-RESULTS I CELLS + @  \\ compare actual with expected\n<> IF S\" INCORRECT RESULT: \" ERROR LEAVE THEN              <> IF S\" INCORRECT RESULT: \" ERROR LEAVE THEN\nLOOP           LOOP\nTHEN        THEN\nELSE                                 \\ DEPTH MISMATCH     ELSE                                 \\ depth mismatch\nS\" WRONG NUMBER OF RESULTS: \" ERROR        S\" WRONG NUMBER OF RESULTS: \" ERROR\nTHEN     THEN\nF} ;     F} ;\nLine 287  HAS-FLOATING-STACK [IF] Line 297  HAS-FLOATING-STACK [IF]\n1 XCURSOR +! ;      1 XCURSOR +! ;\n\n: X}T XTESTER ...}T ;  : X}T XTESTER ...}T ;\n: R}T FTESTER ...}T ;\n: XX}T XTESTER XTESTER ...}T ;  : XX}T XTESTER XTESTER ...}T ;\n: XXX}T XTESTER XTESTER XTESTER ...}T ;\n: XXXX}T XTESTER XTESTER XTESTER XTESTER ...}T ;\n\nHAS-FLOATING [IF]\n: R}T FTESTER ...}T ;\n: XR}T FTESTER XTESTER ...}T ;  : XR}T FTESTER XTESTER ...}T ;\n: RX}T XTESTER FTESTER ...}T ;  : RX}T XTESTER FTESTER ...}T ;\n: RR}T FTESTER FTESTER ...}T ;  : RR}T FTESTER FTESTER ...}T ;\n: XXX}T XTESTER XTESTER XTESTER ...}T ;\n: XXR}T FTESTER XTESTER XTESTER ...}T ;  : XXR}T FTESTER XTESTER XTESTER ...}T ;\n: XRX}T XTESTER FTESTER XTESTER ...}T ;  : XRX}T XTESTER FTESTER XTESTER ...}T ;\n: XRR}T FTESTER FTESTER XTESTER ...}T ;  : XRR}T FTESTER FTESTER XTESTER ...}T ;\nLine 300  HAS-FLOATING-STACK [IF] Line 313  HAS-FLOATING-STACK [IF]\n: RXR}T FTESTER XTESTER FTESTER ...}T ;  : RXR}T FTESTER XTESTER FTESTER ...}T ;\n: RRX}T XTESTER FTESTER FTESTER ...}T ;  : RRX}T XTESTER FTESTER FTESTER ...}T ;\n: RRR}T FTESTER FTESTER FTESTER ...}T ;  : RRR}T FTESTER FTESTER FTESTER ...}T ;\n: XXXX}T XTESTER XTESTER XTESTER XTESTER ...}T ;\n: XXXR}T FTESTER XTESTER XTESTER XTESTER ...}T ;  : XXXR}T FTESTER XTESTER XTESTER XTESTER ...}T ;\n: XXRX}T XTESTER FTESTER XTESTER XTESTER ...}T ;  : XXRX}T XTESTER FTESTER XTESTER XTESTER ...}T ;\n: XXRR}T FTESTER FTESTER XTESTER XTESTER ...}T ;  : XXRR}T FTESTER FTESTER XTESTER XTESTER ...}T ;\nLine 316  HAS-FLOATING-STACK [IF] Line 328  HAS-FLOATING-STACK [IF]\n: RRXR}T FTESTER XTESTER FTESTER FTESTER ...}T ;  : RRXR}T FTESTER XTESTER FTESTER FTESTER ...}T ;\n: RRRX}T XTESTER FTESTER FTESTER FTESTER ...}T ;  : RRRX}T XTESTER FTESTER FTESTER FTESTER ...}T ;\n: RRRR}T FTESTER FTESTER FTESTER FTESTER ...}T ;  : RRRR}T FTESTER FTESTER FTESTER FTESTER ...}T ;\n[THEN]\n\n\\ Set the following flag to TRUE for more verbose output; this may\n\\ allow you to tell which test caused your system to hang.\nVARIABLE VERBOSE\nFALSE VERBOSE !\n\n: TESTING       \\ ( -- ) TALKING COMMENT.  : TESTING       \\ ( -- ) TALKING COMMENT.\nSOURCE VERBOSE @     SOURCE VERBOSE @\nLine 324  HAS-FLOATING-STACK [IF] Line 342  HAS-FLOATING-STACK [IF]\nTHEN ;     THEN ;\n\nBASE !  BASE !\n\\ end of ttester.fs\n\n Removed from v.1.11 changed lines Added in v.1.16\n\nFreeBSD-CVSweb <[email protected]>" ]

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[ "", null, "english accueil réunion accueil canadam\n\nGraph Searching Games - Part I\nOrg: Anthony Bonato (Ryerson University) et Danielle Cox (Mount Saint Vincent University)\n[PDF]\n\nANTHONY BONATO, Ryerson University\nBounds and algorithms for graph burning  [PDF]\n\nGraph burning models the spread of contagion in a network. The burning number of a graph $G$, written $b(G)$, measures the speed of the contagion. The Graph Burning Conjecture, which states that $b(G) \\le \\lceil \\sqrt{n} \\rceil$ for a connected graph of order $n$, remains open. We prove the conjecture for spider graphs.\n\nComputing the burning number is NP-hard even for spiders and path forests. We present new approximation algorithms for graph burning, giving an approximation ratio of 3 for general graphs. We present an algorithm for trees with approximation ratio 2, and consider approximation schemes on path forests.\n\n$\\ell$-Visibility Cops and Robber  [PDF]\n\nA variation of the Cops and Robber game is considered in which the cops can only see the robber when the distance between them is at most a fixed parameter $\\ell$. The cops' strategy consists of a phase in which they need to see\" the robber (i.e.~move within distance $\\ell$), followed by a phase in which they capture the robber. We present a variety of results, including a characterization of those trees on which $k$ cops are sufficient to guarantee a win for all $\\ell \\geq 1$.\n\n\\medskip\n\nThis is joint work with D.~Cox, C.~Duffy, D.~Dyer, S.L.~Fitzpatrick, & M.E.~Messinger.\n\nSEAN ENGLISH, Ryerson University\nCatching Robbers Quickly and Efficiently  [PDF]\n\nCops and Robbers is a game played on a graph in which a team of cops try to catch a moving robber. In this talk we will discuss cop throttling, in which we are concerned with catching the robber quickly. The capture time with $k$ cops, $\\mathrm{capt}_k(G)$, is the length of the longest game of Cops and Robbers possible, assuming optimal play. The cop throttling number is given by $\\mathrm{th}_c(G):=\\min_{k}\\{k+\\mathrm{capt}_k(G)\\}.$ We will give background on Cops and Robbers, and then show that the cop throttling number grows sublinearly with $|V(G)|$.\n\nThis project was joint work with Anthony Bonato.\n\nNATASHA KOMAROV, St. Lawrence University\nContaining a robber on a graph  [PDF]\n\nWe consider Containment'': a variation of the graph pursuit game of Cops and Robber in which cops move from edge to adjacent edge, the robber moves from vertex to adjacent vertex (but cannot move along an edge occupied by a cop), and the cops win by containing'' the robber---that is, by occupying all of the edges incident with a vertex v while the robber is at v. We develop several bounds on the minimal number of cops required to contain a robber, in particular relating this number to the well-studied cop-number'' in the original Cops and Robber game. (Joint work with John Mackey of Carnegie Mellon University and Danny Crytser of St. Lawrence University.)" ]

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[ "", null, "3 x 3 = 9.\n\n# The 03 Times Table\n\nLearning the three times table involves multiplying numbers by 3, or tripling them. Knowing how to do that helps with all kinds of maths at KS3 level and beyond. Even if you get all the questions right the first time you play this quiz, keep on coming back to it as you can improve the time it takes you to answer all the questions. Once you've memorised the three times table it will make multiplying numbers, and so your maths lessons, a lot easier!\n\nThere are many things that come in threes. There are three primary colours: red, green and blue. A triangle has three sides. Three-dimensional (3D) means that something has length, width and height. Three is quite an important number.\n\nSo, even if you think you already know the three times table, take your time and make sure that you read every question carefully before choosing your answer. Overconfidence can lead to careless mistakes!\n\n1.\nWhat is 2 x 3\n6\n9\n12\n8\nMost dice have 6 sides - that's because cubes have 6 faces\n2.\nWhat is 5 x 3\n25\n15\n5\n30\nTo times a number by 5, times it by 10 and then halve your answer\n3.\nWhat is 1 x 3\n6\n156\n2\n3\nAny number multiplied by one remains the same\n4.\nWhat is 10 x 3\n33\n36\n60\n30\nTo multiply any number by 10, just add a zero to its end\n5.\nWhat is 9 x 3\n21\n27\n28\n29\nYou can work this out by first multiplying 3 x 10 and then subtracting 3\n6.\nWhat is 3 x 3\n12\n9\n6\n15\n3 is the square root of 9\n7.\nWhat is 4 x 3\n9\n12\n14\n16\nThere are 12 months in a year - 4 seasons of 3 months\n8.\nWhat is 6 x 3\n30\n24\n16\n18\nThere are 18 holes on a golf course\n9.\nWhat is 7 x 3\n19\n16\n21\n24\n21 used to be the age at which we became adults. Nowadays it's 18\n10.\nWhat is 8 x 3\n18\n16\n20\n24\nPure gold is 24 carat\nAuthor:  Frank Evans" ]

[ null, "https://www.educationquizzes.com/library/KS3-Maths-Tables/3-times-1.jpg", null ]

[ " heat of solution equation\n•", null, "### Heat of Solution | Chemistry for Non-Majors\n\nThis is a multiple-step problem: 1) the grams NaOH is converted to moles; 2) the moles is multiplied by the molar heat of solution; 3) the joules of heat released in the dissolving process is used with the specific heat equation and the total mass of the solution to calculate the ; 4) the is determined from . Step 2: Solve .\n\nChat Online\n•", null, "### Solving the heat equation | DE3 - YouTube\n\n6/16/2019· Boundary conditions, and setup for how Fourier series are useful. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/de3thanks More...\n\nChat Online\n•", null, "### The fundamental solution of the heat equation\n\nMake a change of variables for the heat equation of the following form: r := x/t 1/2, w := u(t,x)/u(0,x). Show that if we assume that w depends only on r, the heat equation becomes an ordinary differential equation, and the heat kernel is a solution. (For students who are familiar with the Fourier transform.)\n\nChat Online\n•", null, "### Heat equation - Wikipedia\n\nMolar heat of solution, or, molar enthalpy of solution, is the energy released or absorbed per mole of solute being dissolved in solvent. Heat of solution (enthalpy of solution) has the symbol 1 ΔH soln; Molar heat of solution (molar enthalpy of solution) has the units 2 J mol-1 or kJ mol-1\n\nChat Online\n•", null, "### Example of Heat Equation - Problem with Solution\n\nExample of Heat Equation – Problem with Solution Consider the plane wall of thickness 2L, in which there is uniform and constant heat generation per unit volume, q V [W/m 3 ] . The centre plane is taken as the origin for x and the slab extends to + L on the right and – L on the left.\n\nChat Online\n•", null, "### DIFFYQS PDEs, separation of variables, and the heat equation\n\nSection 4.6 PDEs, separation of variables, and the heat equation. Note: 2 lectures, §9.5 in , §10.5 in . Let us recall that a partial differential equation or PDE is an equation containing the partial derivatives with respect to several independent variables. Solving PDEs will be our main application of Fourier series. A PDE is said to be linear if the dependent variable and its derivatives ...\n\nChat Online\n•", null, "### Math 241: Solving the heat equation\n\na solution of the heat equation that depends (in a reasonable way) on a parameter , then for any (reasonable) function f( ) the function U(x;t) = 2 1 f( )u (x;t)d is also a solution. D. DeTurck Math 241 002 2012C: Solving the heat equation 3/21\n\nChat Online\n•", null, "### Differential Equations - The Heat Equation\n\nSection 9-1 : The Heat Equation. Before we get into actually solving partial differential equations and before we even start discussing the method of separation of variables we want to spend a little bit of time talking about the two main partial differential equations that we’ll be solving later on in the chapter.\n\nChat Online\n•", null, "### Simple Heat Equation solver - File Exchange - MATLAB Central\n\nI have to solve the exact same heat equation (using the ODE suite), however on the 1D heat equation. So du/dt = alpha * (d^2u/dx^2). I already have working code using forward Euler, but I find it difficult to translate this code to make it solvable using the ODE suite.\n\nChat Online\n•", null, "### 2 Heat Equation - Stanford University\n\nwill be a solution of the heat equation on I which satisfies our boundary conditions, assuming each un is such a solution. In fact, one can show that an infinite series of the form u(x;t) · X1 n=1 un(x;t) will also be a solution of the heat equation, under proper convergence assumptions of this series. We will omit discussion of this issue here.\n\nChat Online\n•", null, "### Heat equation | Definition of Heat equation at Dictionary.com\n\nHeat equation definition, a partial differential equation the solution of which gives the distribution of temperature in a region as a function of space and time when the temperature at the boundaries, the initial distribution of temperature, and the physical properties of the medium are specified. See more.\n\nChat Online\n•", null, "### What's the equation for finding heat of solution? (delta H ...\n\n7/27/2010· The heat of solution is generally expressed in terms of kJ/mol. Convert the total heat released to kJ (multiply calories by 4.186 to change to joules, then divide by 1000 to change to kilojoules). Next calculate the number of moles of NaOH in solution (divide 2.0 g …\n\nChat Online\n•", null, "### The 1-D Heat Equation - MIT OpenCourseWare\n\nThe 1-D Heat Equation 18.303 Linear Partial Differential Equations Matthew J. Hancock Fall 2006 1 The 1-D Heat Equation 1.1 Physical derivation Reference: Guenther & Lee §1.3-1.4, Myint-U & Debnath §2.1 and §2.5 [Sept. 8, 2006] In a metal rod with non-uniform temperature, heat (thermal energy) is transferred\n\nChat Online\n•", null, "### Solutions to Problems for The 1-D Heat Equation\n\nSolutions to Problems for The 1-D Heat Equation 18.303 Linear Partial Differential Equations Matthew J. Hancock 1. A bar with initial temperature profile f (x) > 0, with ends held at 0o C, will cool as t → ∞, and approach a steady-state temperature 0o C.However, whether or\n\nChat Online\n•", null, "### Solution of the HeatEquation by Separation of Variables\n\nlinear equation, P i aiXi(x)Ti(t) is also a solution for any choice of the constants ai. Step 2 We impose the boundary conditions (2) and (3). Step 3 We impose the initial condition (4). The First Step– Finding Factorized Solutions The factorized function u(x,t) = X(x)T(t) is a solution to the heat equation …\n\nChat Online\n\n### Related Products\n\n• purell hand sanitizer dispenser manual" ]

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[ "# Theory Seminar: Pseudorandomness when the Odds are Against You\n\nSpeaker:\nRonen Shaltiel (Haifa University)\nDate:\nWednesday, 30.11.2016, 12:30\nPlace:\nTaub 201\n\nA celebrated result by Impagliazzo and Wigderson is that under complexity theoretic hardness assumptions, every randomized algorithm can be transformed into one that uses only logarithmically many bits, with polynomial slowdown. Such algorithms can then be completely derandomized, with polynomial slowdown. In the talk I will discuss recent work attempting to extend this approach to:\n\n1. Randomized algorithms that err with probability $1-\\epsilon$ for small $\\epsilon$. (Here, the goal is to minimize the number of random bits/slowdown as a function of $\\epsilon$).\n\n2. Known SAT-solving randomized algorithms. (Here, polynomial slowdown is a deal breaker as it gives trivial algorithms that run in super exponential time).\n\n3. Randomized algorithms that sample from probability distributions. (Here, the goal is to sample a statistically-close distribution using only few random bits).\n\nBased on joint work with Artemenko, Impagliazzo and Kabanets.\n\nBack to the index of events" ]

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[ "## Section: New Results\n\n### Asymptotic methods and approximate models\n\n#### Multiscale modelling in electromagnetism\n\nParticipants : Bérangère Delourme, Patrick Joly.\n\nThis topic is developed in collaboration with the CEA-Grenoble (LETI) and H.Haddar (INRIA-Saclay-DEFI) and is dedicated to the study of asymptotic models associated with the scattering of electromagnetic waves from a complex periodic structure. More precisely, this structure is made of a dielectric ring that contains two layers of wires winding around it (see figure 3 ). We are interested in situations where the thickness of the ring and the distance between two consecutive wires are very small compared to the wavelength of the incident wave and the diameter of the ring. One easily understands that in those cases, direct numerical computations of the solution would become prohibitive as the small scale (denoted by", null, ") goes to 0, since the used mesh would need to accurately follow the geometry of the heterogeneities.\n\nFigure 3. the periodic ring", null, "In order to overcome this difficulty, we derive approximate models where the periodic ring is replaced by effective transmission conditions. The numerical discretization of approximate problems is expected to be much less expensive than the exact one, since the used mesh has no longer to be constrained by the small scale.\n\nIn a first part, we have studied a simplified 2D case: we have constructed a complete and explicit expansion of the solution with respect to the small parameter", null, "and we have derived approximate models. These models are theoretically and numerically validated. For one year, we have been interesting in the 3D Maxwell case (which is the interesting model for the application) which presents new difficulties. The first one is due to the finite length of the ring: we need to understand the behavior of the electromagnetic field in the vicinity of the two extremities of the ring. This work has been partially done in collaboration with X.Claeys: we have studied a simplified two dimensional case and proved the relative accuracy of the first order intuitive approximate model. However, the building of approximate models of higher orders seems to be difficult. To avoid this first difficulty, we now consider the 3D Maxwell case with periodic boundary conditions on the extremities of the ring. We have derived an asymptotic expansion of the solution and an approximate model. From both hand computations and functional analysis points of view, the study of Maxwell's equations is more difficult than the study of Helmholtz equation.\n\n#### Quasi-singularities and electrowetting\n\nParticipants : Patrick Ciarlet, Thu Huyen Dao.\n\nA collaboration with Claire Scheid (Nice Univ.).\n\nThis is a twofold work.\n\nFirst, the Master internship of Thu Huyen Dao. Following the PhD thesis of Samir Kaddouri (2007), she studied quasi-singularities for the 2D-cartesian electrostatic model around rounded tips, using the electric field as the primary unknown, instead of the potential. To complement this work, we are investigating the computation of accurate maps of the values of the electric field, to model corona discharge phenomena around 2D and 2", null, "D tips.\n\nHandling very small amount of liquid on a solid surface is of great industrial interest. In this field, electrowetting process is now broadly used: one charges a droplet posed on a solid by applying a given voltage between this droplet and a counter-electrode placed beneath the insulator. This allows one to control precisely the wetting of the drop on the solid. For modeling purposes, one has to compute very accurately the shape of the drop near the counter-electrode by solving an electrostatic problem with a piecewise constant electric permittivity. We recently considered 3D configurations, based on the numerical approximation of the electric field, using a generalized Weighted Regularization Method (see §  6.2.1 ). A paper on this topic has been accepted for publication in M2AN.\n\n#### Asymptotic models for junctions of thin slots\n\nParticipants : Katrin Boxberger, Patrick Joly, Adrien Semin.\n\nWe have almost finished the work started in 2007 for the acoustic case. We have considered the most general possible case (a finite number of slots and junctions, and the slots may have different width). We have studied the two differents aspects of this problem:\n\n• the theoretical point of view: as for the case of two junctions and one slot, we completly justify the asymptotic expansion. We plan to publish (at least) one INRIA Research Report and one article in Asymptotic Analysis,\n\n• the numerical point of view: with the fellowship of Katrin Boxberger, we developed a C++ oriented-object code named \"Net Waves\" (this code is available on the INRIA GForge web site at url http://gforge.inria.fr/projects/netwaves ). This code is particular in the sense that there's no code at our knowledge which solves acoustic wave equation on a general finite network, even with classical Kirchhoff conditions. This code boards graphical output and is still maintained in the project.\n\n#### Wave propagation on infinite trees\n\nParticipants : Patrick Joly, Adrien Semin.\n\nWe have continued the work started in 2007, on two different ways.\n\n• Firstly, we have implemented an approximation of transparent boundary conditions for the Helmoltz equation on a self-similar p -adic tree in the code \"Net Waves\" mentionned in §  6.5.3 . We are currently making some regressions tests to be able to test these conditions. The next step, to be able to do many computations, is to write a GPU version of this code.\n\n• Secondly, we started a collaboration with Serge Nicaise from the University of Valenciennes since July 2009 to look the functionnal framework and the notion of trace at infinity on a general (not necessarily self-similar) p -adic tree.\n\n#### Approximate models in aeroacoustics\n\nParticipants : Anne-Sophie Bonnet-Ben Dhia, Patrick Joly, Lauris Joubert, Ricardo Weder.\n\nThis is the subject of the PhD thesis of Lauris Joubert and the object of a collaboration with M. Duruflé.\n\nTwo aspects of the subject have been considered.\n\nFirst we have completed our work on a simplified model for the propagation of acoustic waves in a duct in the presence of a laminated flow. The theoretical analysis of this model has been completed in two directions:\n\n• The stability analysis of the model in function of the Mach profile has been achieved completely. In the unstable case, an analogy with the known results about Kelvin-Helmholtz instabilities for incompressible fluids (Rayleigh anf Fjorjtoft criteria) has been established. An article has been submitted for publication.\n\n• We have developed a general method for obtaining a quasi-analytic representation of the solution that results into a priori estimates. This method in based on the use of the Fourier-Laplace transform and complex analysis methods. An article has been submitted.\n\nThe quasi-analytic representation of the solution has been exploited numerically (see for instance the result of figure in the case of a parabolic Mach profile). The comparison with results obtained by discretizing the full model (Galbrun's equations) is under way.\n\nThe second aspect we have first developed is the construction of effective boundary conditions for taking into account boundary layers in aeroacoustics. On the basis of the analysis of the thin duct problem, we have proposed a first effective condition whose stabilty has been proven. This condition has the practical disadvantage to be nonlocal with respect to the normal coordinate inside the boundary layer. One can obtain a local condition after approximating the exact Mach profile by a piecewise linear profile. The study and the implementation of this new condition will be the subject of our next contribution to the problem.\n\nFigure 4. Asymptotic wave propagation in a thin duct. We plotted solution with two differents times.", null, "", null, "", null, "#### Impedance boundary conditions for the aero-acoustic wave equations in the presence of viscosity\n\nParticipants : Bérangère Delourme, Patrick Joly, Kersten Schmidt.\n\nThis is a joint work with Sébastien Tordeux (INSA Toulouse).\n\nIn compressible fluids the propagating sound can be described by linearised and perturbed Navier-Stokes equations. This project is dedicated to the case of viscous fluid without mean flow. By multiscale expansion and matched asymptotic expansion we are deriving impedance boundary conditions taking into account the viscosity of the fluid. The first case is a plain wall and the second a wall with periodic perforations where we apply surface homogenisation.\n\nLogo Inria" ]

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[ "# galpy.df.evolveddiskdf.sigmaT2¶\n\nevolveddiskdf.sigmaT2(R, t=0.0, nsigma=None, deg=False, phi=0.0, epsrel=0.01, epsabs=1e-05, grid=None, gridpoints=101, returnGrid=False, surfacemass=None, meanvT=None, hierarchgrid=False, nlevels=2, integrate_method='dopr54_c')[source]\n\nNAME:\n\nsigmaT2\n\nPURPOSE:\n\ncalculate the rotational-velocity variance of the velocity distribution at (R,phi)\n\nINPUT:\n\nR - radius at which to calculate the moment (can be Quantity)\n\nphi= azimuth (rad unless deg=True; can be Quantity)\n\nt= time at which to evaluate the DF (can be a list or ndarray; if this is the case, list needs to be in descending order and equally spaced) (can be Quantity)\n\nsurfacemass, meanvT= if set use this pre-calculated surfacemass and mean rotational velocity\n\nnsigma - number of sigma to integrate the velocities over (based on an estimate, so be generous)\n\ndeg= azimuth is in degree (default=False); do not set this when giving phi as a Quantity\n\nepsrel, epsabs - scipy.integrate keywords (the integration calculates the ratio of this vmoment to that of the initial DF)\n\ngrid= if set to True, build a grid and use that to evaluate integrals; if set to a grid-objects (such as returned by this procedure), use this grid\n\ngridpoints= number of points to use for the grid in 1D (default=101)\n\nreturnGrid= if True, return the grid object (default=False)\n\nhierarchgrid= if True, use a hierarchical grid (default=False)\n\nnlevels= number of hierarchical levels for the hierarchical grid\n\nintegrate_method= orbit.integrate method argument\n\nOUTPUT:\n\nvariance of vT\n\nHISTORY:\n\n2011-03-31 - Written - Bovy (NYU)" ]

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[ "# Understanding elliptic curve point addition over a finite field\n\nI am new to elliptic curve cryptography as well as finite field theory. I am trying to understand point addition in affine coordinates.\n\nI understand, that for an elliptic curve $y^{2}=x^{3}+ax+b$ over $\\mathbb R$ the sum of two points $P=(x_{p},y_{p})$ and $Q=(x_{q},y_{q})$ is $R=(x_{r},y_{r})$: $$x_{r}=\\lambda^{2}-x_{p}-x_{q}$$ $$y_{r}=\\lambda(x_{p}-x_{r})-y_{p}$$\n\nwith the slope $$\\lambda=\\frac{y_{q}-y_{p}}{x_{q}-x_{p}}$$\n\nExcluding the cases: $P=Q$ (e.g. tangent slope), $P=0$ and $Q=0$ (e.g. $R=0$). If however the elliptic curve is defined over a finite field with prime size $n$: $$y^{2}=x^{3}+ax+b\\pmod n$$\n\nCan I just compute the slope for the \"standard case\" as follows (source: Slide 6)?\n\n$$\\lambda=\\frac{y_{q}-y_{p}}{x_{q}-x_{p}} \\pmod n$$\n\nI understand that for an element in a finite field (f.e. point $P=(x_{p},y_{p})$) amongst other things an multiplicative inverse has to exist. However the formula for the slope $\\lambda$ does only include coordinates of the point, not the element itself.\n\n• The formula for $\\lambda$ w/o the $\\bmod n$ is exactly the same, the modular reduction is just implicit (if this was your question), assuming you're operating over a prime field.\n– SEJPM\nMar 1 '17 at 14:39\n• Your formula for $\\lambda$ has numerator and denominator swapped (in both instances). Mar 1 '17 at 14:54\n\nYour coordinates are elements of the finite field. For a point $P = (x_p, y_p)$ with $x_p,y_p \\in \\mathbb{F}_n$, where $\\mathbf{F}_n$ is the finite field of order $n$ over which the elliptic curve is defined.\nSince $n$ is prime, your slope will also be an element of the field $\\mathbb{F}_n$. Even if $n$ was composite and $\\gcd(x_q - x_p, n) = 1$, $\\lambda$ is still an element of your field since an inverse of $(x_q - x_p)$ would still exist in this case. To compute the slope, you must find the multiplicative inverse of $(x_q-x_p)$ in your field $\\mathbb{F}_n$. Then $$\\lambda \\equiv (y_q - y_p)\\cdot(x_q - x_p)^{-1} \\pmod n \\text.$$\n• Thank you. So if all coordinates, such as $x_p,y_p$ are $\\in \\mathbf{F}_n$, then every calculation has to be done in the field $\\mathbf{F}_n$? Since however $(x_q - x_p)$ are not points I can use \"normal\" subtraction / addition here, right? Also including the modulo operation already here is possible to calculate with smaller numbers, but not necessary? Like this: $(x_q - x_p) \\pmod n$ Mar 1 '17 at 17:22\n• @floyd Be sure every operation is done modular $n$. Mar 1 '17 at 20:53\n• As $n$ is a prime larger than both $x_p,x_q$ this won't happen unless $x_p=x_q$ and in that case you're trying to do a point-doubling and there's a different formula for that." ]

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[ "Breaking News\n\n# 604800 Seconds To Days\n\n604800 Seconds To Days. 9 rows 604800 seconds equals 7 days or 604800 s = 7 d. Enter a value in the seconds field and click on the calculate days button. So for 104800 we have: Convert 874800 seconds to days.\n\n(604800 × 1) ÷ 60 = 604800 ÷ 60 =. 604,800 seconds it's only a week. So for 104800 we have:\n\n## Crikey, i've got to get the jog in.\n\nIf we want to calculate how many days are 104800 seconds we have to multiply 104800 by 1 and divide the product by 86400. 9 rows 604800 seconds equals 7 days or 604800 s = 7 d. Therefore, 604800 seconds is equal to 604800/86400 = 7 days.\n\n## To Convert 604800 D To Sec Use Direct Conversion Formula Below.\n\nThis online date calculator will help you calculate how many minutes/hours/days are a given number of seconds.\n\n### There Are 7 Days In 604800 Seconds.\n\nConvert 604,800 seconds to days.\n\n### Kesimpulan dari 604800 Seconds To Days.\n\nSo for 104800 we have: 504000 second to day 40 minute to minute 25920000000 millisecond to day 129.6 second to minute 365 year to millisecond 180 day to millisecond 99999840 second to hour 99999840. Convert 604800 seconds to minutes | convert 604800 sec to min with our conversion calculator and conversion table." ]

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[ "# Intuitive explanation for slit separation affecting fringe separation?\n\nI know the formula which proves fringe separation is inversely proportional to slit separation in the double slits, but is there an intuitive explanation to show that as slit separation increases, fringe separation decreases?\n\nThe following animation shows the fact you mentioned, namely the separation scales inversely for the interference pattern on the screen. The Blue curve is the norm-squared of the Fourier transform of a single slit (a single rectangular function), and the orange curve is the norm-squared of the Fourier transform of two rectangles separated by a distance $$d$$. For the purpose of aesthetic, I multiplied the blue curve by a factor of two ( thanks to Pieter for pointing out that )", null, "" ]

[ null, "https://i.stack.imgur.com/XapIL.gif", null ]

[ "# Coding period week 1\n\nI spent the community bonding period learning more about Jderobot’s Behavior Studio which focuses on using deep learning for self driving cars. It was also great to talk to my mentors and meet other members from Behavior Studio, they are all very kind and supportive. and know more about the Jderobot community.\n\nThe first week of the coding period, I started by studying the tensorflow agents library which has a set of great tutorials, and implemented some basic examples with Deep Q-Networks (DQN), Additionally I set up a Dockerfile to ease my work.\n\nExploring tensorflow agents and DQN in an easier environment like cartpole, would help me translate the implementation to more complex environment like Formula 1 environment. Additionally, I set the environment where I will be working using a GPU.", null, "## Reinforcement Learning", null, "Figure the book, Reinforcement Learning: An Introduction by Andrew Barto and Richard S. Sutton\n\nIn a previous post I wrote more about it, but to sum up reinforcement learning (RL) algorithms unlike supervised learning, learns from trial and error.\n\nAs shown in the figure, an agent acts based in an observation given by the environment, this action gives the agent a new observation and a reward signal which is a way to tell the agent how good was the action taken at that particular observation.\n\n## Q-Learning\n\nA $Q^{*}$ represents the optimal return to get from a state $s$ and an action $a$ also denoted as $Q^{*}(s, a)$. Hence in Q-Learning we tried to get the $Q_{*}$ for each step, it can be done using a simple matrix mapping states and actions.\n\nThe bellman equation is used to approximate to the optimal value $Q^{*}$, taking the reward $r$ in the current state $s$ and the maximum $Q^{*}$ of the next state $s’$ discounted by gamma $\\gamma$ .\n\n$\\begin{equation}Q^{*}(s, a) = \\mathbb{E}\\left[ r + \\gamma \\max_{a'} Q^{*}(s', a') \\right]\\end{equation}$\n\n## Deep Q-Network\n\nDeep Q-Network was developed by Deepmind in 2015, combining deep neural networks and Q-learning .\n\nMore complex environments like games or embodied robots using cameras generate observation that cannot longer be stores in a tabular setting, hence deep learning comes to the rescue.\n\n# Implemented\n\n## Environment\n\nI mainly used tensorflow 2 and tensorflow agents which works with openai-gym!. An environment from gym can easily be loaded to tf-agents by using suite_gym.load then this python environment that uses numpy arrays can be converted to a tensor environment.\n\nenv = suite_gym.load('CartPole-v0')\ntrain_env = tf_py_environment.TFPyEnvironment(env)\n\n\n## Network\n\nQNetwork class provides by tf-agents makes easy to implement the DQN, here we are creating from the specifications of the Carpole environment with a fully connected layer with 100 units.\n\nfc_layer_params = (100,)\n\nq_net = q_network.QNetwork(\ntrain_env.observation_spec(),\ntrain_env.action_spec(),\nfc_layer_params=fc_layer_params)\n\n\n## Agent\n\nJust like QNetwork there is a class DqnAgent uses the q_net previously instantiated, an optimizer and the time step specifications. Later on it would be easy to try new agents that are already implemented in the library.\n\noptimizer = tf.compat.v1.train.AdamOptimizer(learning_rate=learning_rate)\ntrain_step_counter = tf.Variable(0)\n\nagent = dqn_agent.DqnAgent(\ntrain_env.time_step_spec(),\ntrain_env.action_spec(),\nq_network=q_net,\noptimizer=optimizer,\ntd_errors_loss_fn=common.element_wise_squared_loss,\ntrain_step_counter=train_step_counter)\n\nagent.initialize()\n\n\n## Policy\n\nPolicies are the behavior that our agent would agent, some policies are already predefined like the random_policy for exploration.\n\neval_policy = agent.policy\ncollect_policy = agent.collect_policy\nrandom_policy = random_tf_policy.RandomTFPolicy(\ntrain_env.time_step_spec(),\ntrain_env.action_spec())\n\n\n## Replay Buffer\n\nThe replay buffer is an important part in the DQN algorithms this is where some trajectories are stored, basically it stores tuples of observations, reward, and actions, and the next state or observation. Then the tuples are sampled during training to about correlation between consecutive states, and make more efficient use of previous experience.\n\nInitially the collect_data function gathers n_step into the buffer using the random policy, also the function as_dataset allow us to iterate (sample) over the replay buffer.\n\nreplay_buffer = tf_uniform_replay_buffer.TFUniformReplayBuffer(\ndata_spec=agent.collect_data_spec,\nbatch_size=train_env.batch_size,\nmax_length=replay_buffer_max_length)\n\ncollect_data(train_env, random_policy, replay_buffer, n_steps=initial_collect_steps)\n\ndataset = replay_buffer.as_dataset(\nnum_parallel_calls=3,\nsample_batch_size=batch_size,\nnum_steps=2).prefetch(3)\n\niterator = iter(dataset)\n\n\n## Training\n\nAfter around ~5min the agent completes 20000 steps and its policy achieves the maximum score 200.\n\n# (Optional) Optimize by wrapping some of the code in a graph using TF function.\nagent.train = common.function(agent.train)\n\n# Evaluate the agent's policy once before training.\navg_return = compute_avg_return(eval_env, agent.policy, num_eval_episodes)\nreturns = [avg_return]\n\nfor _ in range(num_iterations):\n\n# Collect a few steps using collect_policy and save to the replay buffer.\nfor _ in range(collect_steps_per_iteration):\ncollect_step(train_env, agent.collect_policy, replay_buffer)\n\n# Sample a batch of data from the buffer and update the agent's network.\nexperience, unused_info = next(iterator)\ntrain_loss = agent.train(experience).loss\n\nstep = agent.train_step_counter.numpy()\n\n\nSince this environment has only to possible actions (left and right), and its observation space are four floats, it is fairly easy to achieve good results in such amount of time.", null, "## Week Highlights\n\n• Studied thoughtfully the tf-agents library which is going to accelerate the development of Deep Reinforcement Algorithms in JdeRobot environments.\n• Implemented a DQN example in the CartPole environment testing the working environment I set up using GPUs in a container along with JdeRobot Libraries.\n• Started the DQN implementation of a environment (BreakOut) which uses images since the Jderobot’s Formula 1 environment uses a camera for perception.\n• Modularized the implementations and added documentation to ease replication.\n• Met with my mentors and the Behavior Studio Team, I understood better the project and how work is going to fit the Behavior Studio tools.\n• Even using docker I had a little bit of trouble to met tensorflow-gpu dependencies, and besides using a GPU training times for DRL last hours so it takes some time to debug.\n\n Deepmind, DQN (Deep Q-Network) algorithm, 2015.\n\n Sergio Guadarrama et at, TF-Agents A library for Reinforcement Learning in TensorFlow, 2018.\n\n Richard S. Sutton and Andrew G. Barto, Reinforcement Learning: An Introduction, 2018" ]

[ null, "https://theroboticsclub.github.io/colab-gsoc2020-Diego_Charrez/assets/images/blogs/cartpole.gif", null, "https://theroboticsclub.github.io/colab-gsoc2020-Diego_Charrez/assets/images/blogs/mdp.png", null, "https://theroboticsclub.github.io/colab-gsoc2020-Diego_Charrez/assets/images/blogs/cartpole_20000.gif", null ]

[ "×\n×\n\n# Solutions for Chapter 9.6: Singular Value Decomposition", null, "## Full solutions for Numerical Analysis | 10th Edition\n\nISBN: 9781305253667", null, "Solutions for Chapter 9.6: Singular Value Decomposition\n\nSolutions for Chapter 9.6\n4 5 0 375 Reviews\n20\n4\n##### ISBN: 9781305253667\n\nThis textbook survival guide was created for the textbook: Numerical Analysis, edition: 10. Numerical Analysis was written by and is associated to the ISBN: 9781305253667. Since 20 problems in chapter 9.6: Singular Value Decomposition have been answered, more than 12850 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.6: Singular Value Decomposition includes 20 full step-by-step solutions.\n\nKey Math Terms and definitions covered in this textbook\n• Associative Law (AB)C = A(BC).\n\nParentheses can be removed to leave ABC.\n\n• Column space C (A) =\n\nspace of all combinations of the columns of A.\n\n• Covariance matrix:E.\n\nWhen random variables Xi have mean = average value = 0, their covariances \"'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x - x) (x - x) T is positive (semi)definite; :E is diagonal if the Xi are independent.\n\n• Factorization\n\nA = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.\n\n• Fibonacci numbers\n\n0,1,1,2,3,5, ... satisfy Fn = Fn-l + Fn- 2 = (A7 -A~)I()q -A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].\n\n• Hermitian matrix A H = AT = A.\n\nComplex analog a j i = aU of a symmetric matrix.\n\n• Indefinite matrix.\n\nA symmetric matrix with eigenvalues of both signs (+ and - ).\n\n• Iterative method.\n\nA sequence of steps intended to approach the desired solution.\n\n• Nullspace matrix N.\n\nThe columns of N are the n - r special solutions to As = O.\n\n• Pascal matrix\n\nPs = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).\n\n• Polar decomposition A = Q H.\n\nOrthogonal Q times positive (semi)definite H.\n\n• Random matrix rand(n) or randn(n).\n\nMATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.\n\n• Row space C (AT) = all combinations of rows of A.\n\nColumn vectors by convention.\n\n• Semidefinite matrix A.\n\n(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.\n\n• Similar matrices A and B.\n\nEvery B = M-I AM has the same eigenvalues as A.\n\n• Subspace S of V.\n\nAny vector space inside V, including V and Z = {zero vector only}.\n\n• Symmetric matrix A.\n\nThe transpose is AT = A, and aU = a ji. A-I is also symmetric.\n\n• Toeplitz matrix.\n\nConstant down each diagonal = time-invariant (shift-invariant) filter.\n\n• Triangle inequality II u + v II < II u II + II v II.\n\nFor matrix norms II A + B II < II A II + II B II·\n\n• Vandermonde matrix V.\n\nV c = b gives coefficients of p(x) = Co + ... + Cn_IXn- 1 with P(Xi) = bi. Vij = (Xi)j-I and det V = product of (Xk - Xi) for k > i.\n\n×" ]

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[ "# Fundamental Theorem of Finitely Generated Abelian Groups\n\n## Primary decomposition\n\nEvery finitely generated abelian group", null, "$G$ is isomorphic to a group of the form", null, "$\\displaystyle \\mathbb{Z}^n\\oplus\\mathbb{Z}_{q_1}\\oplus\\dots\\oplus\\mathbb{Z}_{q_t}$ where", null, "$n\\geq 0$ and", null, "$q_1,\\dots,q_t$ are powers of (not necessarily distinct) prime numbers. The values of", null, "$n, q_1, \\dots, q_t$ are (up to rearrangement) uniquely determined by", null, "$G$.\n\n## Invariant factor decomposition\n\nWe can also write", null, "$G$ as a direct sum of the form", null, "$\\displaystyle \\mathbb{Z}^n\\oplus\\mathbb{Z}_{k_1}\\oplus\\dots\\oplus\\mathbb{Z}_{k_u},$ where", null, "$k_1\\mid k_2\\mid k_3\\mid\\dots\\mid k_u$. Again the rank", null, "$n$ and the invariant factors", null, "$k_1,\\dots,k_u$ are uniquely determined by", null, "$G$.", null, "## Author: mathtuition88\n\nhttps://mathtuition88.com/\n\nPosted on Categories mathTags\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed." ]

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[ "# 熊猫加入问题：列重叠但未指定后缀\n\n## 问题：熊猫加入问题：列重叠但未指定后缀\n\n``````df_a =\n\nmukey DI PI\n0 100000 35 14\n1 1000005 44 14\n2 1000006 44 14\n3 1000007 43 13\n4 1000008 43 13\n\ndf_b =\nmukey niccdcd\n0 190236 4\n1 190237 6\n2 190238 7\n3 190239 4\n4 190240 7``````\n\n``join_df = df_a.join(df_b,on='mukey',how='left')``\n\n``*** ValueError: columns overlap but no suffix specified: Index([u'mukey'], dtype='object')``\n\nI have following 2 data frames:\n\n``````df_a =\n\nmukey DI PI\n0 100000 35 14\n1 1000005 44 14\n2 1000006 44 14\n3 1000007 43 13\n4 1000008 43 13\n\ndf_b =\nmukey niccdcd\n0 190236 4\n1 190237 6\n2 190238 7\n3 190239 4\n4 190240 7\n``````\n\nWhen I try to join these 2 dataframes:\n\n``````join_df = df_a.join(df_b,on='mukey',how='left')\n``````\n\nI get the error:\n\n``````*** ValueError: columns overlap but no suffix specified: Index([u'mukey'], dtype='object')\n``````\n\nWhy is this so? The dataframes do have common 'mukey' values.\n\n## 回答 0\n\n``````In :\n\ndf_a.join(df_b, on='mukey', how='left', lsuffix='_left', rsuffix='_right')\nOut:\nmukey_left DI PI mukey_right niccdcd\nindex\n0 100000 35 14 NaN NaN\n1 1000005 44 14 NaN NaN\n2 1000006 44 14 NaN NaN\n3 1000007 43 13 NaN NaN\n4 1000008 43 13 NaN NaN``````\n\n`merge` 之所以有效，是因为它没有此限制：\n\n``````In :\n\ndf_a.merge(df_b, on='mukey', how='left')\nOut:\nmukey DI PI niccdcd\n0 100000 35 14 NaN\n1 1000005 44 14 NaN\n2 1000006 44 14 NaN\n3 1000007 43 13 NaN\n4 1000008 43 13 NaN``````\n\nYour error on the snippet of data you posted is a little cryptic, in that because there are no common values, the join operation fails because the values don't overlap it requires you to supply a suffix for the left and right hand side:\n\n``````In :\n\ndf_a.join(df_b, on='mukey', how='left', lsuffix='_left', rsuffix='_right')\nOut:\nmukey_left DI PI mukey_right niccdcd\nindex\n0 100000 35 14 NaN NaN\n1 1000005 44 14 NaN NaN\n2 1000006 44 14 NaN NaN\n3 1000007 43 13 NaN NaN\n4 1000008 43 13 NaN NaN\n``````\n\n`merge` works because it doesn't have this restriction:\n\n``````In :\n\ndf_a.merge(df_b, on='mukey', how='left')\nOut:\nmukey DI PI niccdcd\n0 100000 35 14 NaN\n1 1000005 44 14 NaN\n2 1000006 44 14 NaN\n3 1000007 43 13 NaN\n4 1000008 43 13 NaN\n``````\n\n## 回答 1\n\n`.join()`函数正在使用`index`传递的参数数据集的，因此您应该改用`set_index`或使用`.merge`function。\n\n``join_df = LS_sgo.join(MSU_pi.set_index('mukey'), on='mukey', how='left')``\n\n``join_df = df_a.merge(df_b, on='mukey', how='left')``\n\nThe `.join()` function is using the `index` of the passed as argument dataset, so you should use `set_index` or use `.merge` function instead.\n\n``````join_df = LS_sgo.join(MSU_pi.set_index('mukey'), on='mukey', how='left')\n``````\n\nor\n\n``````join_df = df_a.merge(df_b, on='mukey', how='left')\n``````\n\n## 回答 2\n\n``df_a.join(df_b, on='mukey', how='left', lsuffix='_left', rsuffix='_right')``\n\nThis error indicates that the two tables have the 1 or more column names that have the same column name. The error message translates to: \"I can see the same column in both tables but you haven't told me to rename either before bringing one of them in\"\n\nYou either want to delete one of the columns before bringing it in from the other on using del df['column name'], or use lsuffix to re-write the original column, or rsuffix to rename the one that is being brought it.\n\n``````df_a.join(df_b, on='mukey', how='left', lsuffix='_left', rsuffix='_right')\n``````\n\n## 回答 3\n\nMainly join is used exclusively to join based on the index,not on the attribute names,so change the attributes names in two different dataframes,then try to join,they will be joined,else this error is raised", null, "" ]

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[ "# jax.scipy.special.spence#\n\njax.scipy.special.spence(x)[source]#\n\nSpence’s function, also known as the dilogarithm for real values. It is defined to be:\n\n$\\begin{equation} \\int_1^z \\frac{\\log(t)}{1 - t}dt \\end{equation}$\n\nUnlike the SciPy implementation, this is only defined for positive real values of z. For negative values, NaN is returned.\n\nParameters:\n\nz – An array of type float32, float64.\n\nReturn type:\n\nArray\n\nReturns:\n\nAn array with dtype=z.dtype. computed values of Spence’s function.\n\nRaises:\n\nTypeError – if elements of array z are not in (float32, float64).\n\nNotes: There is a different convention which defines Spence’s function by the integral:\n\n$\\begin{equation} -\\int_0^z \\frac{\\log(1 - t)}{t}dt \\end{equation}$\n\nthis is our spence(1 - z).\n\nParameters:\n\nx (Array) –" ]

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[ "Looking at Quantization Conditions, for a Wormhole Wavefunction, While Considering Differences between Magnetic Black Holes, Versus Standard Black Holes as Generating Signals from a Wormhole Mouth\nAbstract: We utilize how Weber in 1961 initiated the process of quantization of early universe fields to the problem of what may be emitted at the mouth of a wormhole. While the wormhole models are well developed, there is as of yet no consensus as to how, say GW or other signals from a wormhole mouth could be quantized or made to be in adherence to a procedure Weber cribbed from Feynman, in 1961. In addition, we utilize an approximation for the Hubble parameter parameterized from Temperature using Sarkar’s H ~ Temperature relations, as given in the text. We review what could be a game changer, i.e. magnetic black holes as brought up by Maldacena, in early 2021, at the mouth of the wormhole, and compare this with more standard black holes, at the mouth of a wormhole, while considering also the Bierman battery effect of an accreditation disk moving charges around a black hole as yet another way to have signals generated. The Maldacena article has good order of estimate approximations as to the strength of a magnetic monopole which we can use, and we also will go back to the signal processing effects which may be engendered by the Weber quantization of a wormhole to complete our model.\n\n1. Introduction\n\nThe template of what we will be looking at will be a wormhole, using a wavefunction quantization procedure, as given in which may also be enhanced by using the suggestion by as to a magnetic wormhole to generate fields for our perusal and signal generation edification. Keep in mind, that concludes as to the following “If Q is the integer magnetic charge, the fermions lead to order Q massless two-dimensional fermions moving along the magnetic field lines. These greatly enhance Hawking radiation effects”. Greatly enhanced Hawking radiation combined with Weber quantization of a wave functional may after certain tweaks allow for observable macroscopically detected quantum gravity effects. In doing so we also will be considering what if a wormhole also has black holes generating a magnetic field according to the Biermann battery effect, where moving charges in an accreditation disk outside the black hole generate a given magnetic field . This also can be compared with what will happen if we have higher dimensional black holes, not necessarily magnetic which can be affected by two different generalized uncertainty principles, whereas the higher dimensions of black hole in the mouth of the wormhole may also give verifiable quantum effects without the need of a magnetic field generating black hole in the mouth of a wormhole and also considering and issues, as in we have a way to make a temperature dependent estimation of effects, and we will be also examining conditions in which a BEC (Bose Einstein condensate) approximation of black holes is as condensate of gravitons in order to estimate in part optimal GW and graviton production from black holes in the mouth of the wormholes. Since Gravitons are quantum mechanical in origin, this will tie into Quantum Gravity in a very natural way . And as a bonus in the conclusion, as far as a black hole in the mouth of a wormhole picture, we will make use of the idea of comparing what we get as a signal from a wormhole mouth, with at least one black hole present to the issue brought up in of what happens if thermal quanta are mined from the so called “atmosphere” of a black hole as seen in page 340, Equation (8.119).\n\n2. That Business of the Weber Technique, Summarized\n\nWe bring up this study first a result given by Weber, in 1961 as to getting an initial wavefunction given in , which may be able to model behavior of what happens in the mouth of a wormhole if we assume as given in that H (Hubble’s parameter) is proportional to Temperature, and then go to Energy ~ Temperature. The last part will be enough to isolate, up to first principles a net frequency value.\n\nThe behavior of frequency, versus certain conditions at the mouth of a wormhole may give us clues to be investigated later as to polarization states relevant to the wormhole as well as examining what may be relevant to measurement of signals from a wormhole .\n\nIn doing all of this, the idea is that we are evolving from the Einstein-Rosen bridge to a more complete picture of GR which may entail a new representation of the Visser “Chronology protection” paper as in .\n\nWhat we are seeing is a version of convolution, which may allow for quantization.\n\n3. Looking at the Weber Book as to Reformulate Quantization Imposed Alteration of the Wave Function\n\nUsing a statement as to quantization for a would-be GR term comes straight from\n\n${\\Psi }_{\\text{Later}}=\\int \\underset{H}{\\sum }{\\text{e}}^{\\left(i{I}_{H}/\\hslash \\right)\\left(t,{t}^{0}\\right)}{\\Psi }_{\\text{Earlier}}\\left({t}^{0}\\right)\\text{d}{t}^{0}$ (1)\n\nThe approximation we are making is to pick one index, to have\n\n${\\Psi }_{\\text{Later}}=\\int \\underset{H}{\\sum }{\\text{e}}^{\\left(i{I}_{H}/\\hslash \\right)\\left(t,{t}^{0}\\right)}{\\Psi }_{\\text{Earlier}}\\left({t}^{0}\\right)\\text{d}{t}^{0}\\underset{H\\to 1}{\\to }\\int {\\text{e}}^{\\left(i{I}_{{H}_{\\text{FIXED}}}/\\hslash \\right)\\left(t,{t}^{0}\\right)}{\\Psi }_{\\text{Earlier}}\\left({t}^{0}\\right)\\text{d}{t}^{0}$ (2)\n\nThis corresponds to say being primarily concerned as to GW generation, which is what we will be examining in our ideas, via using\n\n${\\text{e}}^{\\left(i{I}_{{H}_{\\text{FIXED}}}/\\hslash \\right)\\left(t,{t}^{0}\\right)}=\\mathrm{exp}\\left[\\frac{i}{\\hslash }\\cdot \\frac{{c}^{4}}{16\\pi G}\\cdot \\underset{M}{\\int }\\text{d}t\\cdot {\\text{d}}^{3}r\\sqrt{-g}\\cdot \\left(\\Re -2\\Lambda \\right)\\right]$ (3)\n\nWe will use the following, namely, if $\\Lambda$ is a constant, do the following for the Ricci scalar \n\n$\\Re =\\frac{2}{{r}^{2}}$ (4)\n\nIf so then we can write the following, namely: Equation (3) becomes, if we have an invariant Cosmological constant, so we write $\\Lambda \\underset{\\text{alltime}}{\\to }{\\Lambda }_{0}$ everywhere, then\n\n${\\text{e}}^{\\left(i{I}_{{H}_{\\text{FIXED}}}/\\hslash \\right)\\left(t,{t}^{0}\\right)}=\\mathrm{exp}\\left[\\frac{i}{\\hslash }\\cdot \\frac{{c}^{4}\\cdot \\pi \\cdot {t}^{0}}{16G}\\cdot \\left(r-{r}^{3}{\\Lambda }_{0}\\right)\\right]$ (5)\n\nThen, we have that Equation (1) is re written to be\n\n$\\begin{array}{l}{\\Psi }_{\\text{Later}}=\\int \\underset{H}{\\sum }{\\text{e}}^{\\left(i{I}_{H}/\\hslash \\right)\\left(t,{t}^{0}\\right)}{\\Psi }_{\\text{Earlier}}\\left({t}^{0}\\right)\\text{d}{t}^{0}\\\\ \\underset{\\text{atwormhole}}{\\to }\\int \\mathrm{exp}\\left[\\frac{i}{\\hslash }\\cdot \\frac{{c}^{4}\\cdot \\pi \\cdot {t}^{0}}{16G}\\cdot \\left(r-{r}^{3}{\\Lambda }_{0}\\right)\\right]{\\Psi }_{\\text{Earlier}}\\left({t}^{0}\\right)\\text{d}{t}^{0}\\end{array}$ (6)\n\n4. Examining the Behavior of the Earlier Wavefunction in Equation (6)\n\n states a Hartle-Hawking wavefunction which we will adapt for the earlier wavefunction as stated in Equation (6) to read as follows\n\n${\\Psi }_{\\text{Earlier}}\\left({t}^{0}\\right)\\approx {\\Psi }_{HH}\\propto \\mathrm{exp}\\left(\\frac{-\\pi }{2G{H}^{2}}\\cdot {\\left(1-\\mathrm{sinh}\\left(Ht\\right)\\right)}^{3/2}\\right)$ (7)\n\nHere, making use of Sarkar , we set, if say ${g}_{\\ast }$ is the degree of freedom allowed \n\n$H=1.66\\sqrt{{g}_{\\ast }}{T}_{\\text{temp}}^{2}/{M}_{\\text{Planck}}$ (8)\n\nWe assume initially a relatively uniformly given temperature, that H is constant.\n\nSo then we will be attempting to write out an expansion as to what the Equation (6) gives us while we use Equation (7) and Equation (8), with H approximately constant. If so then.\n\n5. Method Used in Calculating Equation (6), with Interpretation of the Results\n\nWe will be considering how, to express Equation (6). And in doing this we will be looking at having a constant value for Equation (8). If so then using numerical integration, on page 751 of this citation\n\n$\\begin{array}{l}{\\Psi }_{\\text{Later}}\\underset{t{}_{M}\\to {\\epsilon }^{+}}{\\to }\\underset{0}{\\overset{{t}_{M}}{\\int }}{\\text{e}}^{i\\cdot \\left(\\stackrel{˜}{\\alpha }1\\right)\\cdot t-\\left(\\stackrel{˜}{\\alpha }2\\right)\\cdot {\\left(1-\\mathrm{sinh}\\left(Ht\\right)\\right)}^{3/2}}\\text{d}t\\\\ \\approx \\frac{{t}_{M}}{2}\\cdot \\left({\\text{e}}^{i\\cdot \\left(\\stackrel{˜}{\\alpha }1\\right)\\cdot {t}_{M}-\\left(\\stackrel{˜}{\\alpha }2\\right)\\cdot {\\left(1-\\mathrm{sinh}\\left(H\\cdot {t}_{M}\\right)\\right)}^{3/2}}-1\\right)\\\\ \\stackrel{˜}{\\alpha }1=\\left[\\frac{{c}^{4}\\cdot \\pi }{16G\\hslash }\\cdot \\left(r-{r}^{3}{\\Lambda }_{0}\\right)\\right],\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\stackrel{˜}{\\alpha }2=\\frac{\\pi }{2G{H}^{2}}\\end{array}$ (9)\n\n6. Using This Wavefunction in the Face of Choices for What Sort of Black Hole May Be in the Wormhole Mouth. Case 1, the Magnetic Monopole Based Black Hole as Given by Maldacena\n\nFirst, we should consider what to do if there is a Magnetic Black hole at the mouth of the wormhole. Then what if there is a Bierman battery generated B field. Then the case of when there is a non-B field generating black hole, which may (or may not) have higher dimensions. The first case to consider is what to do if there is a magnetic “monopole” based black hole generating magnetic field, using .\n\nIn the supposition is that the following will be used for a magnetic charge, as given by\n\n$e\\cdot |B|=\\frac{{e}^{2}}{2\\pi {l}_{P}^{2}Q}$ (10)\n\nHere, we have that the charge, Q as so stated by will lead to an energy, E\n\n$E\\left(\\text{black hole}\\right)\\approx {m}_{H}{Q}^{3/2}={m}_{H}\\cdot {\\left(\\frac{{e}^{2}}{2\\pi {l}_{P}^{2}\\cdot e\\cdot |B|}\\right)}^{3/2}$ (11)\n\nThe implication, rides as to the ${m}_{H}$ value picked which will be as the mass of the Higgs boson to be 125.35 GeV , whereas we can make use of a simple uncertainty principle to obtain a first order time contribution to the wave function Equation (9) above .\n\n$\\Delta t\\approx \\frac{\\hslash }{{m}_{H}}\\cdot {\\left(2\\pi {l}_{P}^{2}\\cdot {e}^{-1}\\cdot |B|\\right)}^{3/2}$ (12)\n\nThis value for time will be placed in Equation (9) above, whereas the time for initial formation of the uncertainty principle for the GUP as in and for refinement will be given in the concluding statements of this document, but it is interesting to note that the strength of a magnetic field, will determine the initial times step as in Equation (9). This magnetic field strength will also be commensurate with the issue of what may be expected in Graviton production due to a “flux” of black holes through/about the wormhole mouth. Note that the B field is not specified here, explicitly but is assumed to be a measurable conundrum to be faced by data set analysis. And to first order, according to the B field would\n\n$B=\\frac{\\aleph \\cdot \\sqrt{M}}{{r}^{2}}\\approx \\frac{{\\mu }^{0}{q}_{m}\\cdot \\sqrt{\\frac{{n}_{\\text{monopoles}}}{{\\rho }_{\\text{PBH}}}}\\cdot \\sqrt{M}}{4\\pi \\cdot {r}^{2}}$ (13)\n\nHere, ${n}_{\\text{monopoles}}$ is the number of magnetic monopoles associated with a magnetic black hole, while, ${q}_{m}$ is a unit of magnetic monopole charge, , and M is the mass of the black hole, and ${\\rho }_{\\text{PBH}}$ is the relevant density of black holes in a wormhole throat area. In addition, M is likely in this configuration to be of the order of 1 to a few Planck masses.\n\n7. What If We Have a Biermann Battery B Field Generation and We Are Looking at the Time Interval as Compared to Equation (12) for Equation (9) Wavefunction?\n\nIn the Biermann battery, the mere act of electric charges in an accreditation disk about a black hole will create magnetic fields. In the case of a magnetic monopole, the B field as for Equation (12) above at least for a short period of time, before decay of the magnetic black hole would be “approximately” constant. This in line with a charge, Q, not decaying rapidly as to what is seen in whereas one has the following situation, i.e.\n\nQuote\n\nHere we show that magnetic fields can be generated in initially unmagnetized accretion disks around PBHs through the Biermann battery mechanism, and therefore provide the small-scale seeds of magnetic field in the universe. The radial temperature and vertical density profiles of these disks provide the necessary conditions for the battery to operate naturally. The generated seed fields have a toroidal structure with opposite sign in the upper and lower half of the disk. In the case of a thin accretion disk around a rotating PBH, the field generation rate increases with increasing PBH spin. At a fixed r/risco, where r is the radial distance from the PBH and risco is the radius of the innermost stable circular orbit, the battery scales as M−9/4, where M is the PBH’s mass.\n\nEnd of quote\n\nThe idea here would be in moving electric charges in a dynamically rotating disc. If we ascertain what is relevant here, the Bierman battery would necessitate a movement beyond the innermost regime of the throat of the wormhole, and would necessitate interfacing with the shape function of the wormhole, as seen in .\n\nWhat and imply is that if one is in the restricted wormhole throat region, that the necessary accreditation disc for the Biermann battery would not form, but if the black hole were say a distance, after $\\Delta t$ traveling time past the wormhole throat then perhaps the geometry of a wormhole shape function would permit forming an accreditation disk, and have movement of electric charges, in a manner about a wormhole which would allow for a B field to form. In doing so, the B field for the accreditation disc would likely linearly grow, as of the form given by and what we have is that there would be a linear growth in the magnitude of the magnetic field, as given by\n\n$B\\left(t\\right)\\approx \\frac{{m}_{e}c}{e}\\cdot \\frac{{v}_{the}^{2}}{{L}_{t}{L}_{n}}\\cdot t$ (14)\n\nWith length of gradients (of material in the Biermann disc defined by)\n\n$\\begin{array}{l}{L}_{t}={T}_{e}/\\nabla T\\\\ {L}_{n}=n/\\nabla n\\end{array}$ (15)\n\nI.e. the B field would grow linearly, as the black hole exited the Wormhole throat regime, whereas we could have an overall magnitude of the B field as established by\n\n$\\frac{B}{\\sqrt{8\\pi {P}_{e}}}\\approx \\frac{c}{\\sqrt{2}\\cdot {L}_{n}\\cdot {\\omega }_{pe}}$ (16)\n\nwhere we would set $c/{\\omega }_{pe}$ as so-called electron inertial length, and ${\\omega }_{pe}$ as an electron plasma frequency\n\nMaking use of Equation (14) we could have a net magnetic field strength as looking like\n\n${E}_{p,m}=-m\\cdot B$ (17)\n\nwhere the term, m, in Equation (17) is a dipole moment, but we can get what we want via the old standby \n\n${\\rho }_{\\text{magnetic}}\\equiv \\frac{1}{2\\cdot \\mu }\\cdot {B}^{2}$ (18)\n\nwhereas we can, up to a point calculate the generated minimum uncertainty of energy and time via\n\n$\\left(\\frac{{V}_{\\text{volume}}}{2\\cdot \\mu }\\cdot {B}^{2}\\right)\\cdot \\Delta t\\approx \\frac{{V}_{\\text{volume}}}{2\\cdot \\mu }\\cdot {\\left(\\frac{{m}_{e}c}{e}\\cdot \\frac{{v}_{the}^{2}}{{L}_{t}{L}_{n}}\\cdot \\Delta t\\right)}^{2}\\cdot \\Delta t\\approx \\hslash$ (19)\n\nThen in this situation, unlike what is in Equation (12) and Equation (13) the Biermann battery approximation would yield an initial delta t value for Equation (9) which is not crazy. This would likely necessitate numerical simulation work. And\n\n$\\Delta t\\approx {\\left(\\frac{e\\cdot {L}_{t}{L}_{n}}{{v}_{the}^{2}\\cdot {m}_{e}c}\\right)}^{2/3}\\cdot {\\left(\\frac{2\\cdot \\mu }{{V}_{\\text{volume}}}\\right)}^{1/3}$ (20)\n\nObviously, the shape of the wormhole function would have to be employed to ascertain a value for ${\\left({V}_{\\text{volume}}\\right)}^{1/3}$. And we then would compare Equation (20) to Equation (13).\n\nNeedless to say, for this situation, the Biermann battery approximation for the magnetic field, for a black hole in a wormhole throat would have a linear link to time and would be growing and would NOT be constant which is tandem to using magnetic dipole approximations, whereas if we have a magnetic monopole, likely up to an initial approximation for the first iteration of Equation (9) the B field would be presentable as a constant. Then spatially it would be decreasing as given in Equation (13). i.e., in the Biermann approximation it is likely that the B field would grow linearly in time, t, whereas it would decrease\n\n8. Examining What to Expect in the Case of a Nonmagnetic Black Hole in a Wormhole Configuration of the Weight of about a Planck Mass\n\nSo far what we have done is to configure energy values associated with a black hole in the absence of, say a strong magnetic field.\n\nA black hole weighing 606,000 metric tons (6.06 × 108 kg) would have a Schwarzschild radius of (0.9 × 10−18 m), a power output of 160 petawatts (160 × 1015 W, or 1.6 × 1017 W), and a 3.5-year lifespan. This is without looking at say a magnetic field, Building on this, if we look at a Planck mass sized black hole, At this stage, a black hole would have a Hawking temperature of (5.6 × 1032 K), which means an emitted Hawking particle would have an energy comparable to the mass of the black hole. If so then the time\n\n$\\Delta t\\approx \\text{Planck time}={t}_{P}=\\sqrt{\\frac{\\hslash G}{{c}^{5}}}\\approx 5.391247\\left(60\\right)×{10}^{-44}\\text{ }\\text{s}$ (21)\n\nThis would be the unit of time placed into Equation (9) above, i.e. assuming we are not looking at magnetic fields, and black holes in the mouth of a wormhole.\n\nHaving specified the input of a brief time interval as to black holes through worm holes, let us guess what they should entail in terms of the number of black holes going through the wormhole mouth, First the case of nonmagnetic field black holes and their rate of production and flow through the wormhole mouth, and then the magnetic field Black hole case which is far harder. We begin with the easy case first.\n\n9. A First Order Guess as to the Rate of Production of Planck Sized Black Holes through a Wormhole, without Referring to Magnetic Fields\n\nIn order to do this, we will be estimating that the temperature would be of the order of Planck temperature, i.e. using ideas from \n\n$\\frac{{\\omega }_{p}}{{T}_{p}}\\equiv \\frac{\\sqrt{G{k}_{B}^{2}}}{\\hslash }\\underset{\\hslash =G={k}_{B}=1}{\\to }1$ (22)\n\nIf so, then there would be to first order the following rate of production\n\n${\\Gamma }_{\\text{rate of production}}\\approx e\\approx 2\\text{\\hspace{0.17em}}\\text{-}\\text{\\hspace{0.17em}}3$ (23)\n\nSome of the considerations given in this could be related to as an afterthought whereas the author in estimated for an LHC that there would be about 3000 gravitons produced per second. Assuming a figure from as to the percentage of black hole mass decaying into gravitons, i.e. , and i.e., 1/1000 of the mass of a Planck sized black hole would delve into gravitons, so if one had 3000 gravitons produced per second, as measured on Earth, one would likely have 2 - 3 black holes of mass of about 10^−5 grams per black hole, producing say 10^57 gravitons, produced per black hole of mass about 10^−62 grams per black hole \n\n$\\Gamma \\approx \\mathrm{exp}\\left({\\omega }_{\\text{signal}}/{T}_{\\text{temperature}}\\right)$ (24)\n\nwhereas we have from a probability for “scalar” particle production from the wormhole given by\n\n$\\Gamma \\approx \\mathrm{exp}\\left(-E/{T}_{\\text{temperature}}\\right)$ (25)\n\nWe next then examine what we can expect if we have black holes producing magnetic fields, and how that would change Equation (23) from considering Equation (24) as a template. Before doing so, let us review what can be stated as far as signal frequencies, as far as Equation (24) and a counterpart, for magnetic field generating black holes.\n\n10. Examining Signal Frequencies in the Case of a Magnetic Monopole Constituent Black Hole and Its Relevance to Black Hole Flux through a Wormhole “Mouth”\n\nAs stated in , page 10, the evaporation timescale of a Schwarzschild black hole of a given radii, of a given radius is Q times larger than the evaporation timescale of a charged (magnetically speaking) black hole. See whereas we also can look at the frequency via the following rule, which has on page 20, via Formula (7.4) and quoting \n\n$|\\omega |\\approx \\frac{{n}_{\\text{quantum}}+\\frac{1}{2}}{4GM}$ (26)\n\nwhereas if we look at what M is, in the case of magnetic black holes, there is in , page 10, Formula (4.1) a mass expression as to collapse to mass extremality for a black hole which we can write as\n\n$\\stackrel{˜}{M}=M-{M}_{e}\\propto \\mathrm{exp}\\left(-t/\\tau \\right)$ (27)\n\n$\\tau \\approx \\frac{8{\\pi }^{5/2}{Q}^{2}{l}_{P}}{3\\cdot \\left({{g}^{\\prime }}^{3}\\right)}$ (28)\n\nIf we make the substitution of $M\\to \\stackrel{˜}{M}$ in Equation (26) we arrive at\n\n$|\\omega |\\approx \\left(\\frac{{n}_{\\text{quantum}}+\\frac{1}{2}}{4G}\\right)\\cdot \\mathrm{exp}\\left(t/\\left\\{\\tau =\\left[\\frac{8{\\pi }^{5/2}{Q}^{2}{l}_{P}}{3\\cdot \\left({{g}^{\\prime }}^{3}\\right)}\\right]\\right\\}\\right)$ (29)\n\nIf ${n}_{\\text{quantum}}$ is set equal to zero, we have then that\n\n$|\\omega |\\approx \\frac{\\mathrm{exp}\\left(t/\\left\\{\\tau =\\left[\\frac{8{\\pi }^{5/2}{Q}^{2}{l}_{P}}{3\\cdot \\left({{g}^{\\prime }}^{3}\\right)}\\right]\\right\\}\\right)}{8G}$ (30)\n\nThe larger t gets, despite the value of Q, the larger the frequency, and we can then compare this Equation (30) with\n\n$\\omega \\approx \\frac{{m}_{H}{Q}^{3/2}}{\\hslash }=\\frac{{m}_{H}}{\\hslash }\\cdot {\\left(\\frac{{e}^{2}}{2\\pi {l}_{P}^{2}\\cdot e\\cdot |B|}\\right)}^{3/2}$ (31)\n\nThen\n\n$\\Gamma \\approx \\mathrm{exp}\\left(\\frac{{m}_{H}}{\\hslash T}\\cdot {\\left(\\frac{{e}^{2}}{2\\pi {l}_{P}^{2}\\cdot e\\cdot |B|}\\right)}^{3/2}\\right)$ (32)\n\nThis will lead to the production rate of Equation (32) being at least Q of Equation (23) per second.\n\nAt the same time, we have that also states that the time of decay decreased by 1/Q, for the black holes, with the time of decay for a non-Magnetic black hole given by, in extra dimensions, of value D\n\n$E~\\frac{\\text{}D{\\left(\\mathrm{dim}\\right)}^{2}}{4\\pi {R}_{H}}\\equiv \\frac{D{\\left(\\mathrm{dim}\\right)}^{2}{T}_{H}}{D\\left(\\mathrm{dim}\\right)-3}\\approx \\frac{\\hslash }{\\Delta t}$ (33)\n\nThen, roughly, the decay in the case of a magnetic field is to first approximation\n\n$\\Delta t\\approx \\frac{D\\left(\\mathrm{dim}\\right)-3}{D{\\left(\\mathrm{dim}\\right)}^{2}{T}_{H}\\cdot \\hslash }\\underset{\\text{Magnetic black hole}}{\\to }{Q}^{-1}\\cdot \\frac{D\\left(\\mathrm{dim}\\right)-3}{D{\\left(\\mathrm{dim}\\right)}^{2}{T}_{H}\\cdot \\hslash }$ (34)\n\nIf a Planck sized black hole disappears after delta t seconds, this means that the same Plank sized black hole will disappear in roughly delta t/Q seconds.\n\nWe will though when having this more rapid decay, have a situation for which there will be Q times the rate of black hole appearance in the throat of the wormhole as given in Equation (32). This is at least Q times the value of the rate of black hole appearance as given in Equation (23), hence the amount of transfer of the black hole stuff through the wormhole remains roughly invariant.\n\n11. Formal Bounding of the Cosmological Constant, in Terms of Two Wavefunctions Plus Analysis of Initial Wormhole Frequency Values\n\n$r\\equiv \\stackrel{⌢}{B}\\cdot {r}_{P}\\underset{{r}_{P}\\to 1}{\\to }\\stackrel{⌢}{B}$ (35)\n\nIf so, then we have the following bounding as far as the value of the cosmological “constant”, namely\n\n$\\begin{array}{l}{\\Psi }_{\\text{Later}}\\underset{t{}_{M}\\to {\\epsilon }^{+}}{\\to }\\underset{0}{\\overset{{t}_{M}}{\\int }}{\\text{e}}^{i\\cdot \\left(\\stackrel{˜}{\\alpha }1\\right)\\cdot t-\\left(\\stackrel{˜}{\\alpha }2\\right)\\cdot {\\left(1-\\mathrm{sinh}\\left(Ht\\right)\\right)}^{3/2}}\\text{d}t\\\\ \\approx \\frac{{t}_{M}}{2}\\cdot \\left({\\text{e}}^{i\\cdot \\left(\\stackrel{˜}{\\alpha }1\\right)\\cdot {t}_{M}-\\left(\\stackrel{˜}{\\alpha }2\\right)\\cdot {\\left(1-\\mathrm{sinh}\\left(H\\cdot {t}_{M}\\right)\\right)}^{3/2}}-1\\right)\\\\ {\\Psi }_{1,\\kappa =n=0}\\approx \\sqrt{\\frac{\\omega }{\\pi }}\\cdot \\left[\\frac{1}{\\omega +i\\cdot \\left(t+r\\right)}-\\frac{1}{\\omega +i\\cdot \\left(t-r\\right)}\\right]\\\\ \\stackrel{˜}{\\alpha }1=\\left[\\frac{{c}^{4}\\cdot \\pi }{16G\\hslash }\\cdot \\left(r-{r}^{3}{\\Lambda }_{0}\\right)\\right],\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\stackrel{˜}{\\alpha }2=\\frac{\\pi }{2G{H}^{2}}\\end{array}$ (36)\n\nWe will be looking at comparing the real values of Equation (36) to obtain a bound on the cosmological constant, to get a bound on the Cosmological constant as given by\n\n$\\begin{array}{l}{\\Lambda }_{0}\\approx {\\stackrel{˜}{B}}^{-2}-\\frac{16}{\\pi }\\cdot {\\stackrel{˜}{B}}^{-2}\\cdot \\left(\\stackrel{˜}{\\alpha }2\\cdot {\\left(1-\\mathrm{sinh}\\left(H\\cdot \\stackrel{˜}{B}\\right)\\right)}^{3/2}\\right)\\\\ \\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}-\\frac{16}{\\pi }\\cdot {\\stackrel{˜}{B}}^{-2}\\cdot {\\mathrm{cos}}^{-1}\\left[\\frac{2\\cdot {8}^{3/4}\\cdot {\\pi }^{1/4}}{8\\pi +{\\left(1+\\stackrel{˜}{B}\\right)}^{2}}-\\frac{2\\cdot {8}^{3/4}\\cdot {\\pi }^{1/4}}{8\\pi +{\\left(1-\\stackrel{˜}{B}\\right)}^{2}}\\right]\\end{array}$ (37)\n\nIn doing this, considering the Planck units and their normalization, we also need to keep in consideration the frequency, which we will denote here as\n\n${\\omega }_{\\text{signal}}\\approx \\frac{{k}_{B}\\cdot \\sqrt{{M}_{\\text{Planck}}H}}{\\hslash \\sqrt{1.66\\sqrt{{g}_{\\ast }}}}\\underset{\\hslash ={\\mathcal{l}}_{P}=G={t}_{P}={k}_{B}=1}{\\to }\\frac{\\sqrt{H}}{\\sqrt{1.66\\sqrt{{g}_{\\ast }}}}\\approx \\frac{{T}_{\\text{temperature}}}{2}$ (38)\n\nWhereas what we will be doing, after we obtain a frequency of a signal near the mouth of a wormhole is to use the following scaling of frequency, near Earth Orbit from this wormhole. First if the wormhole is right at the start of the Universe , we use\n\n$\\begin{array}{l}\\left(1+{z}_{\\text{initial era}}\\right)\\equiv \\frac{{a}_{\\text{today}}}{{a}_{\\text{initial era}}}\\approx {\\left(\\frac{{\\omega }_{\\text{Earth orbit}}}{{\\omega }_{\\text{initial era}}}\\right)}^{-1}\\\\ ⇒\\left(1+{z}_{\\text{initial era}}\\right){\\omega }_{\\text{Earth orbit}}\\approx {10}^{25}{\\omega }_{\\text{Earth orbit}}\\approx {\\omega }_{\\text{initial era}}\\end{array}$ (39)\n\nIf we are say far closer to the Earth, or the Solar system, then we would likely see \n\n$10\\cdot {\\omega }_{\\text{Earth orbit signal}}\\approx {\\omega }_{\\text{wormholemouthsignal}}$ (40)\n\nOur derivation so far is to obtain the initial signal frequency for Equation (39) and Equation (40). Our next task is to obtain some considerations as to the Polarization, of say GW to observe and look for, in conclusion of this document.\n\n12. The Big Picture, Polarization of Signals from a Wormhole Mouth May Affect GW Astronomy Investigations\n\nWe have a rate of production from the worm hole mouth we can quantify as\n\n$\\Gamma \\approx \\mathrm{exp}\\left({\\omega }_{\\text{signal}}/{T}_{\\text{temperature}}\\right)$ (41)\n\nwhereas we have from a probability for “scalar” particle production from the wormhole given by\n\n$\\Gamma \\approx \\mathrm{exp}\\left(-E/{T}_{\\text{temperature}}\\right)$ (42)\n\nwhereas if we assume that there is a “negative” temperature in Equation (41) and say rewrite Equation (42) as obeying having\n\n$\\left({\\omega }_{\\text{signal}}/{T}_{\\text{temperature}}\\right)\\approx \\left(-E/{T}_{\\text{temperature}}\\right)$ (43)\n\nThis is specifying a rate of particle production from the wormhole. And so then:\n\nWhereas what we are discussing in Equation (41) and Equation (42) is having a rate of, from a wormhole mouth, presumably from graviton production. If as an example, we are examining the mouth of a wormhole as being equivalent of a linkage between two black holes, or a black hole—white hole pair, we are presuming a release from the mouth of the wormhole commensurate with an eye to “white holes” for a black hole model as of probability for “scalar” particle production given as, if M is the mass of the black(white) hole, m is the mass of an emitted “particle”, $\\omega$ is frequency of emitted particles,\n\n$\\Gamma \\propto \\mathrm{exp}\\left(-8\\pi M\\cdot \\omega \\cdot \\left[1+\\frac{\\beta }{4}\\cdot \\left({m}^{2}+4{\\omega }^{2}\\right)\\right]\\right)$ (44)\n\nwhereas we define the parameter $\\beta$ via a modified energy expression, as in given by $\\stackrel{˜}{E}$ as a modified energy expression in \n\n$\\stackrel{˜}{E}=E\\cdot \\left(1-\\beta \\cdot \\left({p}^{2}+{m}^{2}\\right)\\right)$ (45)\n\nOur Equations (28), (41) and (42), which are for wormholes, as well as Equation (43) should encompass the same information of Equation (44) which would be consistent with a white hole at the mouth of a worm hole, as would be expected from Equation (44), whereas reviewing a linkage between black holes and white holes as may be for forming a wormhole may give more credence to the information loss criteria as given in .\n\nOur next step is to ask if this permits speaking of say GW polarization in the mouth of a worm hole. To do this, first of all, note that in that the simplest version of a worm hole is one of two universes connected by a “throat” of the form of a “ball” given by $\\pi {b}^{2}$, whereas the term b, is in a diagram, consigned to be the radius, or shape of the initial “ball” joining two “universes”.\n\nIn the case of extending b to become the “shape” of the mouth of a wormhole, we would likely be using for what is called by Visser the “shape” function of the wormhole , whereas what we are referring to in Equation (46) below comes straight from .\n\n$b\\left(r\\right)={\\left[{r}_{0}^{\\frac{\\gamma -1}{\\gamma }}+\\gamma \\cdot {\\frac{\\left(8\\pi G\\right)}{{\\stackrel{˜}{\\stackrel{˜}{\\omega }}}^{1/\\gamma }}}^{\\frac{\\gamma -1}{\\gamma }}\\cdot \\left({r}^{3}-{r}_{0}^{3}\\right)\\right]}^{\\frac{\\gamma }{\\gamma -1}}\\underset{r\\to {r}_{0}}{\\to }{r}_{0}$ (46)\n\nwhereas we need to keep in mind the equation of state for pressure and density of \n\n$p=\\stackrel{˜}{\\stackrel{˜}{\\omega }}\\left(r\\right)\\cdot \\rho$ (47)\n\nThe long and short of it is as follows. Following we have that\n\n${\\rho }_{\\stackrel{˜}{\\alpha }}=\\frac{M}{{\\left(4\\pi \\stackrel{˜}{\\alpha }\\right)}^{3/2}}\\cdot \\mathrm{exp}\\left(-{r}^{2}/4\\stackrel{˜}{\\alpha }\\right)$ (48)\n\nwhereas the b coefficient in the case of noncommutative geometry is chosen \n\n$\\begin{array}{c}b\\left(r\\right)=\\frac{2{r}_{s}}{\\sqrt{\\pi }}\\cdot \\stackrel{⌢}{\\gamma }\\left(\\frac{3}{2},\\frac{{r}^{2}}{4\\stackrel{˜}{\\alpha }}\\right)\\\\ \\equiv \\frac{2{r}_{s}}{\\sqrt{\\pi }}\\cdot {\\left(\\frac{{r}^{2}}{4\\stackrel{˜}{\\alpha }}\\right)}^{3/2}\\cdot \\stackrel{˜}{\\Gamma }\\left(3/2\\right)\\cdot {\\text{e}}^{-3/2}\\cdot \\underset{k=0}{\\overset{\\infty }{\\sum }}\\left(\\frac{{\\left(\\frac{{r}^{2}}{4\\stackrel{˜}{\\alpha }}\\right)}^{k}}{\\stackrel{˜}{\\Gamma }\\left(\\left(3/2\\right)+k+1\\right)}\\right)\\end{array}$ (49)\n\nThis is called the incomplete lower gamma function, with $\\stackrel{˜}{\\Gamma }$ being a gamma function .\n\nFrom here, using that Equation (49) is to be included in the following metric, as given by.\n\nThe coefficient $\\left[\\stackrel{˜}{\\alpha }\\right]=\\left[{r}^{2}\\right]$ in terms of dimensional analysis is chosen so that the dimensions of $\\left[\\stackrel{˜}{\\alpha }\\right]=\\left[{r}^{2}\\right]$ are chosen to contain M as mass in a wormhole.\n\ni.e., the denominator of Equation (48) ${\\left(4\\pi \\stackrel{˜}{\\alpha }\\right)}^{3/2}$ is chosen so that M is within the volume of space so subscribed. And this is for line element . With Equation (48) and Equation (49) fully described in and .\n\n$\\text{d}{S}^{2}=-\\mathrm{exp}\\left(-2\\Phi \\left(r\\right)\\right)\\text{d}{t}^{2}+\\frac{\\text{d}{r}^{2}}{1-b\\left(r\\right)/r}+{r}^{2}\\cdot \\left(\\text{d}{\\theta }^{2}+\\left({\\mathrm{sin}}^{2}\\theta \\right)\\text{d}{\\phi }^{2}\\right)$ (50)\n\nIf we refer to black holes, with extra dimension, n, of Planck sized mass, we have a lifetime of the value of about\n\n$\\begin{array}{l}\\tau ~\\frac{1}{{M}_{*}}{\\left(\\frac{{M}_{\\text{BH}}}{{M}_{*}}\\right)}^{\\frac{n+3}{n+1}}\\underset{{M}_{\\text{BH}}\\approx {M}_{\\text{Planck}}}{\\to }{10}^{-26}\\text{ }\\text{seconds}\\\\ {M}_{*}\\text{\\hspace{0.17em}}\\text{isthelowenergyscale},\\text{}\\\\ \\text{whichcouldbeaslowasafewTeV},\\end{array}$ (51)\n\nThe idea would be that there would be n additional dimensions, as given in Equation (51) which would then lay the door open to investigating and in terms of applications, with of additional polarization states to be investigated, as to signals from the mouth of the wormhole. We will next then go into some predictions into first, the strength of the signals, the frequency range, and several characteristics as to the production rate of Planck sized black holes.\n\n13. Conclusion: A First Order Guess as to the Rate of Production of Planck Sized black Holes through a Wormhole\n\nTo do this, we will be estimating that the temperature would be of the order of Planck temperature, i.e., using ideas from and \n\n$\\frac{{\\omega }_{p}}{{T}_{p}}\\equiv \\frac{\\sqrt{G{k}_{B}^{2}}}{\\hslash }\\underset{\\hslash =G={k}_{B}=1}{\\to }1$ (52)\n\nIf so, then there would be to first order the following rate of production\n\n${\\Gamma }_{\\text{rate of production}}\\approx e\\approx 2\\text{\\hspace{0.17em}}\\text{-}\\text{\\hspace{0.17em}}3$ (53)\n\nSome of the considerations given in this could be related to as an afterthought whereas the author in estimated for an LHC that there would be about 3000 gravitons produced per second. Assuming a figure from as to the percentage of black hole mass decaying into gravitons, i.e. , i.e., 1/1000 of the mass of a Planck sized black hole would delve into gravitons, so if one had 3000 gravitons produced per second, as measured on Earth, one would likely have 2 - 3 black holes of mass of about 10^−5 grams per black hole, producing say 10^57 gravitons, produced per black hole of mass about 10^−62 grams per black hole \n\nHaving said, that what about frequencies? Here, if we have a wormhole throat of about 2 - 3 Planck lengths in diameter, with a frequency of emitted gravitons of about 1019 GHz initially, it is realistic, using the following, to expect in many cases a redshift downscaling of frequencies of about 10^−18, if the worm holes are close to the initial near singularity, so then that we could be looking at approximately 10 to 12 GHz, on Earth, for frequencies, of initially about 10^19 GHZ. So then note at inflation we have\n\n$\\begin{array}{l}\\left(1+{z}_{\\text{initial era}}\\right)\\equiv \\frac{{a}_{\\text{today}}}{{a}_{\\text{initial era}}}\\approx {\\left(\\frac{{\\omega }_{\\text{Earth orbit}}}{{\\omega }_{\\text{initial era}}}\\right)}^{-1}\\\\ ⇒\\left(1+{z}_{\\text{initial era}}\\right){\\omega }_{\\text{Earth orbit}}\\approx {10}^{25}{\\omega }_{\\text{Earth orbit}}\\approx {\\omega }_{\\text{initial era}}\\end{array}$ (54)\n\nIn our situation, the figure would likely be instead of 10^25 times Earth orbit detected frequency, something closer to 10^18 to 10^19 times Earth orbit GW frequencies detected as given by . The relative GW strength of the signal, if one uses while assuming approximately 10 to 12 GHz, for initially about 10^19 GHz GW signals would be about h ~ 10^−26 and this could change an order of magnitude given instrument sensitivity. In any case it would be well worth our while to look closely at for additional clues and insights to consider while commencing this investigation, as well as details given in . Finally, the references - are referencing situations which are natural extensions of this present document and which will be used in future publications. We include them for the readers to review as to consider on their own what may be following up to our first order approximations given for Equation (52), Equation (53) and Equation (54).\n\nCite this paper: Beckwith, A. (2022) Looking at Quantization Conditions, for a Wormhole Wavefunction, While Considering Differences between Magnetic Black Holes, Versus Standard Black Holes as Generating Signals from a Wormhole Mouth. Journal of High Energy Physics, Gravitation and Cosmology, 8, 67-84. doi: 10.4236/jhepgc.2022.81005.\nReferences\n\n   Weber, J. (2004) General Relativity and Gravitational Waves. Dover Publications, Incorporated, Mineola.\n\n   Maldacena, J. 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Annual Review of Nuclear and Particle Science, 70, 355-394.\nhttps://arxiv.org/abs/2006.02838\nhttps://doi.org/10.1146/annurev-nucl-050520-125911\n\n   Giddings, S.B. and Mangano, M.L. (2008) Astrophysical Implications of Hypothetical Stable TeV-Scale Black Holes. Physical Review D, 78, Article ID: 035009.\nhttps://doi.org/10.1103/PhysRevD.78.035009\n\n   Shao, L., Wex, N. and Zhou, S.-Y. (2020) New Graviton Mass Bound from Binary Pulsars. Physical Review D, 102, Article ID: 024069.\nhttps://arxiv.org/abs/2007.04531\nhttps://doi.org/10.1103/PhysRevD.102.024069\n\n   Bonanno, A. and Reuter, M. (2006) Spacetime Structure of an Evaporating Black Hole in Quantum Gravity. Physical Review D, 73, Article ID: 083005.\nhttps://doi.org/10.1103/PhysRevD.73.083005\n\n   Perkins, S. and Yunes, N. (2019) Probing Screening and the Graviton Mass with Gravitational Waves. Classical and Quantum Gravity, 36, Article ID: 055013.\nhttps://arxiv.org/abs/1811.02533\nhttps://doi.org/10.1088/1361-6382/aafce6\n\n   Maggiore, M. (2008) Gravitational Waves, Volume 1: Theory and Experiment. Oxford University Press, Oxford.\n\n   Hawking, S. and Ellis, G.F.R. (1973) The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge.\nhttps://doi.org/10.1017/CBO9780511524646\n\n   Shin’ichi Nojiri, S.D., Odintsov, V.K. and Oikonomou, T.P. (2019) Nonsingular Bounce Cosmology from Lagrange Multiplier F(R) Gravity. Physical Review D, 100, Article ID: 084056.\nhttps://arxiv.org/abs/1910.03546\nhttps://doi.org/10.1103/PhysRevD.100.084056\n\n   Wang, Q., Zhu, Z. and Unruh, W.G. (2017) How the Huge Energy of Quantum Vacuum Gravitates to Drive the Slow Accelerating Expansion of the Universe. Physical Review D, 95, Article ID: 103504. arXiv:1703.00543.\nhttps://doi.org/10.1103/PhysRevD.95.103504\n\n   Astier, P., Guy, J., Regnault, N., Pain, R., Aubourg, E., Balam, D., Basa, S., et al. (2006) The Supernova Legacy Survey: Measurement of ΩM, ΩΛ and W from the First Year Data Set. Astronomy & Astrophysics, 447, 31-48. arXiv:astro-ph/0510447.\nhttps://doi.org/10.1051/0004-6361:20054185\n\n   Chen, P. (1994) Resonant Photon-Graviton Conversion in EM Fields: From Earth to Heaven. SLAC PUB 6666 T/E/A).\nhttps://www.slac.stanford.edu/pubs/slacpubs/6500/slac-pub-6666.pdf\n\nTop" ]

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[ "# A resistance is shown in the figure. Its value and tolerance are given respectively by:\n\nmore_vert\n\nA resistance is shown in the figure. Its value and tolerance are given respectively by:", null, "(1) 27 k$\\Omega$, 20%\n\n(2) 270 k$\\Omega$, 5%\n\n(3) 270 k$\\Omega$, 10%\n\n(4) 27 k$\\Omega$, 10%\n\nmore_vert\n\nverified\n\nAns: (4) 27 k$\\Omega$, 10%\n\nSol: Color code :\n\nRed violet orange silver\n\nR = 27 × 103 $\\Omega$ ± 10%\n\n= 27 k$\\Omega$ ± 10%" ]

[ null, "https://jeeneetqna.in/", null ]

[ "## ››Convert pound/square inch to millitorr\n\n pound/square inch millitorr\n\nThe above form works if you are measuring differential pressure, such as the difference in psi between two points. It also gives the correct answer for absolute pressure, assuming you are measuring psia, which is the pressure relative to absolute zero vacuum.\n\nIf you are measuring relative to vacuum and want to resolve the pressure relative to the atmosphere, then you should use the form below.\n\npound/square inch (relative to atmosphere)\nmillitorr (relative to vacuum)\n\n Did you mean to convert pound/square inch pound/square inch [gauge] pound/square inch [absolute] to millitorr\n\nHow many pound/square inch in 1 millitorr? The answer is 1.9336774970561E-5.\nWe assume you are converting between pound/square inch and millitorr.\nYou can view more details on each measurement unit:\npound/square inch or millitorr\nThe SI derived unit for pressure is the pascal.\n1 pascal is equal to 0.00014503773800722 pound/square inch, or 7.5006167382113 millitorr.\nNote that rounding errors may occur, so always check the results.\nUse this page to learn how to convert between pounds/square inch and millitorr.\nType in your own numbers in the form to convert the units!\n\n## ››Quick conversion chart of pound/square inch to millitorr\n\n1 pound/square inch to millitorr = 51714.93186 millitorr\n\n2 pound/square inch to millitorr = 103429.86372 millitorr\n\n3 pound/square inch to millitorr = 155144.79558 millitorr\n\n4 pound/square inch to millitorr = 206859.72744 millitorr\n\n5 pound/square inch to millitorr = 258574.6593 millitorr\n\n6 pound/square inch to millitorr = 310289.59116 millitorr\n\n7 pound/square inch to millitorr = 362004.52302 millitorr\n\n8 pound/square inch to millitorr = 413719.45488 millitorr\n\n9 pound/square inch to millitorr = 465434.38674 millitorr\n\n10 pound/square inch to millitorr = 517149.3186 millitorr\n\n## ››Want other units?\n\nYou can do the reverse unit conversion from millitorr to pound/square inch, or enter any two units below:\n\n## Enter two units to convert\n\n From: To:\n\n## ››Definition: Pound/square inch\n\nThe pound per square inch or, more accurately, pound-force per square inch (symbol: psi or lbf/in² or lbf/in²) is a unit of pressure or of stress based on avoirdupois units. It is the pressure resulting from a force of one pound-force applied to an area of one square inch.\n\n## ››Definition: Millitorr\n\nThe SI prefix \"milli\" represents a factor of 10-3, or in exponential notation, 1E-3.\n\nSo 1 millitorr = 10-3 torrs.\n\nThe definition of a torr is as follows:\n\nThe torr is a non-SI unit of pressure, named after Evangelista Torricelli. Its symbol is Torr.\n\n## ››Metric conversions and more\n\nConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3\", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!" ]

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[ "Cody\n\n# Problem 1558. Power The Product\n\nEXAMPLE: INPUT x=10 & y=10 OUTPUT z=1000000 or, INPUT x=2 & y=3 OUTPUT z= 216 you just need to calculate the product first then find the value of the power.\n\n### Solution Stats\n\n40.43% Correct | 59.57% Incorrect\nLast Solution submitted on Dec 02, 2019" ]

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[ "", null, "C Programming MCQ Questions | c interview questions\n\nIntroduction\n\nIn this article, you will find basic to most puzzled interview queries questions. This article is very useful for those who are preparing for an interview in IT company. Whether you are experienced or\n\n1) What are the types of linkages in C programming language?\n1. Internal\n2. External and None.\n3. External, Internal and None.\n4. Internal and External.\n\n⇒ Answer: (C) External, Internal and None.\n\n2) Which of the following special symbol allowed in C programming language variable name?\n1. _ (underscore)\n2. - (hyphen)\n3. | (pipeline)\n4. * (asterisk)\n\n⇒ Answer: (A) _ (underscore).\n\n3) Which of the following statements should be used in C programming to obtain a remainder after dividing 4.14 by 2.3 ?\n1. rem = fmod(3.14, 2.1);\n2. rem = modf(3.14, 2.1);\n3. rem = 3.14 % 2.1;\n4. Remainder cannot be obtain in floating point division.\n\n⇒ Answer: (A) rem = fmod(3.14, 2.1);\n\n4) Which of the following is true for variable names in C programming language?\n1. Variable can be of any length\n2. Variable names cannot start with a digit\n3. It is not an error to declare a variable to be one of the keywords(like goto, static)\n4. They can contain alphanumeric characters as well as special characters.\n\n⇒ Answer: (B) Variable names cannot start with a digit\n\n5) Which of the following is not a valid C programming language variable name?\n1. int \\$main;\n2. int variable_count;\n3. float rate;\n4. int number;\n\n⇒ Answer: (A) int \\$main;\n\n6) What will be the output of the following C code?\n\n1. #include <stdio.h>\n2. int main()\n3. {\n4. printf(\"Hello World! %d \\n\", a);\n5. return 0;\n6. }\n1. Hello World!\n2. Compile time error\n3. Hello World! followed by a junk value\n4. Hello World! a;\n\n⇒ Answer: (B) Compile time error\n\nExplanation: since a is used without declaring the variable a.\n\n7) What will be the output of the following C code?\n\n1. #include <stdio.h>\n2. int main()\n3. {\n4. int a = 10000;\n5. int a = 34;\n6. printf(\"Hello World! %d\\n\", a);\n7. return 0;\n8. }\n1. Hello World! followed by a junk value\n2. Hello World! 1000\n3. Hello World! 34\n4. Compile time error\n\n⇒ Answer: (D) Compile time error\n\nExplanation: Since a is already defined, redefining variable a results in an error.\n\n8) What will be the output of the following C code?\n\n1. #include <stdio.h>\n2. int main()\n3. {\n4. int a = 10000;\n5. int a = 34;\n6. printf(\"Hello World! %d\\n\", a);\n7. return 0;\n8. }\n1. 10\n2. 20\n3. The program will have a runtime error\n4. Compile time error\n\n⇒ Answer: (A) Variable names Number and number are both distinct as C is case sensitive programming language.\n\n9) What will be the output of the following C code?\n\n1. #include <stdio.h>\n2. int main()\n3. {\n4. int main = 20;\n5. printf(\"%d\", main);\n6. return 0;\n7. }\n1. It will experience infinite looping\n2. It will run without any error and prints 20\n3. It will cause a run-time error\n4. It will cause a compile-time error\n\n⇒ Answer: (B) It will run without any error and prints 20\n\n10) Which of the following is not a valid variable name declaration in C programming language?\n\n1. #include <stdio.h>\n2. int main()\n3. {\n4. int main = 20;\n5. printf(\"%d\", main);\n6. return 0;\n7. }\n1. #define PI 3.14\n2. int PI = 3.14;\n3. double PI = 3.14;\n4. float PI = 3.14;\n\n⇒ Answer: (A) #define PI 3.14" ]

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[ "# Mathematical background – Part 1 - PowerPoint PPT Presentation", null, "", null, "Download Presentation", null, "Mathematical background – Part 1\n\nMathematical background – Part 1\nDownload Presentation", null, "## Mathematical background – Part 1\n\n- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -\n##### Presentation Transcript\n\n1. Mathematical background – Part 1 Miloš Nováček Chair of Programming Methodology [email protected]\n\n2. Classes • Every Tuesday 1pm – 2pm (starting 1.15pm) • Hand in your solution to me via email [email protected] by Monday 9am • Homework is optional but helpful • You can submit also partial solutions • Master solutions and slides from classes will be published after each class on the course web-page http://www.pm.inf.ethz.ch/education/courses/spa/exercises • Feedback!!!\n\n3. Any questions about the content of the last lecture?\n\n4. Exercise 1 Show that on is a partial order.\n\n5. on is a partial order • As pointed out by Stephan at the lecturewe can use the above definition and use the fact that logical implication () is already partial order. Hence, we have a one step proof. • Definition of\n\n6. Exercise 1 - proof • By definition of partial order, prove that • is reflexive • is antisymmetric • Statement: • Proof: By definition of, we have to prove that. • This is true since trivially implies that , so the right side of the implication is true. • Statement: • Proof: • Therefore, we have • Hence, .\n\n7. Exercise 1 – proof (cont’d) • is transitive • Hence, on is a partial order. • Statement: • Proof: By definition of, we know that • Therefore, by transitive property of logical implication we know that • that, by definition of, means that\n\n8. Exercise 2 Show that the inverse of a partial order on a set is a partial order on . Notation:\n\n9. Inverse relation Definition: Let be a binary relation. Then is an inverse relation of the relation . Furthermore, .\n\n10. Exercise 2 - proof • Let be a poset. Then we need to show that the inverse relation • is reflexive • is antisymmetric • Statement: • Proof: Since than so by the definition of an inverse relation • Statement: • Proof: • Let and . • Then and . • Hence, by antisymmetry of .\n\n11. Exercise 2 – proof (cont’d) • is transitive • Hence, inverse of a partial order on a set is a partial order on . • Statement: • Proof: By definition of , we know that • Therefore, by transitivity of , we know that . • Hence, by the definition of the inverse of a relation.\n\n12. Exercise 3 Show that is glb of .\n\n13. Exercise 3 - proof • is the glb of iff: • (lower bound) • (greatest) • is glb of • Statement: • Proof: By definition of • If then , that is, . • By definition of , and . • Statement • Proof: • Combining:By def. of: • By def. of we have that Can also be proven by contradiction.\n\n14. Questions?" ]

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[ "views updated\n\n# TURáN, PAUL\n\n(b. Budapest, Hungary, 28 August 1910; d. Budapest, 26 September 1976)\n\nmathematics.\n\nTurán was the eldest son of Aranha Beck and Béla Turán. He had two brothers and a sister, none of whom survived World War II. While in high school he showed considerable mathematical ability. Turán received his teaching diploma in 1933 and his Ph.D. (under Lipöt Féjer) at Pázmány Páter University, Budapest, in 1935. Because of the semi-fascist conditions in Hungary, Turán, who was Jewish, could not obtain a post even as high school teacher, and had to support himself by private tutoring. In 1938, when he was an internationally known mathematician, he finally became a teacher in the Budapest rabbinical high school.\n\nAfter thirty-two months in a Nazi labor camp in Hungary in the years 1941–1944, Turán was liberated. He became a Privatdozent at the University of Budapest. In 1947 he went to Denmark for about six months and then spent six months at the Institute for Advanced Study at Princeton (during this period he completed two papers on polynomials and number theory). In 1948 he was elected corresponding member of the Hungarian Academy of Sciences, and became a full member in 1953. In 1948 and 1952 he received the Kossuth Prize, the highest scientific award in Hungary at that time. He became a full professor at the University of Budapest in 1949 and was the head of the department of algebra and number theory at the university and the head of the department of the theory of functions at the Mathematical Institute of the Hungarian Academy of Sciences.\n\nTurán’s first major result, produced when he was twenty-four, was his simple proof of the Hardy-Ramanujan result that the number of prime factors of almost all integers is (1 + 0(l))loglog n. Further developments led to the Turán-Kubilius inequality, one of the starting points of probabilistic number theory.\n\nBy 1938 Turán had developed the basic ideas of his most important work, the power-sum method, on which he published some fifty papers, both alone and with collaborators (Stanislav Knapowski, Vera T. Sós [his wife], János Ptntz. Gabor Halász, and Istvàn Danes, among others). Turán worked on the power-sum method until his death (his last paper was a survey of the application of the method in explicit formulas for prime numbers). The method has its most significant applications in analytic number theory, but it also led to many important applications in the theory of differential equations, complex function theory, numerical algebra (approximative solution of algebraic equations), and theory of trigonometric series. Tur´n devoted three books (with the same title but different—increasingly rich—contents) to this subject. The last and most comprehensive one, On a New Method in Analysis and Its Applications, was published in 1984.\n\nThe essence of the method is to show that the power sum of n arbitrary complex numbers z1, . . ., zn—that is, the sum —cannot be small for all v (compared with the maximal or minimal term, say). In fact, to cite just one (perhaps the most important) result of this theory, choosing v suitably from any interval of length n, we have\n\nIn order to understand this estimate, it should be noted that g(m + 1)= g(m + 2) = . . . g(m + n - 1) = 0 is certainly possible—for instance, the zj’s are nth roots of unity. Similar results can be proved if we consider generalized power sums of the type , supposing very general conditions on the coefficients bj.\n\nTo give an idea of the connection between the theory and its applications, it should be noted that these oscillatory results concerning power sums of complex numbers lead directly to oscillatory results on the solutions of some differential equations; but through a rather sophisticated technique (developed by Turán and Knapowski), via the connection of zeros of Riemann’s zeta function and primes, it is also possible to detect irregularities in the distribution of primes using these results. The variety of known applications is so rich that it is difficult to mention any area of classical analysis where the method would have no possible applications.\n\nIn 1952 Turán wrote a book in Hungarian and German on the power-sum method. A Chinese translation with some new results of this work appeared in 1954. An English version. On a New Method of Analysis and Application, completed by Halász and Pintz, appeared in 1984.\n\nBesides his power-sum method, Turán did work in comparative prime number theory, analytic and quasi-analytic functions, differential equations, and other areas of analysis. In comparative prime number theory inequalities about the distribution of primes in different arithmetic progressions are studied. The subject goes back to Pafhuty Chebyshev and Edmund Landau, but Tur´n and Knapowski (his student and collaborator, who died young) developed it into a systematic theory.\n\nAn elementary power-sum problem posed by Turán in 1938 is the following:\n\nLet |z1|= 1, |zi| ≤ 1 (1 < i < n) be n complex numbers.\n\nLet where max ∣sλ∣ = f(z1, . . . . zn).\n\nTurán conjectured first of all that f(n) > c for all n. This was proved by F. V, Atkinson in 1960.\n\nTurán further conjectured that This problem is still open.\n\nExtremal graph theory was begun by Turán while he was in a labor camp. He wrote the first paper on this subject, and several more followed. Finally he gave birth to statistical group theory, in which he wrote seven fairly substantial papers with the author of this essay.\n\nPaul ErdÖs" ]

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[ "If you're seeing this message, it means we're having trouble loading external resources on our website.\n\nХэрэв та вэб шүүлтүүртэй газар байгаа бол домэйн нэрийг *.kastatic.org and *.kasandbox.org блоклосон эсэхийг нягтална уу.\n\nҮндсэн товъёог\n\n# Age word problem: Imran\n\n## Video transcript\n\nWe're told that in 40 years, Imran will be 11 times as old as he is right now. And then we're asked, how old is he right now? And so I encourage you to try this on your own. Well, let's see if we can set this up as an equation. So let's figure out what our unknown is first. Well, our unknown is how old he is right now. I'm just arbitrarily using x. We always like to use x. But I could've really set it to be anything. But let's say x is equal to how old he is right now. How old-- not how hold. How old he is now. Now, what do we know about how old he will be in 40 years? Well, he's going to be how old he is now plus 40. So let me write that down. So in 40 years Imran is going to be x plus 40, plus this 40 right over here. But they give us another piece of information. This by itself isn't enough to figure out how old he is right now. But they tell us in 40 years, Imran will be 11 times as old as he is right now. So that's saying that this quantity right over here, x plus 40, is going to be 11 times x. In 40 years, he's going to be 11 times as old as he is right now. So this is going to be times 11. You take x, multiply it times 11, you're going to get how old he's going to be in 40 years. So let's write that down as an equation. You take x, multiply it by 11, so 11 times as old as he is right now is how old he is going to be in 40 years. And we have set up a nice little, tidy linear equation now. So we just have to solve for x. So let's get all the x's on the left-hand side. We have more x's here than on the right-hand side. So we avoid negative numbers, let's stick all the x's here. So if I want to get rid of this x on the right hand side, I'd want to subtract an x. But obviously, I can't just do it to the right. Otherwise, the equality won't be true anymore. I need to do it on the left as well. And so I am left with-- if I have 11 of something and I take away 1 of them, I'm left with 10 of that something. So I'm left with 10 times x is equal to-- well, these x's, x minus x is just 0. That was the whole point. It's going to be equal to 40. And you could do this in your head at this point, but let's just solve it formally. So if we want a 1 coefficient here, we'd want to divide by 10, but we've got to do that to both sides. And so we are left with-- and we could have our drum roll now. We are left with x is equal to 4 years old. x is equal to 4. So our answer to the question, how old is Imran right now? He is 4 years old. And let's verify this. If he's 4 years old right now, in 40 years he's going to be 44 years old. And 44 years old is indeed 11 times older than 4 years old. This is a factor of 11 years, so it all worked out." ]

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[ "# Number systems presentation\n\n• View\n1.050\n\n2\n\nTags:\n\nEmbed Size (px)\n\nDESCRIPTION\n\n### Text of Number systems presentation\n\n• Used by Used inSystem Base Symbols humans? computers?Decimal 10 0, 1, 9 Yes NoBinary 2 0, 1 No YesOctal 8 0, 1, 7 No NoHexa- 16 0, 1, 9, No Nodecimal A, B, F\n• Hexa-Decimal Binary Octal decimal 0 0 0 0 1 1 1 1 2 10 2 2 3 11 3 3 4 100 4 4 5 101 5 5 6 110 6 6 7 111 7 7\n• Hexa-Decimal Binary Octal decimal 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F\n• Hexa-Decimal Binary Octal decimal 16 10000 20 10 17 10001 21 11 18 10010 22 12 19 10011 23 13 20 10100 24 14 21 10101 25 15 22 10110 26 16 23 10111 27 17 Etc.\n• The possibilities: Decimal Octal Binary Hexadecimal pp. 40-46\n• 2510 = 110012 = 318 = 1916 Base\n• Decimal OctalBinary Hexadecimal Next slide\n• Weight12510 => 5 x 100 = 5 2 x 101 = 20 1 x 102 = 100 125 Base\n• Technique Multiply each bit by 2n, where n is the weight of the bit The weight is the position of the bit, starting from 0 on the right Add the results\n• Bit 01010112 => 1 x 20 = 1 1 x 21 = 2 0 x 22 = 0 1 x 23 = 8 0 x 24 = 0 1 x 25 = 32 4310\n• Technique Multiply each bit by 8n, where n is the weight of the bit The weight is the position of the bit, starting from 0 on the right Add the results\n• 7248 => 4 x 80 = 4 2 x 81 = 16 7 x 82 = 448 46810\n• Technique Multiply each bit by 16n, where n is the weight of the bit The weight is the position of the bit, starting from 0 on the right Add the results\n• ABC16 => C x 160 = 12 x 1 = 12 B x 161 = 11 x 16 = 176 A x 162 = 10 x 256 = 2560 274810\n• Technique Divide by two, keep track of the remainder First remainder is bit 0 (LSB, least-significant bit) Second remainder is bit 1 Etc.\n• 12510 = ?2 2 125 2 62 1 2 31 0 2 15 1 2 7 1 2 3 1 2 1 1 0 1 12510 = 11111012\n• Technique Convert each octal digit to a 3-bit equivalent binary representation\n• 7058 = ?2 7 0 5 111 000 101 7058 = 1110001012\n• Technique Convert each hexadecimal digit to a 4-bit equivalent binary representation\n• 10AF16 = ?2 1 0 A F 0001 0000 1010 1111 10AF16 = 00010000101011112\n• Technique Divide by 8 Keep track of the remainder\n• 123410 = ?8 8 1234 8 154 2 8 19 2 8 2 3 0 2 123410 = 23228\n• Technique Divide by 16 Keep track of the remainder\n• 123410 = ?16 16 1234 16 77 2 16 4 13 = D 0 4 123410 = 4D216\n• Technique Group bits in threes, starting on right Convert to octal digits\n• 10110101112 = ?8 1 011 010 111 1 3 2 7 10110101112 = 13278\n• Technique Group bits in fours, starting on right Convert to hexadecimal digits\n• 10101110112 = ?16 10 1011 1011 2 B B 10101110112 = 2BB16\n• Technique Use binary as an intermediary\n• 10768 = ?16 1 0 7 6 001 000 111 110 2 3 E 10768 = 23E16\n• Technique Use binary as an intermediary\n• 1F0C16 = ?8 1 F 0 C 0001 1111 0000 1100 1 7 4 1 4 1F0C16 = 174148\n• Hexa-Decimal Binary Octal decimal 33 1110101 703 1AF Dont use a calculator! Skip answer Answer\n• Answer Hexa-Decimal Binary Octal decimal 33 100001 41 21 117 1110101 165 75 451 111000011 703 1C3 431 110101111 657 1AF\n• Base 10 Power Preface Symbol Value 10-12 pico p .000000000001 10-9 nano n .000000001 10-6 micro .000001 10-3 milli m .001 103 kilo k 1000 106 mega M 1000000 109 giga G 1000000000 1012 tera T 1000000000000\n• Base 2 Power Preface Symbol Value 210 kilo k 1024 220 mega M 1048576 230 Giga G 1073741824 What is the value of k, M, and G? In computing, particularly w.r.t. memory, the base-2 interpretation generally applies\n• In the lab1. Double click on My Computer2. Right click on C:3. Click on Properties / 230 =\n• Determine the free space on all drives on a machine in the lab Free space Drive Bytes GB A: C: D: E: etc.\n\nRecommended", null, "##### Number Systems and Codes. CS2100 Number Systems and Codes 2 NUMBER SYSTEMS & CODES Information Representations Number Systems Base Conversion Negative\nDocuments", null, "##### Unit 7 Number Systems and Bases Presentation 1Binary and Base 10 Presentation 2Adding Binary Numbers Presentation 3Subtracting Binary Numbers Presentation\nDocuments", null, "##### Number Systems and Number .Number Systems and Number Representation. 1. Princeton University. Computer\nDocuments", null, "##### NUMBER SYSTEMS CONCEPTS Systems...Number Systems Page 2 Number Systems Concepts The study of number\nDocuments", null, "Documents" ]

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[ "top of page\n\n## Overview\n\n###### Likelihood Methods for Measuring Statistical Evidence\n\nScience looks to Statistics for an objective measure of the strength of evidence in a given body of observations. The Law of Likelihood (LL) provides an answer; it explains how data should be interpreted as statistical evidence for one hypothesis over another. Although likelihood ratios figure prominently in both Frequentist and Bayesian methodologies, they are neither the focus nor the endpoint of either methodology. A defining characteristic of the Likelihood paradigm is that the measure of the strength of evidence is decoupled from the probability of observing misleading evidence. As a result, controllable probabilities of observing misleading or weak evidence provide quantities analogous to the Type I and Type II error rates of hypothesis testing, but do not themselves represent the strength of the evidence in the data.\n\nThe Law of Likelihood is often confused with the Likelihood Principle. I discuss the likelihood principle (LP) and its relation to the third evidential metric - false discovery rates - on this page.\n\n## Evidential Axiom\n\n###### The Law of Likelihood\n\nThe Law of Likelihood is an axiom for the interpretation of data as statistical evidence under a probability model (Royall 1997, Hacking 1965).\n\nThe Law of Likelihood (LL): If the first hypothesis, H1, implies that the probability that a random variable X takes the value x is P1(x|H1), while the second hypothesis, H2, implies that the probability is P2(x|H2), then the observation X=x is evidence supporting H1 over H2 if and only if P(x|H1)>P(x|H2), and the likelihood ratio, P(x|H1)/P(x|H2), measures the strength of that evidence.\n\nHere P(x|H) is the probability of observing x under hypothesis H. The ratio of conditional probabilities, P(x|H1)/P(x|H2), is the likelihood ratio (LR). LL reasons that the hypothesis that more accurately predicted the observed data is the hypothesis that is better supported by the data. This is an intuitive proposition and is already routine reasoning in the sciences.\n\nFor the purpose of interpreting and communicating the strength of evidence, it is useful to divide the likelihood ratio scale into descriptive categories, such as ``weak\", ``moderate\", and ``strong\" evidence. A LR of 1 indicates neutral evidence and benchmarks of k = 8 and 32 are used to distinguish between weak, moderate, and strong evidence.\n\nLL only applies to 'simple' hypotheses that specify a single numeric value for the probability of observing x. While the reason for the precondition is obvious - the LR is not computable if P(x|H) is undefined - it does exclude 'composite' hypotheses that specify a set, or range, of probabilities. For example, if x~N(mu,1), probability statements such as P(x|mu>0), P(x|mu=1 or mu=-1), and P(x|mu=sample mean) are undefined.\n\nThis problem is not unique to LL; every statistical method that depends on a likelihood ratio - and that is the majority of them - has the same problem. The general solution is to pick one simple hypothesis to represent the set and then treat the chosen representative as if it were the pre-specified hypothesis. Examples include hypothesis testing, where the maximum is chosen as the representative, and Bayesian methods, where the prior-weighted average is chosen as the representative. Each has it's pros and cons. The obvious concerns are that the maximum will exaggerate the evidence against the null and the average will be sensitive to the choice of the prior.\n\nEssentially, the Frequentist and Bayesian solution is to change the model/hypotheses so that the LR is computable. Likelihoodists, on the other hand, have sought to display and report all the evidence. They do this in the same way that power curves - another statistical quantity that is undefined for composite hypotheses - are displayed and summarized.\n\n## Examples\n\n###### Likelihood Functions and Support Intervals\n\nThe graph below shows the likelihood function from a fictitious study where 10 out of 205 people had a cardiovascular event (black curve). The likelihood function is scaled to a maximum of 1 so it is easier to display. The x-axis is the hypothesis space: the numerical possibilities for the probability of having a cardiovascular event. All of the hypotheses under the crest of the curve (probabilities of CV event near 0.05) are well supported by the data.", null, "Data were collected from three sites and the grey lines represent the site specific likelihoods (data were 0 out of 30, 2 out of 70 and 7 out of 105). Judging by the maxima alone, some sites appear to be doing better than others. However, this inference ignores the sampling variability. A better approach is to assess the overlap in the base of the curves, where it is clear the evidence is too weak to distinguish sites based on their performance alone.\n\nThe best supported hypothesis is the maximum likelihood estimator of 0.049 (=10/205). The relative measure of support for H1: prob=0.06 over H2: prob=0.3 is weak, with a likelihood ratio of only 2.24 =L(0.06)/L(0.03)=0.784/0.35. In fact, any two hypotheses under the blue line will have a likelihood ratio of 8 or less. The comparative likelihood ratio for any two hypotheses under the red line is 1/32 or less. These sets of hypotheses are called support intervals (SI), as they contain the best supported hypothesis up to the stated level of evidence. Hypotheses in a 1/k SI are inferentially equivalent in the sense that the data do not favor any hypothesis in the set over another by a factor of k or more. The blue interval is the 1/8 support interval; the red is the 1/32 support interval.\n\nUnder a normal model, support intervals and unadjusted confidence intervals (CI) have the same mathematical form. A 95% CI corresponds to a 1/6.8 SI, a 96% CI corresponds to a 1/8 SI (blue line), and 99% CI corresponds to a 1/32 SI (red line). The SI is defined relative to the likelihood function while the CI is defined relative to its coverage probability. Recall that the coverage probability of a CI can change even when the data, and the likelihood function, do not. The natural interpretation of an unadjusted CI as the 'collection of hypotheses that are best supported by the data' is justified by the Law of Likelihood.\n\n###### The Probability of Observing Misleading Evidence\n\nAn important aspect of the likelihood paradigm is how it controls the probability of observing misleading and weak evidence. Misleading evidence is defined as strong evidence in favor of the incorrect hypothesis over the correct hypothesis. After the data have been collected, the strength of the evidence will be determined by the likelihood ratio. Whether the evidence is weak or strong will be clear from the numerical value of the likelihood ratio. However, it remains unknown if the evidence is misleading or not.\n\nOne nice feature of likelihoods is that they are seldom misleading. The probability of observing misleading evidence of k-strength is always bounded by 1/k, the so-called universal bound (Royall 1997, Blume 2002). LL also has strong ties to classical hypothesis testing. It is the solution that minimizes the average error rate (Cornfield, 1966) and allows both error rates to converge to 0 as the sample size grows. It is not necessary to hold the Type I Error rate fixed to maintain good frequentist properties.\n\nThe universal bound applies to both fixed sample size and sequential study designs. In a sequential study, the probability of observing misleading evidence does increase with the number of looks at the data. However, the amount by which it increases shrinks to zero as the sample size grows. As a result, the overall probability can remain bounded (Blume 2007). The probability of observing misleading evidence in a fixed sample size study is less than the corresponding probability in a sequential study, and both are less than 1/k. This is shown below, where the subscript on P denotes the \"true\" hypothesis.", null, "bottom of page" ]

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[ "# 12546\n\n## 12,546 is an even composite number composed of four prime numbers multiplied together.\n\nWhat does the number 12546 look like?\n\nThis visualization shows the relationship between its 4 prime factors (large circles) and 24 divisors.\n\n12546 is an even composite number. It is composed of four distinct prime numbers multiplied together. It has a total of twenty-four divisors.\n\n## Prime factorization of 12546:\n\n### 2 × 32 × 17 × 41\n\n(2 × 3 × 3 × 17 × 41)\n\nSee below for interesting mathematical facts about the number 12546 from the Numbermatics database.\n\n### Names of 12546\n\n• Cardinal: 12546 can be written as Twelve thousand, five hundred forty-six.\n\n### Scientific notation\n\n• Scientific notation: 1.2546 × 104\n\n### Factors of 12546\n\n• Number of distinct prime factors ω(n): 4\n• Total number of prime factors Ω(n): 5\n• Sum of prime factors: 63\n\n### Divisors of 12546\n\n• Number of divisors d(n): 24\n• Complete list of divisors:\n• Sum of all divisors σ(n): 29484\n• Sum of proper divisors (its aliquot sum) s(n): 16938\n• 12546 is an abundant number, because the sum of its proper divisors (16938) is greater than itself. Its abundance is 4392\n\n### Bases of 12546\n\n• Binary: 110001000000102\n• Base-36: 9OI\n\n### Squares and roots of 12546\n\n• 12546 squared (125462) is 157402116\n• 12546 cubed (125463) is 1974766947336\n• The square root of 12546 is 112.0089282155\n• The cube root of 12546 is 23.2363777295\n\n### Scales and comparisons\n\nHow big is 12546?\n• 12,546 seconds is equal to 3 hours, 29 minutes, 6 seconds.\n• To count from 1 to 12,546 would take you about three hours.\n\nThis is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)\n\n• A cube with a volume of 12546 cubic inches would be around 1.9 feet tall.\n\n### Recreational maths with 12546\n\n• 12546 backwards is 64521\n• 12546 is a Harshad number.\n• The number of decimal digits it has is: 5\n• The sum of 12546's digits is 18\n• More coming soon!\n\nMLA style:\n\"Number 12546 - Facts about the integer\". Numbermatics.com. 2022. Web. 1 July 2022.\n\nAPA style:\nNumbermatics. (2022). Number 12546 - Facts about the integer. Retrieved 1 July 2022, from https://numbermatics.com/n/12546/\n\nChicago style:\nNumbermatics. 2022. \"Number 12546 - Facts about the integer\". https://numbermatics.com/n/12546/\n\nThe information we have on file for 12546 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!\n\nKeywords: Divisors of 12546, math, Factors of 12546, curriculum, school, college, exams, university, Prime factorization of 12546, STEM, science, technology, engineering, physics, economics, calculator, twelve thousand, five hundred forty-six.\n\nOh no. Javascript is switched off in your browser.\nSome bits of this website may not work unless you switch it on." ]

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[ "# [R] Referencing function name from within function\n\nrolf at math.unb.ca rolf at math.unb.ca\nTue Apr 3 18:18:44 CEST 2007\n\n```Wott about this then?\n\nmyfunction <- function(x){\ntemp <- sys.calls()[]\nnm <- temp[length(temp)]\na <- TRUE\nif (a){\nstop(paste(nm,\"requires xyz!\"))\n}\n}\n\n> myfunction()\nError in myfunction() : myfunction requires xyz!\n\n> lapply(1:10,myfunction)\nError in FUN(c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)[], ...) :\nmyfunction requires xyz!\n\ncheers,\n\nRolf Turner\nrolf at math.unb.ca\n\n===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===\nProf Brian Ripley wrote:\n\n> This presumes a function is always called by name. Try\n>\n> > lapply(1:10, myfunction)\n> Error in FUN(c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)[], ...) :\n> FUN requires xyz!\n>\n> to see a (simple case of) the problem.\n>\n> On Tue, 3 Apr 2007, rolf at math.unb.ca wrote:\n>\n> > I dunno much about such things, but a wee experiment seems to\n> > indicate that the following structure does what you want:\n> >\n> > myfunction <- function(x){\n> > nm <- as.character(match.call())\n> > a <- TRUE\n> > if (a){\n> > stop(paste(nm,\"requires xyz!\"))\n> > }\n> > }\n> >\n> > cheers,\n> >\n> > Rolf Turner\n> > rolf at math.unb.ca\n> >\n> > ===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===\n> > Original message:\n> >\n> >> For verbose coding I'd like to do something like:\n> >>> myfunction <- function(x){\n> >>> if (a){\n> >>> stop(paste(myfunction_name_here,\"requires xyz!\")\n> >>> }\n> >> Is that possible?\n> >\n> > (Note: In R *all* things are possible!)\n>\n> I don't believe so.\n\n```" ]

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[ "# Why is the limit of the factorial function divided by stirling's approximation the 12th root of e?\n\nI was interested in the limit definition of $$e$$, where as $$x$$ tends towards infinity, the limit of $$1$$ plus $$x$$ to the negative first power, all to the power of $$x$$, is in fact $$e$$. I was wondering if the limit of the ratio between the factorial function and Stirling's approximation would converge in a similar manner. The formula in question and the Wolfram Alpha result are: $$\\lim_{x\\to\\infty} (\\frac {x!}{\\sqrt{2\\pi x}(\\frac{x}{e})^x})^x = \\sqrt{e}$$\n\nWolfram Alpha evaluated this limit as being the 12th root of $$e$$. My question being, why is this? I understand that this would normally be equal to $$e$$ itself, but what is it about the difference between this approximation and the actual factorial function that takes $$e$$ to the 12th root? Why 12 of all roots? Why not 13? or 14? I'm sure there is an explanation for this, I am just unsure why.\n\nIt comes from the next order Stirling approximant. To that order, $$x!=e^{x \\ln(x) - x + \\frac{1}{2} \\ln(2\\pi x) + \\frac{1}{12x}+o(1/x)}$$. The denominator cancels the first three terms in the exponent, so you're left with $$e^{\\frac{1}{12x}}$$ to leading order, and raising that to the $$x$$ gives the result.\nThis is actually related to the $$(1+1/x)^x$$ definition of $$e$$, in that the inside of the parentheses behaves to leading order like $$1+1/(12x)$$." ]

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[ "# A container holds three gases: helium, argon, and xenon. The partial pressures are 0.450 atm helium and 0.350 atm argon. The total pressure is 3.00 atm. What is the partial pressure of xenon?\n\nDec 1, 2014\n\nThe sum of the partial pressures is equal to the total pressure. $\\text{P\"_\"total}$ = ${\\text{P}}_{1}$ + ${\\text{P}}_{2}$ + ${\\text{P}}_{3}$... .To calculate the partial pressure of one of the components of a mixture, subtract the sum of known partial pressures of the other components from the total pressure.\n\nGiven/Known:\n\n$\\text{P\"_\"He}$ = 0.450atm\n\n$\\text{P\"_\"Ar}$ = 0.350atm\n\n$\\text{P\"_\"total}$ = 3.00 atm\n\nUnknown:\n$\\text{P\"_\"Xe}$\n\nSolution: Determine the sum of the partial pressures of helium and argon, then subtract the sum from the total pressure.\n\nThe sum of the partial pressures of He and Ar = 0.800atm.\n\n$\\text{P\"_\"Xe}$ = 3.00atm - 0.800 = 2.20atm\n\nDec 1, 2014\n\npartial pressure = total pressure x mole fraction\n\nfor He: mole fraction(A)= 0.45/3=0.15atm\nfor Ar: mole fraction (B)=0.35/3=0.117atm\n\nsum of mole fractions =1\n(C)=1-(0.15+0.117)\n\npartial pressure of Xe= 3 x C\n=2.199 atm" ]

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[ "We didn't find any results\nopen map\nView Roadmap Satellite Hybrid Terrain My Location Fullscreen Prev Next\n\n# What Is Geometry in Math? Definition, Solved Examples, Facts\n\nPosted by Test on November 28, 2022\n0\n\nIt has the same sides as an angle that is not reflex, but the angle is measured the long way around; there is certainly a difference between a book opened 340° and one opened 20°. Once coordinates are computed, field stakeout is much more flexible using Coordinate Geometry (COGO). Compute coordinates of EC using direction of the tangent PI-EC and T. Compute coordinates of BC using back-direction of the tangent BC-PI and T.\n\n• In several ancient cultures there developed a form of geometry suited to the relationships between lengths, areas, and volumes of physical objects.\n• It is represented using the dot and is named using capital English alphabets.\n• However, some problems turned out to be difficult or impossible to solve by these means alone, and ingenious constructions using neusis, parabolas and other curves, or mechanical devices, were found.\n• If a vertical line and horizontal line intersect, they will form right angles.\n\nHere are the solid versions of the six basic plane figures described in the previous section of this lesson. Geometry is the study of shapes, namely points, lines, angles, surfaces, and solids. In addition to endless practical applications, geometry also helps us train our minds to think analytically about all kinds of problems, even problems that do not seem to be directly related to mathematics. Opposite angles are two angles that are across from each other. Opposite angles formed by intersecting lines are congruent, which means they have the same angle measurement, or number of degrees.\n\n## Finding the right angle\n\nHere, our triangle is represented by 3 points A, B and C and 3 line segments AB, AC and BC. With this information, we can definitely calculate the required measures for this triangle. Though more on this later For now, let us stick to our Quadrant system with the following example. These concepts constitute the basic objects from which all Geometry can be constructed, in other words, any other geometrical object can be defined in terms of a combination of these three concepts. Square     (in geometry) A rectangle with four sides of equal length. (In mathematics) A number multiplied by itself, or the verb meaning to multiply a number by itself.\n\nA plane has only two dimensions length and breadth and it can be infinitely stretched in these two dimensions. Geometry can be applied to many areas such as architecture, electronics, engineering, and construction. It can also be used in fields like science to develop projects or programs for space exploration. Rectangle AECB, Rectangle DCEF, Rectangle ABDF form the rectangular faces of the prism. Examples of different Polygons with their angles and sides are as shown below. Tilings, or tessellations, have been used in art throughout history.\n\n## Circles\n\nAn exterior angle is an angle between any side of a shape and a line extended from the next side of the polygon. Vertical     A term for the direction of a line or plane that runs up and down, as the vertical post for a streetlight does. It’s the opposite of horizontal, which would run parallel to the ground. Pyramid     A monumental structure with a square or triangular base and sloping sides that meet in a point at the top. The best known are those made from stone as royal tombs in ancient Egypt.", null, "In hyperbolic geometry, one of the Euclidean postulates is replaced. In hyperbolic geometry, parallel lines will become further and further apart. And triangles will have angles that are less than 180 degrees in total. One of the better-known facts of Euclidean geometry is that the angles of a triangle add up https://simple-accounting.org/ to one straight angle, or 180°. This may appear to have nothing to do with parallel lines, but the relationship cannot be proved without Euclid’s parallel postulate. A special definition of angles must be used for spherical geometry because the directions of lines change (as viewed from outside the surface).\n\n## Other types of Angles\n\nThe Greek mathematician Archimedes, who lived about the same time as Euclid, extended the investigation to solids that are almost regular and found them closely related to the regular ones. https://simple-accounting.org/points-lines-and-curves/ For two examples, consider the cube and the regular octahedron. One can be put inside the other so that all 12 edges of each solid touch the edges of the other exactly at their midpoints.\n\nIn Physics, it is used to find the center of mass and points of equilibrium. Technically speaking once again, a line has no beginning or end. The imaginary, invisible line stretches out to infinity in both directions. Such a thing has no practical application in the real-world, so we draw lines on paper, on a computer screen, or in the sand.\n\nOne way to stake a horizontal curve is by the radial chord method, Figure C-24. Since the deflection angle occurs across the curve’s length, the deflection rate can also be written as Equation C-12. Then the alignment is stationed from its beginning to its end through the curves, Figure C-18. A circular arc has a fixed radius which means a driver doesn’t have to keep adjusting the steering wheel angle as the car traverses the curve.\n\nWhen the measurement of the angle is between 90 degrees and 180 degrees. When the measurement of the angle is between 0 degrees and 90 degrees. For example, L1, L2, and L3 are parallel lines in the below diagram. A solid is called three-dimensional as it is described by an object in three dimensions.\n\nThe figure shows a natural rock formation that is much like a triangle in saddle geometry. While spherical geometry has no parallels, in saddle geometry many lines can be drawn through the same point, all parallel to the same line. This work of Gauss, published after his death in 1855, led many mathematicians to take non-Euclidean geometry seriously. The roots of elliptic geometry go back to antiquity in the form of spherical geometry. In spherical geometry everything resides on the surface of a sphere, making spherical geometry central for cartography and astronomy.", null, "" ]

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", null, 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Js5RAPh9/v8Az/HXn6HuY5aPbkhPbS+nyX4F5h7nlmL7x7KSOj6cifcDj92vvHsn/wBeRc+mFd/w1Rfoc7/YPPIGNfCz3Mpw2eeRxo/aEq+4vMnc6bl6ZFkgA/TsbA8glX8NL94shSOkV+MOOxSrJ/LQ6LRWeC0e/lpSrOWOkeAMnntkEaD7Ql7C8wLA/wAmEHvNkE9Ca5G74Hwqxn8Nee9WRjiuxuRk/Crnj7NUP6HuAAlonBBHHGNem0HCrCmSSOc47nS/aD9heYe46yL9Emyl8CvRR5jKVj7fL5eekpk2WtzmuRwABgKSr0+zVALQczksflrz9FXiQ2GexwTjtqfaD9heYfR6/EFlQcskIjD6bYT1tdWFBX5ZGoYk2WCD9Oxhg4PBP92q2q2u4pMZpLa/1TKQBj5ag/oa9gKDWVEdgMZ1XDjmlTihng29GFCHLKKuj6eh59QT6/Zr3rslZx+kEP7yR/doZRZ7iclUc5I/v16LRdHHgnJHB+WdN9oPbIhVgdGE5NlKQUpr0H0wTjn1z6a9LdmFQSm4YfqML7DQx+iTqjlTBweDzr79EHk8qaIUORgHTLtBv8CJ3L6hKG7NBymvwFZByPEHHfSwiyQMKuaED5gKGBoW/Q9zpGGMH0x304LSdAA6V8D56sXaH+CElw7n+ImbW7sMWNdcW7qDElJnUs+8MkoGMpPbvyCOCPt1db3b+0bd/cSffblqSqWuahlJihaXOkobSkkq4znBPb8dCdrrpFArLFURPgrVHWlwBwocRkKB+JJykj7eNWF7SqBcF1zK2avSEiarxAmO40htPwg4ATgDHpjvnXOwuJl6JN5lo0q509fla/2zZiYaeNF1yev++8pWrtoSj/8AJM35DpTz+enP0rooGfoabjGf2f46fZpEB9sLhSo8hs8daFdQz9o4179HR2z0vthPzOub6dCLpmr0eTVoiqvWkI4+gpa/llOmTftKa6ki3pROSeVpH56tBT6UpJyrsPT+OvBSqMs5U8kf6SdT06HUr9GxOZVDcanJ6Uotl4+oLw/fjSkbhsEFKLXUD/8Aahz/ALOp6qLRFSUsonMoT09SipBJPPYAfv1JTRKKRhEgLxnOEYH56PpsFzD6NLoV6b9QSSLUJ7H/AI1z/wBjTqb4ThOLUKRjn+t/wANSzBprXJSTgenH89tR3DTmwUhsk/b31PT4LmD0eSWx9+mo+EptUDBPeWDxz/ma9/TVwcqthI+XvJ4/wBnTYm09Ax7qvvk/ENfCo0tJCjEc/6J1PT11F9Hl0FOXpOBGLcZwDzl08fcBptd51tSikUCFgEfW6yRz9un/pajpGPdjkeRVzqQzVqH+2zgZPH8jU9PjWrI+HlyRXm8bgCh00SCMcY6F8/7Wki87lyT9DU3J/8Ao3M4/wBbV2irW55svdv2U5xqQ3VLc6QfCeyR3KO/z76np8OUgLh5XogeVed0pJKqNTD6fqXP8f8AONfC9bnyFCk0vpPl4Lgz/t6IvpK2DnqYeAPbCARpxNQtjlXgv4/0Bz+eiu0Ic2H0aW1A1+m10kpIpdMyP/oXO/8Ar69Vet1nJFNpwKvMNK/xc6JET7a5BZfUD2PQBp1uTbiycMPfL4R29e+p9oQ9oD4eXQExeV2kKKafTU8dvBV2/wBbXirxvBQ+GHCRgZOGD/edFpdoKV9KIrvSDjyGvQu3yOoR3efLgaX7Qj1J6NLoCIvG8uyWYSTjyi/79JN3XkkdPRFGcf8Am40XA0QkpTEX1epx30stUdR6UxVAccg6H2hDqT0aXQDhdV55z1RSPXwEjSv0uvfGAuKB6e7p/howW1S+oExyScdla8DdJBKvdSPTJxqfaEd7J6NLYEjdl5hJIci4xkn3VPfPftr79Lb0V3djkgclUdBI/LRkiNSlA4jkD7cY02YUAnpS0Cntzzx/ONT7Qg+YfR5dASF13oMnx4+D6R0D+e2lC6bzzjxWCPQx08fPtouTApyhlUfOPLq7+unkUynLOTH6T548tT7Qj1YfRpdAMVdN4KKSJDPzxHTj7+Ne/pReABPjxz9sdP8ADto4TRKacFTIwD686kN29S1nhrGR6jQ+0Y+IPRmZ+m6LvUMmQyQeCPd0cflr4XVeAOFPsjPl7unn08taOm1qMsnCVnHOM8fu06m0qIr41JcJPkSMfu1F2hHqyejNozJV23gcjxI/xZ493Tx+I0gXdd4OQ8x8P9qOnI+/GtQFm0VR5LoHqcAdvs00xZ1vSgVRpfidKilRSUkD7/LU+0I9Q+jMzQ3feSlDEiP8wIyf4a+/TG8enoEhgnnkx0/w/njWmqsekg5C198cgZGvv0ApqvjDhSCRxj+Go+0IdSLhZPkZibzvQnoLzH/V0Dn+RqN+m93NDq64wUPPwE8a1Nzb6mgYLigc8EJ4Oorm28FTiHPfFAeWEA40n2jDqF8NLoZ/Wr9vEOshiTHwlhAJ92QecZP9+q1W418BRCHIwSog/wDFU60esWC3H/XKHithP1wO2OMkfnqoes+MAAhpK8D+0BnSR42K2kM+Hk+QEncu+EkYdjE4AyYyfX7NKTudffUR1RM/ZU8aJXrSeTkN05JJGAQ6nt66Zbt1tYWyaY6FsKwpXipPVwDx+OmfGr2gejtPYpf6T73URhUPy7Rk6dTuVfA/wAo5DPT6xkj7NX7VqFSsmmqx3Pxp+7z1L/RFII/qKsp5PxJ00eMT/EHuGtUgVTuXeWQopiKwewjD8c6WNz7rAALUIkf/Vxpx+dbsOS9GegyOpslB+AHt9h019KWp/6NK/Afx1phxar7xnxOHcnsUtrW+1KqZjyUKDTnwHHBwSB56iV+hR6dVpkKH1qZacUEKUDkj56uqXdRecV7rS1BxCCoHxAcn04HGoj1xL94cVJpPxuEk9ax+P1dcqEJZHS1s6LaUk70L2x2zHouHU4CXT0+ZHY9vv1bvSErHSpIwTylQ89V9svoqNPLimvD6VEFIP8Afq1VCjKOQtPfnj+fXWZqpNPcvi7SK1cZlwBcdZQT3Tjj8dJbj4T1ZJSOO/bU9xlBPqQPixxrxaQ2nB5A4+elafIN8imkgonfAAD4fHOeedSKU+6/DS658TmD1ceemJjoaqDSUAfGhQORjnS6UsiO4BghLhSfloPRAuh6c/0IJScnnVM/JPUT3x8vLUioSSVfBx37arD1qWVJyQew1EBybHFOZBznkdu/hr1CSs/B6dsef8AHS2oWVAqTx389WLMIgYTgED78aOomzBeVQa3IuCPUGphRGRjrT1HpGO4x55zoiLBAI6E4zx/I1ZtwCopPV5gYA7fPUhFMT5E8cZOi7ZFoVIYSkZA7Dy9c6UG8DlWRjsDq7TTG8fWUoHg58zpxFLZzkpUMZ8tRIl0Uob6j8RGT5aeZa6sYPOe3lq6bpbGEko4B7ny0v6PZScFvAPz0aJfUqfCJTjpHp9mvgy4kgo7eeNXYhsEjqRjz7cac91Y6QPDzjjJ1BWylSlxPJTnB8tLbUrq+Lt5/LV0IbPZLYGvUwUK+LoyRpaJZVJSVHCuBjPHfSm1KCh05x5kat0wEE8pwewH3a+TSupeee/A7aNEuivSvqOFJOfXTyUjGUp+XbU76OCARjAPYgd9LTESnOEn5alAvWyCltZTkqKfs1IbaUCec5HJOpiYaSerpAzjOdSGo6U/sg9Pf0xo5Q2Qm0KBIKcnnHGnUtuehwPnqxDKTwEHtj1x6aQWnUj4R1DscnjUygzDIZK0ZV1JOD2/n5aUhbjOAefQjUlLSikYA/nOviyoEnHPz8x/dqV1JY6zJUkhJwkZzwOcaltvjjkfFyeMnVYhJJwUnHpqW3nAKTgcj11KDZPdDEiOuO51AOpIPT35HkfsOqu1rXhW206hiY8+p5WSHEgBI+7U9kk9POT6j008ltSMLSCR6jgJ06bimlsDRu3yH+hIRzk/Ia+UElOAEg+QBxpSUkjueRn/AMdOJZ4+IpPOTqtxsdMaAdJAJI6vM9sa9SlSFdOBx/P26kBs/WHV9meBr1TRCeSARz3/AJ8tUyix073GypQR09I6fQ+eqmq06MpHistAY4441al8Nk9SjzwR202+5HebJUnCj66ododbgRKUUVBppCufDUSkH63xDn9+oEZRMub8Y6S8MDnOekfz6anVxoNVdoBzA8JXY4/aHOqpmQ2yH3HxkuvK5PbgAf3atjsBotA6EhKjwQeMH9+nFz0/FyAR28xodfq61LKWs5znnP7tQ5EipKjuuN9fwoVhRHY40ySI2yG7bq5cp19RSStZIyfX004LO4GVgH/2n+/Q+mZcCE9P0g+nngE99O+9V88moyBn/O1pWi1M0kmVduMLiylPdeelJ7eWCNHHtBT7duK7YFatSczITIo8MTA02UhuSlvpcTyOT8IOfnpm2rZSZwalkttKBClAgkDIzrTPaZ2TtzbK+2KPZMiXIo86mRqjFXNWC90OJP1sBPPGfqjvrp4EZrhZtaq17/8AdSrErvIrnqZNYrKhSldZyfFOQe+r9xg4PwEfP/fpy16I+1SnAkYWVqUkJ7Z8v36Atu6Te+4tQrK67dcyKxSJyogiwAhorIJ5UvGSPs1zXC5N2ac+VJJbhwmGtWCcJx24znTjlJfWn4WuoEHHGec6qLkoNz7ZJ/SdqqzarQUKHv0WSUrdjpJx4jayMkDzSfx1ptHpkepQY9SiSnHGJLSXWlhIwUqGR5ajg1qRSvStTNZ9u1TxUSUQn1hAOQ22pZ7eQHfnUZq1rjW0/IRAlNsuuAoS6wpBPHPBGR289bWxTFt8JkOZHyT/AA1KREkpRhUhznn9njH3aHdrmBy1Ofl29W3HxHFPfStXAygjq+zPfVpEsmrJ5XFUOMHnPlqyvWM5I35suKhaiUxJLmeM59Naz9DLUCFPufeB/DReFpoKp234GUsWlLSRmOT0jtqUi2ZCeCyM9vn+GtHVRHCoDx3B8sJ5/LTRorwOepfyOBz+WgsIOcAk0GTgjwwojtjnTiaK/wBQIbA8+OdGyqI4g9SnF8c/I68+hnADnJz55xxp+5oDkB30QtIypBJ78jGNLTSnVAqLZIxntot+h1AZyv5HOlfRwx0KCgf9I/no90BzYIqpMlIPQMgjHbtpxFKfIAUkjnnntosRTAO6VE+WVH+OnUU5JJCGyM+XJOj3aFcmB5pXPYn935aUKYc/Ck+ucdtCXtBP1OkQ7Zj0mfIhvzq2yyVtOFBKMHIOPLka1FNJbT4bK0jKh8IUrHWQOcfjovBpCd5rQPN084HwgnuPnpz3PpypCMdsZ7aIPoUJWFBkqz2yTg69+iDgj3JXYYxorD6jZmUCYqhhRQCePLP56UmOpZ4T0nPmONEP0T8JV7ooDXgoqlHHuwHOORqd1YFKyiTFxgKRnPn/ALtK93OPiITj8vt0QJorhIzFBA9E6rblpaRbNXU60UhEGQSR8OD4Z5BHbR7lAc6RDTGznJSOnvga8S0M4JSOeedDPs7MyaltHRZ850vurVJHiPKyogSHEjJPJwBj7BrSV0XxklTfhJOAAOM9vLReGkCM3JWDn6ppQAXjHHfXnjdJJLieQcEkaIRQinBLjXBxnI04mkA/D4iPl/HGh3cQqTBxPWCCFI6lc4GO2pTQKyevowO/OrpNMdaJwtBAHppbUcZwpRJT3GNHu0g2ygXGQCSDknIwB+Q1423nJ6Vg5HZJPH4aKHIMZQ6icD0xpAisJ4T1+npn79F4cUTM9yibZWD9RYx5hKvw7aktlaFFPhq5Gf8AJq4/LVw0hpGT0qA8gcd9PoXGUCAklQOc9/y0mSKGUmVgbChkB0EeqD31JZbUkYU272/snt+Gp6G2j3bwSPXz1LS2yQkeGrPnpJJWFNoqUpHA8Nzk+bSsn8tfSIqVgrcWEYGT18fv1etRWTkJCsnntxxpxMN1aVeGU5Gc84JA1TKK3GUgPMAPfElaT5ccjVDddShWhBZq1Ze8CEp9DJeOelsq7ZwCQPnrSk0pwoy8yPPuNZT7SlOT/Rk/hsYRMjqOAOPjA/v0kcKM2kxnNxTaJ9dsmtT/AAqjDaTILbKkhLbqM8kYPJAx31HpWzVYkx23Km+G1nKlNoUF9OTnk9j38taBT4OIzaA2n6gPbHGNPBksn4UDGecJ03dJKhnJ3bBeJs000oApWrPngca9ru2rdLoUuV4JCY7RWoqTgdI5OjJl2UMdKcfd21GrrsmTR50RbSFhxhxA47ZSf3aMMCLkk2xu8dGBYoKT/wAYhp483hnP46UDb4GPeoX/AL7/AH6XJs95SigNef8AZ+eo/wChL3/o3+yddD0JJVmMb4h70JstN6XZcEe3qNT2XahOWliK00ghS3lEBI745JHy1cbmSt24N1v0TcbxXKzTm0RlpmhanGmwkdCBlX1QkjGOMHV5tld9nWTelHuyBUW5LlImtTS2EqHV4awrHbgHGPv0Ze0Luztbu5uXKvSjTXo7D0dhpQkMEOFTbYSSQMjy9ew128HhodzKK5/lXL4v5GSeK3iLoCtgFaaH1To7RcLiiMDAxn0zoR2Bkxo9SvzqQlPVcLuArHHfWpWzAtmZREPxqnHKFZwfCVk8+fGsY2u28sW4L13BauBuNIVErRSz1IcwW1Ak4Ax+euPiwjGcoo2xbag0EO9N5wa5Rl7bWk2zPrlcIirbaPUIrJICnHD2SO/fWj2zToVBtun28VNuphxW4xXnHV0pxnWLzKRErW669trImsW7b9HZRIrMqntKZfkLV2bStCeoHHnkefOiW6aqztDXqRIauKo1S2au4YUlExS3XYTygehxDiviUkngpUT8vTSpKqEztNyYdWfbFEs2LLjwqnLkNy31SCmZIC0tEnlKOB0p+WrqPVqTJSoRJEV5SThQbcSrB9OPPXKTd73PdNp23S5131Btus3NIpk5baQFmJlOE9QwfXtj79aTu7b9lbZItK6dvmXaW/EqrEGWGUdAkxl8KDgBws8Zyrn56bKmKsR7rYk37IZjb/WHPUlIQ9GlR+CCM4/362cVOmpyt5xhtB5HUsDPGsM3pobSL/27mx73qJdmVhbKFIhMIVGQoDlGchR7D4s6qKBGsuFubX52/NfqUpMB3wKIipRU+6yI5B/WBKQGyrPcAY551FFC52m0dJtyoLvxN+AUHjqyCNeOv09CCp1TaUoGSe2Bz9mhm0XNnKpUG6zZFdyltktuQqettLCx5KWyOyvIKwDgenGjKW5bC4y2Hm5TjbyCkgoTggggjv20cq3ZYpMAJO7lgfSK6VTZblXlt4626ZEclBH+kptJSD8ic6uaBd1o3GHhTZjKnIqsSWHUlt1g+QW2oBSfvGs79lBFAp1l1mmyYzqVxq/MaUEYwlIKQBzzqi3polBvve+37OtOZUaVKk09SrimRnegrg9RIaISeVHBHPqNOkmVOcqs24Vy2y34gnQClThZBDyOkL/s9+/HbvqHctz2tadKXW7gkR4MNpaEKeUgkJKiAM4B4yRz21hNCsS0qtuTuVthCYeh0OPSoSYCErypqWlCSh/J56urJJzzk51GvXcJm9NhqZa9ajufpKi441AqKQQepTS1ErAPmoISTnzJ0tJaCvFZv1bu61rdpQrFYq0GBBVjpfcKQkhWMY9dSYVShTo7M2BNadZeSFNrbUMKSex48tYI2up1HcCoX7uttHc9Qt23wTRqehbBYiR0ZJdW2pQDrhCQSP34A10zbN1WBdFDg3BQorzsGc0HGVdIT8PbkeRHPHljRSXMEcRtnPHtGrU7cW3ccuhSTXUE8/NPOtCrlk2zXbuo911KpzE1Gkg+6MImdDR7k5bH1jz6+Wh72kHKF+mm1TjUZ5CP0jSHOop5TlHYa8vSXSle1bZqWm3gwzQpS3E5GSelzB9NGkhc1WaHOrlKpLaHKnV40RDiulKn5CUBR+WTzp9NShmMJaai0WOjxA6HQUYAz1Z7Y+eubfZXpSd0LwrtxbkPza/CoSVRobE94yEpW8pWcBzPZKCMf5w9NCdcu5qkV2V7PkuqOU6327rKnJjr2CxTeoEsdR9PrD56GVE717nWVPrdIrXWaTXI0tKPreDISvBz8j6jUCo3ZbFIqjFEqVxwYs+Uf1Edb4Di/n09/LWXbs3/ALZ0VdlP7IS4T1wQpyKa3DivAtvRFpILTmByOvpwT2JyOdWGzlOn2ZJqlybh7V3TXbwq8hxcyosmItptoq+BtordBCcAEgAeQ7AaFWg947o1sNlfSPFUM+WdDl+RvCtCuOFeEimSuecD9Ur10b2lfdjXjHlro8N8PQXjHlxnyW34zg/YWgjg/kccE6jbqOUhO2N2uNU9bakUKcpJU7+0GF89vs0KTC5WtDn/AGbg0KbsDQWrmqaoELxnleOJa4pCxKc6R1pIPfyzzrWX6nRKNEbkzazGjsttpV4j8gABJHBJJ5+099Y1VEwo3sLxmFwAp91toodJyQVVHPA+zOp90UGhVLfPaaHWKS1JjGiAyI7nxIfW00ooKh2I6gDjQcUIpuJqNGvG0rjkCPSLkgSnVDrS208CpQ9QO5HzGo95Xta1hMxHLiqC0SJqw1EissqdffVnshCQSeSPlqr9qNFPptjU+/qDTGIVZtepR5USQ3wotqWEqaJH7B4yO3H26znbfcdq9t3K9vBPsSv3C3DIptvtQIYcajISD1Ky4pKUKIIPfOXFH7YoKhu9d0bhQa5SbjBjxkS2ZbSA6uJKYWy+hJ7KKFYODzgjjVmaXILilKaWAcdgdDFLr98XXvBQrse26k29RqdTJcR9yW40XJJc6VISpKFEgJKcg5PJPbJ1od/XdW6bZdZqNs0hl2rR4biobSG+ol0JPTx5884+WjSWjHU3Rn9fv2yrWqCaNV6+w3Oc5TGbQt137ehAKh+Gva9etr29ay7zqU8ppSUgpdCFErUTgJSMZKs+X7tCGxNdtvb6g/SFbtW45t2VcmVWKi/QZDjviK5LYcKSSkZ8jgnJ1Q7/AG5NG3AuqwLWtuOqsR26k5MnUllsNPOKa6SlpaHOnpyPEBCvI8aDiL3rSNJtS76RdCYqG4FVp0ucz7yxEqERTLjrX9tPdKhjn4SccZ1WDdm1PpifS4seoSY9LeRHn1JhgKiRXVq6UoWvOc5wDgEDPJGhLfy+926rZjdah7ZvW3+j8hEtuqrqDKnWEEFtSQ2kZwoOAHk8d9OItFNv+yTUY0CQpL1QpSarLkDHU66spcUCfMdOE/dpcsQrEk9A8qV31xyryqHZVnPV+RTEJXPWJTbLTKiMpaCzkFwjnp8sjJ1Sw/aGsqapkJpVaQhrpFUdMUdFLUpZQlL5CsglQI4zxob9k+tXDElV6g1WrOTGpUaBXG1uIHUHJTalu891c9I59NRm4bf9E281XbYQkT6/MUF4HUtLTiMc/JfUR9p0rhF7hWJKrs2iu3rQbamxKXUnZK5s5BdjxY0Zb7qkAnK+lsEhI751NRdNBepkeqIrLKIsxwMsPO9TYW4c4R8QHxfCrg88Hz1hGx927nXFVqlubE2+iV0SWWqVGck1dMcRmmUgKSkFJzk4JPHOdW+7armqdmyaLclhsUFFZuOB7oqJUkSUeIvh3AASUk9JV2wSpRznVfdxGjiOrNOtndO163VPopqTLZWtakRHJDCm2Z/QcLLK+y8Edjg+YGOdZ37QW51iVTb2sUCFcMVVR6muiP0LS4VIdSexHHn+GtH3aoFu0faJc+kyHGZVqtsTqflvHS4yU4AI7Ap6kn5E+und3qJQrr2Sr9UpzzS3H6QZzY8E9kpS5jOPQHUhCNpodybtFFb+/W1cyNDaXddPbkPNto6HUlHxkDjKgPPjUupb22ZDq5otP97rMxvAfbpkQyPdx6rKRgfYMn5aJaRZ1GurauGukVKHFnVCithh5TBIadU1hKzgeSjzjWcWVZ9/7Z0xm32toY05DBPvVShV5pS5a/2nQhxCV8nkJURgYGnyRaDnktDS6PctKrUFuo0qWFsOZAJbUgggkFJSoBSSCCCCAQRyNeVmoOtU6S5HU34oaV0gpyCcHAxpyyZFq19MqJEZfodQhq8SXTJ8UMSGlLyQspSVIUFcnrSognOTnI1fVSjUaPFfkTKvGQwhClLUc8JAySeDo4cVmS8S3N6tnPsm6btadOWISlE+cfkfgdMfpfdn/o8EfL3c/wAdaHLc2zU51puqnZ7E5Pn92mR/RuRkXbTvxP8ADXeeCuhyXNcyl2S28ozW5lupuaEy9SHqjHamNyCUtqZU4kL6jn6uM5+zRf7SOx1Fs/eOq0+2IQbpbyWZcdpPIbDiASkfIK6sfLGs02wpu41/3hTbQRdS4jlUfQwy+/8AAhLiiAnkDOc9uO+NWu4lA3msK9qhaFyXRPdm05SUeIXAoKRgKQpJI7FJBH263YMYqLWtfXbX4bfEWTeZNP4BLQ7ecpdPajJjPkAkghBOT6dtZjtTAc/pY3Jh+6ySpMuO50+GokApOcjGRzrXrRqlyposZqZV33HiDkqxnvp+bTnqnFqMR11bAqLZZlOxz4LziVcfXThX35153HrvZV1Z1I3kj4GI1mjVjbPdap3jIoM+db1fYbRJfiRlOriOoyMrQB1dJHmPXQtuNcKN3XaZaVkwJbsJuY3JnVR+MtlhlKD9VKlgZP3a1JXs17YS14n0ypzTz8UiqyVk8f6f850kezBswgE/ogePWW+e/wD09V0UyjPVHMcwsWzAdjyXij9HrwTIaC+OthecrT6jgcj1GtX39vC06jZNPFMuamyXWarDkFtqUhSwnJ+LAOcDPOtF/wDixbN9XWmzmsZ/5905/FWvV+zJtAhKR+hUfPc5ecIHz+to5Rcs1oCW4FUte5a5Z9Wpd+2ylFBqAmyQ7U2knwyBwBnk8aNpG7+3EV5aP0mYmltsLWqEy5JQAoHHxtJKQTjtnUN72b9p0JP/AJGxgCSQOtfI/HV3Zu11sbdTH6nZdNNMflo8GQpmQvpWkHIyCrGRnT5aG9a/eZtUZk+9b5om4FrWtVqNQLfDsmr3FIgrjokRgOWgMZdTxzwcd+Ma6Eg0uRUWGpMUePGfQl1pxGSlaVDIIPnkc6Dtw6Bdd92w5bMC5nqazMUlExwguLWx+0hOVADPHPPGdENKYfpdNi0qO++iPFabYbAWQQhCQE9vkNFKwW4mY7UUOo2/vFuHYK4a0tuvNVqN8JwA4Pi8vmnUKu2/cm3m+lWvqp2vWanR6pS22I0imw1zCh1PTlCkt5Kc9J5PHOtdqTS6rBk02c8t2PKaUy8jqPxJIIIP3E6xxPslbThRUum1NwHjHvq8Jz9nPn66RpbFcrqkRbIsPeRu9J29KLdaCK88qPJoEl5EeUiEkJDTgKuAsdPKFY8+2eBTeTbyt21vnasumwi9BuupM1D3BLjaSZrOAvzwCQrOc4JJ0cueyNtSArw6ZUUZx0qE5eQf541mF/8As/W5QdzLKtmiza1GarDsguLEslbYQEn9Wop+HueedRrQrd0bxecfey7KPItS1NtZNIcqSFRX6pVJ0bw47SvhUpKWlrKjgny4+ei7Z227bjWPFoVnVuNVo9BUumynG8BSZLRw4FpJyk9XPPkRjPfWT0nZm7bGqZr1q7lV+oLYZcDVMqr5daeUpJCQteRgBRSchOeOO+ifZuyKhtpZ6qdNlCXUJ8t2dPdbz0reWecH0AA7/wB+nSrcKbuy03m2dvO87ksao29FYeZolWEyd4khKMNgp5SM8nAPGo9c2rrLm/NKv96XTGqPEpTsN4uzG0OB0hQx0k5I5HOjQ1J9ACsLUcdtZjU/Z+2crdTl1qo2X4sya8uQ+szJA6nFklSsBeByTwNGS8CNc0WXs8bTL2qo9ZpdTuShyHqjUlymvdpaFYa6QE9RJAzwT9+s3mez7e0zc+4dyqVWaJHqcWsNy6O3JqLRbmskEOIX0qJRkdI59To4Z9m3Y1SUpTYqFnOOZkj/AB6fZ9mjZVeU/oKjBPGJb/8Aj0tCtOqLmBN3DqFSpzMvaakNpDqS9KXX4ygyARlbeElSu/Gen7dXtwXZNoTzsWLt5dtUf5DYhQkOtu88EOBfSB8yRoQT7M+ySj0psopOOSJsgEff16vLI2H25sG427ptWlzoc1DS2sCa8ttSF9wUqUersO/nj5aCQbaBTa2JWLY3GrNY3QhG26vuI6yql08p8RpAYC0hpT4PQXykg9PB8/PA1zcCyarXtvLlo1JaC5s6ky40dtS0JCnFsqSkEk4GScarrt24p9512363VplS8O3Jfv0aIytKWHJHHStzKSo9ODjBA5+Z0ZJbdQ109DgB5PGf3aiSIrqjmLeCwavZHsiwKJWA03UKSYXvcdt5LnSov88p7jKhoir1rmdultnfEap0pNGptKWJ8p6ew0GutohIwpQJPxDsNHdw+z9tbc1WlV6vWiJ86a74jzrsh5WT6AFWAOOwxqNH9mzZ5GG29uqcsA9i2tXn586D3Ikyh9oJdmXhtRW7etq9bdm1ZYYLTAq0ZJJDqfMrAH36DNnGKttBTGrRpdWs+54lRcblNsN3CxHmRpLjaetjB6kujqScdJz+PGuL9nLaJK+g7aUnkDOGO32c6aR7NW1LMqPPi7fwWnI7iXmltoUkpUk5BwD5EZ0Q027L+z5d01WRLbu6z41CjNpSYy26siWp/nkKSlCejA+Z0Q1Klsu099qnVBESSpsht9bXipbV5Eo6h1eXGR9unWqNMVwhpZPf6px+OvFUuo5KelRyPJJ9dTRIe2tDlq/vaJuuxbon2lJk0B+bBc8Ncg0SYlJBGQoBLqgcgg9/PWV1S77MueqObh3FfteF6xC0qlOQbf8ABhxy2rqCVDqK3Ae2TjjuFa7wct2oqJdTDHUr6xCR3/DT5t+YR1KY6STgnvn+c6DoTLJnE9f9qy4bst9yz6zZVOMae2Y0+WhEg9bZThSm28AoX5jJVggcaC61u3eU/bVG1jXUikQ2ywqaiA6JEqOjlpsg/CkABIJz2H25/QlVuPFZUmODnk8YydUl7UNce0q28+0ENop8krUo4AHhKyc/jpaQXGT5nJmye7dtWrUxWqhalyS4i7eptMSqJCC0l5lJDiu/bkYP26Lty95tvqntjWLPsiyLjgSao4FLS/BKEJK3Qt1ZOTycH7zrXfZ7oU5Gzdq9TJIcgpcSSc5Sokj8jrUmaZLaSE+ASMHAxz9uq21ZZGEmtzjazt6re2m8ej2pCk1qgSnjJZjS21xJMRagCtIPSpK05GR2PJ0R3Lvlbd9wLZk1CIaaul3EzPkxQ6X1JjtpWOrPSkdRKh8Izx566rNLyMe6DqIIIUkHXqaYnoLYjJz3I6Rk6DSGjGW1nOe7e9lh3NtzWLdoNRefn1GN4LSSyUpySPrKJwOP3alM737YR7HTaLlSfLqaUKecxVeGo+F0Zzjtro1hmc18LXwYGfhPlr1xpx7CnkBZwSUqSFZz376KqOg+Vs5Zsjem06FtpRbbVuQzRa3TGEtqcMBcpklJOEqGBlJH9lQPz0X2fvxXrmddptLtyNdcqI2lbztuzUHqST9YsyOhTY8vrK58+RraJVo0Kop8Kdb1MfB4/WQWVHH2lOotAsC17Tqbtatm3YFMnvN+C49GjpQtScg44HbIBx8vlotaaEjGV7ma2zCv65t0VXrWrJl25TYdLVTW2pDiFPy1KdSsKUEKIAT0nAye+tAqdLemxH4QjujxklIBHy0YOVKstjqEoHHIKm0H+7VTctyXQikSnIcppt9KD4azGbVhX3jnVmDG8WPvQ0vVgzEJ21kguqIj/gjHnquO2LwJBjq4/wA0/wANW8vcvdaO8rrnQ19/rQG+fwGkf0p7s/24P/UW/wCGvWKEVyOHKTZTWbu5bVIuGDWLbo9ZFQp76JTJVHaPxoIUnA6zk58ux0X7n+0jaW5V3quar2pWIctTDTDiGo7fJQOnJJc7/L7tNbM2unbzcOh3c/CUtmny23XEBpJKkAgqSM+ZT1D79H/tG7d2jcu6b1zWUIrsGqRmZLyIzfSlp8p6Vgpxwo9IUfmo6OFDFvbX3bbafHT5Fs3FNfUHLbuyzJ0BqU1RauhK05SFJaB+8derFy67PYacekUyqpbbSVLVhoY+/r47aTS9taoxCQ3FigoSkKwRzrNvaQYrNnbfLp0ZtQq1xPIpVPaQPjccc4PT9gJ515fiXWNO+rOvF1hp+BYbRb+2Juj9MBi26nHVSJhYSUutrDzZz0r5IwSB25+3Wlpr9nKbClUiohR7Hpb/AMeuaPZ72qrG2u79wbWyUFch6kRKkkqxlRxhePsUoj7tdPDb2rq6R4ODx92q4tJCwbklYyitWnkKVRqnjnOPD7/6+pJuCz1tBKaLVCR6eFx/t6SuxKskqaWgJJ4x6fLvr1mwasgBSmBznBJ08aGdjhqFkvICV0iqIOPRrj/b0y7OspRWg0qrnIyCENY/7epEWzKmHfhQnJ9Tp56xas2jIZycdWCR9vH3abQRt2VxmWUWgPouqdY7Aoa4+/r02KpaiHFddHqhSR8J6W8H/b1W7cRLkviNUpMy05lEVAmORUomdSfGSn9tOUjj8R8zouXt5VwkAsIKvPkcaWMoyVoOPhYvDYjwsRVJf7yBKmXNY9QLj8KlVJxLLzjC+ptAIWg9JHK8986sBWbUSR00OeE4wSfDGT9yidRbBsCovt1xstpV7tWpiFDPOSrqH79ED+3lQCgS0Mp4IT3B5xpYtNWDisPucWWGtkVibltVoELoU/qGAD1N/wCL+7Tb1asmVJblv2lIW+wFeA6Q0pxGe/SrPGdXqtv3lpSpTORjBB9e3Gkq24nZSGUo+EfV6vLViyMzasq03Daa0KUq2phAHBKkd+P87Xkar2uS4+bfkqychPWjjjyGfXVp/R7UEjoU0kKz2z3+/Q7a6qBdNZrNvUCuRJdQoT/gVCMhXxsL8goH7DyPQ6aocw3Kiz/Si2+G2bXewTg5UjgY+3SEV63FlaP0aeOf89Azq0G307pUtIQDnjOvRYM4qLQWkq4zgjv9ui3EGvUqE1qghRcTbjmBzlTif7j2027cMJJKI1IKBgYBcHfPbjV8zYjyFYdebwOFfEOPU40l6wpDjp6VtYUT8QIzqt5egLlzYPm5WkK5oCFA4PxOD8f59NfC7wlB/wCB0EduF51eKsmRkoLiD3B0tG3jhIPiJSOQrkAaFR2oHrdSjXe3hpWhFFQrGcEuYAGlIvmV0lKaS0cDjC+CPw1cL28d/WBLrZSBwCocjy0wbGcSnpS63nJ56hwM6NxvYmvUqnL6mFJH0YyknnlX+7QTdftGS7Ovm2LJctlqSm5FOITIQ6AWlhQwSMcjn+edaULFQ4vw3X0AD9rq1z7uTbcSV7Wm3VtOLQtEanS5hJUMAhDqgfxQNB5d0iO0tzdkXvVSklUKOolWQMnPP3aecvmqhtKkwmElIOMqx/dqE1+i67mlWc1WEmrwozcx5gNKwhpRwkleOnPbjOfPGro2pCV8Pv7SvhBHxDRbi+QbfUrmr3qiUk+7R8gA4yfX7NLRfVRWrCmWE9PP1u3rzjU79EKbgOCe3nz6Vef8/v18bJjHCnJbPfPwny+elTiuQdeoD2Xv3Ouu4brto0ZuHJticIyyV9SX0LBKFjjIzgnHz0XqvaqONAutNcHgBXb8tYttFbbD2/28dMMttAZfpTgyeD1MuZ1uqLPjhSWjLbIwM5UM/nqWuaAsz5gjc79euExX6VdE+hTIpV0SIS0KC0qxlLjTiFIWMjIyMjyPJ0J1Sxbju3pibh7j1m4KahYUqnJDMKM9jsl4MNpU4n5FWNa2bNpzZClyQMHOEq404q2KWpSSZ7YwMkZye2ltdBsre7KWn12ZTWGIMGHEjxo6EstNNDpS2gDASkY4AA40UUy55cpAX4EZSh/azknVcu36c2k9Mlsk8EqIH26capMNlQKJ6W1gdwf3/jpPVeyLUn1CNFxOdJQ7S4wz6LI/u0l+4o5+IUeKCnsQ4fw7arUQg40gmoNuHywvnOkSaUkApVKTk/53n/OdB10GVlk3c8ZtKQ9SGCoc5DnB/LQMN64qd4ndr3LQjrirpCKk1MbkkKSrrKShQ6cc44x66J0W+5JbV4cponOe4zrEaDb1Ske1ddMdCAtUC3oiAodh1KB/joWgu1szoNV0UVJC10dSeACEug5HqONNvXXbfQkop75J9Veeq79EqvkqU11A+YHbTS7OqrRx7ss9WcYHBGiNqWqK9bEhOHWHm8nnOcAfh/dqPUpVlojrfk1gMtITleW3D0/MgI50wi0ar0ZTEUAfUYzqNUbMqMuI7BdhKwtPxfDxq/hleNFeKFxW8j15AnKn7QPOq6bxgAnJJUhwD/s6YxtIrn9O6UM88ur/AIaqp+zz5dK/dQU59PPUMbPSyMiArH/sc/3a9p3cnyPOTko1qZ1tdZVRuG9qRRbmuGpRabUJbTEl9UhR8FC1gKWOo4yASQTo73v2LufaTcJ23YV1VabT3mkS4clchaFLaVkYVhWMhSVJ+eM6GbZ3Ln3HVYtHom3alTpDiUx22ZSnXHnM/ChKQ3nJOAMZ76Ntwt/L5k3AmnbhbePCqUllMDwpEkNuNoTkgKHhDPKicnJOe+suHGGbR6c/Kq8/mbcRy0oh0hqtRoTTL8hxxxCR1rdWpSyPmScnWF1qoV+/N+feodGfrNLsZHR0R1oRiWvnP6xQBxj18tbZc+9kS3bGqV0y7SYZ8GKtbaTKzhZ4SM9PPONCPsyL/Rrb01Kt28JNUuKU5VJLynuhR8Q5SCOk9gfXz15biFWNOurOpH1oRT6Gf3/cN2UDdu09wDZ8yCZfVR3RJlNID3WfhypKlAd/PjXRMOZU3Ira5CDHcWlJU2TnpJ7jIODj5aCfaQc/THamot023PBqFLWipxXUO9S0raPUcDp9M6M9ud1KPeNmUa4RbIdMqKhThD2B1gYX3T6g6WGmlDKOVtWVV6XPU7ToD1cZge+racbSlgPFvq6lBOerBx31EjRtzJTP0nIu6IxKUPERCEUuRmx/zZX1BZ+agR9mibcm4KLM2/rbJthaViIpxB94+qpJCgfq+WNXtDvG35MKFKVa6SmRHbcP64EYKQfT+caDblOn0OjCUcLhFiQScnJptq9Ek1vtz8TK63uHXo9MVGp8JhFyOSm4KIjjiihLq+Q5kd0YyoHjt8jqRGuC/LWkRHb2q8OowZa0sGUyyplUV1RwlKhkgoJwnqGCCRkakXtcVoxt4rRqX0CGnOh9uUkPDo6SnDJWcYB61KAz/aONEu6182q1Z8+nvWyTLqTfuURpDwUpbznwoKRjJwcEkdsZ1Rnlcm3sbO5wqwMKMNMXV6arVx0fRVfx1BGduzW26LEmwaIqRLl1R6keD74Qlt1ClhKlEj6pKBnzGfPS4967l0yWaBVKbSqjVHo3vcZMWW5GbWhKkpcSSsKPUnqBz2IPlqIupUOBRrmgyKE+HKZX4FRbV4o46vAUvPHYnxDn56Ma7c1vt7i2m9Ht9zqVGqDSx4gx0FCDk8eqRoKc3q/D9B8bheGw3kjFNPM715RU1z2p0BNq3LumKncUaHbUFK1VAPvIcrCsJWppJxkNnPrnjvowrV212iWzNuGrRel2DCXKfZbkqIBQkqKQrp57Yzgal2zdNJi3ldrbVvKWlTkNw/rAMfqiPTzwNX1RuG3anBegTraLkaWytl1HifWQpJBB49CdXYMZRXXf6nJ7UnCWKlGKWkXpfOKfNs/NW/Paf3gveoOyBeFSo0MqPgwqZLcYQhPl1KSQpR+ZP4a032Zfae3BN0xrCu6vzKvEqh8GI/KfUp5l7HwgrOSpJGRzkg4+ehTdP2TL4olblTLAprtZojrqlMIDiBIYTnIStJI6sdsp7+g0W+zH7O13UHcSm3zuBR1QINIWX2Yq3kF2Q7jCcgZ6UjOTnBONWapnFV2dlGrV1KTlSgRwP1yhz6njWNU32kaU3bF2X7Ot5yEqi1U0l1TToU7PdRgNgKCQT3/a+qM66BavChtr6lUBRR5/rOTrjGzLZoW5NmXfZhrzVFnNX9KqkBTgQ4HAlKR4ZbJBUB8tPmfQslpszf8Ab/cncm5ksP3Dty/Q4dQa8WO+amHiBjIDqehJQSO2Afu0aTK3Np8KRUJslEeNGbU684t5QSlAGVEnHbA1h1aujdjZ6PT7sr+5jF0Mu1KPFk0h6lsx23WXFdP6hScKC09+OMDkca0f2jryjO7HXY3S6Spp9+nlPUFAlKSoBXb5E6GeS5C2mjMUb/bq1+lVjce2bcp4sagJW54k5x1MuopQfjLJHCB9qT2+4bXY98Sb3tWn3XSg/wC5VFgPNJeWQvHI+Lg+Y1iV4bhWbbnsWxKBCaZQ5UbfiwmVJcHU7IWElzA79/EJ1pvs5XnSqfstaMBVNQ8Waa2FOZGVKyf3aGeXQVU3uNb0bu1PaC0mrskUFdTZXNbiqbTLLRAWFHqBKCO6e356p7d3T3wqluMXpK2vYNInIEpmHFqSvpBEcjKVqSpHSslODgFJ+Wk+2FccOubDVNhikBlcSXDlJcJz2fSn/vHWjxN47aoVgRbqqVOQ3Aj0tqW4suYyPCBx9/b7ToXJsml7mZSvaYptYl0SibfU1y465XQotQkySx7slGesyFFJLeMHjBJx9hN1Sd4pLjt20e6IDMOrWXG98qLEWSXUuMeEXPEaylKiMAggjgkeusH9jSsQ6rvbeu4dXpLLTsplyQ1FA6Us+9P+JlAPOAlJSD6K+eiO2Lij3Luh7QPvlOL0eqUtdPb+Mjwh4a0pTkdux/DUzMCDe3d49z7to4v23duBNtNxzwo7SJRVUn0BXQp9CMdGAQfgz1HHB1m9Tu25a57TtNrMPbm4npVJoa1fRy0NtSOhXUjxCFrASn9YByQe2th9lK94ELYC1oApaHFx0yU9XVk595d/v0O2/e0Zz21rlqjlPSWmrSajeGDnGVRlZ/Mj79RuTVDadS5oO7kyr7gs7Y3BZVWoVTlQjNjmU+hYcQAer6hVjscd+3lqBWt9qdTLvk2vQ7YrFyfRjjbNVl0toutQlrV0hJwCVKzkEDtg98HQ7u1uEKN7R6LrgwQzIi2LUfcArCgl5Lbykq+eDzjRl7IlfpFsbL0x5untvTKo8/NnSCf1j7qnCMrPc4AA1M0ugHT0ssBuZU0byo2iVbikLNKNUTOMrunOOnwyjIweO/lohi3vBmXlM28ivKNbp8VE1+OUrH6hXSAoKxjHxp4786zetXzDg+2fQK09Sx4dStNyI02VY+MOPLJ+3CDpW0N+w6p7Ue7N0v01DhaYhU1pP/NoQkIVj7S0DoZnYV0IFhVNdA3r3jq1T6WI8FmnSpa1FR8JtEdairgc8f7tPwd/9wl2s7u3UbUpsWxfe247aHHHBUFMqcCDJB5QQCR8GMnnB4yc03dvpcG9N9moUZttNbpNMaIBHwgFpJI+5ZH36Lt4rkgU72QbXtanQEMiWzSW1EHAVlKXFH71AnQUmG/EO65v6pN4psK1LPqVxVpTLMwNR1JaaMVbSHA94iuAMKA5HfjzGtHocuvVqnMzpVDfprziSDGkYLjZGfhJQSk/cdZFt5VI1N9qa8Ji6ekNN23TI8ZgHCUoS00k49eUH89dDpveA2k5pYyTjOcDUzPoWQ05mXXhuZHtOrxbVRGk1W4J6fEYpcFvreLfPxqJIShPf4lEahVvcC8bQtKrXxflmimwKeltSW4swS3lpUsJ+IYQlOMg/WPc6fuawTO3Bm7mWdec+3a1UozcWR/U48tlTaMYAS4nKRwCcHnA0Eb57qXJTtork263CgU+VNqEELplZgpLTcpKHmutDjRJLboCgeD0qzxjBGi2+hNuZZ0jd3cup0pF2Rto5At91ovtvJnpMxbGMhwR8c8c4Cycds9tIuf2iLft+qUijx486rSK/DTNhIgx/EU4FqwhOCoHJwfwOda5tjd1s0faq3jUKclLMaix1PrWoAdCWgVE58sZ1y/7Lsiju7+Vur1+I4llVOedoEd8YKYjsnqBbzzgJUcY8lHy1XKVrVDK00rNYXutfrL8SjU6xH49amAux4lSnJipdaSn41IdR4iVKSSnKOCAQe2gK2Lp3sa33uybT7XpbVZcpsT3qO7V1dDbYGEqDgQOrP2DGt93irtk+BbDjFOdbq6K9CMFPSCtQKwHQkd8eCXM+XGT5aE7LnW077Vt8PSmpCY/0DBQhAQCc8E+el3Ww733D+yrv3JmUvxLmQaXNSshbEecX21AYwoKwDz6EZHz76KkXLdxQemoqI8snJ+fcato0+x/qFiVjPCg0Mefz1Obk2OMgNyiRyD4Xl8+dFNLSiymUiLxuxs9JqpJSDgYBGfXtqLWNwL3ap77sWeDISPhK2woZ8+COdEnvVjocypEok8glvH9+mqhUduYsRcqc+9FbRyt1bC1geXZGT+WtPCtPHhpzQmNphv3GLTd1t4UE/12H3I5p7eB+WoR3c3fyf63A/8Aw9v+GtBmXbsapxRN2oCicnNMl+Xf/ktQv0q2LPP6VtffT5ef/wDlr2qS6nnJtdDPbQgW/aVdp1zUy46YmVBkIfbU3JQSkhQIPfWtb6VvbreO66ddNImw48j6Objy0uPtAqcSpRzkKIVwoDJ5wAPLXOtrbcCHVorlShKXESsJdSkYKk/tAY57a3T2gfZ7s60rgolY28hlmkVqEJKGFrKy2sHkjPISUqRwSeQrWWH9RXHrX5/t7jbLZNMGbv8AZ0t/cm2G7dn3mIEN11D6wwtB6gg5CDxyD3/DRbD2fp0GMxDi3RCDDCEtIHUnhKUgDjHy1Cp0aXFjMxlPNp6EBOOseQxj/dqwaiSiDh9tWew6xrymJKUsWUvFnchGMYr3I9d2lZlociuXFDUhaSkgrRhSSDwePTQ7tx7Nbe3NFkUCm3i3KhqlLksoddR+pCzkoBx2zop+jZ/BCgonvg5xr73OoJIKVlWFcYPCtLFyu2wSSexBuXZyfKoM6IKzEUh6O6lX65OCCk6w+nbP70VC36FUrJW8/CmUxlxS1XE20ltQHSUhtwKIGADxxz5a3SdHrb0SQwhSyXUKRgc8kYxqh23g3TSbHo1PqEV2PIjxw0W3BgjpJAz+Gs+LGU8Ra8jrcDxy4LhZvKpPMtJarVS5X7gCpOxO/wBT4khP6IWjLcqOEy36nWVSXXQM4Cz09ueAngemvqZ7O+/tInpqVLtjb9mQMlDr0yY+pH+iVA9H/R1tCJ1fQ4lKms/tAkcfz20tNUrnBXF6hz5Z/ntoLh73b8gS7em7rCir3+9/9jDqnsJ7S1RNTW9FspH0uhpEgNuyuQj6pTx8J/h+Mibsr7UbtZp9fXRbRlPUxp5CEMPvoSsOAA5Kx3HSMc63Biu1MKKXIivh8h6/3afFbmoX1Flw5GRjPGm9E55mBdvzpJ4MHSa2ezWXr0VGaWBtHueHKvWr2oDVNqdRfQkR2Vh5vw20YSQoKJ5JPGjBe1lxobKvBWE+alNk/d30RJrUlR6TEcVnscnn79PfSa1KLJZeJHOM5z+etMIuEaTONxOP6TivEca20WySVJK7+oInau48ZDWQCc4QTx+OmF7Z1tJPhpKVDzLZwB699G6ZpSoktvpJ47nvp/qdwMokjjuHFfx01vYzNroZ4nbi41r6OgDt8Sm+B+B1m9O9j+gUxqrxXaU9ParM1VRUZOSph455ZUnpU337g5+fGuilfGD0KlgkYx4qsfv0oLWAErfmAHnh1QP79C5Abiznqi+yXRaZVGK5LaqdXmQldcVdVluyUxiDx0JUrp4xwSCfno2n7V1aqxnYs1tp6M6gtvNOM9SFoI5BBPI1p6WFKKk++zU+eQ+sf36QacvxFBEyoJyMFIkLGTn7dK20iu4s5zg+xtt5DkoeZtFp3w0qDbch195prq79La1lKc59Ne0X2OqPQJ0WbDn19qHTpAkxqeKk6IzbgORhAOSMgcZx65Guhk0qQhwKE+oZI6eZCu3mO+kP2/MkqS6ajU1HyPvC9C2yNxOdPaX23mTtlbnefDyUwIZmjoKkYLZCsKAPxDjsePPyGg6x/ZquHcLb+0Jl2X3WapQnqbCnN0oIaaZVlpKkoUUgKWkZxg84HfXUF9bcuXnZ1ZtR+tVBr6Xhuw1OLcUsALSRkpzzjOceemNv9tJ9jWXRbQNx1OWaPCahh4EtBYQnpGEAkAYAGM+WprdslxRhly+yRW6pdSrstC551rSpcIQZXuDCShxoABIGfqEAAZHbAxjVfB9iGPRpAdpNwXNEW8lJn+DMP9fUCSFO8ZOSTwMcffnqo0GpIb6TWKoEg+bysH7NOClVU8JrVV7ZB8def36LTJmj0MKsDYipbdWnCtGmLkPR4XiFLshOVqK1lZ7Y81HHy1Ap3s3Vmmbp1PdYz3i7UqcmAqEWPhSB4XxdWc8+GD9+ug10ysqBKK1UQEjH+VVx668EKvYCVVuoqB4IL6tDULlE57vT2aKld9129eT77kaRRQ4262GAtMpheMtqye2Cr/W0NW17MG7thRpFMsW9YzdEdcW8xFqNN8ZUbqJJCVBST5+fHy11cI9QQEtuT55SOP8AKq1Iai1Y/wCSqU4IV3/XK9dK026JmicjXv7L+5N0M0Cspuplq8KC+VR6mIXhtLQVE9CkAnj8jznvpi0/ZA3Gse4VXVRtxZvv1TJcrZVAQpEtZcKyAFZ6RyRnv3x3xrr5dOq7n/zjOBPOfFOT/I02aRWVOpQarPKunnLyvT7dRpjJxfI5nuD2So1y1m4q7UkTm5txQEwXyFfq2wOgpUlOPrZbSeSfz0Lv+xNdtft6Jbt2bhVee1S2gzSmkMJbaiYPwqKR/lFY+Hk8DXX7tFrTiwV1Wd1nJBU8rnXpodaSgEVacHDkH9crt+OhqtQ6c0YJb/s/XHRrsZu2dWXpU/6HapMla4yUJkFtRUHTjsrnGB6aNmrAuNQOMHByFeGfXR99A1gcKqMwnOc+KrTjNvVrnNQmg/J5X8dBMdZTDa7szuy/Vn5lG3Mlw2XFZRDcpcd5prywFFIX+J1k2/3s93JC20uO+r6vKpV6ZSoYMJsspjRo3U6gLUG28dSiMDKs/kMdiPW/WHFltVRnAY8nVfx0K7nbQ1Lcyw6nYkq5J0NmohtDjoJdASlaV/VJAOenHPrnQzOwtJmHWP7OVz3PZ1vm6Nwq3UaEuBGkJpBQ2y0tJbCg24tsBbiO3BPloyvb2eabeL9OR0P0mpU0BNNn079U+wlPHSkg4KR6H7sc51qj2VU6NRoNGYqs1TcCM3GRlZGUoSEj8hp0W7WESUr+kJf6sYT8ajj10rbQ8VEzm1PZ9ft6pquOrVioXDXFILSKhVMLUyj+w0hOEtg+eBk+up0H2eJ0e+qtuG1VJbcyswE09SEIAS0lOMLT59WQO+daM1Sa00AoVKYFcZSXlcfZp3or6SEpqczg/wDOKxqWMlEGbO2tui16CzSpdwTKw5GKszaggKecBJOCU+nYHV4m1a4CG+pvHfJR5fjqQ61XFBKl1KV0jGP1isabDFYSpQ+k5Q9MuK4A0czLYnzlo1j66C2QOeW/9+q6dY9UqDLkZ4hSVeQRjqI1ZLZqy2un6SlEY4w6rH79VVYm3lRoa51Iq8hqUngLUhLox5/CsEflrRwcr4iHvKsfTClXQCp2zkxxa1Ijr5ycdHfUE7MS88tf7P8Au05M3N3obcX0XGDwR/8AJ8fn/wDL1XK3W3o6j/w8g8/+rWP8Gvbpp8jzk4zYAWtfe59frEajrkwSX1+Gk+5oSQo9uR88fjrQ9wXt/tr7ij27eTsAueCHIyhHQ4240SRlBHzB+/y0MUq+tr/e2lU5dRElCkrQFRCFcc9+2tQ3C9ouytx2aJCud2SxIo7CmlvrhO+I4pXTkqHTwfhHbvrHBz75JS9+vyN02sl0CUO5qw8pLj8hxC1nqUE5ABPoPL/dq0buOqNgdMx4gjAwdC6r7tJqc57uzJeZCv1bgZKQofYRkakHcG2/ECXYMnw8nBCDnOvJzzRnJPqzuRkpQT8AibuetKPiIludxkk99S2K5W0q6nJrmPLIzoCou++01ZuGZa8F996pU4f1mOY60lHlnOMEA98aLmL2tF1s9caUkk8YZI8vnpVKXQqk4vmWC67VChQMjHPxYSBn59tOGuVcJAS+FJA4ygcD8NNR7ys1xSU+A+BjnLXOedSHLnst1zKfHbAA/wCT/nnRbe9FcveMorNT6j1KaBPc+En+GvFVup9ScIYSRnCiynk/hqa3WbLWv4n14SM4I/M6dM+zVHmYBwfLP7tFN9BVXUrzclUC+nwWM47+Cn92O+nP0lqyiAlpgnGCSyP5OrBp6xyhIM4g4yfh0/4tjp+NuoJIPbg/Cc+emTfQGiKgXJPSgISGkpJxwjkZ0v8ASeqeIVthtKRx9TGrZyTZSWOlNRTkDHT0+Z08n9CFJBM9Bz8tO5PahHS5lO3c1SCskNfMdGR9/wCOpzN31RJKlIbBxwQMd9S1x7ISA8moZCvkeM/dpL7dnkhLU/GQBz5+mluW9FbrqQ03jVFJUpSWwpI4JB5B+/Ub9MKop0BTSCgHPAPkft1btw7Vcj+GqqICj2JGMaT9E2oClIrDZyM5Ixx/HSuT6C1fMr/01qKT1oaSMHP1jgfn9mlm8ZsjH6kE8k/Gvk+vfU9qk2eo4NXZGRxk9/5OlfRFss9S01ZhKfNXWMDUUn0Fa8SA3fM9kJbS0PhBSPiVx+epkTcarlRHgBSFAj4lKwPz00qnW4oZRU2CD2KVA/z207Hp1rMoCTU2sk85V+7Uz+AcviPov6plZWlhOAcAfEefx0y5uJU/Gy60AAeMZ4+Xz06iDa/UvpqCR59/PSHaNby1pJqbBB8urnUzabEp3uSEbnTCMrZbVjkqJPb8dPL3ReeQFeA31DggZ51BVbVtpClKqTPPPwq7D+RpsW1b3vBIqjeMfWBxj5amfqha8SzG6hXkmMwUcBQz5j56da3RaUnw0xmvhOc4/LVWLUoIUUonNHGSfjyO+kuWtQUOqSJ7Ks85B7aVy8A14l+5uKCgf1dkq9DrwbjI6i2Y6UqUcq8+dUDlBpBZSkVBtGPQ6dZoVFSMLqDajjkDOTqN3sgqLrcIG9wwlIAQ0VHnB8x/J043uAeg9DDOcc9PlzoebolFDK+mchPOO4z/AD214ml0VLZP0mgODkZOQefL8dDXoOk+oUHcBXUCthkhPrzwdepvsufEUM5J4we4GhP3SlhfU7NQcAZyrHGn0tUQIUGpjYT2wT+WlfuGS8QsRfHPSppnB7DHbTovlRV1Kbaz26QDgaEo7tGSA65KQAPhA8ydNurpAUFCSnIPcqA5/doNvoMq6hci9yXCTGR8XkM8c6c/TL4uGWwCcfWz6aDmX6QXFBUpASPRQP4adek0gEFuQ2MnAz/fpPEdJXuGCLwbW4OthnjjvwNKVczbpCgykY57kjv+WhN2dQm20BL6SrPJChqkq9/WFbtXpVArVwR4c6tqUmC25kB5ScZSFY6Qr4hgEgnyB1HYUkaWxczQScR0DzBydSkV9hOP1CCQe+ToPj1KjtI61PJBOSBkYOPTT6a1R1E/rQkgZ4OQNRJjaBYmqxlDmA2CODpszIawUCKE9XJAV5euqFirUjp6UyE5I8yPuzp5FXpCcKElJPIznjSuyyKRZrMNST0shIHf4/LPrqtrFRpEGG5JraC3CQPiU2grVnywBpKq/SOnq8dvv6g6iTXId0xn6JGKFOOcpAVycc60cC2uIh70Ljq8KV9ARnXrtAlfxzJo75/qK+dQv072a/8AWEsf/wCG5/DT8/ZyStSgGsY8gNV52alZP9TWfsGvepS5HmpOPUzah7XOUmoxqmuL8Md1CyFDIODnW9e0dZtj7gvW9eFqRITNRlximosx0BKsgJ6etKeAoZIyeSAPIDXLNAp97P1WLEm3PXDFdeSh0LnvFPSTg5BVg8a27fXZq7drK3TV2pflzTKLVIyXo7iqi6lSFjhSD0rwRgpUDgcKx5EnnNYfpEbVPp1Ok7eHqwKqOzVbRIDkSIotlIPIPf5aoq1tjc9LgSqk42ptmIyt9xah8ISkZPP3a0+3qpdkajsR5NdqLrieSt6c6pROfMk6yf2ntx7zjWkxt1b1QmSK3eLn0exGRMV1Fo/5Q88Ac4z89eW4uvSJ11f1OrCWXBV9Dk22bPva26B/8Y6JHkOw11Z1mWlQ4cirV09f+scfbjXV1Hsu+KhAj1WnxXXY0hpLzbnSCFJIBBGPt1CQq9WNm3dnl7SXKiE5S1QCGp0R1vrKcdf+UGPi57asPZR3Vvyt2L+h0+HLjO2ko01x915pSSUcBBScrSQPkRx38tUxTbopVLQnCztxW8JFIUtWM4x/I04q3Nx2kBDlvOKJ7KAyMfjrYhc13gDoqQykYA8JtWR96NVTm516NTzT2GXpLjQypQZZ6QMdslPz1k43tDB7PhGXEOszpUm22+SStsvwsGWM2octWZszTdzGkgC2Xz0Y56CONfe/7gRG+l21JJCcZ+A57601jcq8XFOJdcfZWj/KtrYZ+H59sY+Y1GG7F2uI8R5h9Eda+lDpiskK+7HHbVON25wGBGMsTESUr68tHfSno7qnpuGPC4km0ovQzs3LdAIU9aktJHn0Ej8h30r9Mp6SG5FGlIwPNJ1prO4VxLfchISOtkdZC4rQ6x6g+evXdw60JHujsKMp1xJXzDaxj0OCP5GtkeO4eUVNTVOWXf8AFdV770opeG06rlfwM1/T1pAAcgyMKOOko/PUli+aWtwpdCmwPVB+/VnuXvpC2wtWbdVwUOnOtMfA217m3l9456UAZwCT3Ppzrkmnf/CC3k3XXJNY22tGRSHV8RWYhbdbTnuHMnqOPUY1qcmjM3FnWzVy0eWEpM1Kcf2uBj0079KU95QbbnRgfmsf36qrQ3K273GoMS5KJQKW4xMHX0pSULQrzQpIXwQf92ryS7aDn6tykw2CoA8Egn8/no+s0VNwTHmHWlEJafZcHGSkg6sG2wD+sDahjHpoe9wtx3/iEhlkkYyjnz+3WR31V96tu5L1ZplKhXbbi1+JmA2pubFR5hSOQ4B5KHJ88alSjzA3hs6AMHrB6W20jPoO+hTd2nLd2vutKEDqRSJSgQenBDZOQdZJbO+VAudhh1u6U0p6QelDVUbcj/GDynrJLZI+StGVxUu9KvbFRiCYmRHnQnmvgcUtCkKQQfl2Oc6PrvZgWTmSvZnpr1R2NtOStXjLdhqJUs5Uf1ixydaem2ZRPSGUHuoceeuH9kt8rutTaxmnwKPW6hAtsuKnSYrCSzEaKyRlRUOo4JOBnA51tVR3eqlOtaNelSrTTVJkIQ61ILih4nVykDzJPoNIs3ULUDem7aqHWW/d845OANK/R+aVdS42AkgY6cawWzd/K7c/vhtqdPechLSmSwptxtbRIyCUrwQDppn2r2lSpFPkXG04th0NvOdKihtzOAlSwOkHy76Lz1uL6h0Sm3ZSiCGAQQOOnn93fTrdsyR8QjA578dzrImd9rlbidLqjg+ZbOR950MxvbIo/wCkKrUXVHPe2HQ0pzwVeCHlHCWyvt15B4/kSprdg9TkdErt2SEZMdCU9jxqN+jL3iKUGAMcj0I1nKd96q4goW7g8Ht6aHrn9rSj2rIahVerBMx4pCIzTSnHV9WcEISCSONR5+pEo8jav0XmuL+GOD9vl/HTwtSYDksJOONZTb/tPU+tQHanBqzK2GSoOqUOnwyPrdYVyjA7519T/apoFWmLgUy66dLdJ4bbeQTkdwnHf7tRd51G9Q1JNpTg50loJCvPH568NnTEL6vA6s6zZ3e64DXYr7FwQ2qeywsPwVsdTjqifhcDnUCgDGMFJB1GrPtZ2nbsxuBXrqix5DoyGkq6lAEZyQnOBjzOND1+Yyy7BXula8pW3d1gpU100eY54iCUqQUsrVkEcjBGdCnsyQq9c+yduVepvOzZLrS0reePWtYS4oAlR78DUPcD2gqBUNu67HVctNAqNGloYy+hJeStlYBSM85zoG9nT2mbQsjZi3aDWbtpkJ6I04gtOOjrALijgp7+fnpXnT1YU4vY6YRZs0Ho92BB5xjSl2bO/wDQwQBkcd9DcLeuPJaamRqg2408ErQoK6g4CMhQPpr2p74w6dAXUqnWI8SO0Opx11wJQnnHc6lTeo6cdi/FoyPCCUsJBOCR0jP899fC05WcJipwCRn+OdC8HeiDVYyalTq1GkRVglLrTgW2R54IONN1Df22qQ8INTuulQ3ljIQ/JQ24c9jgnt89J6yHUohU5a8tBChGSrB7Y7D11gHtI0d1vcbaSKlgIW9XlchIyf8AJ/jrZhukwIy5a6k0llCCtThV8ISBkkn07nOubN1N87V3D3N2wftqoSJaKTXl9T5iOIjqPwAhDigErxjyzoPPzGbjVnWbVuOKwSlGPQJ8/s1ITa7vADKVAf5o51QsbgNnpIlpGf8AOyB/POpDd+joUhqWkZ5wSAfx/nvqLOx04l1+jbqD0+EhPIyMaeVbjyE9Cm0gHnISNUK76eDSle+NhROMk8/36dZvhaj8U1GAOD1ZB0PXHTiWkm2lnKSE8/jqsnUiu0aMqdR5D0GQOEusEoVg9+Rr1V9px/xlnvz8Y41PgbkUGGVuV1EmZHCSAiGlC1hXHOFKSMffrTwOZ8TC9rBxDj3Mn4AJMuDdZClpavCsHCuxdyT958tRP0p3iHAvGq/gj/DrQJm7u0oWUrolwYGckQ2jz/73tqH/AEs7Rq5FLroB5A93QP8A9TXuPVo825NcjH6VvHGrMtmlw9r1pelOJabKKp1HqJAACfBGT9/mNaXe+8F+UWbEsvdDb2oNOUtCVR2H6ilXwHgKSotfEOMZycYx5aD6TbVmwZbU6n3fQVvR1B1vw6kypWRyCMK78a2jdS6rP3mZoMxRp7NVp7RZkSRNZWHBxxwc/WyeRx1HWZ976RHZ/LQ3ycO78AMZv+C5HEgW8y00tPWErdyU/bxrBNtbkibqb/17dqfSmnaTbKDR6QyF/D4nPW5nHJ+t+I1tNds+mSqPPosW7RCefZXHQ6hKF+CSkjqA8wPtH26HNqdlqFtrZzNtwryRNWl1b70lSENqdWs5JKT1Y8h3OvGcR/Wm29bf1OxG3CNbUacm9qMtSeq3E8Dj9d2Py4+Wue6NdFI2h9pmotvUjotzceOl5hC3eG6gjIIBxj4s/ioa2j9GIKyVfpC0B81o9O3bQbun7PtJ3SpcCIu7G6ZNpUxudGmNJSpaCggkAZHceeeMA86XKuoGn0NRbu+1FEf8CvA9RwOtPb07aqYNy2eu5ZzsimScKSkYSpJ+3jOvGbKDUdtv6ahuqSkAqJGVnHJx1d9VFWtM0KUJ4ntuGSnoJSkKTkH/AEted/iLDw8L0bjcaajh4WIpSbdUnFx+rRt4NzefDirco0vmn+RdXDXLIXHkTmKZLbdUkJUrAPUM8g86ZrVwWR9ANNMRZhKA3hOEg9x89DyonvDamXlBSVJAP6vv/tai/o4+tCWZMiTJZb5QgtgAfPvrwPb3bXYeLi48uExoy77DyaOlF5m3J6c7VtW7Wp0uG4fioqHexfqu+t6bBZW6lZbRiVmMia0poAOpU3jKT5Zz9unKTLsGdUJc5UqR4SiG0EtY47k/u0L/AEJUFwnWFMF9IScFfw4Hlz21Z2/trcn0S06G0hTo8TBJ7HtjXR7H4nhO1+3Iy4HGzYdd7OPs4ijk87T96sy8VHEwOFfexp/dT6pu/wDfeZ57X+19J3R2u+jtvJTztWp0pE1uM6jwxKSEkKQDnAVg5GfTX56K2T3aTMFP/o2uXxirpGKY8UZz/b6enHzzjX6t/oJc7Sf1bbfSruVE9/w1IVZdwJPSqOCpPYZP5ca+pZV1PNyu9jANh/ZC2cp+3FOb3epUSXdEla35WfF/q6VH4GspUASkYyR5k60M+yV7KvK0W/C4/wA6T/i0fx7Qr5SQYo+HkjJ/hqSm0bgLJcMFPzWFn+GmjBXuLmfQzA+yZ7LDgz9Awcj62HZAOfvOh+9fZ69kmwLel3XcCTTqfDSkqW1Ik9alE4CUgHJUT2GtjdtKvIVhEMZ6hnk/uxph6y6u+w5Hl0xt1lY6VtuDqSflgjB0ci6kcn0ONNv9gRvFccyZapqe3m2dQwHPfZTr0qrthWQsNq+EZxwo8Aeatdn2ntjttYdmsWhbda6abCZW22HXFurPVknJI8yT2wPTXybVrLCEhuEEISOkJSrHSM8Dtxp5u2K2pLjQgqOfhGVefn5aVRV7gbdbGC+xna9r3TsBU6HXKqwymZPqEN5LgxlCwEnIx6HWNbMqpm4dz7UbWV+e0qn27UqvJkuOfUdSweqP3+YPB8jro/2f9jL82vtSr2/cDEJ0v1SRLjGM6o4ZWBjqyBg8dhrNqD7IG7NmsUS4bXrdKNz0Koy5OX2l+7PMPhILasfFxhX+v5Y0nLcFu9ihRb8y5PaM33plnSW/fRbbkWC8lYT1vBphASlR7FSgfw0U7ZuI242pi0i4NgK6iFSoiHK3KWqItTzvd15LJc63Ug5OcZAAAHGpNg+zV7QNlXXVr8i3jQ11i4wtdSbkU5x5kr6yUhJC0kDtz5DjBxnRndNg+0tdFAmWvKes2nN1Foxn6hFbk+IhlQIX0NLJHURkZKiOfv0UvEVvXYLK7HsSp7K1TdG1KzTZ0VmhyavDRlI61IZUtKCnuFdQwU98gjXNMbZy0qR7DlV3Jlz4LteqiU1UuqdT44fVKQhGDnqykH8SfU66SoOzX6Obao2whMSXKammuU8urIKlhxKgtZ8skqJx251jVO9lXeOuWdTNrL4uGBFtKjrccCKYhapc09Si2FlY6UpSTnAH9xAyvqMpeBsG2mw9Eq23tsVKoXBHXJnUuM+64qQnrWtTYKiee+sVvjZOkwPbKsy3WapHWxUqLId8VTiSlCkNvHvnA7fnrcNqNvtxbIoCLcuutR60xCaaYp6mofgLbZQOkBZ6j1k4HPHbWQ790y64XtDbYzLahQhV5TMyMwmZ1eC4cHIV089lHtou+pFLwMg9r2x1bM3DNpdHqDTsW96WiQ82ytJ6H23kpUogHjqRwT5n7NdHQfZIt9dhwracqEEsw4jYQ8l1CFodAB8VKgcpX1c8aad9lysXqzXq1vDKRUq7XoogsGnt9EelMJV1pSwFkknqAJUrv28zn5vZn2gP0ebsh3cinM0hDYjfSLNKUKkY4HT05LnQFY46sZ+epUg5l0Oe6TatRurdOwG5lUYU9No9chyXw6Al/wB0XKayecfEW+ofbop9lzYem1ja+bdUlML3mqSJkRx95aS54KFFHSCeQn4T9utQr3s6VmkX5tg7ZFvu/QltMTYk51x5AKG3WiAVAkFSlKUonAPJJ40T7ObLXVYO3jlpVqG05J97luoUwrrQlLqypPJxzgjPGhq+Y11sjnTaPZSiXVsDIumrUmkyZMWPUm470hCFOpQ11lOCeeDnGiz2e9nqDP2mtyurpdJMqWwtxTzjLRdJ6z3VjPlrTtq9kLstDaV6wbmhoVLcTLa8SOepIS8VY7+fxab9nmybppG1FHo1z2tNpk6EHWCy+gJUpIcV0qwTnkYP36lMZSS5Fkuw1RmEeHOjJSEgfA4kDA4xjOue4tvOb77q1umVKeBaFkygwIpUOidMBIUpfkpIIXj5Y9TrriRacoJJTTXQkdxgd/x1y1bpi7AX7fNAvajVXwaxLNUorkWGt73tKyohpJSD8eVAc8Zzoyb2IpIHbJoLdVpO9sSJOYYokSTNZgxUlKW0uIbcLhQB2BIR2441O2E2ZsCr7PtXPXIMSbNqzD4felpDi20jKQEZ+pgJBBGDq72s2p3npdHuBda2+Z90vVx+pK65QYegKeQv4FNEEknKfh4I5BwdFG2mz180rYFy2Z1tyYtwO0+Y3HjOLQkhxzr8MFXVgckd+3noDJmHyLjrp9nu0bQiVRfv92T1UlDinD1Ji+OpOCfQp6U/6JI0dXXbdHod87SWRTHWRGpjz72EHCcNtBRUSO5KgT8ydEz3sr3FUtsbUoLkh2k3JbfRJZfSgOtpfB6ik8jIz5j005Tdhd1qrfdBvC8ahR1IoDbzaG6dDcBfDiSnKitwgHnPH4aFDpmntMttpLpqLDiQAQPPPlxnUmM4kLSgzmCSckdX1f5GvhZE3qJ+jJaur/NGB+evBZNTSnrRTZRxwPqknv250yiOpJciSuSyE/raiwACMDIz9379OR6hGPxiSgJB7Zyfy1WG0aqQMUqTk9jhPH56hOWtVmz4P0c+nk4GB/HUap2OpIun6vEaKkoltlR/ZPGPljy0X7c2q9e3v5Q2HGogSCpP9pWSB+WsqdtysMkf1F884GEjn7NFdrUK6G6O/JpU2owEvOHqTHkONdWBwT0kZ8++tvZeG5cSmuWpVxcsuA/E02Vsi91qHuvGODj89Qf6C3R/yX5DQE9TNw0uEfpRXuDz/X3/APFpr3bcYcC7bgGP/rzv8dewUpc0eenFvmANA2rkwqnGkSoSiy06laxj6yQR5/droD2gNkrEUuhXnt0zCixapHSiVBiudQQ4BnrAycZBwR6pz3J1gdN3X3XcIjyJsNaHD0nNPaHB4PYD11st+0vd7a6j29XnptCq9NrcdLrT6IJBaWUg+EvkZ4PBHfB7efPfdLHjq1v8TpSc3BoGottVeIwGjG+FPwjB9NPpplQQSFxVDp9RqnNy3NNdXOkFptbx6iltASgH5J5wONSU3FXUpAU8kZA5DSe2vK8Ql30q6s7OHrCN9C0ahSj8SoygO/b5eem3IczrCiwpI7kY4xpDFy1lZC+psfY0BjTzty1R0BRbQSng/B6/fqUquxXo9BhUKSUlYbXgchWOe2deKpcw+Gl1CykjIB76zz2jbruSNs7V51FqUqlzIRYfbkwpLrLqcOpyApKhwQSCPQ60azr3mVG1qVMlRWnnXoTDpeK3OpRUhJJ+t3OpLLJZXqity10EppchB6kpcT6jUtEKYBw++keeVHvq8j3WptbfVRmCnzBWv+OpaLtQ4eKNHCTnKUqVgE/bnVPc4KVKK+SK5YknzBWoR6m9FWxHee/WJ6RlasD89WEaVVGG22BKk4QgJ+uR2HGr4XM2gdJozJCR38x+WdYvuDulctE37sKiQHlNUSusym58AhtSXigfAsKKCpBBP7JGcDOs0eDwcPiHxUV6zSj8E2/qxZY0pQ7tvS7NOTJrS1dCJ8wZ5H608HSnXK+4roVUJv3uq76vmrojeEULoiSAPJxIJP8Aq8afRc0FCF9dIWScjPiJ4/2ddCK0M7vqDhqlxcoNUlq8s+IfLS2K7dDTeBWJgBGOXDjtq7TclKDhWqiLwDyQpPb706mJuqjKT0/Qik9QwrlPAx9mnSFb5WDwuK5T0rNVknjzUT5a+duO41cfScpQJ/tavU3NQm0kfRCz0nKeE4H5aULlt8spd+inisHHKUc+upp0A5NcwW/SO5ypJFUkp5zjPA045cl0LHUKrJyrg+Whqib0syt9ri2xqdCjopUOksVOnSGW8Pq6ilLiXMnBHUVYx5Y17snvM3fi7siXLRo7KrduCTSmFxWcB5lCyEKUFE4VjvjjVb0Bb3sJ0XFc6Ufq5shJyRk+fH2aSi57sbwkTZKseeB+fGis161HEJQmE+jyGGk8+XrpJrdqE+GuO8pP9rw0/wAdK/cLb6g6i57xWo/1iSEnkfAnH7tfPXbd7hyuWsJSMZKU/h21Lu+6qXSLVq9VosL3idEhOvxWX0YbWtKSQlXScgHGONUe0W6dtbo7d0e83qcIMioNKD0ZodYZdQsoUnJIJGU558saOj5EV1dlk3et1AJ6ZCvh4CShJGPw06m9rkJyqSev1CE8au2ZtpKdc6w6cnj9R3+7OnM2ePj6nOeOnwCft5zoaPkS31KRF63OHgWpnSUjA/VJ4H4azTcq3LtvjdLb2/YtShstWfLfffQtrC3UrCAEpCRg5wc5PGto/wDIxZUhL6+kDOfBUOfUc/dplSbRU51+8qCR36mFfx0dK2GTfUrlX3ci1KBda+LyDI0tF/19ZKH/AAFnOBlkDGNTw3ZiEqWJSgtODywec/LOnOm0SB4csZxnPgq0vwCm+pBRuDW0r6VIYJ9SyMDT6b+raTnointwGRjOpQjWetOTUE/WHJZVxrwwrUSSlM8K8+W1DP5alKtg5n1Gv0/q7g6lsRFHHH6kZ0pd+1RQTmHDGBk/qu/56UabbaAPDqyCoEZylQ/u0v6PtlSwRUmeoHJyFAfu0KVBUpdRKb6qiEZVBggEc/qyc8/bptN6S1frHaRTlqHA6myDyfLnVPf1SpVnWTcF1QnYsx+j0+ROajKcWkPKaQVdHV08ZwdSrImW5eFo0S6m5bERNYgMTiwtaiWvEQFdOQnkjqx92pUR1JotG72f6gldHgJAHACD8vnqUi8n0BOaRAJ/0Vcfnppyi0HqKkVWOQDjAcVn7fq6+NLoSCB9KR/g7K8U/wCHUUYosUmjx28nHcqdo0LrIwPhVj9+m4d3+Eypr6IhKyrOcK/jpC6ZSMFKalFKknv4ysfd8OmYtPpDiiXKhFQeQMunP5J/nOklFNlkZMsG7wQg/rKJDKiPPqAwfv76movKMpvpFBhpCvP4vy51mO2d90vces3jQjDZpzto1hdJW4qZ1okgEgOJ+AdPCeRzj11oppVIB6HKjGyAAMSPL8NFRQVJktN6ROjoTb8U47qOR31GcuaAtxTiaDEHODjJI0wmjwEq6UVCIUp+sVSfX/o6cbokDJCqjBGRnmQe5/6OlcVepZFijcNJV0pVb0VeOMdWOrGo0rdG3aCwIblkOvFIyVtSAkEc8Y6Tp00KEpRV79AyMgf1sgf9nGrmHtWis0pM1oMuBzOFIX1ZGfI411Oxorv22+X6GTtCX8pe8Bl762slxRVt5M+331H+HUI75Wxk/wD9Pp3/AFls/wDc0dSNjS4c+ByTk4GmBsS1j4kKB8wE9teti4+0cKcoI58ibk7QOpKRErDThGEFUNP1j27K1pU7fWkz7PpNl3gqqx4EZKJETx6WQpSAClKkrH1k8kZ/hrPGtkFt5eS2klIzwR+Ottud6lbi7MW7asukq+nqE6hpmQGx0+7hJBwryz8GR6pzrHNY3ewcop/l4nS9TI9TM3azYciWt2AiU6wsgoUWunq49Dpl68dpYc5ikVKuRok2ScNRnpLaHHR/moKgo/cNDG8lEq22221wXJCKDIpkJTjSCeUk4AOPlnOsX2t2T3RkWizcE2z7Dry6+gTHJ9UfcekPpcGRlRSQng4wOONeT4l/z52ub+p2YSahFR10R1RMrO11JguTqlVkQozCetx6Q6202keqlKIA1Fl3LtVEpZrL1xsIg+GHve1Oo8INnsrq6sdPz1lm2e0+6cQ1e2L8olGctWY2TDioqKpRjgjCmfjQCps9wD9XGBkdsB3FoFwWdecb2ZGblhKt2uVCPKjrek4cp8dSyTGWT2BIBSCecj11W5IWUpLVo6H33unZWtbQ3LR6XuFR3qhJpa3YsdM1krdPCkFKQvJBxxjU/ZbcXZp/bC0kVncOixamaZGZdjPzmkuBwICSkpKsg5HbGe2k3xsfbr231TaetKmuvQqQ40w+uK2p5AQ0QjCyOrjHGsZs+hWXbPsrM7lzrAp1UlRo7jZdcgtuKLviqQlSyRnAOMnSWiqTaZ2B/wCRylJU3VM8D9g9vw18Y1qpx4dZ+Mjn9WeNcPWhb6GbEXcknb/c83zNY97iVuPbkossqx1NNtFPwqZ4SCMYIOnKdaVZ3X32ocC4GazQPpW3GZ9WppQ9CXIcaKkqSpBwekkZzjt29dS01qVW7O5GW7eKUk1lKgchQ6Dz89YPvCxRG/aS2meFVQYjiZzSncHhYSnGftzoMtas1nbaLuzbVRedns2LiXTlTOpx1DLqOptBUrJUkEpAJ+fOhen7cVymRNpt0Lin1CXWK3XEe9+NIWtvw5KFKbCUE9KMBIHwgd+ew0+lVYmrd0dusxbYdABrbeVdyc4H5afcjW6lsJRV2FEn9r11yVYkGi7p1GpVe/dxPAkuVSTDp1vsV0QVRG2llA6mm1pcU4cZOflroKDaM2FT2IkZl1bLLSUIUt0uKKAMAlSiSrjzOdWRa6grwDaPSrfWOpVXj5UP7Xz1I+jLecWG/paLgfDnq57a4+3cvF6obwU/aSRfsaz6NCiCoVqY7UUQ3HgT8DDbi1DBIweOcEny1Nl3rZ9lXRbjVnbqUyuUuszUUubSxXUT3WVLB8OS2rxFLSAoBKgSUnqB4OjmS2YjV8jqxy26KV9CK1Fxz3UONe/ovSkk/wDDUUnyBV31xtajG9O7F+3vQ37/AJ1Hp1mzn4cUU9ptDjjqlK8IO8ELSlKRkcdXy5OocHevca7bft/bu31Nt37V6hKpcyWkDpjNRlYdk9GcAlPI47g4HbS5kuYlPoarRqJDd9sq5GU1BhSINoxk9fiDBKnEnH3aV7IVBiVi27uuBc9ps1G66g6nKh9Xr74PlzoGsG06rbPtH3BSJVbqVVkPWrFke8zXAp5eFhBPAHGQcDnGdZ1am4lT292PlwKDLTGr9auqXTILjqwEtKKx1unJx8I8zwCoZ0jp8w8qo76NpMuNZTUYxxkZCwOPP92ogthPSR9IR8eoV5a4jk717g0yypNOoNwuVJudXk0OlXTNwhgIDaS++pWAjpStR6VHjB8+nRjuved3WpS7KsC3r2DMm4ElEu65jyfCbbSB1KC/qBSirjn0A5OdH4iZXtR1O7aYkxJKHZTHQplSCOoHIIPz1h3sWURyo7TSmkyEJTGrs5hAWQAAFJOOfmToloNJqlEtVDKa/Ua10RlEzpLoWt74SSSUADHp8jrmna2/ro202Xi3fTI0d+jm6349YLiXCtplxaUh1tSVAAg8HIOeoemp8QqmnSO9WbRBKQw8wo54UFjGdV9yUWp0eh1GrUymKq0yHGdfZgx1pDklxKSUtJKjgFRAAJ9dc/7v7m3NY7tn020yiRUroq7UNlD4WptbBA61jpIxytHPz0cXlcNw0CzK7Xaa8579T6bJlseMVKb8RtpSh1AEHGRzyNGkuYFW9GiWvRqrXaJCq8qjyaPJmNpcegy1JLsZR7oWUkjP2HVmLRnuEKHSBnHB41xlQPaD3Z3SqlrWXbTybem1in/S86qIw+lMZCloX4Ta84PiIUnnPOOe+tH203Kvhi/67tNftWXMqlLjoqUGoNthr3yGogAqQOAtJUAccd+ONBb7jNJK6Og12jUwolxpPSCRka8NpzgCtGOTxk+Wsw3M3R/o4sypXjVZMx1untdTbAcCS84eEIyR5qI58udZXQdyPaHplto3XvCZGmUGYlE1+hQWCmTCgqGfFQ5+2pKcKUk5yM8jtqc9yKnyOqBZ9QTlSAFn+/T7do1LpUFMpSruPs/8Nckwd2d490Nwa3Z+3t4wqFTaCw3ORUiyJTk9p5tK46elWAgHq+Ijt92DFZ9qa+Iu0Ldadd8a9JFXct2NDQr9U9LQoAuAd+gApJGe5Azg6FeIdK2OulWvUklKcZ6ge3b56Ui1KmTksY9B5/brBrK3H3Og3W3t9uNWm5dZkUsVOJNgtFtp5KSEvIKCThSVKGCMBSTnA7a0xy5as1HW/IrMhCUJKlKUQAkDknkaCjfMlpchG8tuVRG014tOR8j6CmqyoZGAyrVZttS7pY2CtSo2tbiKtOTQYC48N2UIqHctoBBcUlXThOT2OcY1jcLc7enfG17tr1ArsClWoUSqfT2ZVPW85UG0tlDjinAtPSD8QHSMZyCDgkt7Zb63rblE2dtGnuNvU2v0pcJ0r6g406wgBJSc4KfhIIx55z5GVruWKq2OqIdArDkNl6VT1xZDjaHHWeoL8NZA6kdQ4Vg8ZHfT6baqriOt6NgDuD5nXMdn7v7871S6w/QbvZsmNb8lymvNCMioPPy09+pSwkJbB7YGe+raJ7Su6CK63tdS2YFzXXBb6qvOjyFRabFRnuokKV14xlAHc4HoF16j2kdA/o5KyEqZ+twOO514m05pUpzwVqCeeO3prne9Pa3uC2LcqML3ZtV6RZ7VLapYd8VlTzqOpt0LGCpopOewOeOO+nLTvH2xri99ZrFcoNruQHiwCaQt0Sk9/FQS4QR5eX56XVDppk72WqDPq53EuXwlpbnXfNIUe/wrI9PnrYLLnU3cOkqr9rTEVCAXVxi4lCgUuIJC0FJAIIOOCNcjbQXn7QNh7cXlX7Tu6giJRKtUJEuHMpqlrfeQQXCFJUMA44GtNie2duJPqll2lR7SbnVW6aY1Unz45YZZCurqCCQoqA6DySPLvplY6kjolVszm2gAyok8caSi3Kk2BmO4CR2we3bWSXN7UdwWbZ1VuWo0aYmZQXo6KjSnkJQ+226oJS62rJQ4g54KeCQeQQRqRI9puq1jZyo7t2RMhzhEiqe92kNlJbWlQC2nOlWUqAz8uQeR3FN0OpLY0l+gzsnDBIPy0NXBt1MqyxJ90SCsZGW+ft/LVjZ26FwXdalHudPhMipwWpXheHkt9aQenOfLOPnq0lbz3RSG0xE25R5fhgDqcbdC1fbheM/drq9iprHk99P0M3HyfdqupmDu0kvxCtMFOc9w3qP/AET1X9mAceWtIX7QdZTxI2/pSykfsuOJB/fpv/4ws/z24hf9bX/h16qMvA4s72aOc4tjXIwQll+UnjnpcUP79bjW9l6YztDRdx7Luirmcp1MSrQXJGUoeIVykJwUjgYBzwoc6zWHvrd7mUvWnRFjJwoMuJOT5cK1oVRrG5tk2vRq7WrGpaqLW0B6I+mQtSV5GQFBKj0qwexx+WsUlhvEglKvz8DotyUXoA86gzarAkUSttuyWZLRZfDyyrrSocg5+Ws8oO2+7m3bC6TY10QqjQm1ERoFZaX1xk5J6W3miD08/tJPby1vrV9KqTbcx2gU9hTicKbSkqAP2k50+u5+pJP0XEBT3PSRxry3F0seddX9TrYcbw4t9EYYuhe0PVX2VvXdRqGylxJcFOge8OqSO46n19JGP80HUlzZKzps+uT6nbkqoSq+AZj8p4LUCBwWyVEtkHkY7YGtqTdCugj6MjntwlB/cNON3M0klRo8VeRkk54+/VFp8hGl1Ml2/tq+LZtqXaVxXFLrEdKnW4Uh3/LNxVDCW3D1HrIB76CaJs7d0PY6sbTVertuKlOyHISmurobSV9SAvI9eTgcZ10mLgiqQVLojCjwcBRGNITX4JWF/QTQHlhwj7u2pfgVyV8znqzt1N17Yt+Datf2quyRVqWwiKl6CppcR8ISEhfilYCMgducatK3b97VbeK091KYHIwiU52BVEvLUHUNrBISnpBCiCo+eOO+tyXcNNcI8SgIznHDh7/hr5ut0ZZIVQh0fJ3BH5anwFq+ZznP2yuu4b83GVVVvih3lSo8VqZklfioSkdJT3+EjOSMEY0Prc3yk0S3NuKjZUuTOtGoxJcSsNvpTAkMRzwSs/EhZTxjBOfIDXWzVZtopIXRVg/5ruONLFRtpRyikqTyM9KwSPXViXgI14nPVbqFxXfT5UKR7P8AHVMqPUl+RVnIBjpWc/GtSFLcWM85SjJ1oO271w2NYlHtKTXXJblMjJZU6eQec4BUM9IzgZPYa0ddQtVspApMgpH+eOf4a9Ei1lJVinSBzkYKcEenfR2ewj23OY7yg3Nbm9c3dmNZ7d4U6uU1uFOjJQyqRGcb6QlxCHcBQISB8Pz0X2tuO/WKwxFTspLpcQZ65lQp8FkMHyPQVdR5/sgkemtrLtpJUSmA+DjgHH79Ol20vDwqNJQogcgA8+nfQtc0VO+pzjtHcNxWtvduhDkw324ldkx6ozKLJ8FxXSQUhRGM/F2+R1jm19P3GsvdSp73Uiz5dcZZrFThSYCAESEtunIebSvHUD1Htntru5pqy1sgBL5xz9QAj89LCbNSgDpfwBjlvvoKnyJma5nO1oXTel378t7nvWPU6DTmbdcpDqqohttx1wvdaQEBRJGPPgax27dpLutisxLlr1qRLjt6mXXOqi4EYJfedhSClRKmscgdAynJ7+nOu6WYNmuoUovOgk8gt5OnHqdZXhgIfUl1Q/5s50NOgFKS5mQRN+bOgWbAfgWpJ/R9XUwGGbdd8NkpA+FbPR1AHPBCSk4POs9sbcZy3K7c1y3DYD1E28uB9pMCnTqaXGmX0pw48Y46iwhzPp0kjy108mkWWhoEzFkEHA8M/mdMuUO0X/gVPTjsR4Z1PVXIiclzMJ2fviKm77uZ2+o8hix5kJAabksraipnkqDnuiFjqSgp6cgADq5A7ZzvahSrn9l2/dsPo9p2oRqjPT0/tpeCg4gY9cpwNdfsW1aIQFmpoxzgdJwNVsy3rAt6FOqKJsWLGQlcuQWmQgKwCpalYHJ7/botxJcjkrZ+/wB3ebduwajIhIci7cWwhEhLiSlJnEBtRPqokJP2I10purd/j7cXYymnxut2iT0gjPBMdY41m/sfWXRaxZle3Lqj8eLMvCtyJnghvp6GUrUEAfLKln79b07ZVrzGnGpNQiOtOgoUhaR0rQRyCCOfPI0vqhbdnFHsxVdhjdawH1Q2nEt7fyWUJVwCsVGRk8eec61mkXFGqHtkVya3S2VNUuzWobyBnAcceadTz/oK1t0Tarb+nPNO0tiixFx2fAaLMdtstNZKihJAGE5JOBxk6dY25tKHMeqLLtKTKldPjPpaQl14AYSFqxlQA7Z7anq8yZmtjA/bXmyK1s237rSyGolWivTfCJPVHAUDx6BRTzosuT2mtpqdbnRSW4txzZUZTcGlUlXvDz6lpwlKkpB6E84JVjAB7njWsu2TQpjS48mRCeQtJCm1dKkqHzB7/ZqJT9sbOpR8SlR6PEVnnwGmmic/6I0PV5EUpczk32RotVsjdW7aFdFM/wCEU0OmlyOVj9RltKkoPf6qVJT92sggqhVndOlGsVqfQ7eVeNVLcyG+ltcZ5SkqSQtYUlB4RyR21+gsPZCy4t4VC+ISmG6zVY7TEqR7ypXWhtICUhPV0jgDkDPGvJuxlk1aI7SKhRqJIgPOKeWwuO2pBcUTlfTjHVkn4u+poG5dAGsSwNvLfveDfpve6rnqrMRyIx9K1pmSjwV8qCQltJ788HGjrcOqQ6tY9xU2mUMmXLpExiKltWCXlsqSnH3kap6B7Mu2lrVD6VoNt0uNMjqBadSsqW2TwejqUenvzjGi9yxupoLEtOATwmQUn8joeqMnJbGCezluTtnSdj4Fl1KXEp9YpcaQzUYkp5LTyHVOOFWUrweerOfz1k1i3HSo9O2Iq7sXxWKfcVXp7y0q4UFvqDYz69JGuuatsZZNyvJfrlt0apvJPwrlR0PEferPnqND9nOybfp7FEpdu04Q48pVRZaWouoakKyS4jrJ6Vc4GMY7DA1HlGWboZFtdXolsXZvrSWKOt15VRXVITRJGfFZWoAY55OO3rqi9mTaDZOvbYwrnu2gS6zXag68ua+KpIbwesgIKEOAZAHcjJzrppO2YCS6gjxFHCyHDlXlzzzoCqnsi7aVSe/UZdrIaekrKnTGqMmOFqPclLbiU/bxqeqth0pGP7kWXsxt/vfthcNMtFNGoJlvmovmQ6ttchKcxytS1qAwvHP4511HG3Bsep9DUZ1h0rACA2+hRV9nPP3aF2dhqFBoDNpIgtuUplGExJTqpLYTnOD4qlZ5PnnUKi+zhY1FntVij2hSY0xhfWy80wlKkKxjKf7J+zQqPMeOZGQW3VaQ3t/7QdFERwLZrFVWwVYylC0E9vLtqqsOVbFl7kbX33c5VFtydZbFMTNd/wAjHmhJJSpXZIVngkjvrfIHs+UmA/cakQXii7XFOVVBkqPjlSSlQHOUjBPb11PpWzcKjURi0qfT+qlRG/BbjyFl9IRzhJ8TJI7986CS5jVIxX2m7s27uxSqNaVZjzZLtvVJM9MZxLnhttBD7KllOQB4jeBk/tHGgvcV2i7Q2xPbpbbrVvbhWu2nwkpy3Gq6G0ZV8g4jqJ+Z9NdKP7AUZ6izqLGt+HDhVJtbMpuJHRH8VCu4JbAI7+uo147Fx7xtRdmVqKtyE4ylpj4ElbKkj4FIOMhQ9fMZB76aknuOk3yC7b1y02NvrcjMPlYapURPWkcKwykenGtAbpu2DkKO9PvOjR3VN9Sm35rSFoJGcKGcgj01idqbKuWc1HVFn1UusU5inKLsglDqGgAhRb+qFDnkDPJ0dSNpqpJZbdKVr6kJJJGc5Guv2JH+ZJxfIx9oN93GMglcom0y1Dpvm3jk8/19o8Y+3SBb21pAP6bUP/r7f8dAb2zNSIJEdQ59OdMf0K1I8+Gv8Br06U1zOPJLqBsS4Njnlc1p5s8crhOD88a0GJuvalZsCHt5U7piJpcKV4zCXYjgWnlZyFAdj1nWao2DqKFFKYqxjB4T561tNCtS4djYllyLf8G5KLKKoc5qMnLyFOErSpzvgBSuDnlKdZsRTzwbhevy8ToerllqC77FpOPYpla8eMQAlbbJ6ew8iM/u0r3ehL5FUJ5ySpvSIu39Sp7aY4TgNjkdXI0EbzVSbtjYdTuR5rD6UBiIjzckL+FCQO5Oefu14/jJf8ifvf1OvhaYUfcgBt/2gYlZ9oaZtIyqAihMocYYqAaX4q5KE5KfrY6c5Hb79b63TKY5kN1+Ok9Pmyv/ABa5CufaCt7P7a2RuVOi/wDC1JrDdRqy8EuESSOtKj344HpnOurqdRJkxhiXHaKkPtpcQrHdJGQfw1QmIr1ssU0yEhWV12OUp4I8M9vx0CXfuFBtDcKg2c7FiyolbAHvgldBZUVY5T0nq8vMd9HItmoLHLKiPn5n+GsN9oC2KjDu6xakiKoOJmqbTlJH7aCP79asCKxJUzl9q48+F4fvYOqcflaTN+XSqKtLZRWYKiSRy7jH5aQLcjq6lNVOnZzjBlY7j/R0IXNttVK6I5Zq9ZpiobnjZgrSnxDjssKSrqT8tXKKJUW2Uthl5RHmpPfAGdCloa1JttNadSzkW06kpDNSgLCs4zJwP+zzpxFvyG2lKE2DgDOEv+fn5aoRS6ilRK2XCn8temBOT05acSDxkJI0FJIkmEYtmW4ghyXGT0AcBwH8Nei1pnhlLa2VAAEfrEgfv0MqiVEE/q3uOAeg86UItTT8aEuf2eEnQzlLaYRm2qm06B7uVp6fJaMEH5Z08m1KkpAcLKlIzgfrEdvx0MhVSaT0qQ7yMcg8jS0v1BlSQfEA5I50M/UQKkWvO8AlUIJPr1J/cDqO5bVQU2Upik48+OD+OhOsXAbdpz1WrVfj02BHSVOPyXw22gfNSiANLplwLq1PZqFJqyJkKSkONSIz3iNuJ8ilSSQR9mipMGgUKtOppaSoRVfEfI6eXatTDaQYTnWkc5T+WdDKarVg4B47vGMfGeDp39JKwHEqVKfGD9bqPf8AHRsGhduW3VvqrgPBIAPA8tIFtVU/CmC7gcn4dVaq7XXFe8JmPknv8Z/k6Wi5K4B/x+QOv/OONBsGhNVQqmy2FphOEK/zfnjQruXZ123DYlboNuxy3PqEJyOwt4KSgFYwScAkcE86IEXBWmupaprpHGMnz+WpKLorS8qcmOZ7cjz0Gw6IFNqLAnWFt1Q7TlR0qk02Ehp9TDayhTvdZSSMkFRPONFYiTeo9UZ0BIyR4Sjj8tSEXDVldp7o8xgAef2aUqv11BUv38kKGD1JGT6aKYraeoyabJJwqI7leCkeGon92ml0mYoHqjOgDIIKDqaLlr5WCuSFEjj4Aee2n27srjS1IS6lSSQTltPf14GpYVRSro85sqLrTienyKTkfbpX0VJT0q8MjJJPrq7VeVc6ypbreSkDIbHJ16i76w4rKlNnOEkBocaAdCiMF8K6FqSk54yf46c8FTYCFqSCngg40QC7qk24FJYjlQPJ8Ln7O+lPXlUnR1liNzgEeH3H92jdKwpK9wXLSuskLTheeerudetBSUAKdb6TnsrRIq6pwAPuscfMt/79LTeUvoSDDin/AO7P8fs0t8xkl1BppC+lKg4np9QsAHnvpXiOownxUlJOBzopRdqwnqdp8VWBjlPc6+cuqM4rxPoeKgjvhJH4DUukMq6gwv3gJCeo5J+qF8D+fXXylSGvgEgq5Az1aIxcUcDq+hISlE8K6c/v147Wqa40EKoERQJ5wMA6Fp8i2K8SiRMWv4V9aiBjIXzpPjujlCnQR2yo5/nnVwqdSgVqFvRSSB5Zxr1moUTKQbejYx2wn1zycaGhYmVKJlSThYkPgpGMdZ/jphc6qJcyl10c4GVE4+WidU+gJHUzbsdCu4xjHfsONepn26pBKqE2nzODxz6emg6W5ZEHm6/UwA374+kJHHxnv20l2tVRbgLcx4lJGCVH01fmbbpIBoylEHPB40lM62C98VIcCQeQleDjGha5DqwdkVasr+Fya7k+ZV31fydz90oaUR401pSWkhCeuG2ogDjPbS1O2YuUgvUp4IQoElKskJzngZ5OimfuJs2hYbkRqrkY/wDMe/8Ata7fYyj67avbkc/tG/VQBO7z7tNKx4kI4OeIKP7tRzvXu+ST4lPH/wDrkaNDfuybpKVOVFv/AEoB/u15+mWx3lVHMfOEv/Dr0Ue7rbyZyJv/ABOUYUbciKB4deq4Pp705j9+tut/b+55WyD+5lv3tWkVal1Ax6hCMhQQUKUgBaMc5/WAnP8AnemgGLvrMeGDt7SU9xgOOgj79GVBuG949nO3qNvm3Lbdklp19iSrpbdyPhUBnAypOCR5jWXESU4+vWv+o6bbyuolGmo1qQkP1ebIkSjjrcecJUrHqdYVecSZvjvFHskVedGoFmtiXNfhu9KhNVjoCVEEBQHy451tV7biNxaRU67Btw9ceKp1qM0FOrWoJ4AwMnJ1nns3xJ1r2O7Vq7Th9N3HMdqU/wAdtSXAVk9KDnGMDy+evI8Tax5+9nTw/WhG+h7eWxU25LcqFFlbtbhTWnmVdMebV23o61gZR1pLWSMgdjn7NT/ZsvKp13beLS5lQmip2+tdLmBclzqSps4T5/2en8NahHuJHQsrprJB7HB/DWDUe4Ye1HtGTYjsNtND3CZEhlHiYQxObz1Aemf+8NVq1rRGknozoKNVKq0kuIlyc9gC8s8c/PWT+0DWKk5OtFT8p1QbqQPKjwcp7a1RV4UVIyYrGePquD8/nrIfaAuijyH7RWiEnCKkCopUOcFPHGtfDNrERxP4gjfATrXWP/sgh3Y3Tvug3BazdGuR+KxPmeFJQG0LDiSpAx8aT6ntqi3D3G3Wk7kQbEt67JEKFUY6FuOBpnxEDKutSV9PUDhJ89L3/lRJMm0pdMpD7ymKh4iktpLnw5QecA+h501etWojO+1oTDEdS29G6Fj/AFx5fbq2MVSdcmcbjuIxljYuGpPLnw1u9mta/Mcua6b12lqlGqNPvSrVKi1B1MWdGnuIf6Fd+tBUnKCeTgccau6zuRfVfvRNlWhcKYLUeOmTMqDkVp1SQcYCUlOM8gcjXntAyrVk7fOKhsuOPpmsFASApQ5Ofq58tCMC1Nso16qrG4tJqK6NWabHkRpyZL7KGHw2nrbcLSxjPl1enz0Ixi8PO1rqVcVxGPgcW+DwpNQbi7tpJNO1erSbS+fiaXSd06/RLojWPdFXYqLspgvxZjbCG/Ex9ZLiBwlXHccH00aovKcQUo93KfIqYGft4Ostp0X2ULfqTNwU6qIYkxElxLpqcl9QHbASXFdXHlg51q9BqG3NfgNVWjTFyIboPhupb4Pke/Ofw1nnlTTUfI7XBTk04Yk4t8qldLx2IL91VR45Q5FCvQR/7s6hVq96vTqXKqaoLcsw2FveAxDK3XSlOQlKQeSew0VsU2xySVyJCT80ZxpLtKtPKgme6cg9J8LH+7VfjRu16n5/v3ZcG8F2t3puvdNpQoMJ5Ri2lXZMiFHaIPBUjpSHe2SQpQPY8fDro+19yd1pdPaZtC3NrajT2EhCU0+svBKGwOAlKGSEj051tRtWx5YzPWy4ojGXGQo/mNMUjb/auhSJEykRaVTpEpI94fiwUNOPAZwFqQkFWM+Z9dFahZlsrdfeWGvwB7P0WWpJ/wArGr0UJP2eIpJx92ktbx7zAAH2ZfEPqq44A7/AHmtpVQ7UWG0orSCBz9U5H46cNuW8p3paqzSMDzVkZ/36GiF1ow1O729qU4T7MbYAPBNzwiT93ifLUmNu/u8kdUv2Y1qB/5u5oB/evWyLtejqQcVljKlDGFYAH5ajmgU5lXSatH6UefVgaV0FNnMm4m5e7jdRRdNu7R3lbUyKyEPx0yI1UpsptJJHjMpOUHJ+u2tJx68YvfZ79qyRu/UnqBVtqFxH4TSlSKjEeKoaVDHCurlJUc4SCo/aATrTN4NkX92LchW7C3INDpipiXao3HaBXMjjnwuvIKR5+YPGQcaIrY2ltCxbejUK0RBgQIyQhLbeMrIAytau6lHzUcknR0ByrmVV/buWhtxQlXBXqMooU4liPFir63pLyjhLbSMfEo/PQ9Ud/v0do9PuS/NpZlDokxxKX30TPenKalX1VyUIR8CckA4KsE4IB40IXu1CV7WVl2xctRYTTGKK/NpZdUkNOTypSTgnjqCRwPUJ1H9sO8LXom3M7bij1Jmq3XcKUR2abEHivMtBQW444kA9I6UnGcHnPYZ0LRFFmw1Hd7aOhUqBWazVoMWFVkhUFxUkZkJIBBbSOV9x2Hnqxt3cbaq7CWKDPZlvBJWplDwS6AT3KFYUPw89ch7AQ4987ubcM3E9GEelWEh+htvr/VuykLU08tIPBWnDox3HhhWPhB1vPtF2XBh7c1K+RV4tMq9st+/0yo9aUONvtnIbCs5Ulf1SjkKz20W0iZWFu4O9O0e3z8Sm11M+RVZpT7tSqaz7zMfzxkNoOQMg8qIBxwc8anW5uhtrX4EupwxJYap2RUGZiUx34KgnqKX23CFNkDnn7Rka5K9mej7y7nG5d3LWlWDIrVVqKmJb9bele8xEJSClptKG1BDWFDAB5CRnPSMaZRvZW3LuOt3zVN1rnoaWrxpseCpFAedSULbWlQUQ4gDgIA7nPUrtqWr1Gyh5Sfab2luesKp1pWne1fjNOeE7U6ZR1PQ2znzX1BRAx3CT8s61FmTbbmFCLLGADylIJz9/HfWQUPZfeSx6TFoto3pbbtMpzIbjxZtFU2VJHA6nGnQB8z4ZPnzqXtPfNRv2tXLZVYp7FNua0nkR6pHjShIjqChlLjTgAODg/CQFJPB50tpkp9DYHBapbSkplgnnGB+GM6zJHtBezq9WplAavZ0y6c8WJRFPk+7tuJ+sFPhvwhyMZKsccHTHtBOXLZWyt03LTHVNymISm23EHCmushBWPQgKyCOxGons/7Ss2dtJQIcCIhxVUhtVOc8Egl955AWST+1gEJHyA1G09gxi6NMh1CyahARVYtUWuKpsupfbQVoKQM5BSDkY1kbO+Uu+Z8gbK7dzLmosN5TD9YmSUwGHXE/WSylYK1dxypI7841B3BgnaC9rckUiOmJSr/mros+CgnwlS1oPhSW2+yFEkIX0gBQwTkjJgexfTKl/RTJRFayGa7PbUAOykqTn+7UTSHys1zbi/bJv6nSUJTPpFYpb5i1alTI6i/CfH7KinKVJPdKwcEc8cjRp9G2+WwoVAn/AO5WMflrnSksVmk+2RVKNCStCa5azcqayf2nWnAlCyB3ITkf9LW/fRtU+oqOrPp5Y1LiNTJoat5RLf0hwCMhTKgf3ae+h6KSlZqaMH0QRqCKY8v6rCyvA7j8dfIpcxIKEhSleQ7aCosVlmu3KQsBQrMdJKQcBWPTTSqDTlpIFVi4H+fyTqJ7lUmx4rkZwYGOdeojTs9TrC048saD12LUie3a8QHqRVoxCcZPWBj8/wB2m1WrEW5lM2OcefiDn89MpRLAylleD3A7jSFtSgonwHAVDAODpW0NGybHspqVJajJlMrU44EhIWPPy1PqGxkpwlYYKufMfw1QmBLLiUhtQWTwexB8sarptPv1o5jVmrNAn/kpjqefuVxr0HYaeWddUc7tHeKLd7YGXkq93Vz2GMeeop2HqOT0snHl8J1QLe3VZ+Fu7bhSD/ZqkgH5ft6j+97u+V2XN99Yk/49ehjn8DlTk47FBFi7LOEFu9qcOexQ6k/h0aMrP3BtWg2pXLCYuylvUirlSQy+06pIJ6f1reE8K4Hf+yONZrF2Aq6cf1ReR5BOD92tXs62bUc2mrlg3Fb4TWmH1SKdUW4oU8lfwnwyvhQHwkHJIws8ax4uZuNwvU3pqn6wKzaXavip9xqrbrASnpcbaICvszpLdFoikpxVU98cgjj+caW1aNVp7SYioilhoY+sB+/XpoFVSQRSiVds9Q7a8lxKviJ+9/U7WFXdRrohC6DRktqCKq2MeiSc86YFr0Vaeo1KMpaeElYBOPlxxqQqhVX4UmnLQfPJGdJ+gaipY/qrg8sd/wANLXiSSSWxEFr05WVCqxe56cLx/PJ0NXztVTL2oq6Qi6BTX23A80+w58SSO+RkZBzq4utybbtuVOvLpMmQ3To65C2kABSkoGSAScZ41lqt54kim2LW4FtzXId6yjEaK3UoXHV9gyF4II4I0yk46pmbGw8PGg8PEWjPWfZao72TVNwZ0xQPKwtII/1grUtj2WrQZcw3cU9ZHfLzXb/UHGtD+iaghKuumyMHsSkc+XrpwU+WroK4zgKicBSe2rVjY3U40+w+znpLCv4v9QCV7L1qKBQirTlev69vH/Z0k+ytbjbilxq7UGyj6qvEa4+/p9NaCuK+jhcdwEHyST/4/d6aqK/XqXalPVWbimmDAQtDa5LzSw2hSiAMnpwBnjJwNDvsbqUvsHs3+0vP9ShR7Ol5Rz7zSt1JzXRhSG3UqXwO3Icx+WjWyLKvSm0VUS5atHqUzxVrEhpZBLZxgHgc/wA51DalKKcoXJU2oBQKWnMEd+OOx06iZLZOAqWBjIHhOD7O41JYk5qmyzheyuF4LE7zBTXhmbXybYSm155RlanM9sB9X9x+zTSbWmr+Fv3rgkjDy/XPrqh+lJyQjrXIwrJGCU9/t04KtLGW1SnEEjkqWe3z7aFSS0NzUS5dt6qeIUJQ+Qkdg+v+OvWLbqiQW/BfAV26iT+86pE1ySy38NUweSf134eevDdU5kBSavgeZ8YanrrUFQRfqt6roBcDUjo8j3GfP8tJRRawhBQFPFZGQMeuqsXbUPDC01V1TZ5wHeOPXy0pV6TEkOCpqQtZHQS4BnjyGleZai1HYlqpVUMgIdS+PI8jH3a9bpFRcUQ2l1QPOT6fhqMbsrCwltUsnOCcnP36c/S2qoTgTCOrg9ufy0LmGoj66ZU8nCVoAGQVADPz0tym1pbKQhbvQBnHQB+WoovOqtJSluVwSOOkeulJversBclMpCUJUc5SOB/DTJySFqIM3rtjQr+p7dNvahsVZiMsrZD7XxNq9UrThSc8ZwRnHnqntnZSxLITNdtOzYtPkTWFMuvhsuulBTgpC1lSgk+YBwfPtq/uy6dx5LUedaFdo0V+O4oPRanCLrElCsYHUhQW2RgkEZHJyDxqkq27288WjvxY21cWdU1JWhoxaqyqOPRS1OBtQHngJPppW2+Q6S5Mx72fLBoG4W1MWlV+G6mdZ9anQoU2K4tmVFX4niktuoIUOXO3bjR/I9mm1a3Pj1G8qpcl0CGorYZrFTfkstZ7gJKhwcDPbOOdWPs621dW09kPUiuPx3qpV6lIrE/wxltDzoSnpSfMBKE/eTjgDWtKu2oloBqNH5JBHRydBX0C2r3MulbJ24ipuVu2XajaU95puO45QJLkJDqUjpQFtoPQoJHABTxqbRttbhhMzWaluxelTiTGCypp6b4Zb5BC23GwlaFDHcK589Houma6SmRDYWVYTnpxgZ7504LnkpUcw4uB8I6kkj0/ho670Be8yyp7ZbmTWVw6dvvdkWAUFCkeAwp8IPHSl7oC0nH7XKvnq92r2uoG0FIkQ7TivF+YvxZ0x91SpEpfOCtX3k4HHJ0dN3N8aU/RzHQU8jt+/Ulu6WFL6TTGfM86VNrkPSfMqKqp24KTMoNYhtTKdPZUxJYecV0uIUMEHA1mbNl7x2bTm6NtduqiHS4oCIsGtRffSwkdkIeASoIAwACFH54wNbOisRO6qY2DxwFYxr012muOJWmmJz1DnOjLM1sNGlzMPtvZq+qhe1O3F3i3CVddTo5LlLhtIMeHCcPPWlIB6iDgg4HIGc4GDXauzjtNSJ1BoMyZJizqk9UlGS+kqS46B1JHSgccfbrQ/pylhXSaf3z3Vnnz+zX0eq0EFDaYK09SjyDqW6qgpXzMpiWHdsX2g5m8hq0d2HKoYpKYwKveG19aFA88FPwq5yDyONag1ddaYX1HxFEcYynOp7lTtr4Ue5rSpXbpH886ktTLUcALsdxsnGMDSq72LVtuU6ryq76gSh5JyAMdPHH26dReFdQAhrxQUZUCQn1+3nU8yLX6x4aCAThfz/u04mqWsB4ZZcGCeQAfz0LT5DpPayEm9a8pQS7z6hQB51IN81RJCijPGB8AP8nTb0+2lpKkeJ6kgcD5aQ1MtVIBC14z8WfL10t1yLKY6L5qiFAmHye58MeWli/5bK+tUNJP9ktd/np7320HSC66tIAxnA7Y1GdFpvvgKmHAxhOOM/boSroNFMn0/c0MVKO/PpIkobcCi2D0FZHYdWDj8Doikb+W806Uv7crBz+xUwfw/UjQzbVDt2r3JDhN1VhHirwFOLSgdicZPH3a0yRstSJRJbmQnSr0fQc/gft13OyXhKEnN1r1o5/H/eSq9AQb38sPJRJsGe0EjJLclC8fikZ1KTvrtYUg/ojXeR/YZP8A3tXTuwcPkoWwQewDicfv1G/oBhnkvN/iP467GfA9vzObPf7pyVQbo3nt+AiDTLsrLMdCirw0yV9z37nW27a0jca6du7mvWNuPVma/RFmUuC4rrakNJQDk5OSrCVAZGOE+us9o2/lLJUisbaR1lR+Ex5amyB280q0aWVXancUC4bvoe3Et6hU9xC5yGKmhK2W+jnKSnKh8JJITxg59dVY2HC081O9zoJyqqKQVu46kr6Rq8956W7hTq1YHOMDt9mpiazVEAAyHRx36u5/k6zfdLfelWa407TaC9Kl1h4R6VSkqSp5xwjzWAAEjuVY+46iNX5uTFpIqVcmWJT5Ck9QhvKd8NJx9UvlY59SEHHlnXk8ZfzpPxf1OvGaUUvA1hFcqfAVJcycgkHOm/p2oJWCmY4fXONYTUPawhR7DrdyUq3oMis20+01UqcZKXE9ClhPW263kLSQThQH2jXkX2n69bzdv3DudYFLpNtXKFCLKhTFuvwzjqR46SkJwoY+r8+PLQ1K5TRrG5NdqQ28uMrlKKPoySfI5/VqGuWqbOmxtsdhGlP8NXEHW8p+rlSvl8+2tNrG695bm7S3ZctHtii02hvQ5LUBMtbpkyY6UkKdyn4UE4JA6SOPLvrMVzYTe0exD4aSBFrzQdVn16hzjQsplK2dpIq9RUB+tQvq75QCMa9VW6mlWEe7Hp8vD5H46y6+d9KRadxRLMtyz5dyXC+3709DiOpaTGjjutbijgE89KfPzIzqHSPai2zuqbDp1pW9cddqctsuPQafEaDkPB6SH1OuobRgg/tn9x0yrcrbZqa7hqHiZLTCPNSS0OdZR7UVfcnbH3VGdjMdPu6CFeEQU4cSRjVpcO+dsUWsQbTj2ZcdTuaoMGQmkxkRiuMjsFPuh4toST5hStDvtD1WHW/Z7ueRIoNTo09DLYchy/DWUnxE8hbalNrSfUH7QDxoxA2zR7Jux6XZlCfXT4xUumRypZRyrLaTk/PRCLhSvDf0VGxwSORoC2pvLb2r0inWdDqC26zTaTEdfivNrbUUFpPS4glOFpPqknHnjV5ct+WJaNwUC3qq+6iZcclUSF0tuOArAz8QSklI5AzgjvnGmikkVybYS/T8NLgL1vxlccd/t451T3JfFv29TkVOo29JkoceQ2sw47shSAo4BKG0lXSPMgcaI0QaW8hK3ZMdJPkHVDp/L0Mbp3pY+1VqO3jX3JMmCzJZjlmnJS48C4rpCulZQnpB785weAdO6EzNloaxSHknFFR0nthXTxx3BGvRVLecY8NdBQhQ5KvE75+0ay+7d4oh3B/ol25oTtVuIsNzVy57iI1LZirSFeKtxJW6cZSCkN5yeM+dlaF4+/3rJ21vWjt0i5W4iZrBjy0vwp0fOC4w6oIVkKBBQpIIx56XnRHYcJn2+CEGi5R5jryMfLjWJe2F+j8jaNNaptFU3OoFZhVJp0HJQA50q8u2F/lreZFqhkDwVdQWMjDrXH+3rK/aYtF9Wyt3JaKVrRTi8P1jZz0EK4AUTnjQaa0ETth3TKnZtSjRKo3SD4L7aXhkpOUqAI/fqcs2R0LK6S5nqynCB+GsD2Zqu+N37d27Vbes21IVJZgMR23a3WnUSZqW0BJebSy0sISSnsvB+0c60e0rxiVqtqsy6aNKti6EoU6KZMIcTIbT3djvI+B5HrjChjlI4JEboLWoZMxLNWD4kV5KzzwlPA0H71Uy1H9qLsRGalBRpUhbfGMKCCR2Oe4GkPbkbWJqkukI3Co4mwXTHlNl04YcCsdK1Ywnnjk41A3ar9CpNjVaBUqifFqtJkiG3HYdkF/rbUEqT4aDkcjnto2ya9DJ6kxSqx7EserJqMxNYiUpqUh9C1dYcbe6TlQ5+qD563jb9doV6yKHX3XnlPz6dGfX8BwFqbBUM/aTrl2zbzoFT9k2daDTs/6Sj0Wd1f8Fygx8ClrI948Pws48uv89aDsnu7ar1jW9b1IpVyVx6nU5pupSaXSnZDEFaUDIcUByQCDhAUcaCbYWq5HQzcG1SOoS3k84I6D+P4akMwbTcUV+/rQoAHlJx21QW4qFddIjXBbNQZqEGRktus5IODgg55CgRgg8g8HVwm3ankt+AoAH7u3GnTfUWvAGN50QLd2suu4rZuBTFTp1MekxXAOrocSnIwFZB+8Y03s6iNeu01s3bX64k1OqQEPSQ2VIBX2PHlnHl92NZrvnuDZ1T2yvy3KFdEKZUIEAtSW45KkoWVYKCsDoKsBXw5zxou2UXGpe1tkUd2ZHbfmUlpcVlx5KFvEIClhAJyrAUM47Z0VKxqSWxpq7doLSuhFZOEoAH6w/wDjpItqnrypmtgE5xyMcfaNZhdtc2+tO+o1buPcFNJqLsMQBTn6qER3UFXUlamCSAoFRwvg4PmNH0OI9PhtzISw/GdbS4hxpQWhSSMhQIOCCDkHS22xtFyJqbbR4pAuAcDByUZPz+rp5+1PDQ2I1wpJJPUQUD7uU6i/RM9IAVGUc89RzjXi6fUUL8PwCceuopNLcOj5GR+1BUrisLbVmq23czsSpv1eFGYdaUjJKldRBGMFOEkEEYOec61yFaVXVSo7r1TaW8WkKcwE8np54yADnXPvtZR3HpG3lBlrCW59yseKlZ8hgZPy+I62ebGueW7T3Lcq1PaisP8A/CDb8dTpfZI4DakrHhq7nJCh5Y0Ldj6MIRZ9b6UOfSLBKOOnpz6ZPfXztqV8YKZTIyn+wec+nxaQfHQEgLcz88414/730gJecSScgDPpoZ2h40xSbXrjY+KU11Hgnp7/AJ69i2zWulTZLeTnjnnSErk9BSH3DjGSDjXjEqUwMolPeYz1Hz0ltOx0k9CQ5a1ajqwptJH7ROcflqO7addSpagwkJ8uknH89vPU1iZUDwZrpyM5Kj+Gn2KhVHFpS5PKwBgJB541LLEimYtS43EFS4uE9+SdSjbNXaa5jqJPY9R+06IG6lOabx7+4OlIwOs8/wAdNprNSBwqU4UjlIwOBpZOkPFIr7ds2rVGqtMBhfWtJVyee2ryftPXVrJS0sAHtqTbV7Vq36iKjTG2ZMhDakpQ+31pwe/GRq7l7/bhtKx9A0Ygdz7mf39evRdjyxVgNxjavqc3jleIteQBO7TV8E/q3Md+Rpr+iK6TyI7xB7fD/u0aL9om/MjrtijK7Z/qqu/+vpY9o+6QMGzKNnz/AFa/467KxcVfg80YJxvn9TMLcpmzFyQvfot5QIKgtTRbmtrZWQB3AKe3PHro42/rFEsmoVek29uDbxi1VoR1NuPktqSpOOrBAGR8XfyPz1mUT2dqupBdisPOJJwFITlI+/GPP92tE2jtKl2mm6bTvS31TY9RhBLSvdUrcae6T0KSSMoPJ5B4xqnGU2vu2r2NUXHXU5W9pjbKIi+KHcMKBHu6mW9JUmoU6KtMgPx3EjKmwDhwpP7Py1Ux5PsWolLnTWbfgyc4dizac42ppX9lTKk4SR5gDW0Vuy5tHqy4j8P40hJ+JGFYI8+M69TSZaXEApXknnCyPT568hxUVHGnF9WdnCVwi10Rkd003Yy7Nq7zibSU+lokmkuOF+nUUx23Sj4gguhtKVHI4BOfTQXujHg3L7GlDrzUxDjsNEIpT1Z6VJX4SgPuzrqBugqdb6HGFqaUnpcHWT1J88gnSZli0iuUj6DqNFYfp5SEGK4kKawk5A6TxgYB7aq06iTTMT2hu/bW4/Z/Yt1++6NSqnGpLtPkQJ8xuM6lzoUDhKyCoHIORnvrNEoYmeydbVzMSG1uWpcaPGCCMoQl5Qzx34Un8ddV1DamzpryX6jZFFlOIQG0qeprS1BKRgJypJ4A4A03a+2Vt2hS3aPblAZiwX3zJcjpSShbpOerpOQMHGMdsDRpFTiznC27Id3C3pv2DWt2UWsmclhYbZS22/UactHUkNPLXlKenHVhJyMZxrYrE9nKwKcZj+ye6D8FThQzNcpNQiz0rKPJfWlzpPckDGjCvbb2vdDzb9x2xBqLjSelC5UZLiwnPYKUM4+WquobFbW1GOmDN27oim0kEeHCQ0on1JQAT+OmUU+YrVABRLeNe35q1iVy5BIual0zxmblt14xloayB7vNZyporSVAgEEE4yBwNUu+VcuugU+5Nl7vqUWuv1GhuVSmVGMylt4NsnqU3JbTwDhJIWkAHB4GtRhbA7cUkLTb9uv0d11HS5Ipk1+K6pPkCttYJGnqDsrtxbypsiBbaHJNTbcYmSpTq5Eh9tfCwpxwqVz5nPOjGF8xXpyMvuSn1GjbYbde0LbkYOSrcp0YVHwuFP05aUpdSrHPwnkemTq4oMn+lr2mo1ZpBTNpNm0FuQysYUgvyk5B/wBVQ+wjWnRrYotEtZVnwYxZoaY7kcwyepvwVZyk9WTjk+esd9jy1Y9Gol13DQVvsw59YejRB1gq8BnITlRHxcqPbRUGnViN+B0yuk1J3qKYoSoEZIT8v36xL2v6TVm9iau47Hw21JiFfn0jxhjWstTauGyPf5ieknAHTn/s6HNw7Md3Ts6XZVzVSpNwZqmy4qMpCXB0KChgqQR3HodPlfUrtJ7GP25TqjH9q6IwqIUOybKjrISMEgADP5audy26pT/aX2seTHcDsmLU4+On6yejPf786PIW2DEHcKnbnIr9Y+lYFJRRUpLrRbdYSDhTg8MEqOe4KRny1Hv2x7uufcmxL+gVmKz+i0iQp1D6FdTjTqEpIRj9rAPfGkceoG1ZorjlULYK4zhA/spyRqmuq3pNzW5U6PJZdU3PivRlHpIx1IKf79FEWtXKz8Qks9R4CiwVYP8AraQq57hT8CpzAAUT/wAV/wD5emrZRb3K1S2OffZJlzKltNHoUpDyZlvT5NLlIOT4akL6uk+mOrt8tee1iymjbdR71Q97rW6FVYsikOZw4p4uAKQnzIKOokeYTozjbSwaLOrVatW4a1b8u4Jbk+oOUyWtCXX1klS/DcK0JOSeydRmdpqDKrlPuC75NXu6oUx3xoyq3OW8yyoYwoMpCWsggc9PlzpMjQ+ZXZm3saQBNtG7JM2CGKq9cT/v8ct4W3lCCEqBHGCV9/no3uH3HaS5bep9MWzHol31BdNVSAvp8B9SFK8eOgfVQSOlxIHTlxJGCTm9uGxYtUuWZdtCl1G161UUBE2bQpYjmUkdvFQptbalf5xT1fPnUey9uLYtK5EXlPpkq5Lga+pVK7PXMeaHP1AUhDf1j9RIxoZWgWrsyLZe3avL2V3I2yYBdlUabWKOlvOCVeGrpyPmonGj/wBld1A2Lts0hoR0hDyXg2MdTwcUFqOPMkd9F1hWtIsfcC970izmJES8348pyme6dCIrzaSFKSvrPV1daiR0jy7692Utc7OWk9ZqXm6zHRUJE2O44wGfAbdIPhABSurBCj1cfW7akYyQXTM39nWoVGm3/uvasJ5xuFFuJUhDaFEJQtzqCyAOOelP4aNfaIve6LN2buWtU+oSESUx24zbgWQpvxnENZB+QXq4sKzKRYt53jeEYuTDeUxM9+K6EBEZY6iUoKeSMqPf5fbq/viJae4do1GyrkoRMKpt+G4lp3pWjnqSpJIOFJUAQcdx56NSoOm9mGV+yVbZ+yjXLXhIbQtdGEioLSP8vJX0lxZVjnngfIDQlX6tU5EH2aOt5ZUxOj+CodwkeACAfsHbWhV61t75O30ralm5bKrFIfgqp6alVKZKbqYaIwnqU28WypIA+Mo5xkjVa/tdebdo7SUpSKZU6tt/cDEyW6wosJdgJWkqQOtRK14QBnCQcj4RyTFFoNrqV2z0JKPaO3eaeixpDzjrTilSGULc8N3lSASPqnqGR2OB31mKVWzUtyKpt9KYvCVtraNQeU1SKdFky2nqgpX6wK8FJ6GwrxMJyPljqVrp+yLRNC9oO/tyJlJR9A3LChswkpdy828002lzqHplKiPloZtSnVjZe+byXAsKbeFtXVOVV4zsF9lmVBfUSVsuIeWkLRyQlSTngZHPCuMlyCmr3Amh74K2wtzcSZQ6NPhUSlLgm14FUp7rPhPyELC220PJCg0HEFfSOBlWMZ0ZbbbCpq1ti6Nyq3XJt21xAfmvoqLrJYQvkx0pQoJCOk9Kk4I7gYGNPbnUaob4WezDplmVS0qlQKxFq0ZmvIQ/HqPhpWC0ox3FFKeecgeXrkGFD3Oub6Qg02vbNT4iJDwafmQ6u3JZjoPBcPUhtagO5AT27aCTY2lbmF787IbV2pdO28ai2cxFj1i5WYs9PjyF+MyVIy2rqWSBgnkYPz0W2zZtqbb+1ZDp9k0JFKgy7SedeitOuqbdcD6Rk9aiewHGccaJfaJocq8avtvLtGlSqgmjXKzNqCwAhLEdKkkqPUQfLyB1YSLTdf8AaapF7IbP6Ms209Bell1CSiQXCpKegkLIIA5AxoU72GAHZhmvbmXBft9y72uemKduF+PT49PqjjcaO238KSWCS25hPSMLSR8I1b70bv39a+3NyUFtosXZS2o8lipwlFtL8IvBJkpQokAgpKHG+cFQPZQ1dxrVqm0d3V+pWG1AuW17ikqqTlK9+TEmQJSsdfhKWPDcQok/CSnHHPHOfb4NXre1rV28avRI1qUqh0Z+KzCfqDUqZNcekMFRWGj0ISkNAgZJzn7hrY9Kgyg7WU1NjovNF23Wxd71MbnKrKq08tfiBvxAhbRPhqZ6sZbKenGdZkx7RF57sG17TTdMHbqG/TTKrVckOtsKlLQ4ptQirdIAyU5HScgk8/Dz0Te7FKibHVyp02otuqbtt5bLbXKir3c4AHf00I7XUnZiDs1Y9sblV61oq5VIalsxa2tpKVOLAK+gu4HXlZGAerv5aW2hkg426pLdIYiSoW4dXuikux+gidKbm+OvPDiJCUhQPkRlQI8hjOjZ2XRvE8UQXFFIx9cYwPu51z9V6BtftnutY8HZy4qQ3LrlRci1mlUqYHGnoZbKvHdbCilBQQOlRwSFEDPOuhoVFpNVhtT6HcEGbFf5RIYkJcbUASCApJwcfI6DdFiEOVWjLU2pqI8jA+LCgSe/y+zS/pSjLVxGfTkckdPf8NKftVTCQBNjlRSMDrHn9+lN2zI8Mlb7JUecdY1G0WJF5t3UrQZrzrlwrdjxAyvp/VdeVEgBOB8s8/L56P3a7sg6rBrhSTx8UVY79vLQTZG28q5JchlvKktNdSugZ5JwAeNEEv2f5a1dXuznfnjXoey+77hXOtX0/NHL4x/zdUTjI2Pe6VC64iOc/EwsZ/2dedWx/wD/AHjT/wD3S/8ADqhkez3OAz4LoKu3w/fqIfZ9mZOW38/JH+7XWWX+6/L9DDJwvVHNlpp3YsiMuJbVdqtNjuK61tRXVoQpXHOEnHprcNnE3ffL1fZu7cq6adXYsP3iC83OAaX0A/C4lYOeSOAQcZ1nll+0XVaXAXHuvbykVt1SwpEghUYpGMYIbISftxrTNurmkbpVCsTqBttRGVwYaXnYjlUebW4gZyW/hOTzg5IHbWfiFD8Vrx0/U3xzUZFcdxXbU6iJV0Tps2WlsNl51WT0jsO+cfdqtFXeS5gLknpyMlpePxxoyu68qPclREym2oiltJQG1tKdLhKhwTnAx9mqU1OOAlCIDaSoYJyTjXluLa7+aS0s6uE33UfcIj1eYG8+8qSgAD4j21Mj1p7qKUTUgjuOoaai1Zppfh+6t4yeo6mIq8YhR90RlXYZAx+GqVTFkvEUm4JLnSDM6kngnA7/AMjUhFanHp8J4qAPkO2mBUoTaggQQcDuk8dtSET4C1J/qhHrg6aNc0I7PnK5OCuHUpcTkEqAOBpKrgqCCepbQVjGekYB9Rqc05Q1qH9VUDnkgg6daaoqicxyR5du+nVC6orBcEpbrZ8VvtyOM51M+n3StISwyrz7A5zqU0xQA5h2Kr0Hw8fz204tiguHrQtxGOeB56bQRtgdunef6KbZ3NcC4rHiRaY+po/5/QQkfiRqu9m2K1bmyFqU/wByZLrkP3pwqGCpThK8n8fy1cbp7e0bcqxZ9mKq8iAzOCQZDTQWpPSsK4BxnOMau7ftq26Fb8CjNSCv3CM2wlSmQCoJSEg47eWoqbKnmYRM1NhQBXTmCAc5Awfs1NRU6csHFJbGRyc8D8dUDUegZS2oo6knOFNjnTqWaEkpYLrYCjjPRgJ8/t0U48xHm5FwZtOQnp+ikKJHrj7tKQ7S1LR1UkLTnqx1541XNMUdKelE9GRyMZHzzp1FLgr6R9LAcDJDqj+edHLErakW7cuglY6qeWkjPAWP3nUOWq11AlEFxJV9YBYOdMfQFMfCQqqH4QRxJcH34B0xMtGKlKXGaqojGcGQ52+fOmeWgK+h6ldvqUG1xngAOQCNNlNsF0IAkfbgccdtKFoh5QU3NBX/AO3V/HXkq0ZjQ6m5AGecFYI+3nS1HqS2+QtDVoKPxmSAO5wDnjUdMa2COlTjyeTklvtpK7UqS0gNSc55HSUcfl9uku2lWUJGJ6yTnKR0dv8AV0fVlzDr0Fe5W2pJCZToyOMtnGlJo1AUATUwrr5I6caYVblZYyCVk9kZA/hjTYolUGEhpXUk5BCe+pGr1Yb8CQ3atEDmBV046scny14m2KY46M1Rgc461HGfLUJ2j1lIJKlIx2JT+XGnmqZVw0T0dXOQej8tBJdQ34HxtSCM9NTZxnHKuT92lHb+I+lDjVUjjzz14540y5T62pQCouCrt8J1DUzX2CAhoo44JR+Hno0+TDfgW6LAfRy3UY68jOOsHTCrJlAlLkhtOVFOQfrHVeJdaaUPERz2x0nvqWqpS1IIWwFFIzyD+/GpVrcMfcKatGb0Ah9IUe2SOf46fNozOStv4ickZGAPnqqflVBR62Wh36h8Z4/2dKTUKyhfQiOMHth05H5arosTXQsHbNqCgCWD8RGOk478aZXadVIISl3pB5I16qp1QJCiXuSc4V2H/jrxur1NSCoiWSnIx1p4/wBrQ9YKpKz5NsVZKPFS0Vo9cahzrYekRlRZtMbfacGFodbCkrHoQRg6sPpuor+FKZqABxkpHH+tqP8AT1XBWla5KwBn4uk5+Y5Og7odNH36OTEx0luOnw08dATjA9Men8NQanYNOr0JcSvW7DmRySQ3JYSsc98AjudT2rtntEJU6+lOcZ6c/jjU4Xs+kI8R54kg5T4Rzj8NDLJ6jqgVtfaCzLTdclWtZVLprzoCXXI8NCCoc8ZA7c6vKfarVHZTAp1KbispUpZaZb8NKSTkkAcDJzq4Zvp9vA8UgcD/ACPl9+n/ANOwlZUp5CurzUj9+o0wqimk0x5Sg0phxKgO/PPpqG61NjtdDQeBBzgEg50TG+wopUS0VKHxfq8efHP2aacuth9YV+pT9379LKch0kJsFd3POTVUiXOYISnJQ4oA8kgHB5/36IpUvdhgktXFVk9P1cPK7+nf56sNvtzYlstTUm3o09Tq05WFkFOM8cfadETvtAUYY67AQrjJIkHH3Dp16bs1TXDR/l3vrp18Tl8U/wCa6YDruPeRK+lN0VgHHk8vB02Lj3rIz+l1a59HlaNT7QNq9avF26WR6iX3/FGvRv5ZRAJsB8fL3ocf7Guhr/Z/9f1Mk83tebMVs65vZ8uZl5VVqFSoLiFhCGpsBK/E8+oFpahjy5weO2ja1KnYNp3O5UbF3BjhpyF4b7op76kIQThXX+rUkfsnJPloBsvYKm3zHekWLWqTXmYqwh9ynT2ZCGyewV0KOCR5emtX2k2+vbZy75ObUmzqdUYhalttMkhSecYUARkHH3E6o4iT1Sav2dP0NUaRlt8U61oFZKaLc0SpMuthwuxm1dIVnkHITg/Z66FFMxysrVMbHPA8MpP7zomvnbiv2tV3GHKO/FbkkutNuII4JJxkgZA7ayndmvzdubGqlxSY2FtNlEZGfrvK4QnHmckca8rxj/5M76nXwK7mLXQqYm8lBl7wSNpobCHSxFL3v/vWEF9PKmejoPIGDnq+7Wkojx0nrcfbHVzgLzyPuGuXKnt3XtstuLS3EmwnW6pSqomq1V3pPUUSSA4knzwMD7tdJRGZkyJHkx2lqZfbS4heDhSSMj8tVUkBW9y5R4PXhKs+nKefz0iDWaVOrEuhR3FCbAaaddBAwEuZ6cHOD2OoLcCoAlaW3ScZPwk5GgujJlR92Lla8MqKqVBe6ACCcKcH8/aNWwipJvp+qK5vK1XM1pEJC1DEhPUSTjvqa1FaaAPjKITjGB+egS2p9fq9Nbl1igOUeYVrSqIt5LxQAogHqSMHIAOr1HvjQPwL4Hz/AIamidMF2rCUR23+ULIA7Ep+tpbUQK4WUoT8zjQ4iZKHUQogD62BjGnjKkk5KjknnPnoPqhHqEwgAoJSlBQBgdKteGnpHdkjJzxngemqQ1BxttJbdOQM4KtetVSVk5kKUc+ec6fYry6F0KShXSspUM54UhXH2caS7QQogoQpfY8oUQfmcjVazXZgR0qkqwCc850oXJIAGXl5zgZ76OhW4tExyD4YSlXSD1HpBHSdIeiR2kg+IQTwfiAH899Rk3A4VhTj6wr9klQ7+unlVxK2Qgun0JKtMtdhWhXuiA2VJkNoB7/rR/HX3hSMhkvowkEjCh92m3LgnhI6ZBSBxjGlJuGatJSqQCDnOQD9uowZWx5KJBVjxCQfMHUgrmo6kuhWE5Oc5zqOi4pC1g5C8jA4GPloS3OuSbDt1idFWhl2PVqYpRRgdSfe2upJI7pKSQQeMHRhDPJRXMWTyxthwy8/19QK0jn1+/UrwlrAUiSoH7SPu/LUAVxAaSoQoxUCf+RA/wDHSkVxHC/c2Ar/ADUAY0saTGpslOsS1I6Pe1JUkcHqPlprM5sEtvuZzyrqPOnBczClFD0ZlKlHPA/n10pytwAekQEHA/tnGdSldkSbIEiRUWspTIcwOe/HfXyatV8KQ3IcSOxCdWJq1Od/+b0gpGM+IcY9Py1HVKo6z1IpxGDzhZ/v0jSHSYwK7WWE58ZayOB14ONSIt5zSlaXlIJIxygHI1IQ/RVpKVxXcqzjDmkORrfdORHkpx/n/v02iGXiMruOSQMNskDsFNjUdysvrST7oyPLAbGDqbEg26oLDvvSeMJyvP5aUWKG2Vp8aUgEgJUSlWPy0Mq6ht7IrhV1tp/4pHAxkgoxzp1FwN4ClwmMI45T56SuHR1KPTUZIIVwAhPf8NRl0ylAApqro5zgtjz+7VdRHSdFoi44XQSqmNEYz3I/fpti4ITaVKdpDZ8xg4OoLdKhlQ6KthJOT1N5Gku0oBaUpq8bCk8fqiCf9rUaQy6F2zV6O4es0tI6u56ux5+WvHZVAKQ4aeoKI/tDHftqjhwV+IkKrMQknkeGrA+0dX9+paoK1KKhUYpA5A9fs0lDXQ/AOTri+lcZ0DskAgY/LX0pu2CyENty85A5I17GhurT1IciHBxy7j+7Uk0R95PKopz6vZ/u0eWg68SqYZoKkFeX8pP9kYH28/bpC41CcJIkPAHkZSOPmNWarcfDqk4ZCjjADg02m3p4dU2YalYPBSsDJ+3SaLmOutEBUa33EdKJjhUnjlHH36QuNb5YyZ5SU5GSnvzqxNszurKaY4kKGcdacnUaRbMtBGYKgrOQdR6a2MqelGl7T0WwH6JLfq9yQGXHX+lLbyulQSB3+w50au2Zti4rqF30Pjn4pbY+zz1mVmbV1WvUNcmOw6keKpBynAUfPUiTsTcBXwh0nnuM99eo4FfyI/zK020OPxCi8WVoPlbfbZukFq8Lf8Ai5A9+a/jr4ba2Bji76Fjy/rrf+LWYubF3InPQl04zgDI/LTP9B1xDgIdH363JYnLF8kZZZOaMToW2F+W8549JlTYa3PgUphwozz2JSR/J1qO0FNkqv8AZpu6dXqzsN+G4hp5yoyGvdlYJSoKQseacYPHI41nW1u7O7u3Cpfu82TWm5YQpaK267ODfTnBQXVFSO5zggHjOSBjatut1r/3WvqBb79v2hT3XWHSmQ/RvG+qkrx9cKGekjg9+cHVXE6p3t1vX6GvDt8zJLpmVpmrvw6pVJk9ppakMPSHlrUWur4cZOe33a5sv1iv7zbpt2ZQK85TqTZ3TMlyktJkD30n4AUL+FRTg8HtzrqTd2+rgrUua27bFHi1SmNvRG0xI3hJdcSSElRySOe326w/2f7dqNjWnIfuKnE16rzHZ1S8TKvjJOE5HBAHp6nXluLTWPNrqdbB9bDimUl07Ybw3NbVRodT3wmzosxhTbkV2jxkoc4+qSnlPlyO2if2f7xqlZ2zprEma573SOqmSU5yUuNHp8/kAdaQmuQlr5gsBR5GAePlrHNt5Tdnb4XdabkMIptfbRWoZUkhCXcdLqUk8Z8/w1VbsjSi9DZEVCoKOPpF4pJ/so/w6A6bVJ7e9FYa94UXF0GIpKilOOkPLyOPt1ozU+lLcwlpo8cgK0CwnqarfGoutxCEptxhOOrzL6v4flrTgy0l7v0KMXePvKJG8u4KqXQl0ij0p+qViqSaU4l1Kw3GLalgOKAUVEAJ5AOT5EaNGdwLxotYhUm6ZFJkt1PrbjyosVcfpeSOooUhbi8ggEggjtjGswpkmnRYT8stKH0VuC4BgZ6W3V4I57f5Q/gNG29Saamh0Say2pLseuQR1k8JLjnhn/ta0vCi5qCS1v8Ab8jOpypyb2LGBvLXZzkisNW2yLZZle6Coqfw6tQX0KdDeMeF18Z6s9zjGjxq45ayVLYi5Pnj8NZHY1rx6xZLNvP3pWIwh5iTYQjQ/wBS4leSknwevB4IJOSDnOtZYjUdSQkPEgJ7kcHHnqniIwhKooOFKclcisu7d2FaYiRXKGuq1SoLKIdOgthT8hQ5J5wlKR5rUQkeepFv3xc9QeCLhsGNTm1tlxCkzW3ukjshYABCvmnqT350LXDa9GuC5kVq1b9FLqsKOuG+EMsSv1ZUFdJQsEoIPmMZ7HONQpSbispyC5VtwzcTtVmNwWoL8CPGUAs4K2y0Ek9APUrPV8IPbTxhCcVGK9bxv/8ABHKUW29vgEFZ37tulVpy30W5MqjsXHvxpkFcluECM9Tykpwnjy5OPLXtw71Uml1KJSqXaD9dmyY4llqn+GfAjD/lVqWUpAPkM5V5aBNubaq0O1wpe4drQxMekLml2CsPokqWouBxSnuVDOOQOANX22FtUe2Yt1qqtbaWKZIZjqmLISFxm4zfhrznHScqI5xzrRLAwYxb3r368ilYuJJq9L9wTOb47aRqZS6q6llyPV21OQS1HcWqRgpBShITkryoDo+t344OPn99dvlIZAt2ovy1ZzTo9MdVNZx3K4+OtAAI5IA54J1ldh0mlVun2JUUKPgouipIbStJSpKXEPrbwDyAUlB+8a0OBZaoO8E2qdKzFm0FhsyCnIDrb68pKvXpWDjRxMHBwHlmndPn0dUIsTExNYvp9LCiTfNkN0M3NIZSxSi2HVSFFKUpGcYIJyFZ46cZzkYzpuk7k7cVegyLiilbdNiAqfdeaLJaAGSVpXhSRjnJHI51jLkGsz74bpNvW01cNPp1XqU8x3qgiMy27lCErV1hXWErU4ekA4JB76L65Z951S0L6mXXDotO+kKO4zFYgzVyFENtuZLilNoGfiAGM8DSz4XDw2k3q/Fc/DckMacta0QY0veXZCq1NmiwbijOTZDnQyUJcLTqj+yh0DoUfkFEnVBvNuVs/Etyp0Q3D0VKPIjFTAZc6k9L7aiD8BxgDOfTXlbtGn1nYhYaRFbbXbYlxy0APAdEfrQtHGElKsEY7Y0m7IjtQ2VjVyQ5HclVGJTipWBkrdcZHn81aOBh4ccWLp71v+xMWU3htabBTbu520dzT0U2jXCiZKWhSgyGXEqwnv3SB6auq9VtvrboU+4a3UPc4UBlUl9xaTgISMnHqfQeunRbbiSlxlpoE/tAAdxqovnbSLe1p1K1qt8MaqRlx3VNqwpIUMdQ+YIB1hl3afq3/vwNMVKvWOQpX/wg0IVpQibWoVSUu4SpdSV7wpvP1sdHSDjy5+3XT9gbzbF7hUOBXod702G5Ma61wpkxtqTHUDylaCrIwQeRwRz564iuz2B9+aNWVw7bpMG4qetR8GYxOZYPTnjrQ8tJSrHp1D5nXVm0fsi2daW39Nol52Tb1drQSpydKfgNvKLilElKVrT1dKQQkdu2qrHpdDY/pTblzK4170opWAQffmyD+eltyrKWnKLxpCsd/wCuo8/v1m072QtkqgtTsva+nJUR/wCbLcZGc+jagNVr3sWbFKWkHbbGc5DdRmJ4/wCi7ouwquRrjCraLhMa5KYpA74lo7/edTWqRT5Sw5GqjKwokYRIBxrEFexfsY2rDFkymR5FFYm8n73TqFM9i/bDBVDVc8IDnEesO4xn/O6tKrYTTN2d0NttkqUxVb7rpY97UtESMwC9IfWkchKU9h2+JRABIyRnQHtF7VG0m8FbbtemyZ1Grb6j7tGqQCUyfkhxJKSrH7JwT5Z1gftDexfcUCkw69th9NVwRgoTIEyV474SeQ41kDI45T35BAPOOWItuXxQbngQ2aNVKfW/eGzDbXHW294oUOgpBHJ6saNkP2LNvS/GISlSjkpGV+frr42/LSvlpZJ7YPbVDT0T2obBmpzJ8NJdKc8LwOr7s6lgzUoPS64OeClRGNJSvcsigetXaq5bYuOt1idfddrUCrr8VFPnBBRDVn/k1JAwnBCenA7DvooXQn221ONsvEq45559NctWbvtd1p7O7h3ncFZqNcl0i7ZlLpqJUpxXSFBkIRnOQhJWpWM9gQMaPLEmXxU4cSr3D7QxXWZraXRS4TsQxGFKGQ14eCtYGcE9SVH1GjVAs1pdMmHs3IR5cDj89NuQ5QJ4d7cAjy1Lj1KuR2W0yp61OdIKldSgkq88DPHOqO+NyY1iW/Oua46m8xEhIK1nAUtw/soTnuSeANL4FiLJMZ0K6+txJJ4AHb8dOdJScLdfCe5wM8/drniVfu+FXses7vVq9lWpTosR+fR6OxBjuKUlKD4SpC3G1E9Rx8I7gg8Htru1O51Svvb+hXVU2mmZNShodeQGkJT4mMKIAHAJBIyexGhTCne4Z9TqOlQfcwnvkD+Gn2J7qB1++vpSB2BGM/LUVy6XMqUpDXA5HQOR92NMJr7yikIajdJGektkdQ8vPQepYtNy4VUZR+P3t3p9Md9eLqzhHSZTq8dweONQP0mKT0LhxzjByBgHntpKbhZJ61U5gg8jBI50GMjQbYua/YdDS3blXntREuKISF5AV59xp9y/t5kABNfn4yefDRnB+1Orexd3rZoNpxIUuylPvIC1OOofACyVZzyn0x+GrpzfXbkN9cix5wWOelC0EEfaSP3a9XwqccGCeDei1qOpxsa3iSafMDf6WN7mkhP0urgclUVkk/ij7dOJ3k3p6R1VJvOOf6gz/h0Tf05bWF39bZVTbRn66fCJ7c8FXr89O/017P8Ala1a/wDdM/8A7mtVQ54HkjNJzv7xzxtVvfaS3ZTO7VltqbKUe7O0NgpKVAkKDiXnDkdiCCMYPByMa9alxbN3hc8VNg0O9fpOM0t3ENtlC2kBQ+PJc9SBwfPWV7YQNlNyZMiKzX028/GQlwJriExkugnHwKJKSRgZGc88Z5xpNIsG3rDuylV20dy7QVIZ6lI66uyEEDBKSOrJCh1DuPPnScQ/WazU/I0wy9LBDcqTt5LrqRbUmqLcbCkzPfGghaX+o5HfJPfP9+g5yDR+rDTroCvMJyBom3dtl+Fcy61GrVGmqrCnZjhhSUPIC1LJV9VXAyePs0HRodSXkLWy6fRJ6QD95OvK8Z/1ErZ2eGaeDEkO02mpUpSJaiAcAFJHGvhSYKlJc96yOeQjJGvjAqDgSVsIP+i5n7zxpPuk8BXTH6xg9iPvz6azpeIzSEu02KhwkSkKHYHGPt/n/wAdCl2be1evTkTaFuHLoqEthtTTMaM6lwjPxHxW1Kz9h0WBD4Th1glRHHbjVBeFxN2XbNQuWZT5L0anMl91LYT1FKfIZIGrIOWG7TKZqMlqgMTsvdsQOKj7svN+8SPeHQmiwAXHeP1isN8r4HJyeBpNS2R3Wq6UR171iTHStLyG5lAjPJC0kFKsBSfiBGQe4IBGNHlrVxi6rfgXDEjPtx6kwiUhLiR1JSoZAOM86tPGeQvwyh1sHPwhKufy1phxWNu6+S/QoeBhtUvqzGK57P8AubW340urXdbNfWlxCXlzaW5GcW0FZKept1XV3OAoY58tbRDtyVTYUeIwpDbbSEobS2cBCQMdIHkPlplMmSXilHUAB5pOmXa211qYXKR1JV0rHiDKSPX8NHEx8TGrNy8KBHBhDbmZnuZs/uDcNxLqFs02yJUVbAbUusRlplNuZOSh1tClY7Y5GDocoWz/ALQFp1A1ehUzbxqYpBSX3HZb7yQeCAtxBIGPIHGtvXVFAgtz055GPFBJ+3TiK0sEJRIKVeeFcfLWjD43FhHJSa8UUT4bDlLNqYtP273xqExVYrtgbVVOYo/rHX4ilrcxjuVNYJHlntpFap+71YmxZ11+z5a9ZVBSENGPLQklCfqpwc9SB5IUkjW7CtSUpHVJX1q4HUrjHy1VTH5rTzk2jV56myXfjX1pD8dSsd1NK/PpKT89Xw42batLT3/kymfCxWzZjbW4u5T9fnRpWw1afkQ5kWqtRmKg2hMZzwy2lWQj4kqCTxj1+WihzendlKUlvYCv5GAUma1jP2gf3aN7VFVoK6hUqxXPpao1NxCpUlMYR2yhAIQhDYUroSkE/tEkkknV6ao6sAIWEg/F0gdtDH4rDlL+mnVe1+pMLh5Jfea+Rz0zcO58Fh5ETY644c0T5E2PMZqLfiMrfV1OJz04Ug5x0FJBwPMA6lsbgb6hExqt7a3TNalx1xyypUUISlSSCvKUJJVjyzjnXQDNUkKJSlYAHfq589S2qh04Dh6ecjCfPU9NjJW8OPn+pFwjW035HPbW4d+R9v02BM2suwITShSjJHhFQT4Xh+J0g98c4/PSq3ubWJNjtWk5t1ekYRUw0tO/Ri3epLC21cpR2z0Y78Z10S3VWkLPS0laljngH7dfO1NkdPS03ySeRpVxkE83drR3u9wS4aTWXP4bIoaNc9enU6LVEwH43vDaXPBkKKXG+oA9KkkcKHmPt1OXctTe6VPsL+fSoHjVoK1FPC47SR08YTzqOqpR8593aIJyfU/P89YZ68jXGL6nzFw1BKyUF8dOOOoH+/Uxq5Kg2sqw4nOMfEM/v1GRVooCk+7IPxZAzyRr0VineKlz3XlPkMHOl2WwUvEvEXbLbGSVZI5OPT01JTeL7jOB4g6fVOqRNWpq05cggenz0+anTD0p92JwecYwdG10Dl8SzRc6wQpwOFR5GU9WpyLmQR+uSFc+bfc6oUTaVnhpY4wCc6lodovSnClDGeoarTV7DZX1LcXFGUg9TaU9s5b76iOVeAqQlxUZhw4ykqa+L92kJdpKl48Z0pIBwk4xny7fLXvuNOWSpMhSQTnlQ7ajyvkFRYh2tRScGOgEfs9Pca+XXackY8FlOc4GeSfLShCpZUcy08YJI9dKVSoPSeiWnJ5zpfVGSZzX7IqLbqlmX/RrqpUCezKvWo+8w5iEONuJLTHC0K4IznuMauy97EUuRLo0m3bJpsxpSkyI8uCmC80rJyMrSlST6YPpjy1uZoEbxOpM1KfE5yeOo41WV/b+27jYZiXFT6VVGm1ZQidHQ+hKvUBYOONJaaCouzFNj9wrdnbs3RtzZlQerNh0yC1Kp8p6St4U94KShUVp1XK2iDlIJPT0EAkaZ3/NBuzefbDbKrMLat2W69U5ZWfhmvNg+Gxk8ZGOQe4cHy1t1D23oNAjqh25S6XS2XFda0Q4zbKFKxjqISACdV99bKW1f9NYplzQm5PuzwkRnWnFNPR3AR8ba0EKSrgdj5D00LQcr2Mh9tauWnRdkp9DZlqZn1h2OxBjJwS6EOoWsgA/VCUkdu+PXWibHUex5Gz9qfQtWTOYZpbDK32MdJdSgBY4PBCgoEHkEc86iW/7MVhW9cKLnTAkVWqoT0syatUHJq2hjHw+KTjufx0mq+ytt/OlrqMOgu0l95fjOqpE12H1qznkNKSPn20My2CovcPjb9DSo9Uh0oSTk9Plr5ygUNxtSW5yk8ZJKedSo9oz2oiUIjFQQkIB7qGB5nuT89fLtSolPQphaVYJPOP79RVuW5b5FY5atLIKGqunqPYcjUcWhDUcitgZHnng6tnLLqaEKIjvZwCT1n1+3UNy1qoFqSGngeMfEc/Lz9NRpIdLkbpZ1g7dptCmMzbtpnimMHHC6+lBBV8RBz2PI/DVk/trtkpR6btoiSODma2P79DdL2Vr71GgLWhzqVGbUoFPmUgn89Rn9iLgJUrwnOOB8J167BUVCKWNWngefm7m9OYTO7T7fKQVfpRRQnOAozUd8eue+lf0K2r5XJTcf+3T/HQY/sXcYIPhu8HqHB9NQ1bI3MCRiT39f9+rsrrTG8l+pXLLzRkdn7Kwbz8U2TXqfXAykLX9HykSSkHzV0EkDOj+ydrrl2wvWmV6q2wupRulxt6M9G60rSpOFAdQPxAHqHzHprFLa2su60ZBnW8mTTZDgCFOxCplSknnBKSCdHFFn7lNVmls1+97mYhB/pLjdTdStA7KKSVHB6SfLV08POsq2fvHTrnqPbk2lIpN0zZzFHkU+n1B92TEZcSUhDZXwn7gfLQRNmMUzCZE2PHWvkJddCOvHpk6Or5ue63pblDr91Sq1Hpzi2oMl5YWpbROAoqxlRPmST9uuV9k7do1QuW9ZN1QfparU+tOx211DL/gMKJKUthWQjg+Xy147j1/yZp6NHb4ZtYMedm6RZDzjIcZX1IUCUlB6gfmMcafbek9XQCvH2nWP7hKk7Oujc6yGlsUyOpCa3Rm1HwHmSoDxW0E9KHE58sA551UULcjdK+KHW90YNys0ejMJccpdLcgsrbdaayVKdUU9eVYI+FQA/fmilvY7k7o3lSHUEeGtZVj1zg6CN5npZ2rupGV4NMfBweB8OgGse0PcdwRbIjWUxEpxvUKbM2Wx4i4amzhZSgEoVznHVnyyNWm49M3PbsS4Yyr9g1aC/S3Q8J1HQmRnoPUEKYU2lIPllCsfPTtUVN2gi2SnVH+ie1i09jFNYTkDsnH8NHjcyopzlZUTyPPWQez9Kv1e31srVV7bco6YaEojmmPCQlKcjBd8bBVx36Pu1oO5m5dvbc2rNuidCS860OiLFCylUh4nCEJxnknz9Bpooieg1fdWrkGza7LYeU2+xAkLaWjhSSEHBHz7azfZXb+15219Gq8uk9VRqLSpMme2841JccUoklTiFBRP36u39z6m/ZvhblWWLe/SKC8xDfbkh1tDy21dDToBy2pQ7E5B7HpPGqj2a61d1R23oscUKhrpUfxI3jGqPIkjpcOSW/BUk49Or7xop0I3bNgpzvu0FiCGi8GkhCXJCy4tQ/zlEknt3PJ06pxCvhMRpWD/Y7al1aoW3bdHk1qsyERoUJlT77qnCAhAGT5cn5aymh7zVN6NTLtuO149JtKv1AU+A8qQpU1CVcNPOo6ekIWeODkZB1ZarUD8DS3BEdws05oLQOfg+ehnc2LDnbf3FB+jklxymyOlaBhQUEKxj79HjjEFGCHVqB8hgD8c6iVemU2dT5jKvE6XI7iehXRzkH/ADvnoNutBaMt9nyrIrW0VuzKkyZEhEYtreW51LUUqIGfnwO+j2j1y1atEdk0gMygh0suFpYPQ4k8pPofkdYfshe9B289nWLc1xMTpESDUnYbqYjaFLbSp3HWQpacgdX262q7rrsyyLaRclXnvrZeLaYcWIwXJEx1wZQ22jIBUfmQPUjRi3QC1Zm009ShCdRjyT58c/fpfv8AS+AmLIKcf2z2+7VZt/cdo7i06TLoNRkNvwXjHmwpcZTMiG8O6HUnsfsJB9eNS03Dt2KpJpCLzpS5kdaWpDYcyWlHslZwQk58jg6KYpKbkUx0guNzE85I61D7++vnE0tKgtBkgckZUo/v1eOW/FbCFiczlKeek55/DUKpUqLTYr06ZU4rMRhtTjrzrgQhKQDlRzgAD10XaWgElZBSxFcbKG5byFJI7pCgfy0puI2sgmqrAPOClH+HQnRt0duasyqVBuZtUcviMiW5GeZiuOE4CUPrQG1EnjhXfjVlWbss63ag3TK9d1KgS3QFNsSJiELUk9jjPn66VtjpdC/+jY6OkieCVJyCQOfQcdtNLp0nxQ2JrPPI+D/fp+LFM9pmXTi3IZdSFIcbUFoUPVJGQR9mq2rViiUOSiLWq1T4Dx+JLcmUhpZB8wCod9C/ElIskQH/AAS6JTCldXAwocfZnSGo8wOdCnGMAckKJzzpbEF55KXGm+tLoCkrQrKVJPIII9deSoEkdGGFoyBxg51HbQUh73Of1pPiMkY4IUTjTxaeQrpUtBUDkhKv92obkSYAEqQoc/DnjXngymR4hLg8sk9tDUlItWUT0q68oX5Y6xnODqk3MuS4LL25r12UiOw7LpUNctCHiVIUU84IBBPGdPJMptJCVKx35zoG3pnTRtHd4e8TpVSJAV5gjp1G9RkjTLVrT91WxRbpbhrQzWKfHnJSFpPSHW0rAznnHVq6acnEFKoTvw47dJ/v1mOydWknaKyWgshKaBASMeojo0dIqMtKAQ4SSOfPOq99BktC8bEnHMR7GRxgYz+Oo1eqC6LRZ9ZXAkPJgRXZRaSPiUlCCogHyPGkMVuWohtT6grHmOBqBdFSlOWpWIxeylcCQg5HJy2Qf36gUjyyb5ou4Fp068aFHmmBUWvEaLrJCwQopIIGeQUkcEjjjVz78XFBKGpA9f1a/wA+NZF7J9bkxthbbjtBJCBJHJ5H9Yc/jrY2KrLOVlpKioZxjtnQ+A0bGPfkjJCHh5n9Wsf3a9YrTiMcukEYz0q41LRUn0rI93ZSk+ie4161L6fhchsKSrsOgEj79Lpew6TGRVkBZUiStLecHCiPw0hVd+LKqgfXPXqcJAUMCIyUgDAI1HekMIdURTGUE8JJB/HUaTGja5jse65LbYS3Ul+YPUvg/j5adTdL6nPilIJ7gFXfUMymOkhVPTnII+I/jqQ3KipUha6a2o5BOTwRntxpXXQdGhJvDdZplp+LWJxQQkp6gkg5HzGmHtyN50EhFWdGORmK0f8Au6L070W/GYaZNjEpQgJSEvDsB/o6hPb8WzkqVt44ojPeSkf93XsoQlSvAX/ieed26l9QaG6m9bQJNRKhyR1QmeePL4NNjeLerA/rDZ47mC3/AIdFje+lhkoEyx5jeR8fQ4lfSfkOMj8NSRvbtVgZtSpA/Jlv/Ho1Hnw/lEEs3tHFG3t5btWDU357VxViuB5osqj3BKeqLSRkHqCXVHCuO45xnWgtbr7i3bWaRT5tLt1pfvXwKVBUy3kgpwsoJPTg+Q8hoW2+3sqbdYKNyLMo82kFCggUWM5HkpXn4cl11aCMcEYH26P6xuTtZcEmlQrcsq5m5SpqE9KzHJcQQQQkhY+Lkd9bJ76r4iLfRFVu9dlQVXxQbgsenUapUhSo75glzof9FfGc4I5B8wRrlO3bmn23vletMgWwajHqiY05xoSUtOoT04KkJUOlfJAwVp8u/bXXG7b9j1CTEcpK661VkdbdSZq8fpdbWMAc858/XsNcr1OPGpvtP0cJkp8Kq0JxoqI+spCsgH8NeJ43Tip/v0XU73D33EGO7vTL03Etddl2paD1MRVMNzZtUlshLTeQcJQytwqz6/loVoVytW7spO2zuK1blbrcWK/TUJjUxx1qQVZ6HEOgdHSc85I10cqjRQQ4mU0Or7j9+kG3EvqKfGZXnuOrj+e2sy8CyUHd2ceUOj3PblsWC27Z9wmp25WVyJKlR21MJjuq5CChZUeCO6R5664nRKTWaHLhCUFCZFcbwU57pOp36LLbIS14WD2wsd9J/RiZ05WlJAyOCDznVmnMryuJmfsyy4i9smaLImpal0SbIp76FdwpLme3fkHVf7RNOUJVl3DKLkih0etIkVQtoK/CRx0uKSO6Rg5PlrURZ0ll1bjMNPUtWVKCAkk/MjudPuW5LaSQ80vpwCQOB/PfTRpslPLRje/m4dh3FYpsu2a7Br9brjzDUCNTlh9TZ6wfEJRno6QDwedP+yUzIgWlXbZqElsSKFW3oq+pfkecj7SDzrS4VhQKfJcmQ6LHjuu/5RxtkNqVz5kd9RLf2yplsSanMoNPdjuViSZUtSlKX1ufLJ40UhNnYNe1A27/AEfU6k+8AR6zWoUGThQz4Sl5I758h/u1U+1g3AomyhpgLLIVNhMQxkApKVg/D6YSk/doxvvbRu+qI5blbdlCOpYeQttRStlxPIWlXkR5cHQjUdh1XNNiO7i3ZVrlj01BREhyAhthORjrX0JBWrGOeO2mp8xWt6NftuLMct2lpZKnkGEynxCoK6vgHOfPVg/Bm+CpoN4C09I6sdznA1nVt2K7aSozFDui40w4qeluA9O8VhIwQAOtJVgDsOrjGjBqVUSQlyS6eOSrA/d9mmSvmSqOWIjL0f2YL/opQVuUuuPsLx+zh9s5/v0QWRR27j9oqg1Kaz44pVnwpzaTynxSjpC8eo6vyGjcbRTWKRf1FTciFQ75kOSAj3M5huLByc9eF5OD2T21M2+2zfse4YF2PXA7Onw6G1Q1JTHCGVtNkkLI6ioHkeeONJHcSnQG3vcdW2w3lu2bblHdku3LbRqKWUupbHvDAKVunq/soSVYHJxjUHaBV7xNj5kSn7YTau5dTEqS5UE1Bj+sOOhQClJUerA4+fB1p1zWPJundGh385LimFT6ZKp0mG4CFPJeSpJwe2Pi7ag2Xbe7m11Ncta0pluVSgNvuOU9uoqeRIjJWoq8IrSCFpBJxwDqO0RK2H21jVxU3bq3KdcfvCKnHp7LUpMhfU4FpSAcnnP251mntVSKjUabZ9hCS8xDui4Y0KapJIKmuoHp/Eg4Pmka0Oz61uwiXLevuNbBiqSn3RNKS+HG1AnPX4hwRjHbHI1D3St6mboUBqiVX3iFJhSEzYFQjFIdiyUHKVgHvz3Hn8jzptaDWgTptqgi22rXVRYkijNMoYTAeYStjw0AdIKCCkgYB5HfWIbERW65uzubetUZbcq0aqKo8dC0DMeG2elCUg9gUttjj+z89H1Jr2+cFHuNVi2XXWUgIbl/1iE+4AfrOJAcT1H/ADcDOq+uWbX4l4vbj7b1CDSazPZS3VqfMYU/AqBSMJUopKVJWnnCwMn0GTlZXoiZS6ulStt4Uu96Cz0U+OfeK3S0IHgus/8AKvto7IdQMqPTgLAPVzhQzL2XLdtG47eue5axSYddluV2VBan1FsS3DCShHhthTnUQnCjnHcYznAxfXDQd59wo67Zu2vW9QKBLSW56aDGeVKkMnhbXW8SEBQyMgefIPbV9sdt2No2bjowcakUeo1Q1CmNNpWXGG1JCShZI5ICUYxnsdSmwUrM6nXtdGx8rc2z7UqKmqfApke4bdjySXUREOOJQ+22knhvr68JHA79yc2DFCuay9mI28tEvGtuXiqG1cFSXInvLYnocCVuRnWVKKClKFFKVABQKQQeeJG8+3lYvC/KrVLepJVBqVjSaN1KV0gTA8XWgQeQCcDPYY0a1Cl+L7PUi258ZYrqLZTCcjs/HmQiOEqQnHfKhxj5aansQBke0rK3Rvtmj0i+oFnWnT4EeZOlPSGESpLrqEq93bLvAxlSVEDIKT6jWi21vRQ27sRaCb8pVw06XAfmx5AksrfjrYwXUOFAAKShQUk4B+BwHIAOufNjbIi7Vwvpnc3a8V+i12Oy/wCOqlolS6RIR1BaHGFJKwhQPV1JHHSM9862Oo1r2ar+os22LJnWxFuGrU+XAppVARHcbkOMLQnp6kJUk5Vjjk9h30E3epFsebYXXuTvJMq1+/pC9QbV95ci0WFGjMqL4bVgvuLWgkjIxgYyQocYyYm5VL3rqO01zyrku6hRkmnyjIpkehBZLaSoAJkeMMdSQD9Q4zjnGnNk9xbKsOz6TtnuFKFo12jMKZdbqn9Wjv4UrLzTysNrSrvkHOSR5a0m45lt3ftvcMi27hhVeLJp0xpDsN9L7alhtWR1JJGc6XZ6j8jJrEuO7tvdnLbv2v3rQn7cp9GhrMBNCKZCm/DSEspeD+FOdkhRTgnkjRtYN3bs3RRv0znxLfpjU1PvMGhux3SrwDgoDkkLHQpQPfw1AcHpPYZSu1avfPsa27GpUR+oSoS2pEmC1w7JjsSHAptHmVdIBA7nHHpo/sywtlb8pqJtm35cCUNoR4kOPc0th2LkcIcZ8QKbOQRgjHHHGlYVbDO5d5rXtbb5zcWZGKo5bAZi9OHXJBJSlkAEjq6wQcdsE+WqGmVTeWpbf1O77ikURqZJhuyo1vsxsIaawSG3H1K6usp8xwk9+rGNBO+G08ey9vqB+jKqjVbfoNxNVaqR1vKlOpjlRU6sFWVKAUVKPfHUSeM416RJoFxWHUa5bVwQKhAkU2Q429GWlaThCsjjsQeCDyDwRprRFZSeyLLiK2Lt5MiO0o9cnP60jH69fH1TraVSIZKXAw2Bkj/Kk8eXdOufvZMbdGyFvK8TqQtcggZyAfHXx/PrrafdlHzQkk+RA5PloJoeKL5ldOcPWttKSOD0OZAH4DUtDUAJ+MK5HBSQTk/boebp83v4qTjuM5Glsw6otakg4GMAqPlpWo8ixJovG26egFKi6V8A5CcH8TpaWqe4fCW06B6lCP46qOmog/AcEH7uO+paFT1pOW1Egc/h89C0MkOTKTDZPixpCigDKkYGft76TSmqdInNNvS0paKx4jhSOBnk9/LTjbEiRhagc5yMH9+oZtiqyahHRBTn3l5LaUJPOVHGhpJjPRHRSaJtQuO2o3DAxgJ6lOJGcj0Prpo2ntMpXh/pNTM+QMhv+OqdzYuetoJ8X4vP4tVzuwNWK8pV2PA6hr1cXh/335Hn7v8ACX/6C7Tujqbu6k49PeWh/wB7TZ272tJJ/S2kf9cb/wAWhZ72e60AodPUM8DOmR7Pldx9Rf8ArAatWXlxH0Ekl7JzLZG4G0dfuRyh3Bb9TtyGkrDNUlth1lwpPw/C0FLHUADyOPPGtGqFA2oZagVS29y7fcdTNZQlJeLa0hRwV4VgpAznJ4wDoHtewLDuq5lWhbF5UmpVlC3Ee5R3x4yi2fiASe+MEnGiO4NkKjZbsaoyWyhUaawMOYwCpeEnB+ZGt7S2Wj6aFVpO2yVvvatWqEmDerN5UOtO1EJYfVS5CHM+GhKUlQTkD4Ujn11h82wIU+46bdlQguv1WkJUiK/4hHQlX1gUpIB+8HWt7nQZceqNVh+lGnfSaAegYAUtAAUpISAADjsBoKMuDGeZYlVBhpb6ulpDjqUqc+QB5J+zXjO04uHFSi/Db3HoeCanw8WNtpq6uS2OkeYbJ/v0+hypNoSDFHPnzp9DRbBDUnyz9bOdPMqWkoAfWUgdurP5ayxrZl0kyGh6WcH3cAjg9JOlIqE1JSlUYjnn4vL7e2rJBfSRhzJzwMc6WHJaSFLWnCfLoH8NS0Vu0Q2aw4g9K2VAnvg/yNOKrjrKh1NP4PcdQ8h9upxW46AgNteYP6sD92vi4nxFdcZlSc5+qdWKmJyIBqziTlan++cdx2+WpjVxj4Shb46E9/CURn8NKcU248P6k31Y8sjPHb8tfJ9yZwhUJOR3HWdMmlqBo9Xc6G2yUS0dunC0/hwRpty4GlI+N2P1eZUkfZpxpmlLV1P04lRGApJwc+X79fKiU8nKWnACBzn/AHabR6i3oMIqzGMFLBH+jp1uaychTMfJ755185Gp5SAhp0AdzxkHXqI9PACSHSR6oB0KTJbFePHdT1JjMLTx9Xj8NLQYCuDCQnjHV1ADOkIjUx0dS1dAHdPhhWNRzDoxUCJbef2R04OjlQLbJD0eAUkuQkgcHOecA6Zc+jELwhhYSBg4ORp4QaYoY96aAAAwAc/lpCKLGfcKkzk4V2/Wr/dnUdLQmp60unhKkuMrzgfD1AjGnUsUZ/AQHG8cnABzpItFJUPCqYGMHPiq/DnUoWrMDZKZ+fLhSfP7RqJJaNgb6DL8GllIAeUkYye3rpxqnUvoIMsjq5Kunn92nG7VnhSuud4nTyQent+GkLoNWQspbcSRj7eNI1ezD70SYtv0txoq+kU5JxykdtKVQoKPh98b44+f26juU2tRW1qbS26Ec4TkHjSQKm2yXlRwQAeMHPy0afUFrcmt2+wWgn3porV8R4xxn108i0Y7vQsuNqHJ5wO/zxqrEmoBJCYSlEDHc99LarFUaPS7Bd+458/s0yVbMZ00SnrVU0CELbPUQeFDgfZpZtlJAdcjtfCPrZGf57ajfSsl/wCrGkDp/ZwB+88aaTVZGQjwngeOFYz+/QaZFQ5MsuFVGi1UKfDlNnnw32UrScH5g6jxrJhUuN7rR6XGiMlRUpqO0lCM+Z6Rgc8akCrFJSMPc8cJUcDJHppaawCgnqXwc8pUPv7Y0lSYVl5nkag+5tpjx46W05wEpGE/h5aHq9stZ9yyUTK1aUCZISesSFsAOg+R6xg57c6IVVB/PV4yklQ4+z114ut1FnAblkgc/wCj8tBphSjRR29tpRrSjSWLdpTkNuW4HHQh1xQWvGM4UT5YGqOfsNt9VpEl921ERnpST470J12KtwHgglpSePlrQI9yuNHpkuAgjOf5/nnU9FejOFKG5DKMjOOr79KszGqFAXatjRbBoMa2LWYci06IFeCyVqc6cqJJ6lZUcknudWq4tTQAr317tjJCPy+HV/8ASgcSQZDRyMZ44P8APlpReccwhTjChnPUcDUt1Q0aKJt2spASJq3AOSMJBP5afarlUbIjKccSRwMo7ccZ0Qs9AR8K2kgHGAOTr5SxwotMKXglRA5POo21uMqYPO1GtBIW08gq9SknI/HXwqdfQjDr6Dz36D2x5c6vfeGy2fDabClHB47ffpCJ8ZZW04wlJSCMcEkfhpbYSAxWq60j4U5I5yMjB/HV7Rrhrrs6K220pLy1pCVg8hROlsusuIGIrak9+rPJ+7tqfQKm1SqzCnRqc089HeS4hCxlJIORn8tGMnnSrmgy1i7Dp+Hug24t5mt1MLwAAJCsZ8vs89RHZO8Da/E/SGppIyR+uURope3yupBOLVp5wBgEr7+uo/8AT9XkA+NZUFWD2C1Z+flr2SWPX9KPziedTjf3vqDD1b3pHUE1+qZPw8KPf8NNi6d70gD6bmnHGSnJ0Tq9oaopB69v4uR2IWe/4aSPaEcIBVt9Gz59/wDDqZcXngL/AMQSev3/AKnIkf2f7lhPe8JhFDoz8aU9Ku/cH79SKhthXoTDap5meEXkkAOLyeRznP2aDqBZV40K8nNw6S7LiXA9IXKcnIwVrdcz1KIxgk5PlrQa1eu8dZieBV7gddaykrK47af2gecAZ5Gt+6eun++BXTuxi8V16nyGAzVqlLpyUJTHalyVuhjCR1JT19hnPb11hvtBvzmqFRL1LZ8a2asxMBSjHS0VdK/s8tdCVy4K9U3W6fcUqBNYjpSuK9HjoZK+oc9XQeSDxzz20B7m0uFc231eo6qc2FOQXgglzsoJyk46fIjXje19ONk14fQ7nAa8Ir8fqWUG5XanCYlpjMONvISsK6AcggH92pIqcZAIRT2AVcfC2ONZlshct43DtvRHYtlQHmY8ZDAkyq2WlPqbyk/AmO508jzPnoypG4FvGuG0rvpj9vVgx1ykCS625GfZT9ZbTwwFBPOQQk8cjWBZnsas0a1CdmoxOjBjqSR5Bahz6akfS9MJwmM8k45BcJ/f/fpmJ+jdVjoqVLqLcuO8MtvslDjbifIhSTgjVNRrktO4bhrdtU2VIMuhLQ3L646ugKUMgJUM5P7tMk61FaVhHHrlLbwPDfTkEj4gR+GNUW5dSZeseufRFSnQpiIDzzD8dXS4haUdQUCPmn7+dXSKNDUekSkEjuVJUkD5EnQPdl2bboh1mgzL5oceezHeZcZfmobUlZQQAAsjn+Ojqo00K0nsWOzt2/pXt1b9wVWpKcmSYifeFFtJy4nKVHj1I0bpVTngjonpB7HxGu/4HXPns53hZSdsaTRZ1629FntuPMCK9VGW3zh0hI6CoKORjHHOdbYaM+4FFuQlxGcZQ4M/LTJ3yFSVBAhuMtgYnMEJJBHQU/vPbXgiSHHVJD0MpOOS8Rn/AGc6oVUitN4JQVp/HPy0hCa40cqYUensAn8dOq00BQTe6yWldJRFIAyVB7OPy0lyGpZCfBSokEJ6HE9vx0Pol1RCS0WlpCRntrxuVLK1KIKTyQQMefrqOUVWgKtBBHo7ziVH3NxPV59SSB+B0uRb4QsKcgPqT3JCND5lVWO6AlxScZBBHf79SG6zVklQW4tJ7Ag/lqJpqqBlaLVdAawVJakDHcdJ1GVSnWUl1xLuE8ghByNRRUavj9VKWsEZVg51MFcqiG0qU8rPT2PcHProScWRJ8j4sOlCVglIIzlWQPzGpTBWB0pktBffp6sHPr89MIr0tXKnusqP1Qr6x9OdMR7ySqVKp8ObHkPRSlMhhtSVLZUoAgLA5TkYPOONBNbsLTLEqm5Li/iHqk9vnrxMzqkGIh9Bf6Ovww5hfSSR1Y74JHf5aYTcsh5RZdjt/FzhbYIGsVuKqFftbWg+202j3WhTCtCB0hQIWOQPmQfu0G0LVG8lEojqbLgyM5zjJzp9DExaAAV5KfM9tMCvRFudTjQz/pH09NPt1qAoEFk9RGR8RzopK6JQpMWUQr4j5nn7NNH3wKBThSgCnkYx/ONSE16nt9RDZUDxgr7n17ay6m3pUdwN2JcSk1uTBtWzV+BN91WAqpVIjJaUojJbaHCkg8q78A6Oi0DqaO4JxUE9QSeQcc500kyfEHW23j1KQCNWInwHJBIU6cjAHH9w0l2dA8QBlSUk4CutOT+8aVpDKyAXnOpKfCR0jj6oPz18VOk+J4COO41KU/D8Tq6wvpHJSnBx950/1wiFLQE9WDwrgH8tBLoSnREZkMJV1pjJV8icYOle8R3AUJgI61DByc4P3jWfbe31Ubh3Cvuy6wzDQza8mGmK4ypSVONSGlLAVnOSkpIyAOCNacj3BCSrxgtWACAoYGPTUigkEe6FYLkcE+ZJGAdfKj05tSSG1d+cE45/u1IK4iVda0/CTwSR/HX3hRVKJDhORnBIyTqNPqMqIwajoA8JKk8YAI/d/HTqW4TqUnwQrpHHHr+/Xq4zMhKcrXkcJ5HHbSUMJbytSVjtjGNVtNPca01qehqFj44qVeePCB59TxjTrTFKVwIyCO2Cjtzz5aAtp9x1blUaq1FVKTTTSKzIpLiS/wCIl0tdJ8QcJ6chY455B5OjB6atLpbb7cc9J1HYYpci+ZgUkIJSGzk4Kegc6iS6dAV1PAuJUQcAHGfXHz0CRNyoQu6dZHiLiVWEymSht9kpElg4y40eygFHpPmDq5euSukKxJTjHALQPI+0fnqU1zGVNk9UqBHQQZcptQPwpLij2+/Vlt1cdFVfNMFfVLNPQ8Cvo5UcDIGPTOM9+M6EU1F+YtPvKGy4rnrDZTyONH2zFmRrmv2EzNlsx2W2nHleKenxCEkBKc91ZVn7ATpsJXixzPSwYrSw37joKTf+zqFHxY8wg5yoRFkaaVeexzyApT7qMjOFRXBj8uP92rN3ZqgOK/VTGhn8fnqG5sRR3FK6ZbOCexyeNelWJwf9yS+P7Hn6xPZRXuXRsN0nqqS8enu6/T/R0gXHsCRn6R7+sdf8NSnfZ9p6iSiU3zz3Ooh9nlnJ6X2seX61Q/u1YsThH/8ANL5/sRxl7BwjTNzt1WNwnLylT3JNLemKkuUAtpEMNqP+SQSlS0JHkckjHnrRLs37j3DRpMNva5FNcWlJQ4xUCrCgRjqC2jkfIY+3QQ1vfCVe7qf6OWEWm5K4UleZ6I+O+M+GpY580j7NGVx7lbHzqZKYpVBuNlxbKulcmG2npVjIGUOK4yOflrr1e/5lDpU6I9crNPqkOn05y3DSZ0dBdddQ+HUSEucgjGMY541UPx4L0VyMqSkpeQUEkHgEYxp+vSrUq1Hp0i1ay9KnpKve4cmM4yuMg4KB1KHSoHn6pPA0POsykH9ay6MeXWfP5Z14ztnXjJfD6Hf7Of8Axo/H6gL7Ms+nRbMqdFfq0Zk0qsyY6Uur6f1fXkd8cc6hbmVCPuDuNZ9vWHMaqs6j1D3qdPiK6o8SPj40KdHwkkZBTk+nfU629mrWos6rS5cJipqqk1Uv+tRW1FnPPSCrJIz+/R/TYDNNQlmnpbit8/C00lIJx8gPkNc7RsvyuqZn6XFbC3uaZNfWizrpcW5CKl/q4E7BKms/soXgkfPtqR7M0CbW6Xct8rSrNwVl95Cu2W0EpT/fqZvmYZ2puBdbixpbLUYqbQ83nDuQElPooE5BGrbZGku21tjb9KSQ2v3NDqgAQOpY6ift50y21FcWpUaMadNCvhQodXkoHOosmlzJLD0dbCltqBSUkdXOMfw043LmJUFKcTgZ5yc6f+kZ6UEMgkgcKLmM/wA86dJS0sbKzn72d7Wo8qi3NRqnQadMVRq9LY/rERtxQSTkdxqZ7OrD02Ze9UjICIKq84xDYRw2ylGQQhHZHcHA0aWLZNcse5LrrRqLD0S5JgmJjpSQpleD1ZJGFEnz40O2nQt0tq3Ljptm0Sk1qn1moOVCE5Kl+AuMtz6wcT0HqGcY6TnU2e5VTVFzY9/VSs3/AHfZFS93UqhusuxSzlKlMODPSrnuk+Yx30xuvPn2JGZ3OprsoJpZSioxUOK6JMVSsE9JOAtGchQ+YOdBdp7c7mbbXId1YpbuG4akXf0gpxeQ026hZBHgKVwCgjjqxn5attyK5uFvTS27Cp23tRtyjTnGxVKlPUyHEtJV1KQ2hpSyc4xnt9mnU2Bq0N7PxL6vy01XhW7+uSK7VZbsmAhmUCmPG6vhR0LSpCu3mnONaRSLlrECqoty5H0qmPMqeiSmepKJSE4C/gUT0rGQSnJGOR6AMsiq3bsvbzVmVnb6qXTR6cVIp1Sojbbj5aKiUoeZccQoKGTkpyDqXSatcm4V/wBKuKo2XKti3aCl1xliepIlzX3ElGVISo+GhIJOCTnIxnyibuwaUjS01uQg9KlLBCRj4UfPzIOsapu4O6m4G5NctGnV6NbNItl4okyWIjMmTM6+WwA6gpQOnvwec984G3ql0ZxZUI/w4GSF4x31z5Yt8WFbm+W5SrguCNTGXn4iGTIdCApSUEKGTjRbdEa2D93ci5NuH4ce9H4tWo0t1MU1pmAGXY7qzhIktJV09JJwFo6QDjKR31Gp2+VXvK6avb9g2VEqMa33/dps2fNVEbW6MgpbAQsqwQeePI+ehzd/cOz74t93b3bJxNy1evFMdT0QhceA2VAqddcHwpIAOBnPn9sTayn07ZGpV6172kSkQqjMM+BXPAW4w/1AdaHVoB8NST5rwD66S2lRK1Niod5xHKmii3JRvoepuBS2EeN4jElPn4buAFKHmk9Ksc9OOdDp3k2jp71yVmqNIpb9DmJptRfcj/rHnMFTaUqQklYOCACe/p5iW5241m3NS2rb2xqMm5rkcksLg/R8ZSmYbqVhQecfIDaQMHIznBwQBnWO3DTG6pUbspkh9HiztxKbFUDkgAgjP2cnTXpTA9Do8b30KIiFULmsWv0Kj1R1MeBUZaG1F1xXKErZbUXGuoDjqSAePXWRy9yaE/7SxuGPa92VCLAt4spixqK8ZQWtwfEWlhKkowcdWO5A0a+1ApiPt5Taa2+lbs+uwIzXT/aDnVkfcjv89MWxCQv2pLkbMhGWLXiIB6s8lbZ4OklexHuHlM3Js6bTX6xWBWLWZiq6XBcNPcgYJzjCnB0q/wCion1xxqdb157e3SMW5dMOeSknpadBUQP2gM5I579tZfuPtxd9V3WhXdUbZTeVswIwRFpMeoMtGPI/adcafKEOeeB1E9s8DGtCtW8aDVpMehSaRLtqp4WY1OqkER1rSByWlJ6ml/YhZOO4GopdQ7F9V5sKm0eoT0SErXEjreSknAPSknnn10B+zzSDS9q6bNlzEJl1ou1eT3JWp9wrSST59BQPu0e3PSJM+16rDbQtxT8J9tABGclBA1nFmXQ5RPZ1pl4QaVIqH0RQktqjMoSpfiMJ8JeQSPhC0knnOAeM8aeyc7NSZlxgtKkVBj62QkHUt1SnlJKXmyD25+fnrl3aeqMVey27guTbO+K/WK487Mk1iPTUqSSVEAMOpcSptKQMAICcHONPXrdO4zWyd1vSqdcdDn0Gaz7hUqiw5Dkvw1OoSlRUj4VODqKVDPIGTydTR6WFSrWjp8tAp/yiRjjKVakMsSS3lC28YIyVj8flxrm257UqtnbUQdxrLrVZZrNLhsVOb41QeebqCCkF9L6HFFKvhUpQIAxjjUyjXnM3ivZNGt6ty4Vr0enx5dVchSVtuTX3kJWiOHEnqSlIz19JCsgp89InzJdhJtlFlK3s3bms/GTIpLWOO4jK5/PWrN+9+ISttScHIODg451yoiu1u2bZ3quGy6rJiVGDX0MMvSJBedQ0ghCuXirrwCcZyQPTjWrRNqI0vb2JW6VUq1Cuh6Ame1V3Ki84+JKm0q/WBSulSMjBQR04JAA0yXiSL6GqKlPnCPDJV3H851X124TbsFVWkwahIbZUkLZhRHJDpBITkIQCo4zk4B4B1i+2G7d+btzW2LXlQI0aj09hdVflMFYkTnE58JvpwUJGCCog85wMDRPfW5Fbtzbyr3JGaXGrdCkxWJlOkpC0pLjyG/hUAOpCkKKkLHyyAQQBux1JLU02NUS6lDzanQh1IWnKSnjAxkHBB57EZ15InzFNOFIWAlBPwjn8B31k9VvbcCo7or25tJ2nRW41KbqkqdMjqeKUqwnwwhBSMkkck9grUaFfW41XmV60C/SKZcNuALlPORXHGJLC0FTbraQ4Ck8K6kknHHJ0stVoFSTPvZnedZ2/nTkp6/f65Okk9skudP8A3BrVPGmdZWtxXw/u1zps7eF2WHslT7qn16kijeNIKIP0c4qXIdXIcw2hwOgFalZx8OAD6AnWwUGv7r1KnJq9UtijseKjxUU4S1mUlGMgKV09HX24zjPdQ8l1saDVeJB3iozjtFj31SkFVctJZqEUhXSp5gf5dgn+wtGfsIBHnorodSjXTRYFdp7zhjVCOh9skgYCgDj7RnHHnqeY70+n9MlJSmQ0Qtt1vCilQ5SoZx8tZ/7Pi5TO3n0KqS31UWoTKZko6uG3lAc59CNR01T5BWktOYbvU6W2QtEpQGcDqBOjbZe1Ktdt1SIin+oRoincH5qSPP7dDi35ISlC3WuR0ghvvoq23g3BNkzlUeVIZW20lK3I6ugkFWcEjnHHy1r7Nhn4qCuirjW48PJo1+TsbX3FDw0EnzPST92dQXNjbsbcLjbbyfhH1c5z58/hqpA3Wpr6noVz11tZzk+8qUCecZBzn79WSL+31hjoFySFdIxhyEwo5+eUE69hJcVXqzi/mvyPPQyvexX9FW4jZ/VzakjA6fhecGB6d9J/o23W8qtVP+sL/jpbe7O+MV0LeqTb6UkEoVAawfllKQdSTvlvADj3Kn/9WP8AHVT9LX4Y/P8AYskoy5s5GqF5bF0+93LOZjVmVDTIQy3XGI7RgrSrH6wqU4FhA8/hzwe+j24LB2lj0GVU6buNQZSg0tSGW5SStQSnP1T+7Wa1aydt7evBVgT78gN1zx244jpQtYUteOkJcCSjknvnHro1rnsxVukU9+U622ltppbyypY+qBnPy+3WmLvSvoVvVaSJVHsa2a2I9WeuykIDoLTQRKQXCkAHC0pJKe+BnRZF2fpUmO3Ni1iK8w4sNhaF9YK/NIOO/fWW0nZSZX3YdQpzaGUBtKGnW8YcPHbHc86I1+z1c/SvMda1ftqIPPcfjqzu4TXrxV+6zM5YkNIToLKlsQacOp+bHbCh1AKfAz8++B/u1Xq2kS11eHXYOUpyUicjI+7q7eXPrqla2YvaKjoiuTUJI+q24sZ9Rwdeq2z3FjOlSZlSC18r/XLyfLB9dGHB8HJViQX/AGgWPxkXpPzFXp7Nczce2nKDIlvrhOuIWfdXAVEoVnvyCM+Wr2LszddMisQ2GnA3GQG0AoyQEjAOqam2zuTQ0uogSH0plZQ/1Moc8QE5+IqSc/fqa5L3hLKmVVucGVEqICAkcf6IHlzpJdl8BJ6JeZYuM4yL+8Tht1eCVgLjEp5Iy1gj+QdOCzbpjkE0pLhzgfByCMai0y496aKrMarylANlsCQhTuO/ISpWAfuzxqVJ3G3gcID8wBXclDPT92Oe/wDfqmXYnBN+rXzZbHtPjFq9T5y3a/8AWXRQc8AAajqos4AJVQ1hSPiz/P3amL3V3W6kl2NCUhJ5/q/KvkSRq0hb23a3JZcqdowJDaEqDrTf6tThyMHqIPSB6Ac/LVMv4e4evVf/AJL80Mu1+J2cV8gbNJdSklyiupwT1cajLo+B1fRshODwEj8f3aO2d8W3SwmpbfpaAIL7jTiF9f8AogpGPxOpLm9NrJW2lNhPLbxl0eGEkEHuCF4PHOMD7dVv+HYcr+aJ9tYvOP1Mvebba+BcKWoDOAGerj7tNtvRVJDwiy0AZGVskcfL8DrXoW6+2sh5z6VtqWy34fwKTHIKlc8cKVx20mVubtQl1Dce3JZQofEvK0dJA7YLZzzgd/XVT/hxy2zfJfqP9tOO8TIEO0qQlQ8ZAUVDOUkZ9dY7YVmzWt69wZ9SgFECYIqokl1r9W9hPxdJI5xrspq69kZ7IXK8WHwklLiMqT5EcDy+37tJTL2JqMl1pMxsKCSU+M2hPUfTqPH7tUS/h7FWqb/7WN9t4b3iYc9bNMAUUCIFeeEAZHr21DVRvd0AMoYKCCFBGADk9tdAu0PZiQphhyqwGfHBKVhbSkDHPKkq+H0Gcc8DVfLtjZVKUluusr8RXQPDUV4PPfB4HBOq32BxD2fk/wBCxds4GzTMMRSUtjrbbLZGBlDhH5Z50GztobTnTHqj9FPNPyagzVHnGZCwVS2s9DmCcDGeccHXWI2c25qKFvRKx4qWAFKDPiKGFHuOkHOflqI/sbYqI5kfTa0pI5Uou/icp7/dqh9jcRejXn+hY+1uHS1OaLusGHezVOaraZTiKbMbmseG4B+sRnGeORyeONV428cjX1O3DiVKU3PqMBNPW10JLQSkghQ4zn4R3ONdQR9gaBVXHGqRewdWhwsrSzLbPS4P2SMd8eWm53s2SoyfBau9tpQyrpfcbUeDyrGU9jqmfZnEQ0dX70NHtPhZPc5gfh7zQABRqrb9XHUTioRnYq0pz262ysE/PoGh+oWru5fFyUCZeqKNSaXQJyaghumvOvPvPJ+oOpSUhKfXHJHGPMdZs+zXdziPFpl3sPpwFJWhgEYPbkLP46jSvZx3VUSGqnCcSRg+IlSfuyAflqr0HiI6NeaLfTuHe0zLfpCoKBSpISMjgrI5/DWWMeLtbMrlv1lhwWRcTzr6JLY6kU917h1l0AApaVnKVdhnB9ddIy/Z53cjjqYEJ0k5OFkZ5x5p1CTsjvIglxdCjLKQSD46Rnkf7/w0nouMvwFnpOA9powWyIm8G0NFRbVvQqRddtx1qVA94nGHKaQsk9BPhrQpOScHjvqLurUN39ytuaxa0qzaNTjNaa8MJrqnnCUuoXgDwEo/ZxysffreH9q92ySF2e84cjJQtGD/ALWosnb3cdlsKdseeCg/sNhRJ/6JPOg8DFX4X8hli4bVKa+Zjt5Va4F7FVG2mKa87VDQ0wVRmk9ZyUJQoAjvxk8fdoI2Pg3bsah9iXa1RqtIr8aLNW/CbQuRDlBpPituNKKT0hSlAEZPA4OTjoZ+zL0bJULFrZwOSIDxGftCTqrfod3RT1P2TW2wT3MF4cY9cap7qcdHFlilGWto5uut+q0vbPdio1GkzYUW47iTLh+PH6FradcB6iknI8sj1OtmrO7lzV20GrK2ytuoCbMiiB9JVCOqIxT2ykILmXAFrUBnp6Unnn0BH977Lvi8rAl29R7XqHvEiQypIcYWgfCsEkkjjjOib6NqqmUqk0moodQOpJUwtJHz7aOR9GSPSwL2V+iPZ5ue6LVuVx4UipKYl06q+ApxpwISQpCikHoVlXY/PGe+oO8t8O3xNn1Kg0aSzbRYp0GTMkRVR/fXvpBlxBQlQCilKfEHVjHxcd9aCmqXFTUj6RhzvDUcfrW1D8yOdSo16xkFIkJcbx2yCMaDg460MqkqTG7CqlPqG+e4c73dpS4kOlwmuc4SULWSPkeO3pqmtBaq5uZuzcL8EqCUsUeMlHCj4TKuofb8SPxGjeJc9CWT0zPCJOSpScAkfv8A92rZqZRJGQJLa+o9X1cDJ9TpdB8rRjG2NiUy5tkrbtC51y6TVqXLdqDSAUoksLTJdLai2sH4Tk904Oiy669dO3tuybjO4UWSzBSXfCqcBoJkEDAa62ikpUTwCAfs0S1+ybOujoTX6HAnpQD0rkR0qLY8+lXdPbyI1Vx9kdqGX2Kg5blPdfYPUyX+t0I9MJWoj08tVqm7DlaVIJ6NuHTKrZcS8arTnKW0uAJj7Lqh1MfB1KBOB29cDy4GdZV7Pl8UGmWhNrlxymKazdNxTJEBLziU9XiKGEjPHkdXO6e3dxX69AtqBXKfS7WXhVVcQD708AeGkeQSQBz6/howpdl2vT6VEokaNETT4iEtNNKQFAJTjB58/wC/TNphqV+4IlVGjulP6t0JxzyP59NaBtXfFStEzpdu0lmYJKUodTIUrpTjkHjz1lf0dT0lXQ4wRg9+/nz+OtM2lvC37Soc9qfSkS33pAW2pKCU9IwCM58sk66PY+H3vFJKN6PQy9pyUeHd+Aet76X02kty7RpT3nlIWnAxjHb79Ui96r9TKL66HEWwVcNKSk4H2hI51Y1Pd6yEKQqLayn0rHUrrCmyM+WOk69p262181woqdvPwelBIKgpeVg8J4RwOc5+3jXslgrDWbufz/M85GUZaWRRvvWmm1mXYsda1KB4cCUgA+Xwn598+XpptXtBSAoj+jKIef8A07H/AOlqVG3C2ckltUqE9FDxUXVFBUU4xg4CeSefw+eo7t+bJB1YTJyAo4JQ4M8+nh6SWFBv7jXzJLrZyVI2GqtNmfR9RDLEtJGWnCA5z247/wDhq0XtBfNPirS2qe030K6ghagCO/kdYZdlYq9Y3KNbq1VmTaipcdSpkl9Tr5KSOklaiVceXOu5rQrVYn2ZNcnVaZIUpggqdfWsn4c9ydVKKvd/M0xnJxzGCQbSvNSaeq36xWI7MZOSymU70BR7kJKsDOfIaIXKTuo6lLT1TqqgkY5fVgJ+f4+frrSaU89F2SpkuM6tp81BpJdQopWRhfGRzjgar6dXK0tLiV1iaoDxRgyFnsePPWrBw8yzJlE526asEWZ27sFCUt1uqJSlPR34A9AMcaWLl3hjKBRclT6gAEhQCsY10RbCUymh7ykO8gfGOrjJ9dXiqZTS26s0+MVAHB8JORwPlqzPiQ2fkitZJLYwunb77v0qnJgPU6jzS0oK8eVAUXTxjBKVpBH3a8G++5xYWh+lUYFQ4WiEoFOTzjqKh+IxxrYnKbTiyMwI3/uk/wBk/LVRUabTk5KYEYduzSfT7NVKda0id3GasAKZv5dcaOtuqWnDnOFXCiUNDtzkBrnnnuNW8Lf1jCUVKwWsBPSvoUlZP2D4ONWb9Pge8hPuUfBU1x4SfX7NVUiFC9z6vdGclByfDHy/jod/Fu3BeYy4dPRNjTm/cF99QVttGDAJKB1kK6fL9vGdXETejap6JmqWRVGZRP1WUJWgDz5znPbjQy5Ch+F/xRnv/wA2NVbkaOmWEJYbCSU5ASMHgajxMOWmWvc2DuXHSw8jbq7My5S2JtCqMJjjpeLC1YHnkJST+GdTnbx9nwu+GzVHQDz1e5SEgnA4PU2O2sllMMhpBDKB8Ofqj5agvoSHSAkD4B5aZRhJ6Wvj+wHCUeZsyqrsRJbDya4lIOSR1IChk9sKIJ+4akuQtly8y0xc8VxT/SeppxtQGRnCulRxx3zrCVIR1/VHYeXy174LPxfqkeX7I9daFw0ZOk3/AL8ChuS5nQSrB21cUSm6IzfSMq6wo4xySVAEfzjSv6IrPksKUxctPKEAlRLgT0DzznsADrnN1llLZ6WkDGcYSOONeqUpkueCot/CfqnGmfByi/VxGVvEadNHQrextAlhIhV2lPFQUvDclslQBIJ79sjH46YTsPGePgRKjTnFpOClDyCfwB/njWASatVUIV0VOWnAOMPKGOft1NgV6uNIQWqzOR1OoUemQsZIHB76SeFj4e2I/wDfiK5qro26R7P09HSUqSnrz05XwpXmNIb2NuJlCkQZL6RgjDLqhj7ge/8Au1mLlfrsmY2ZNanultK1o65K1dKiBkjJ4PA5+Q1pdGnTQpShMfyWGyT4hyT4yRn8z+J0ubiFHNn8v3EeLFK8o2dmb1ZdUtiRLSpXdSXlgn8+T207+ge5kdfWmuVjKU4SfHUo4x888aMbNnzl0SOVzX1HDgyXCf8Azg6JLcnz1hAXNfVnpzlxR8kfP5nWTG43GhJ5ndaEw5wnLLl2MmVbm67XiIRXqoPEHStPWOR9401Ggbq08ONsVWWWucodbS4jtjIBHBGBz8uNaRW6zWGrglstVWYhtMaUoIS+oJBHY4z5eWimLIkORGFOPuKUpPJKiSeDpJdoT5xT+C/Q0Rw4vYwtTu7KcONVV9soQEfCwBgZz9X7++M6kRbm3oiO+IqruvJSQQhyOMZ+7+eddNtRIpSjMZo5Rk5QOdMKgQVBfVDYOFebY9dD7QzKnBfJfoRYMWjneRuZu6WvDdahKIThSvBWCRnJ7H5/b388aqaTfG69GeR1SnJraRjw5fWodyeSCD2wOT2Hrk66NlQIIUsCExgAYHhp+fy1VSYMEDIhsDJOf1Y/ztWQ4iCjlWHH5E7pdTG42724rCFom0qK+pRPSUhaT5epIPY/zzpqRu3fK3krbo7DY6QnpJCwecknKTyRnkcfLy1rUinwOl3+pR+ArH6tPp9mqx6BB8VA9yY7A/5Meo1bDEwt+7iDutN2Z8jea6EpWg0FsKBylaktK6Bx8OOgZGM9z3x2181vHWmpDYk2wh5oJJWVJaGVZGOAkcAD5d+/bBfMgwgU4hscq5/VjTMqFDLmDEZI68Y8MemmvBa/przJ3bUvvMGm96lIblF60EvLJR7upTAHTgAKCglQKgSDgjGMjvjTE/dW3amGUz9vIDueHfGglwEFP7OV8fFn144476tW4cQh3MVk4QCMoHqdVrkSLlY92axnt0D+yNTLgN6w82WZZJVYPzbn2gntOOXDtpAYawrBjQfjSeg4HJH7QAzjsflzFU9sQqKUHbRYeBKf1JWwCAOD1JVnJ5yPl89Ju6NGTTJnTHaGI6yMIHf104wwwUskst5yf2RpXw3CzeuH5jxniqOk2JRK2UQ2x4dkVRguKIdT9KOnwxnHBVnq8z9nz40txGySphaNMqHgKPCm5rmRkE/VKBzwPPSHWGUvlKWUADyCR6aQ6y0lKQGkDKV5wkc6X7P4B6LC8/2HXE8Tqu8ZKTTthnpQZzWmWy0HApTpxnqAKCCk4Iz5cYB1OcsvYstvPxrgmLDKFrS2ZqEFYSewCk5yRyAefkDoaWy1yfCRnoB+qO+oyo8cucsN/VH7I9NR9j8HPaFfL9B1xnE2vXYXosLYtyjtVj9Iqkha1paMVU1gvDqIGSk84GQSfIffq+oltbTU6IzGjVvLb6lKQXn2VqSfVXSvIHHfGORnHlljkeP0A+A3nqHPSPTUN9hgOugMoAGSB0jjnT4XZWBgvNh6P4AlxWNjLLKWhsblE238RCPpFSlOKCUHpSSs5xkYVnHB51GXbO25kJYfryGF84D7akgkYyM9gcEcd+dY9IYZ6M+CjJB/ZHodUtQQgF4hCcjjt8tavRVdKTEUmtzanLW27lPrix7gbW82lSijwXAQADk8p8sE6pzQrBSSn9L4gxxjkf8Ad1hcuTJacQpqQ6g9KhlKyD21SOSpJcUTId7n9s6qnDJVMNuZ/9k=", 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[ "# Confidence interval for polynomial linear regression\n\nI have a model which is not linear but rather polynomial, and I have to estimate the parameters by giving a 95% confidence interval. There are plenty of formulas for regression of the type $Y = \\beta_0 + \\beta_1 X$, but do they apply in my case (where $Y = \\beta_1 X + \\beta_2 X^2$)?\n\nOf course, R gives me a pretty output:\n\nCall:\nlm(formula = dN ~ 0 + I(N) + I(N^2))\n\nResiduals:\n1 2 3 4 5 6 7\n0.02456 -0.10512 -0.12136 0.01848 0.24056 -0.11465 0.02646\n\nCoefficients:\nEstimate Std. Error t value Pr(>|t|)\nI(N) 2.977e-02 6.596e-04 45.14 1.01e-07 ***\nI(N^2) -4.440e-05 1.770e-06 -25.08 1.88e-06 ***\n---\nSignif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n\nResidual standard error: 0.1403 on 5 degrees of freedom\nMultiple R-squared: 0.9992, Adjusted R-squared: 0.9989\nF-statistic: 3173 on 2 and 5 DF, p-value: 1.739e-08\n\n\nI have read on some PDF file (page 13) that one can simply get the confidence intervals by taking the standard error (given by R): $\\hat{\\beta_1} \\pm t_{\\alpha/2} \\times Std. Error$. Does it always hold?\n\nIn the same way, are the confidence intervals for the model prediction the same?\n\nThank you in advance for any clarification.\n\nPolynomial regression is in effect multiple linear regression: consider $X_1=X$ and $X_2=X^2$ -- then $E(Y) = \\beta_1 X + \\beta_2 X^2$ is the same as $E(Y) = \\beta_1 X_1 + \\beta_2 X_2$.\n\nAs such, methods for constructing confidence intervals for parameters (and for the mean in multiple regression) carry over directly to the polynomial case. Most regression packages will compute this for you. Yes, it can be done using the formula you suggest (if the assumptions needed for the t-interval to apply hold), and the right d.f. are used for the $t$ (the residual d.f. - which in R is available from the summary output).\n\nThe R function confint can be used to construct confidence intervals for parameters from a regression model. See ?confint.\n\nIn the case of a confidence interval for the conditional mean, let $X$ be the matrix of predictors, whether for polynomial regression or any other multiple regression model; let the estimated variance of the mean at $x_i=(x_{1i},x_{2i},...,x_{pi})$ be $v_i=\\hat{\\sigma}^2x_i(X'X)^{-1}x_i'$ and let $s_i=\\sqrt v_i$ be the corresponding standard error. Let the upper $\\alpha/2$ $t$ critical value for $n-p-1$ df be $t$. Then the pointwise confidence interval for the mean at $x_i$ is $\\hat{y}_i\\pm t\\cdot s$.\n\nAlso, the R function predict can be used to construct CIs for E(Y|X) - see ?predict.lm.\n\n[At least when doing polynomial regression with an intercept, it makes sense to use orthogonal polynomials but if the spread of $X$ is large compared to the mean, and the degree is low (such as quadratic), it won't be so critical (I tend to do so anyway, because it's easier to interpret the linear and quadratic).]\n\nIt is somewhat of a lengthy procedure to verify that the linear model obeys a t-distribution. To do so for the quadratic would be tedious. I do not think the above suggestion that one can simply substitute for the quadratic term is sound. There are methods involving Taylor expansions to make the conversion. See the following resource; http://fmwww.bc.edu/RePEc/esAUSM04/up.11216.1077841765.pdf\n\n• Welcome to Cross Validated! At a glance, this looks wrong. The regression is perfectly linear, just with a nonlinear basis function. Perhaps you can expand on why you think Glen_b got it wrong.\n– Dave\nSep 20, 2021 at 1:53" ]

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[ "Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange\nScilab 6.0.1\nChange language to: English - Français - Português - 日本語 -\n\nSee the recommended documentation of this function\n\n# sylv\n\nSylvester equation.\n\n### Syntax\n\n`sylv(A, B, C, flag)`\n\n### Arguments\n\nA,B,C\n\nthree real matrices of appropriate dimensions.\n\nflag\n\ncharacter string (`'c'` or `'d'`)\n\n### Description\n\n`X= sylv(A, B, C, 'c')` computes `X`, solution of the \"continuous time\" Sylvester equation\n\n`A*X+X*B = C`\n\n`X=sylv(A, B, C, 'd')` computes `X`, solution of the modified \"discrete time\" Sylvester equation\n\n`A*X*B+X = C`\n\n`X=-sylv(-A, B, C, 'd')` computes `X`, solution of the real \"discrete time\" Sylvester equation\n\n`A*X*B-X = C`\n\n### Examples\n\n```// Continuous time Sylvester equation:\nA = rand(4, 4); C = rand(4, 3); B = rand(3, 3);\nX = sylv(A, B, C, 'c');\nnorm(A*X+X*B-C)\n\n// Modified Discrete time Sylvester equation:\nX = sylv(A, B, C, 'd');\nnorm(A*X*B+X-C)\n\n// Real Discrete time Sylvester equation:\nX = -sylv(-A, B, C, 'd');\nnorm(A*X*B-X-C)```" ]

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[ "### Hereditary property of semi-separation axioms and its applications\n\nSang-Eon Han\n\n#### Abstract\n\nThe paper studies the open-hereditary property of semi-separation axioms and\napplies it to the study of digital topological spaces such as an $n$-dimensional Khalimsky topological space,\na Marcus-Wyse topological space and so on.\nMore precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms\nsuch as $T_{\\frac{1}{2}}$, semi-$T_{\\frac{1}{2}}$, semi-$T_1$, semi-$T_2$, {\\it etc}.\nBesides, using the finite or the infinite product property of the semi-$T_i$-separation axiom, $i\\in \\{1, 2\\}$,\nwe confirm that the $n$-dimensional Khalimsky topological space is a semi-$T_2$-space.\nAfter showing that not every subspace of the digital topological spaces satisfies the semi-$T_i$-separation axiom, $i\\in \\{1, 2\\}$,\nwe prove that the semi-$T_i$-separation property is open-hereditary, $i\\in \\{1, 2\\}$.\nAll spaces in the paper are assumed to be nonempty and connected.\n\nPDF\n\n### Refbacks\n\n• There are currently no refbacks." ]

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[ "# My Blog\n\n### cronbach alpha formula\n\n28 The Cronbach's alpha coefficient is typically in the range of 0-1, but it may also take negative values when the elements are not positively correlated with each other. 2003, research design course. Cronbach’s alpha is a test reliability technique that requires only a single test administration to provide a unique estimate of the reliability for a given test. Cronbach's alpha, a measure of internal consistency, tells you how well the items in a scale work together. res[step+n_var-2,2]=n_var #save number of variables in the scale. Also, the formula CALPHA(B4:L15) can be used to produce the results shown in range B43:L43 of Figure 3 of Cronbach’s Alpha Basic Concepts. res[step+n_var-2,3]=psych::alpha(mat)\\$total\\$raw_alpha #save Cronbach's alpha. The α was calculated in cell E13 when we put the cell formula as “= B12* (1- (E12/B13))”. The general rule of thumb is that a Cronbach’s alpha of .70 and above is good, .80 and above is better, and .90 and above is best. Cronbach’s (1951) alpha was developed based on the necessity to … c̄] Where N is the number of scale or items, c-bar is the average inter-item covariance among the scale items, and v-bar … Formula Used: Reliability = N / ( N - 1)x (Total Variance - Sum of Variance for Each Question )/Total Variance where, N is no of questions, Calculation of Cronbach's Alpha Coefficient is made easier. assalamualaykum pak, maaf mau nanya tentang uji alpha cronbach ini. #both ggplot2 and psych packages … The Cronbach's alpha computed by cronbach.alpha () is defined as follows α = p p − 1 ( 1 − ∑ i = 1 p σ y i 2 σ x 2), where p is the number of items σ x 2 is the variance of the observed total test scores, and σ y … Cronbach’s alpha is … The calculated value of α in E13 was 0.835. Cronbach’s alpha does come with some limitations: … kuesioner penelitian saya ketika diuji muncul hasilnya macam ini Reliability Statistics Cronbach's Alpha = 6,997E-6 N of Items = 107 … Before alpha, researchers were limited to estimating internal consistency of only dichotomously scored items using the KR-20 formula. Those who have access to Microsoft Excel, they can carry out the same … Example 1 : Calculate Cronbach’s alpha for a 10 …" ]

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[ "## Data Preprocessing\n\nMean subtraction is the most common form of preprocessing. It involves subtracting the mean across every individual feature in the data, and has the geometric interpretation of centering the cloud of data around the origin along every dimension. In numpy, this operation would be implemented as: X -= np.mean(X, axis = 0). With images specifically, for convenience it can be common to subtract a single value from all pixels (e.g. X -= np.mean(X)), or to do so separately across the three color channels.\n\nNormalization refers to normalizing the data dimensions so that they are of approximately the same scale. There are two common ways of achieving this normalization. One is to divide each dimension by its standard deviation, once it has been zero-centered: (X /= np.std(X, axis = 0)). Another form of this preprocessing normalizes each dimension so that the min and max along the dimension is -1 and 1 respectively. It only makes sense to apply this preprocessing if you have a reason to believe that different input features have different scales (or units), but they should be of approximately equal importance to the learning algorithm. In case of images, the relative scales of pixels are already approximately equal (and in range from 0 to 255), so it is not strictly necessary to perform this additional preprocessing step.\n\nCommon pitfall. An important point to make about the preprocessing is that any preprocessing statistics (e.g. the data mean) must only be computed on the training data, and then applied to the validation / test data. E.g. computing the mean and subtracting it from every image across the entire dataset and then splitting the data into train/val/test splits would be a mistake. Instead, the mean must be computed only over the training data and then subtracted equally from all splits (train/val/test).\n\n## Dropout\n\nDropout is an extremely effective, simple and recently introduced regularization technique by Srivastava et al. While training, dropout is implemented by only keeping a neuron active with some probability $P$ (a hyperparameter), or setting it to zero otherwise.\n\nwe must scale the activations by $p$ at test time. Since test-time performance is so critical, it is always preferable to use inverted dropout, which performs the scaling at train time, leaving the forward pass at test time untouched. Additionally, this has the appealing property that the prediction code can remain untouched when you decide to tweak where you apply dropout, or if at all. Inverted dropout looks as follows:\n\n## Loss functions\n\nIt is important to note that the L2 loss is much harder to optimize than a more stable loss such as Softmax. Intuitively, it requires a very fragile and specific property from the network to output exactly one correct value for each input (and its augmentations). Notice that this is not the case with Softmax, where the precise value of each score is less important: It only matters that their magnitudes are appropriate. Additionally, the L2 loss is less robust because outliers can introduce huge gradients. When faced with a regression problem, first consider if it is absolutely inadequate to quantize the output into bins. For example, if you are predicting star rating for a product, it might work much better to use 5 independent classifiers for ratings of 1-5 stars instead of a regression loss. Classification has the additional benefit that it can give you a distribution over the regression outputs, not just a single output with no indication of its confidence. If you’re certain that classification is not appropriate, use the L2 but be careful: For example, the L2 is more fragile and applying dropout in the network (especially in the layer right before the L2 loss) is not a great idea.\n\nWhen faced with a regression task, first consider if it is absolutely necessary. Instead, have a strong preference to discretizing your outputs to bins and perform classification over them whenever possible.\n\nIn theory, performing a gradient check is as simple as comparing the analytic gradient to the numerical gradient. In practice, the process is much more involved and error prone. Here are some tips, tricks, and issues to watch out for:\n\nUse the centered formula. The formula you may have seen for the finite difference approximation when evaluating the numerical gradient looks as follows:\n\nWhere $h$ is a very small number, in practice approximately 1e-5 or so. In practice, it turns out that it is much better to use the centered difference formula of the form:\n\nUse relative error for the comparison.\n\n• relative error > 1e-2 usually means the gradient is probably wrong\n• 1e-2 > relative error > 1e-4 should make you feel uncomfortable\n• 1e-4 > relative error is usually okay for objectives with kinks. But if there are no kinks (e.g. use of tanh nonlinearities and softmax), then 1e-4 is too high.\n• 1e-7 and less you should be happy.\n\n## Annealing the learning rate\n\n• Step decay: Reduce the learning rate by some factor every few epochs. Typical values might be reducing the learning rate by a half every 5 epochs, or by 0.1 every 20 epochs. These numbers depend heavily on the type of problem and the model. One heuristic you may see in practice is to watch the validation error while training with a fixed learning rate, and reduce the learning rate by a constant (e.g. 0.5) whenever the validation error stops improving.\n• Exponential decay. has the mathematical form $\\alpha = \\alpha_0 e^{-k t}$. where $\\alpha_0, k$ are hyperparameters and $t$ is the iteration number (but you can also use units of epochs).\n• 1/t decay has the mathematical form $\\alpha = \\alpha_0 / (1 + k t )$ where $a_0, k$, are hyperparameters and $t$ is the iteration number.\n\nIn practice, we find that the step decay is slightly preferable because the hyperparameters it involves (the fraction of decay and the step timings in units of epochs) are more interpretable than the hyperparameter $k$.\n\n## Second order methods\n\nA second, popular group of methods for optimization in context of deep learning is based on Newton’s method, which iterates the following update:\n\nHere,$H f(x)$ is the Hessian matrix, which is a square matrix of second-order partial derivatives of the function. The term\n$\\nabla f(x)$ is the gradient vector, as seen in Gradient Descent. Intuitively, the Hessian describes the local curvature of the loss function, which allows us to perform a more efficient update. In particular, multiplying by the inverse Hessian leads the optimization to take more aggressive steps in directions of shallow curvature and shorter steps in directions of steep curvature.\n\nHowever, the update above is impractical for most deep learning applications because computing (and inverting) the Hessian in its explicit form is a very costly process in both space and time. For instance, a Neural Network with one million parameters would have a Hessian matrix of size [1,000,000 x 1,000,000], occupying approximately 3725 gigabytes of RAM. Hence, a large variety of quasi-Newton methods have been developed that seek to approximate the inverse Hessian. Among these, the most popular is L-BFGS, which uses the information in the gradients over time to form the approximation implicitly (i.e. the full matrix is never computed).\n\nIn practice, it is currently not common to see L-BFGS or similar second-order methods applied to large-scale Deep Learning and Convolutional Neural Networks. Instead, SGD variants based on (Nesterov’s) momentum are more standard because they are simpler and scale more easily.\n\n## Per-parameter adaptive learning rate methods\n\nAdam. Adam is a recently proposed update that looks a bit like RMSProp with momentum. The (simplified) update looks as follows:\n\nNotice that the update looks exactly as RMSProp update, except the “smooth” version of the gradient m is used instead of the raw (and perhaps noisy) gradient vector dx. Recommended values in the paper are eps = 1e-8, beta1 = 0.9, beta2 = 0.999. In practice Adam is currently recommended as the default algorithm to use, and often works slightly better than RMSProp. However, it is often also worth trying SGD+Nesterov Momentum as an alternative. The full Adam update also includes a bias correction mechanism, which compensates for the fact that in the first few time steps the vectors m,v are both initialized and therefore biased at zero, before they fully “warm up”. With the bias correction mechanism, the update looks as follows:\n\n## Hyperparameter optimization\n\nAs we’ve seen, training Neural Networks can involve many hyperparameter settings. The most common hyperparameters in context of Neural Networks include:\n\n• the initial learning rate\n• learning rate decay schedule (such as the decay constant)\n• regularization strength (L2 penalty, dropout strength)\n\nBut as we saw, there are many more relatively less sensitive hyperparameters, for example in per-parameter adaptive learning methods, the setting of momentum and its schedule, etc.\n\nHyperparameter ranges. Search for hyperparameters on log scale. For example, a typical sampling of the learning rate would look as follows: learning_rate = 10 ** uniform(-6, 1).\n\nPrefer random search to grid search. As argued by Bergstra and Bengio in Random Search for Hyper-Parameter Optimization, “randomly chosen trials are more efficient for hyper-parameter optimization than trials on a grid”. As it turns out, this is also usually easier to implement.\n\nCareful with best values on border. Sometimes it can happen that you’re searching for a hyperparameter (e.g. learning rate) in a bad range. For example, suppose we use learning_rate = 10 ** uniform(-6, 1). Once we receive the results, it is important to double check that the final learning rate is not at the edge of this interval, or otherwise you may be missing more optimal hyperparameter setting beyond the interval.\n\nStage your search from coarse to fine. In practice, it can be helpful to first search in coarse ranges (e.g. 10 ** [-6, 1]), and then depending on where the best results are turning up, narrow the range. Also, it can be helpful to perform the initial coarse search while only training for 1 epoch or even less, because many hyperparameter settings can lead the model to not learn at all, or immediately explode with infinite cost. The second stage could then perform a narrower search with 5 epochs, and the last stage could perform a detailed search in the final range for many more epochs (for example).\n\n## Model Ensembles\n\nIn practice, one reliable approach to improving the performance of Neural Networks by a few percent is to train multiple independent models, and at test time average their predictions. As the number of models in the ensemble increases, the performance typically monotonically improves (though with diminishing returns). Moreover, the improvements are more dramatic with higher model variety in the ensemble. There are a few approaches to forming an ensemble:\n\n• Same model, different initializations. Use cross-validation to determine the best hyperparameters, then train multiple models with the best set of hyperparameters but with different random initialization. The danger with this approach is that the variety is only due to initialization.\n• Top models discovered during cross-validation. Use cross-validation to determine the best hyperparameters, then pick the top few (e.g. 10) models to form the ensemble. This improves the variety of the ensemble but has the danger of including suboptimal models. In practice, this can be easier to perform since it doesn’t require additional retraining of models after cross-validation\n• Different checkpoints of a single model. If training is very expensive, some people have had limited success in taking different checkpoints of a single network over time (for example after every epoch) and using those to form an ensemble. Clearly, this suffers from some lack of variety, but can still work reasonably well in practice. The advantage of this approach is that is very cheap.\n• Running average of parameters during training. Related to the last point, a cheap way of almost always getting an extra percent or two of performance is to maintain a second copy of the network’s weights in memory that maintains an exponentially decaying sum of previous weights during training. This way you’re averaging the state of the network over last several iterations. You will find that this “smoothed” version of the weights over last few steps almost always achieves better validation error. The rough intuition to have in mind is that the objective is bowl-shaped and your network is jumping around the mode, so the average has a higher chance of being somewhere nearer the mode.\n\nreference https://zhuanlan.zhihu.com/p/27919794\ncs231n lecture notes" ]

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[ "You are viewing the RapidMiner Studio documentation for version 9.0 - Check here for latest version\n\n#", null, "Explain Predictions (Model Simulator)\n\n## Synopsis\n\nThis operator identifies the attributes that play the largest role when making a prediction.\n\n## Description\n\nGiven a model and an input, you can generate a prediction, but which of the attributes plays the largest role in forming that prediction? This operator takes a model and an ExampleSet as input, and generates a table highlighting the attributes that most strongly support (green) or contradict (red) each prediction. Alternatively, the table can be displayed with two extra columns (support and predict) containing numeric details.\n\nFor each Example in an ExampleSet, this operator generates a neigboring set of data points, and uses correlation to identify the local attribute weights in that neighborhood. Although the relationship between attributes and predictions may be highly non-linear globally, the local linear relationship is more than powerful enough to explain the predictions.\n\nThis operator works with all data types and data sizes. It supports both classification and regression problems. The only model type which is not recommended is k-Nearest Neighbors, since this model typically suffers from long runtimes.\n\n## Input\n\n•", null, "model (Model)\n\nThis input port expects a model.\n\n•", null, "training data (Data Table)\n\nThis input port expects an ExampleSet identical to the one that trained the model.\n\n•", null, "test data (Data Table)\n\nThis input port expects an ExampleSet with test data.\n\n## Output\n\n•", null, "visualization output\n\nThis output port displays the test data with predictions and color highlighting of attributes: green when the value of the attribute supports the prediction, and red when the value of the attribute contradicts the prediction.\n\n•", null, "example set output (Data Table)\n\nThis output port displays the test data with predictions and two extra columns: one that details the attributes that support the prediction and one that details the attributes that contradict the prediction.\n\n•", null, "importances output (Data Table)\n\nThis output port displays the test data in a long table format including the importance of all attributes for each row. This can be useful if the data should be visualized later on.\n\n## Parameters\n\n• maximal explaining attributes The maximal number of attributes used to support the predictions, also the maximal number of attributes used for contradicting it. The whole point about explanations is that they allow you to focus on the factors that matter in each particular case. We recommend a value of 3 to achieve this but you can increase this number if you feel that you need more factors to explain the predictions to you. Please note that you might end up with less factors if only less attribute values than the maximal number support or contradict a prediction in this case. Range: integer\n• local sample size The number of locally generated samples around each prediction data point to identify the attributes with the biggest impact on this decision. You might want to increase this number for high-dimensional data sets in case the quality of predictions become worse. Please note that the runtime of this algorithm slows down with higher numbers. In general, a value of around 500 delivers high-quality explanations in a reasonable amount of time. Range: integer\n\n## Tutorial Processes\n\n### Explaining Predictions for Titanic\n\nThis process trains a Naive Bayes model on the Titanic data. It then uses the Explain Predictions operator to create the predictions and all local explanations for the second data set.\n\nYou can see the two results. First the data with additional columns for the predictions, the confidences, and the new explanations. The other result directly visualizes the explanations with colors. Green means a value which strongly supports the prediction. Red means that this value contradicts the prediction. Have a look at the 3rd row for example. The model predicts \"Yes\" for survival despite the fact that the gender is male. In general, most men died during the accident though so the model made this prediction based on the other values. In this case, this would be the age of 71, the amount of money paid, and the fact that this person traveled without parents or children.", null, "" ]

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[ "# Iterator pattern\n\n### 1. Usage\n\n• Provide a way to access the elements of an aggregate object sequentially without exposing its underlying representation.\n• makes possible to decouple collection classes and algorithms.\n• Promote to “full object status” the traversal of a collection.\n• Polymorphic traversal\n\n### 2. UML class diagram", null, "", null, "### 3. Pros\n\n• shields the client from the internal representation of aggregator.\n• aggregate can be iterated in many different ways.\n• more than one iterator can be active – the iterator stores the current state so each is self contained.\n\n### 4. Cons\n\n• uses AbsractFactory so have to define a ConcreteAggregate in addition to ConcreteIterator\n• if the underlying aggregate is updated while using an Iterator, the operation of the Iterator may be undefined.\n\n### 5. Source code\n\n```// http://patterns.pl/iterator.html\n#include <iostream>\n#include <vector>\n#include <memory>\n#include <stdexcept>\nusing namespace std;\ntemplate<typename T>\nclass Iterator\n{\npublic:\nvirtual void first() = 0;\nvirtual void next() = 0;\nvirtual bool isDone() const = 0;\nvirtual T& current() = 0;\n};\ntemplate<typename T>\nclass VectorIterator : public Iterator<T>\n{\nvector<T> vect;\nsize_t position;\npublic:\nVectorIterator(vector<T> & v) : vect(v), position(0) {}\nvoid first() override\n{\nposition = 0;\n}\nvoid next() override\n{\n++position;\n}\nbool isDone() const override\n{\nreturn !(position < vect.size());\n}\nT& current() override\n{\nif (!isDone())\n{\nreturn vect.at(position);\n}\nthrow out_of_range(\"out of range\");\n}\n};\nint main()\n{\nvector<int> v{ 1, 2, 3 };\nVectorIterator<int> vIter(v);\n// use interface so you can switch easly in case different implementation\nIterator<int> &iter = vIter;\nfor (iter.first(); !iter.isDone(); iter.next())\n{\ncout << iter.current() << endl;\n}\nreturn 0;\n}\n```" ]

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[ "Search a number\nBaseRepresentation\nbin101110011010100…\n…1111111111011101\n311000112122022121000\n41130311033333131\n511142202304010\n6414313500513\n753411134320\noct13465177735\n94015568530\n101557463005\n1172a16900a\n12375711739\n131ba891557\n1410abc07b7\n1591aea7c0\nhex5cd4ffdd\n\n1557463005 has 64 divisors (see below), whose sum is σ = 3170119680. Its totient is φ = 710690112.\n\nThe previous prime is 1557463001. The next prime is 1557463021. The reversal of 1557463005 is 5003647551.\n\n1557463005 is a `hidden beast` number, since 15 + 5 + 7 + 4 + 630 + 0 + 5 = 666.\n\nIt is not a de Polignac number, because 1557463005 - 22 = 1557463001 is a prime.\n\nIt is a super-3 number, since 3×15574630053 (a number of 29 digits) contains 333 as substring.\n\nIt is a congruent number.\n\nIt is not an unprimeable number, because it can be changed into a prime (1557463001) by changing a digit.\n\nIt is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 685882 + ... + 688148.\n\nIt is an arithmetic number, because the mean of its divisors is an integer number (49533120).\n\nAlmost surely, 21557463005 is an apocalyptic number.\n\n1557463005 is a gapful number since it is divisible by the number (15) formed by its first and last digit.\n\nIt is an amenable number.\n\n1557463005 is an abundant number, since it is smaller than the sum of its proper divisors (1612656675).\n\nIt is a pseudoperfect number, because it is the sum of a subset of its proper divisors.\n\n1557463005 is a wasteful number, since it uses less digits than its factorization.\n\n1557463005 is an evil number, because the sum of its binary digits is even.\n\nThe sum of its prime factors is 3015 (or 3009 counting only the distinct ones).\n\nThe product of its (nonzero) digits is 63000, while the sum is 36.\n\nThe square root of 1557463005 is about 39464.7058141829. The cubic root of 1557463005 is about 1159.1489509280.\n\nThe spelling of 1557463005 in words is \"one billion, five hundred fifty-seven million, four hundred sixty-three thousand, five\"." ]

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[ "## Avogadro’s Number and the Mole\n\n#### Learning Objective\n\n• Define and memorize Avogadro’s number\n\n#### Key Points\n\n• The mole allows scientists to calculate the number of elementary entities (usually atoms or molecules) in a certain mass of a given substance.\n• Avogadro’s number is an absolute number: there are 6.022×1023 elementary entities in 1 mole. This can also be written as 6.022×1023 mol-1.\n• The mass of one mole of a substance is equal to that substance’s molecular weight. For example, the mean molecular weight of water is 18.015 atomic mass units (amu), so one mole of water weight 18.015 grams.\n\n#### Term\n\n• moleThe amount of substance of a system that contains as many elementary entities as there are atoms in 12 g of carbon-12.\n\nThe chemical changes observed in any reaction involve the rearrangement of billions of atoms. It is impractical to try to count or visualize all these atoms, but scientists need some way to refer to the entire quantity. They also need a way to compare these numbers and relate them to the weights of the substances, which they can measure and observe. The solution is the concept of the mole, which is very important in quantitative chemistry.\n\nAmadeo Avogadro first proposed that the volume of a gas at a given pressure and temperature is proportional to the number of atoms or molecules, regardless of the type of gas. Although he did not determine the exact proportion, he is credited for the idea.\n\nAvogadro’s number is a proportion that relates molar mass on an atomic scale to physical mass on a human scale. Avogadro’s number is defined as the number of elementary particles (molecules, atoms, compounds, etc.) per mole of a substance. It is equal to 6.022×1023 mol-1 and is expressed as the symbol NA.\n\nAvogadro’s number is a similar concept to that of a dozen or a gross. A dozen molecules is 12 molecules. A gross of molecules is 144 molecules. Avogadro’s number is 6.022×1023 molecules. With Avogadro’s number, scientists can discuss and compare very large numbers, which is useful because substances in everyday quantities contain very large numbers of atoms and molecules.\n\n## The Mole\n\nThe mole (abbreviated mol) is the SI measure of quantity of a “chemical entity,” such as atoms, electrons, or protons. It is defined as the amount of a substance that contains as many particles as there are atoms in 12 grams of pure carbon-12. So, 1 mol contains 6.022×1023 elementary entities of the substance.\n\n## Chemical Computations with Avogadro’s Number and the Mole\n\nAvogadro’s number is fundamental to understanding both the makeup of molecules and their interactions and combinations. For example, since one atom of oxygen will combine with two atoms of hydrogen to create one molecule of water (H2O), one mole of oxygen (6.022×1023 of O atoms) will combine with two moles of hydrogen (2 × 6.022×1023 of H atoms) to make one mole of H2O.\n\nAnother property of Avogadro’s number is that the mass of one mole of a substance is equal to that substance’s molecular weight. For example, the mean molecular weight of water is 18.015 atomic mass units (amu), so one mole of water weight 18.015 grams. This property simplifies many chemical computations.\n\nIf you have 1.25 grams of a molecule with molecular weight of 134.1 g/mol, how many moles of that molecule do you have?\n\n$1.25g \\times \\frac{ 1 \\text{ mole}}{134.1g}=0.0093 \\text{ moles}.$" ]

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[ "# Difference between revisions of \"Lab 13 RS\"\n\nDC Bipolar Transistor Curves\n\nData sheet for transistors.\n\nUsing 2N3904 is more srtaight forward in this lab.\n\n# Transistor circuit\n\n1.) Identify the type (n-p-n or p-n-p) of transistor you are using and fill in the following specifications.\n\nI am going to use n-p-n transistor 2N3904. Below are some specifications from data shits for this type of transistor:\n\nValue Description\nCollector-Base breakdown voltage\nEmitter-Base Breakdown Voltage\nMaximum Collector-Emitter Voltage\nMaximum Collector-Emitter Voltage\nMaximum Collector Current - Continuous\nTransistor Power rating()\n,\n40 300 ,\n70 300 ,\n100 300 ,\n60 300 ,\n30 300 ,\n\n2.) Construct the circuit below according to the type of transistor you have.\n\nLet .\n\nvariable power supply\n\n.\n\nFind the resistors you need to have\n\n, , and\n\nBy measurements I was able to find that . So I am going to use this value. Also let picks up . So my current .\n\nNow to get I need to use\nTo get I need to use\nTo get I need to use\n\n\n3.) Measure the emitter current for several values of by changing such that the base current A is constant.\n\nI used:\n\n\n\n\n\nand\n\n\n\n\nBelow is the table with my measurements:\n\nAnd below is my currents and power calculation:\n\nHere:\n\n\n\n\n\n4a.) Repeat the previous measurements for . Remember to keep so the transistor doesn't burn out\n\nI used:\n\n\n\n\nand\n\n\n\n\nBelow is the table with my measurements:\n\nAnd below is my currents and power calculation:\n\nHere:\n\n\n\n\n\n4a.) Repeat the previous measurements for . Remember to keep so the transistor doesn't burn out\n\nI used:\n\n\n\n\nand\n\n\n\n\nBelow is the table with my measurements:\n\nAnd below is my currents and power calculation:\n\nHere:\n\n\n\n\n\n5.) Graph -vs- for each value of and above. (40 pnts)\n\nBellow is my plot for the case of\n\nBellow is my plot for the case of\n\nBellow is my plot for the case of\n\n6.) Overlay points from the transistor's data sheet on the graph in part 5.).(10 pnts)\n\n# Questions\n\n1. Compare your measured value of or for the transistor to the spec sheet? (10 pnts)\n\nI will calculate my from my measurements above in saturation region:\n\n1):\n\n2):\n\n3):\n\n\nAnd this values of in agreement with range of from spec sheet which is from 30 to 300. But I can not say nothing more because 1) my current doesn't corresponds to published in data sheet. 2) my calculation for specific value of current but in data sheet we have the range of for specific values of currents.\n\n1. What is for the transistor? (10 pnts)\n2. The base must always be more positive (negative) than the emitter for a npn (pnp) transistor to conduct I_C.(10 pnts)\n3. For a transistor to conduct I_{C} the base-emitter junction must be forward biased.(10 pnts)\n4. For a transistor to conduct I_{C} the collector-base junction must be reversed biased.(10 pnts)\n\n# Extra credit\n\nMeasure the Base-Emitter breakdown voltage. (10 pnts)\n\nI expect to see a graph and a linear fit which is similar to the forward biased diode curves. Compare your result to what is reported in the data sheet.\n\nI used:\n\n\n\n\n\nBelow is the table with my measurements and current calculations:\n\nHere:\n\n\n\n\nAnd bellow is my plot for the Base-Emitter breakdown voltage\n\nThe fitting line is . The intersection this line with x-axis gives the forvard turn on voltage:" ]

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[ "# Global\n\n## Location\n\n• Reference:\n• Go.dll  .NET, .NET Standard 2.0\n• Go.fx  Island\n• Namespace: go.compress.lzw\n• Platforms: .NET, .NET Standard 2.0, Island\n\n## Constants\n\nLSB\n\n``const LSB: Order = 0;``\n\n``const Order LSB = 0``\n\n``static let LSB: Order = 0``\n\n``const LSB Order = 0``\n\n``Dim LSB As Order = 0``\n\nMSB\n\n``const MSB: Order = 1;``\n\n``const Order MSB = 1``\n\n``static let MSB: Order = 1``\n\n``const MSB Order = 1``\n\n``Dim MSB As Order = 1``\n\n## Methods\n\n``class method NewReader(r: Reader; order: Order; litWidth: int): ReadCloser``\n\n``static ReadCloser NewReader(Reader r, Order order, int litWidth)``\n\n``static func NewReader(_ r: Reader, _ order: Order, _ litWidth: int) -> ReadCloser``\n\n``func NewReader(r Reader, order Order, litWidth int) ReadCloser``\n\n``Shared Function NewReader(r As Reader, order As Order, litWidth As int) As ReadCloser``\n\nParameters:\n\n• r:\n• order:\n• litWidth:\n\nNewWriter\n\n``class method NewWriter(w: Writer; order: Order; litWidth: int): WriteCloser``\n\n``static WriteCloser NewWriter(Writer w, Order order, int litWidth)``\n\n``static func NewWriter(_ w: Writer, _ order: Order, _ litWidth: int) -> WriteCloser``\n\n``func NewWriter(w Writer, order Order, litWidth int) WriteCloser``\n\n``Shared Function NewWriter(w As Writer, order As Order, litWidth As int) As WriteCloser``\n\nParameters:\n\n• w:\n• order:\n• litWidth:" ]

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[ "# Distinguish between returns to a factor and returns to scale. Use isoquants to explain constant returns to scale and diminishing returns to a factor can they exist together?\n\nReturns to a factor studies the behavior of output when more and more units of the variable factor is combined with the fixed factor. Here, scale of production remains constant but factor ratio changes. Whereas the returns to scale studies the behavior of output when the scale of output changes. Here scale changes but the factor ratio remains constant.\n\n#### Returns to a factor is a short -run concept. It has three situations namely;\n\n1. Increasing Returns to a factor : Total output tends to increase at a increasing rate when more of the variable factor is combined with the fixed factors of production.\n2. Constant Returns to a factor : It’s a situation when increasing application of the variable factor no more results in increasing marginal product of the factor, rather marginal product of the factors tends to stabilize.\n3. Diminishing Returns to a factor : Total output tends to increase at the diminishing rate when more of the variable factor is combined with the fixed factors of production. Marginal product of the variable factor must be\n\nReturns to scale is a long run concept as in the long run all factors of production are variable. The response of output to changes in the scale or size of all factors in the same proportion is termed as returns to scale. It has three situations i.e.,\n\n1. Increasing Returns to scale: It occurs when a given percentage increase in all factor inputs causes proportionately greater increase in output.\n2. Constant Returns to Scale : It occurs when a gives percentage increase in all factor inputs causes equal percentage increase in output.\n3. Diminishing Returns to Scale : It occurs when a given percentage increase in all factor inputs (in some constant ratio) cause proportionately lesser increase in output.\n\nThe main cause of the application of Returns to a factor is the variation or the change in the proportion of different factors. Whereas, Returns to scale are caused by change in the scale of production.\n\nConstant Returns to Scale : It refers to a situation in which expansion in output happens to be just proportionate to the expansion in factor inputs. Constant returns to scale means that the size of inputs and the size of the output increases in the same proportion. Doubling the input, doubles the output.\n\nDiminishing Returns to a factor : It is a situation when increasing application of the variable factor increases total output only at the\ndiminishing rate. When capital is held constant at OR and production is expanded by adding more labour, the distance between successive isoquants become increasingly greater, that is, more and more labour is required for every 100 additional units of output. This means a diminishing Marginal product of labour. The distance EF is less than FG and FG is less than GH.\n\nIt means that 100 units increase in output can be obtained by using successively greater increments of labor. Between E & F additional\n10 units of labor. Between F to G additional 100 units of output is obtained by applying 20 units of additional labor. Thus, the marginal product of labor diminishes when output is expanded along the output path RP.\n\nTags: Ba Economics", null, "Enable registration in settings - general\n• Total (0)\n0" ]

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[ "# 可加範疇\n\n（重定向自加法範疇\n\n## 可加函子\n\n$B$ $A_{1},\\ldots ,A_{n}$ ${\\mathcal {C}}$ 中的雙積，設$p_{j}$ 為相應的投影而$i_{j}$ 為相應的內射，則$F(B)$ $F(A_{1}),\\ldots ,F(A_{n})$ 的雙積，使得$F(p_{j})$ 為相應的投影而$F(i_{j})$ 為相應的內射。\n\n## 文獻\n\n• Nicolae Popescu, 1973, Abelian Categories with Applications to Rings and Modules, Academic Press, Inc.（已絕版） 該書對此主題有仔細介紹" ]

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[ "Successfully added the following line to the database.\n\n\\n\"; print \"```\\n\"; print \\$words,\"\\n\"; print \"```\"; } else { # Put the words on the matrix \\$wordcount = 0; foreach \\$w (@wordarray) { @where = (1,1,1,0); &scanboard(\\$w); if (\\$where<0) { } else { \\$goodwords[\\$wordcount] = \\$w; &putword (\\$w); \\$wordcount = \\$wordcount + 1; }; }; @wordarray = @goodwords; # sort out the word list if (\\$dosort == 1) { sortwordlist; }; # backup the matrix to the solution @solution = @searcharray; # fill the letters not used with a random number. if (\\$fillspaces == 1) { for (\\$i=0; \\$i<=\\$matrixsize; \\$i++) { if (\\$searcharray[\\$i] eq \".\") { \\$searcharray[\\$i] = \\$chars[random_uniform_integer(1,1,26)]; }; }; }; \\$title = join (\"\", \"Puzzle: \",\\$wordsearchname); &printheader; print \"```\\n\"; for (\\$y = 1; \\$y <= \\$height; \\$y++) { # print \" \"; if (\\$printlinenumbers == 1) { print \"0\" if (\\$y < 10); print \\$y,\" \"; }; for (\\$x = 1; \\$x <= \\$width; \\$x++) { print &getletter(\\$x,\\$y),\" \"; }; # print \"\"; print \"\\n\"; }; print \"```\\n\"; print \"\n\\n\"; print \"```\\n\"; \\$i = 0; foreach \\$w (@wordarray) { \\$i = \\$i + 1; print \"0\" if (\\$i<10); print \\$i,\") \",\\$w,\"\\n\"; }; print \"```\\n\"; print \"\n\\n\"; # print the solution if (\\$printsolution == 1) { @searcharray = @solution; for (\\$i=1; \\$i<51; \\$i++) { print \"\n\\n\"; }; print \"```\\n\"; for (\\$y = 1; \\$y <= \\$height; \\$y++) { if (\\$printlinenumbers == 1) { print \"0\" if (\\$y < 10); print \\$y,\" \"; }; for (\\$x = 1; \\$x <= \\$width; \\$x++) { print &getletter(\\$x,\\$y),\" \"; }; print \"\\n\"; }; print \"```\\n\"; print \"\n\\n\"; print \"```\\n\"; \\$i = 0; foreach \\$w (@wordarray) { \\$i = \\$i + 1; print \"0\" if (\\$i<10); print \\$i,\") \",\\$w,\"\\n\"; }; print \"```\\n\"; print \"" ]

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[ "Here are some scripts related to Hit/Miss Ratios .\n\n## Buffer Hit Ratio\n\nBUFFER HIT RATIO NOTES:\n\n• Consistent Gets - The number of accesses made to the block buffer to retrieve data in a consistent mode.\n• DB Blk Gets - The number of blocks accessed via single block gets (i.e. not through the consistent get mechanism).\n• Physical Reads - The cumulative number of blocks read from disk.\n\n• Logical reads are the sum of consistent gets and db block gets.\n• The db block gets statistic value is incremented when a block is read for update and when segment header blocks are accessed.\n• Hit Ratio should be > 80%, else increase DB_BLOCK_BUFFERS in init.ora\n\n```select sum(decode(NAME, 'consistent gets',VALUE, 0)) \"Consistent Gets\", sum(decode(NAME, 'db block gets',VALUE, 0)) \"DB Block Gets\", sum(decode(NAME, 'physical reads',VALUE, 0)) \"Physical Reads\", round((sum(decode(name, 'consistent gets',value, 0)) + sum(decode(name, 'db block gets',value, 0)) - sum(decode(name, 'physical reads',value, 0))) / (sum(decode(name, 'consistent gets',value, 0)) + sum(decode(name, 'db block gets',value, 0))) * 100,2) \"Hit Ratio\" from v\\$sysstat ```\n\n## Data Dict Hit Ratio\n\nDATA DICTIONARY HIT RATIO NOTES:\n\n• Gets - Total number of requests for information on the data object.\n• Cache Misses - Number of data requests resulting in cache misses\n\n• Hit Ratio should be > 90%, else increase SHARED_POOL_SIZE in init.ora\n\n```select sum(GETS), sum(GETMISSES), round((1 - (sum(GETMISSES) / sum(GETS))) * 100,2) from v\\$rowcache ```\n\n## SQL Cache Hit Ratio\n\nSQL CACHE HIT RATIO NOTES:\n\n• Pins - The number of times a pin was requested for objects of this namespace.\n• Reloads - Any pin of an object that is not the first pin performed since the object handle was created, and which requires loading the object from disk.\n\n• Hit Ratio should be > 85%\n\n```select sum(PINS) Pins, sum(RELOADS) Reloads, round((sum(PINS) - sum(RELOADS)) / sum(PINS) * 100,2) Hit_Ratio from v\\$librarycache ```\n\n## Library Cache Miss Ratio\n\nLIBRARY CACHE MISS RATIO NOTES:\n\n• Executions - The number of times a pin was requested for objects of this namespace.\n• Cache Misses - Any pin of an object that is not the first pin performed since the object handle was created, and which requires loading the object from disk.\n\n• Hit Ratio should be < 1%, else increase SHARED_POOL_SIZE in init.ora\n\n```select sum(PINS) Executions, sum(RELOADS) cache_misses, sum(RELOADS) / sum(PINS) miss_ratio from v\\$librarycache ```" ]

[ null ]

[ "# Patterns", null, "In one of the previous lessons, you learnt about the properties of objects and how they are related to maths. In this lesson, you will learn the concept called a mathematical pattern.\n\nA pattern is a constantly repeating interconnection of phenomena, actions or properties of objects.\n\nPatterns like object properties are related to maths and logic. Knowing the pattern, you can know exactly what will happen next. Friday will come after Thursday, 11 o'clock comes after 10 o’clock in the morning. The sequence of actions, phenomena, properties or events in the patterns is always defined. That is why, we know exactly what will happen next.\n\n## Types of patter\n\nThere are several types of patterns: decreasing, increasing, cyclic and complex patterns. Let's learn with each of them in details.\n\n### Increasing pattern\n\nThe pattern where the numerical property increases according to a law or a formula is called increasing.\n\nFor example, a tree grows and one new ring is added to its trunk every year. This process is called a simple increasing regularity. In this pattern, it is easy to calculate how many rings will appear in 2 years or in 10 years. The number of rings in the trunk corresponds to the age of the tree.", null, "Let's give an example of an increasing pattern that is more complicated than the one in the example with a tree. Imagine a single-celled organism that is divided into two cells every minute. The picture clearly shows that during the first minute we see 1 cell, during the second minute - already 2 cells, and then 4 cells, 8, 16. Every minute the amount increases twice. If you know the previous number, you can find out how many cells will appear within the next minute. This process is also called an increasing pattern. For true mathematicians, it will not be difficult to find out a formula for increasing the pattern for this example. This task is still difficult for you, since you have just started to study maths. The main thing is to understand what a pattern means.", null, "### Decreasing pattern\n\nThe pattern where the numerical property decreases according to a law or a formula is called decreasing.\n\nImagine a competition of eating sausages at a speed where there are two participants. Everyone has 10 sausages on a plate (it is as much as your fingers). The first one eats one sausage per minute, and the second one eats 2 sausages per minute. It is clear that the second participant will win as he eats more sausages per minute than the first one. But it is important to study the pattern. On the picture, we can see how the number of sausages decreases on each plate. This process is called a decreasing pattern. The second participant ate a plate whole of sausages in five minutes and won!", null, "### Cyclic pattern\n\nThe pattern repeating every time is called cyclic. The entire circle in a cyclic pattern is called the pattern cycle.\n\nYou know exactly the pattern of this type - this is the change of seasons. Spring-Summer-Autumn-Winter and then it repeats.\n\nLet’s consider an example with objects of different shapes. On the picture, you see a chain of different numbers of objects. Try to find the pattern in the picture below. Continue the chain.", null, "Subjects are repeated every three cells. If we know the pattern, we can assume which objects will come later. After the last link you will find a triangle, then a circle, then a square.", null, "### Complex patterns\n\nPatterns that consist of several types of patterns or have several properties are called complex.\n\nLet’s check the example of patterns on the same chain. But we will search for patterns depending on the properties of the links. Try to find the next link in the example below.", null, "#### Pattern by form", null, "We see how the chain links alternate. We know for sure that a circle will follow by shape. Let’s define it as a large circle.\n\n#### Pattern by size", null, "We see how the chain links alternate: big and then two small figures, it means, the next one will be a small figure.\n\n#### Pattern by color", null, "We got the longest pattern in the chain, select it and determine what the next color will be.\n\nAs you can see, the pattern depends on the properties of the chain elements. For the same chain, we found different patterns depending on the property. Combine the results and find out which link will be next.", null, "## Algorithm for finding patterns\n\nLet's repeat once again all the steps to reveal the patterns.\n\n1. Let’s determine the number of properties of the chain;\n2. Let’s determine the pattern for each property;\n3. Let’s compare the patterns to determine all the properties of the next link in the chain.\n\nSearch for patterns is a very good skill for a young mathematician. In the future, when you study the numbers, you will definitely need this skill. We have created a set of tests where you can practice in the search for patterns. Try to pass all the tests with a good result and move on in the study of maths.\n\n## Test to define the element in patterns with geometric figures.\n\nIt's time to try finding patterns in real time. First of all, you will see a sequence of geometric figures different in color, shape and size. Try to find the pattern for each property and to define the element hidden behind the question mark. If y...", null, "## Test to define the element in patterns with sweets.\n\nIn this test, you will need to find sweets behind a question mark. All the sweets vary in color and size. The main feature of the test is that sweets can be hidden anywhere within the sequence. You should be very attentive. The task is pretty complicat...", null, "## Math Tower of Hanoi\n\nThe Tower of Hanoi is a puzzle game invented in 19th century by the French mathematician Eduard Lucas. This guy got inspired by the legend about priests in Hindi castle. Those priests got 3 bars, one ...", null, "", null, "" ]

[ null, "https://playcoolmath.com/cdn/lessons/images/20/thumbnail/patterns.png", null, "https://playcoolmath.com/cdn/lessons/images/20/counting-tree-rings.png", null, "https://playcoolmath.com/cdn/lessons/images/20/cells.png", null, "https://playcoolmath.com/cdn/lessons/images/20/math-sausages.png", null, "https://playcoolmath.com/cdn/lessons/images/20/pattern-question.png", null, "https://playcoolmath.com/cdn/lessons/images/20/pattern-answer.png", null, "https://playcoolmath.com/cdn/lessons/images/20/hard-pattern-question.png", null, "https://playcoolmath.com/cdn/lessons/images/20/hard-pattern-answer-01.png", null, "https://playcoolmath.com/cdn/lessons/images/20/hard-pattern-answer-02.png", null, "https://playcoolmath.com/cdn/lessons/images/20/hard-pattern-answer-03.png", null, "https://playcoolmath.com/cdn/lessons/images/20/hard-pattern-answer-04.png", null, "https://playcoolmath.com/cdn/tasks/32/images/test-on-the-determination-pattern-element-pattern-with-geometric-shapes-by-shape-color-and-size-thumbnail.png", null, "https://playcoolmath.com/cdn/tasks/31/images/test-on-the-determination-pattern-element-pattern-with-sweets-by-shape-color-and-size-thumbnail.png", null, "https://playcoolmath.com/cdn/games/3/images/thumbnail/hanoi-tower-math-thumbnail.jpg", null, "https://server.cpmstar.com/action.aspx", null ]

[ "# Qlik Sense Enterprise Documents & Videos\n\nDocuments & videos about Qlik Sense.\n\n# How to Develop Qlik Sense Extensions from D3.js: Customizing the D3 with Qlik's data", null, "Not applicable\n\n## How to Develop Qlik Sense Extensions from D3.js: Customizing the D3 with Qlik's data\n\n1 - Introduction\n\n2 - Testing the D3 visualization in HTML\n\n3 - Importing the D3 visualization into Qlik Sense\n\n[4 - Customizing the D3 with Qlik's data]\n\n5 - Drawing a second indicator as a reference line [coming soon]\n\n6 - Creating Custom Settings by editing CSS from Javascript [coming soon]\n\n4 - Customizing the D3 with Qlik's Data:\n\nNow that we have our visualization working in Qlik Sense, let's inject Qlik's data in there. After increasing our max/min number of measures and creating a new object, we can add any measure we want, it could be a count, sum, average, of the selected data field. For simplicity, we can add our own number such as \"=90\" as a measure. We'll start by checking out the measure we just added in the hypercube in layout:", null, "Inside layout, we have our extension's qHypercube, that includes the selected data input to the extension, the dimension and measures' labels as well as metadata. The data is divided in data pages. In this extension, we're using only one data page, the initial data page we pulled near the top of our code, Inside each data page in qDataPages is a qMatrix and some metadata about it, such as the number of rows and columns included in this data page. Inside our qMatrix is all the individual rows in the data page. Inside each row, is all the column values for this row. And finally, inside each of these column values is a qNum, a numeric version of the value, and a qText, a textual version of the value. Note that the column values are not defined as a dimension or a measure, it is up to us to use the qText for dimensions and qNums for measures. If we would use the qText of a measure, we would be retrieving the formatted version of the value (for instance 2 decimal places) while the qNum value itself could include many more.\n\nSo, we'll start by defining the path to our qMatrix and the data itself (one measure in this case) in variables, so we'll be adding this code snippet to the end of our paint function:\n\n```         var qMatrix = layout.qHyperCube.qDataPages.qMatrix;\n\nvar data = qMatrix.map(function(d) {\nreturn {\n\"Metric1\":d.qNum\n}\n});\n\n```\n\nNow that we have our data ready, let's prepare our extension to receive our data. We'll start by adding more parameters to our function to get access to the data, layout, and the width/height of the object. We'll create a kpi variable that maps to our measure's data in the data variable. Width and height are currently hardcoded in pixels in the first block of code so we'll use the width/height parameters we just added to make the size of the visualization dynamic.\n\n```var vizwithoutref = function(data,layout,width,height,id) {\n\nvar kpi = data.map(function(d){return d.Metric1;});\n\nvar svg = d3.select(\"#\" + id)\n.append(\"svg\")\n.attr(\"width\", width)\n.attr(\"height\", height);\n\nvar gauge = iopctrl.arcslider()\n.radius(120)\n.events(false)\n.indicator(iopctrl.defaultGaugeIndicator);\ngauge.axis().orient(\"in\")\n.normalize(true)\n.ticks(12)\n.tickSubdivide(3)\n.tickSize(10, 8, 10)\n.tickPadding(5)\n.scale(d3.scale.linear()\n.domain([0, 160])\n.range([-3*Math.PI/4, 3*Math.PI/4]));\n\nvar segDisplay = iopctrl.segdisplay()\n.width(80)\n.digitCount(6)\n.negative(false)\n.decimals(0);\n\nsvg.append(\"g\")\n.attr(\"class\", \"segdisplay\")\n.attr(\"transform\", \"translate(130, 200)\")\n.call(segDisplay);\n\nsvg.append(\"g\")\n.attr(\"class\", \"gauge\")\n.call(gauge);\nsegDisplay.value(kpi);\ngauge.value(kpi);\n}\n\n```\n\nDon't forget to actually give the function these parameters by adding them in the function call:\n\n```     vizwithoutref(data,layout,width,height,id);\n\n```\n\nNow we can go to Qlik Sense, open DevTools, and refresh the page using F5, change our measure to \"=30\", and watch our speedometer change from 90 (that we set earlier) to 30.\n\nIn order to size the gauge itself correctly however, we could either create a formula that dynamically sizes it based on the width and height, or create a sizing map where we size it a certain way if it's between a certain set of heights and a certain set of widths. In our example, we'll be using a sizing map to keep things clean. If we had gone the formula route, we'd have a hard time finding a formula that fits all kinds of width/height combinations. Since the gauge is circular, we'll be checking if the width or height is shorter and draw the circle's radius using that factor. Once we're done drawing out our sizing map, we can add its variables in the place of hardcoded variables, such as the gauge's radius, gauge's tickPadding, the segDisplay's width, and both the segDisplay and the gauge's tranform statement that tells the D3 library where to paint them in our visualization. Here is our resizable function with the sizing map and the changes in the D3 code:\n\n```var vizwithoutref = function(data,layout,width,height,id) {\n\nvar kpi = data.map(function(d){return d.Metric1;});\n\nvar widthOrHeight = (width<=height)? width: height;\n\n//Resizing Map Declarations\nvar fontPercentage = \"60%\";\nvar tickPadding = widthOrHeight/200;\nvar gaugeWidthTransform = -30;\nvar gaugeHeightTransform = -30;\nvar displayWidthTransform = ((widthOrHeight/2)*0.8);\nvar displayHeightTransform = ((widthOrHeight/2)*0.8);\n\n//Resizing Map\nif(widthOrHeight<=151){\nfontPercentage = \"40%\";\ntickPadding = 1;\ngaugeWidthTransform = -37;\ngaugeHeightTransform = -35;\ndisplayWidthTransform = ((widthOrHeight/2)*0.825);\ndisplayHeightTransform = ((widthOrHeight/2)*1.45);\n}\nelse if(widthOrHeight>151 && widthOrHeight<=213){\nfontPercentage = \"50%\";\ntickPadding = 2;\ngaugeWidthTransform = -32;\ngaugeHeightTransform = -25;\ndisplayWidthTransform = ((widthOrHeight/2)*0.775);\ndisplayHeightTransform = ((widthOrHeight/2)*1.45);\n}\nelse if(widthOrHeight>213 && widthOrHeight<=276){\nfontPercentage = \"60%\";\ntickPadding = 3;\ngaugeWidthTransform = -27;\ngaugeHeightTransform = -20;\ndisplayWidthTransform = ((widthOrHeight/2)*0.775);\ndisplayHeightTransform = ((widthOrHeight/2)*1.375);\n}\nelse if(widthOrHeight>276 && widthOrHeight<=338){\nfontPercentage = \"70%\";\ntickPadding = 4;\ngaugeWidthTransform = -20;\ngaugeHeightTransform = -9;\ndisplayWidthTransform = ((widthOrHeight/2)*0.8);\ndisplayHeightTransform = ((widthOrHeight/2)*1.375);\n}\nelse if(widthOrHeight>338 && widthOrHeight<=422){\nfontPercentage = \"80%\";\ntickPadding = 4;\ngaugeWidthTransform = -10;\ngaugeHeightTransform = 0;\ndisplayWidthTransform = ((widthOrHeight/2)*0.825);\ndisplayHeightTransform = ((widthOrHeight/2)*1.4);\n}\nelse if(widthOrHeight>422 && widthOrHeight<=504){\nfontPercentage = \"90%\";\ntickPadding = 4;\ngaugeWidthTransform = 0;\ngaugeHeightTransform = 10;\ndisplayWidthTransform = ((widthOrHeight/2)*0.825);\ndisplayHeightTransform = ((widthOrHeight/2)*1.425);\n}\nelse if(widthOrHeight>504){\nfontPercentage = \"100%\";\ntickPadding = 4;\ngaugeWidthTransform = 20;\ngaugeHeightTransform = 20;\ndisplayWidthTransform = ((widthOrHeight/2)*0.825);\ndisplayHeightTransform = ((widthOrHeight/2)*1.4);\n}\n\nvar svg = d3.select(\"#\" + id)\n.append(\"svg\")\n.attr(\"width\", width)\n.attr(\"height\", height);\n\nvar gauge = iopctrl.arcslider()\n.radius((widthOrHeight/2)*0.8)\n.events(false)\n.indicator(iopctrl.defaultGaugeIndicator);\ngauge.axis().orient(\"in\")\n.normalize(true)\n.ticks(12)\n.tickSubdivide(3)\n.tickSize(10, 8, 10)\n.tickPadding(tickPadding)\n.scale(d3.scale.linear()\n.domain([0, 160])\n.range([-3*Math.PI/4, 3*Math.PI/4]));\n\nvar segDisplay = iopctrl.segdisplay()\n.width((widthOrHeight)/5)\n.digitCount(6)\n.negative(false)\n.decimals(0);\n\n//Preparing transform statements\nvar transform = \"translate(\";\nvar gaugePlacement = transform.concat(gaugeWidthTransform, \",\",gaugeHeightTransform,\")\");\nvar displayPlacement = transform.concat(displayWidthTransform, \",\",displayHeightTransform,\")\");\n\n//Applying CSS properties and transform statements\nsvg.append(\"g\")\n.attr(\"class\", \"gauge\")\n.attr(\"transform\", gaugePlacement)\n.call(gauge);\n\nsvg.append(\"g\")\n.attr(\"class\", \"segdisplay\")\n.attr(\"transform\", displayPlacement)\n.call(segDisplay);\n\nsegDisplay.value(kpi);\ngauge.value(kpi);\n}\n\n```\n\nNow that we've identified the variables in the D3 code that affect the resizing of the visualization, and changed them from being hardcoded to a dynamic variable that we can control, we can go to our app to test the resizing:", null, "In the next section, we’ll be modifying the D3 code to add another gauge indicator for a reference line, as well as edit the CSS file for styling our visualization.\n\nComments\nNew Contributor II\n\nHello!\n\nI have been following along with this tutorial up until the point of the qmatrix and have hit a wall. I copied into my java script everything you have up through changing the call script to vizwithoutref(data,layout,width,height,id);\n\nWhen I open the visualization in Qlik Sense, I am not given an option to edit the measure =\"30\" (You can see that the measures section is grayed out. I am also attaching my java script file. Please let me know what I am doing wrong. I think it has to do with the calling of my qmatrix variable placement.", null, "The link to my .js file:\n\nhttps://www.dropbox.com/home?preview=speedometerd3twoindicators.js", null, "Not applicable\n\nHi Nicole,\n\nThanks for following along. Unfortunately, I can't seem to download the file you linked on dropbox, possibly because you moved the file later? If you can send another link to the file, I can certainly check it out.\n\nOne of the things you should check is the initialproperties near the top of the javascript file. If the properties of max measures and min measures are set to 0, that would be the problem:", null, "New Contributor II\n\nThank you Fady. This actually solved the missing measure piece. My next question is where I need to put the hypercube code in my .js script. This code:\n\nvar qMatrix = layout.qHyperCube.qDataPages.qMatrix;\n\nvar data = qMatrix.map(function(d) {\n\nreturn\n\n\"Metric1\":d.qNum\n\n}\n\n});", null, "Not applicable\n\nI'm glad that helped, Nicole.\n\nYou would put this code snippet in the paint function before you call the visualization function:", null, "Contributor\n\nHow do I find this layout-viewer that you're referring to?\n\n*Never mind, I found it under Console in the developer tools!\n\nNew Contributor III\n\nVery helpful and neatly put post, eagerly waiting for next sections.\n\nThanks\n\nRaja\n\nValued Contributor\n\nHi,\n\nI have changed the max measures to 1 but still the \"add measure\" is greyed out. Have I done anything wrong? I am doing this in Sense June 2017 desktop.\n\nThank you very much!\n\nFei\n\n//Declaring all files we'll be using\ndefine([\"jquery\",\n\"text!./speedometerd3twoindicators.css\",\n\"text!./googleplay.css\",\n\"./d3.min\",\n\"./iopctrl\",\n\"./pointergestures\",\n\"./pointerevents\"\n],\nfunction(\\$, cssContent) {\n\n'use strict';\n\\$(\"<style>\").html(cssContent).appendTo(\"head\");\n\nreturn {\ninitialProperties : {\nqHyperCubeDef : {\nqDimensions : [],\nqMeasures : [],\nqInitialDataFetch : [{\nqWidth : 10,\nqHeight : 1000\n}]\n}\n},\n//definition is the function that gets called only when\n//the extension is created. If you resize or update the\n//variables or selections, it doesn't get called again.\ndefinition : {\ntype : \"items\",\ncomponent : \"accordion\",\nitems : {\ndimensions : {\nuses : \"dimensions\",\nmin : 0,\nmax : 0\n},\nmeasures : {\nuses : \"measures\",\nmin : 0,\nmax : 1\n},\nsorting : {\nuses : \"sorting\"\n},\n//Custom Settings\nsettings : {\nuses : \"settings\",\nitems : {\n}\n}\n}\n},\n\nsnapshot : {\ncanTakeSnapshot : true\n},\n\n//paint is the function that gets called every time the\n//variables or selection changes, or if you resize the window.\npaint : function(\\$element,layout) {\n//element is what holds the chart's width and length\n//layout is what holds Qlik's dimensions and measures as well as\n//the custom settings selected\n\n//Pushing element and layout to the console for\n//reference-finding and debugging\nconsole.log(\\$element);\nconsole.log(layout);\n\nvar width = \\$element.width();\nvar height = \\$element.height();\n//From element, we'll extract our chart's ID\nvar id = \"container_\" + layout.qInfo.qId;\n//Check if the chart has already been created\nif (document.getElementById(id)) {\n//If it has, empty it so we can repaint our visualization\n\\$(\"#\" + id).empty();\n}\nelse {\n//If it hasn't, create it with our id, width, and height\n\\$element.append(\\$('<div />;').attr(\"id\", id).width(width).height(height));\n}\n\nvar qMatrix = layout.qHyperCube.qDataPages.qMatrix;\n\nvar data = qMatrix.map(function(d) {\nreturn {\n\"Metric1\":d.qNum\n}\n});\n\nvizwithoutref(data,layout,width,height,id);\n}\n};\n});\n\nvar vizwithoutref = function(data,layout,width,height,id) {\n\nvar kpi = data.map(function(d){return d.Metric1;});\n\nvar svg = d3.select(\"#\" + id)\n.append(\"svg\")\n.attr(\"width\", width)\n.attr(\"height\", height);\n\nvar gauge = iopctrl.arcslider()\n.radius(120)\n.events(false)\n.indicator(iopctrl.defaultGaugeIndicator);\ngauge.axis().orient(\"in\")\n.normalize(true)\n.ticks(12)\n.tickSubdivide(3)\n.tickSize(10, 8, 10)\n.tickPadding(5)\n.scale(d3.scale.linear()\n.domain([0, 160])\n.range([-3*Math.PI/4, 3*Math.PI/4]));\n\nvar segDisplay = iopctrl.segdisplay()\n.width(80)\n.digitCount(6)\n.negative(false)\n.decimals(0);\n\nsvg.append(\"g\")\n.attr(\"class\", \"segdisplay\")\n.attr(\"transform\", \"translate(130, 200)\")\n.call(segDisplay);\n\nsvg.append(\"g\")\n.attr(\"class\", \"gauge\")\n.call(gauge);\nsegDisplay.value(kpi);\ngauge.value(kpi);\n\nNew Contributor III\n\nHi,\n\nHope you had refreshed the Qlikense app after the JS Script change, you can cross check the changes using Console.-> Sources.", null, "Thanks\n\nRaja", null, "Luminary\n\nYou have to go out of the app and in again. The dimension/measure  info only gets loaded when you open the app.\n\nNew Contributor III\n\nNo not required, simple refresh (F5) will do, if Disable Cache is checked as shown.\n\nShow dev tools -> Settings ->  Disable cache (while DevTools is open)", null, "Thanks\n\nRaja\n\nVersion history\nRevision #:\n1 of 1\nLast update:\n‎06-13-2016 02:04 PM\nUpdated by:" ]

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[ "base-4.6.0.0: Basic libraries\n\nData.Complex\n\nContents\n\nDescription\n\nComplex numbers.\n\nSynopsis\n\n# Rectangular form\n\ndata Complex a Source\n\nComplex numbers are an algebraic type.\n\nFor a complex number `z`, `abs z` is a number with the magnitude of `z`, but oriented in the positive real direction, whereas `signum z` has the phase of `z`, but unit magnitude.\n\nConstructors\n\n !a :+ !a forms a complex number from its real and imaginary rectangular components.\n\nInstances\n\n Typeable1 Complex Eq a => Eq (Complex a) (Fractional (Complex a), RealFloat a) => Floating (Complex a) (Num (Complex a), RealFloat a) => Fractional (Complex a) (Typeable (Complex a), Data a) => Data (Complex a) RealFloat a => Num (Complex a) Read a => Read (Complex a) Show a => Show (Complex a)\n\nrealPart :: RealFloat a => Complex a -> aSource\n\nExtracts the real part of a complex number.\n\nimagPart :: RealFloat a => Complex a -> aSource\n\nExtracts the imaginary part of a complex number.\n\n# Polar form\n\nmkPolar :: RealFloat a => a -> a -> Complex aSource\n\nForm a complex number from polar components of magnitude and phase.\n\ncis :: RealFloat a => a -> Complex aSource\n\n`cis t` is a complex value with magnitude `1` and phase `t` (modulo `2*pi`).\n\npolar :: RealFloat a => Complex a -> (a, a)Source\n\nThe function `polar` takes a complex number and returns a (magnitude, phase) pair in canonical form: the magnitude is nonnegative, and the phase in the range `(-pi, pi]`; if the magnitude is zero, then so is the phase.\n\nmagnitude :: RealFloat a => Complex a -> aSource\n\nThe nonnegative magnitude of a complex number.\n\nphase :: RealFloat a => Complex a -> aSource\n\nThe phase of a complex number, in the range `(-pi, pi]`. If the magnitude is zero, then so is the phase.\n\n# Conjugate\n\nconjugate :: RealFloat a => Complex a -> Complex aSource\n\nThe conjugate of a complex number." ]

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[ "# #00e517 Color Information\n\nIn a RGB color space, hex #00e517 is composed of 0% red, 89.8% green and 9% blue. Whereas in a CMYK color space, it is composed of 100% cyan, 0% magenta, 90% yellow and 10.2% black. It has a hue angle of 126 degrees, a saturation of 100% and a lightness of 44.9%. #00e517 color hex could be obtained by blending #00ff2e with #00cb00. Closest websafe color is: #00cc00.\n\n• R 0\n• G 90\n• B 9\nRGB color chart\n• C 100\n• M 0\n• Y 90\n• K 10\nCMYK color chart\n\n#00e517 color description : Pure (or mostly pure) lime green.\n\n# #00e517 Color Conversion\n\nThe hexadecimal color #00e517 has RGB values of R:0, G:229, B:23 and CMYK values of C:1, M:0, Y:0.9, K:0.1. Its decimal value is 58647.\n\nHex triplet RGB Decimal 00e517 `#00e517` 0, 229, 23 `rgb(0,229,23)` 0, 89.8, 9 `rgb(0%,89.8%,9%)` 100, 0, 90, 10 126°, 100, 44.9 `hsl(126,100%,44.9%)` 126°, 100, 89.8 00cc00 `#00cc00`\nCIE-LAB 79.669, -78.993, 74.252 28.172, 56.097, 10.154 0.298, 0.594, 56.097 79.669, 108.412, 136.772 79.669, -75.235, 95.884 74.898, -63.93, 44.391 00000000, 11100101, 00010111\n\n# Color Schemes with #00e517\n\n• #00e517\n``#00e517` `rgb(0,229,23)``\n• #e500ce\n``#e500ce` `rgb(229,0,206)``\nComplementary Color\n• #5ce500\n``#5ce500` `rgb(92,229,0)``\n• #00e517\n``#00e517` `rgb(0,229,23)``\n• #00e58a\n``#00e58a` `rgb(0,229,138)``\nAnalogous Color\n• #e5005c\n``#e5005c` `rgb(229,0,92)``\n• #00e517\n``#00e517` `rgb(0,229,23)``\n• #8a00e5\n``#8a00e5` `rgb(138,0,229)``\nSplit Complementary Color\n• #e51700\n``#e51700` `rgb(229,23,0)``\n• #00e517\n``#00e517` `rgb(0,229,23)``\n• #1700e5\n``#1700e5` `rgb(23,0,229)``\nTriadic Color\n• #cee500\n``#cee500` `rgb(206,229,0)``\n• #00e517\n``#00e517` `rgb(0,229,23)``\n• #1700e5\n``#1700e5` `rgb(23,0,229)``\n• #e500ce\n``#e500ce` `rgb(229,0,206)``\nTetradic Color\n• #00990f\n``#00990f` `rgb(0,153,15)``\n• #00b212\n``#00b212` `rgb(0,178,18)``\n• #00cc14\n``#00cc14` `rgb(0,204,20)``\n• #00e517\n``#00e517` `rgb(0,229,23)``\n• #00ff1a\n``#00ff1a` `rgb(0,255,26)``\n• #19ff30\n``#19ff30` `rgb(25,255,48)``\n• #33ff47\n``#33ff47` `rgb(51,255,71)``\nMonochromatic Color\n\n# Alternatives to #00e517\n\nBelow, you can see some colors close to #00e517. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #22e500\n``#22e500` `rgb(34,229,0)``\n• #0fe500\n``#0fe500` `rgb(15,229,0)``\n• #00e504\n``#00e504` `rgb(0,229,4)``\n• #00e517\n``#00e517` `rgb(0,229,23)``\n• #00e52a\n``#00e52a` `rgb(0,229,42)``\n• #00e53d\n``#00e53d` `rgb(0,229,61)``\n• #00e550\n``#00e550` `rgb(0,229,80)``\nSimilar Colors\n\n# #00e517 Preview\n\nText with hexadecimal color #00e517\n\nThis text has a font color of #00e517.\n\n``<span style=\"color:#00e517;\">Text here</span>``\n#00e517 background color\n\nThis paragraph has a background color of #00e517.\n\n``<p style=\"background-color:#00e517;\">Content here</p>``\n#00e517 border color\n\nThis element has a border color of #00e517.\n\n``<div style=\"border:1px solid #00e517;\">Content here</div>``\nCSS codes\n``.text {color:#00e517;}``\n``.background {background-color:#00e517;}``\n``.border {border:1px solid #00e517;}``\n\n# Shades and Tints of #00e517\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, #000d01 is the darkest color, while #f9fff9 is the lightest one.\n\n• #000d01\n``#000d01` `rgb(0,13,1)``\n• #002103\n``#002103` `rgb(0,33,3)``\n• #003405\n``#003405` `rgb(0,52,5)``\n• #004807\n``#004807` `rgb(0,72,7)``\n• #005c09\n``#005c09` `rgb(0,92,9)``\n• #006f0b\n``#006f0b` `rgb(0,111,11)``\n• #00830d\n``#00830d` `rgb(0,131,13)``\n• #00970f\n``#00970f` `rgb(0,151,15)``\n• #00aa11\n``#00aa11` `rgb(0,170,17)``\n• #00be13\n``#00be13` `rgb(0,190,19)``\n• #00d115\n``#00d115` `rgb(0,209,21)``\n• #00e517\n``#00e517` `rgb(0,229,23)``\n• #00f919\n``#00f919` `rgb(0,249,25)``\nShade Color Variation\n• #0dff26\n``#0dff26` `rgb(13,255,38)``\n• #21ff37\n``#21ff37` `rgb(33,255,55)``\n• #34ff49\n``#34ff49` `rgb(52,255,73)``\n• #48ff5a\n``#48ff5a` `rgb(72,255,90)``\n• #5cff6c\n``#5cff6c` `rgb(92,255,108)``\n• #6fff7e\n``#6fff7e` `rgb(111,255,126)``\n• #83ff8f\n``#83ff8f` `rgb(131,255,143)``\n• #97ffa1\n``#97ffa1` `rgb(151,255,161)``\n• #aaffb3\n``#aaffb3` `rgb(170,255,179)``\n• #beffc4\n``#beffc4` `rgb(190,255,196)``\n• #d1ffd6\n``#d1ffd6` `rgb(209,255,214)``\n• #e5ffe8\n``#e5ffe8` `rgb(229,255,232)``\n• #f9fff9\n``#f9fff9` `rgb(249,255,249)``\nTint Color Variation\n\n# Tones of #00e517\n\nA tone is produced by adding gray to any pure hue. In this case, #6a7b6b is the less saturated color, while #00e517 is the most saturated one.\n\n• #6a7b6b\n``#6a7b6b` `rgb(106,123,107)``\n• #618464\n``#618464` `rgb(97,132,100)``\n• #588d5d\n``#588d5d` `rgb(88,141,93)``\n• #4f9656\n``#4f9656` `rgb(79,150,86)``\n• #469f4f\n``#469f4f` `rgb(70,159,79)``\n• #3ea748\n``#3ea748` `rgb(62,167,72)``\n• #35b041\n``#35b041` `rgb(53,176,65)``\n• #2cb93a\n``#2cb93a` `rgb(44,185,58)``\n• #23c233\n``#23c233` `rgb(35,194,51)``\n• #1acb2c\n``#1acb2c` `rgb(26,203,44)``\n• #12d325\n``#12d325` `rgb(18,211,37)``\n• #09dc1e\n``#09dc1e` `rgb(9,220,30)``\n• #00e517\n``#00e517` `rgb(0,229,23)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #00e517 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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[ "# Cross-hemisphere comparison¶\n\nThis example illustrates how to visualize the difference between activity in the left and the right hemisphere. The data from the right hemisphere is mapped to the left hemisphere, and then the difference is plotted. For more information see mne.compute_source_morph().", null, "Out:\n\nUsing control points [ 3.70314401 4.48867635 13.29875944]\n\n\n# Author: Christian Brodbeck <[email protected]>\n#\n\nimport mne\n\ndata_dir = mne.datasets.sample.data_path()\nsubjects_dir = data_dir + '/subjects'\nstc_path = data_dir + '/MEG/sample/sample_audvis-meg-eeg'\n\n# First, morph the data to fsaverage_sym, for which we have left_right\n# registrations:\nstc = mne.compute_source_morph(stc, 'sample', 'fsaverage_sym', smooth=5,\nwarn=False,\nsubjects_dir=subjects_dir).apply(stc)\n\n# Compute a morph-matrix mapping the right to the left hemisphere,\n# and vice-versa.\nmorph = mne.compute_source_morph(stc, 'fsaverage_sym', 'fsaverage_sym',\nspacing=stc.vertices, warn=False,\nsubjects_dir=subjects_dir, xhemi=True,\nverbose='error') # creating morph map\nstc_xhemi = morph.apply(stc)\n\n# Now we can subtract them and plot the result:\ndiff = stc - stc_xhemi\n\ndiff.plot(hemi='lh', subjects_dir=subjects_dir, initial_time=0.07,\nsize=(800, 600))\n\n\nTotal running time of the script: ( 0 minutes 24.842 seconds)\n\nEstimated memory usage: 22 MB\n\nGallery generated by Sphinx-Gallery" ]

[ null, "https://mne.tools/stable/_images/sphx_glr_plot_xhemi_001.png", null ]

[ "Aviator on the BBC Micro\n\n# The Theme: GetAlienWeakSpot\n\n``` Name: GetAlienWeakSpot [Show more]\nType: Subroutine\nCategory: The Theme\nSummary: Calculate the coordinates of an alien's weak spot\nDeep dive: Detecting alien hits\nContext: See this subroutine in context in the source code\nReferences: This subroutine is called as follows:\n* CheckIfAlienIsHit (Part 2 of 2) calls GetAlienWeakSpot\n\nThe alien's weak spot is calculated as follows:\n\n* x-coordinate = (xObjectHi xObjectLo) + (5 Q)\n\n* y-coordinate = (yObjectHi yObjectLo)\n\n* z-coordinate = (zObjectHi zObjectLo) + (5 Q)\n\nwhere Q is\n\nThis is called STIP in the original source code.\n\nArguments:\n\nY The object ID of the alien (30 to 33)\n\nQ The low byte of the amount to add\n\nReturns:\n\n(I+2 W+2) The x-coordinate of the alien's weak spot\n\n(I+1 W+1) The y-coordinate of the alien's weak spot\n\n(I W) The z-coordinate of the alien's weak spot\n\n.GetAlienWeakSpot\n\nLDX #2 \\ Set a counter in X to iterate through 2, 1, 0, which\n\\ has the following effect:\n\\\n\\ When X = 2:\n\\\n\\ * (I+2 W+2) = (xObjectHi xObjectLo) + (5 Q)\n\\\n\\ When X = 1:\n\\\n\\ * (I+1 W+1) = (yObjectHi yObjectLo)\n\\\n\\ When X = 0:\n\\\n\\ * (I W) = (zObjectHi zObjectLo) + (5 Q)\n\\\n\\ note that\n\n.weak1\n\nLDA xObjectLo,Y \\ Set (I+X W+X) = (xObjectHi xObjectLo) + (5 Q)\nCLC \\\nADC Q \\ starting with the low bytes\nSTA W,X\n\nLDA xObjectHi,Y \\ And then the high bytes\nSTA I,X\n\n.weak2\n\nTYA \\ Point Y to the next axis (xObject, yObject, zObject)\nCLC\nTAY\n\nDEX \\ Decrement the loop counter\n\nBPL weak3 \\ If we haven't yet done all three calculations, jump\n\\ to weak3\n\nRTS \\ Return from the subroutine\n\n.weak3\n\nBEQ weak1 \\ If X = 0, jump up to weak1 to add (5 Q)\n\nLDA xObjectLo,Y \\ If we get here then X = 1, so do the calculation\nSTA W,X \\ without adding (5 Q)\nLDA xObjectHi,Y\nSTA I,X\n\nJMP weak2 \\ Jump back to weak2 to move on to X = 0\n```" ]

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[ "Volume 13 Supplement 13\n\nBM-BC: a Bayesian method of base calling for Solexa sequence data\n\nAbstract\n\nBase calling is a critical step in the Solexa next-generation sequencing procedure. It compares the position-specific intensity measurements that reflect the signal strength of four possible bases (A, C, G, T) at each genomic position, and outputs estimates of the true sequences for short reads of DNA or RNA. We present a Bayesian method of base calling, BM-BC, for Solexa-GA sequencing data. The Bayesian method builds on a hierarchical model that accounts for three sources of noise in the data, which are known to affect the accuracy of the base calls: fading, phasing, and cross-talk between channels. We show that the new method improves the precision of base calling compared with currently leading methods. Furthermore, the proposed method provides a probability score that measures the confidence of each base call. This probability score can be used to estimate the false discovery rate of the base calling or to rank the precision of the estimated DNA sequences, which in turn can be useful for downstream analysis such as sequence alignment.\n\nIntroduction\n\nNext generation sequencing (NGS) such as Solexa sequencing (http://www.illumina.com) is a powerful tool producing massive sequences of short reads. It is considered the “digital” version of the classic microarray technology because in principle it measures the exact number of gene copies rather than relative abundances. NGS can be used for studies of sequence variations in genomes ([1, 2]), protein-DNA interactions ([3, 4]), transcriptome analysis (), and de novo genome assembly . The full potential of the technology is still being explored as quantitative researchers try to find efficient ways to streamline the sample processing and model the processed data.\n\nMany challenges remain in processing NGS data. We consider one of the important problems, namely base calling. Base calling refers to the estimation of the true sequences of DNA or RNA based on the intensity scores measuring the signal strength of four nucleotides, A, C, G, and T. One of the most popular NGS technology is the Solexa/Illumina sequencing, in which intensity data from a standard run consist of millions of intensity measurements for the four bases of short reads spanning across the genome. For each short read, the measurements of their intensities are stored in an I × 4 matrix, where I is the length of the read (e.g., I = 36). Such a matrix corresponds to a colony. The positions i = 1, ..., I in the short read are sequenced in cycles. As a result, each row of the colony matrix contains measurements from a cycle in the experiment in which the sequence of a single base is synthesized. At each cycle, all four nucleotides (A, C, G, and T) labeled with four different fluorescent dyes are probed, thus producing a quadruple vector of fluorescent intensity scores. Figure 1 plots the A intensities versus the C intensities (top left panel) and the G intensities versus the T intensities (top right panel) for 1,000 arbitrarily chosen colonies. The four colors used in the bottom two panels represent the estimated base calls from the proposed BM-BC method. Figure 1 exhibits two main features. First, the A and C intensities are highly correlated as are the G and T intensities, which is known as the “cross talk” between channels . Second, when the A or C intensity is large, both the G and T intensities are small; similarly, when G or T is large, both A and C are small.\n\nIn summary, the final data are millions of quadruple vectors. Each vector contains four continuous scores that represent the fluorescent intensities of nucleotides A, C, G, and T. Using these data, our task is to estimate the sequence of each short read.\n\nWe acknowledge that the proposed method in this paper deals with the data from Solexa genome analyzer. New sequencing technologies have been developed by Solexa/Illumina, such as the HiSeq series. However, numerous data sets have already been generated using the genome analyzer, which need to be properly analyzed. We believe that our proposed base-calling approach will contribute to the analysis of the existing data and also future data from experiments that still use the genome analyzer for sequencing. To our knowledge, a few methods for base calling are available in the literature. Most researchers use the default procedure, Bustard, built into the commercial software of the Illumina Genome Analyzer. The procedure yields an estimated base for each cycle along with a quality score called fast-q. The fast-q score measures the most likely base intensity relative to the three other intensities on a logarithmic scale from –5 to 40. In practice, DNA tags with small fast-q scores are discarded in Solexa base calling. A more recent statistical method of base calling is by , who considered a variety of issues in the sequencing data including the base calling. Other works include [11, 12]. A recent addition to this group of methods is Ibis (Improved Base Calling for Genome Sequence Analyzer) . Ibis applies multiclass Support Vector Machines to raw cluster intensities. The model is trained from data obtained from a reference genome.\n\nIn this paper, we propose a model-based Bayesian method of base-calling (BM-BC) for Solexa sequencing data. The BM-BC method presents a hierarchical model that applies a probabilistic-based inference for base calling. The estimation of model parameters is computed via Markov chain Monte Carlo (MCMC) simulations and the posterior samples are used to compute the probability that each base is A, C, G, or T. These posterior probabilities are used to estimate the true DNA sequences, to rank the base calls, and to compute the false discovery rates (FDR). The remainder of this paper is organized as follows: The Methodology section presents a probability model for base calling, and the posterior inference procedure. The section on Numerical examples presents the base-calling results for a Solexa sequencing data set using the BM-BC method and three other methods as comparison. The Discussion sections ends the paper.\n\nMethodology\n\nTo start, we introduce the three known sources of noise in the Solexa data that motivated the proposed probability models. The first type of noise is called fading (see e.g., ), which refers to a decay in the intensity as a function of cycle number. That is, for a colony, as the cycle number increases, the intensity measurement decreases. This is usually caused by material loss during the sequencing process. The second source is phasing, a well-known source of noise in Solexa sequencers that use cyclic reversible termination (CRT) ([14, 15]). Basically, errors in the CRT cause stochastic failures in base-binding that is supposed to incorporate only one nucleotide per cycle. Instead, the errors may lead to incorporation of none or more than one nucleotide in one cycle, thus increasing the noise in the signal output for down-stream cycles. As a result, the precision of base calling drops as the cycle number increases (see Figure 2). The third important source of noise is a fluorophore cross talk between channels A and C, and channels G and T. The cross talk induces high correlations between A intensities and C intensities, and between G intensities and T intensities (see Figure 1). There are many factors that contribute to cross-talk between channels, one of them being an overlap in the wavelengths of the dye schemes used to mark different nucleotides.\n\nOther important systematic biases also affect the accuracy of base calling. For a discussion, see [14, 15]. However, these biases can be removed or reduced using standard statistical techniques. We assume that these biases have been removed and now the goal is to model the intensity scores.\n\nHierarchical models\n\nWe first consider models for sequence data of a single colony, i.e., measurements corresponding to a short read, with say I = 36 bases. Let y = {y1, , y36} represent the 36 quadruplets of nucleotide intensity measurements, where y i = (y i 1, y i 2, y i 3, y i 4)′ is the 4 × 1 vector for cycle i, respectively representing the intensities of four nucleotides, A, C, G, and T at location i of the short reads. Therefore, strong signals are indicated by large positive values of y ij . Because for each cycle only one true nucleotide is present, ideally only one of the four y ij ’s should be positive and the remaining three should be zero. In the presence of noise, this is not the case. First, due to channel cross-talk, y i 1 and y i 2 are positively correlated, as are y i 3 and y i 4. Second, because of fading, the intensities decay over cycles; that is, for later cycles, the values of y i ’s are smaller on average. Last, when phasing is present, the intensity scores at cycle i depend on the ones at cycle (i – 1).\n\nLet k i {1, 2, 3,4} indicates the true base of cycle i, where {1, 2, 3, 4} correspond to {A, C, G, T}. The main feature of the sampling model for y i is given by an auto-regression consisting of a mixture of four multivariate normal distributions, with each normal distribution describing the case when the true base is one of {A, C, G, T}. Specifically, letting MVN4(µ, Σ) denote a 4-dimensional normal with mean vector µ and covariance matrix Σ, we assume that for i = 2, …, 36,", null, "(1)\n\nand", null, "(2)\n\nwhere I j ’s are four indicator functions Ind(·) that truncate the multivariate normal. Here,", null, ". These indicators reflect the prior belief that the true base should have the largest intensity. Models (2) and (2) attempt to account for three sources of noise in the data. Specifically, due to fading, the intensity signals weaken as the cycle indicator i gets larger. Therefore, we include the exponential factor exp(–β · iλ) to describe the decay of the mean signal. Note that we specify an exponent λ to allow for more flexibility. For the phasing, we add a term α · y i –1, j to the mean of the multivariate normal (thus autoregressive), i.e., the intensity of the current cycle i depends on the intensity of the previous cycle (i – 1) for i ≥ 2.\n\nThe cross talk is accounted for by constructing appropriate priors for μ j ’s, as described next. We assume that the mean intensities when the true base is A, C, G, or T are given by", null, "When the true base is A (i.e., j = 1), the intensities at channels A and C are modeled by µ11 and µ12 while the intensities at channels T and G will be close to zero, parametrized as ε11 and ε12. In addition, the mean intensity µ11 at channel A should be larger than µ12 at channel C. Therefore, the prior for µ1 is given by", null, "(3)\n\nWe use a log N(0,1) prior for µ11. Here, g1 accounts for the cross talk from channel C to channel A. We assign a beta(1, 1) as its prior. For g ε 1 and g ε 2, we use beta(2,10) to reflect our strong belief that the intensities at channels G and T are much smaller than the intensity at channel A. We have tried other beta priors beta(a, b) with a b and obtained similar results in base calling.\n\nThe model is completed by specifying the discrete uniform prior for k i , i.e., Pr(k i = j) = 1/4 for j = 1, 2, 3, 4, a beta(1, 1) prior for λ, α, and β, and an inverse Wishart(diag(1, 4), 6) prior for ∑ j , where diag(1, 4) is the 4 × 4 identity matrix.\n\nThe models above are built for one colony of sequencing data. With multiple colonies, we use y ic = (yic,1, …, yic,4) to denote the quadruple intensities of cycle i in colony c, and k ic to represent the latent indicator of the true base of cycle i in colony c. The models for y ic are the same as in (2) and (2), with y ic and k ic replacing y i and k i . The priors for k ic , µ j , λ, α, β, and ∑ j remain unchanged. Since y ic ’s are conditionally independent, the joint likelihood for all the data is simply the product of the likelihood function for each y ic . For simplicity, the mathematical expression of the models is omitted.\n\nPosterior inference\n\nInference is carried out via MCMC simulations. The probability models are coded in C (now included in an R package). The MCMC simulations output provides Monte Carlo posterior samples of all the parameters from the joint posterior distribution. These samples can be used to perform posterior inference. For example, we obtain random samples of k ic from its marginal posterior, denoted as", null, ", where B is the number of MCMC samples. We can compute", null, "(4)\n\nas the posterior probability that the i th cycle in colony c has a true base of A, C, G, or T, respectively. These samples can be used to perform base calling. Specifically, the Bayesian base call corresponds to the nucleotide with the largest posterior probability in its cycle. That is, we assign base A, C, G, or T to cycle i in colony c if s ic equals 1, 2, 3, or 4, where", null, ". In addition, one can assess the accuracy of the proposed method by computing an estimated Bayesian FDR ([16, 17]) using the ξ’s. We will demonstrate this feature with a concrete example in the next section.\n\nNumerical examples\n\nWe compared the performance of the BM-BC method with currently leading methods, including the Solexa Bustard, the Rolexa method , and the B-I method .\n\nData\n\nWe obtained Solexa DNA sequencing data from the control lane for a bacteria phage. This is part of the standard Solexa protocol. To illustrate the performance of base calling methods, we randomly selected three subsets, with each containing 1,000 colonies of the sequence data.\n\nThe control lane sequences the genome of an enterobacteria phage, phiX174, which is composed of 5,386 bases of single stranded DNA sequences and has no polymorphism. DNA preparation follows Illumina Control DNA library protocol (Illumina Cat. No CT-901-1001). DNA are broken to a size of 200 nucleotides and are subject to 18 cycles of polymerase chain reaction (PCR) amplification before the generation of DNA colonies by single molecule PCR. The sequences of DNA colonies are probed by 36 cycles of sequencing by synthesis.\n\nEach DNA read is compared to the entire phage genome of 5,386 positions to search for the best matches. This is done using the Solexa software PhageAlign. After a tag is aligned to the phage genome, the matched sequence on the phage genome is considered to be the true sequence and any mismatched nucleotide is considered a sequencing error. The assignment of the true sequence is correct because 1) the phage genome contains no polymorphism and 2) the small genome size makes a mistaken sequence match over 36 nucleotides highly unlikely. Note that this is not the case for the human genome, where polymorphism occurs (). Here, we treat the bases obtained from the above procedure as the “true” ones and compare the performance of base calling methods based on the deviation from these bases.\n\nAnalysis with random subsets\n\nWe first applied all the methods to a small data set for illustration purpose. We then implemented the BM-BC method on a data set from the control lane of the Solexa sequencing, consisting of about 5 million short reads. We compare the following four base-calling methods using the phage sequencing data.\n\n• Bustard from Solexa’s Genome Analyzer: this is the commercial software provided by Illumina. More detailed information about the Genome Analyzer can be found at http://www.illumina.com.\n\n• Rolexa: this is a method building upon model-based clustering , which assumes that the quadruplets of intensities follow four-component univariate Gaussian mixture models. Instead of performing a full Bayesian inference using the joint posterior distribution, the Rolexa method applies the EM algorithm to obtain point estimates of the parameters.\n\n• B-I: this is the intensity model proposed in Bravo and Irrizary (2010). The authors carefully examined potential noises in the intensity data and proposed a linear mixture model with different means given the indicator of true bases. They applied the EM algorithm to obtain the posterior probabilities of the true base calls. See .\n\n• BM-BC: our proposed method.\n\nWe applied all four methods to the three random subsets of phage sequencing data, each with 1,000 colonies.\n\nFor the BM-BC method, we performed base calling using 100 colonies at a time. The Markov chains converged fast and mixed extremely well. We only needed to throw away 100 burn-in samples with a total of 600 iterations for every 100 colonies.\n\nWe compared the estimated bases from the four methods with the true bases. Table 1 shows the number of wrong calls for each of the four methods. The BM-BC method had the smallest number of wrong calls for two subsets and a close second for the third subset, in which the Rolexa yields the smallest number of wrong calls.\n\nIn Table 1, we used ACGT as the base calls for the Rolexa method. In the original paper by Rougemont et al. (2008), the authors focused on using the International Union of Pure and Applied Chemistry (IUPAC) symbols (http://www.bioinformatics.org/sms/iupac.html) as base calls. These symbols include not only ACGT, but other ambiguous calls that represent more than one base within ACGT. The authors stated that the IUPAC symbols gave the Rolexa better performance. For a fair comparison, we used the ACGT symbols for the Rolexa.\n\nFor ease of exposition, we now focus on the results of an arbitrary subset, data set 1 in Table 1. We computed the difference in the number of correct calls per colony between the BM-BC method and each of the other three methods.\n\nWe can see that the BM-BC method is more likely to make right calls for a given colony than the other three methods. In addition, in extreme cases the BM-BC method could make more than 20 more correct calls (out of a total of 36) than the other methods. In contrast, the largest number of more wrong calls the BM-BC method could make is only 6. Figure 2 compares the error rates by cycle, defined as the proportion of wrong calls for each cycle across all colonies. Interestingly, the error rate for the Solexa calls has a large increase after cycle 26. See Figure 5 for more results related to this. This seems to suggest that the Solexa base calling is more sensitive to the phasing noise in the data. In contrast, the error rates for the other three methods increase gradually over the cycles. Both BM-BC and Rolexa methods are also robust to phasing as it is specifically accounted for in the probability models. We can estimate the FDR based on the posterior probabilities ξ’s for base calls from the BM-BC method. Because we know the true bases, we can precisely compute the FDR of the BM-BC method. The idea is to treat", null, "as the local FDR. We present the following algorithm for computing the FDR based on the true bases.\n\n1. 1.\n\nLet the true base be t ic for cycle i in colony c.\n\n2. 2.\n\nCompute", null, "; then", null, "is the local FDR denoting the posterior probability of making a wrong call.\n\n3. 3.\n\nRank the pairs (i, c) according to the increasing values of", null, ".\n\n4. 4.\n\nStarting from the highest ranking pair (i, c) with the smallest", null, ", move down to the G th highest ranking pair. The estimated FDR is given by the sum of", null, "for all G pairs divided by G.\n\nFigure 3 plots the estimated FDR versus the number of calls (ranked based on increasing values of", null, "). We can see that the FDR is controlled by 0.04. This seems to agree with the error rate in Table 1. In cases where we do not know the true base calls, we only need to replace t ic with", null, ", the estimated base call by the BM-BC, in the above FDR algorithm to estimate the Bayesian FDR. This new value will be smaller because the errors in s ic are not accounted for.\n\nFull data analysis\n\nWe implemented the BM-BC method on a data set consisting of 5,120,000 colonies. The data are from a control lane in a standard Solexa run, in which the true sequences are known. We first splitted the data into 8 equal parts, each comprising of 640,000 colonies. We then applied the BM-BC method to each of the eight subsets in parallel. The eight jobs were executed on an iMAC with 2.8 GHz Intel Core i7 and 16 GB of memory. It took about 4 hours to complete the computation. We have built an R package “BM-BC”, available to be downloaded from http://odin.mdacc.tmc.edu/~yuanj/soft.html\n\nWe computed", null, "as the posterior probability that the base of cycle i in colony c is j, for j = 1, 2, 3, or 4. The base call is", null, ", the base with the largest posterior probability. We found that almost all the largest posterior probabilities were greater than 0.95, thus implying that our model was able to predict most bases with high degrees of confidence. Since we knew the true sequences for the data, we compared our predicted calls to the true sequences. Table 2 cross-tabulates the comparison results. In Figure 4, we see that the B-I error curves, though showing no such drastic jumps, still fares poorly compared to the BM-BC method. For this dataset the B-I also has a larger overall error rate of 8% compared to that of BM-BC, which has an overall error rate of of 5%. Figure 5 plots the error rates by cycle for the BM-BC and Solexa methods using the entire dataset. Although the overall error rates for the BM-BC and the Solexa methods are comparable, the A-C substitution rate for the Solexa calls show a large increase after cycle 26.\n\nDiscussion\n\nAn important feature of the BM-BC method is that it yields marginal posterior probabilities of the four nucleotides for each base. This allows a full probability-based inference for base calling and subsequent analysis. For example, one can associate the posterior probability of the base call with the estimated base and use it as a quality control measure for downstream sequence alignment. Sequences mapped to a genome with overall high posterior probabilities are more reliable than those with lower probabilities.\n\nWe also compared our method with the Bayesian classifier BayesCall in . The computation was slow compared to the other methods. The slow speed could be a potential shortcoming for its application to data from NGS platforms, typical consisting of about millions of clusters. Naive Bayes classifiers, on the other hand, suffer from the simplistic assumptions of independence which are grossly violated in datasets of these type. One important feature of BM-BC is that it does not require any prior learning for its application to GA-I data. However, unsupervised clustering is not always feasible for data from newer sequencing technologies. Ibis specifically uses large training data sets to analyze GA-II control lanes. In addition, certain platforms possess unique features and need algorithms specially tailored to their specific requirements. Ibis, for example, is designed to model the features of bi-directional phasing and T accumulation which are present in GA-II. On the other hand, BM-BC is more suited towards addressing the issues of phasing, fading and cross talk that arise in the context of modeling GA-I data.\n\nWe acknowledge that there is a scope of improving the model by incorporating the error sources unique to the latest sequencing platforms.\n\nReferences\n\n1. 1.\n\nKorbel JO, Urban AE, Affourtit JP, Godwin B, Grubert F, Simons JF, Kim PM, Palejev D, Carriero NJ, Du L, Taillon BE, Chen Z, Tanzer A, Saunders AC, Chi J, Yang F, Carter NP, Hurles ME, Weissman SM, Harkins TT, Gerstein MB, Egholm M, Snyder M: Paired-end mapping reveals extensive structural variation in the human genome. Science 2007, 318(5849):420–426. 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Genome Res 2005, 15(12):1767–1776. [http://www.hubmed.org/fulltext.cgi?uids=16339375] 10.1101/gr.3770505\n\n16. 16.\n\nNewton M, Noueiry A, Sarkar D, Ahlquist P: Detecting differential gene expression with a semi-parametric hierarchical mixture method. Biostatistics 2004, 5: 155–176. 10.1093/biostatistics/5.2.155\n\n17. 17.\n\nJi Y, Yin G, Tsui K, Kolonin M, Sun J, Arap W, Pasqualini R, Do KA: Bayesian mixture models for complex high-dimension count data in phage display experiments. Journal of the Royal Statistical Society, Series C (Applied Statistics) 2007, 56(2):139–152. 10.1111/j.1467-9876.2007.00570.x\n\n18. 18.\n\nJi Y, Xu Y, Zhang Q, Tsui KW, Yuan Y, Liang S, Liang H: BM-Map: Bayesian mapping of multireads for next-generation sequencing data. Tech. rep The University of Texas M. D. Anderson Cancer Center; 2010. [http://odin.mdacc.tmc.edu/~ylji]\n\nAcknowledgement\n\nYuan Ji’s and Peter Müller’s research is partly supported by NIH/NCI R01 CA132897. Shoudan Liang’s research is partly supported by NIH/NCI K25 CA123344. Fernando Quintana’s research is partly supported by grants FONDECYT 1100010.\n\nThis article has been published as part of BMC Bioinformatics Volume 13 Supplement 13, 2012: Selected articles from The 8th Annual Biotechnology and Bioinformatics Symposium (BIOT-2011). The full contents of the supplement are available online at http://www.biomedcentral.com/1471-2105/13/S13/S1\n\nAuthor information\n\nAuthors\n\nCorresponding authors\n\nCorrespondence to Yuan Ji or Riten Mitra.\n\nCompeting interests\n\nThe authors declare that they have no competing interests.\n\nAuthors' contributions\n\nConceived and designed the method: YJ FQ AJ SL. Performed the data analysis: YJ RM FQ AJ PL. Wrote the paper: YJ RM FQ PM YL SL.\n\nRights and permissions\n\nReprints and Permissions\n\nJi, Y., Mitra, R., Quintana, F. et al. BM-BC: a Bayesian method of base calling for Solexa sequence data. BMC Bioinformatics 13, S6 (2012). https://doi.org/10.1186/1471-2105-13-S13-S6", null, "" ]

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[ "# Extract intervals from an array of numbers\n\nLet’s assume you have an array of numbers and you want to extract intervals from this array. For example, from such an array: 2,3,4,5,8,9,10,11,12,15,18,19,20 you should be getting (2-5), (8-12), (18-20) as intervals.\n\nMore bioinformatic case: Let’s assume you ran samtools pileup format and want to extract intervals from the genomic coordinates that has at least one hit.\n\nThe following one-liner will give you what you want: (I used `seq` to generate array of numbers and concatenated multiple seq)\n\n``````cat <(seq 3 23) <(echo 25) <(seq 40 50) | perl -ne 'BEGIN{our \\$i=1}; chomp ; if((\\$_ - (\\${\\$hash->{\\$i-1}}[-1]))==1){push @{\\$hash->{\\$i-1}},\\$_}else{push @{\\$hash->{\\$i++}},\\$_}; END {print join\"\\n\", map {\\${\\$hash->{\\$_}}.\"\\t\".\\${\\$hash->{\\$_}}[-1]} grep { scalar(@{\\$hash->{\\$_}}) > 1} sort {\\$a <=> \\$b} keys %\\$hash; print \"\\n\"}'\n``````\n\nAnd the result is:\n\n``````3\t23\n40\t50\n``````\n\n`map` was used to get first and last element of array, `grep` is used to filter out arrays that has less than 2 elements.", null, "##### Alper Yilmaz\n###### Assist.Prof.Dr. Alper YILMAZ\n\nMy research interests include genome grammar and NGS analysis." ]

[ null, "http://alperyilmaz.site/author/admin/avatar_hu33d8f2710ea4928d295bd08cdc05f6eb_10738_250x250_fill_q90_lanczos_center.jpg", null ]

[ "", null, "# Mathematical Sciences Research Institute\n\nHome » Hamiltonian systems, from topology to applications through analysis\n\n# Program\n\nHamiltonian systems, from topology to applications through analysis August 13, 2018 to December 14, 2018\nOrganizers Rafael de la Llave (Georgia Institute of Technology), LEAD Albert Fathi (Georgia Institute of Technology; École Normale Supérieure de Lyon), vadim kaloshin (University of Maryland), Robert Littlejohn (University of California, Berkeley), Philip Morrison (University of Texas, Austin), Tere Seara (Polytechnical University of Cataluña (Barcelona)), Sergei Tabachnikov (Pennsylvania State University), Amie Wilkinson (University of Chicago)\nDescription\nHamiltonian mechanics was born out of optics. Sir William Rowan Hamilton developed a theory for studying the propagation of the phase in optical systems guided by Fermat's principle for light rays (i.e. high frequency systems). Shortly afterwards, he realized that ,based on the similarity of Fermat's principle with the action principle, one could adapt the machinery to mechanics. Hamiltonian methods are now a central topic in dynamics and mechanics. Many interesting PDE's appear as a limit of mechanical systems of many small particles (e.g. water waves, fluid mechanics, the equations of plasma physics), and therefore the Hamiltonian setting is essential for studying these types of PDE’s. It is interesting to note that Maxwell spent some time developing mechanical models for his equations for the electromagnetic field. Practical scientists appreciate the magic cancellations in the Hamiltonian setting that lead to efficient calculations. The interdisciplinary nature of Hamiltonian systems is deeply ingrained in its history. It is remarkable that the discovery in the 1980’s of the celebrated Aubry-Mather theory (one of the most important developments in decades) was accomplished simultaneously by a Physicist Serge Aubry and a Mathematician John Mather. Many of the people working in this area can talk to both mathematicians and physicists. This program is designed to mix the pure mathematical viewpoint with applications in physics, space mechanics, and theoretical chemistry. The two communities will be completely integrated for synergy. Workshops are designed with the priority of fomenting interactions.  We envision that during the whole semester the visitors will present tutorials aimed also to the people from different scientific backgrounds. The selection of the majority of visitors will be based on potential interactions. Mathematical topics include: 1) Arnold diffusion (using both the geometric and variational methods, including examples of diffusion in celestial mechanics). 2) Celestial mechanics (with a particular emphasis on minimizing orbits, and other surprising trajectories). 3) Connections between the weak (viscosity) solutions of the Hamilton-Jacobi equation and the Aubry-Mather theory of Lagrangian systems (Weak KAM theory). 4) PDE’s that can be thought of as infinite dimensional Hamiltonian Systems, to which the KAM methods can be applied. Applications include: 1) Astrodynamics and motions of satellites. 2) Plasma Physics and accelerator Physics confinement. 3) Theoretical Chemistry and atomic Physics.  Bibliography\nKeywords and Mathematics Subject Classification (MSC)\nTags/Keywords\n• Hamiltonian systems\n\n• Celestial Mechanics\n\n• Arnold diffusion\n\n• Hamilton-Jacobi\n\n• Aubry-Mather\n\n• KAM methods\n\n• Lagrangian systems\n\n• astrodynamics\n\n• plasma physics\n\n• accelerator physics\n\n• theoretical chemistry\n\n• atomic physics\n\n• weak KAM\n\n• viscosity solutions\n\n• symplectic\n\n• Poisson brackets\n\n• barriers and transport\n\n• perturbation theory\n\n• billiards\n\n• invariant manifolds\n\n• spectral rigidity\n\n• Hamiltonian invariants\n\n• twist maps\n\nPrimary Mathematics Subject Classification\nSecondary Mathematics Subject Classification\nLogistics Program Logistics can be viewed by Members. If you are a program member then Login Here.\nProgrammatic Workshops\n August 16, 2018 - August 17, 2018 Connections for Women: Hamiltonian Systems, from topology to applications through analysis August 20, 2018 - August 24, 2018 Introductory Workshop: Hamiltonian systems, from topology to applications through analysis October 08, 2018 - October 12, 2018 Hamiltonian systems, from topology to applications through analysis I November 26, 2018 - November 30, 2018 Hamiltonian systems, from topology to applications through analysis II" ]

[ null, "https://www.msri.org/assets/msri/logo-700e44004610ddac7cc20843a05755bcc98ec19f00a3b938096366f100d8bf88.png", null ]

[ " Efficient Generalized Inverse for Solving Simultaneous Linear Equations\n\nJournal of Applied Mathematics and Physics\nVol.04 No.01(2016), Article ID:62628,5 pages\n10.4236/jamp.2016.41003\n\nEfficient Generalized Inverse for Solving Simultaneous Linear Equations\n\nS. Kadiam Bose1, D. T. Nguyen2\n\n1Structural Technologies Strong Point LLC, Baltimore, MD, USA\n\n2Department of Civil and Environmental Engineering, Old Dominion University, Norfolk, VA, USA", null, "", null, "", null, "Received 22 November 2015; accepted 5 January 2016; published 12 January 2016\n\nABSTRACT\n\nSolving large scale system of Simultaneous Linear Equations (SLE) has been (and continue to be) a major challenging problem for many real-world engineering and science applications. Solving SLE with singular coefficient matrices arises from various engineering and sciences applications -. In this paper, efficient numerical procedures for finding the generalized (or pseudo) inverse of a general (square/rectangle, symmetrical/unsymmetrical, non-singular/singular) matrix and solving systems of Simultaneous Linear Equations (SLE) are formulated and explained. The developed procedures and its associated computer software (under MATLAB computer environment) have been based on “special Cholesky factorization schemes” (for a singular matrix). Test matrices from different fields of applications have been chosen, tested and compared with other existing algorithms. The results of the numerical tests have indicated that the developed procedures are far more efficient than the existing algorithms.\n\nKeywords:\n\nGeneralized Inverse Algorithms, Simultaneous Linear Systems, Matrix Inverse, Singular Matrix, Pseudo Inverse, Cholesky Factorization", null, "1. Introduction\n\nIn scientific computing, most computational time is spent on solving system of Simultaneous Linear Equations (SLE) which can be represented in matrix notations as", null, "(1.1)\n\nwhere", null, "is a singular/non-singular matrix, and b is a given vector in", null, ". For practical engineering/ science applications, matrix A can be either sparse (for most cases), or dense (for some cases). For a non-sin- gular coefficient matrix A, direct methods (Cholesky factorization,", null, "algorithm,", null, "decomposition, etc) or iterative methods (Conjugate Gradient algorithm, Bi-Conjugate Stabilization, GMRES, etc.) are used to solve Equation (1.1). If the coefficient matrix is singular or rectangular, the above mentioned direct and iterative methods cannot be used to solve Equation (1.1) and thus generalized inverse is needed to solve the unknown solution vector x in Equation (1.1).\n\nThe generalized (or pseudo) inverse of a matrix is an extension of the ordinary/regular square (non-singular) matrix inverse, which can be applied to any matrix (such as singular, rectangular etc.). The generalized inverse has numerous important engineering and sciences applications. Over the past decades, generalized inverses of matrices and its applications have been investigated by many researchers -. Generalized inverse is also known as “Moore-Penrose inverse” or “g-inverse” or “pseudo-inverse” etc.\n\nIn this paper we introduce an efficient (in terms of computational time and computer memory requirement) generalized inverse formulation to solve SLE with full or deficient rank of the coefficient matrix. The coefficient matrix can be singular/non-singular, symmetric/unsymmetric, or square/rectangular. Due to popular MATLAB software, which is widely accepted by researchers and educators worldwide, the developed code from this work is written in MATLAB language.\n\nThe rest of this paper is organized as follows. In Section 2, we discuss background of generalized inverse. In Section 3, we give a description of the algorithm. This section also describes the efficient generalized inverse formulation (which uses modified Cholesky factorization). In Section 4, we present comparison of numerical performances of the proposed algorithm with other existing algorithms. Extensive set of coefficient matrices (including rectangular, square, symmetrical, non-symmetrical, singular, non-singular matrices) obtained from well-established/popular websites were tested and the numerical performance in terms of timings, error norm were compared with other algorithms. Finally, conclusions are drawn in Section 5.\n\n2. Singular Value Decomposition (SVD) and the Generalized Inverse\n\nA general (square or rectangular) matrix", null, "can be decomposed as", null, "(2.1)\n\nwhere", null, "(2.2)", null, "", null, "(2.3)\n\nLet A be a singular matrix of size", null, "and let k be the rank of the matrix. Based on Equation (2.1), one has", null, "", null, "with", null, "(2.4)\n\nand", null, "Note: Eigen-values of", null, "and Eigen-values of", null, "are the same. However, the Eigen-vectors of and Eigen-vectors of are “NOT” the same.\n\nThen, the generalized inverse of is the matrix and is given as\n\n(2.5)\n\nwhere\n\nand is the diagonal matrix, with.\n\n3. Efficient Generalized Inverse Algorithms - \n\nMoore-Penrose inverse can be computed using Singular Value Decomposition (SVD), Least Squares Method, QR factorizations, Finite Recursive Algorithm , etc. In this work, our numerical algorithms have been based on:\n\n(a) The “special Cholesky factorization” (for symmetrical/singular coefficient matrix), and\n\n(b) The generalized inverse of a product of 2 matrices and can be described in the following paragraphs.\n\nThe Moore-Penrose inverse (or generalized inverse or pseudo inverse) of a matrix (not necessarily a square matrix) is the unique matrix which satisfies the following four conditions:\n\n1. General condition:\n\n2. Reflexive condition:\n\n3. Normalized condition:\n\n4. Reverse normalized condition:\n\nConsider with a square coefficient matrix, and let the rank be less than the size of the matrix (if r is the rank of the matrix, then). Let the size of the known right-hand-side vector be. Consider a symmetric positive matrix with rank (here, the matrix plays the same role as matrix in Equation (1.1)), then based on the theorem presented in , there exists a unique such that:\n\n(3.1)\n\nIn Equation (3.1), matrices have the dimensions, respectively.\n\nM is the upper triangular (special) Cholesky factorized matrix and contains exactly zero rows. Removing the zero rows from M, one obtains a (upper, rectangular) matrix.\n\n(3.2)\n\nIn this work, the upper triangular (special) Cholesky factorized matrix can be obtained by the regular/ standard Cholesky factorization, with the following modifications:\n\na) When the diagonal term of the current row is very close to zero, then factorization of this dependent row is skipped.\n\nb) When the current row is factorized, all previous rows were used except those dependent row(s).\n\nConsider the generalized inverse of a matrix product \n\n(3.3)\n\nFrom Equation (3.3), if then\n\n(3.4)\n\nIf and A is a matrix of rank r, then one obtains from Equation (3.3)\n\n(3.5)\n\nLet us consider regular inverse in Equation (3.5) in place of generalized inverse\n\n(3.6)\n\nUsing Equation (3.4),\n\n(3.7)\n\nFrom Equations (3.1)-(3.2) and Equation (3.6) one obtains,\n\n(3.8)\n\nThus, Equation (3.7) becomes\n\n(3.9)\n\nWhile MATLAB solution can be obtained by implying the generalized inverse [see Equation (3.9)] to be formed explicitly, our main idea is to solve SLE where is a known right-hand-side vector.\n\n4. Numerical Performance of ODU Generalized Inverse Solver\n\nBased on the detailed algorithms explained in Section 3, the numerical performance of our proposed procedures are evaluated in this section. The known RHS vector can be random vector, or can be chosen such a way that the unknown solution vector.\n\nWe also compared the performance of our algorithm with the efficient algorithm described in and also with MATLAB built-in function for computing the generalized inverse explicitly. We use MATLAB version 7.6.0.324 (R2008a) on Intel Core 2 CPU, 2.13 GHZ, 2GB RAM, Windows XP Professional SP3 for numerical comparisons.\n\nTable 1 and Table 2 records the times (in seconds) taken by our proposed algorithm, the algorithm mentioned in and MATLAB built-in function . For our convenience, we represent our algorithm with, algorithm in with and MATLAB built-in function with. In addition, we have also presented the error norm for all the test matrices.\n\nTable 1. Computational times (in seconds) for symmetric rank-deficient test matrices with RHS Vector as linear combination of columns of coefficient matrix.\n\nTable 2. Computational times (in seconds) for rectangular rank-deficient test matrices (Tall type: Rows >> Cols) with RHS Vector as linear combination of columns of coefficient matrix.\n\n5. Conclusion\n\nIn this paper, various efficient algorithms for solving SLE with full rank, or rank deficient have been reviewed, proposed and tested. The developed numerical procedures can be applied to solve “general” SLE (in the form, where the coefficient matrix could be square/rectangular, symmetrical/unsymmetrical, non-singular/singular). The users have option to choose either a direct solver or an iterative solver inside the generalized inverse to solve for SLE. Numerical results have shown that the proposed algorithms are highly efficient as compared to existing algorithms (including the popular MATLAB built-in function) .\n\nAcknowledgements\n\nThe authors would like to acknowledge Gelareh Bakhtyar for her useful discussions.\n\nCite this paper\n\nS. Kadiam Bose,D. T. Nguyen, (2016) Efficient Generalized Inverse for Solving Simultaneous Linear Equations. Journal of Applied Mathematics and Physics,04,16-20. doi: 10.4236/jamp.2016.41003\n\nReferences\n\n1. 1. Nguyen, D.T. (2006) Finite Element Methods: Parallel-Sparse Statics and Eigen-Solutions. Springer Publisher.\n\n2. 2. Golub, G.H. and Loan, C.F.V. (1996) Matrix Computations. The John Hopkins University Press.\n\n3. 3. Heath, M.T. (1997) Scientific Computing: An Introductory Survey. McGraw Hill Publisher.\n\n4. 4. Hou, G. and Wang, Y. (2004) A Substructuring Technique for Design Modifications of Interface Conditions. Structural Dynamics & Materials Conference, Palm Springs, California, 19-22 April 2004. http://dx.doi.org/10.2514/6.2004-2010\n\n5. 5. Farhat, C. and Roux, F.X. (1994) Implicit Parallel Processing in Structural Mechanics. Computational Mechanics Advances, 2, Elsevier Publisher.\n\n6. 6. Pierre, C. (2005) Fast Computation of Moore-Penrose Inverse Matrices. Neural Information Processing—Letters and Reviews, 8.\n\n7. 7. MATLAB, MATLAB—The Language of Technical Computing.\n\n8. 8. Davis, T. University of South Florida Matrix Collection.\n\n9. 9. SJSU, SJSU—Singular Matrix Database." ]

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[ "# How to force weights to add to $1$ in Linear regression\n\nI am using a linear regression using scikit-learn in python. However, I would like to force the weights to add to $$1$$. Is there a way to do this? I know that I need to add a constraint but am not able to figure out how. My regression looks something like this $$Y= a_0 + bX_1 + (1-b)X_2$$\n\n• Linear Regression estimator has a coef_ attribute and an intercept_ attribute. coef_ contains the estimated weights, whereas the intercept_ contains the bias(es). You can directly modify their values by adding a 1. But I'm more interested in knowing that why would you do such a nasty thing in the first place? Feb 22 '19 at 19:51\n• Welcome to the site! Are you able to share your use case? Asking weights to add up to a certain number doesn't really make a whole lot of sense and it basically makes this no longer be a data science effort. What exactly are you trying to achieve here? Feb 22 '19 at 19:57\n• @SyedAliHamza he doesn't want to add a 1 he wants the sum of the weights to add up to 1. So, it's a slight correction to how you understood the question, but an equally nasty request :-) Feb 22 '19 at 19:58\n• Hi @I_Play_With_Data, I am working with some interest rate data. In interest rate shock scenarios, the shock for the dependant variable would be inconsistent if the weights do not add to 1. Feb 22 '19 at 20:03\n• Interesting. I don't know a lot about that particular domain so maybe someone else can give you better guidance. But, my gut tells me that maybe regression wouldn't be the best approach for this. You're implying that your dependent results have a limited/restricted range, and that's OK, it may be that another model would be better suited for this. Is there a reason why you picked regression? Is it for transparency purposes? Feb 22 '19 at 20:06\n\nSuppose the problem formulation is\n\n$$\\min_{a,b} \\sum_{i=1}^n(y_i -a_0-\\sum_{j=1}^pb_jx_{ij} )^2$$\n\nsubject to $$\\sum_{j=1}^p b_j=1$$ $$b \\ge 0$$\n\nthen this is an instance of a quadratic programming problem.\n\nThere are solvers such as Gurobi (free for academia) and CVXOPT (freeware) that can manage a quadratic programming problem. An example of CVXOPT code to solve a QP can be found here.\n\nNote that the objective function can be written as\n\n\\begin{align}&\\|Y-a_0e-Xb\\|^2\\\\&=\\left\\|Y-\\begin{bmatrix}e & X \\end{bmatrix}\\begin{bmatrix}a_0 \\\\ b\\end{bmatrix}\\right\\|^2\\\\ &=\\begin{bmatrix}a_0 & b \\end{bmatrix}\\begin{bmatrix} e^T\\\\X^T\\end{bmatrix}\\begin{bmatrix} e &X\\end{bmatrix}\\begin{bmatrix}a_0 \\\\ b \\end{bmatrix}-2Y^T\\begin{bmatrix} e &X\\end{bmatrix}\\begin{bmatrix}a_0 \\\\ b \\end{bmatrix}+\\|Y\\|^2\\end{align}\n\nAlso, you might like to check with people in your field what is the common package that they use.\n\n• great answer! I would also like to add a C++/python solver that I have found useful for optimization problems esa.github.io/pagmo2 Feb 23 '19 at 16:09" ]

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[ "# -*- coding: utf-8 -*-\n#\n#\n# pylint: disable= no-member, arguments-differ, invalid-name\n\nimport dgl\nimport torch.nn as nn\n\n# pylint: disable=W0221\n\nThis layer updates node representations with a MLP and computes graph representations\nout of node representations with max, mean or sum.\n\nParameters\n----------\nnode_feats : int\nSize for the input node features.\nhidden_feats : int\nSize for the hidden representations.\ngraph_feats : int\nSize for the output graph representations.\nactivation : callable\nActivation function. Default to None.\nmode : 'max' or 'mean' or 'sum'\nWhether to compute elementwise maximum, mean or sum of the node representations.\n\"\"\"\ndef __init__(self, node_feats, hidden_feats, graph_feats, activation=None, mode='sum'):\n\nassert mode in ['max', 'mean', 'sum'], \\\n\"Expect mode to be 'max' or 'mean' or 'sum', got {}\".format(mode)\nself.mode = mode\nself.in_project = nn.Linear(node_feats, hidden_feats)\nself.activation = activation\nself.out_project = nn.Linear(hidden_feats, graph_feats)\n\n[docs] def forward(self, g, node_feats):\n\"\"\"Computes graph representations out of node features.\n\nParameters\n----------\ng : DGLGraph\nDGLGraph for a batch of graphs.\nnode_feats : float32 tensor of shape (V, node_feats)\nInput node features, V for the number of nodes.\n\nReturns\n-------\ngraph_feats : float32 tensor of shape (G, graph_feats)\nGraph representations computed. G for the number of graphs.\n\"\"\"\nnode_feats = self.in_project(node_feats)\nif self.activation is not None:\nnode_feats = self.activation(node_feats)\nnode_feats = self.out_project(node_feats)\n\nwith g.local_scope():\ng.ndata['h'] = node_feats\nif self.mode == 'max':\ngraph_feats = dgl.max_nodes(g, 'h')\nelif self.mode == 'mean':\ngraph_feats = dgl.mean_nodes(g, 'h')\nelif self.mode == 'sum':\ngraph_feats = dgl.sum_nodes(g, 'h')\n\nreturn graph_feats" ]

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[ "HDK\nImathMatrixAlgo.h File Reference\n`#include \"ImathEuler.h\"`\n`#include \"ImathExport.h\"`\n`#include \"ImathMatrix.h\"`\n`#include \"ImathNamespace.h\"`\n`#include \"ImathQuat.h\"`\n`#include \"ImathVec.h\"`\n`#include <math.h>`", null, "Include dependency graph for ImathMatrixAlgo.h:", null, "This graph shows which files directly or indirectly include this file:\n\nGo to the source code of this file.\n\n## Functions\n\ntemplate<class T >\nbool extractScaling (const Matrix44< T > &mat, Vec3< T > &scl, bool exc=true)\n\ntemplate<class T >\nMatrix44< T > sansScaling (const Matrix44< T > &mat, bool exc=true)\n\ntemplate<class T >\nbool removeScaling (Matrix44< T > &mat, bool exc=true)\n\ntemplate<class T >\nbool extractScalingAndShear (const Matrix44< T > &mat, Vec3< T > &scl, Vec3< T > &shr, bool exc=true)\n\ntemplate<class T >\nMatrix44< T > sansScalingAndShear (const Matrix44< T > &mat, bool exc=true)\n\ntemplate<class T >\nvoid sansScalingAndShear (Matrix44< T > &result, const Matrix44< T > &mat, bool exc=true)\n\ntemplate<class T >\nbool removeScalingAndShear (Matrix44< T > &mat, bool exc=true)\nRemove scaling and shear from the given 4x4 matrix in place. More...\n\ntemplate<class T >\nbool extractAndRemoveScalingAndShear (Matrix44< T > &mat, Vec3< T > &scl, Vec3< T > &shr, bool exc=true)\n\ntemplate<class T >\nvoid extractEulerXYZ (const Matrix44< T > &mat, Vec3< T > &rot)\n\ntemplate<class T >\nvoid extractEulerZYX (const Matrix44< T > &mat, Vec3< T > &rot)\n\ntemplate<class T >\nQuat< T > extractQuat (const Matrix44< T > &mat)\n\ntemplate<class T >\nbool extractSHRT (const Matrix44< T > &mat, Vec3< T > &s, Vec3< T > &h, Vec3< T > &r, Vec3< T > &t, bool exc, typename Euler< T >::Order rOrder)\n\ntemplate<class T >\nbool extractSHRT (const Matrix44< T > &mat, Vec3< T > &s, Vec3< T > &h, Vec3< T > &r, Vec3< T > &t, bool exc=true)\n\ntemplate<class T >\nbool extractSHRT (const Matrix44< T > &mat, Vec3< T > &s, Vec3< T > &h, Euler< T > &r, Vec3< T > &t, bool exc=true)\n\ntemplate<class T >\nbool checkForZeroScaleInRow (const T &scl, const Vec3< T > &row, bool exc=true)\n\ntemplate<class T >\nMatrix44< T > outerProduct (const Vec4< T > &a, const Vec4< T > &b)\nReturn the 4x4 outer product two 4-vectors. More...\n\ntemplate<class T >\nMatrix44< T > rotationMatrix (const Vec3< T > &fromDirection, const Vec3< T > &toDirection)\n\ntemplate<class T >\nMatrix44< T > rotationMatrixWithUpDir (const Vec3< T > &fromDir, const Vec3< T > &toDir, const Vec3< T > &upDir)\n\ntemplate<class T >\nvoid alignZAxisWithTargetDir (Matrix44< T > &result, Vec3< T > targetDir, Vec3< T > upDir)\n\ntemplate<class T >\nMatrix44< T > computeLocalFrame (const Vec3< T > &p, const Vec3< T > &xDir, const Vec3< T > &normal)\n\ntemplate<class T >\nMatrix44< T > addOffset (const Matrix44< T > &inMat, const Vec3< T > &tOffset, const Vec3< T > &rOffset, const Vec3< T > &sOffset, const Vec3< T > &ref)\n\ntemplate<class T >\nMatrix44< T > computeRSMatrix (bool keepRotateA, bool keepScaleA, const Matrix44< T > &A, const Matrix44< T > &B)\n\ntemplate<class T >\nbool extractScaling (const Matrix33< T > &mat, Vec2< T > &scl, bool exc=true)\n\ntemplate<class T >\nMatrix33< T > sansScaling (const Matrix33< T > &mat, bool exc=true)\n\ntemplate<class T >\nbool removeScaling (Matrix33< T > &mat, bool exc=true)\n\ntemplate<class T >\nbool extractScalingAndShear (const Matrix33< T > &mat, Vec2< T > &scl, T &shr, bool exc=true)\n\ntemplate<class T >\nMatrix33< T > sansScalingAndShear (const Matrix33< T > &mat, bool exc=true)\n\ntemplate<class T >\nbool removeScalingAndShear (Matrix33< T > &mat, bool exc=true)\nRemove scaling and shear from the given 3x3e matrix in place. More...\n\ntemplate<class T >\nbool extractAndRemoveScalingAndShear (Matrix33< T > &mat, Vec2< T > &scl, T &shr, bool exc=true)\n\ntemplate<class T >\nvoid extractEuler (const Matrix22< T > &mat, T &rot)\n\ntemplate<class T >\nvoid extractEuler (const Matrix33< T > &mat, T &rot)\n\ntemplate<class T >\nbool extractSHRT (const Matrix33< T > &mat, Vec2< T > &s, T &h, T &r, Vec2< T > &t, bool exc=true)\n\ntemplate<class T >\nbool checkForZeroScaleInRow (const T &scl, const Vec2< T > &row, bool exc=true)\n\ntemplate<class T >\nMatrix33< T > outerProduct (const Vec3< T > &a, const Vec3< T > &b)\nReturn the 3xe outer product two 3-vectors. More...\n\ntemplate<class T >\nMatrix44< T > addOffset (const Matrix44< T > &inMat, const Vec3< T > &tOffset, const Vec3< T > &rOffset, const Vec3< T > &sOffset, const Matrix44< T > &ref)\n\ntemplate<typename T >\nM44d procrustesRotationAndTranslation (const Vec3< T > *A, const Vec3< T > *B, const T *weights, const size_t numPoints, const bool doScaling=false)\n\ntemplate<typename T >\nM44d procrustesRotationAndTranslation (const Vec3< T > *A, const Vec3< T > *B, const size_t numPoints, const bool doScaling=false)\n\ntemplate<typename T >\nvoid jacobiSVD (const Matrix33< T > &A, Matrix33< T > &U, Vec3< T > &S, Matrix33< T > &V, const T tol=std::numeric_limits< T >::epsilon(), const bool forcePositiveDeterminant=false)\n\ntemplate<typename T >\nvoid jacobiSVD (const Matrix44< T > &A, Matrix44< T > &U, Vec4< T > &S, Matrix44< T > &V, const T tol=std::numeric_limits< T >::epsilon(), const bool forcePositiveDeterminant=false)\n\ntemplate<typename T >\nvoid jacobiEigenSolver (Matrix33< T > &A, Vec3< T > &S, Matrix33< T > &V, const T tol)\n\ntemplate<typename T >\nvoid jacobiEigenSolver (Matrix33< T > &A, Vec3< T > &S, Matrix33< T > &V)\n\ntemplate<typename T >\nvoid jacobiEigenSolver (Matrix44< T > &A, Vec4< T > &S, Matrix44< T > &V, const T tol)\n\ntemplate<typename T >\nvoid jacobiEigenSolver (Matrix44< T > &A, Vec4< T > &S, Matrix44< T > &V)\n\ntemplate<typename TM , typename TV >\nvoid maxEigenVector (TM &A, TV &S)\n\ntemplate<typename TM , typename TV >\nvoid minEigenVector (TM &A, TV &S)\n\n## Variables\n\nIMATH_EXPORT_CONST M22f\nidentity22f\nM22f identity matrix. More...\n\nIMATH_EXPORT_CONST M33f identity33f\nM33f identity matrix. More...\n\nIMATH_EXPORT_CONST M44f identity44f\nM44f identity matrix. More...\n\nIMATH_EXPORT_CONST M22d identity22d\nM22d identity matrix. More...\n\nIMATH_EXPORT_CONST M33d identity33d\nM33d identity matrix. More...\n\nIMATH_EXPORT_CONST M44d identity44d\nM44d identity matrix. More...\n\n## Function Documentation\n\ntemplate<class T >\n Matrix44 addOffset ( const Matrix44< T > & inMat, const Vec3< T > & tOffset, const Vec3< T > & rOffset, const Vec3< T > & sOffset, const Vec3< T > & ref )\n\nAdd a translate/rotate/scale offset to a 4x4 input frame and put it in another frame of reference\n\nParameters\n [in] inMat Input frame [in] tOffset Translation offset [in] rOffset Rotation offset in degrees [in] sOffset Scale offset [in] ref Frame of reference\nReturns\nThe offsetted frame\ntemplate<class T >\n Matrix44 addOffset ( const Matrix44< T > & inMat, const Vec3< T > & tOffset, const Vec3< T > & rOffset, const Vec3< T > & sOffset, const Matrix44< T > & ref )\n\nAdd a translate/rotate/scale offset to an input frame and put it in another frame of reference.\n\nParameters\n inMat input frame tOffset translate offset rOffset rotate offset in degrees sOffset scale offset ref Frame of reference\nReturns\nThe offsetted frame\n\nDefinition at line 1027 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n void alignZAxisWithTargetDir ( Matrix44< T > & result, Vec3< T > targetDir, Vec3< T > upDir )\n\nConstruct a 4x4 matrix that rotates the z-axis so that it points towards `targetDir`. You must also specify that you want the up vector to be pointing in a certain direction `upDir`.\n\nNotes: The following degenerate cases are handled: (a) when the directions given by `toDir` and `upDir` are parallel or opposite (the direction vectors must have a non-zero cross product); (b) when any of the given direction vectors have zero length\n\nParameters\n [out] result The output matrix [in] targetDir The target direction vector [in] upDir The up direction vector\n\nDefinition at line 908 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool checkForZeroScaleInRow ( const T & scl, const Vec3< T > & row, bool exc = `true` )\n\nReturn true if the given scale can be removed from the given row matrix, false if `scl` is small enough that the operation would overflow. If `exc` is true, throw an exception on overflow.\n\nDefinition at line 828 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool checkForZeroScaleInRow ( const T & scl, const Vec2< T > & row, bool exc = `true` )\n\nReturn true if the given scale can be removed from the given row matrix, false if `scl` is small enough that the operation would overflow. If `exc` is true, throw an exception on overflow.\n\ntemplate<class T >\n Matrix44< T > computeLocalFrame ( const Vec3< T > & p, const Vec3< T > & xDir, const Vec3< T > & normal )\n\nCompute an orthonormal direct 4x4 frame from a position, an x axis direction and a normal to the y axis. If the x axis and normal are perpendicular, then the normal will have the same direction as the z axis.\n\nParameters\n [in] p The position of the frame [in] xDir The x axis direction of the frame [in] normal A normal to the y axis of the frame\nReturns\nThe orthonormal frame\n\nDefinition at line 985 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n Matrix44< T > computeRSMatrix ( bool keepRotateA, bool keepScaleA, const Matrix44< T > & A, const Matrix44< T > & B )\n\nCompute 4x4 translate/rotate/scale matrix from `A` with the rotate/scale of `B`.\n\nParameters\n [in] keepRotateA If true, keep rotate from matrix `A`, use `B` otherwise [in] keepScaleA If true, keep scale from matrix `A`, use `B` otherwise [in] A Matrix A [in] B Matrix B\nReturns\nMatrix `A` with tweaked rotation/scale\n\nDefinition at line 1060 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractAndRemoveScalingAndShear ( Matrix44< T > & mat, Vec3< T > & scl, Vec3< T > & shr, bool exc = `true` )\n\nRemove scaling and shear from the given 4x4 matrix in place, returning the extracted values.\n\nParameters\n [in,out] mat The matrix to operate on [out] scl The extracted scale [out] shr The extracted shear [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 523 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractAndRemoveScalingAndShear ( Matrix33< T > & mat, Vec2< T > & scl, T & shr, bool exc = `true` )\n\nRemove scaling and shear from the given 3x3 matrix in place, returning the extracted values.\n\nParameters\n [in,out] mat The matrix to operate on [out] scl The extracted scale [out] shr The extracted shear [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 1182 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n void extractEuler ( const Matrix22< T > & mat, T & rot )\n\nExtract the rotation from the given 2x2 matrix\n\nParameters\n [in] mat The input matrix [out] rot The extracted rotation value\n\nDefinition at line 1269 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n void extractEuler ( const Matrix33< T > & mat, T & rot )\n\nExtract the rotation from the given 3x3 matrix\n\nParameters\n [in] mat The input matrix [out] rot The extracted rotation value\n\nDefinition at line 1290 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n void extractEulerXYZ ( const Matrix44< T > & mat, Vec3< T > & rot )\n\nExtract the rotation from the given 4x4 matrix in the form of XYZ euler angles.\n\nParameters\n [in] mat The input matrix [out] rot The extracted XYZ euler angle vector\n\nDefinition at line 636 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n void extractEulerZYX ( const Matrix44< T > & mat, Vec3< T > & rot )\n\nExtract the rotation from the given 4x4 matrix in the form of ZYX euler angles.\n\nParameters\n [in] mat The input matrix [out] rot The extracted ZYX euler angle vector\n\nDefinition at line 679 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n Quat< T > extractQuat ( const Matrix44< T > & mat )\n\nExtract the rotation from the given 4x4 matrix in the form of a quaternion.\n\nParameters\n [in] mat The input matrix\nReturns\nThe extracted quaternion\n\nDefinition at line 722 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractScaling ( const Matrix44< T > & mat, Vec3< T > & scl, bool exc = `true` )\n\nExtract the scaling component of the given 4x4 matrix.\n\nParameters\n [in] mat The input matrix [out] scl The extracted scale, i.e. the output value [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 419 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractScaling ( const Matrix33< T > & mat, Vec2< T > & scl, bool exc = `true` )\n\nExtract the scaling component of the given 3x3 matrix.\n\nParameters\n [in] mat The input matrix [out] scl The extracted scale, i.e. the output value [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 1089 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractScalingAndShear ( const Matrix44< T > & mat, Vec3< T > & scl, Vec3< T > & shr, bool exc = `true` )\n\nExtract the scaling and shear components of the given 4x4 matrix. Return true if the scale could be successfully extracted, false if the matrix is degenerate.\n\nParameters\n [in] mat The input matrix [out] scl The extracted scale [out] shr The extracted shear [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 473 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractScalingAndShear ( const Matrix33< T > & mat, Vec2< T > & scl, T & shr, bool exc = `true` )\n\nExtract the scaling and shear components of the given 3x3 matrix. Return true if the scale could be successfully extracted, false if the matrix is degenerate.\n\nParameters\n [in] mat The input matrix [out] scl The extracted scale [out] shr The extracted shear [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 1143 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractSHRT ( const Matrix44< T > & mat, Vec3< T > & s, Vec3< T > & h, Vec3< T > & r, Vec3< T > & t, bool exc, typename Euler< T >::Order rOrder )\n\nExtract the scaling, shear, rotation, and translation components of the given 4x4 matrix. The values are such that:\n\n```M = S * H * R * T\n```\nParameters\n [in] mat The input matrix [out] s The extracted scale [out] h The extracted shear [out] r The extracted rotation [out] t The extracted translation [in] exc If true, throw an exception if the scaling in `mat` is very close to zero. [in] rOrder The order with which to extract the rotation\nReturns\nTrue if the values could be extracted, false if the matrix is degenerate.\n\nDefinition at line 777 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractSHRT ( const Matrix44< T > & mat, Vec3< T > & s, Vec3< T > & h, Vec3< T > & r, Vec3< T > & t, bool exc = `true` )\n\nExtract the scaling, shear, rotation, and translation components of the given 4x4 matrix.\n\nParameters\n [in] mat The input matrix [out] s The extracted scale [out] h The extracted shear [out] r The extracted rotation, in XYZ euler angles [out] t The extracted translation [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the values could be extracted, false if the matrix is degenerate.\n\nDefinition at line 809 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractSHRT ( const Matrix44< T > & mat, Vec3< T > & s, Vec3< T > & h, Euler< T > & r, Vec3< T > & t, bool exc = `true` )\n\nExtract the scaling, shear, rotation, and translation components of the given 4x4 matrix.\n\nParameters\n [in] mat The input matrix [out] s The extracted scale [out] h The extracted shear [out] r The extracted rotation, in Euler angles [out] t The extracted translation [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the values could be extracted, false if the matrix is degenerate.\n\nDefinition at line 816 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool extractSHRT ( const Matrix33< T > & mat, Vec2< T > & s, T & h, T & r, Vec2< T > & t, bool exc = `true` )\n\nExtract the scaling, shear, rotation, and translation components of the given 3x3 matrix. The values are such that:\n\n```M = S * H * R * T\n```\nParameters\n [in] mat The input matrix [out] s The extracted scale [out] h The extracted shear [out] r The extracted rotation [out] t The extracted translation [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the values could be extracted, false if the matrix is degenerate.\n\nDefinition at line 1311 of file ImathMatrixAlgo.h.\n\ntemplate<typename T >\n void jacobiEigenSolver ( Matrix33< T > & A, Vec3< T > & S, Matrix33< T > & V, const T tol )\n\nCompute the eigenvalues (S) and the eigenvectors (V) of a real symmetric matrix using Jacobi transformation, using a given tolerance `tol`.\n\nJacobi transformation of a 3x3/4x4 matrix A outputs S and V: A = V * S * V^T where V is orthonormal and S is the diagonal matrix of eigenvalues. Input matrix A must be symmetric. A is also modified during the computation so that upper diagonal entries of A become zero.\n\ntemplate<typename T >\n void jacobiEigenSolver ( Matrix33< T > & A, Vec3< T > & S, Matrix33< T > & V )\ninline\n\nCompute the eigenvalues (S) and the eigenvectors (V) of a real symmetric matrix using Jacobi transformation.\n\nJacobi transformation of a 3x3/4x4 matrix A outputs S and V: A = V * S * V^T where V is orthonormal and S is the diagonal matrix of eigenvalues. Input matrix A must be symmetric. A is also modified during the computation so that upper diagonal entries of A become zero.\n\nDefinition at line 1474 of file ImathMatrixAlgo.h.\n\ntemplate<typename T >\n void jacobiEigenSolver ( Matrix44< T > & A, Vec4< T > & S, Matrix44< T > & V, const T tol )\n\nCompute the eigenvalues (S) and the eigenvectors (V) of a real symmetric matrix using Jacobi transformation, using a given tolerance `tol`.\n\nJacobi transformation of a 3x3/4x4 matrix A outputs S and V: A = V * S * V^T where V is orthonormal and S is the diagonal matrix of eigenvalues. Input matrix A must be symmetric. A is also modified during the computation so that upper diagonal entries of A become zero.\n\ntemplate<typename T >\n void jacobiEigenSolver ( Matrix44< T > & A, Vec4< T > & S, Matrix44< T > & V )\ninline\n\nCompute the eigenvalues (S) and the eigenvectors (V) of a real symmetric matrix using Jacobi transformation.\n\nJacobi transformation of a 3x3/4x4 matrix A outputs S and V: A = V * S * V^T where V is orthonormal and S is the diagonal matrix of eigenvalues. Input matrix A must be symmetric. A is also modified during the computation so that upper diagonal entries of A become zero.\n\nDefinition at line 1501 of file ImathMatrixAlgo.h.\n\ntemplate<typename T >\n void jacobiSVD ( const Matrix33< T > & A, Matrix33< T > & U, Vec3< T > & S, Matrix33< T > & V, const T tol = `std::numeric_limits< T >::epsilon()`, const bool forcePositiveDeterminant = `false` )\n\nCompute the SVD of a 3x3 matrix using Jacobi transformations. This method should be quite accurate (competitive with LAPACK) even for poorly conditioned matrices, and because it has been written specifically for the 3x3/4x4 case it is much faster than calling out to LAPACK.\n\nThe SVD of a 3x3/4x4 matrix A is defined as follows: A = U * S * V^T where S is the diagonal matrix of singular values and both U and V are orthonormal. By convention, the entries S are all positive and sorted from the largest to the smallest. However, some uses of this function may require that the matrix U*V^T have positive determinant; in this case, we may make the smallest singular value negative to ensure that this is satisfied.\n\nCurrently only available for single- and double-precision matrices.\n\ntemplate<typename T >\n void jacobiSVD ( const Matrix44< T > & A, Matrix44< T > & U, Vec4< T > & S, Matrix44< T > & V, const T tol = `std::numeric_limits< T >::epsilon()`, const bool forcePositiveDeterminant = `false` )\n\nCompute the SVD of a 3x3 matrix using Jacobi transformations. This method should be quite accurate (competitive with LAPACK) even for poorly conditioned matrices, and because it has been written specifically for the 3x3/4x4 case it is much faster than calling out to LAPACK.\n\nThe SVD of a 3x3/4x4 matrix A is defined as follows: A = U * S * V^T where S is the diagonal matrix of singular values and both U and V are orthonormal. By convention, the entries S are all positive and sorted from the largest to the smallest. However, some uses of this function may require that the matrix U*V^T have positive determinant; in this case, we may make the smallest singular value negative to ensure that this is satisfied.\n\nCurrently only available for single- and double-precision matrices.\n\ntemplate<typename TM , typename TV >\n void maxEigenVector ( TM & A, TV & S )\n\nCompute a eigenvector corresponding to the abs max eigenvalue of a real symmetric matrix using Jacobi transformation.\n\ntemplate<typename TM , typename TV >\n void minEigenVector ( TM & A, TV & S )\n\nCompute a eigenvector corresponding to the abs min eigenvalue of a real symmetric matrix using Jacobi transformation.\n\ntemplate<class T >\n Matrix44< T > outerProduct ( const Vec4< T > & a, const Vec4< T > & b )\n\nReturn the 4x4 outer product two 4-vectors.\n\nDefinition at line 847 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n Matrix33< T > outerProduct ( const Vec3< T > & a, const Vec3< T > & b )\n\nReturn the 3xe outer product two 3-vectors.\n\nDefinition at line 1349 of file ImathMatrixAlgo.h.\n\ntemplate<typename T >\n M44d procrustesRotationAndTranslation ( const Vec3< T > * A, const Vec3< T > * B, const T * weights, const size_t numPoints, const bool doScaling = `false` )\n\nComputes the translation and rotation that brings the 'from' points as close as possible to the 'to' points under the Frobenius norm. To be more specific, let x be the matrix of 'from' points and y be the matrix of 'to' points, we want to find the matrix A of the form [ R t ] [ 0 1 ] that minimizes || (A*x - y)^T * W * (A*x - y) ||_F If doScaling is true, then a uniform scale is allowed also.\n\nParameters\n A From points B To points weights Per-point weights numPoints The number of points in `A`, `B`, and `weights` (must be equal) doScaling If true, include a scaling transformation\nReturns\nThe procrustes transformation\ntemplate<typename T >\n M44d procrustesRotationAndTranslation ( const Vec3< T > * A, const Vec3< T > * B, const size_t numPoints, const bool doScaling = `false` )\n\nComputes the translation and rotation that brings the 'from' points as close as possible to the 'to' points under the Frobenius norm. To be more specific, let x be the matrix of 'from' points and y be the matrix of 'to' points, we want to find the matrix A of the form [ R t ] [ 0 1 ] that minimizes || (A*x - y)^T * W * (A*x - y) ||_F If doScaling is true, then a uniform scale is allowed also.\n\nParameters\n A From points B To points numPoints The number of points in `A` and `B` (must be equal) doScaling If true, include a scaling transformation\nReturns\nThe procrustes transformation\ntemplate<class T >\n bool removeScaling ( Matrix44< T > & mat, bool exc = `true` )\n\nRemove scaling from the given 4x4 matrix in place. Return true if the scale could be successfully extracted, false if the matrix is degenerate.\n\nParameters\n [in] mat The matrix to operate on [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 453 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool removeScaling ( Matrix33< T > & mat, bool exc = `true` )\n\nRemove scaling from the given 3x3 matrix in place. Return true if the scale could be successfully extracted, false if the matrix is degenerate.\n\nParameters\n [in] mat The matrix to operate on [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 1123 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool removeScalingAndShear ( Matrix44< T > & mat, bool exc = `true` )\n\nRemove scaling and shear from the given 4x4 matrix in place.\n\nParameters\n [in,out] mat The matrix to operate on [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 510 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n bool removeScalingAndShear ( Matrix33< T > & mat, bool exc = `true` )\n\nRemove scaling and shear from the given 3x3e matrix in place.\n\nParameters\n [in,out] mat The matrix to operate on [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\nReturns\nTrue if the scale could be extracted, false if the matrix is degenerate.\n\nDefinition at line 1169 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n Matrix44< T > rotationMatrix ( const Vec3< T > & fromDirection, const Vec3< T > & toDirection )\n\nReturn a 4x4 matrix that rotates the vector `fromDirection` to `toDirection`\n\nDefinition at line 869 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n Matrix44< T > rotationMatrixWithUpDir ( const Vec3< T > & fromDir, const Vec3< T > & toDir, const Vec3< T > & upDir )\n\nReturn a 4x4 matrix that rotates the `fromDir` vector so that it points towards `toDir1. You may also specify that you want the up vector to be pointing in a certain direction 1upDir`.\n\nDefinition at line 878 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n Matrix44< T > sansScaling ( const Matrix44< T > & mat, bool exc = `true` )\n\nReturn the given 4x4 matrix with scaling removed.\n\nParameters\n [in] mat The input matrix [in] exc If true, throw an exception if the scaling in `mat`\n\nDefinition at line 432 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n Matrix33< T > sansScaling ( const Matrix33< T > & mat, bool exc = `true` )\n\nReturn the given 3x3 matrix with scaling removed.\n\nParameters\n [in] mat The input matrix [in] exc If true, throw an exception if the scaling in `mat`\n\nDefinition at line 1102 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n Matrix44< T > sansScalingAndShear ( const Matrix44< T > & mat, bool exc = `true` )\n\nReturn the given 4x4 matrix with scaling and shear removed.\n\nParameters\n [in] mat The input matrix [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\n\nDefinition at line 485 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n void sansScalingAndShear ( Matrix44< T > & result, const Matrix44< T > & mat, bool exc = `true` )\n\nExtract scaling and shear from the given 4x4 matrix in-place.\n\nParameters\n [in,out] result The output matrix [in] mat The return value if `result` is degenerate [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\n\nDefinition at line 499 of file ImathMatrixAlgo.h.\n\ntemplate<class T >\n Matrix33< T > sansScalingAndShear ( const Matrix33< T > & mat, bool exc = `true` )\n\nReturn the given 3x3 matrix with scaling and shear removed.\n\nParameters\n [in] mat The input matrix [in] exc If true, throw an exception if the scaling in `mat` is very close to zero.\n\nDefinition at line 1155 of file ImathMatrixAlgo.h.\n\n## Variable Documentation\n\n IMATH_EXPORT_CONST M22d identity22d\n\nM22d identity matrix.\n\nDefinition at line 37 of file ImathMatrixAlgo.h.\n\n IMATH_INTERNAL_NAMESPACE_HEADER_ENTER IMATH_EXPORT_CONST M22f identity22f\n\nM22f identity matrix.\n\nDefinition at line 31 of file ImathMatrixAlgo.h.\n\n IMATH_EXPORT_CONST M33d identity33d\n\nM33d identity matrix.\n\nDefinition at line 39 of file ImathMatrixAlgo.h.\n\n IMATH_EXPORT_CONST M33f identity33f\n\nM33f identity matrix.\n\nDefinition at line 33 of file ImathMatrixAlgo.h.\n\n IMATH_EXPORT_CONST M44d identity44d\n\nM44d identity matrix.\n\nDefinition at line 41 of file ImathMatrixAlgo.h.\n\n IMATH_EXPORT_CONST M44f identity44f\n\nM44f identity matrix.\n\nDefinition at line 35 of file ImathMatrixAlgo.h." ]

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[ "# Summary of correct responses\n\nHi guys! Sorry for so many answers and thank you,\n\nThe only thing I miss in Desmos, are things that could be easily implemented. The correctness mark that we teachers get in preview mode\n\nsometimes I would like the students to see it to have more feedback. I end up programming it using graph labels or subtitles which is time consuming and “ugly”.\n\nAlso it would be great to have the number of correct questions answered, for the student or the teacher.\n\nI am trying to program it but I got stuck in:\n\n``````number(\"g\"):\n\nwhen table4.cellContent(2,1)=\"✓\" numericValue(\"\\${graph1.number(\"g\")}+1\")\n\notherwise numericValue(\"\\${graph1.number(\"g\")}\")\n``````\n\nBecause it says there is circular dependecy. So it looks like the programming structure:\n\n``````variable=variable+1\n``````\n\nis not possible in here.\n\nI was thinking on creating a numberList and aggregate every correct answer and at the end check the numberList lenght. I don’t even know if it’s possible.\n\nWhat’s the purpose here? If you have an action button, you can use capture. Instead of your essentially `g=g+1` (which would infinitely increase by 1 because it doesn’t read through the code just once), you could have `g={last g captured} +1`.\n\nin most slides I don’t use buttons. I just program what is correct, and that’s it.\n\nThe last slide I wanted to be a summary of correct responses with the grade, so student can go back and correct whatever she/he wants. (Similar of what you get as a teacher)\n\nFor every question I check the answer and I write a check mark if it’s right or a x if it’s wrong. (That’s already done)\n\nThe question here is how I add all the correct answers from the table to get a grade. So my first intention was to define a variable in any of the graphs and just add one for every correct answer.\n\nThank you\n\nThis is the activity. It’s all finished, except that last slide where I wanted to summarize the student work:\n\nI would make variables for each answer (e.g. a1, a2, a3, a4). Then, use the same conditionals that you used for the table in slide 31, but instead of checkmark or X use 1 and 0. Create a total:\n\n`total=numericValue(\"\\${a1}+\\${a2}+\\${a3}+\\${a4}\")`\n\nUse this for g in your graph:\n`number(\"g\")=table4.script.total`\n\nThank you Daniel, I finally succeeded:\n\nCan you assign points to each slide and at the end have the final slide add up all the points with a final grade?", null, "Yes, that’s what I have been doing lately. The grade it’s at the beginning:\n\nWow! Looks great! Thank you for sharing. I plan to analyze your CL. I would like to be able to create some activities like yours. I’m hoping it will make my inputting grades easier. Thx", null, "again.\n\nThank you", null, "for sharing.\n\nI have a bunch done in different topics. Let me know which topic and I might have it.\n\nOh that is awesome! Do you have solving multi-step equations. Possibly with distributive property. Multiplying polynomials, simplifying exponents (using rules of exponents). Exponential equations and Finally factoring quadratics. I teach math 8 and Algebra 1. I would greatly appreciate it.\n\nThis is what I have. I will have power rules by the end of the week.\n\n2 Likes\n\nAWESOME! Thank you for sharing!\n\n1 Like\n\nHi Roger\nYour work is awesome! Thank you for sharing.\n\nHi Roger\n\nI really appreciate you sharing these activities with me. I see that you have done a lot of CL in your Desmos activities. I like that you incorporate a timer and multiple problems in one slide. To be honest that is truly way advanced for me. I would like something really simple to begin to understand. I like that you have a table with the problems that the students got correct and a final grade at the end. Could you, would you be willing to help me attach something like that to my Desmos activity? I would like for each slide that has a correct answer to be assigned 1 point. Then at the end, a grade after the assignment is done. I am attaching my most recent work.\n\nhttps://teacher.desmos.com/activitybuilder/custom/6058034aa4e2e40ca4fca177\n\nThanks again for all your help,\nClaudia Fuentes\n\nYou need something like this\n\nThank you! I will take a look at it.\n\nSorry Claudia I sent the wrong one!\n\nThis is the one working!" ]

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[ "# A Ray Of Light Passes From Air Right Into Water The Case Angle Is 30 Degrees. Locate The Index Of Refraction Of Water If The Angle Of Refraction Is 22 Degrees.", null, "It will certainly flex inwards a little, considering that this outside’s going to impend a bit longer, if you purchase right into my vehicle taking a trip right into the mud example. So it will certainly after that bend a bit. And also I want to figure out what this new angle will be.\n\n## What is the relation between critical angle and refractive index?\n\nThe ratio of velocities of a light ray in the air to the given medium is a refractive index. Thus, the relation between the critical angle and refractive index can be established as the Critical angle is inversely proportional to the refractive index.\n\nI’ll simply round a little bit. So I’ll get– I’ll change colors– 0.4314 is equal to sine of theta 2. And also now to fix for theta, you just have to take the inverse sine of both sides of this. This does not imply sine to the adverse 1.\n\nI want to find out the angle of refraction. I’ll call that theta 2. What is this? This is simply directly applying Snell’s regulation. And we understand what the refraction index for air and also for water is, and afterwards we just need to fix for theta 2. So allow’s just do that. The refraction index for air is this number right over here, 1.00029.\n\nI’m just separating by the numerator below. When you just separate this response, it suggests your last solution. That’s the numerator up right here separated by that . Therefore I get 0.4314.\n\nSo it’s mosting likely to be, there’s three 0’s, 1.00029 times the sine of 35 levels, is mosting likely to amount to the refraction index for water, which is 1.33. So it’s 1.33 times sine of theta 2. Currently we can divide both sides of this equation by 1.33. On this side, we’re simply left with the sine of theta 2. On the left-hand side, let’s get our calculator out for this. So let me get the convenient calculator.", null, "As guaranteed, allow’s do a number of easy Snell’s regulation instances. So allow’s state, that I have two media– I presume the plural of mediums. So let’s claim I have air right below. And after that right below is the surface area. Allow me do that in a more appropriate shade. That is the surface area of the water.\n\n## What is the value of angle of minimum deviation?\n\nYou will see that there is a minimum angle of deviation, about 37.2 degrees. If you drag the prism either direction from orientation that gives this minimum deviation, you find that the deviation is quite insensitive to the change. That is just a familiar fact of calculus: at a minimum, the derivative is zero.\n\nAs well as I know that I have a light ray, can be found in with an occurrence angle of– so about the vertical– 35 levels. As well as what I wish to know is what the angle of refraction will be. So it will certainly refract a little.\n\n## When light passes from air into water at an angle of 30 from the normal What is the angle of refraction?\n\nThe unknown in this problem is Θ2 , which should be isolated. Since 30o only contains 2 significant digits, the answer needs to be rounded to 2 significant digits, which means the angle of refraction in air is 42o ." ]

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", null, 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null ]

[ "LINEAR INTEGRAL EQUATIONS KANWAL PDF\n\nOriginally published in , Linear Integral Equations is ideal as a text for a beginning graduate level course. Its treatment of boundary value. Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems. Linear integral equations: theory and technique. Front Cover. Ram P. Kanwal. Academic Press INTEGRAL EQUATIONS WITH SEPARABLE. 4. METHOD OF .", null, "Author: Arashicage Arashijin Country: Zambia Language: English (Spanish) Genre: Career Published (Last): 24 May 2006 Pages: 349 PDF File Size: 15.68 Mb ePub File Size: 10.94 Mb ISBN: 691-9-45763-956-1 Downloads: 3134 Price: Free* [*Free Regsitration Required] Uploader: Meztishicage", null, "The chapters dealing with differential equations and singular integral equations have been expanded considerably.\n\nShopbop Designer Fashion Brands. Among the applications addressed are electrostatics pp. Common terms and phrases 2-function 2-kernel algebraic system analysis approximation arbitrary axially symmetric boundary condition boundary value problem Cauchy Cauchy principal value chapter circular disk coefficients complete constant converges defined denote derivative differential equation Dirichlet problem eigenfunctions eigenvalue electrostatic evaluate Examples Example finite follows Fourier Fredholm integral equation function f s given grad Green’s function Hilbert Hilbert-Schmidt theorem homogeneous equation identity infinite inhomogeneous initial value problem integral equation g s integral representation formula inverse iterated kernels kernel K s Km s Laplace transform linear linearly independent method Neumann problem obtain order ilnear integration orthogonal orthonormal system potential preceding proved radius relation resolvent kernel result satisfies second kind Section 6.\n\nFourier and Laplace transforms, pp. I wish to thank Professor B. Many physical problems that are usually lniear by differential equation methods can be solved more effectively by integral equation methods.\n\nCATALOGO BURNDY 2012 PDF", null, "Most helpful customer reviews on Amazon. From inside the book.", null, "Last but not least, I am grateful to the editor and kanwsl of Birkhauser for inviting me to prepare this new edition and for their support in preparing it for publication.\n\nSee our Returns Policy.\n\nIts treatment of boundary value problems and an extended and up-to-date bibliography will also make the book useful to research workers in many applied fields.\n\nContents Integral Equations with Separable Kernels.\n\nLinear Integral Equations: Theory & Technique – Ram P. Kanwal – Google Books\n\nKanwal Snippet view – Share your thoughts with other customers. Be the first to review this item Amazon Bestsellers Rank: If you are a seller for this product, would you like to suggest updates through seller support? Read more Read less.\n\nThis second edition of Linear Integral Equations continues the emphasis that the first edition placed kansal applications. Thus the book is ideal as a text for a beginning graduate level course. Its excellent treatment of boundary value problems and an equtaions bibliography make the book equally useful for researchers in many applied fields.\n\nLinear integral equations: theory and technique – Ram P. Kanwal – Google Books\n\nHere’s how terms and conditions apply. Significant new material has been added in Chapters 6 and 8. Theory and Technique Ram P. Visit our Help Euqations. Integral Equations with Separable Kernels. Indeed, many more examples have been added throughout the text. Audible Download Audio Books. Account Options Sign in.\n\nEM HAUPTKURS PDF\n\nFor instance, in Chapter 8 we have included the solutions of the Cauchy type integral equations on the real equatons. Such problems abound in applied mathematics, theoretical mechanics, and mathematical physics.\n\nAmazon Prime Music Stream millions of songs, ad-free. Definition An integral equation is an equation in which an unknown function appears under one or more integral signs Naturally, in such an equation there can occur other terms as well.\n\nReview “A nice introductory text Presents the basics of linear integral equations theory in a very comprehensive way Customers who viewed this item also viewed.", null, "The second edition of this widely used book continues the emphasis on applications and presents a variety of techniques with extensive examples. See all free Kindle reading apps. Linear Integral Equations Ram P. Cashback will be credited as Amazon Pay balance within 10 days.\n\nWould you like to tell us about a lower price? Method Of Successive Approximations. Eqquations this page volume, the author presents the reader with a number of methods for solving linear integral equations, which are often discussed within the context of Fredholm janwal using matrix, integral transforms e." ]

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[ "This one will be a quick post. In effect, we continue with last time, where we defined the relative homotopy groups, and now describe a practical means of determining when something in one of these relative groups is zero or not. This will become useful in the future.\n\nThe compression criterion\n\nWe have defined the group", null, "${\\pi_n(X, A)}$ above, but we still need a good criterion for knowing when something in", null, "${\\pi_n(X, A)}$, represented by", null, "${f: (D^n, S^{n-1}) \\rightarrow (X, A)}$ , is zero. Or, when", null, "${n = 1}$, when it represents the base element. The obvious reason is that if there is a homotopy", null, "${H: (D^n, S^{n-1}) \\times I \\rightarrow (X, A)}$ starting with", null, "${f}$ and ending at the constant map. Here is another that will be useful.\n\nTheorem 1 (Compression criterion) A map", null, "${f: (D^n, S^{n-1}) \\rightarrow (X, A)}$ represents zero in", null, "${\\pi_n(X, A)}$ if and only if", null, "${f}$ is homotopic relative", null, "${S^{n-1}}$ to a map", null, "${g: D^n \\rightarrow A}$.\n\nProof: This is one of those things which is not really all that hard to prove, but for which pictures help significantly. So I will try to draw pictures. (more…)\n\nToday, we will define relative versions of the homotopy groups, and show that they fit into an exact sequence. So let", null, "${X}$ be a pointed space and", null, "${A \\subset X}$ a subspace containing the basepoint. Let", null, "${n \\geq 1}$. Then we define", null, "$\\displaystyle \\pi_n(X, A)$\n\nto be the pointed homotopy class of maps", null, "${(D^n, S^{n-1}) \\rightarrow (X, A)}$. Here", null, "${D^n}$ has a basepoint, which is located on the boundary", null, "${S^{n-1}}$.\n\nDefinition 1", null, "${\\pi_n(X, A)}$ is called the", null, "${n}$-th relative homotopy group of the pair", null, "${(X, A)}$. (We have not yet shown that it is a group.)\n\nAnother perhaps more geometric way of thinking of the relative homotopy groups is as follows. Namely, it is the homotopy class of maps", null, "${(I^n, I^{n-1}, J^n) \\rightarrow (X, A, x_0)}$, where", null, "${I^n}$ is the", null, "${n}$-cube and", null, "${J^n}$ is the complement of the front face", null, "${I^{n-1}}$. So on the boundary, such a map is", null, "${x_0}$ except possibly on the front face, where it is at least in", null, "${A}$. The reason is that if we quotient by", null, "${J^{n-1}}$, we get the pair", null, "${(D^n, S^{n-1})}$. (more…)\n\nThe Whitehead theorem states that a map of connected CW complexes that induces an isomorphism in homotopy groups is a homotopy equivalence. In particular, isomorphisms in the homotopy category of pointed CW complexes can be detected by homming out of spheres", null, "$S^n$. But the equality of two morphisms cannot. The fact that this “relative Whitehead theorem” fails was the subject of a MO question. Today, I want to discuss another example along these lines. (I will assume a little more familiarity with algebraic topology than I have in previous posts.)\n\nRecall that a common technique to show that a map is not nullhomotopic is to show that it does not induce the trivial morphism on some functor in algebraic topology. For instance, the fact that", null, "${\\pi_1(S^1) \\neq 0}$ is used to show that", null, "${S^1}$ is not contractible; this is probably the most basic example. But the basic invariants of algebraic topology can be insufficient. Here is an example which Eric Larson showed me yesterday.\n(more…)\n\nLast time, we defined two functors", null, "${\\Omega}$ and", null, "${\\Sigma}$ on the category", null, "${\\mathbf{PT}}$ of pointed topological spaces and (base-point preserving) homotopy classes of base-point preserving continuous maps. We showed that they were adjoint, i.e. that there was a natural isomorphism", null, "$\\displaystyle \\hom_{\\mathbf{PT}}(X, \\Omega Y) \\simeq \\hom_{\\mathbf{PT}}(\\Sigma X, Y).$\n\nWe also showed that", null, "${\\Omega Y}$ is naturally an H group, i.e. a group object in", null, "${\\mathbf{PT}}$, for any", null, "${Y}$. So, given that we have a group operation", null, "${\\Omega Y \\times \\Omega Y \\rightarrow \\Omega Y}$, it follows that", null, "${\\hom_{\\mathbf{PT}}(X, \\Omega Y)}$ is naturally a group for each", null, "${Y}$. (more…)" ]

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[ "## Class 11 Maths Exercise 3.3 Introduction (Part 1)\n\nClass 11 Maths Chapter 3 Exercise 3.3 Introduction (Part 1) Explanation In this video I have taught Trigonometric Functions Chapter 3 Exercise 3.3 Introduction of class 11 Maths NCERT.   Class 11 Maths (All Chapters) https://www.youtube.com/MathsTeacher/playlists Website (official) https://www.mathsteacher.blog Mail-id (Official) mathsteacher.blog Instagram (Official) https://www.instagram.com/mathsteacher.blog Facebook (Official) https://www.facebook.com/mathsteacher01 #TrigonometricFunctionsClass11 #MathsTeacher About MathsTeacher: In this channel […]\n\n## Class 11 Exercise 3.3 Introduction\n\nClass 11 Ex 3.3 Intro (Part 1) Chapter 3 Trigonometric Functions NCERT Maths For more videos, click here\n\n## Class 11 Exercise 3.2 Introduction\n\nClass 11 Ex 3.2 Introduction Chapter 3 Trigonometric Functions NCERT Maths Class 11 Maths NCERT Solutions Chapter 3  is devised accurately as per the latest CBSE syllabus introduced. The Trigonometry Class 11 in Chapter 3 of the syllabus comprises of step by step shortcut techniques. Our study material is available for free for all the […]\n\n## Class 11 Trigonometric Functions Ex 3.1 Q5 Q6 and Q7 NCERT Maths\n\nClass 11 Ex 3.1 (Q5, Q6, Q7) Chapter 3 Trigonometric Functions NCERT Maths Question 5: In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord Question 6: If in two circles, arcs of the same length subtend angles 60° and 75° […]\n\n## Class 11 Ex 3.1 Q3 and Q4 Chapter 3 NCERT Maths\n\nClass 11 Ex 3.1 (Q3, Q4) Chapter 3 Trigonometric Functions NCERT Maths Question 3: A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second? Question 4: Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc […]\n\n## Class 11 Ex 3.1 Q1 and Q2\n\nClass 11 Ex 3.1 (Q1, Q2) Chapter 3 Trigonometric Functions NCERT Maths Question 1: Find the radian measures corresponding to the following degree measures: (i) 25° (ii) – 47°30′ (iii) 240° (iv) 520° Question 2: Find the degree measures corresponding to the following radian measures Use π=22/7. (i) 11/16 (ii) -4 (iii) 5π/3 (iv) 7π/6 […]\n\n## Class 11 Exercise 3.1 Introduction\n\nClass 11 Ex 3.1 Introduction Chapter 3 Trigonometric Functions NCERT Maths Class 11 Maths (All Chapters): https://www.youtube.com/MathsTeacher/playlistsWebsite (official) – https://www.mathsteacher.blogMail-id (Official) – [email protected] (Official) – https://www.instagram.com/mathsteacher.blogFacebook (Official) – https://www.facebook.com/mathsteacher01 #TrigonometricFunctionsClass11 #MathsTeacher" ]

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[ "# Stiff delay equations\n\nPost-publication activity\n\nCurator: Nicola Guglielmi\n\nA system of delay differential equations in a quite general form is given by $\\tag{1} \\left\\{ \\begin{array}{rcl} M \\dot{y}(t) & = & f\\Big(t,y(t), y \\big( \\alpha(t,y(t)) \\big) \\Big), \\quad t_{0} \\leq t\\leq t_f \\\\ y(t) & = & \\phi(t), \\quad t < t_{0}, \\qquad y(t_0) = y_0 \\end{array} \\right.$\n\nwhere $$y(t) \\in \\R^d\\ ,$$ $$M$$ is a constant square matrix, $$f$$ a real vector function, $$\\phi$$ a given initial function, and $$y_0$$ a given initial vector. The deviating argument $$\\alpha(t,y(t))$$ is assumed to be bounded above by $$t\\ .$$ The corresponding delay is given by the non-negative function $$\\tau (t,y(t))= t - \\alpha(t,y(t)).$$ All statements of this article extend to the case of several deviating arguments. If the matrix $$M$$ is the identity then the problem is said to be explicit (see Delay Differential Equations), while in all the other cases is said to be in implicit form.\n\nAs for ordinary differential equations (see Stiff Systems) a rigorous mathematical definition of stiffness is not possible. Stiffness is characterized by phenomena such as: strong contractivity of neighbouring solutions, multiple time scales (fast transient phases) and the fact that explicit numerical integrators are not able to reproduce a correct approximation of the solution in an efficient way. A general reference for the numerical treatment of delay equations (including stiff problems) is the book by Bellen and Zennaro (2003), and for stiff ordinary differential equations is the book by Hairer & Wanner (1996).\n\n## Stability of linear delay equations\n\nMuch insight can be gained by considering linear delay equations with constant delay, whose exact solution is well understood.\n\n#### The scalar case\n\nIt is common to start by studying the scalar equation $\\tag{2} \\dot y (t) = a y(t) + b y(t-1) ,$\n\nwhere $$a$$ and $$b$$ are real (or complex) numbers. Without loss of generality the delay can be assumed to be $$\\tau = 1\\ ,$$ because any constant delay can be reduced to it by a linear time transformation. Searching for solutions of the form $$y(t)=c e^{\\lambda t}\\ ,$$ one is lead to the characteristic equation $\\tag{3} \\lambda -a -b \\, e^{-\\lambda} = 0 ,$\n\nwhich for $$b\\ne 0$$ possesses infinitely many solutions. The general solution is then obtained as a sum of such exponentials. The zeros of (3) are plotted in the left picture of Figure 2 for the case $$(a,b)=(0.5,-1)\\ .$$ Notice that they all lie in the left half-plane, so that the solution will tend to zero for $$t\\to\\infty$$ (despite a positive $$a$$).\n\nThe white region in the right picture of Figure 2 shows the values of real pairs $$(a,b)$$ for which all solutions of the delay equation tend to zero. The shaded regions correspond to pairs, where the characteristic equation has zeros with positive real part (increasing darkness indicates an increasing number of unstable modes), so that solutions are unstable. The boundary of the stability domain can be obtained by the root locus technique: put $$\\lambda = i\\theta$$ with real $$\\theta\\ ,$$ and solve the characteristic equation for $$(a,b)\\ .$$\n\nEquation (2) gives the simplest prototype of stiff problem for large values of $$a<0$$ and $$b\\ ,$$ but also for $$(a,b)$$-pairs close to lower boundary of the stability region (white set in the right picture of Figure 2). The stability restrictions associated to a numerical integration by means of forward Euler method are illustrated in Figure 3.\n\n#### Linear systems\n\nThe stability of a linear system of delay equations $\\tag{4} \\dot y (t) = A y(t) + B y(t-1) ,$\n\n(with square matrices $$A$$ and $$B$$) can be analyzed in a similar way. Setting $$I$$ the identity matrix, the characteristic equation has just to be replaced by $${\\rm det}\\,\\Big( \\lambda I - A - B\\,e^{-\\lambda} \\Big) = 0\\ .$$ The main difficulty here is that in general the matrices $$A$$ and $$B$$ do not commute, so that they cannot be transformed simultaneously to a simple (diagonal) form. This is in contrast to the situation of linear ordinary differential equations.\n\nSuitable algorithms for the numerical computation of the characteristic roots of a linear system have been developed recently (see e.g. Engelborghs and Roose, 2002 and Breda, Maset and Vermiglio, 2004).\n\nSuch linear systems of delay equations, when the solution is stable and the matrices $$A$$ and/or $$B$$ contain elements of large modulus, are the first candidates of stiff delay equations. They can arise in the space discretization of partial delay differential evolution equations (see e.g Wu, 1996 and van der Houwen, Sommeijer and Baker, 1986).\n\n## Further examples of stiff delay equations\n\nAll situations that can be simulated by stiff ordinary differential equations will sooner or later also lead to the consideration of stiff delay equations (delayed phenomena are often present in the physical problem, but their simulation is suppressed to keep the model as simple as possible).\n\n#### Singularly perturbed problems\n\nAn important class of stiff problems are equations in singularly perturbed form: $\\begin{array}{rcl} \\dot y (t) &=& f\\Big( y(t),z(t),y(\\alpha (t)),z(\\alpha (t))\\Big) \\\\ \\varepsilon\\,\\dot z (t) &=& g\\Big( y(t),z(t),y(\\alpha (t)),z(\\alpha (t))\\Big) \\end{array}$ where $$0<\\varepsilon \\ll 1$$ is a positive, very small parameter, and the derivative of $$g$$ with respect to the $$z$$ variables is such that the solutions are stable when $$\\varepsilon\\to 0\\ .$$ Of course, $$\\alpha (t)$$ can be replaced by a state-dependent delay. This system is of the from (1) with a matrix $$M={\\rm diag}(I,\\varepsilon I)\\ .$$\n\n#### Differential algebraic equations\n\nPutting formally $$\\varepsilon =0$$ in the above singularly perturbed problem, one obtains a delay differential equation coupled with a delay algebraic equation. It is in some sense infinitely stiff. The system is still of the form (1), but the matrix $$M$$ is singular. Any system (1) with singular matrix $$M$$ is called a delay differential algebraic equation. In the absence of delayed terms (see Hairer and Wanner, 1996) such systems are well understood, and they are classified in terms of the index. Most of these results carry over to our situation as long as the delay is bounded away from zero. Applications to control theory are discussed in (Shampine and Gahinet, 2006).\n\n#### Neutral problems\n\nIf the right-hand side of a delay equation also depends on the derivative of the solution, it is called neutral. A typical problem is $\\dot y (t) = f\\Big( y(t),y(\\alpha (t)),\\dot y (\\alpha (t))\\Big) .$ Introducing $$z(t)=\\dot y(t)$$ as new variable, this neutral equation is seen to be equivalent to the system $\\begin{array}{rcl} \\dot y (t) &=& z(t) \\\\ 0 &=& f\\Big( y(t),y(\\alpha (t)),z(\\alpha (t))\\Big) - z(t) , \\end{array}$ which is a differential algebraic delay equation with matrix $$M={\\rm diag}(I,0)\\ .$$\n\nExample. Consider the neutral equation analyzed in (Enright and Hayashi, 1997) and (Castleton and Grimm, 1973) $\\tag{5} \\begin{array}{rcl} \\dot y (t) &=& z(t) \\\\ 0 &=& \\cos{(t)} \\Big( 1 + y( t y(t)^2 ) + 0.6 y(t) z( t y(t)^2 )\\Big) - z(t), \\end{array}$\n\nwith initial function $$y(t)=-t/2$$ and $$z(t)=-1/2$$ for $$t \\le 0.25\\ .$$ Notice that at $$t=4.09...$$ a classical solution ceases to exist.\n\nThe component $$z(t)$$ is plotted in Figure 1. The blue and red circles indicate simultaneously the values of $$z(t)$$ and $$z( t y(t)^2 )\\ ,$$ respectively.\n\n## Breaking points\n\nDiscontinuities may occur in various orders of the derivative of the solution, independently of the regularity of the right hand side. In fact, if either $$y_0 \\ne \\phi(t_0)$$ or some right-hand derivative of the solution at $$t_0$$ is different from the corresponding left-hand derivative the discontinuity at $$t_0$$ may propagate along the integration interval by means of the deviating argument $$\\alpha(t,y(t))\\ .$$ Evidently, as soon as $$\\alpha(\\xi,y(\\xi)) = t_0$$ for some $$\\xi \\ge t_0\\ ,$$ due to the fact that $$y$$ is not regular at $$t_0\\ ,$$ $$f\\Big(t,y(t),y\\big( \\alpha (t,y(t))\\big) \\Big)$$ is not smooth at $$\\xi\\ .$$ Such discontinuity points are referred in the literature as breaking points (see for example Bellen and Zennaro, 2003 and Baker, Paul and Willé, 1995).\n\n#### Determination of breaking points\n\nIf the deviating arguments do not depend on the solution itself, that is $$\\alpha = \\alpha(t)\\ ,$$ such points may be computed and possibly inserted in advance into a mesh of integration. This allows for decomposing the Cauchy problem (1) into a finite (if the number of breaking points is finite) sequence of regular problems. But in the general state-dependent case this computation is not possible and one has to deal with a truly non-smooth problem.\n\n#### Termination and bifurcation\n\nIf some component of the solution $$y$$ has a jump discontinuity at some breaking point $$\\zeta\\ ,$$ the right hand side of (1) can be discontinuous at $$t = \\xi$$ as soon as $$\\alpha(\\xi,y(\\xi)) = \\zeta\\ .$$ Usually, a classical solution will continue to exist, but when the delay depends on the solution $$y(t)$$ is might either cease to exist (termination) or lose the uniqueness (bifurcation). The loss of uniqueness is not generic. Detecting automatically the occurrence of these situations is an important prerogative of a numerical code and should be a by-product of an accurate computation of breaking points (c.f., Guglielmi and Hairer, 2007).\n\n## Numerical stability of simple integrators\n\nNumerical phenomena that can be observed in solving stiff ordinary differential equations (see e.g., Hairer and Wanner, 1996), are also relevant for stiff delay equations. We concentrate here on aspects that are particular to delay equations.\n\n#### Stability domains\n\nLet us apply the explicit Euler discretization to the scalar test equation (2) with a step size $$h=1/m\\ ,$$ so that the delay $$\\tau =1$$ is an integral multiple of the step size. This yields the recursion $y_{n+1} = y_n + h\\Big(a y_n + b y_{n-m}\\Big) .$ To study its stability one looks for solutions of the form $$y_n=\\zeta^n\\ ,$$ and so obtains the characteristic equation $\\zeta^{m+1} = \\zeta^m \\Big( 1+ \\frac am \\Big)+ \\frac bm .$ This polynomial equation has $$m+1$$ solutions which are related to the dominant roots of (3) via $$\\zeta =e^{\\lambda /m}\\ .$$ If all of them lie inside the unit disc, a stable numerical solution is obtained. The set of real pairs $$(a,b)\\ ,$$ for which the numerical solution is stable, is called the stability region of the method. It is plotted for $$m=2,3,4,5$$ as a red shaded region in Figure 3. For increasing $$m\\ ,$$ the stability region becomes larger and asymptotically tends to the set of pairs for which the analytic solution is stable (white region in the right picture of Figure 2). Notice that there exist pairs $$(a,b)$$ (with $$a$$ not necessarily large and negative), so that the numerical solution solution diverges but the analytic solution is stable.\n\nA similar analysis can be done for other numerical methods. It is interesting to note that the implicit Euler method, the mid-point rule and the trapezoidal rule have the property that whenever the analytic solution of (2) is stable, also the numerical solution is stable for every integer $$m\\ ,$$ see Guglielmi (1998).\n\nAnother interesting topic, which is not discussed here for the sake of conciseness, is the stability behavior of numerical integrators applied to neutral delay differential equations (the reader is referred e.g. to Bellen, Jackiewicz and Zennaro (1988), Koto (1996) and Guglielmi (2001)).\n\n#### One-sided Lipschitz conditions\n\nFor linear systems, the stability analysis is rather involved. It is therefore common to restrict the class of problems (4) to matrices satisfying $\\tag{6} \\mu (A) + \\| B \\| \\le 0 ,$\n\nwhere $$\\mu (A) = \\sup \\{ \\langle v,Av\\rangle ; \\| v\\| =1 \\}$$ is the logarithmic norm and $$\\| B\\| = \\sup \\{ \\| Bv\\| ; \\| v\\| =1 \\}$$ the matrix norm corresponding to a scalar product. This condition implies stability of the analytic solution, even when the lag-term $$y(t-1)$$ is replaced by $$y(t-\\tau )$$ with an arbitrary non-negative $$\\tau\\ .$$ This is the reason why a stability analysis based on this condition is often called stability for all delays or delay-independent stability. For the scalar case, this restriction corresponds to the sector $$|b|\\le -a$$ which covers a large part of the analytic stability region (Fig.Figure 2). The implicit Euler method, the trapezoidal rule, and the mid-point rule produce stable numerical solutions when applied to linear systems of delay equations satisfying (6).\n\nFor an analysis of the stability properties of A-stable methods under condition (6) the reader is referred to (Zennaro, 1986), (Koto, 1994) and to (Bellen and Zennaro, 2003).\n\n## Stiff integrators\n\nA natural approach consists in suitably extending stiff integrators for ordinary differential equations (ODEs) to delay differential equations (DDEs).\n\n#### Implicit Runge-Kutta methods (Radau IIA)\n\nLet us explain such an extension for the example of a stiffly-accurate $$s$$-stage implicit Runge-Kutta method with abscissae $$\\{c_{i} \\}$$ and coefficients $$\\{a_{ij} \\}\\ .$$ Using the step size $$h_{n}=t_{n+1}-t_{n}$$ and an approximation $$y_n$$ to the solution at time $$t_n\\ ,$$ one step of the method is given by $\\tag{7} M \\left( Y_i^{(n)} - y_n \\right) \\, = \\, h_{n}\\sum_{j=1}^{s} a_{ij} f \\Big( t_n+c_j h_n, Y_j^{(n)}, Z_{j}^{(n)} \\Big), \\qquad i=1,\\ldots ,s$\n\nwhere $$Z_{j}^{(n)}$$ has to approximate $$y\\Big( \\alpha (t,y(t))\\Big)$$ at $$t=t_n+c_j h_n$$ and $$y_{n+1} = Y_s^{(n)}$$ approximates the solution at time $$t_{n+1}\\ .$$\n\nFor ordinary differential equations, where $$f$$ only depends on $$t,y\\ ,$$ this represents a nonlinear system for the internal stage values $$\\{ Y_i^{(n)} \\}\\ .$$ For delay equations instead, it is necessary to define $$Z_{j}^{(n)}\\ .$$ Setting $$\\alpha_{j}^{(n)} = \\alpha(t_{n} + c_{j}\\,h_{n}, Y_{j}^{(n)})\\ ,$$ it is usual to put $$Z_{j}^{(n)} = \\phi \\left( \\alpha_{j}^{(n)} \\right)$$ if $$\\alpha_{j}^{(n)} < t_{0}$$ and $\\tag{8} Z_{j}^{(n)} = u_m \\left( \\alpha_{j}^{(n)} \\right) \\qquad \\mbox{if } \\quad t_{m} \\le \\alpha_{j}^{(n)} < t_{m+1} \\quad \\mbox{for some } \\ 0\\le m\\le n,$\n\nwhere $$u_m(t)$$ is a continuous extension of the solution computed at the $$m$$-th step (which is available for $$t_m \\le t \\le t_{m+1}$$). For a collocation method, $$u_m(t)$$ can be the Lagrange polynomial interpolating the $$s+1$$ pairs $$(t_m,y_m)$$ and $$\\{ (t_m + c_j h_m, Y_j^{(m)} ) \\}_{j=1}^{s}\\ .$$\n\nOn a general mesh, due to the dependence of the right hand side on the dense output, the order of convergence is usually reduced with respect to the case of ODEs. But on specially constrained meshes it is possible to preserve the classical order (see Bellen, 1984).\n\nStability. An analysis of Runge-Kutta methods applied to (2) with a step size $$h=1/m$$ shows that Gauss methods and Radau IIA methods of any order are stable for all $$m$$ (see Guglielmi and Hairer, 1999). This means that they preserve the correct asymptotic vanishing behavior of the true solutions for all pairs$$(a,b)$$ in the white region in Figure 2. This is not true for all A-stable Runge-Kutta methods (e.g. Lobatto IIIC methods). Recall that a method is A-stable if, when applied to the test equation $$\\dot y = \\lambda y$$ with $$\\Re \\lambda < 0$$ with an arbitrary step size, the numerical solution tends to zero.\n\nFor linear systems of delay equations a stability analysis is much more complicated and the results are negative. It is for example known (Guglielmi, 2001 and Maset, 2002) that for every numerical method and for every $$m$$ there exists a real linear system (4) in dimension $$2\\ ,$$ such that the analytic solution is stable but the numerical solution diverges. Assuming instead delay independent asymptotic stability conditions, i.e., condition (6), it is known that all A-stable methods preserve the correct asymptotically vanishing behavior of true solutions (see Zennaro, 1986 and Koto, 1994).\n\nWhen passing to nonlinear systems it is common to make use of a one-sided Lipschitz condition combined with a standard Lipschitz condition for arguments with delay. In this situation, many contractivity results (B-stability, algebraic stability) for numerical methods applied to stiff ordinary differential equations can be extended to stiff delay equations (see e.g. Zennaro, 1997 and Bellen and Zennaro, 2003 with the bibliography included therein).\n\n#### Multistep methods (BDF)\n\nThe same idea can be applied to multistep stiff integrators such as BDF schemes. One step of the $$k$$-step BDF method is given by $\\tag{9} M \\Big( y_{n+1} - \\sum_{j=1}^{k} \\alpha_{n,j} y_{n+1-j} \\Big) \\, = \\, h_{n}\\,\\beta_{n} f \\big( t_{n+1}, y_{n+1}, z_{n+1} \\big),$\n\nwhere $$\\{ \\alpha_{n,j} \\},\\beta_{n}$$ denote the coefficients (depending on the stepsize ratios) of the BDF formula and $$z_{n+1}$$ approximates $$y\\Big( \\alpha (t,y(t))\\Big)$$ at $$t_{n+1}=t_{n}+h_{n}\\ .$$ Similarly to the previous case, with $$\\alpha^{(n)} = \\alpha (t_{n+1}, y_{n+1})\\ ,$$ $\\tag{10} z_{n+1} = v_m \\left( \\alpha^{(n)} \\right) \\qquad \\mbox{if } \\quad t_{m} \\le \\alpha^{(n)} < t_{m+1} \\quad \\mbox{for some } \\ 0\\le m\\le n,$\n\nwhere $$v_m(t)$$ is a continuous extension of the solution computed at the $$m$$-th step.\n\nFor a discussion the reader is referred to (Bocharov, Marchuk and Romanyukha, 1996) and - for differential algebraic equations - to (Ascher and Petzold, 1995).\n\n#### Implementation issues\n\nThe numerical integration of a stiff delay differential equation presents several new difficulties compared to the treatment of stiff ordinary differential equation.\n\nNonlinear equations. Explicit numerical integrators are not suitable for solving stiff problems. As long as the step size is smaller than the delay, the same difficulties are encountered as for ordinary differential equations and there are well-established techniques (simplified Newton method, defect correction) to solve the arising nonlinear equations. If the step size is larger than the delay, one has to take care of the fact that the vectors $$Z_j^{(n)}$$ in the Runge-Kutta formula (or the vector $$z_{n+1}$$ in the BDF scheme) also depend on the unknown variables, and it may be necessary to use a more sophisticated Jacobian approximation during the simplified Newton iterations.\n\nImplicit computation of breaking points. For state-dependent delay equations, where the breaking points are not known in advance, the step sizes may be severely restricted near the jump discontinuities of the solution or some low order derivative. It is therefore important to detect and accurately compute them during the integration. It is possible to take advantage of the use of an implicit method. Once the presence of a breaking point in the current interval is detected (a zero of the equation $$\\alpha(\\xi,y(\\xi)) = \\zeta ,$$ where $$\\zeta$$ is a previous breaking point), a natural idea is to consider the step size $$h_n$$ as a new variable and to add the scalar equation $\\tag{11} \\alpha \\Big( t_n+h_n, u_n(t_n+h_n) \\Big) = \\zeta$\n\nto the system (7) (or (9)). This yields the breaking point $$t_n+h_n$$ at the same time as the numerical solution of the implicit integrator (see Guglielmi and Hairer, 2007 and Enright, Jackson, Nørsett and Thomsen, 1988 for details of this strategy).\n\nVanishing or small delays. It is essential that a stiff integrator can deal with vanishing or small delays. A typical situation for stiff problems is the existence of quasi-stationary solutions, where extremely large step sizes have to be used. If the solution is sufficiently smooth in such a region, the method of steps strategy would be very inefficient.\n\nError control. Step size selection strategies for stiff ordinary differential equations are usually based on error estimations at grid points. For delay equations the accuracy of the dense output strongly influences the performance. Thus suitable uniform error estimates have to be provided in order to control the error. For BDF formulas an accurate uniform error estimate (of the same order as that obtained at grid points) is immediately available. For Runge-Kutta methods one has to pay attention because the dense output is usually less accurate than the numerical solution at grid points (see Enright, 1989 and Guglielmi and Hairer, 2001).\n\n#### An example from immunology\n\nThis is a system of delay equations which models the antibody response to antigen challenge (see Waltman, 1978).\n\nThe problem consists of six equations $\\begin{array}{rcl} \\dot{y}_1(t) & = & -r y_1(t) y_2(t) - s y_1(t) y_4(t)\\\\[1mm] \\dot{y}_2(t) & = & -r y_1(t) y_2(t) + \\alpha r y_1\\big( y_5(t)\\big) y_2\\big( y_5(t)\\big) H(t-t_0)\\\\[1mm] \\dot{y}_3(t) & = & r y_1(t) y_2(t)\\\\[1mm] \\dot{y}_4(t) & = & -s y_1(t) y_4(t) - \\gamma y_4(t) + \\beta r y_1\\big( y_6(t)\\big) y_2\\big( y_6(t)\\big) H(t-t_1)\\\\[1mm] \\dot{y}_5(t) & = & H(t-t_0) \\big( y_1(t) y_2(t) + y_3(t)\\big) \\big/ \\big( y_1\\big( y_5(t)\\big) y_2\\big( y_5(t)\\big) + y_3\\big( y_5(t)\\big) \\big) \\\\[1mm] \\dot{y}_6(t) & = & H(t-t_1) \\big( y_2(t)+y_3(t)\\big) \\big/ \\big( y_2\\big( y_6(t)\\big)+y_3\\big( y_6(t)\\big)\\big) \\end{array}$ where $$H(x)$$ is the Heavyside function ($$H(x)=0$$ if $$x<0$$ and $$H(x)=1$$ if $$x\\ge 0$$). Choosing $$\\alpha =1.8\\ ,$$ $$\\beta =20\\ ,$$ $$\\gamma =0.002\\ ,$$ $$r=5\\cdot 10^4\\ ,$$ $$s=10^5\\ ,$$ $$t_0=35\\ ,$$ $$t_1=197$$ and the initial functions $$y_1(t)=5\\cdot 10^{-6}\\ ,$$ $$y_2(t)=10^{-15}\\ ,$$ and $$y_3(t)=y_4(t)=y_5(t)=y_6(t)=0$$ for $$t\\le 0$$ the obtained solutions are shown in the plot.\n\nThis problem has several difficulties: the delay is state-dependent, it becomes very small and vanishes asymptotically (see Fig.Figure 4). The functions $$y_2$$ and $$y_4, y_6$$ are extremely steep at the values $$t_0=35$$ and $$t_1=197\\ ,$$ respectively, and the problem is very stiff (as already observed by Waltman (1978)).\n\n## Software\n\n• Dde-Stride: a Fortran77 code by Baker, Butcher and Paul (1992) for the integration of stiff delay and neutral differential equations. The algorithm extends Butcher's Stride code for ODEs and is based on a SIRK method.\n• Delh: a Fortran77 code by Weiner and Strehmel (1988) for the integration of partitioned stiff/nonstiff systems. The algorithm is based on Rosenbrock type methods.\n• Difsub-dde: a Fortran77 code by Bocharov, Marchuk and Romanyukha (1996) for the integration of non-neutral stiff delay differential equations. The algorithm suitably extends Gear's code Difsub for ODEs which is based on BDF formulas.\n• Radar5: http://www.unige.ch/~hairer/software.html. A Fortran90 code by Guglielmi and Hairer (2001,2007) for the integration of implicit problems of the form (1). The algorithm extends Hairer and Wanner's Radau5 code, and is based on the $$3$$ stage Radau IIA collocation method.\n• Snddelm: a Fortran77 code by Jackiewicz and Lo (1993) for the integration of systems of neutral delay differential equations. The algorithm is based on Adams predictor corrector methods.\n• Baker C.T.H., Butcher J.C. and Paul C.A.H. (1992) Experience of Stride applied to delay differential equations. Tech. Rep. 208, Univ. of Manchester..\n• Baker C.T.H., Paul C.A.H. and Willé D.R. (1995) Issues in the numerical solution of evolutionary delay differential equations. Adv. Comput. Math. 3:171-196.\n• Bellen A. (1984) One-step collocation for delay differential equations. J. Comput. Appl. Math. 10:275-283.\n• Bellen A., Jackiewicz Z. and Zennaro M. (1988) Stability analysis of one-step methods for neutral delay-differential eqautions. Numer. Math. 52:605-619.\n• Bellen A. and Zennaro M (2003) Numerical solution of delay differential equations. Oxford University Press, Oxford. \n• Bocharov G.A., Marchuk G.I. and Romanyukha A.A. (1996) Numerical solution by LMMs of a stiff delay-differential system modelling an immune response. Numer. Math. 73:131-148.\n• Breda D., Maset S. and Vermiglio R. (2004) Computing the characteristic roots for delay differential equations. IMA J. Numer. Anal. 24:1-19.\n• Castleton R.N. and Grimm L.J. (1973) A first order method for differential equations of neutral type. Math. Comp. 27:571-577.\n• Engelborghs K. and Roose D. (2002) On Stability of LMS-methods and Characteristic Roots of Delay Differential Equations. SIAM J. Numer. Anal. 40:629-650.\n• Enright W.H., Jackson K.R., Nørsett S.P. and Thomsen P.G. (1988) Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants. Appl. Math. Comput. 27:313--335\n• Enright W.H. (1989) Analysis of error control strategies for continuous Runge-Kutta methods. SIAM J. Numer. Anal. 26:588--599.\n• Feldstein A., Neves K.W. and Thompson, S. (2006) Sharpness results for state dependent delay differential equations: an overview. Appl. Numer. Math. 56:472--487.\n• Guglielmi N. (1998) Delay dependent stability regions of Theta-methods for delay differential equations. IMA J. of Numer. Anal. 18:399--418.\n• Guglielmi N. (2001) Asymptotic stability barriers for natural Runge-Kutta processes for delay equations. SIAM J. Numer. Anal. 39:763-783.\n• Guglielmi N. and Hairer E. (1999) Order stars and stability for delay differential equations. Numer. Math. 83:371-383.\n• Guglielmi N. and Hairer E. (2001) Implementing Radau IIa methods for stiff delay differential equations. Computing 67:1-12.\n• Guglielmi N. and Hairer E. (2007) Computing breaking points in implicit delay differential equations. Adv. Comput. Math. in press.\n• Hairer E. and Wanner, G. (1996) Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer-Verlag, Berlin. \n• Jackiewicz Z. and Lo E. (1993) The algorithm SNDDELM for the numerical solution of systems of neutral delay differential equations, Appendix in: Kuang Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, Boston.\n• Koto T. (1994) A stability property of A-stable natural Runge-Kutta methods for systems of delay differential equations. BIT 34:262-267.\n• Koto T. (1996) A stability property of A-stable collocation-based Runge-Kutta methods for neutral delay differential equations. BIT 36:855-859.\n• Maset S. (2002) Instability of Runge-Kutta methods when applied to linear systems of delay differential equations. Numer. Math. 90:555-562.\n• Shampine L.F. and Gahinet P. (2006) Delay-differential-algebraic equations in control theory. Appl. Numer. Math. 56:574--588.\n• van der Houwen P.J., Sommeijer B.P. and Baker C.T.H. (1986) On the stability of predictor-corrector methods for parabolic equations with delay. IMA J. Numer. Anal. 6:1--23.\n• Waltman P. (1978) A threshold model of antigen-stimulated antibody production. Theoretical Immunology, Immunology Series 8:437-453. Dekker, New York.\n• Weiner R. and Strehmel K. (1988) A type insensitive code for delay differential equations basing on adaptive and explicit Runge-Kutta interpolation methods. Computing 40:255--265.\n• Wu, J. (1996) Theory and applications of partial functional-differential equations. Applied Mathematical Sciences, 119. Springer-Verlag, New York. \n• Zennaro M. (1986) P-stability properties of Runge-Kutta methods for delay differential equations. Numer. Math. 46:305-318.\n• Zennaro M. (1997) Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations. Numer. Math. 77:549-563.\n\nInternal references" ]

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[ "IBM Developer Blog\n\nFollow the latest happenings with IBM Developer and stay in the know.\n\nAIF360 now works with scikit-learn\n\nScikit-learn is a very popular data science library which is enormously useful for training established machine learning algorithms, computing basic metrics, and building model pipelines. In fact, many of our example notebooks already use scikit-learn classifiers with pre-processing or post-processing workflows.\n\nUnfortunately, switching between AIF360 algorithms and scikit-learn algorithms breaks the workflow and forces the user to convert data structures back and forth. We’re also unable to leverage some of the powerful meta-programming tools from scikit-learn like pipelines and cross validation.\n\nThe latest version release of AIF360, 0.3.0, brings a number of changes, but the highlight is the addition of the new aif360.sklearn module. This is where you can find all the currently completed scikit-learn-compatible AIF360 functionality.\n\nNote: This is still a work-in-progress and not all functionality is yet migrated. Interested developers can also check out the “sklearn-compat” development branch to get the latest features and make contributions.\n\nThe vision for this update is to make AIF360 functionality interchangeable with scikit-learn functionality. Algorithms can be swapped with debiasing algorithms and metrics can be swapped with fairness metrics. For example, instead of a simple LogisticRegression classifier, you can use an AdversarialDebiasing classifier instead of just the recall_score, you can measure the equal_opportunity_difference or difference in recall between protected groups. All of this should be as easy as swapping a line of code.\n\nHowever, in order to incorporate fairness features into algorithms, we are not able to ensure complete compatibility with scikit-learn in some cases. For example, some scikit-learn preprocessors like sklearn.decomposition.pca will strip the sample properties such as protected attributes and thus cause errors to AIF360 algorithms later in the pipeline. Read on to learn about workarounds and other caveats for working with scikit-learn.\n\nOld API remains\n\nThe old API will remain for the foreseeable future as we continue to replicate its functionality in the new API. Once this is completed, we may choose to deprecate support for the old API within a few versions but this will be communicated clearly when the time comes and depends on feedback from the community.\n\nCapabilities overview\n\nAgain, this is a work-in-progress. Many features are still missing and the API is still somewhat experimental. User feedback and contributions are critical for this project.\n\nFor more in-depth explanations of the capabilities, see the API reference. For an interactive demonstration of the capabilities, we have an example notebook.\n\nDatasets\n\nFour of the five datasets included in AIF360 are replicated here: Adult Census Income, German Credit, Bank Marketing, and COMPAS Recidivism. They now download automatically from OpenML the first time the corresponding function is called and are cached for later reuse.\n\nThe data structure is simplified as well. The data is separated into familiar X features and y target values as well as sample_weight if available. Each variable is returned as a Pandas DataFrame object with the original data values (e.g. string category values) by default and protected attribute values per sample in the index.\n\nFor example, if this is the input:\n\nfrom aif360.sklearn.datasets import fetch_compas\n\nX, y = fetch_compas(binary_race=True)\n\nThe output would be something like this:\n\nsex age age_cat race juv_fel_count juv_misd_count juv_other_count priors_count c_charge_degree c_charge_desc\nid sex race\n3 Male African-American Male 34 25 – 45 African-American 0 0 0 0 F Felony Battery w/Prior Convict\n4 Male African-American Male 24 Less than 25 African-American 0 0 1 4 F Possession of Cocaine\n8 Male Caucasian Male 41 25 – 45 Caucasian 0 0 0 14 F Possession Burglary Tools\n10 Female Caucasian Female 39 25 – 45 Caucasian 0 0 0 0 M Battery\n14 Male Caucasian Male 27 25 – 45 Caucasian 0 0 0 0 F Poss 3,4 MDMA (Ecstasy)\n\nNow, let’s encode the protected attributes as 0 or 1. Since the default ordering of the categories assigns 0 to unprivileged attributes and 1 to privileged ones, this will make things easier when calculating metrics as we can make use of the default priv_group=1.\n\nimport pandas as pd\n\nX.index = pd.MultiIndex.from_arrays(X.index.codes, names=X.index.names)\ny.index = pd.MultiIndex.from_arrays(y.index.codes, names=y.index.names)\n\nWe can also flip the labels since recidivism is unfavorable. This isn’t strictly necessary but it saves us from having to provide the pos_label for all the metrics.\n\ny = 1 - pd.Series(y.factorize(sort=True), index=y.index)\n\nAs previously mentioned, some scikit-learn steps will strip the formatting containing protected attribute information from the data. This makes it difficult to use most sklearn.preprocessing steps such as input normalization and one-hot encoding. Below, we show another workaround but in the interest of simplicity, we hope to work closer with the scikit-learn community to make this work seamlessly.\n\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.compose import make_column_transformer\nfrom sklearn.preprocessing import OneHotEncoder, StandardScaler\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1234567)\ndata_preproc = make_column_transformer(\n(OneHotEncoder(sparse=False, handle_unknown='ignore'), X_train.dtypes == 'category'),\nremainder=StandardScaler())\n\nX_train = pd.DataFrame(data_preproc.fit_transform(X_train), index=X_train.index)\nX_test = pd.DataFrame(data_preproc.transform(X_test), index=X_test.index)\n\nAlgorithms\n\nThree algorithms are included in the initial release of aif360.sklearn: one pre-processor (Reweighing), one in-processor (Adversarial Debiasing), and one post-processor (Calibrated Equalized Odds). We welcome contributions from the community as we work to make all 11 of the algorithms available (and any new ones as well, of course).\n\nAdversarial Debiasing works very much like any other scikit-learn Estimator – it trains with the fit() method and can return both “hard” (predict()) and “soft” (predict_proba()) predictions.\n\nimport tensorflow as tf\ntf.logging.set_verbosity(tf.logging.ERROR)\n\nReweighing breaks the scikit-learn API conventions a bit since it needs to return new sample weights from transform(). As a workaround, we have included a meta-estimator which combines the reweigher and an arbitrary estimator in a single fit() step.\n\nfrom aif360.sklearn.preprocessing import ReweighingMeta, Reweighing\nfrom sklearn.linear_model import LogisticRegression\n\nlr = LogisticRegression(solver='liblinear')\nrew = ReweighingMeta(estimator=lr, reweigher=Reweighing('race'))\nrew.fit(X_train, y_train)\ny_pred_REW = rew.predict(X_test)\n\nThe Calibrated Equalized Odds post-processor also requires a workaround. Post-processors train on predictions from a black-box estimator and ground-truth values to produce fairer predictions. This alone is without precedent in scikit-learn. Furthermore, to avoid data leakage, the training set for the post-processor should differ from the training set of the estimator. The PostProcessingMeta class takes care of both of these issues by combining the training and prediction of an arbitrary estimator and the post-processor while seamlessly splitting the dataset.\n\nfrom aif360.sklearn.postprocessing import CalibratedEqualizedOdds, PostProcessingMeta\n\npp = CalibratedEqualizedOdds('race', cost_constraint='fnr', random_state=1234567)\nceo = PostProcessingMeta(estimator=lr, postprocessor=pp, random_state=1234567)\nceo.fit(X_train, y_train)\ny_pred_CEO = ceo.predict(X_test)\ny_proba_CEO = ceo.predict_proba(X_test)\n\nMetrics\n\nMost of the fairness metrics have been reproduced as standalone functions. This means it is no longer necessary to create an object for each pair of predictions and ground-truth labels but it does make each function call’s syntax longer. Furthermore, since the inputs are also valid for functions from sklearn.metrics, we avoid reimplementing functions like accuracy_score and recall_score.\n\nAdditionally, the newly ported metrics can be used as scorers in a grid search, for example.\n\nfrom aif360.sklearn.metrics import disparate_impact_ratio\n\ntrain_di = disparate_impact_ratio(y_test, prot_attr='race')\n\nprint(f'Training set disparate impact: {train_di:.3f}')\n\nTraining set disparate impact: 0.773\n\nfrom aif360.sklearn.metrics import average_odds_error\nfrom sklearn.metrics import accuracy_score\n\n[Adversarial Debiasing] Test equal odds measure 0.091\nacc_REW = accuracy_score(y_test, y_pred_REW)\ndi_REW = disparate_impact_ratio(y_test, y_pred_REW, prot_attr='race')\n\nprint(f'[Reweighing] Test accuracy: {acc_REW:.2%}')\nprint(f'[Reweighing] Test disparate impact: {di_REW:.3f}')\n[Reweighing] Test accuracy: 66.64%\n[Reweighing] Test disparate impace 0.893\nfrom aif360.sklearn.metrics import difference, generalized_fnr\n\nacc_CEO = accuracy_score(y_test, y_pred_CEO)\ndfnr_CEO = difference(generalized_fnr, y_test, y_proba_CEO[:, 1], prot_attr='race')\n\nprint(f'[Calibrated Equalized Odds] Test accuracy: {acc_CEO:.2%}')\nprint(f'[Calibrated Equalized Odds] Test FNR difference: {dfnr_CEO:.3f}')\n[Calibrated Equalized Odds] Test accuracy: 63.99%\n[Calibrated Equalized Odds] Test FNR difference 0.053\n\nLooking for contributions\n\nOn that note, we’re always looking for new open-source contributors! Now that we have examples of how to modify each algorithm type, if you would like to help improve the project, feel free to choose an unimplemented algorithm by posting on the GitHub issue and migrate it. We also have a Slack channel devoted to this undertaking, #sklearn-compat, where you can ask questions and provide feedback." ]

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[ "# UEFA, what were the odds ?\n\nOk, I was supposed to take a break, but Frédéric, professor in Tours, came back to me this morning with a tickling question. He asked me what were the odds that the Champions League draw produces exactly the same pairings from the practice draw, and the official one (see e.g. dailymail.co.uk/…).\n\nTo be honest, I don’t know much about soccer, so here is what happened, with the practice draw (on the left, on December 19th) and the official one (on the right, on December 20th),", null, "Clearly, the pairs are identical, but not the order. Actually, at first, I was suprised that even which team plays at home first, was iddentical. But (it seams that) teams that play at home first are the ones that ended second after the previous stage of the competition.\n\nAnd to be more specific about those draws, those pairs were obtained using real urns, real balls, so it is pure randomness (again, as far as I understood). But with very specific rules. For instance, two teams from the same country cannot play together (or one against the other) at this stage. Or teams that ended first after the previous turn can only play with (or against) teams that ended second. Actually, Frederic sent me an xls file, with a possibility matrix.\n\nLet us find all possible pairs, regardless which team plays at home first (again, we do not care here since the order is defined by the rule mentioned above). Doing the maths might have been a bit complicated, with all those contraints. With a small code, it is possible to list all possible pairs, for those eight games. Let us import our possibility matrix,\n\n``` > n=16\n+ \"http://freakonometrics.blog.free.fr/public/data/uefa.csv\",\n> LISTEIMPOSSIBLE=matrix(\n+ (rep(1:n,n))*(uefa[1:n,2:(n+1)]==\"NON\"),n,n)```\n\nI can fix the first team (in my list, the fourth one is the first team that ended second). Then, I look at all possible second one (that will play with the first one),\n\n``` > a1=1\n> \"%notin%\" <- function(x, table){x[match(x, table, nomatch = 0) == 0]}\n> posa2=((a1+1):n)%notin%LISTEIMPOSSIBLE[,a1]```\n\nThen, consider the second team that ended second (the sixth one in my list). And look at all possible fourth team (that will play this second game), i.e exluding the one that were already drawn, and those that are not possible,\n\n``` > b1=6\n> posb2=(1:n)%notin%c(LISTEIMPOSSIBLE[,b1],a2)```\n\nEtc. So, given the list of home teams,\n\n``` > a1=4\n> b1=6\n> c1=8\n> d1=9\n> e1=12\n> f1=14\n> g1=15\n> h1=16```\n\nconsider the following loops,\n\n``` > posa2=(1:n)%notin%c(LISTEIMPOSSIBLE[,a1])\n> for(a2 in posa2){\n+ posb2=(1:n)%notin%c(LISTEIMPOSSIBLE[,b1],a2)\n+ for(b2 in posb2){\n+ posc2=(1:n)%notin%c(LISTEIMPOSSIBLE[,c1],a2,b2)\n+ for(c2 in posc2){\n+ posd2=(1:n)%notin%c(LISTEIMPOSSIBLE[,d1],a2,b2,c2)\n+ for(d2 in posd2){\n+ pose2=(1:n)%notin%c(LISTEIMPOSSIBLE[,e1],a2,b2,c2,d2)\n+ for(e2 in pose2){\n+ posf2=(1:n)%notin%c(LISTEIMPOSSIBLE[,f1],a2,b2,c2,d2,e2)\n+ for(f2 in posf2){\n+ posg2=(1:n)%notin%c(LISTEIMPOSSIBLE[,g1],a2,b2,c2,d2,e2,f2)\n+ for(g2 in posg2){\n+ posh2=(1:n)%notin%c(LISTEIMPOSSIBLE[,h1],a2,b2,c2,d2,e2,f2,g2)\n+ for(h2 in posh2){\n+ s=s+1\n+ V=c(a1,a2,b1,b2,c1,c2,d1,d2,e1,e2,f1,f2,g1,g2,h1,h2)\n+ cat(s,V,\"\\n\")\n+ M=rbind(M,V)\n+ }}}}}}}}```\n\nWith the print option, we end up with\n\n```5461 4 13 6 11 8 5 9 2 12 10 14 3 15 7 16 1\n5462 4 13 6 11 8 5 9 2 12 10 14 7 15 1 16 3\n5463 4 13 6 11 8 5 9 2 12 10 14 7 15 3 16 1```\n\ni.e.\n\n```> nrow(M)\n 5463```\n\npossible pairs (the list can be found here, where numbers are the same as the one in the csv file). Which was the probability mentioned in acomment in the article mentioned previously dailymail.co.uk/…. So the probability to have exactly the same output after the practise and the official draws was (in %)\n\n```> 100/nrow(M)\n 0.01830496```\n\nWhich is not that small when we think about it….\n\nAnd if someone has a mathematical expression for this probability, I am interested. The only reliable method I found was to list all possible pairs (the csv file is available if someone wants to check). But I am not satisfied….\n\n## 6 thoughts on “UEFA, what were the odds ?”\n\n1.", null, "Mehmet Suzen says:\n\nI did simple direct monte carlo simulations on this before the draws.\nHere is my post dated 7.12.2012:\nhttp://memosisland.blogspot.de/2012/12/uefa-champions-league-knockout-phase.html\n\nThis is a direct simulation that repeatedly creates possible pairs randomly, I run this 20M times.\n\n2.", null, "Kl says:\n\nFrom my understanding this result assumes all pairings are equally likely (?), which is not really obvious to me…i dont think its true actually and in that case i wonder how far from uniform distribution we could get (depending on possibility matrix)\n\n3.", null, "DiffusePrior says:\n\nInteresting. I wrote a computational solution to this problem a few days ago. However, the probability I calculated was much lower: 0.00011. I am wondering why our answers are so different. My calculation was performed via MC methods wherein I assumed that ordering was unimportant. The advantage of the MC method (in my head anyway) is that all I needed to do was write a function that performs random draws while adhering to UEFA’s rules without worrying about complex condition probabilities. Perhaps there is an error in my code but if there is, it’s not one I can see. My post is here:\n\nhttp://diffuseprior.wordpress.com/2012/12/24/identical-champions-league-draw-what-were-the-odds\n\n1.", null, "Arthur Charpentier says:\n\nWe have almost the same probability, I just use a percentage notation…\n\n4.", null, "Amit Gal says:\n\nI’ve read your uefa blog post. You ask for a mathematical solution for the counting all possible matchings under constraints. Actually there is a simple solution to that.\nIf you create an 8*8 matrix with teams who finished 1st as rows an those who finished second as columns, then Aij=1 means that team i can face team j, and Aij=0 means they are constrained an cannot face each other.\nnow, the number of possible legit draws (the number of options you simulated) is exactly the permanent of that matrix.\nmore generally, permanents can be used to count maximal matchings in bipartite graphs.\n\n5.", null, "Joël says:\n\nA precision taht might be useful to some:\n\nthe %notin% function is not a standard one, it needs to be defined as:\n\n`%notin%` <- function(x,y) !(x %in% y)\n\nThanks for your very nice blog anyway!\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed." ]

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[ "HPS 0410 Einstein for Everyone\n\nBack to main course page\n\n# Philosophical Significance of the General Theory of RelativityorWhat does it all mean, again? Ontology of Space and Time: The Hole Argument\n\nJohn D. Norton\nDepartment of History and Philosophy of Science\nUniversity of Pittsburgh\n\nIn the last chapter, we saw a migration in Einstein's understanding of the foundations of his developing general theory of relativity. His initial hope in 1907 was for a theory that would eliminate the absoluteness of acceleration that still remained in his special theory of relativity. By 1915, when the theory was complete, those aspirations had migrated into the requirement that his spacetime coordinate systems lose their independent existence. This, he achieved, through the general covariance of his final theory.\n\nIt was not so clear to him initially just what that loss of independence meant when carried through to the fullest extent. Its full import was revealed only after Einstein had taken an embarrassing detour through his \"hole argument,\" which he initially believed renderred all generally covariant theories physically uninteresting. With its repudiation, Einstein felt he had now established the loss of independent existence for spacetime coordinate systems. That loss became the revised version of Einstein's generalized principle of relativity.\n\nThis chapter tells the story. We will use some of the technical details developed in the last chapter.\n\n## The Disaster of 1913\n\nWe saw in an earlier chapter that Einstein's investigations on gravity and spacetime did not proceed smoothly. In 1913, together with the mathematician, his friend Marcel Grossmann, Einstein published his \"Entwurf...\" paper. It contained all the essential  components of the general theory of relativity but one. That one was the most important. It was the generally covariant gravitational field equations of the final theory. In spite of all of Einstein's efforts, the theory of 1913 was not generally covariant.", null, "This failure was a source of continuing trouble for Einstein. He alternated between concern that something was wrong in the theory; and confidence that all was right. A major contribution to this latter confidence was an argument he hit upon shortly after completing the \"Entwurf...\" and which he ended up publishing four times in 1914. This argument purported to establish that Einstein's failure to find a generally covariant theory was no failure at all, for a generally covariant theory would be physically uninteresting.\n\nMore specifically, what this \"hole argument\" purported to show was that a generally covariant theory would contradict what Einstein called the \"law of causality.\" In more modern terms, what it purported to show was that such a theory suffered a severe form of indeterminism.\n\nA common form of indeterminism arises in quantum mechanics. In standard accounts, we can specify the present state of the quantum system. However that will not fix what later measurements might return on the system. The best we can have are probabilities for different measurement outcomes.\n\nThe form of indeterminism of the hole argument was more severe. We specify the metric of spacetime everywhere in the past; and everywhere in the future, excepting a tiny region of spacetime: \"the hole.\" This near complete specification is insufficient to determine what the metric will be in the hole. Worse, there are no probabilities supplied for the different possibilities.\n\nThis failure of determinism was so calamitous a defect that, Einstein felt, it made generally covariant theories physically uninteresting.\n\n## The Hole Argument\n\nThe machinery of the hole arguments depends only on the most basic facts of a generally covariant theory. The metric tensor in a generally covariant theory will be governed by gravitational field equations, such as the Einstein gravitational field equations we saw in an earlier chapter. What this means is that we can apply the field equations in any coordinate system we choose.\n\n For example, the field equations might tell us that some metric g can arise in some coordinate system x. That means that, for each event with coordinate x in the spacetime, there is a particular metric g. We write this as g(x). Because the theory is generally covariant, we can also solve the field equations in another coordinate system x' for the same physical case. We would then recover a metric g'(x'), where the tables of values in g' assigned to the coordinates will, in general differ from those assigned by g. If we transform from the coordinate system x to the coordinate system x', then the rules for transforming tensors will transform g to g'. For more on transforming tensors between coordinate systems, see the Technical Appendix of the last chapter. These two assignments of tables of numbers g(x) and g'(x') to the coordinates are merely two different coordinate-based representations of the same set of facts about proper times and distances in spacetime. To recall: the metric g is just a compact way of writing the 4x4 table of numbers gμν that comprise the metric tensor in this coordinate system. The quantity x represents the four coordinates assigned to an event in spacetime: x = xμ = (x0, x1, x2, x3). The quantity \"g(x)\" represents the assigning of a 4x4 table to each value of the quadruple(x0, x1, x2, x3). In special cases, the same table will be assigned to every quadruple of coordinates. Here's an example in the last chapter (Minkowski spacetime metric in inertial coordinates). In general, there might be a different table for each value of the quadruple of coordinates. Here's an example in the last chapter. The tables are different according to the value of x = x1 in the quadruple. (Minkowski spacetime metric in uniformly accelerated coordinates.)\n\nEinstein applies these basic facts of a generally covariant theory to a quite particular pair of coordinate systems x and x'. The two systems agree everwhere except in some very small region of spacetime where they come smoothly to differ.\n\nAn example of  two such systems of coordinates is shown in the figures. For simplicity, only the t=x0 and x=x1 coordinates of x are shown. Here is the spacetime with this coordinate system and the hole marked.", null, "The metric g induces spatial distances and proper times elapsed onto the spacetime as well all distinguishing the trajectories of light signals. These trajectories form the light cone structure of the spacetime, as represented below. We will track the alterations in the metric tensor g visually by tracking changes in these light cones.", null, "We now introduce a transformation to a new coordinate system (t', x') that is the same everywhere outside the hole but comes smoothly to differ from it inside the hole. In this example, the transformation leaves t unchanged, since t = t'. The coordinate values of x' however are smoothly shifted towards the -x direction of the original coordinate system, so that, at t=0, the origin of the x' coordinate system is located in x at x = -1.", null, "The metric in this new coordinate system, g'(x'), will consist of an assignment of table of numbers to the coordinates that differ from those in the original coordinate system, g(x). However nothing has been done, so far, to alter the physical facts about times and spaces represented. In the figure, this is seen in the way the light cones are unaltered. All that has happened is that we have labeled the events of the spacetime with different numbers. The event that was labeled t=0, x=0 in the original coordinate system, for example, is now labeled t'=0, x'=1. To preserve the physical facts about spaces and times, we have had to make adjustments to the tables assigned in g(x), which becomes those assigned in g'(x').\n\n It now follows that the g(x) and g'(x') agree everywhere in spacetime except when the coordinates x and x' are those of events within the hole. For when we transform to a new coordinate system, we must also transform the table of numbers comprising g. Here \"agree\" means just this. Take an event where x and x' have the same values, that is, they are set of four numbers. The same table of values gμν is assigned to x by g(x) and to x' by g'(x').\n\ng(x) ≠ g'(x')   when  x = x' for events within the hole\notherwise\ng(x) = g'(x')   when  x = x'\n\nThat they differ within the hole is no special cause for concern. g(x) and g'(x') represent the same spacetime metric, but in different coordinate systems, so there is no necessity for them to be the very same table of numbers. Indeed, for events within the hole, when x = x', the two sets of coordinates x and x' are, by construction, labeling different events.\n\nNow comes the most delicate point in Einstein's argument. It is a point that was overlooked in later commentaries, where Einstein's argument was initially dismissed incorrectly as trivially flawed. When generally covariant field equations allow some metric in some coordinate system, all that matters to the field equations is the particular functional dependence of the g on x or the g' on x'. The field equations are satisfied by any pair of g* and x* that stand in the right functional relationship. There is no extra condition that the coordinate system x* must satisfy.\n\nThis means that we can take the functional dependence of g' on x' and recreate it in the first coordinate system x. That is, we form the metric tensor g'(x) in the first coordinate system x. We do this by taking the table assigned by g'(x') to coordinate  x' and reassigning it to the coordinate x in the old system, where the coordinate x has the same numerical values as x'. For example, imagine that g'(x') assigns some particular table of values \"G\" to the origin of its coordinates x' = (0, 0, 0, 0). The new assignment g'(x) will now assign that same table of values G to the origin x = (0, 0, 0, 0) of the first coordinate system.\n\nWe now have a set of conditions that look quite like the first set, but differ in an important way:\n\ng(x) ≠ g'(x for events with coordinate x within the hole\notherwise\ng(x) = g'(x)   for events with coordinates x outside the hole\n\nThis new inequality is troubling. For it tells us that there are two solutions of the gravitational field equation in the same coordinate system x such that the two solutions g(x) and g'(x) differ within the hole, but agree everywhere outside it.\n\nThe figure below is an attempt to show how the creation of this new metric g'(x) appears. The effect of the creation is equivalent to taking the original metric g(x) and smoothly dragging to the right, that is, to the +x direction, all its physical content. For example, the new coordinate system assigns t'=0, x'=+1 to the origin event of the old coordinate system t=0, x=0. So the dragging takes the metrical structure at t=0, x=0 and drags it one coordinate unit to the right, leaving it a t=0, x=+1. The lines depicting the coordinate system x are also shown dragged to help visualize the dragging.", null, "To see these effects a little more clearly, we should restore the dragged lines of the original coordinate system x  to their correct disposition.", null, "The light cones appear distorted by this dragging. This distortion of the light cones is no longer an artifact of being in a different coordinate system. The distortion is a real difference. For now there is only the original coordinate system. These light cones show that the metric g'(x) disagrees with the original g(x) on how the trajectories of light signals and proper times and distances are spread over the spacetime.\n\nTo make the difficulty more concrete, consider the two light signals shown in the figure. If they follow the light cone structure arising from g(x), they intersect at the origin event E of the coordinate system at t = x = 0. There is also a massive body shown in the figure whose timelike worldline takes it through the same event E:", null, "If however they were to follow the light cone structure arising from g'(x), that intersection event would be displaced by one coordinate unit to the right in the +x direction to the point E'. That is to be expected, for we saw above that the dragging effect took the structures at t=0, x=0 and moved them to t=0, x=+1.", null, "Where will the light signals meet? At the event E? Or at the event E'? Nothing in the full specification of the spacetime outside the hole determines it. For g(x) = g'(x) outside the hole, where the two spacetimes they represent agree in all physical properties. This is the troubling form of indeterminism that Einstein felt sufficiently worrisome to render a generally covariant theory g(x) = g'(x).\n\n## Einstein's Statement of It\n\nHere is Einstein's most careful and complete version of the hole argument from a paper of 1914:", null, "Here is my translation:\n\n\"§12. Proof of the necessity of a restriction on the choice of coordinates.\n\nWe consider a finite region of the continuum Σ, in which no material process takes place. Physical happenings in Σ are then fully determined if the quantities gμν are given as functions of the xν in relation to the coordinate system K used for description. The totality of these functions will be symbolically denoted by G (x).\nLet a new coordinate system K' be introduced, which coincides with K outside Σ, but deviates from it inside Σ in such a way that the g'μν related to the K' are continuous everywhere like the gμν (together with their derivatives). We denote the totality of the g'μν symbolically with G'(x'). G'(x') and G(x) describe the same gravitational field. In the functions g'μν we replace the coordinates x'ν with the coordinates xν i.e., we form G'(x). Then, likewise, G'(x) describes a gravitational field with respect to K, which however does not correspond with the real (or originally given) gravitational field.\nWe now assume that the differential equations of the gravitational field are generally covariant. Then they are satisfied by G'(x') (relative to K') if they are satisfied by G (x) relative to K. Then they are also satisfied by G'(x) relative to K. Then relative to K there exist the solutions G(x) and G'(x), which are different from one another, in spite of the fact that both solutions coincide in the boundary region, i.e., happenings in the gravitational field cannot be uniquely determined by generally covariant differential equations for the gravitational field.\"\n\nA. Einstein, \"Die formale Grundlage der allgemeinen Relativitätstheorie.\" Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1914): 1030-1085 on p. 1067.\n\nMy presentation has simplified Einstein's original argument by considering the \"source free\" case in which the source term in Einstein's gravitational field equations, the stress-energy tensor Tμν, is zero.  In Einstein's original argument above, he considers the more general case in which the source Tμν is non-zero outside the hole, but is zero within the hole. (\"no material processes\") In hindsight, the complication adds nothing to the argument, so I have presented a simpler version above. For Einstein in 1913, the difference may have been important. It meant that he could show that the matter distribution outside the hole fails to fix the structure of spacetime within it. This would not have sat well with his early Machian sensibilities. It would directly contradict the version of Mach's principle given in Einstein's 191 paper.\n\n## The Point-Coincidence Argument\n\nThe hole argument provided only temporary relief for Einstein's enduring doubts about this theory. By November 1915, Einstein had realized that his abandoning of general covariance was mistaken. He made his celebrated return to general covariance and completed the general theory of relativity.\n\nEinstein now had a new problem. In 1915, he announced to his colleagues in physics a generally covariant theory. The previous year he had given apparently compelling reasons against such a theory. Einstein needed to retract the hole argument and to do it in an equally compelling way.\n\nThat retraction came in the form of the \"point-coincidence\" argument, which appeared in his 1916 review article. It was offered as an argument for general covariance and read:\n\n\"That this requirement of general co-variance, which takes away from space and time the last remnant of physical objectivity, is a natural one, will be seen from the following reflexion. All our space-time verifications invariably amount to a determination of space-time coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meetings of two or more of these points. Moreover, the results of our measurings are nothing but verifications of such meetings of the material points of our measuring instruments with other material points, coincidences between the hands of a clock and points on the clock dial, and observed point-events happening at the same place at the same time.\n\nThe introduction of a system of reference serves no other purpose than to facilitate the description of the totality of such coincidences. We allot to the universe four space-time variables x1, x2, x3, x4 in such a way that for every point-event there is a corresponding system of values of the variables x1 ... x4. To two coincident point-events there corresponds one system of values of the variables x1 ... x4, i.e. coincidence is characterized by the identity of the co-ordinates. If, in place of the variables x1 ... x4, we introduce functions of them, x'1, x'2, x'3, x'4, as a new system of co-ordinates, so that the systems of values are made to correspond to one another without ambiguity, the equality of all four co-ordinates in the new system will also serve as an expression for the space-time coincidence of the two point-events. As all our physical experience can be ultimately reduced to such coincidences, there is no immediate reason for preferring certain systems of co-ordinates to others, that is to say, we arrive at the requirement of general co-variance.\"\n\nA. Einstein, \"The Foundation of the General Theory of Relativity,\" 1916 as translated in H. A. Lorentz et al. The Principle of Relativity. New York: Dover on p. 117.\n\n Here Einstein does not say explicitly that this argument is to supercede the hole argument. However it is clear that it does. For the two spacetimes associated with g(x) and g'(x) in the hole argument agree on all coincidences. For example, the meeting of the two light signals coincides with their meeting the worldline of the massive point particle. That is true in the spacetime associated with g(x); and it is equally true in the spacetime associated with g'(x). The only difference between the two spacetimes lies in how the tables of numbers forming g(x) and g'(x) are spread over the one coordinate system x. Those differences are invisible to the point-coincidences of physical systems like light signals and massive particles. For when g(x) is dragged and spread anew over x to form g'(x), all these material coincidences are carried along with the new spreading. Nothing in them is changed. Why might Einstein not link the point-coincidence argument explicitly to the hole argument in his 1916 review article? Perhaps he hoped that the completion of the theory would wipe away the dead end turnings in the pathway that brought him to it. The positive result asserted in the point-coincidence argument is important in its own right, so readers would need to know of it. But why trouble them with what proved to be an unfortunate distraction?\n\nThis resolution of the hole argument could be put in positive terms concerning the ontology of coordinate systems. In his generally covariant theory, the coordinate systems have no independent physical reality. Here is how he put it in a letter to his friend and confidant, Michele Besso in early 1916:\n\n\"There is no physical content in two different solutions G(x) and G'(x) existing with respect to the same coordinate system K. To imagine two solutions simultaneously in the same manifold has no meaning and the system K has no physical reality.\"\n\nEinstein to Michele Besso, January 3, 1916 (Papers, Vol. 8A, Doc. 178.)\n\nThe same point was made more figuratively by Einstein much later in a 1952 appendix to his popular text on relativity:\n\n\"On the basis of the general theory of relativity, on the other hand, space as opposed to \"what fills space\", which is dependent on the co-ordinates, has no separate existence. Thus a pure gravitational field might have been described in terms of the gik (as functions of the coordinates), by solution of the gravitational equations. If we imagine the gravitational field, i.e. the functions gik, to be removed, there does not remain a space of the type (1) [Minkowski spacetime], but absolutely nothing and also no topological space.\n...\n\nThere is no such thing as an empty space, i.e. a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field.\"\n\nAlbert Einstein, Relativity: the Special and the General Theory. Trans. R. W. Lawson. 15th rev. ed. London: Methuen, 1954 (1977) on p. 155.\n\nWhat Einstein says here gives a vivid picture of the precise step in the hole argument where it fails. Figuratively speaking, the hole argument asks us to start with a metric g(x) in a coordinate system x, remove g(x) from x and replace it with g'(x), in the same coordinate system x.", null, "THEN", null, "THEN", null, "The failure comes with the intermediate step. We are supposed to make physical sense of the coordinate system x without the metric g. Then we are apply the new metric g' to this very same coordinate system. Einstein repudiates the idea of the coordinate system x existing independently of g. As he says, taking away g does not leave us with a bare coordinate system x upon which we can carry out further operations. It leaves us with nothing.", null, "THEN", null, "THEN NOTHING\n\n## The Modern Hole Argument\n\nThe account above describes the hole argument and Einstein's resolution of it, at it appeared in 1914-1916. The modern literature in philosophy of space and time also draws on the hole argument and offers a solution. The issues in both literatures are essentially the same. This sameness, however, is obscured by the more sophisticated mathematical clothing used in the modern literature.\n\nFor an introduction to the modern formulation and a survey of responses, see my \"The Hole Argument,\" Stanford Encyclopedia of Philosophy.\n\n Readers who know the modern version of the hole argument can see the similarity of the two literatures once they know how to translate Einstein's considerations into the modern context. The modern context represents the events of spacetime as a mathematical object known as a manifold. Call it \"M.\" It is a set of events along with a specification of the particular way those events can be collected into neighborhoods. The metric is then introduced as a codification of intervals between nearby events. What can mislead mathematically sophisticated, modern readers is that the term \"coordinate system\" or \"coordinate chart\" designates a structure within the modern notion of manifold. So it is natural to associate Einstein's coordinate system with these coordinate charts. The association fails since the modern concept of manifold is built around a mathematical set of events that are in turn the mathematical representation of the physical events of spacetime. In Einstein's treatments, there is no such separate set. That mathematical set of events is better associated with the quadruples of numbers assigned as coordinate labels. These quadruples form what is, in modern language, a manifold that is the closest Einstein's treatment has to the manifold M of the modern treatments. For more on this way of reading Einstein, see my \"Coordinates and Covariance: Einstein's View of Spacetime and the Modern View Foundations of Physics19 (1989), pp. 1215-63.\n\nThe structure corresponding to this spacetime manifold is the coordinate system Einstein uses in formulating the hole argument. For in both Einstein's original formulation and in the modern formulation, the essential manipulation is to spread a metric g in two different ways over a coordinate system x or a spacetime manifold M.\n\n Einstein concludes through the point-coincidence argument that the coordinate system x has no existence independently from the metric tensor g associated with it. In the modern literature, the initial reading of the import of the hole argument was similar. One  might imagine that the spacetime manifold of events has an existence independent of what is in spacetime. Since independent existence is a defining characteristic of substances, this amounts to a \"substantival\" view of the manifold. The the indeterminism of the hole argument is escaped by denying the independent existence of the spacetime manifold. That is, we deny \"spacetime substantivalism\" or, more exactly, \" spacetime manifold substantivalism.\"\n\nCopyright John D. Norton. November 12, 2019." ]

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[ "# Using burnout current sources for Wheatstone bridge detection\n\nMany recent high-performance ADCs like the AD7190 include a builtin so-called burnout current source that can allegedly be used to detect an open circuit in the sensor. However, most vendors don’t provide an easy explanation on how this can be done.\n\nIn this blogpost I will attempt to explain how those current sources can be useful for practical applications. For this example, we will assume the ADC has one idealized differential channel and is connected to a simple wheatstone bridge strain gauge:", null, "", null, "### What is a burnout current source?\n\nMost ADC include two burnout current sources:\n\n• One sourcing from the analog supply voltage and sinking into the positive input\n• One sourcing from the negative input and sinking into the analog ground\n\nThose burnout current sources usually have very low and fixed current value – for the AD7190, it is $500\\,nA$.\n\nApplying this to the Wheatstone bridge, we get:", null, "The balanced Wheatstone bridge without any current sources forms two equal voltage dividers with a division ration of 2: Both the positive and the negative ADC input are biased at $\\frac{1}{2} V_{DDA} = 2.5\\,V$ (with $V_{DDA}$ being the analog supply voltage of the ADC and the bridge excitation voltage. While they might not be the same for many practical applications, for this example we will assume they are equal for simplicity). We could also say equivalently: The current flowing through R1 and R2 causes a voltage drop of $2.5\\,V$ over R3 and R4 respectively.\n\nWe can use a simplified model to understand what is happening qualitatively:", null, "By ignoring any current flowing through R1 and R4, the current through R2 and R3 is equal to I1 and I2 respectively. By using Ohm’s lawwhich can be expressed as $U = I{\\cdot}R$, we can calculate:\n\n$U_{R2,R3} = 500\\,\\text{nA} \\cdot 350\\,\\Omega = 175\\,{\\mu}\\text{V}$\n\nAs we assume no current flows through R1 and R4 and the IN(+) and IN(-) nodes are biased at $2.5\\,V$, adding the burnout current sources yields $$V_{IN(+)} = 2.5\\,V + 175\\,{\\mu}\\text{V}$$ and $$V_{IN(-)} = 2.5\\,V - 175\\,{\\mu}\\text{V}$$, yielding a difference of $$V_{IN(+)} - V_{IN(-)} = 2\\cdot175 {\\mu}\\text{V}$$\n\nNow we need to take into account the current flowing through R1 and R4. Although the mathematics of this exceed the scope of this article, we can easily use a LTSpice simulation (download simulation file) to see the numbers. Running this simulation shows that $V_{IN(+)} - V_{IN(-)} = 175\\,{\\mu}\\text{V}$. This applies independently of the supply voltage as long as $I_{R1,R4} \\gg I_{Burnout}$. This condition can be assumed to apply for any realistic setup if $V_{DDA} \\gt 1\\,\\text{V}$\n\nWe can therefore conclude that if a balanced Wheatstone bridge is connected and the burnout current sources are enabled: $$V_{IN(+)} - V_{IN(-)} = \\frac{I_{Burnout} \\cdot (R_3 + R_2)}{2}$$ If $R_3 \\approxeq R_2$, this can be simplified to: $$V_{IN(+)} - V_{IN(-)} = I_{Burnout} \\cdot R_{2,3}$$\n\n### Open circuit detection\n\nNow we assume that no sensor is connected at all, i.e. R1 to R4 are assumed to be infinite resistances.\n\nAn ideal current source would yield an infinitely high voltage when trying to push a constant current through an infinite ohmic resistance. The burnout current sources in ADCs do not exhibit this property: The maximum voltage they can possibly generate is $V_{DDA}$ while the minimum voltage is $0\\,\\text{V}$. While in practice these values will usually not reach the rails, we can ignore this fact for most practical configurations.\n\nThis means that an open-circuit scenario would mean that $V_{IN(+)} = V_{DDA}$ and $V_{IN(-)} = 0\\,\\text{V}$ and therefore $$V_{IN(+)} - V_{IN(-)} = V_{DDA} - 0\\,\\text{V} = V_{DDA}$$\n\nThis means that the ADC will therefore show the maximum possible value (e.g. 0xFFFFFF for a 24-bit ADC).\n\nWhen the burnout current sources are disabled, the voltage on the input terminals is undefined and depends on leakage currents being present on the PCB and on the input stage of the ADC.\n\nBased on this information, we can conclude that an open circuit condition can be detected by activating the burnout current sources and checking if the ADC shows the maximum possible digital output value. In most cases, a value very close to the maximum can be considered an open circuit condition as well.\n\n### Quantitative estimation of bridge resistances using burnout current sources\n\nFor many circuits it is useful to get an estimate on the actual resistance of the Wheatstone bridge in use – this may be useful, for example, to automatically configure the excitation voltage.\n\nBy using the burnout current source value and the equation we derived above $$V_{IN(+)} - V_{IN(-)} = I_{Burnout} * R_{2,3}$$ we can easily see that the differential voltage induced by the burnout currents depend on the resistors $R_2$ and $R_3$ of the bridge.\n\nUsually the burnout current sources have wide tolerance ranges and must be expected to device up to 20% over the full operating range and due to manufacturing tolerances. For open circuit detection, the exact current does not matter as long as $I_{burnout} \\gg I_{leakage}$ However, a current mismatch between the two current sources introduces a significant error in the observed voltage drop: $$E = \\frac{|I_a - I_b|}{}$$ For quantitative measurements these tolerances need to be taken into account – without individual calibration this means we won’t be able to determine the exact resistance of the bridge. However, it is still easily possible to classify the bridge resistance into one of several classes, for example strain gauges with a resistance of:\n\n• $120\\,\\Omega$\n• $350\\,\\Omega$\n• $1200\\,\\Omega$\n\nThis can be done using the following algorithm:\n\n• for i in 1..n\n• Disable burnout current source\n• Measure ADC voltage $V_{a,i}$\n• Enable burnout current source\n• Measure ADC voltage $V_{b,i}$\n• Compute burnout difference ${\\Delta}V_i = V_{b,i}\\,-\\,V_{a,i}$\n• Compute average additional voltage drop due to burnout: $$\\overline{{\\Delta}V}\\,=\\,\\sum^{n}_{i=0}{\\Delta}V_i$$\n\nNote that, in order to account for a potentially unbalanced bridge, we must only interpret the difference between the ADC value with burnout current enabled and the one with burnout current disabled.\n\nThe averaging is performed so sensor value changes during the measurement period (which are translated into resistance changes for at least one bridge element) an noise are eliminated from the equation as far as possible. A larger value for $n$ leads to lower errors in the resulting value. For fast-changing input signals, using a high sampling rate is recommended in order to minimize the time between aand b measurements. For multi-channel ADCs it also is recommended to measure only one channel at a time and disable zero-latency mode for this reason.\n\nWe can then calculate the observed resistance using $$R_{observed}\\,=\\,\\frac{\\overline{{\\Delta}V}}{I_{burnout}}$$\n\nFor example, if $\\overline{{\\Delta}V} = 165\\,{\\mu}V$ and $I_{burnout} = 500\\,nA$, $R_{observed} = 330\\,\\Omega$. This value is sufficiently close to $350\\,\\Omega$. The difference might be caused by ADC errors, burnout current deviations and resistance deviations in the sensor itself (caused by both static manufacturing tolerances and dynamic resistance changes).\n\nNote that many ADCs including the AD7190 series only specify nominal values and no guaranteed tolerance for the burnout currents." ]

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[ "# Warm-up Coding Interview: Dynamic Programming\n\n## Longest Increasing Sequence\n\nThere are three steps involved in solving a problem by dynamic programming:\n\n1. Formulate the answer as a recurrence relation or recursive algorithm.\n2. Show that the number of different parameter values taken on by your recurrence is bounded by a (hopefully small) polynomial.\n3. Specify an order of evaluation for the recurrence so the partial results you need are always available when you need them.\n\nTo see how this is done, let’s see how we would develop an algorithm to find the longest monotonically increasing subsequence within a sequence of n numbers. Still, it is instructive to work it out from scratch. Indeed, dynamic programming algorithms are often easier to reinvent than look up.\n\nWe distinguish an increasing sequence from a run, where the elements, must be physical neighbors of each other. The selected elements of both must be sorted in increasing order from left to right. For example, consider the sequence\n\nThe longest increasing subsequence of S has length 5, including {2, 3, 5, 6, 8}. In fact, there are eight of this length (can you enumerate them?).\n\nFinding the longest increasing run in a numerical sequence is strightforward. Indeed, you should longest increasing subsequence is considerably tricker. How can we identify which scattered elements to skip? To apply dynamic programming, we need to construct a recurrence that computes the length of the longest sequence. To find the right recurrence, ask what information about the first n-1 elements of S would help you to find the answer for the entire sequence?\n\n• The length of the longest increasing sequence in [katex]s_1, s_2, \\cdots, s_{n-1}[/katex] seems a useful thing to know. In fact, this will be longest increasing sequence in S, unless [katex]s_n[/katex] extends some increasing sequence of the same length.\n\nUnfortunately, the length of this sequence is not enough information to complete the full solution. Suppose I told you that the longest increasing sequence in [katex]s_1, s_2, \\dots, s_{n-1}[/katex] was of length 5 and that [katex]s_n = 9[/katex]. Will the length of the final longest increasing subsequence of S be 5 or 6?\n\n• We need to know the length of the longest sequence that [katex]s_n[/katex] will extend. To be certain we know this, we really need the length of the longest sequence that any possible value of [katex]s_n[/katex] can extend.\n\nThis provides the idea around which to build a recurrence. Define [katex]l_i[/katex] to be the length of the longest sequence ending with [katex]s_i[/katex].\n\nThe longest increasing sequence containing the nth number will be formed by appending it to the longest increasing sequence to the left of n that ends on a number smaller than [katex]s_n[/katex]. The following recurrence computes [katex]l_i[/katex]:\n\n[katex]l_i = \\max_{0<j<i} l_j + 1, \\text{ where } (s_j < s_i),[/katex]\n\nWhat auxiliary information will we need to store to reconstruct the actual sequence instead of its length? For each element [katex]s_i[/katex], we will store its predecessor — the index [katex]p_i[/katex] of the element that appears immediately before [katex]s_i[/katex]. Since all of these pointers go towards the left, it is simple matter to start from the last value of the longest sequence and follow the pointers so as to reconstruct the order items in the sequence.\n\nIn fact, by using dictionary data structures in a clever way, we can evaluate this recurrence in O(n lg n) time. However, the simple recurrence would be easy to program and therefore is a good place to start.\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed." ]

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[ "Cody\n\n# Problem 63. Encode Roman Numerals\n\nSolution 1639924\n\nSubmitted on 8 Oct 2018 by Philippe S.\n• Size: 7\n• This is the leading solution.\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 = 1990; y_correct = 'MCMXC'; assert(isequal(dec2rom(x),y_correct))\n\n[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In dec2rom (line 2) In ScoringEngineTestPoint1 (line 3) In solutionTest (line 3)]\n\n2   Pass\nx = 2008; y_correct = 'MMVIII'; assert(isequal(dec2rom(x),y_correct))\n\n[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In dec2rom (line 2) In ScoringEngineTestPoint2 (line 3) In solutionTest (line 5)]\n\n3   Pass\nx = 1666; y_correct = 'MDCLXVI'; assert(isequal(dec2rom(x),y_correct))\n\n[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In dec2rom (line 2) In ScoringEngineTestPoint3 (line 3) In solutionTest (line 7)]\n\n4   Pass\nx = 49; y_correct = 'XLIX'; assert(isequal(dec2rom(x),y_correct))\n\n[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In dec2rom (line 2) In ScoringEngineTestPoint4 (line 3) In solutionTest (line 9)]\n\n5   Pass\nx = 45; y_correct = 'XLV'; assert(isequal(dec2rom(x),y_correct))\n\n[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In dec2rom (line 2) In ScoringEngineTestPoint5 (line 3) In solutionTest (line 11)]\n\n6   Pass\nx = 0; y_correct = ''; assert(isempty(dec2rom(x)))\n\n[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In dec2rom (line 2) In ScoringEngineTestPoint6 (line 3) In solutionTest (line 13)]" ]

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[ "# Lesson 13\n\nGraphing the Standard Form (Part 2)\n\n### Lesson Narrative\n\nThis lesson is optional because it goes beyond the depth of understanding required to address the standards. In this lesson, students continue to examine the ties between quadratic expressions in standard form and the graphs that represent them. The focus this time is on the coefficient of the linear term, the $$b$$ in $$ax^2+bx+c$$, and how changes to it affect the graph. Students are not expected to know how to modify given expressions to transform the graphs in certain ways, but they will notice that adding a linear term to the squared term translates the graph in both horizontal and vertical directions. This understanding will help students to conclude that writing an expression such as $$x^2+bx$$ in factored form can help us reason about the graph.\n\nStudents also practice writing expressions that produce particular graphs. To do so, students make use of the structure in quadratic expressions (MP7) and what they learned about the connections between expressions and graphs.\n\n### Learning Goals\n\nTeacher Facing\n\n• Describe (orally and in writing) how the $b$ in $y=ax^2+bx+c$ affects the graph.\n• Write quadratic expressions in standard and factored forms that match given graphs.\n\n### Student Facing\n\n• Let’s change some other parts of a quadratic expression and see how they affect the graph.\n\n### Required Preparation\n\nAcquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)\n\n### Student Facing\n\n• I can explain how the $b$ in $y=ax^2+bx+c$ affects the graph of the equation.\n• I can match equations given in standard and factored form with their graph." ]

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[ "# What is a potentiometric transducer\n\n## Potentiometry\n\nPotentiometry is a form of titration in which you use a Voltage measurement determine the concentration of your sample solution. You can find all the details here in our article.\n\nIf you prefer to see the entire content in audiovisual form, just have a look at our video!\n\n### Potentiometry simply explained\n\nSince potentiometry is a form of titration, the basic titration process is the same. The only difference to traditional titration is the recording of the equivalence point. You no longer determine this via an indicator, but by measuring the electrochemical potential difference between Customized solution and one Reference electrode on constant potential.\n\nYou always use this titration method if you cannot find a suitable indicator or if the strong color of the sample solution makes it impossible to see the color change. If you would like to have the basics of titration explained again before reading on, then take a look at our article on titration.\n\n### Potentiometry experiment setup\n\nIf you do the titration potentiometric want to perform, then you need both a reference electrode and a measuring electrode. The reference electrode is usually an electrode of the 2nd type. These are characterized by the fact that their potential constant and not concentration dependent is. The measuring electrode, on the other hand, has a potential that depends on the concentration in your measuring solution. So if you change the concentration of the sample solution through neutralization, the potential of your measuring electrode also changes. In potentiometry, you record this change by continuously measuring the voltage of the constant potential against your reference electrode.\n\nIf you are already well versed in electrochemistry, then you probably also know that a current flow would also change this voltage difference over time. But since you want the neutralization of the sample solution to be the only source of your potential changes, you block this current with a Voltage compensation circuit. You can use this to measure the voltage without the risk of falsifying your results.\n\n### Potentiometry basics\n\nNow that you have understood the basic processes, you are probably wondering how you can tell from the recorded voltage curve when you have reached the equivalence point. To answer that, you have to look at the Nernst equation look at. If this equation doesn't mean anything to you, then take a look at the article here to do this.\n\n### Voltage determination\n\nThe Nernst equation describes the voltage curve of an electrode that is in contact with an electrolyte solution, depending on the concentration.", null, "Using this equation, you can convert the voltage of your measuring electrode into a Normal electrode comprehend. Usually, however, your experiment setup consists of both a measuring electrode and a reference electrode. So you record the voltage difference between these two electrodes. But since the voltage of the reference electrode is always constant, you can easily calculate the voltage curve. For this, one also assumes that the substance to be titrated is present as an ion in a solution and, by adding the standard solution, afterwards equation will react.", null, "Ox = oxidized form; Red = reduced form n = whole number; e = electron\n\nIf this is the case, you can easily calculate the voltage by subtracting the constant potential of the reference electrode from the concentration-dependent measuring electrode.", null, "### Equivalence point determination\n\nThe potential of the reference electrode varies depending on the material used. Frequently used electrodes are the Ag / AgCl electrode or the Calomel electrode (Hg / HgCl).\n\nIf you now look at this equation, you can see that the voltage value will change significantly if the concentrations of the oxidized and reduced form are the same. As the reaction progresses, the ln function falls below the value 1 and its slope increases sharply as a result. This increase is then clearly visible in the measurement curve. Within this jump of tension you will then also find your equivalence point. If you would like to take a closer look at the equivalence point, then click here.\n\n### Potentiometry evaluation of the measurement curve\n\nIf the measured voltage is now plotted against the added volume of standard solution, the result is again a for the titration typical course.\n\nAs you can see here, there is again a course with a steep climb. Similar to acid-base titration, this increase occurs when the equivalence point is reached. You can also go through this curve graphical determination of the turning point the curve to find out the equivalence point. This is an example of this Tangent method or that Circular process at.\n\nIf you want to use the tangent method, you only have to add two tangents to the Breakpoints of the curves. These should form an angle of approximately 45 ° with the x-axis. Then you just have to draw a third straight line that is parallel to the other two tangents. This should be exactly in the middle of the two. The Intersection of this third straight line is then your equivalence point.\n\nIf you know the voltage at which the equivalence point has been reached, you can rearrange the Nernst equation and thus calculate the concentration of the sample solution at the equivalence point. In order to determine the original concentration, you now have to add the amount of substance that has already reacted with the standard solution when the equivalence point is reached. Since you can read from the diagram how much standard solution has already dripped into the sample solution at the equivalence point, you can also calculate the amount of reacted substance:", null, "• n = amount of substance of the measuring reagent in the sample solution at the equivalence point\n•", null, "= added volume of standard solution at the equivalence point\n•", null, "= Concentration of the standard solution\n\nYou can then use the reaction equation for the titration to calculate the amount of substance used in the sample solution. You then only have to add this to the already known equivalence point amount of substance. You will then receive the initial concentration based on the volume of the sample solution.\n\n### Potentiometry fields of application\n\nSince potentiometry is a very versatile method, it can also be found in many fields of application. You can use it for example Solubility products measure or determine the concentrations of any solution in the classic way. A very important area of ​​application is above all that Acid-base titration.\n\n### Acid-base titration using potentiometry\n\nSince the use of indicators often leads to somewhat inaccurate titration results, alternative measurement methods were sought early on and found in potentiometry. A special one is normally used for the measurement even during the titration Glass electrode.\n\nThis electrode is designed so that it can both electrodes, so reference and measuring electrode, contains at the same time. However, these two are spatially separated from each other and only connected by a conductive wire to measure the voltage between the two. As before, the reference electrode is an Ag / AgCl or a calomel electrode. The measuring electrode itself is immersed in a solution with the pH 7 a. In addition, the solution contains a bufferto keep the pH stable. If you want to repeat the term pH value again, then click here.\n\nThe crucial part of the glass electrode is one Glass membraneimmersed in the sample solution. One side of the glass membrane is immersed in the sample solution. The other side, on the other hand, is in contact with the Buffer solutionwhich also contains the measuring electrode. Now you have to know that ions are stored in most glasses, like", null, "-Ions. But these are due to the amorphous structure of the glass very agile. In addition, the oxonium ions can adhere to a solution Surface of the glass membrane attach, but this not penetrate.\n\nDue to the additional charge on the surface, the Li ions in the glass are pushed back from the surface. How many oxonium ions accumulate depends on the respective concentration of the oxonium ions in the adjacent solution. The higher it is, the more will accumulate. If the pH value on the two sides of the glass membrane is different, then the tendency of the oxonium ions to attach to the membrane is also different. Accordingly, there is also a charge difference between the two sides of the glass membrane and a resulting voltage above it. This voltage can then be recorded using the two electrodes.\n\n### Donnan's equation\n\nSince there is no redox process per se, the Nernst equation cannot be used without problems to calculate the voltage. Instead, you have to Donnan's equation draw in. But this looks very similar to the Nernst equation:", null, "•", null, "= Activity of the oxonium ions outside\n•", null, "= Activity of oxonium ions inside\n\nIf you now want to titrate a solution, you can easily measure the pH value changes with this method, since the activity of the inside always remains the same due to the buffer and the impermeability of the membrane. A change in the measured voltage on the glass electrode can only come about through a change in the pH value of the solution on the outer layer. If you now want to track the pH value, which is necessary for an acid-base titration, you can easily change the above equation according to the activity / concentration of the oxonium ions on the outer layer." ]

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[ "# Divisors of 136\n\n## Divisors of 136\n\nThe list of all positive divisors (that is, the list of all integers that divide 22) is as follows :\n\nAccordingly:\n\n136 is multiplo of 1\n\n136 is multiplo of 2\n\n136 is multiplo of 4\n\n136 is multiplo of 8\n\n136 is multiplo of 17\n\n136 is multiplo of 34\n\n136 is multiplo of 68\n\n136 has 7 positive divisors\n\n## Parity of 136\n\nIn addition we can say of the number 136 that it is even\n\n136 is an even number, as it is divisible by 2 : 136/2 = 68\n\n## The factors for 136\n\nThe factors for 136 are all the numbers between -136 and 136 , which divide 136 without leaving any remainder. Since 136 divided by -136 is an integer, -136 is a factor of 136 .\n\nSince 136 divided by -136 is a whole number, -136 is a factor of 136\n\nSince 136 divided by -68 is a whole number, -68 is a factor of 136\n\nSince 136 divided by -34 is a whole number, -34 is a factor of 136\n\nSince 136 divided by -17 is a whole number, -17 is a factor of 136\n\nSince 136 divided by -8 is a whole number, -8 is a factor of 136\n\nSince 136 divided by -4 is a whole number, -4 is a factor of 136\n\nSince 136 divided by -2 is a whole number, -2 is a factor of 136\n\nSince 136 divided by -1 is a whole number, -1 is a factor of 136\n\nSince 136 divided by 1 is a whole number, 1 is a factor of 136\n\nSince 136 divided by 2 is a whole number, 2 is a factor of 136\n\nSince 136 divided by 4 is a whole number, 4 is a factor of 136\n\nSince 136 divided by 8 is a whole number, 8 is a factor of 136\n\nSince 136 divided by 17 is a whole number, 17 is a factor of 136\n\nSince 136 divided by 34 is a whole number, 34 is a factor of 136\n\nSince 136 divided by 68 is a whole number, 68 is a factor of 136\n\n## What are the multiples of 136?\n\nMultiples of 136 are all integers divisible by 136 , i.e. the remainder of the full division by 136 is zero. There are infinite multiples of 136. The smallest multiples of 136 are:\n\n0 : in fact, 0 is divisible by any integer, so it is also a multiple of 136 since 0 × 136 = 0\n\n136 : in fact, 136 is a multiple of itself, since 136 is divisible by 136 (it was 136 / 136 = 1, so the rest of this division is zero)\n\n272: in fact, 272 = 136 × 2\n\n408: in fact, 408 = 136 × 3\n\n544: in fact, 544 = 136 × 4\n\n680: in fact, 680 = 136 × 5\n\netc.\n\n## Is 136 a prime number?\n\nIt is possible to determine using mathematical techniques whether an integer is prime or not.\n\nfor 136, the answer is: No, 136 is not a prime number.\n\n## How do you determine if a number is prime?\n\nTo know the primality of an integer, we can use several algorithms. The most naive is to try all divisors below the number you want to know if it is prime (in our case 136). We can already eliminate even numbers bigger than 2 (then 4 , 6 , 8 ...). Besides, we can stop at the square root of the number in question (here 11.662 ). Historically, the Eratosthenes screen (which dates back to Antiquity) uses this technique relatively effectively.\n\nMore modern techniques include the Atkin screen, probabilistic tests, or the cyclotomic test." ]

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[ "### thank you to the person who will help me include include using namespace std int mai 3806568", null, "Thank you to the person who will help me :))\n\n#include\n\n#include\n\nusing namespace std;\n\nint main()\n\n{\n\n//variable initialization\n\ndouble rate=0.05;//\n\ndouble bal=100;\n\ndouble interest;\n\ndouble totalInterest=0;\n\ncout\n\ncout\n\n//Running for loop for ten times\n\nfor(int i=0;i{\n\n//compound interest calculation\n\n//find interest\n\ninterest=bal*rate;\n\nbal=bal+interest;\n\n//adding interest to find total interst\n\ntotalInterest+=interest;\n\ncout\n\n}\n\ncout\n\nsystem(“pause”);\n\nreturn 0;\n\n}" ]

[ null, "https://authoritypapers.com/thank-you-to-the-person-who-will-help-me-include-include-using-namespace-std-int-mai-3806568/", null ]

[ "# pdist2 equivalent in MATLAB version 7\n\nI need to calculate the euclidean distance between 2 matrices in matlab. Currently I am using bsxfun and calculating the distance as below( i am attaching a snippet of the code ):\n\n``````for i=1:4754\ntest_data=fea_test(i,:);\nd=sqrt(sum(bsxfun(@minus, test_data, fea_train).^2, 2));\nend\n``````\n\nSize of fea_test is 4754x1024 and fea_train is 6800x1024 , using his for loop is causing the execution of the for to take approximately 12 minutes which I think is too high. Is there a way to calculate the euclidean distance between both the matrices faster?\n\nI was told that by removing unnecessary for loops I can reduce the execution time. I also know that pdist2 can help reduce the time for calculation but since I am using version 7. of matlab I do not have the pdist2 function. Upgrade is not an option.\n\nAny help.\n\nRegards,\n\nBhavya\n\nYou could fully vectorize the calculation by repeating the rows of `fea_test` 6800 times, and of `fea_train` 4754 times, like this:\n\n``````rA = size(fea_test,1);\nrB = size(fea_train,1);\n\n[I,J]=ndgrid(1:rA,1:rB);\n\nd = zeros(rA,rB);\n\nd(:) = sqrt(sum(fea_test(J(:),:)-fea_train(I(:),:)).^2,2));\n``````\n\nHowever, this would lead to intermediary arrays of size 6800x4754x1024 (*8 bytes for doubles), which will take up ~250GB of RAM. Thus, the full vectorization won't work.\n\nYou can, however, reduce the time of the distance calculation by preallocation, and by not calculating the square root before it's necessary:\n\n``````rA = size(fea_test,1);\nrB = size(fea_train,1);\nd = zeros(rA,rB);\n\nfor i = 1:rA\ntest_data=fea_test(i,:);\nd(i,:)=sum( (test_data(ones(nB,1),:) - fea_train).^2, 2))';\nend\n\nd = sqrt(d);\n``````\n• `repmat` is never good for performance. You're better off inlining in this case: replace `repmat(test_data,nB,1)` with `test_data(ones(1,n8), :)`. – Nzbuu Oct 8 '11 at 13:31\n• @Jones thank you for this reply, but this does not reduce the number of for loops i have in my code. I already have a for loop within which this loop is found and the execution time is still the same. – bhavs Oct 8 '11 at 15:01\n• @BhavyaPH: The solution that reduces the number of `for` loops will most likely not run on your computer due to not enough RAM. The other solution should reduce the execution time. Have you used the profiler to compare? – Jonas Oct 8 '11 at 15:49\n• Removing for loops isn't always fastest due to the JIT. See stackoverflow.com/questions/7569368/…, and many other questions on SO. – Nzbuu Oct 8 '11 at 17:32\n\nHere is vectorized implementation for computing the euclidean distance that is much faster than what you have (even significantly faster than PDIST2 on my machine):\n\n``````D = sqrt( bsxfun(@plus,sum(A.^2,2),sum(B.^2,2)') - 2*(A*B') );\n``````\n\nIt is based on the fact that: `||u-v||^2 = ||u||^2 + ||v||^2 - 2*u.v`\n\nConsider below a crude comparison between the two methods:\n\n``````A = rand(4754,1024);\nB = rand(6800,1024);\n\ntic\nD = pdist2(A,B,'euclidean');\ntoc\n\ntic\nDD = sqrt( bsxfun(@plus,sum(A.^2,2),sum(B.^2,2)') - 2*(A*B') );\ntoc\n``````\n\nOn my WinXP laptop running R2011b, we can see a 10x times improvement in time:\n\n``````Elapsed time is 70.939146 seconds. %# PDIST2\nElapsed time is 7.879438 seconds. %# vectorized solution\n``````\n\nYou should be aware that it does not give exactly the same results as PDIST2 down to the smallest precision.. By comparing the results, you will see small differences (usually close to `eps` the floating-point relative accuracy):\n\n``````>> max( abs(D(:)-DD(:)) )\nans =\n1.0658e-013\n``````\n\nOn a side note, I've collected around 10 different implementations (some are just small variations of each other) for this distance computation, and have been comparing them. You would be surprised how fast simple loops can be (thanks to the JIT), compared to other vectorized solutions...\n\n• @Alex: thanks. I see your solution is basically the same, only I avoid creating temp matrices in memory by using BSXFUN (instead of using REPMAT and the like) – Amro Jun 29 '12 at 17:27\n• Agree, bsxfun is one of the underrated and unknown functions in MATLAB. It doesn't waste memory like repmat. More users need to learn how to use it when 'vectorizing' their code. – Alexey Jun 29 '12 at 19:31\n• Just a quick note, I compared both PDIST2 and your method using bsxfun and serially bsxfun is much faster. However, inside of a parfor loop performance actually got worse using your bsxfun method for DD. – brown.2179 Mar 2 '14 at 17:14\n• but vectorized code can be used to have even better performance if GPUs are around and for loops aren't...right? – Charlie Parker Mar 24 '16 at 5:08\n• @CharlieParker I guess, you'd have to benchmark and see.. My point was that for-loops in MATLAB had gotten a bad reputation in the past, but they're not as bad nowadays. – Amro Mar 24 '16 at 5:13\n\nTry this vectorized version, it should be pretty efficient. Edit: just noticed that my answer is similar to @Amro's.\n\n``````function K = calculateEuclideanDist(P,Q)\n% Vectorized method to compute pairwise Euclidean distance\n% Returns K(i,j) = sqrt((P(i,:) - Q(j,:))'*(P(i,:) - Q(j,:)))\n\n[nP, d] = size(P);\n[nQ, d] = size(Q);\n\npmag = sum(P .* P, 2);\nqmag = sum(Q .* Q, 2);\n\nK = sqrt(ones(nP,1)*qmag' + pmag*ones(1,nQ) - 2*P*Q');\n\nend\n``````" ]

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[ "Like logic, the subject of sets is rich and interesting for its own sake. We will need only a few facts about sets and techniques for dealing with them, which we set out in this section and the next. We will return to sets as an object of study in chapters 4 and 5.\n\nA set is a collection of objects; any one of the objects in a set is called a member or an element of the set. If $a$ is an element of a set $A$ we write $a\\in A$.\n\nSome sets occur so frequently that there are standard names and symbols for them. We denote the real numbers by $\\R$, the rational numbers (that is, the fractions) by $\\Q$, the integers by $\\Z$ and the natural numbers (that is, the positive integers) by $\\N$.\n\nThere is a natural relationship between sets and logic. If $A$ is a set, then $P(x)=$\"$x\\in A$'' is a formula. It is true for elements of $A$ and false for elements outside of $A$. Conversely, if we are given a formula $Q(x)$, we can form the truth set consisting of all $x$ that make $Q(x)$ true. This is usually written $\\{x:Q(x)\\}$ or $\\{x\\mid Q(x)\\}$.\n\nExample 1.5.1 If the universe is $\\Z$, then $\\{x:x>0\\}$ is the set of positive integers and $\\{x:\\exists n\\,(x=2n)\\}$ is the set of even integers. $\\square$\n\nIf there are a finite number of elements in a set, or if the elements can be arranged in a sequence, we often indicate the set simply by listing its elements.\n\nExample 1.5.2 $\\{1,2,3\\}$ and $\\{1,3,5,7,9,…\\}$ are sets of integers. The second is presumably the set of all positive odd numbers, but of course there are an infinite number of other possibilities. In all but the most obvious cases, it is usually wise to describe the set (\"the set of positive odd numbers, $\\{1,3,5,7,9,…\\}$'') or give a formula for the terms (\"$\\{1,3,5,7,9,\\ldots,2i+1,\\ldots\\}$''). $\\square$\n\nExample 1.5.3 We indicate the empty set by $\\emptyset$, that is, $\\emptyset=\\{\\}$ is the set without any elements. Note well that $\\emptyset\\ne\\{\\emptyset\\}$: the first contains nothing, the second contains a single element, namely the empty set. $\\square$\n\nThe logical operations $\\lnot, \\land, \\lor$ translate into the theory of sets in a natural way using truth sets. If $A$ is a set, define $$A^c=\\{x: x\\notin A\\},$$ called the complement of $A$. If $B$ is a second set, define $$A\\cap B=\\{x:x\\in A\\land x\\in B\\},$$ called the intersection of $A$ and $B$, and $$A\\cup B=\\{x:x\\in A\\lor x\\in B\\},$$ called the union of $A$ and $B$.\n\nExample 1.5.4 Suppose $U=\\{1,2,3,\\ldots,10\\}$, $A=\\{1,3,4,5,7\\}$, $B=\\{1,2,4,7,8,9\\}$; then $A^c=\\{2,6,8,9,10\\}$, $A\\cap B=\\{1,4,7\\}$ and $A\\cup B=\\{1,2,3,4,5,7,8,9\\}$. Note that the complement of a set depends on the universe $U$, while the union and intersection of two sets do not. $\\square$\n\nWe often wish to compare two sets. We say that $A$ is a subset of $B$ if $$\\forall x (x\\in A\\implies x\\in B),$$ and write $A\\subseteq B$. This is not only a definition but a technique of proof. If we wish to show $A\\subseteq B$ we may start with an arbitrary element $x$ of $A$ and prove that it must be in $B$. We say the sets $A$ and $B$ are equal if and only if $A\\subseteq B$ and $B\\subseteq A$, that is, $$\\forall x (x\\in A\\iff x\\in B).$$ So to show two sets are equal one must verify that a biconditional is satisfied, which often needs to be done in two parts, that is, the easiest way to show that $A=B$ often is to show that $A\\subseteq B$ and $B\\subseteq A$. If $A\\subseteq B$ and $A\\ne B$, we say $A$ is a proper subset of $B$ and write $A\\subset B$.\n\nExample 1.5.5 $\\N\\subset\\Z\\subset\\Q\\subset\\R$. $\\square$\n\nFinally, we say that $A$ and $B$ are disjoint if $A\\cap B=\\emptyset$.\n\nIn section 1.1 we learned that logical operations are related by many tautologies, the study of which is called Boolean Algebra. These tautologies can be interpreted as statements about sets; here are some particularly useful examples.\n\nTheorem 1.5.6 Suppose $A$, $B$ and $C$ are sets. Then\n\na) $A\\cap B\\subseteq A$,\n\nb) $A\\subseteq A\\cup B$,\n\nc) $A\\cap(B\\cup C)=(A\\cap B)\\cup (A\\cap C)$,\n\nd) $A\\cup(B\\cap C)=(A\\cup B)\\cap (A\\cup C)$,\n\ne) $(A\\cap B)^c=A^c\\cup B^c$,\n\nf) $(A\\cup B)^c=A^c\\cap B^c$,\n\ng) $A\\subseteq B$ iff $B^c\\subseteq A^c$.\n\nProof. Suppose $P(x)=$\"$x\\in A$'', $Q(x)=$\"$x\\in B$'', $R(x)=$\"$x\\in C$''. To prove (a), suppose that $a\\in A\\cap B$. Then by definition, $P(a)\\land Q(a)$ is true. Since $P(x)\\land Q(x)\\implies P(x)$ is a tautology, $P(a)$ is true, or $a\\in A$. As noted above, this proves that $A\\cap B\\subseteq A$. Similarly, (c) follows since $P(x)\\land(Q(x)\\lor R(x))\\iff (P(x)\\land Q(x))\\lor (P(x)\\land R(x))$ is a tautology. All the other statements follow in the same manner. $\\qed$\n\nAs in the case of logic, (e) and (f) are called De Morgan's laws. Theorem 1.5.6 certainly is not an exhaustive list of set identities, it merely illustrates a few of the more important ones.\n\nIf $a,b\\in U$ we can form the ordered pair $(a,b)$. The fundamental property of ordered pairs is that $(a_1,b_1)=(a_2,b_2)$ if and only if $a_1=a_2$ and $b_1=b_2$. If $A$ and $B$ are sets, the set $$A\\times B=\\{(a,b): a\\in A\\land b\\in B\\}$$ is called the Cartesian product of $A$ and $B$." ]

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[ "Courses\nCourses for Kids\nFree study material\nOffline Centres\nMore\n\n# RD Sharma Class 11 Solutions Chapter 32 - Statistics (Ex 32.4) Exercise 32.4 - Free PDF", null, "Last updated date: 04th Dec 2023\nTotal views: 519.3k\nViews today: 9.19k\n\n## Vedantu’s RD Sharma Free PDF For Class 11 Solutions Available\n\nStatistics is the way of summarizing in brief; the way to know and measure. You know a few things about any item or object; like the temperature of the air is 70 degrees Celsius, it can be measured through a thermometer; you can also know about a person; you can know the height of the person, weight, age of the person, income and all that.\n\nFrom the above definition, we can understand what Statistics is. It is the process of analyzing and recording information to understand how it affects the decisions that we make and how we choose to live our life. It is a science that studies and looks for patterns, to find connections, relationships and trends among things. Statistics can be a bit daunting, so here are some points to help you to understand the subject better.\n\n## Statistical Terms and Definitions\n\nBefore starting, we will take a look at some basic terms and definitions that are mostly used in statistics and to understand the subject better.\n\n• Data: Data can be anything that is collected or observed. It can be information collected from the observations of a particular set of objects. It includes both tangible and intangible things.\n\nExample: The data is the source of information that is collected and analyzed. It is information that shows us about our world. The data we have in our minds, the experiences that we have, the books we read, the conversations that we hear, the things we see, everything is our data.\n\n• Records: Records are considered as the list of collected data or information that is recorded on a particular topic or subject. It includes data about all the facts about a particular thing. It is important to know that every record contains several pieces of data.\n\nExample: An internet history is a record of what has happened on the internet.\n\n• Variables: Variables are the elements that we will use to measure. It can be an answer that we want to get and the variables that will be used to solve the problem.\n\nExample: The total population of the world is the variable that we will use to find out how many people are left in the world.\n\n• Variance: The variance is the variation or the difference in the values of the variable. The value of the difference in one variable and its average. The higher the variance, the higher the variation in that set of values.\n\nExample: When we take the average of 3 numbers then the difference is between 2 and 3. If we multiply the numbers then it is the number in the last row minus the number in the first row.\n\n• Standard Deviation: The standard deviation is a measure of the standard of the variation that exists in the data set.\n\nExample: If there are 50 data in our set, then we will use the average of the set as a mean and we will find the standard deviation using the average of the set.\n\n• Normal Distribution: It is one of the five common distributions of continuous data. The Normal Distribution has a bell-like shape with most of its data on one side. There are two peaks of the distribution. The peak at the mean is most of the data points. The peak at the mean is not symmetrical. The variance of the distribution is 1.0.\n\nExample: If we want to find out the number of people in the group, then the mean of this group is 100 people and the standard deviation is 10 people. This means that most of the people are concentrated at the right side of the bell-like distribution. The mean will be approximately a value of 60 people.\n\n• Percentiles: The percentiles are numerical values that are associated with points in the distribution. These points are chosen to represent the distribution.\n\nExample: There are four numbers which have an average of 15. Suppose that these numbers are 15, 17, 20, and 30. Then these are the percentiles.\n\n• InterQuartile Range: The InterQuartile Range is the difference between the 25th percentile and the 75th percentile. It is equal to the 75th percentile - 25th percentile. If the IQR is 0, then the 25th and 75th percentiles are equal.\n\nExample: Given the average of the four numbers is 15 and suppose the 25th percentile is 10 and the 75th percentile is 20, then the IQR is 15 - 10 = 5 and the InterQuartile Range is 75th percentile - 25th percentile = 5. The difference between the 75th percentile and the 25th percentile is 50%.\n\n• Variance: The variance is a mathematical measure of how much one measurement varies from the average.\n\nExample: If we assume that the standard deviation of four numbers are 10, 5, 4, and 3, then the variance will be\n\n• Skewness: Skewness is the measure of the shape of the distribution.\n\nExample: The skewness of a distribution is equal to (Median - Average) / Standard Deviation. Suppose we have two groups of 30 numbers. One group consists of numbers from 5 to 30 and the other group consists of numbers from 20 to 30. The average of the first group is equal to 15 and the average of the second group is equal to 25. The median of the first group is 15 and the median of the second group is 25. The standard deviation of the first group is equal to 5. The standard deviation of the second group is equal to 2. Then the skewness of the first group of 30 numbers is (15 - 15) / (5) = 0 and the skewness of the second group of 30 numbers is (25 - 15) / (2) = 10. The skewness of the first group of 30 numbers is less than 0 and the skewness of the second group of 30 numbers is greater than 0.\n\nFree PDF download of RD Sharma Class 11 Solutions Chapter 32 - Statistics Exercise 32.4 solved by Expert Mathematics Teachers on Vedantu. All Chapter 32 - Statistics Ex 32.4 Questions with Solutions for RD Sharma Class 11 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.\n\n## FAQs on RD Sharma Class 11 Solutions Chapter 32 - Statistics (Ex 32.4) Exercise 32.4 - Free PDF\n\n1. What are the primary topics in Statistics?\n\nData is everywhere around us, the whole task is to make it usable. For this purpose students of class 11 have a chapter in their mathematics syllabus. The initial topics one should know in the chapter statistics are the Collection of data and its organization. The collection is the process of gathering and measuring information on diverse topics. The second step in the study related to data is an organization of data which is all about categorizing and classifying data to make it more usable.\n\n2. Why should students learn Statistics?\n\nStudents of class 11 enter into their higher secondary education which gives them an idea about various subjects which can be pursued in their further education as well for research purposes. Therefore Statistics is included in their curriculum to let them know about the basics of statistics. Statistics is such a subject that is used everywhere, for instance, CGPA is an example. Hence students should know the basics of this chapter which is used in day to day life.\n\n3. Where can I find solutions for class 11 Statistics?\n\nStatistics is a chapter in class 11 is a chapter primarily focused on the collection of data, organizing, presentation and interpretation of it to make it understandable. Vedantu is a platform that aims at making students well prepared for the final exams and therefore it provides answers to all the questions of previous year question papers obtained from expert teachers in the subject which can be downloaded either through the app or website.\n\n4. How to score well in class 11 Statistics?\n\nStudents face little confusion in Statistics as this chapter is primarily focused on collecting, organizing, presenting and interpreting data to make it understandable due to the similar formulas. So, students need to pay attention to the minute differences in using the formulas and solving the problems. This can be done effectively if planned daily with proper notes. At Vedantu, we provide students with adequate study material and notes which helps them grasp and retain the concepts for a longer period. To find notes, visit the Vedantu app or website.\n\n5. Where can I find notes for class 11 Statistics?\n\nStatistics is a very interesting and important chapter in the class 11 curriculum which the majority of students enjoy doing. Also, it has a lot of practical applications that become one of the reasons to score well in this chapter. Students. At Vedantu, we provide students with adequate study material and notes which makes it not only easier but also interesting to the students and helps them grasp and retain the concepts for a longer period of time. To find notes, visit the Vedantu app or website." ]

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