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# Posts tagged programming
## 5 things I learned at SciPy
I’ve finally decompressed after my first go-around with Scipy. For those who haven’t heard of this conference before, Scipy is an annual meeting where members of scientific community get together to discuss their love of Python, scientific programming, and open science. It spans both academics and people from industry, making it a unique place in terms of how software interfaces with scientific research. (if you’re interested the full set of Scipy conferences, check out here.
It was an eye-opening experience that I learned a lot from, so here’s a quick recap of some things that I learned during my first rodeo.
## The beauty of computational efficiency
When we discuss “computational efficiency”, you often hear people throw around phrases like $$O(n^2)$$ or $$O(nlogn)$$. We talk about them in the abstract, and it can be hard to appreciate what these distinctions mean and how important they are. So let’s take a quick look at what computational efficiency looks like in the context of a very famous algorithm: The Fourier Transform.
Briefly, A Fourier Transform is used for uncovering the spectral information that is present in a signal. AKA, it tells us about oscillatory components in the signal, and has a wide range of uses in communications, signal processing, and even neuroscience analysis.
## Scraping craigslist
In this notebook, I’ll show you how to make a simple query on Craigslist using some nifty python modules. You can take advantage of all the structure data that exists on webpages to collect interesting datasets.
First we need to figure out how to submit a query to Craigslist. As with many websites, one way you can do this is simply by constructing the proper URL and sending it to Craigslist. Here’s a sample URL that is returned after manually typing in a search to Craigslist:
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# SIP-88: ExchangeRates patch - Chainlink aggregator V2V3
Author Clement Balestrat Implemented Governance Ethereum TBD TBD 2020-10-06
## Simple Summary
During the Formalhaut release, an update was made to the ExchangeRates contract to be using Chainlink's aggregator V2V3 (SIP-86).
Just after the change was made, we found an edge case where transfers are reverting if a price has not been updated after a user exchanges into a Synth. The issue relates to how fee reclamation is calculated.
## Abstract
This SIP will fix the issue by using low level calls to the Chainlink aggregator's latestRoundData and getRoundData functions in order to avoid any reverts in case the requested round ID does not exist.
This will act as a try/catch method which will allow the ExchangeRates contract to only update a rate if the previous call to the aggregator was successful.
## Motivation
In the previous version of Chainlink's aggregator interface, the function getRoundData(uint roundId) was returning 0 in case roundId was not found.
This was helpful for the ExchangeRates contract to know if a new round ID existed or not during the calculation of fee reclamation, by calling getRoundData(roundId + 1). If the result was returning 0, the current round ID was kept for the next steps.
However, this logic was changed in the latest aggregator interface. Calling getRoundData(roundId) is now reverting if roundId cannot be found, which makes the current logic obsolete.
## Specification
### Overview
This SIP will implement low-level calls to Chainlink aggregator's getRoundData() and getLatestRoundData() functions in order to suppress any reverts.
bytes memory payload = abi.encodeWithSignature("getRoundData(uint80)", roundId);
As shown above, staticcall is used here to avoid getRoundData() from reverting, returning success and returnData.
If success is true, ExchangeRates will then update the rates with returnData. If success is false, we do nothing.
### Test Cases
A production test will need to be added with the following scenario:
• Exchange a synth from sUSD to sETH
• Wait the required amount of time for a transaction to be allowed to settle (SystemSettings.waitingPeriodsSecs())
• Settle sETH
This scenario will only pass if the patch described in this SIP is implemented. It will fail otherwise.
N/A
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# Curious about an empirically found continued fraction for tanh
First of all, and since this is my first question in this forum, I would like to specify that I am not a professional mathematician (but a philosophy teacher); I apologize by advance if something is wrong in my question.
I enjoy doing numerical computations on my leisure time, and at the end of the last summer, I was working on some personal routines related to the world of ISC. With the help of these pieces of code, I detected algorithmically several identities, among which the following one $$\tanh z = \operatorname*{K}_{n=1}^{\infty} \frac{1 + \left((n-1) \frac{\pi}{4} z^{-1}\right)^2}{(2n-1) \frac{\pi}{4} z^{-1}} \tag{1} \label{1}$$
The previous notation is the one I use; I find it convenient and it can be found for instance in Continued Fractions with Applications by Lorentzen & Waadeland, but I know that some people don't like it; it has to be read the following way: $$a_0 + \operatorname*{K}_{n=1}^{\infty} \frac{b_n}{a_n} = a_0 + \cfrac{b_1}{a_1 + \cfrac{b_2}{a_2 + \cfrac{b_3}{a_3 + \dotsb}}}$$
This continued fraction is nice when used for computing the hyperbolic tangent of numbers like $\pi/4$ and other simple multiples of $\pi$ since it will only involve integer numbers in the expansion of the continued fraction.
Of course I browsed a little in order to see what was known about it, for example here, but I didn't find anything similar. I also sent it to several professional mathematicians, who told me that it could be difficult to recognize easily whether this continued fraction was equivalent to some other identity or not.
I haven't myself the required skills to study further this expression, but I would be very happy to know more about it: is it something well-known? Is it something that comes trivially from some other identity? Is it (who knows?) something new?
Edit 1: I posted myself an answer to the question by thinking something new was found; but it happened to be related to the precision in the computation. For that reason I may delete this answer in the future.
Edit 2: In this edit I am going to explain more how I came up with the identity and to add a code that can be used to test the identity.
I will not post my C code here because it is too long but I can really share it if someone wants it. Basically: I coded in the end of last summer a program in C computing very quickly millions of random continued fractions; each one was computed up to its 36th convergent; convergence was checked by looking at the difference between 35th and 36th convergent. Any quadratic value was discarded as not interesting for my purpose. Remaining values were matched against all non-quadratic values in Shamos's catalogue of real numbers by computing the PSLQ vector for $[z,1,S]$ (where $z$ was a continued fraction and $S$ a number from Shamos's book). I used a personal hygienic C macro for the pslq algorithm that I share here. The precision when computing the PSLQ algorithm on double-precision numbers was "poor" (about 12 digits) but I focused on speed for this project. Whenever an interesting result was returned by the PSLQ algorithm (low norm of the returned vector), the continued fraction was computed a second time with the dd type from D.H. Bailey's libqd library (about 32 exact digits only but much quicker than any arbitrary precision library; furthermore precision in Shamos's book is only 20 digits). If the coefficients previously returned by the PSLQ algorithm were able to find again the relation with at least 17 exact digits, current parameters were printed. I made this program run for several weeks on three cores of a Raspberry Pi 2 (which is rather slow but which can compute long tasks without getting warm). Results had to be later generalized "by hand" when similar values were noticed by me. What I finally got was much more than I could expect. Above is one of these results.
Below is some code for Maxima (using the bfloat types):
/* Set the precision of the computation with bfloat numbers */
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location: Publications → journals
Search results
Search: All articles in the CJM digital archive with keyword toroidal filling
Expand all Collapse all Results 1 - 1 of 1
1. CJM 2008 (vol 60 pp. 164)
Lee, Sangyop; Teragaito, Masakazu
Boundary Structure of Hyperbolic $3$-Manifolds Admitting Annular and Toroidal Fillings at Large Distance For a hyperbolic $3$-manifold $M$ with a torus boundary component, all but finitely many Dehn fillings yield hyperbolic $3$-manifolds. In this paper, we will focus on the situation where $M$ has two exceptional Dehn fillings: an annular filling and a toroidal filling. For such a situation, Gordon gave an upper bound of $5$ for the distance between such slopes. Furthermore, the distance $4$ is realized only by two specific manifolds, and $5$ is realized by a single manifold. These manifolds all have a union of two tori as their boundaries. Also, there is a manifold with three tori as its boundary which realizes the distance $3$. We show that if the distance is $3$ then the boundary of the manifold consists of at most three tori. Keywords:Dehn filling, annular filling, toroidal filling, knotCategories:57M50, 57N10
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# American Institute of Mathematical Sciences
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January 2018, 14(1): 309-323. doi: 10.3934/jimo.2017048
## On analyzing and detecting multiple optima of portfolio optimization
1 China Academy of Corporate Governance & Department of Financial Management, Business School & Collaborative Innovation Center for China Economy, Nankai University, 94 Weijin Road, Tianjin, 300071, China 2 Department of Financial Management, Business School, Nankai University, 94 Weijin Road, Tianjin, 300071, China
* Corresponding author: Su Zhang
Received July 2016 Revised November 2016 Published June 2017
Fund Project: The first author is supported by Social Science Grant of the Ministry of Education of China grant 14JJD630007. The third author is supported by National Natural Science Foundation of China grant 11401322 and Fundamental Research Funds for the Central Universities grant NKZXB1447
Portfolio selection is widely recognized as the birth-place of modern finance; portfolio optimization has become a developed tool for portfolio selection by the endeavor of generations of scholars. Multiple optima are an important aspect of optimization. Unfortunately, there is little research for multiple optima of portfolio optimization. We present examples for the multiple optima, emphasize the risk of overlooking the multiple optima by (ordinary) quadratic programming, and report the software failure by parametric quadratic programming. Moreover, we study multiple optima of multiple-objective portfolio selection and prove the nonexistence of the multiple optima of an extension of the model of Merton. This paper can be a step-stone of studying the multiple optima.
Citation: Yue Qi, Zhihao Wang, Su Zhang. On analyzing and detecting multiple optima of portfolio optimization. Journal of Industrial & Management Optimization, 2018, 14 (1) : 309-323. doi: 10.3934/jimo.2017048
##### References:
[1] Z. Bodie, A. Kane and A. J. Marcus, Investments, 10th edition, McGraw-Hill/Irwin, Boston, 2013. [2] S. P. Boyd and L. Vandenberghe, Convex Optimization, 1st edition, Cambridge University Press, Cambridge, Britain, 2004. doi: 10.1017/CBO9780511804441. [3] P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, 1st edition, Springer Verlag, New York, 1987. doi: 10.1007/978-1-4899-0004-3. [4] V. DeMiguel, L. Garlappi, F.J. Nogales and R. Uppal, A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms, Management Science, 55 (2009), 798-812. [5] V. DeMiguel, L. Garlappi and R. Uppal, Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?, Review of Financial Studies, 22 (2009), 1915-1953. doi: 10.1093/acprof:oso/9780199744282.003.0034. [6] D. Disatnik and S. Katz, Portfolio optimization using a block structure for the covariance matrix, Journal of Business Finance & Accounting, 39 (2012), 806-843. [7] P. H. Dybvig, Short sales restrictions and kinks on the mean variance frontier, The Journal of Finance, 39 (1984), 239-244. doi: 10.1111/j.1540-6261.1984.tb03871.x. [8] M. Ehrgott, Multicriteria Optimization, Volume 491 of Lecture Notes in Economics and Mathematical Systems, 2nd edition, Springer Verlag, Berlin, 2005. doi: 10.1007/978-3-662-22199-0. [9] E. J. Elton, M. J. Gruber, S. J. Brown and W. N. Goetzmann, Modern Portfolio Theory and Investment Analysis, 9th edition, John Wiley & Sons, New York, 2014. [10] J. B. Guerard, Handbook of Portfolio Construction: Contemporary Applications of Markowitz Techniques, Springer, New York, 2010. [11] G. Hadley, Nonlinear and Dynamic Programming, Addison Wesley, Reading, Massachusetts, 1964. [12] F. S. Hillier and G. J. Lieberman, Introduction to Operations Research, Third edition. Holden-Day, Inc., Oakland, Calif., 1980. [13] M. Hirschberger, Y. Qi and R. E. Steuer, Large-scale MV efficient frontier computation via a procedure of parametric quadratic programming, European Journal of Operational Research, 204 (2010), 581-588. doi: 10.1016/j.ejor.2009.11.016. [14] C. Huang and R. H. Litzenberger, Foundations for Financial Economics, Prentice Hall, Englewood Cliffs, New Jersey, 1988. [15] B. I. Jacobs, K. N. Levy and H. M. Markowitz, Portfolio optimization with factors, scenarios, and realistic short positions, Operations Research, 53 (2005), 586-599. doi: 10.1287/opre.1050.0212. [16] H. M. Markowitz, Portfolio selection, The Journal of Finance, 7 (1952), 77-91. doi: 10.1111/j.1540-6261.1952.tb01525.x. [17] H. M. Markowitz and A. F. Perold, Portfolio analysis with factors and scenarios, The Journal of Finance, 36 (1981), 871-877. doi: 10.1111/j.1540-6261.1981.tb04889.x. [18] H. M. Markowitz and G. P. Todd, Mean-Variance Analysis in Portfolio Choice and Capital Markets, Frank J. Fabozzi Associates, New Hope, Pennsylvania, 2000. [19] R. C. Merton, An analytical derivation of the efficient portfolio frontier, Journal of Financial and Quantitative Analysis, 7 (1972), 1851-1872. [20] K. Miettinen, Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Boston, 1999. [21] Y. Qi, R. E. Steuer and M. Wimmer, An analytical derivation of the efficient surface in portfolio selection with three criteria, Annals of Operations Research, 251 (2017), 161-177. doi: 10.1007/s10479-015-1900-y. [22] M. Rubinstein, Markowitz's "portfolio selection": A fifty-year retrospective, The Journal of Finance, 57 (2002), 1041-1045. [23] M. Stein, J. Branke and H. Schmeck, Efficient implementation of an active set algorithm for large-scale portfolio selection, Computers & Operations Research, 35 (2008), 3945-3961. doi: 10.1016/j.cor.2007.05.004. [24] R. E. Steuer, Multiple Criteria Optimization: Theory, Computation, and Application, John Wiley & Sons, New York, 1986. [25] R. E. Steuer and P. Na, Multiple criteria decision making combined with finance: A categorized bibliography, European Journal of Operational Research, 150 (2003), 496-515. doi: 10.1016/S0377-2217(02)00774-9. [26] J. Vörös, The explicit derivation of the efficient portfolio frontier in the case of degeneracy and general singularity, European Journal of Operational Research, 32 (1987), 302-310. doi: 10.1016/S0377-2217(87)80153-4. [27] J. Vörös, J. Kriens and L. W. G. Strijbosch, A note on the kinks at the mean variance frontier, European Journal of Operational Research, 112 (1999), 236-239. [28] P. Wolfe, The simplex method for quadratic programming, Econometrica, 27 (1959), 382-398. doi: 10.2307/1909468. [29] C. Zopounidis, E. Galariotis, M. Doumpos, S. Sarri and K. Andriosopoulos, Multiple criteria decision aiding for finance: An updated bibliographic survey, European Journal of Operational Research, 247 (2015), 339-348. doi: 10.1016/j.ejor.2015.05.032.
show all references
##### References:
[1] Z. Bodie, A. Kane and A. J. Marcus, Investments, 10th edition, McGraw-Hill/Irwin, Boston, 2013. [2] S. P. Boyd and L. Vandenberghe, Convex Optimization, 1st edition, Cambridge University Press, Cambridge, Britain, 2004. doi: 10.1017/CBO9780511804441. [3] P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, 1st edition, Springer Verlag, New York, 1987. doi: 10.1007/978-1-4899-0004-3. [4] V. DeMiguel, L. Garlappi, F.J. Nogales and R. Uppal, A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms, Management Science, 55 (2009), 798-812. [5] V. DeMiguel, L. Garlappi and R. Uppal, Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?, Review of Financial Studies, 22 (2009), 1915-1953. doi: 10.1093/acprof:oso/9780199744282.003.0034. [6] D. Disatnik and S. Katz, Portfolio optimization using a block structure for the covariance matrix, Journal of Business Finance & Accounting, 39 (2012), 806-843. [7] P. H. Dybvig, Short sales restrictions and kinks on the mean variance frontier, The Journal of Finance, 39 (1984), 239-244. doi: 10.1111/j.1540-6261.1984.tb03871.x. [8] M. Ehrgott, Multicriteria Optimization, Volume 491 of Lecture Notes in Economics and Mathematical Systems, 2nd edition, Springer Verlag, Berlin, 2005. doi: 10.1007/978-3-662-22199-0. [9] E. J. Elton, M. J. Gruber, S. J. Brown and W. N. Goetzmann, Modern Portfolio Theory and Investment Analysis, 9th edition, John Wiley & Sons, New York, 2014. [10] J. B. Guerard, Handbook of Portfolio Construction: Contemporary Applications of Markowitz Techniques, Springer, New York, 2010. [11] G. Hadley, Nonlinear and Dynamic Programming, Addison Wesley, Reading, Massachusetts, 1964. [12] F. S. Hillier and G. J. Lieberman, Introduction to Operations Research, Third edition. Holden-Day, Inc., Oakland, Calif., 1980. [13] M. Hirschberger, Y. Qi and R. E. Steuer, Large-scale MV efficient frontier computation via a procedure of parametric quadratic programming, European Journal of Operational Research, 204 (2010), 581-588. doi: 10.1016/j.ejor.2009.11.016. [14] C. Huang and R. H. Litzenberger, Foundations for Financial Economics, Prentice Hall, Englewood Cliffs, New Jersey, 1988. [15] B. I. Jacobs, K. N. Levy and H. M. Markowitz, Portfolio optimization with factors, scenarios, and realistic short positions, Operations Research, 53 (2005), 586-599. doi: 10.1287/opre.1050.0212. [16] H. M. Markowitz, Portfolio selection, The Journal of Finance, 7 (1952), 77-91. doi: 10.1111/j.1540-6261.1952.tb01525.x. [17] H. M. Markowitz and A. F. Perold, Portfolio analysis with factors and scenarios, The Journal of Finance, 36 (1981), 871-877. doi: 10.1111/j.1540-6261.1981.tb04889.x. [18] H. M. Markowitz and G. P. Todd, Mean-Variance Analysis in Portfolio Choice and Capital Markets, Frank J. Fabozzi Associates, New Hope, Pennsylvania, 2000. [19] R. C. Merton, An analytical derivation of the efficient portfolio frontier, Journal of Financial and Quantitative Analysis, 7 (1972), 1851-1872. [20] K. Miettinen, Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Boston, 1999. [21] Y. Qi, R. E. Steuer and M. Wimmer, An analytical derivation of the efficient surface in portfolio selection with three criteria, Annals of Operations Research, 251 (2017), 161-177. doi: 10.1007/s10479-015-1900-y. [22] M. Rubinstein, Markowitz's "portfolio selection": A fifty-year retrospective, The Journal of Finance, 57 (2002), 1041-1045. [23] M. Stein, J. Branke and H. Schmeck, Efficient implementation of an active set algorithm for large-scale portfolio selection, Computers & Operations Research, 35 (2008), 3945-3961. doi: 10.1016/j.cor.2007.05.004. [24] R. E. Steuer, Multiple Criteria Optimization: Theory, Computation, and Application, John Wiley & Sons, New York, 1986. [25] R. E. Steuer and P. Na, Multiple criteria decision making combined with finance: A categorized bibliography, European Journal of Operational Research, 150 (2003), 496-515. doi: 10.1016/S0377-2217(02)00774-9. [26] J. Vörös, The explicit derivation of the efficient portfolio frontier in the case of degeneracy and general singularity, European Journal of Operational Research, 32 (1987), 302-310. doi: 10.1016/S0377-2217(87)80153-4. [27] J. Vörös, J. Kriens and L. W. G. Strijbosch, A note on the kinks at the mean variance frontier, European Journal of Operational Research, 112 (1999), 236-239. [28] P. Wolfe, The simplex method for quadratic programming, Econometrica, 27 (1959), 382-398. doi: 10.2307/1909468. [29] C. Zopounidis, E. Galariotis, M. Doumpos, S. Sarri and K. Andriosopoulos, Multiple criteria decision aiding for finance: An updated bibliographic survey, European Journal of Operational Research, 247 (2015), 339-348. doi: 10.1016/j.ejor.2015.05.032.
A feasible region Z of portfolio selection
The S, E, Z, and N of the example in subsection 3.1
The Z and N of the example in subsection 3.2
Incorrectly approximating the N of the example in subsection 3.1 by the major style of portfolio optimization
Incorrectly approximating the N of the example in subsection 3.2 by the major style of portfolio optimization
The Z and N of the generalization of the example in subsection 3.2
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2017 Impact Factor: 0.994
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# Is any linear combination of arbitrary elements in a vector space also arbitrary?
Assuming $K$ is some vector space, is it valid to say the following:
If $a, b, c \in K$ are arbitrary and $\gamma$ and $\phi$ are scalars, then $a+b$, $a+c$, $a+b+c$, $\gamma a$, $\gamma b$, $\gamma a+\phi b$, etc. are also arbitrary.
Put another way, is any linear combination of arbitrary vectors in a vector space also arbitrary? I am mainly interested in the case that $K$ is a vector space, but does it necessarily have to be a vector space?
I am probably over-thinking my introductory linear algebra homework problem, but the following is the context I'd like to know this for:
Show that
$$\begin{pmatrix}1\\1\\0\\0\end{pmatrix}, \begin{pmatrix}1\\0\\1\\0\end{pmatrix}, \begin{pmatrix}1\\0\\0\\1\end{pmatrix}, \begin{pmatrix}0\\1\\1\\0\end{pmatrix}, \begin{pmatrix}0\\1\\0\\1\end{pmatrix}, \begin{pmatrix}0\\0\\1\\1\end{pmatrix}$$
span $\mathbb{C}^4$; i.e., every vector on $\mathbb{C}^4$ can be written as a linear combination of these vectors. Which collections of those six vectors form a basis for $\mathbb{C}^4$?
You might say, well just show those column vectors span $\mathbb{C}^4$ by simply row reducing a matrix of those column vectors to show there is a trivial solution and thus these are independent vectors and so on. I technically haven't learned that in this class yet, so I would like to be more "rigorous" and prove it by showing that there exists scalars along with those vectors that form a linear combination for all vectors in $\mathbb{C}^4$.
My proof would go something like this:
Let $x_1, x_2, x_3, x_4 \in{\mathbb{C}}$ be arbitrary. Thus, $x_1+x_2+x_3$, $x_1+x_4$, and $x_2+x_4$ are also arbitrary elements of $\mathbb{C}$.
This means that $x=\begin{pmatrix}x_1+x_2+x_3\\x_1+x_4\\x_2+x_4\\x_3\end{pmatrix} \in{\mathbb{C}^4}$ is also arbitrary.
So a linear combination of $x$ with the given vectors is simply
$x_1\begin{pmatrix}1\\1\\0\\0\end{pmatrix}+ x_2\begin{pmatrix}1\\0\\1\\0\end{pmatrix}+ x_3\begin{pmatrix}1\\0\\0\\1\end{pmatrix}+ x_4\begin{pmatrix}0\\1\\1\\0\end{pmatrix}+ 0\begin{pmatrix}0\\1\\0\\1\end{pmatrix}+ 0\begin{pmatrix}0\\0\\1\\1\end{pmatrix}$
Therefore, the given vectors span $\mathbb{C}^4$ for all $x_i$. $\blacksquare$
For the second question, I'd argue that any 4 of those given vectors can be shown to span $\mathbb{C}^4$ in a similar manner. So there are ${6}\choose{4}$ ways 4 of those vectors form a basis for $\mathbb{C}^4$.
• Could you define what you mean by arbitrary? – YoTengoUnLCD Jul 15 '15 at 2:43
• I might be abusing that word in my example, but I'm taking it to mean that if $z\in{Z}$ is arbitrary , then whatever result I get for $z$ extends to all elements of the set $Z$. Would you say "$z\in{Z}$ is arbitrary" is the functional equivalent of "$\forall z \in{Z}$"? – gbrlrz017 Jul 15 '15 at 2:48
• I see what you mean, I would avoid using that word altogether, it causes confusion. Also, there aren't 6 choose 4 ways to pick those vectors to form a basis, pick vectors 2,3,4 and 5. Do those form a basis? However, there are infinite ways to form a basis from those vectors, let $x_1=6y_1 \in \Bbb C$, and you have a different basis than your original one. – YoTengoUnLCD Jul 15 '15 at 2:58
• You can't just generalize from a single example willy-nilly...maybe in science...but in math you need to show how being true for $z$ logically implies it holds for all Z – user237392 Jul 15 '15 at 2:59
• @ YoTengoUnLCD @ Bey, would you say my proof at the end is essentially correct? If it is, I think a better way of making the final conclusion is if I prove that there is a unique linear combination involving the vectors 1, 2, 3, and 4, so these four vectors form a basis. After this I'd say that there are ${6}\choose{4}$ possible $\bf{unordered}$ bases involving any 4 out of those 6 vectors. – gbrlrz017 Jul 15 '15 at 3:21
Your concept of "arbitrary" makes sense as long as you're talking about one value at a time; then it can be made rigorous, e.g., by saying "if $x_1$ traverses all of $\mathbb C$, so does $x_2+x_1$".
However, you then start talking about several things at a time, and at that point you're begging the question, since what you're supposed to show is precisely that these things independently traverse all $\mathbb C$ (that they're "independently arbitrary"), and that's not at all obvious. For instance, there are six different sums $x_i+x_j$ for $1\le i\le j\le 4$, and they're all individually "arbitrary" in that they traverse all of $\mathbb C$ as the $x_i$ do, but that doesn't mean you can span a six-dimensional vector space using them as coefficients; it will still be just four-dimensional because there are really only four coefficients.
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EDASeq, RUVSeq and edgeR together
1
0
Entering edit mode
@zoppoli-pietro-4792
Last seen 4.0 years ago
United States
Hi,
I'd like to use together EDASeq,RUVSeq and edgeR
I'd like to know if It's correct to run the folling code
According to EDASeq manual:
dataOffset <- withinLaneNormalization(data,"gc",which="upper",offset=TRUE)
dataOffset <- betweenLaneNormalization(dataOffset,which="upper",offset=TRUE)
then according to RUVSeq using control genes taken from
Eisenberg E, Levanon EY. Human housekeeping genes, revisited. Trends Genet. 2013
I do:
set1 <- RUVg(x = dataOffset cIdx = HKgenes, k=1)
RUVg does NOT fill the offset slot of the EDASeq object.
To use the offsets I need the result from EDASeq but I still want to Remove Unwanted Variation
so I modify the edgeR paragraph of the EDASeq manual:
W_1 <- pData(set1)$W_1 pData(dataOffset) <- cbind(pData(dataOffset),W_1) design <- model.matrix(~conditions + W_1, data=pData(dataOffset)) then all by manual disp <- estimateGLMCommonDisp(counts(dataOffset), design, offset=-offst(dataOffset)) fit <- glmFit(counts(dataOffset), design, disp, offset=-offst(dataOffset)) lrt <- glmLRT(fit, coef=2) topTags(lrt) By the way other than common dispersion (estimateGLMCommonDisp ) in edgeR manual there are 2 other steps (raccomanded): To estimate trended dispersions: y <- estimateGLMTrendedDisp(y, design) To estimate tagwise dispersions: y <- estimateGLMTagwiseDisp(y, design) I need to integrate these steps too ? Thank, Pietro edaseq ruvseq edgeR • 1.5k views ADD COMMENT 1 Entering edit mode davide risso ▴ 900 @davide-risso-5075 Last seen 11 months ago University of Padova Hi Pietro, I think that your code is fine. And yes, it's likely better to have a tagwise and possibly trended dispersion and not a global dispersion parameter. I believe that edgeR now offers a simpler wrapper function to carry out the three steps that you describe. Have a look at ?edgeR::estimateDisp. Best, Davide ADD COMMENT 0 Entering edit mode Hi Davide, following your tips I changed this dispersion: disp <- estimateGLMCommonDisp(counts(dataOffset), design, offset=-offst(dataOffset)) with this dispersion disp2 <- estimateDisp(counts(dataOffset),design, offset=-offst(dataOffset)) and changed the fit step: fit <- glmFit(counts(dataOffset), design, disp, offset=-offst(dataOffset)) with this: fit2 <- glmFit(counts(dataOffset), design, disp2$tagwise.dispersion,
offset=-offst(dataOffset))
Thanks,
Pietro
0
Entering edit mode
Hi Davide,
I'm going to visualize the results of the analysis using a simple boxplot and I find a myself troubled to decide which matrix to use.
Let's say I get lrt2 from glmLRT and I want to plot geneA
contrast_BvsA <- makeContrasts(TvsN=conditionsB-conditionA, levels=design)
contrast_BvsA
# Contrasts
# Levels BvsA
# conditionA -1
# conditionsB 1
# W_1 0
# W_1 is a vector to Remove Unwanted Variation
lrt2 <- glmLRT(fit2,contrast = contrast_BvsA )
lrt2$table["geneA",] logFC logCPM LR PValue geneA 5.605485 27.49028 580.2279 3.3458e-128 I need to give a vector to boxplot. According to manuals you can use the log2(normCounts) or better use something like rld <- rlogTransformation(dataOffset@assayData@normalizedCounts, blind=TRUE) or vsd <- varianceStabilizingTransformation(dataOffset@assayData@normalizedCounts, blind=TRUE) I check for geneA FC FC <- aggregate(vsd["geneA",] ~ (conditions),FUN= mean) BvsA vsd ["geneA", ] 1 A 8.710527 2 B 9.881888 FC[2,2]-FC[1,2] # 1.171361 such FC is very different from the lrt2 FC so if I plot this any reviewer can argument boxplot is NOT representative of the reported FC. I try to use counts or normalizedCounts (though if they worked I could not explain myself why adopt the discussed pipeline) log2(mean(Data2@assayData$counts["geneA",names(which(condition=="B"))],na.rm=T)
/
mean(Data2@assayData$counts["geneA",names(which(condition=="A"))],na.rm=T)) # 3.312596 log2(mean(Data2@assayData$normalizedCounts["geneA",names(which(condition=="B"))],na.rm=T)
/
mean(Data2@assayData$normalizedCounts["geneA",names(which(condition=="A"))],na.rm=T)) # 1.673753 Also these FCs are far away from the lrt2 result. So I try to get the data from lrt2 results, in particular i extract fitted.values and coefficients FC <- aggregate(log2(lrt2$fitted.values["geneA",])~ (conditions),FUN= mean)
FC[2,2] - FC[1,2]
# 3.146288
lrt2$coefficients["geenA",2] - lrt2$coefficients["geneA",1]
# 3.885426
these values are still very different from logFC = 5.605485 from glmLRT function.
Worst scenario is geneB
lrt2$table["geneB",] logFC logCPM LR PValue geneB -1.088669 31.60722 23.45083 1.281471e-06 vsd FC is 0.42 counts FC is 1.95 normalizedCounts is 0.51 lrt2$coefficients is -0.75
ltr2$fitted.values FC is 1.93 As u can see only lrt2$coefficients goes near the value reported by lrt2 while the others have even different sign
I think I'm missing something, maybe more than that.
Please can you comment these results and pinpoint the correct matrix to use for boxplot.
Best,
Pietro
0
Entering edit mode
Hi Pietro, the issue here is in the terminology. What edgeR calls "logFC" is not a log-fold-change per se but the estimated value of the particular contrast based on the estimates of the coefficient of the regression model. When you use the additional covariates from RUV, you are changing the value of the estimated coefficient, because these coefficients are "adjusted" by the presence of the confounding factors from RUV. Obviously, none of your manual log-fold-changes are. The interpretation of the values in this case would be something along the lines of "the value that the log-fold-change would have if the data weren't influenced by the unwanted variation". I hope this helps.
0
Entering edit mode
Hi Davide,
thanks for your reply. I explained myself the discrepancy in the same way BUT this means I can't use boxplot or similar plots to show the data.
I can do a HM of the genes using the edgeR "logFC" but i have no way to show the distribution of the samples around that value, right ?
By the way, is there no way to generate a "corrected" matrix using the confounding factors from RUV together with the estimates of the coefficient of the regression model ?
How you would visualize the result and explain it to a review asking to look at distribution of the expression of a gene in the two tested conditions ?
Here seems that RUV strongly changes the expression values (maybe because the total reads of the first condition are the double of the other condition).
Thank you very much,
P
0
Entering edit mode
You can of course look at the "corrected" values once you fit the model, by looking at $Y - W alpha$, or you could plot the fitted values for the model instead of the observed data. Note that neither RUV nor any other statistical method will tell you if the difference is biological or technical if you have complete confounding. But if that's not the case, then, $Y - W alpha$ is probably what you want to plot to show the estimated effect.
0
Entering edit mode
Hi Davide,
my bad but i really can't understand the formula $Y - W alpha$. Can you please explain it to me ?
Please consider that in my example fit2 is the result of the glmFit having pData(set1)$W_1 integrated into design and set1 is the result of RUVg. Sorry to bother but i'd really like to fully implement and standardize the pipeline so I can use it every time (when reasonable). Best, P ADD REPLY 0 Entering edit mode Sorry, I was assuming that you were familiar with the notation we use in RUV, where$W$is the matrix with the unwanted variation factors and$\alpha$its associated parameter vector.$Y - W \alpha$essentially means to look at the coefficient estimates related to the unwanted variation factors in the glmFit result object, %*% that by the related columns of your design matrix and subtract the resulting matrix from the matrix of observed counts. This would be almost like we provide as "normalizedCounts" in RUV, but after fitting the full model (including the variable of interests). I hope this is more clear, sorry that there isn't an automated function to do that, but it would work on edgeR objects so I always thought it is out of the scope of the RUVSeq package. But if you want to contribute a PR to the RUVSeq package I would consider adding it to the package. ADD REPLY 0 Entering edit mode Hi Davide, if I understand correctly, in my example:$Y is the fit2$counts$W$is the lrt2$coefficients (Ngenes X 3conditions)
$\alpha$ is the design$W_1 (W_1 is a vector result of RUVg) (Nsamples X 1) so MatrixByDavide <- fit_TvsN$coefficients[,W_1]%*%t(design$W_1) MatrixToMakePlots <- log2(fit_TvsN$counts)- MatrixByDavide
bb <- aggregate(log2(MatrixToMakePlots [geneB,])~ (conditions),FUN= mean)
bb[2,2]-bb[1,2]
# 0.074 instead of -1.088669
if I use all the columns of fit_TvsN$coefficients then MatrixByDavide2 <- fit_TvsN$coefficients%*%t(design$W_1) MatrixToMakePlots2 <- log2(fit_TvsN$counts)- MatrixByDavide2
bb <- aggregate(log2(MatrixToMakePlots2 [geneB,])~ (conditions),FUN= mean)
bb[2,2]-bb[1,2]
# 0.5405 instead of -1.088669
Please let me know if I made something wrong because I'm still not able to get a matrix I can use to plot the results.
Best,
P
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# Lending Rates for Bitcoin and USD on Cryptoexchanges
We are going to take a look at the current interest rates in bitcoin lending. Why is this important? In addition to being a way to make extra income from your fiat (“real” currency) or bitcoin holdings without selling them, these interest rates indicate traders sentiment about the relative values of these currencies in the future. We will look at bitcoin in this post, because it is the largest cryptocurrency, both in terms of market cap and trading volume. As of the date of this writing here are the top 4 cryptocurrencies by total market cap. Information from http://coinmarketmap.com.
Crypto-Currency Market Cap ($USD, billion) 24 Hr Trading volume ($USD, billion) Bitcoin (BTC) 45 1.0 Ethereum (ETH) 32 0.78 Ripple 11 0.18 Litecoin (LTC) 2.5 0.37
The Bitfinex Exchange is one of the exchanges that allows margin trading, and also customer lending of fiat and crytpocurrencies. They call the lending exchange funding and it works with an order book just like a regular trading exchange. Customers submit funding offers and requests, and the exchange matches the orders. So, for example, I could offer $USD800 for 4 days at .0329% per day (12% annually). This get placed on the order book. Someone else could accept that offer, and then the loan happens. As the lender, I get paid interest daily at the contract rate, paid by the borrower. Now, what does the borrower do with the proceeds? They can’t withdraw the money from Bitfinex, this is not a general personal loan. They could use this money to buy bitcoins on margin. There are specific rules on how much they can borrow at purchase, and how much margin they must maintain in the future. We won’t go into the specifics of those rules in this post, but just be aware that the exchange can liquidate, or sell, a position to maintain margin requirements. In fact, this is what caused the recent meltdown in the Ethereum market at one exchange (GDAX) Ethereum Flash Crash, as traders had their positions liquidated automatically for margin calls. So, show me the data! In this chart, fUSD is the funding rate as an APR for$USD, and fBTC is the funding rate for bitcoin (BTC). These are based on a small sample of 2 day loans actually traded on that day. The first thing to note is that the rates are quite volatile, reaching highs of over 100% (USD) and 50% (BTC) during the last year. The current rates (June 2017) are around 40% (USD) and 4% (BTC).
One more thing we might want to look at. We might wonder about the difference between the two rates and what that means. In economics, there is something called uncovered interest rate parity, which normally looks at the difference in interest rates between 2 currencies, say the USD and the Euro (EUR). This difference is related to the relative inflation expected between the 2 currencies in the future. In fact, futures contracts for the currencies should have a price related to this difference in such a way as to make arbitrage not possible. Here is the difference graph.
Note that it switches around both sides of zero. Between approximately 15 Mar 2017 and 1 May 2017, it was negative, meaning people were demanding higher rates to lend BTC than to lend USD. Perhaps this is an indication that people wanted to short BTC at that time – although we don’t know which fiat currency they were shorting it against.
Another thing that we can pull from the data is the yield curve. In the bond market, this indicates the interest rates for bonds at different maturities, for example, a 30 day, 60 day, 1 year, etc. In the case of Bitfinex, the loans can only be made for 2-30 days, so we have a more limited set of possibilities.
You can see the curves are relatively flat, but they only go out to 30 days, so we can’t say much about 1 year rates. Note that most of the volume is at the extremes, that is 2 days or 30 days, so the numbers in between are not that meaningful.
In post to come, we will look at Bitcoin futures, to see how their pricing might be related to the uncovered interest rate parity. Stay tuned.
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## Saturday, 1 June 2013
### Clipboard Processing with AutoHotkey
I've been doing a lot of text processing recently, and a lot of it has been to convert a column of cells from Excel into a comma separated list. Well, I used to do that with Notepad++, but last week I bit the bullet and wrote an AutoHotkey script to do it for me. Without further ado, here are the goods:
#v::
StringReplace, Clipboard, Clipboard, rn, ,%A_Space%, All
Clipboard := RTrim(Clipboard, ", n")
; Gets rid of the annoying trailing newline that Office programs put in.
Send ^v
Return
It will paste the converted clipboard contents when you press Windows+V. Also, I found a way to get text/content copied from MS Office to plain, plain text by removing the trailing newline character.
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# covariate selection for a cox model by Lasso using glmnet
I would like to use model selection through shrinkage (Lasso) using glmnet. So far I did the following:
> library(glmnet)
> library(survival)
> d <- myTestData
> x <- model.matrix( ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8, d)
> y <- Surv(d$time, d$status)
> fit <- glmnet(x, y, family="cox", alpha=1)
> plot(fit, label=T)
> cv.fit <- cv.glmnet(x, y, family="cox", alpha=1)
> plot(cv.fit)
Question #1: How would you interpret the model selection by Lasso in this case?
Then I retrieved the variables with nonzero coefficients at lambda.min and compared themwith the coefficients of an coxph model using the same variables.
> coef(cv.fit, s = "lambda.min")
9 x 1 sparse Matrix of class "dgCMatrix"
1
(Intercept) .
x1 0.575711489
x2 0.292638801
x3 .
x4 0.004826889
x5 .
x6 .
x7 -0.045450370
x8 -0.032665220
> m1 <- coxph(Surv(time, status) ~ x1 + x2 + x4 + x7 + x8, data=d) # selected by LASSO
> coef(m1)
x1 x2 x4 x7 x8
0.72538227 0.30256729 0.01394998 -0.09512841 -0.03507133
The Lasso coefficients are smaller than the coxph coefficients, which is for my understanding to avoid overfitting.
Question #2: Is the way of variable selection by Lasso correct this way?
Question #3: Would it be possible to get an coxph or cph object from the Lasso objects?
Question #4: How can I get the HR, its CI andP-value for presentation from this?
Then I did also a backward selection:
> fastbw(fit, type="individual", rule="aic")
Deleted Chi-Sq d.f. P Residual d.f. P AIC
x3 0.02 1 0.8897 0.02 1 0.8897 -1.98
x5 0.03 1 0.8701 0.05 2 0.9773 -3.95
x6 0.18 1 0.6701 0.23 3 0.9730 -5.77
x4 0.72 1 0.3974 0.94 4 0.9182 -7.06
x7 1.49 1 0.2221 2.43 5 0.7863 -7.57
Approximate Estimates after Deleting Factors
Coef S.E. Wald Z P
x1 0.70903 0.32241 2.199 2.787e-02
x2 0.32185 0.06857 4.694 2.680e-06
x8 -0.03761 0.01446 -2.601 9.308e-03
Factors in Final Model
[1] x1 x2 x8
The resulting coefficients are similar to the coefficients obtained from coxph.
Question #5: Is the slight difference due to rounding error or is there more?
I really looking forward to your replies ... I find it hard to get into this subject together with R and need some help. ;-)
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# Luogu P1361 small M's gift
P1361
##### Meaning:
There are \ (n \) points. They need to be divided into two point sets, and the contribution of each point in the two point sets is given. At the same time \ (m \) rules are given. Each rule gives some points. When these points are in the same point set, they will have additional contributions. The contributions of the points of each rule in the two point sets are given. Please maximize your contribution and.
##### analysis:
(pictures and ideas from Luogu)
The minimum cut can be used to divide some points into two point sets, so consider the minimum cut. Only minimize the "loss contribution".
If we divide a point into the point set on the left, the contribution on the right will be lost. Therefore, without considering additional rules, we can build such a model:
The middle is the point, and the flow of the left and right edges is the contribution to the left and right point set, so the minimum cut is the minimum "loss contribution".
Then consider additional rules.
The contribution of a rule to the point set can be divided into three cases: contribution to the point set \ (S \), contribution to the point set \ (T \), or no contribution, which means that we cannot deal with it through one state. We can consider it in two parts: contribution to \ (S \) and contribution to \ (T \).
Because this contribution cannot be connected to the existing edge, we first connect to an imaginary point and consider the contribution to \ (S \) separately. As long as a point is divided into the point set \ (T \), the contribution should be "lost", so each point should be connected to this imaginary point, so:
As long as a point is assigned to the point set \ (T \), the contribution should be "lost", so the "lost contribution" should be on the yellow side rather than the blue side. If a point \ (c \) is assigned to the point set \ (T \), any path from \ (S \) to \ (c \) should be disconnected. For \ (S\rightarrow X\rightarrow c \) , we want to cut off the yellow edge and keep the blue edge, so we set the flow of the yellow edge as the contribution. At the same time, in order to avoid cutting off the blue edge, we set its flow as inf.
The contribution to \ (T \) is the same, so the final model is:
To sum up:
The basic two take the problem model, that is, the minimum cut partition point set.
The application of virtual points is used to deal with some rules based on the basic model.
##### Algorithm:
Build a model and run the maximum flow.
The calculated minimum cut is the contribution of loss. The answer is obtained by subtracting the total contribution.
In addition, note that the number of points required by the topic is 3e3 and the number of sides is 2e6+4e3
##### code:
#include<bits/stdc++.h>
using namespace std;
#define int long long
inline int read(){
int p=0,f=1;
char c=getchar();
while(!isdigit(c)){if(c=='-')f=-1;c=getchar();}
while(isdigit(c)){p=p*10+c-'0';c=getchar();}
return p*f;
}
const int N=3e3+5;
const int M=2e6+4e3+5;
const int inf=0x7fffffff;
int n,m,s,t,cnt,maxflow;
struct edge{
int v,w,nxt;
}e[M<<1];
int head[N],en=1;
void insert(int u,int v,int w){
e[++en].v=v;
e[en].w=w;
e[en].nxt=head[u];
head[u]=en;
}
void add(int u,int v,int w){
insert(u,v,w);
insert(v,u,0);
}
int cur[N],dis[N];
queue<int> q;
bool bfs(){
for(int i=1;i<=cnt;i++)
dis[i]=0,cur[i]=head[i];
while(!q.empty())q.pop();
q.push(s);dis[s]=1;
while(!q.empty()){
int u=q.front();q.pop();
for(int i=head[u],v=e[i].v;i;i=e[i].nxt,v=e[i].v){
if(!dis[v]&&e[i].w){
dis[v]=dis[u]+1;
if(v==t)return true;
q.push(v);
}
}
}
return false;
}
int dfs(int u,int in){
if(!in||u==t){return in;}
int out=0;
for(int i=cur[u],v=e[i].v;i;i=e[i].nxt,v=e[i].v){
cur[u]=i;
if(dis[v]!=dis[u]+1||!e[i].w)continue;
int tmp=dfs(v,min(in-out,e[i].w));
e[i].w-=tmp;
e[i^1].w+=tmp;
out+=tmp;
if(in==out)break;
}
return out;
}
void dinic(){
while(bfs()){maxflow+=dfs(s,inf);}
}
int ans;
signed main(){
n=read();s=n+1,cnt=t=n+2;
for(int i=1;i<=n;i++){int tmp=read();add(s,i,tmp);ans+=tmp;}
for(int i=1;i<=n;i++){int tmp=read();add(i,t,tmp);ans+=tmp;}
m=read();
for(int i=1,k,c;i<=m;i++){
k=read();
c=read();add(s,++cnt,c);ans+=c;
c=read();add(++cnt,t,c);ans+=c;
for(int j=1,x;j<=k;j++){
x=read();
add(cnt-1,x,inf);
add(x,cnt,inf);
}
}
dinic();
cout<<ans-maxflow;
return 0;
}
##### Digression:
Personally, I feel that modeling is more difficult than some template questions.
Posted on Tue, 02 Nov 2021 23:10:47 -0400 by Rushy
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From Single-Bit to Multi-Bit Public-Key Encryption via Non-Malleable Codes
Sandro Coretti, Ueli Maurer, Björn Tackmann, and Daniele Venturi
Abstract
One approach towards basing public-key encryption (PKE) schemes on weak and credible assumptions is to build stronger'' or more general schemes generically from weaker'' or more restricted ones. One particular line of work in this context was initiated by Myers and shelat (FOCS '09) and continued by Hohenberger, Lewko, and Waters (Eurocrypt '12), who provide constructions of multi-bit CCA-secure PKE from single-bit CCA-secure PKE. It is well-known that encrypting each bit of a plaintext string independently is not CCA-secure---the resulting scheme is *malleable*. We therefore investigate whether this malleability can be dealt with using the conceptually simple approach of applying a suitable non-malleable code (Dziembowski et al., ICS '10) to the plaintext and subsequently encrypting the resulting codeword bit-by-bit. We find that an attacker's ability to ask multiple decryption queries requires that the underlying code be *continuously* non-malleable (Faust et al., TCC '14). Since, as we show, this flavor of non-malleability can only be achieved if the code is allowed to self-destruct,'' the resulting scheme inherits this property and therefore only achieves a weaker variant of CCA security. We formalize this new notion of so-called *self-destruct CCA security (SD-CCA)* as CCA security with the restriction that the decryption oracle stops working once the attacker submits an invalid ciphertext. We first show that the above approach based on non-malleable codes yields a solution to the problem of domain extension for SD-CCA-secure PKE, provided that the underlying code is continuously non-malleable against a *reduced* form of bit-wise tampering. Then, we prove that the code of Dziembowski et al.\ is actually already continuously non-malleable against (even *full*) bit-wise tampering; this constitutes the first *information-theoretically* secure continuously non-malleable code, a technical contribution that we believe is of independent interest. Compared to the previous approaches to PKE domain extension, our scheme is more efficient and intuitive, at the cost of not achieving full CCA security. Our result is also one of the first applications of non-malleable codes in a context other than memory tampering.
Available format(s)
Category
Public-key cryptography
Publication info
A major revision of an IACR publication in TCC 2015
Contact author(s)
corettis @ inf ethz ch
History
2015-08-03: last of 10 revisions
See all versions
Short URL
https://ia.cr/2014/324
CC BY
BibTeX
@misc{cryptoeprint:2014/324,
author = {Sandro Coretti and Ueli Maurer and Björn Tackmann and Daniele Venturi},
title = {From Single-Bit to Multi-Bit Public-Key Encryption via Non-Malleable Codes},
howpublished = {Cryptology ePrint Archive, Paper 2014/324},
year = {2014},
note = {\url{https://eprint.iacr.org/2014/324}},
url = {https://eprint.iacr.org/2014/324}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.
|
# Math Help - Direct variation help
1. ## Direct variation help
Do the following equations represent direct variations? If so, find the constant of variation
1. 3x-4y=9
2. y=1/5y
3. 8x=4y
thanks
3. two variables, y and x, are in a direct variation if y and x can be written in the form y = kx , where k is any constant.
4. Originally Posted by ssppsabres
-Dan
6. Look at the first equation. Solve it for y. Is this in the form y = kx? Use the same method for the other two. Post your solution for #1 (or either of the others) so we can see if you err at some point.
-Dan
7. y=1.5?
8. Originally Posted by ssppsabres
y=1.5?
how did you get that from the equation 3x - 4y = 9 ?
9. y=3?
10. Originally Posted by ssppsabres
y=3?
no. you are guessing.
$3x - 4y = 9$
$3x - 9 = 4y$
$\dfrac{3x}{4} - \dfrac{9}{4} = y$
or
$y = \dfrac{3x}{4} - \dfrac{9}{4}$
now ... is this equation in the form $y = kx$ ?
11. No, so therefore it is not a DV and has no constant?
12. So no its not?
Question #1 asked "Do the following equations represent direct variations? If so, find the constant of variation
1. 3x-4y=9"
and when asked to post your solution, you posted, in three separate posts,
"y=1.5? "
"y=3? "
"So no its not?"
The first two make no sense because you were not asked to find a value of y. The last makes no sense because it is not a complete sentence- "so no its not" what?
Since the questions asks, first whether or not the relation given is a "direct variation", you should start by stating what a direct variatio is and then show how the given relation does or does not satisfy that. If it is a direct variation, then you should give the constant of variation, which is NOT "y".
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# Grassmannian.info
A periodic table of (generalised) Grassmannians.
## Lagrangian Grassmannian $\LGr(3,6)$
Basic information
dimension
6
index
4
Euler characteristic
8
Betti numbers
$\mathrm{b}_{ 0 } = 1$, $\mathrm{b}_{ 2 } = 1$, $\mathrm{b}_{ 4 } = 1$, $\mathrm{b}_{ 6 } = 2$, $\mathrm{b}_{ 8 } = 1$, $\mathrm{b}_{ 10 } = 1$, $\mathrm{b}_{ 12 } = 1$
$\mathrm{Aut}^0(\LGr(3,6))$
$\mathrm{PSp}_{ 6 }$
$\pi_0\mathrm{Aut}(\LGr(3,6))$
$1$
$\dim\mathrm{Aut}^0(\LGr(3,6))$
21
Projective geometry
minimal embedding
$\LGr(3,6)\hookrightarrow\mathbb{P}^{ 13 }$
degree
16
Hilbert series
1, 14, 84, 330, 1001, 2548, 5712, 11628, 21945, 38962, 65780, 106470, 166257, 251720, 371008, 534072, 752913, 1041846, 1417780, 1900514, ...
Exceptional collections
• Fonarev constructed a full exceptional sequence in 2019, see arXiv:1911.08968.
• Samokhin constructed a full exceptional sequence in 2001, see MR1859740.
Quantum cohomology
The small quantum cohomology is generically semisimple.
The big quantum cohomology is generically semisimple.
The eigenvalues of quantum multiplication by $\mathrm{c}_1(\LGr(3,6))$ are given by:
Homological projective duality
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# Question ba256
Jun 27, 2016
$\text{D.F.} = 3$
#### Explanation:
The dilution factor essentially tells you by what factor the concentration of the diluted solution decreased compared with the concentration of the initial solution.
A dilution is based on the principle that you can decrease the concentration of a solution by
• keeping the number of moles of solute constant
• increasing the volume of the solution
The dilution factor can thus be calculated by dividing the volume of the target solution, i.e. the diluted solution, by the volume of the initial solution, i.e. the concentrated solution.
$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{D.F." = V_"diluted"/V_"concentrated} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
In your case, you are adding $\text{200 mL}$ of pure water to a $\text{100 mL}$ sample of treated waste water.
The total volume of the diluted solution will be
${V}_{\text{diluted" = "100 mL" + "200 mL" = "300 mL}}$
The dilution factor will thus be
"D.F." = (300 color(red)(cancel(color(black)("mL"))))/(100color(red)(cancel(color(black)("mL")))) = 3#
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# GlobPattern¶
class GlobPattern
This class can be used to test for string matches against standard Unix- shell filename globbing conventions. It serves as a portable standin for the Posix fnmatch() call.
A GlobPattern is given a pattern string, which can contain operators like *, ?, and []. Then it can be tested against any number of candidate strings; for each candidate, it will indicate whether the string matches the pattern or not. It can be used, for example, to scan a directory for all files matching a particular pattern.
Inheritance diagram
GlobPattern(std::string const &pattern = string())
GlobPattern(GlobPattern const ©)
bool get_case_sensitive(void) const
Returns whether the match is case sensitive (true) or case insensitive (false). The default is case sensitive.
std::string get_const_prefix(void) const
Returns the initial part of the pattern before the first glob character. Since many glob patterns begin with a sequence of static characters and end with one or more glob characters, this can be used to optimized searches through sorted indices.
std::string const &get_nomatch_chars(void) const
Returns the set of characters that are not matched by * or ?.
std::string const &get_pattern(void) const
Returns the pattern string that the GlobPattern object matches.
bool has_glob_characters(void) const
Returns true if the pattern includes any special globbing characters, or false if it is just a literal string.
int match_files(vector_string &results, Filename const &cwd = Filename()) const
PyObject *match_files(Filename const &cwd = Filename()) const
Treats the GlobPattern as a filename pattern, and returns a list of any actual files that match the pattern. This is the behavior of the standard Posix glob() function. Any part of the filename may contain glob characters, including intermediate directory names.
If cwd is specified, it is the directory that relative filenames are taken to be relative to; otherwise, the actual current working directory is assumed.
The return value is the number of files matched, which are added to the results vector.
bool matches(std::string const &candidate) const
Returns true if the candidate string matches the pattern, false otherwise.
bool matches_file(Filename candidate) const
Treats the GlobPattern as a filename pattern, and returns true if the given filename matches the pattern. Unlike matches(), this will not match slash characters for single asterisk characters, and it will ignore path components that only contain a dot.
void output(std::ostream &out) const
void set_case_sensitive(bool case_sensitive)
Sets whether the match is case sensitive (true) or case insensitive (false). The default is case sensitive.
void set_nomatch_chars(std::string const &nomatch_chars)
Specifies a set of characters that are not matched by * or ?.
void set_pattern(std::string const &pattern)
Changes the pattern string that the GlobPattern object matches.
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# Calculating morphometric properties
Is it possible to calculate segment length, segment diameter and branch angles for three dimensional geometry. Geometry contains vertex points and polygon surfaces as
file = "http://i.stack.imgur.com/N6RYT.png";
Import[file, "Graphics3D"]
data = Import[file, "VertexData"];
polysurface = Import[file, "PolygonData"];
Graphics3D[Point@data]
-
Six hours ago you asked a question. In the answers to that question you can find at least two different ways to calculate segment lengths and angles. Could you please specify why this question is different? – belisarius Sep 21 '12 at 5:18
@belisarius: That question was for 2d image, which had center line in the image. This question have 3d geometry and it doesnt have flat plane 2d image, I think this is entirely a different problem. – mathew Sep 21 '12 at 5:27
One possible approach is to Rasterize the 3D graphics with various rotations applied, and use the thinning and morphological operations you already have for 2D. It should be relatively easy to solve for the 3D vertex positions from a set of known rotations and corresponding 2D vertex positions. I guess the tricky part will be to identify the same vertices in multiple views. Sorry, I don't have time to write any actual code... – Simon Woods Sep 21 '12 at 7:47
@Jay, just to let you know I had a go using my idea, and there were more complications than I realised! In particular, the number of vertices found by MorphologicalGraph varies with the rotation of the object. It's an interesting problem. – Simon Woods Sep 22 '12 at 17:44
@SimonWoods see my (partial) answer. Perhaps inspires you some idea on how to get there – belisarius Sep 24 '12 at 9:53
I decided to post another answer for several reasons:
• I made up a full working contraption by using another approach
• The previous answer could be useful for others, so I prefer to leave it there
• Both answers are quite long, and having both in one post will clutter it
That said, the plan is the following:
1. Collapse the points as before, pre-clustering them over an skeleton
2. Calculate real clusters and collapse each point to the Center of Mass of its cluster
3. From the polygon's description, get the surviving lines that form a 3D skeleton for the figure
4. Find the branch points in the skeleton, and the incoming lines to each branch point
5. Calculate the angles
Limitations/ To-dos:
1. The method used is purely metric, without regarding the topological characteristics of the body. It works very well here, because the branches are not nearby parallel structures. May fail for tangled things
2. There are two iterative loops that (perhaps) will be converted to something more Mathematica-ish if I find time/momentum and a way to do it.
Note: As the code here will be interspersed with graphics and comments, you may like to download a fully functional .nb in only one step. For that, execute the following and you'll get a new notebook ready for running, downloaded from imgur:
NotebookPut@ImportString[Uncompress@FromCharacterCode@
TakeWhile[Flatten@ImageData[Import["http://i.stack.imgur.com/tP8xo.png"],"Byte"],#!=0&],"NB"]
Ok. Let's get something done:
i = Import["http://dl.dropbox.com/u/68983831/final.vtk", "GraphicsComplex"];
j = i[[1]]; (*Point coordinates*)
(*Number of Nearest neighbors to take in account for collapsing the 3D structure*)
nn = 40;
j1 = j/2; (*some initial value for the iteration stopping test*)
(*Search for a quasi fixed point by moving towards the CoM of NN*)
While[Total[Abs[j1 - j], -1] > Length@j/100,
j1 = j;
(j[[#]] = Mean[Nearest[j, j[[#]], nn]]) & /@ Range@Length@j]
jp = j; (*To preserve j for later use*)
(*Show our proto-clusters*)
Show[Graphics3D[{Opacity[.1], EdgeForm[None],
GraphicsComplex[i[[1]], i[[2]]]}], ListPointPlot3D[j]]
Now we have a nice arrangement of all our points over one skeleton, we need to proceed further and collapse each cluster to its Center of Mass, to reduce the number of points drastically and allow us to have segments linking those points. Sorry, iteration follows:
(*Now collpse every point to its corresponding CoM*)
(*maxdist is an estimation of a safe intercluster distance*)
maxdist = Mean[EuclideanDistance[j[[#]], First@Complement[
Nearest[j, j[[#]], 81],
Nearest[j, j[[#]], 80]]] & /@
RandomSample[Range@Length@j, IntegerPart[Length@j/5]]]/2;
h = 0;
agg (*buckets for clusters*) = n = {};
(*Calculate clusters, FindClusters[] doesn't do any good here :( *)
While[j != {},
h++;
AppendTo[agg, {First@j}];
While[j != {} && EuclideanDistance[agg[[h, 1]],
n = (Nearest[j, agg[[h, 1]], 1][[1]])] < maxdist,
j = DeleteCases[j, n];
AppendTo[agg[[h]], n];
]
];
(*Clusters calculated, collapse each cluster to its mean*)
rules = (Thread[Rule[#, x]] /. x -> Mean[#]) & /@ agg;
j = (jp /. Flatten[rules, 1]);
Now we have our points completely collapsed. Lets see what we found:
(*A plot showing the lines found*)
vl = (i[[2]] /. rul) /. {a_List, b_List, c_List} /; a != b != c -> Sequence[];
uniLines = Union[Sort /@ Flatten[Subsets[#, {2}] & /@ vl[[1, 1]], 1]] /. {a_, a_} -> Sequence[];
Graphics3D@Table[{Thick, Hue@RandomReal[], Line@l}, {l, uniLines}]
Nice. Now we can explore the endpoints for each segment:
Manipulate[Show[
Graphics3D@{Opacity[.1], EdgeForm[None], GraphicsComplex[i[[1]], i[[2]]]},
Graphics3D@Table[{Hue[o/Length@uniLines], Line@uniLines[[o]]}, {o, 1, Length@uniLines}],
Graphics3D[{PointSize[Medium], Point[Union@Flatten[uniLines, 1]]}],
Graphics3D[{Red, PointSize[Large], Point[uniLines[[w]]]}]
], {w, 1, Length@uniLines, 1}]
We are almost there, now we identify the branch points and the related lines:
(*Now get and process the bifurcation points*)
branchPt = First /@ Extract[#, Position[Length /@ #, 3]] &@(Gather@Flatten[uniLines, 1]);
(*Get the incoming lines to each point *)
branchLn = Extract[uniLines, #] &/@ ((Position[uniLines, #] & /@ branchPt)[[All,All,1 ;;1]]);
Let's see if we identified our branch points correctly:
(*Plot Bifurcations*)
Show[Graphics3D[{Opacity[.1], EdgeForm[None],GraphicsComplex[i[[1]], i[[2]]]}],
Graphics3D[Line /@ branchLn],
Graphics3D[{Red, PointSize[Large], Point[branchPt]}]]
Now we get normalized vectors along the lines, outgoing from each branch point
(*Get the normalized vectors at the branch points*)
aux[x_] := Map[# - First@Commonest[Flatten[x, 1]] &, x, {2}];
nv = Map[Normalize, ((Select[Flatten[aux[#], 1], # != {0, 0, 0} &]) & /@ branchLn), {2}];
Finally we are going to get our desired 9 angles. As you can observe, in all cases the three segments at each branch point are almost coplanar, so the sum of the angles ought to be near 2 Pi. We now calculate the angles and verify the coplanarity observation:
(*Angles and kind of Coplanarity test*)
(VectorAngle @@@ Subsets[#, {2}]) & /@ nv
Total /@ ((VectorAngle @@@ Subsets[#, {2}]) & /@ nv)
(* Angles: {{2.0326, 2.54025, 1.70803},
{1.71701, 2.4161, 2.14805},
{2.14213, 1.98282, 2.158}}*)
(* Coplanarity test (Very near 2 Pi): {6.28087, 6.28115, 6.28295} *)
-
does angles are in degrees? – mathew Sep 29 '12 at 20:57
@Jay Nope. In radians – belisarius Sep 29 '12 at 20:58
+1 Excellent stuff :-) – Simon Woods Sep 30 '12 at 14:30
Great effort, +1 ;-) – Vitaliy Kaurov Sep 30 '12 at 17:04
Not a full answer, but gotta something and perhaps it's useful so someone else can help to finish.
The idea is trying to get a skeleton by collapsing the points to the mass center of a group of nearest neighbors. Like this:
file = "http://dl.dropbox.com/u/68983831/final.vtk";
i = Import[file, "GraphicsComplex"];
j = i[[1]];
k = 1 ;(*A parm. In this set up we collapse immediately*)
iter = 4; (*Number of iterations*)
nn = 40; (*Nearest neighbors to take in account*)
(* Apply elastic pressure *)
For[h = 1, h <= iter, h++,
For[s = 1, s <= Length@j, s++,
j[[s]] = (Mean[Nearest[j, j[[s]], nn]]) - j[[s]] (1 - k)]]
(*Show*)
Show[Graphics3D[{Opacity[.1], EdgeForm[None],
GraphicsComplex[i[[1]], i[[2]]]}], ListPointPlot3D[j]]
Now we have a useless set of scattered points. But not so useless if you remember that they were originally part of polygons. So:
Graphics3D@GraphicsComplex[j, i[[2]]]
And now we have a nice alien creature:
I think if one can figure out which sides of the triangles to keep, and which ones to discard, then we can replace polygons by lines. After that, an intelligent way to take means on those lines can get us somewhere ...
My 2 cents.
Edit
One step further, getting rid of some polygons:
rul = Thread[Rule[Range@Length@j, j]];
vl = i[[2]] /. rul /. Polygon -> List; (*Polygons as vertices*)
herons[{a_, b_, c_}] := Module[{n, s}, (*Heron's area formula*)
n = Norm /@ {a - b, b - c, c - a};
s = Total@n/2;
Return[Sqrt[s (s - n[[1]]) (s - n[[2]]) (s - n[[3]])]]
]
(*Get rid of fat triangles*)
Graphics3D[{Polygon@Select[vl[[1, 1]], herons[#] < 1/100 &],
Opacity[.1], EdgeForm[None], GraphicsComplex[i[[1]], i[[2]]]}]
Our alien is getting thinner
Edit 2
Getting rid of the polygons, going to lines.
(*discard the big area polygons as before*)
ps = Select[vl[[1, 1]], herons[#] < 1/100 &];
(*get the lines of those polygons*)
lines = Flatten[Subsets[#, {2}] & /@ ps, 1];
(*discard the crunched lines in the skeletonization process*)
selLines = Select[lines, EuclideanDistance[Sequence @@ #] > 1/3 &];
Graphics3D[{Line /@ selLines, Opacity[.1], EdgeForm[None], GraphicsComplex[i[[1]], i[[2]]]}]
Now we have only 1500 lines to deal with.
-
plus one thanks – mathew Sep 24 '12 at 15:30
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# SCTF 2018 Quals Write-up
## Mic Check
Category: none
Difficulty: easy
Solvers: 533
The problem description contains the flag. It gives information about the format of the flags.
Flag: SCTF{you_need_to_include_SCTF{}_too}
## BankRobber
Category: defense
Difficulty: easy
Solvers: 141
The problem asks us to fix a vulnerable Solidity smart contract. I patched four functions.
• Check sender’s balance in donate function
• Avoid integer overflow in multiTransfer function
• Use msg.sender instead of tx.origin in deliver function
• tx.origin returns the address that kicked off the transaction, not the address of the caller. Therefore, if the contract owner triggers a smart contract which is under an attacker’s control, the attacker can invoke our deliver function in their contract with malicious parameters and pass through tx.origin check.
• Prevent reentrancy attack in withdraw function by swapping line 22 and 23
• An attacker can setup a fallback function that calls withdraw to perform reentrancy attack on the contract. When the attacker calls withdraw function, address.call.value(value)() will invoke the attacker’s fallback function and the control flow will enter withdraw function again. The balance update of the first call has not happened at the time of the balance check of the second call, which allows the attacker to withdraw more money than the balance.
Overall, security considerations page of the Solidity documentation was very helpful to solve this problem. The server gives us the flag when we submit the correctly patched source file.
Flag: SCTF{sorry_this_transaction_was_sent_by_my_cat}
## dingJMax
Category: reversing
Difficulty: easy
Solvers: 94
We are given a binary file of a music game. It says that it will give the flag of the problem when we get the perfect score in the game.
The UI is updated per 20 ticks using the game data at 0x603280, and one tick is slightly longer than 0.01 seconds. We get a PERFECT judgement when a correct keypress happens exactly at an update tick. Getting one PERFECT is already nearly impossible for a human, so I wrote a python script that attaches GDB to the binary and plays the game instead of me.
solver.py
It adds a breakpoint just before wgetch call in main function(line 16), finds a correct key to press(line 33-48), and patches the wgetch call with mov %eax, (keycode)(line 50-52).
When the script finishes the game with the perfect score, the FLAG region contains the flag of the problem.
Flag: SCTF{I_w0u1d_l1k3_70_d3v3l0p_GUI_v3rs10n_n3x7_t1m3}
## HideInSSL
Category: coding
Difficulty: easy
Solvers: 35
We are given a pcap file. Some TCP streams contain a lot of Client Hello messages like below:
JFIF in Random section of the handshake protocol looks familiar. It looks like a JPEG file header!
I wrote a python script to collect and concatenate random bytes in all packets from the dumped stream. TCP streams were extracted as hexdump format by right clicking a packet and choose Follow > TCP Stream. There was one more condition, though. We have to concatenate the bytes in a packet only when the response for the packet is 1.
After confirming that this approach gives a valid JPEG file, all similar streams were identified and extracted from the pcap file. This command will show all TCP streams and the number of packets belong to them in descending order:
tshark -r HideInSSL.pcap -T fields -e tcp.stream | sort -n | uniq -c | sort -nr
I manually checked and extracted the candidates with high counts. There were 22 of them. I had to persuade myself not to automate this, because manual work is faster at this scale but programmers like to automate everything.
solver.py
Each JPEG file contains one letter of the flag. Joining them reveals the flag for the problem.
Flag: SCTF{H3llo_Cov3rt_S5L}
## Tracer
Category: crypto
Difficulty: easy
Solvers: 5
What_I_did file shows the scenario of the problem. A person encrypted the flag file by a binary named my_secure_encryptor. We are given the public key and the cipher text in What_I_did file, and also all instruction pointer traces (except library call) in a file named pc.log.
The binary consists of several complicated arithmetic routines with GMP, which seems to require a lot of effort to understand at first. I think that is why the number of solvers are small despite of the problem difficulty indicator is easy. Reverse engineering uncovered that they are actually elliptic-curve arithmetic functions. Once I realized this, the analysis of the binary became much easier.
These are elliptic-curve arithmetic routines in the binary:
• 0x402019 is a curve initialization function.
• 0x6032B0 is A, 0x6031A0 is B, and 0x6031B0 is P of curve parameters(Weierstrass form).
• This curve is named P521.
• 0x4018A0 is a point addition function.
• It takes a point $P$(2nd parameter) and a point $Q$(3rd parameter).
• It stores the result $P + Q$ to a point(1st parameter).
• 0x401EE8 is a multiplication function.
• It takes a point $P$(2nd parameter) and a number $k$(3rd parameter).
• It stores the result $k \cdot P$ to a point(1st parameter).
0x401196 is the main encryption routine. First, the binary reads ./flag file and convert it to the point on the curve. The x coordinate will be the content of the file converted to an integer, and y coordinate will be calculated from the x coordinate using the curve equation. After the binary finds the point which corresponds to the flag, the public key and the cipher text are calculated as follows:
Three random values are used here. Let’s respectively call them $r_0$, $r_1$, and $r_2$. These values were not recorded directly, but we can recover them using pc.log. Specifically, we can calculate the value of $k$ for the multiplication function by investigating whether jump is taken or not at 0x401F8E. One check will reveal a bit, and repeating it reconstructs the whole value of $k$.
The encryption routine gives $Pub = r_1 \cdot G$, $CT_0 = r_0 \cdot G$ and $CT_1 = r_0 \cdot Pub + flag = r_0 \cdot r_1 \cdot G + flag$. We can calculate the flag point by a formula $CT_1 - r_1 \cdot CT_0$. Then, the x coordinate of the point represents the content of the flag file.
solver.py
Flag: SCTF{Ev3r_get_th4t_feelin9_of_dejavu_L0LOL}
## WebCached
Category: attack
Difficulty: medium
Solvers: 13
The main page of the website contains a text field and a submit button. Submitting a URL redirects us to view page, which renders the content in the original URL.
There is a trivial local file read vulnerability with file:// scheme. I leaked the source code of the problem with following steps:
1. Reading file:///proc/self/cmdline gives uwsgi --ini /tmp/uwsgi.ini.
2. /tmp/uwsgi.ini file shows that the entry source file location is /app/run.py.
3. run.py imports RedisSessionInterface from session_interface.py.
/app/run.py and /app/session_interface.py are code files for the server. The server uses Flask framework with Redis as a session backend. They also give important information about Redis interaction:
• Python session data is stored in Redis under session:{SESSION_ID} key. Session data is pickled and base64 encoded before storing.
• The server uses Python’s urllib to fetch data from the provided URL and saves the data in Redis with a key {REMOTE_ADDR}:{URL} with 3 seconds expiration time.
I used Python pickle deserialization as an attack vector for the problem. This payload will create a pickle, which connects a reverse shell to port 46845 of example.com server when deserialized.
Our goal is to register this malicious pickle under session:{SOME_STRING} key. Then, setting the value of our session cookie to {SOME_STRING} and visiting any webpage inside the server will trigger the deserialization of the crafted pickle.
We cannot use the server’s caching feature to inject our payload, because {REMOTE_ADDR} would never be equal to session. However, Python urllib‘s CRLF injection vulnerability makes it possible to send commands to the Redis server. When urllib reads data from a URL 'http://127.0.0.1\r\n SET session:' + bad_session_id + ' ' + bad_pickle_b64 + '\r\n :6379/foo', it connects to 127.0.0.1:6379 while containing a line SET session:{BAD_SESSION_ID} {BAD_PICKLE_B64} in the request packet.
solver.py
Running the script successfully creates a reverse shell! ls / command shows that there exists a file named flag_dad9d752e1969f0e614ce2a4330efd6e. Reading it gives the flag for the problem.
Flag: SCTF{c652f8004846fe0e3bf9571be26afbf1}
## λ: Beauty
Category: coding
Difficulty: hard
Solvers: 5
The server evaluates a lambda calculus formula that we send. There are two servers; repl server, which just executes our payload and shows the result of the evaluation, and chal server, which applies the flag term to our payload but only gives information whether timeout happened.
This function is where the problem encodes string data as a lambda calculus term. Evaluating string true returns the first bit of the string, string false true returns the second bit, and so on. Here, true is λa.λb.a and false is λa.λb.b. The bit of the string is represented as a church numeral, which represents a nonnegative integer n as a function that takes f, x and applies f n times to x. In a nutshell, 0 is λf.λx.x and 1 is λf.λx.f x.
We can trigger timeout by calculating (λx.x x x) (λx.x x x). Let’s call this term timeout. Then, the term 'λflag.(flag %s) timeout false' % ('false ' * N + 'true') provides an oracle to n-th bit of the flag on the chal server; it reaches timeout if the bit is 1 and returns successfully in the other case. With this oracle, we can recover the whole contents of the flag.
solver.py
Flag: SCTF{S0_L0ng_4nd_7h4nks_f0r_A11_7h3_L4mbd4}
## Slider
Category: crypto
Difficulty: hard
Solvers: 3
The server implements a block cipher based on feistal construction. It uses three 2 bytes keys $k_0$, $k_1$, and $k_2$. AES based pseudo-random function is used as a round function, whose input and output are both 2 bytes. Overall, the cipher implements pseudo-random permutation of 4 bytes block. There are 16 rounds in total. The encryption routine cyclically uses $k_0$, $k_1$, $k_0$, $k_2$ and the decryption routine do the same thing with the reversed key order.
We can send maximum 1024 encryption/decryption queries, and one additional guess query at last. If we guess all three keys correctly in the last query, the server gives us the flag.
Slide attacks make it possible to tackle only one (or few) rounds of the cipher when the construction has self-similarity. In this problem, all rounds use the same round function whose domain has only $2^{16} = 65536$ elements(2 bytes). Thus, slide attacks are applicable, and if we find the input and the output for one specific round, it is easy to recover the key which is used in that round.
The first step of a slide attack is to find a slid pair. We call plain text-cipher text pairs $$ and $$ a slid pair if they satisfy two conditions $Round(P) = P'$ and $Round(C) = C'$. These pairs can be found efficiently by a birthday attack.
We can leverage advanced slide attacks suggested by Alex Biryukov and David Wagner to solve this problem, namely the complementation slide and sliding with a twist.
The first step is to recover $k_2$. The requirements of a slid pair are:
• $R = L'$
• $M = N'$
• $M' = N \oplus F(M \oplus k_2)$
• $R' = L \oplus F(R \oplus k_2)$
We query to the server with $dec(random_1 \parallel fix)$ and $enc(fix \parallel random_2)$ format, both 256 times, to maximize the number of pairs that satisfies the first requirement. Then, for each pair that satisfies the first requirement, we check whether the second requirement $M=N'$ is satisfied. Since the second requirement is a 16 bit condition, it is very likely that a pair which satisfies both first and second requirements is an actual slid pair. Based on the fact, we speculate that the found pair is a slid pair and calculate $k_2$ from third and fourth requirements. Reverse table of $F$ is used in the calculation.
The next step is to recover $k_0$ and $k_1$. Note that this is a complementation slide and there are rounds where decryption routine uses $k_2$ and encryption routine uses $k_1$. However, we can also find a slid pair on this setup similarly. Let $\Delta = k_1 \oplus k_2$. Then, the requirements of a slid pair are:
• $R = L'$
• $M = N'$
• $L \oplus F(R \oplus k_0) = R' \oplus \Delta$
• $N \oplus \Delta = M' \oplus F(N' \oplus k_0)$
Similar to the previous step, we query the server with $enc(random_1 \parallel fix)$ and $dec(fix \parallel random_2)$ format, both 256 times. Once we find a pair that satisfies the first the second requirement, we calculate $k_0$ and $k_1$ from the third and fourth requirements.
We can use an equation $N \oplus R' = L \oplus M' \oplus F(R \oplus k_0) \oplus F(N' \oplus k_0)$ to brute-force a valid $k_0$ value. When we have a candidate for $k_0$, we can calculate corresponding $k_1$ from $\Delta$ and $k_2$.
Finally, we check again that calculated keys actually generates the collected pairs. After the verification, send the last guess query to the server and receive the flag!
solver.py
Flag: SCTF{Did_y0u_3nj0y_my_5lid3r?}
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# How do you simplify (2sqrt3+sqrt2)/(sqrt3+2sqrt2)?
$\frac{2 \sqrt{3} + \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}} \cdot \frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - 2 \sqrt{2}}$
$= \frac{2 \left(3\right) + \sqrt{2} \sqrt{3} - 4 \sqrt{2} \sqrt{3} - 2 \left(2\right)}{3 - 8}$
$= \frac{10 - 3 \sqrt{6}}{- 5}$
$= \frac{3}{5} \sqrt{6} - 2$
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# Tag Info
6
It is hard to say what "official" means exactly, it is not like there was a bureau of terminological standards. But "real numbers", "real values" and "real quantities" were certainly widely used long before Dedekind, and the erasure of the distinction between rationals and irrationals where it is not relevant is even ...
6
I do not think it is a virtue to make unsupported assertions just because we happen to believe them now. Following available evidence does not makes one not smart or disappointing, that is how science should be done. Galileo deserves credit for moving the question from armchair speculations to observations and experiments, and honestly surmising what they ...
5
See more detail about this anagram (there were actually two of them) here: https://mathoverflow.net/questions/140327/arnold-on-newtons-anagram Whatever the literal translation of the anagrams is, Newton indeed discovered a method of solving "all equations" algebraic, differential, functional, whatever. The method consisted in plugging a power ...
5
The motivation for applying derivatives to polynomials over general fields is their use in detecting multiple roots: if $K$ is a general field, a polynomial $f(x)$ in $K[x]$ has no repeated roots if and only if $f(x)$ is relatively prime to $f'(x)$ in $K[x]$. Formal derivatives on polynomials in $K[x]$ for a general field $K$ were introduced by Steinitz in ...
4
Maybe some of Newton's prisms were preserved. An article by A.A. Mills (1981) shows images. He writes: Newton appears to have purchased all his prisms: there is no intimation that he made any of them, although he was obviously skilled at grinding lenses and mirrors. This availability of ready-made glass prisms is rather puzzling, for the period in question ...
3
Following up on Carl Witthoft's lead, I found another image at this link. To locate the image, you can search the page for the text "第五章：科技筑梦" to avoid lots of scrolling. The image, shown below, provides the full background text: 没有大胆的猜测 就没有伟大的发现 (paraphrasing google translate, this comes out to: "Without bold guesses, there is no great ...
3
Perhaps this is a lead: I found an article which includes the following text [emphasis mine] . The campus of Broad Group in Changsha was designed to reflect Zhang Yue’s eclectic influences and his passion for the environment. It encompasses a sprawling organic garden that provides up to half of the food consumed by his workers, and the grounds are dotted ...
3
I'm not a historian, but I have to answer this because the previous answers have gotten it completely wrong. Leibniz's $\displaystyle \frac{df}{dx}$ is not equal to $f'(x)$. I think there are two main differences between Newton's calculus and Leibniz's: Newton's calculus is about functions. Leibniz's calculus is about relations defined by constraints. In ...
3
See Sir Isaac Newton's two treatises of the quadrature of curves and analysis by equations of an infinite number of terms (1745).
2
Chrandrasekhar's Newton's Principia for the Common Reader p. 370: 104. Proposition VII: the universal law of gravitation We have now reached the climactic point of Philosphie naturalis Principia Mathematica. After establishing the preceding propositions, particularly, Propositions IV and VI, Newton, at long last, is ready to enunciate his law of gravitation....
2
The first main point to make in answer is : beware Newton myths -- there are far too many of them, and people have made money and (flaky) reputations fabricating catchpenny fake history about Newton. The 'apple' story has been plenty embroidered over time. But there is a source, a notebook handwritten by Newton's friend William Stukeley. It was written ...
2
This explanation helped me understand Newton's language and answered my question: "the excess of the degrees of the heat … were in geometrical progression when the times are in an arithmetical progression (by 'degree of heat' Newton meant what we now call 'temperature', so that 'excess of the degrees of the heat' means ‘temperature difference')." ...
2
The definitions related to Newton's laws of motion do not require the use of any units. The concepts of force, velocity, distance and time are expressed in general terms. Units are unnecessary.
2
It's very doubtful that the engraving/diagram had anything to do with Newton. "The system of the world" was a posthumous publication from 1728-9 onwards. It was derived (with a little editorial amendment including a new title) from a manuscript of 1685 of Newton's (written out by his secretary/amanuensis but bearing corrections in Newton's hand). ...
1
Mirowski P., More heat than light (1989 Cambr.UP), Chap.2. pp.11-98 The history of the energy concept.< It's a great book for various other reasons.> For Ernst Mach, energy was more or less defined as the ability to do work. Although "work" could mean many things to many people, Mach felt it was merely an historical accident that the term ...
1
There seem to be alternative versions of this illustration: this one from page 6 of the Second Edition of On the System of the World [from the ResearchGate site]. I've always just taken this to be a "generic" planet for illustrative purposes. I've been looking for information on the engraver, in case anything was ever said about the intent of the ...
1
After a bit of research I stumbled across this paper which might be a good starting point. As often in mathematics, Newton discovered his method of divided differences through pattern finding whereby the paper gives a slightly adjusted approach after some examination of Newton's thoughts which will give you a good idea why his method works.
1
Full details in my paper: Historical Development of the Newton-Raphson Method, published in SIAM Review in 1995. Deuflhard's paper is basically a summary of that work.
Only top voted, non community-wiki answers of a minimum length are eligible
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# Gray Morphology
TODO component: {"content"=>"sc.fiji:Gray\\_Morphology"} This plugin performs mathematical morphology on grayscale images. It only works on 8-bit grayscale images.
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# di52, the PHP 5.2 compatible DI container, is getting IDE autocompletion
Autocompletion for the win.
## Guess the class
The more I use the PHP 5.2 compatible container project di52 the more I fill a list of the things I’d like it to do for me.
I’ve been working on it to make it auto-generate metadata files that IDEs like PhpStorm, Sublime Text or vim are able to consume to suggest sane and useful auto-completion while typing.
Below is a PhpStorm example:
[caption id=“attachment_3313” align=“aligncenter” width=“1784”] di52 auto completion at work on PhpStorm[/caption]
## Next
For the time being I’ve been able to generate PhpStorm metadata files pretty easily and I will publish that code soon.
Next on the list is Sublime Text and then vim; the latter will require more work to play nice with the various plugins offering autocompletion functionalities.
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• 问题讨论 •
### 庐山地区混杂沉积的特征和成因
1. 兰州大学地质地理系
• 出版日期:1984-03-20 发布日期:1984-03-20
### FEATURES AND GENESES OF THE DIAMICTON IN THE LUSHAN REGION
Zhang Linyuan, Mu Yunzhi
1. Department of Geology and Geography, Lanzhou University
• Online:1984-03-20 Published:1984-03-20
Abstract: The glacial problem of the Quaternary in the eastern part of China,especially in the mountains at low latitudes and low altitudes,has been debated among domestic and foreign researchers.The points in debate are those of glaciation and non-glaciation.This paper deals with the problem in the light of some features of the diamietons of the region. The allitic weathering of the diamicton is very obvious in the region. However,a key question for determining the sedimentary environment and its genesis is of period over which warm,humid weathering prevailed.Those who advocate glaciation of the Lushan have already pointed out that under the condi-tion of warm,humid weathering the deposition of diamictons often occurred. Based on analysis of data,however,the following is proposed:the composition of diamicton of Dagu period on the piedmont came from the weathered crust constructed by vermicular red soil,in the mountains.that is to say,lt had gone through strong warm and humid weathering before deposition.This proves that the warm,humid weathring prevailed in the region in the early period. Based on its generation and development process,the original diamictons of different ages and colours in the region can be divided into three types: modern slope sediments laid down by creep,slope sediments which came from earlier diamicton and crept slowly along the slopes cut by stream,and debris-mud flow sediments. Based on a series of charateristics of the diamictons,it is considerable that the diamicions in the Lushan are not of glacial origin,however,they can not be explained by any single non-glacial process.Diamictons of different ages and geomorphological expression have been produced by various mechanisms. The Dagu diamicton(corresponding to Mindel glaciation)which was said to be typical morainedebris is really a sediments of piedmont fan.Its main features can be explained by the mechanism of debris-mud flow accumulation.
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시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB222100.000%
문제
Modeling sandpiles is an interesting problem in statistical physics. When dropping a sand grain on an existing pile, most of the time the grain will stick to it or a couple of grains will slide down. Occasionally, however, adding one extra grain to a pile will lead to a huge avalanche of sand grains falling down.
A simple way to model sandpiles is the Abelian Sandpile Model. In this simple model the sandpile is described as a two-dimensional lattice with on each lattice site a height (the number of sand grains on that lattice site). When an additional grain is dropped on a lattice site, its height is increased by one. If the height becomes larger than a certain critical height, sand grains begin to topple. This is modeled by reducing the number of sand grains on the site that is too high by four, and increasing the heights of its four neighbors by one. If some of the neighbors exceed the critical height after this toppling, sand grains topple from those points too until the situation is stable again. If a sand grain falls off the lattice, the grain is gone.
Given an initial sandpile and the positions where the grains are dropped, determine the final sandpile.
입력
The first line of the input file contains a single number: the number of test cases to follow. Each test case has the following format:
• One line with four integers, y, x, n and h with 1 ≤ y, x ≤ 100, 0 ≤ n ≤ 100 and 3 ≤ h ≤ 9: the dimensions of the sandpile, the number of dropped sand grains and the critical height.
• y lines, each with x characters in the range ’0’. . . ’9’: the heights of the initial sandpile. Each height is less than or equal to the critical height.
• n lines with two integers yi and xi with 1 ≤ yi ≤ y and 1 ≤ xi ≤ x: the positions where the grains are dropped.
출력
For every test case in the input file, the output should contain y lines, each with x characters in the range ’0’. . . ’9’: the heights of the final sandpile.
예제 입력 1
3
3 4 1 5
1023
2344
0000
2 3
3 4 1 4
1023
2344
0000
2 3
7 7 1 9
9999999
9999999
9999999
9999999
9999999
9999999
9999999
4 4
예제 출력 1
1023
2354
0000
1034
2421
0011
7999997
9799979
9979799
9996999
9979799
9799979
7999997
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dc.creator Keutsch, F. N. en_US dc.creator Fellers, R. S. en_US dc.creator Petersen, P. B. en_US dc.creator Viant, Mark R. en_US dc.creator Brown, M. G. en_US dc.creator Saykally, R. J. en_US dc.date.accessioned 2006-06-15T19:55:42Z dc.date.available 2006-06-15T19:55:42Z dc.date.issued 2000 en_US dc.identifier 2000-MF-07 en_US dc.identifier.uri http://hdl.handle.net/1811/19666 dc.description $^{a}$W. Klopper, M. Schutz, H. P. Luthi, S. Leutwyler, J. Chem. Phys. 103, 1085 (1995). $^{b}$A. Luzar, D. Chandler, Nature 379, 55(1996). en_US dc.description Author Institution: Department of Chemistry, University of California Berkeley en_US dc.description.abstract We report the observation of a new vibration-rotation-tunneling (VRT) band of $(D_{2}O)_{3}$ at $142.8 cm^{-1}$ and a set of four bands of $(H_{2}O)_{3}$ around $520 cm^{-1}$. These new bands represent the first observation of a translational and librational vibration for a water cluster. The observed VRT spectrum of $(D_{2}O)_{3}$ at $142.8 cm^{-1}$, in the translational band of the liquid, is assigned to a combination band or mixed level of the asymmetric hydrogen bond stretch and a torsional vibration. The predicted frequencies of the hydrogen bond stretching modes are too high, presumably because calculations fail to include the necessary coupling between stretching and torsional $motions^{a}$. The bands of $(H_{2}O)_{3}$ around $520 cm^{-1}$ lie in the librational band region of liquid water and are tentatively assigned to the our of plane librational vibration. The observation of at least four bands within $8 cm^{-1}$ is explained by a dramatically increased splitting of the excited state rovibrational levels by bifurcation-tunneling. The experimental results presented should therefore allow for the first exact determination of the height of the bifurcation tunneling barrier. The tunneling time scale is estimated at 2-4ps, similar to those of several important dynamical processes in bulk $water^{b}$. en_US dc.format.extent 140914 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title VRT-SPECTROSCOPY IN THE TRANSLATIONAL AND LIBRATIONAL BAND REGION OF LIQUID WATER: HYDROGEN BOND TUNNELING DYNAMICS IN WATER CLUSTERS en_US dc.type article en_US
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chapter 3
23 Pages
## Commodity Movements: Consumption and Welfare Aspects
The reader will recall that, whereas productive efficiency is affected by substitution between sources of supply of the same commodity, efficiency in exchange relates to substitution between consumer goods that are different in kind. Tariffs created intercountry differences between the price ratios of traded commodities; hence their removal will improve the efficiency of exchange through the equalization of these ratios. In common-sense terms, the domestic consumers were restricted in their demand for imported goods by the tariff, and, after tariffs have been eliminated, they can adjust consumption by purchasing more of higher-valued imported, and less of lower-valued domestic, goods.1
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A photon is a particle of electromagnetic radiation that has zero mass and carries a quantum of energy. In 1905, Albert Einstein (1879-1955) proposed that light be described as quanta of energy that behave as particles. The threshold frequency depends on the metal or material of the cathode. The photoelectric effect was explained by Albert Einstein. As e and h are also constant, V0 turns out to be a linear function of the frequency f. A graph of V0 as a function of frequency (f) is a straight line. At or above the threshold frequency (green) electrons are ejected. Work function (ϕ) for a surface is defined as the minimum amount of energy required by an individual electron in order to escape from that particular surface. Classical physics was unable to explain the photoelectric effect. Particle nature of Electromagnetic radiations :There were two important phenomenon that couldn’t be explained by considering Light with wave character: The phenomenon is: Black body radiation; Photoelectric effect; Lets first study about the nature … Main Uses of Ceanothus Americanus in Homeopathy, Implementing Agile Offshore Software Development, Top 9 Reasons To Go For Scrum Master Certification, Particulate Matter (PM) Air Pollution – A Serious Health Hazard, Publicly-Funded Homeopathy Comes to An End in England, Copyright © Adidarwinian - Health, Biology, Science 2020. Unfair Opposition to Homeopathic ADHD Treatment. Light with energy above a certain point can be used to knock electrons loose, freeing them from a solid metal surface, according to Scientific American. A photon is a particle of electromagnetic radiation that has zero mass and carries a quantum of energy. This process is also often referred to as photoemission, and the electrons that are ejected from the metal are called photoelectrons. This minimum frequency needed to cause electron ejection is referred to as the threshold frequency. When metal absorbs light, the light mediates a transfer of energy from the source of that light to that metal. How to check PHP version that a website is using? Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Einstein proposed photons to be quanta of electromagnetic radiation having energy E = h ν is the frequency of the radiation. self-propagating electromagnetic waves. The photoelectric effect is defined as a phenomenon in which the emission of electrons occurs when a beam of light strikes a metal or a cathode surface. Missed the LibreFest? In the photoelectric effect, electrons are emitted from a metal’s surface when it absorbs electromagnetic radiation. Contrarily, wave nature is prominent when seen in the field of propagation of light. For most of the metals, threshold frequency is in the ultraviolet range (wavelengths between 200 nm to 300 nm). The higher the intensity of radiation, the higher the number of photons (quanta) in an electromagnetic wave, but individual quanta still carry the same amount of energy (from the Planck equation). Perl As Programming Language of Choice for Biologists!! Particle Nature of Electromagnetic Radiation. As the frequency increases beyond the threshold, the ejected electrons simply move faster. It's light! Experiments showed that light exhibited wavelike properties of diffraction and interference. Thus, photocurrent is directly proportional to the intensity of light. particle nature of electromagnetic radiation and planck's quantum theory The electromagnetic wave theory of radiation believed in the continuous generation of energy. If we imagine light as photon bullets or stream of particles, therefore we can imagine photoelectric effect as well. Each particle of light, called a photon, collides with an electron and uses some of its energy to dislodge the electron. The phenomenon is studied in condensed matter physics, and solid state and quantum chemistry to draw inferences about the properties of atoms, molecules and solids. Still, the particle theory of light got a boost from Albert Einstein in 1905. Explains the particle nature of light and the photoelectric effect. Look, up in the sky, it's a particle! Actually it's both. In old science fiction stories (1950's), one of the space travel themes was the use of solar sails for propulsion. This theory explained the phenomenon of propagation of light such as diffraction and interference" quote successfully but it failed to explain many phenomena such as black body radiation and photoelectric effect. The photoelectric effect is produced by light striking a metal and dislodging electrons from the surface of the metal. Thus, putting Kmax = eV0 we get the equation of photoelectric effect: For a given cathode material, work function (ϕ) is constant. If you illuminate a metallic surface with photons of electromagnetic radiation above a threshold frequency, the photons are absorbed and electrons are emitted from the surface . The phenomena such as interference, diffraction, and polarization can only be explained when light is treated as a wave whereas the phenomena such as the photoelectric effect, line spectra, and the production and scattering of x rays demonstrate the particle nature of light. The idea was that the photon pressure from the sun would push the sail (like wind sails) and move the spacecraft. vmax = maximum velocity attained by an emitted electron, The maximum kinetic energy (Kmax) of a photoelectron can also be measured as eV0, e is the magnitude of electron charge and is = 1.602 x 10-19 C. The stopping potential (V0) is the potential required to stop the emission of an electron from the surface of a cathode towards the anode. Watch the recordings here on Youtube! Einstein used the particle theory of light to explain the photoelectric effect as shown in the figure below. The true nature of light is difficult to assess. Besides, photons assume an essential role in the electromagnetic propagation of energy. If the frequency is equal to or higher than the threshold frequency, electrons will be ejected. The photoelectric effect is light incident on a metal’s surface causing the spontaneous emission of electrons. While investigating the scattering of X-rays, he observed that such rays lose some of their energy in the scattering process and emerge with slightly decreased frequency. Electrons emitted in this manner are called photoelectrons. Aditya Sardana is a Medical, Science and Technology Writer, Books' Author, Alternative Medicine and Homeopathy Practitioner, Naturalist, Pharmacist, Bioinformaticist, and Science Enthusiast. The photoelectric effect is studied in part because it can be an introduction to wave-particle duality and quantum mechanics. When light shines on a metal, electrons can be ejected from the surface of the metal in a phenomenon known as the photoelectric effect. However, this phenomenon can be explained by the particle nature of light, in which light can be visualized as a stream of particles of electromagnetic energy. If classical physics applied to this situation, the electron in the metal could eventually collect enough energy to be ejected from the surface even if the incoming light was of low frequency. If the frequency of the incident light is too low (red light, for example), then no electrons were ejected even if the intensity of the light was very high or it was shone onto the surface for a long time. Your email address will not be published. Photoelectric effect, phenomenon in which electrically charged particles are released from or within a material when it absorbs electromagnetic radiation. Planck’s Quantum Theory – It states, “One photon of light carries exactly one quantum of energy.” Wave theory of radiation cannot explain the phenomena of the photoelectric effect and black body radiation. A photon is a particle of electromagnetic radiation that has zero mass and carries a quantum of energy. If the intensity of light (I) is increased while keeping the frequency same, more electrons are emitted per unit time. If the frequency of the light was higher (green light, for example), then electrons were able to be ejected from the metal surface even if the intensity was very low or it was shone for only a short time. Aditya Sardana – Author, Editor, Consultant, Quotes of Aditya Sardana on Homeopathy and Alternative Medicine, Bioinformatics and Charles Darwin – Biological Approach of the New Age, Rationally Coping With High Blood Pressure or Hypertension. If the incoming light's frequency, $$\nu$$, is below the threshold frequency, there will never be enough energy to cause electrons to be ejected. The $$E$$ is the minimum energy that is required in order for the metal's electron to be ejected. Photoelectric Effect and the Particle Nature of Light In 1905 Albert Einstein (1879 - 1955) proposed that light be described as quanta of energy that behave as particles. When a surface is exposed to sufficiently energetic electromagnetic energy, light will be absorbed and electrons will be emitted. Both effects demonstrate the particle nature of electromagnetic waves. It was observed that only certain frequencies of light are able to cause the ejection of electrons. The diagram below shows this. Modern physics fully accepts the concept of wave-particle duality in case of light and other electromagnetic radiation. Planck’s constant (h) = 6.6260755(40) x 10-34. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Classical wave theory of light fails to explain some phenomenons of photoelectric effect but the quantum theory, which assumes particle nature of light, explains them fruitfully. The photoelectric effect is a phenomenon that occurs when light shined onto a metal surface causes the ejection of electrons from that metal. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Even higher frequency incoming light (blue) causes ejection of the same number of electrons but with greater speed. Before quantum mechanics, we used to think that light delivered that energy in a continuous stream. This value is known as the threshold frequency. Some phenomena (reflection, refraction, diffraction) were explained using wave nature of electromagnetic radiation and some phenomena (photoelectric effect and black body radiation) were explained by using particle nature of radiation. All electromagnetic radiation is composed of photons. The classical wave theory of electromagnetic radiation predicted the kinetic energy of emitted electrons was dependant on the intensity, and the number of emissions dependant on the frequency of the incident wave. In the photoelectric effect, electrons, called [photoelectrons], are emitted from a metal's surface when light of a certain frequency, or higher than a certain frequency, [shines] on the surface. Electromagnetic Radiation (a.k.a. Compton effect Convincing evidence of the particle nature of electromagnetic radiation was found in 1922 by the American physicist Arthur Holly Compton. This experiment investigates the photoelectric effect, which can be understood in terms of the particle nature of light. Einstein explained the reaction by defining light as a stream of photons, or energy packets. The photoelectric effect is an important concept explained considering the dual nature of matter. Photoelectric cells convert light energy into electrical energy which powers this calculator. The electron gets all of the photon’s energy or none at all. de Broglie wavelength. Main Difference – Photoelectric Effect vs Compton Effect. Compton effect was observed and explained by Arthur Compton. James Clerk Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their symmetry. Back in 1887 when Hertz discovered the Electromagnetic Radiation (EM-R) scientists thought the nature of EM-Wave finally settled, but when Max Planck published his ideas about the discrete nature of electromagnetic radiation energy in 1900 (Planck, 1901), Einstein saw in it the tool to tackle the photoelectric effect in 1905 (Einstein & into English, 1965). The photoelectric effect typically requires photons with energies from a few electronvolts to 1 MeV for heavier elements, roughly in the ultraviolet and X-ray range. The photoelectric effect is applied in devices called photoelectric cells, which are commonly found in everyday items such as a calculator which uses the energy of light to generate electricity. This suggests that … Details of particular methods of particle diffraction are not expected. Low frequency light (red) is unable to cause ejection of electrons from the metal surface. Required fields are marked *. The photoelectric effect cannot be explained by considering light as a wave. Light has properties of both a wave and a particle. Dual Nature of Radiation and Matter and Relativity. An increase in the intensity of incoming light that is above the threshold frequency causes the number of electrons that are ejected to increase, but they do not travel any faster. Consider the $$E = h \nu$$ equation. Photons do not give their energy in parts, they either will give all the energy or none at all. Seahorse – Male Endurance – Roles Swapped!! Electrons are emitted from matter when light shines on a surface . The photoelectric effect is the emission of electrons by substances, especially metals, when light falls on their surfaces. On the other hand, photoelectric effect indicates that light has the aspects of a particle … The effect has found use in electronic devices specialized for light detection and precisely timed electron emission. It is interesting to know that Einstein was awarded the Nobel Prize in Physics 1921 for his work on photoelectric effect. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave. Study of the photoelectric effect led to important st… A photon, present in a beam of light, is absorbed by an electron present at a cathode or metal surface. Electrons are emitted from matter that is absorbing energy from electromagnetic radiation, resulting in the photoelectric effect. What once was science fiction is now reality as solar sails are being developed and tested for modern space travel. The photoelectric effect is defined as a phenomenon in which the emission of electrons occurs when a beam of light strikes a metal or a cathode surface. The energy of photons of light is quantized according to the $$E = h \nu$$ equation. Frequency (f) of photon = speed of light (c)/wavelength of photon (λ). This is called the photoelectric effect, and the electrons emitted in this manner are called photoelectrons. For many years light had been described using only wave concepts, and scientists trained in classical physics found this wave-particle duality of light to be a difficult idea to accept. Explaining the Photoelectric Effect: The Concept of Photons. In 1905 Albert Einstein (1879 - 1955) proposed that light be described as quanta of energy that behave as particles. If the energy absorbed by the electron is greater than the work function for that particular metal or cathode surface, the electron may escape from the surface. For the emission of electrons to take place, the frequency of incident light is required to be greater than a certain minimum value. Have questions or comments? The Photoelectric Effect 5. Originally Answered: how dose photoelectric effect give the evidence of the particle nature of electromagnetic raditaion? Einstein figured out that a beam of light comprises of small packages of energy known as photons or quanta. For the emission of electrons to take place, the frequency of incident light is required to be greater than a certain minimum value. Light’s Dual Nature 6. A key concept that was explained by Einstein using light's particle nature was called the photoelectric effect. These ‘particles’ of light are called photons. A photon is a particle of electromagnetic radiation that has zero mass and carries a quantum of energy. Photoelectric Effect and the Particle Nature of Light. Wave-particle duality. The photoelectric effect and Compton effect are two types of interactions between light and matter. Maxwell (1850's) showed that light is energy carried in the form of opposite but supporting electric and magnetic fields in the shape of waves, i.e. In this article, in order to show the particle nature of light, I have discussed the photoelectric effect along with the necessary equations. Your email address will not be published. How do we know about this stuff? For more information contact us at [email protected] or check out our status page at https://status.libretexts.org. It's a wave! The Photoelectric effect provides evidence that electromagnetic waves have particle-like behaviour. The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. This value is known as the threshold frequency. Well, because of Einstein for one. Now that you know the relation between photoelectric effect particle nature of light it is time … [ "article:topic", "photoelectric effect", "showtoc:no", "license:ccbync", "program:ck12" ], https://chem.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FIntroductory_Chemistry%2FBook%253A_Introductory_Chemistry_(CK-12)%2F05%253A_Electrons_in_Atoms%2F5.04%253A_Photoelectric_Effect, Photoelectric Effect and the Particle Nature of Light, information contact us at [email protected], status page at https://status.libretexts.org. Students should know that electron diffraction suggests that particles possess wave properties and the photoelectric effect suggests that electromagnetic waves have a particulate nature. The energy of a photon (E) is equal to the product of the Planck’s constant (h) and the frequency of a photon (f). Photoelectric Effect – Definition: When an electromagnetic radiation of particular frequency and above strikes a given metal, the photons from that radiation knock out electrons from the metal and provide them with a certain kinetic energy.. He observed the photoelectric effect in which ultraviolet light forces a surface to release electrons when the light hits. Legal. where mv is the momentum p CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon. Photoelectric Effect and the Particle Nature of Light In 1905 Albert Einstein (1879–1955) proposed that light be described as quanta of energy that behave as particles. The threshold frequency is different for different materials. Maxwell's equations were confirmed by Heinrich Hertz through experiments with radio waves. The photoelectric effect was correctly explained by the world-famous physicist, Albert Einstein, in the year 1905. The effect is often defined as the ejection of electrons from a metal plate when light falls on it. Much of the initial confirmation of the wave nature of electromagnetic radiation is attributed to experiments performed by Heinrich Hertz around 1888. The electrons that get emitted from the metal surface are called photoelectrons. Applying the law of conservation of energy, Einstein stated that the maximum kinetic energy (Kmax) for an electron emitted from a surface (a photoelectron) can be calculated by subtracting the work function (ϕ) from the energy gained from a photon (hf). What is Black Body Radiation? The photoelectric effect is a phenomenon of emission of electrons from the surface of metals when the light of suitable frequency is incident on the metal surface. The above equation of photoelectric effect also show that greater the work function of a metal or material, the higher the minimum frequency of light required to induce photoelectric effect, i.e., to cause emission of electrons (photoelectrons). Light): Roemer (1680's) was the first to measure the speed of light using Jupiter's moons -> c=299,790 km/sec or about 185,000 mi/sec . The photoelectric effect is the process in which electromagnetic radiation ejects electrons from a material. Black body radiation and Photoelectric effect .
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• question_answer A refrigerating machine in heat pump mode has a C.O.P. of 4. If it is worked in refrigerating mode with a power input of 3 kW, what is the heat extracted from the food kept in a refrigerator? A) 180 kJ/min B) 360 kJ/minC) 540 kJ/min D) 720 kJ/min
${{(COP)}_{HP}}=4$ ${{(COP)}_{\text{Ref}}}={{(COP)}_{HP}}-1=4-1=3$ $\frac{Q}{W}=\frac{Q}{3}$ $Q=9\,kW\,\,or\,\,540\,kJ/min$
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# Solving multivariate linear regression using Gradient Descent
Note: This is a continuation of Gradient Descent topic. The context and equations used here derive from that article.
When we regress for y using multiple predictors of x, the hypothesis function becomes:
$$h_{\theta}(x) = \theta_{0} + \theta_{1}x_{1} + \theta_{2}x_{2} + \theta_{3}x_{3} + … + \theta_{n}x_{n}$$ If we consider $x_{0} = 1$, then the above can be represented as matrix multiplication using linear algebra.
$$x = \begin{bmatrix} x_{0}\ x_{1}\ \vdots\ x_{n} \end{bmatrix} \ and \ \theta=\begin{bmatrix} \theta_{0}\ \theta_{1}\ \vdots\ \theta_{n} \end{bmatrix}$$
Thus, $$h_{\theta}(x) = \theta^{T}x$$ Here the dimensions of $\theta$ and x is n+1 as this goes from 0 to n.
### Loss function of multivariate linear regression¶
The loss function is given by
$$J(\theta_{0}, \theta_{1},…,\theta_{n}) = \frac{1}{2m}\sum_{i=1}^{m}[h_{\theta}(x^{(i)}) - y^{(i)}]^{2}$$
which you can simplify to
$$J(\theta) = \frac{1}{2m}\sum_{i=1}^{m}[h_{\theta}(x^{(i)}) - y^{(i)}]^{2}$$
The gradient descent of the loss function is now
$$\theta_{j} := \theta_{j} - \alpha\frac{\partial}{\partial\theta_{j}}J(\theta)$$ Note: Here j represents the n+1 features (attributes) and i goes from 1 -> m representing the m records.
Simplifying the partial differential equation, we get the n+1 update rules as follows
$$\theta_{0} := \theta_{0} - \alpha \frac{1}{m}\sum_{i=1}^{m}[h_{\theta}(x^{(i)}) - y^{(i)}]x_{0}^{{(i)}}$$ $$\theta_{1} := \theta_{1} - \alpha \frac{1}{m}\sum_{i=1}^{m}[h_{\theta}(x^{(i)}) - y^{(i)}]x_{1}^{{(i)}}$$ $$\vdots$$ $$\theta_{n} := \theta_{n} - \alpha \frac{1}{m}\sum_{i=1}^{m}[h_{\theta}(x^{(i)}) - y^{(i)}]x_{n}^{{(i)}}$$
The equations above are very similar to ones from simple linear equations.
### Impact of scaling on Gradient Descent¶
When the data ranges of features varies quite a bit from each other, the surface of GD is highly skewed as shown below:
This is because $\theta$ (which is our weights) will descend quickly on small ranges and slowly on large ranges, and so will oscillate inefficiently down to the optimum when the variables are very uneven. When scaled, the surface takes a healthier shape, allowing the algorithm to converge faster. Ideally scale values so they fall within -1 to 1.
#### Scaling methods¶
Feature Scaling is simply dividing values by range. Normalization is when you transform them to have a mean = 0.
Mean normalization $$scaled \ x_{j} = \frac{(x_{j} - \mu_{j})}{s_{j}}$$ where $\mu$ is mean and s is range.
Standard normalization is similar to above, except, s is standard deviation.
The exact range of normalization is less important than having all features follow a particular range.
The general premise is, as number of iterations increase, the loss should reduce. You can also declare a threshold and if the loss reduces below that for n number of iterations, then you can declare convergence. However, Andrew Ng suggests against this and suggests visualizing the loss on a chart to pick LR.
When LR is too high: If you have a diverging graph - loss increases steadily or if the loss is oscillating (pic below), it is likely the the rate is too high. In case of oscillation, the weights sporadically hit the local minima but continue to overshoot.
Iterating through a number of LRs: Andrew suggests picking a range of LRs 0.001, 0.01, 0.1, 1, ... and iterating through them. He typically bumps rates by a factor of 10. For convenience, he picks ..0.001, 0.003, 0.01, 0.03, 0.1, 0.3.. where he bumps by ~3 which is also effective.
### Non-linear functions vs non-linear models¶
A linear function is one which produces a straight line. It is typically of the form $y = \theta_{0} + \theta_{1}x_{1}$. A non-linear function is something that produces a curve. It is typically of the from $y = \theta_{0} + \theta_{1}x^{k}$. A linear model is when the model parameters are additive, even though individual parameters are non-linear. It takes form $y = \theta_{0} + \theta_{1}x_{1} + … + \theta_{n}x_{n}$. A non-linear model is when the model parameters are multiplicative even though they are of order 1. It typically takes form $y = \theta_{0}x_{1}theta_{1}x_{2}^{k}x_{3}$ etc.
### Representing non-linearity using Polynomial Regression¶
Sometimes, when you plot the response variable with one of the predictors, it may not take a linear form. You might want an order 2 or 3 curve. You can still represent them using linear models. Consider the case where square footage is one of the parameters in predicting house price and you notice a non-linear relationship. From the graphic below, you might try a quadratic model as $h_{\theta}(x) = \theta_{0} + \theta_{1}x_{1} + \theta_{2}x_{2}^{2}$. But this model will eventually taper off. Instead, you may try a cubic model as $h_{\theta}(x) = \theta_{0} + \theta_{1}x_{1} + \theta_{2}x_{2}^{2} + \theta_{3}x_{3}^{3}$.
The way to represent non-linearity is to sequentially raise the power / order of the parameter, represent them as additional features. This is a step in feature engineering. This method is called polynomial regression. When you raise the power, the range of that parameter also increases exponentially. Thus you model might become highly skewed. It is vital to scale features in a polynomial regression.
Another option here is, instead of raising power, you take square roots or nth roots, such as: $h_{\theta}(x) = \theta_{0} + \theta_{1}x_{1} + \theta_{2}\sqrt{x_{2}} + \theta_{3}\sqrt[3]{x_{3}}$
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Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
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• # Artykuł - szczegóły
## Colloquium Mathematicum
2016 | 145 | 1 | 1-13
## The structure of split regular Hom-Poisson algebras
EN
### Abstrakty
EN
We introduce the class of split regular Hom-Poisson algebras formed by those Hom-Poisson algebras whose underlying Hom-Lie algebras are split and regular. This class is the natural extension of the ones of split Hom-Lie algebras and of split Poisson algebras. We show that the structure theorems for split Poisson algebras can be extended to the more general setting of split regular Hom-Poisson algebras. That is, we prove that an arbitrary split regular Hom-Poisson algebra 𝔓 is of the form $𝔓 = U + ∑_{j} I_{j}$ with U a linear subspace of a maximal abelian subalgebra H and any $I_{j}$ a well described (split) ideal of 𝔓, satisfying ${I_{j},I_{k}} + I_{j}I_{k} = 0$ if j ≠ k. Under certain conditions, the simplicity of 𝔓 is characterized, and it is shown that 𝔓 is the direct sum of the family of its simple ideals.
1-13
wydano
2016
### Twórcy
• Department of Mathematics, Faculty od Sciences, University of Cádiz, 11510 Puerto Real, Cádiz, Spain
• Department of Mathematics, Faculty od Sciences, University of Cádiz, 11510 Puerto Real, Cádiz, Spain
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# Meeting Details
Title: Heavy-traffic limits for a fork-join network in the Halfin-Whitt regime Probability and Financial Mathematics Seminar Hongyuan Lu, PSU, Industr. & Manufact. Engineering We study a fork-join network with a single class of jobs, which are forked into a fixed number of parallel tasks upon arrival to be processed at the corresponding parallel service stations. After service completion, each task will join a buffer associated with the service station waiting for synchronization, called unsynchronized queue". The synchronization rule requires that all tasks from the same job must be completed, referred to non-exchangeable synchronization". Once synchronized, jobs will leave the system immediately. Service times of the associated parallel tasks of each job can be correlated and form a sequence of i.i.d. random vectors with a general continuous joint distribution function. Each service station has multiple statistically identical parallel servers. We consider the system in the Halfin-Whitt (Quality-and-Efficiency-Driven, QED) regime, in which the arrival rate of jobs and the number of servers in each station get large appropriately so that all service stations become critically loaded asymptotically. We develop a new method to study the joint dynamics of the service processes and the unsynchronized queueing processes at all stations and the synchronized process. The waiting processes for synchronization after service depend on the service dynamics at all service stations, and thus are extremely difficult to analyze exactly. The main mathematical challenge lies in the resequencing of arrival orders after service completion at each station. We represent the dynamics of all the aforementioned processes via a multiparameter sequential empirical process driven by the service vectors of the parallel tasks. We show a functional law large number (FLLN) and a functional central limit theorem (FCLT) for these processes. Both the service and unsynchronized queueing processes in the limit can be characterized as unique solutions to the associated integral convolution equations driven by the arrival limit process and a generalized multiparameter Kiefer process driven by the service vectors.
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# Orthogonal projector
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
orthoprojector
A mapping of a Hilbert space onto a subspace of it such that is orthogonal to : . An orthogonal projector is a bounded self-adjoint operator, acting on a Hilbert space , such that and . On the other hand, if a bounded self-adjoint operator acting on a Hilbert space such that is given, then is a subspace, and is an orthogonal projector onto . Two orthogonal projectors are called orthogonal if ; this is equivalent to the condition that .
Properties of an orthogonal projector. 1) In order that the sum of two orthogonal projectors is itself an orthogonal projector, it is necessary and sufficient that , in this case ; 2) in order that the composite is an orthogonal projector, it is necessary and sufficient that , in this case .
An orthogonal projector is called a part of an orthogonal projector if is a subspace of . Under this condition is an orthogonal projector on — the orthogonal complement to in . In particular, is an orthogonal projector on .
#### References
[1] L.A. Lyusternik, V.I. Sobolev, "Elements of functional analysis" , Wiley & Hindustan Publ. Comp. (1974) (Translated from Russian) [2] N.I. [N.I. Akhiezer] Achieser, I.M. [I.M. Glaz'man] Glasman, "Theorie der linearen Operatoren im Hilbert Raum" , Akademie Verlag (1958) (Translated from Russian) [3] F. Riesz, B. Szökefalvi-Nagy, "Functional analysis" , F. Ungar (1955) (Translated from French)
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A. Parity Game
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
You are fishing with polar bears Alice and Bob. While waiting for the fish to bite, the polar bears get bored. They come up with a game. First Alice and Bob each writes a 01-string (strings that only contain character "0" and "1") a and b. Then you try to turn a into b using two types of operations:
• Write parity(a) to the end of a. For example, .
• Remove the first character of a. For example, . You cannot perform this operation if a is empty.
You can use as many operations as you want. The problem is, is it possible to turn a into b?
The parity of a 01-string is 1 if there is an odd number of "1"s in the string, and 0 otherwise.
Input
The first line contains the string a and the second line contains the string b (1 ≤ |a|, |b| ≤ 1000). Both strings contain only the characters "0" and "1". Here |x| denotes the length of the string x.
Output
Print "YES" (without quotes) if it is possible to turn a into b, and "NO" (without quotes) otherwise.
Examples
Input
010110110
Output
YES
Input
00111110
Output
NO
Note
In the first sample, the steps are as follows: 01011 → 1011 → 011 → 0110
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time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Xenia the beginner mathematician is a third year student at elementary school. She is now learning the addition operation.
The teacher has written down the sum of multiple numbers. Pupils should calculate the sum. To make the calculation easier, the sum only contains numbers 1, 2 and 3. Still, that isn't enough for Xenia. She is only beginning to count, so she can calculate a sum only if the summands follow in non-decreasing order. For example, she can't calculate sum 1+3+2+1 but she can calculate sums 1+1+2 and 3+3.
You've got the sum that was written on the board. Rearrange the summans and print the sum in such a way that Xenia can calculate the sum.
Input
The first line contains a non-empty string s — the sum Xenia needs to count. String s contains no spaces. It only contains digits and characters "+". Besides, string s is a correct sum of numbers 1, 2 and 3. String s is at most 100 characters long.
Output
Print the new sum that Xenia can count.
Examples
Input
3+2+1
Output
1+2+3
Input
1+1+3+1+3
Output
1+1+1+3+3
Input
2
Output
2
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# resizing plot panels to fit data distribution
March 3, 2013
By
(This article was first published on metvurst, and kindly contributed to R-bloggers)
I am a big fan of lattice/latticeExtra. In fact, nearly all visualisations I have produced so far make use of this great package. The possibilities for customisation are endless and the amount of flexibility it provides is especially valuable for producing visualisations in batch mode/programatically.
Today I needed to visualise some precipitation data for a poster presentation of climate observations at Mt. Kilimanjaro. I wanted to show monthly precipitation observations in relation to long term mean monthly precipitation in order to show which months have been particularly wet or dry.
The important point here is that by combining two different visualisations of the same data, we need to make sure that we make these directly comparable. This means that the scales of the absolute rain amounts and the deviations need to be similar, so we can get an instant impression of the deviation in relation to the absolute amounts.
Here's what I've done with latticeExtra (using mock data):
First, we need some (semi-) random data.
## LOAD PACKAGE
library(latticeExtra, quietly = TRUE)
## CREATE MOCK DATA
# precipitation long term mean
pltmean <- 800
# precipitation long term standard deviation
pltsd <- 200
# precipitation observations
pobs <- rnorm(12, pltmean, pltsd)
# preceipitation deviation from long term mean
pdev <- rnorm(12, 0, 150)
# months
dates <- 1:12
Then we calculate the panel heights to be relative to the (precipitation) data distribution. This is crucial because we want the deviation data to be directly comparable to the observed values.
## CALCULATE RELATIVE PANEL HEIGHTS
y.abs <- max(abs(pobs))
y.dev <- range(pdev)[2] - range(pdev)[1]
yy.aspect <- y.dev/y.abs
Then, we create the bar charts as objects.
## COLOUR
clrs <- rev(brewer.pal(3, "RdBu"))
## CREATE THE PLOT OBJECTS
abs <- barchart(pobs ~ dates, horizontal = FALSE, strip = FALSE, origin = 0,
between = list(y = 0.3),
ylab = "Precipitation [mm]", xlab = "Months", col = clrs[1])
dev <- barchart(pdev ~ dates, horizontal = FALSE, origin = 0,
col = ifelse(pdev > 0, clrs[1], clrs[length(clrs)]))
Now, we combine the two plot objects into one and also create strips to be plotted at the top of each panel with labels providing some detail about the respective panel.
## COMBINE PLOT OBJECTS INTO ONE AND CREATE CUSTOM STRIPS FOR LABELLING
out <- c(abs, dev, x.same = TRUE, y.same = FALSE, layout = c(1,2))
out <- update(out, scales = list(y = list(rot = 0)),
strip = strip.custom(bg = "grey40",
par.strip.text = list(col = "white",
font = 2),
strip.names = FALSE, strip.levels = TRUE,
factor.levels = c("observed",
"deviation from long term monthly mean")))
As a final step, we re-size the panels according to the panel heights calculated earlier.
## RESIZE PANELS RELATIVE TO DATA DISTRIBUTION
out <- resizePanels(out, h = c(1,yy.aspect), w = 1)
And this is what the final product looks like.
## PRINT PLOT
print(out)
Note: I suggest you rerun this example a few times to see how the relative panel sizes change with the data distribution (which is randomly created during each run). This highlights the usefulness of such an approach for batch visualisations.
sessionInfo()
## R version 2.15.3 (2013-03-01)
## Platform: x86_64-pc-linux-gnu (64-bit)
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=C LC_NAME=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] grid parallel stats graphics grDevices utils datasets
## [8] methods base
##
## other attached packages:
## [1] gridBase_0.4-6 abind_1.4-0 fields_6.7
## [4] spam_0.29-2 reshape_0.8.4 plyr_1.8
## [7] latticeExtra_0.6-19 lattice_0.20-13 RColorBrewer_1.0-5
## [10] RWordPress_0.2-3 rgdal_0.8-5 raster_2.0-41
## [13] sp_1.0-5 knitr_1.1
##
## loaded via a namespace (and not attached):
## [1] digest_0.6.3 evaluate_0.4.3 formatR_0.7 markdown_0.5.4
## [5] RCurl_1.95-3 stringr_0.6.2 tools_2.15.3 XML_3.95-0
## [9] XMLRPC_0.2-5
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Best container for me.
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Hi, Let my illustrate my problem, i need to make a list of "products" groups like for example for "SuperGLU", each product has its unique SERIAL_ID_START, and SERIAL_ID_END. Example: Product: "SuperGlue" SERIAL_ID_START: 0 SERIAL_ID_END: 100 Product: "BluePaint" SERIAL_ID_START: 101 SERIAL_ID_END: 120 etc. etc. And now the client wants to get the single product where SERIAL_ID is 105. The search process should return "BluePaint" product. Of course this can be easily done by implementing normal std:list container, but the problem is SPEED. There could be an N products in the shop (for example a >million), and each element in the product "list" should be erasable, also user may add an new element at any time. Std:map is fast, but the problem in this implementation is the key value. Any idea what container should i use? Binary trees maybe? Please note this program must be done in c++, no SQL is alowed :) Thanks!!
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Well, with the std::map you could make your key value an std::pair, or other struct, which contains the upper and lower limits and you test against that when finding.
The other option might be boost's Multi-index container. You should be able to index on the two values and force them both to be unique in the container meaning you can't duplicate them.
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Quote:
Original post by phantomWell, with the std::map you could make your key value an std::pair, or other struct, which contains the upper and lower limits and you test against that when finding. The other option might be boost's Multi-index container. You should be able to index on the two values and force them both to be unique in the container meaning you can't duplicate them.
I'm not sure if i got you correctly, is that the thing you were talking about?:
typedef std::pair<int, int> MyPair;typedef std::map<MyPair, DWORD> MyMap; // at this moment the second DWORD param is not importantMyMap product_map;product_map.insert(make_pair(MyPair(PRODUCT1_SERIALID_START,PRODUCT1_SERIALID_END ),0));product_map.insert(make_pair(MyPair(PRODUCT2_SERIALID_START,PRODUCT2_SERIALID_END ),0));
How does this simplify the finding the specific map entry like PRODUCT1_SERIALID_START+1? You were thinking about using "find" method or iterating all the map entries?
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A binary search tree would work. Create the tree using the minimum number as the primary value, then add a second value to each node which would be the maximum. When traversing the tree, you'd need to check the maximum at each node before moving to the right.
There's probably a better solution, but that should work fairly well.
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Yeah, std::pair wouldn't work, however if you did it with a struct and implimented the function/operator 'find' uses to find matches and have it do the right thing you might be able to get away with it.
Although you still have the potential for overlapping ranges if you aren't careful.
Boost::Multi-index container might well be a better solution as you can do all manner of lookups on that; it does come with a bit of a learning curve however.
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thanks for replying phantom and drakostar.
I was thinking about binary tree, but in bit different manner, for example
instead of finding the correct value, i would request the binary tree to find the nearest one, and then do manual check with the "neareast one" element size.
If that would fail, it means that the element is not in list. What do you think?
Now i will try to play with this BOOST library!
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Assuming non-overlapping intervals:
struct edge { product_id product; enum type { START, END } side; };typedef std::map<int,edge> intervals;void add_interval(intervals& i, product_id id, int min, int max){ edge start = { id, START }; edge end = { id, END ]; i[min] = start; i[max] = end;}boost::optional<product_id> get(const intervals& i, int pos){ intervals::const_iterator found = i.lower_bound(pos); if (found == i.end() || found -> second.side == START) return boost::optional<product_id>(); return found->second.product;}
Of course, if there are no holes between intervals, you can get away with storing only the end edge. Both methods get even faster if the list of products changes infrequently, since you can then use an array with the std::lower_bound function for improved speed.
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ToohrVyk:
I've modified your idea a bit works like a charm! Thank you! Silly me i didnt remember the "lower_bound" method!
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## Characteristic function for Dirichlet distribution
I've been unable to find the characteristic function for the Dirichlet distribution. Does anyone have any reference to where this function has been derived?
Thanks!
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How do I change the thickness and color of \hline on a table simultaneously?
It is easy to change the color or thickness of \hline in a table, but I want to change color and thickness which is hard for me...
\documentclass{article}
\usepackage{colortbl}
\begin{document}
\begin{tabular}{c}
\arrayrulecolor{red}\hline
a \\
\arrayrulecolor{green}\hline
\end{tabular}
\end{document}
The thickness of \hline is controlled by \arrayrulewidth. It can be changed globally inside \noalign:
\documentclass{article}
\usepackage{colortbl}
\begin{document}
\begin{tabular}{c}
\noalign{\global\arrayrulewidth=2mm}
\arrayrulecolor{red}\hline
a \\
\noalign{\global\arrayrulewidth=1mm}
\arrayrulecolor{green}\hline
\end{tabular}
\end{document}
• Is there anyway to change the color of \hhline? Also, is there any way to change the thickness locally? – H. R. Sep 22 '17 at 14:45
• @H.R. a) The method of the answer should also work for \hhline, see also "9 More fun with \hhline" in the documentation of package colortbl. – Heiko Oberdiek Sep 22 '17 at 16:28
• b) Also \arrayrulecolor uses a global definition internally. At the start of a new table row, TeX expands tokens. An assignment ends the expansion mode and starts the new cell already. As a workaround, the previous thickness can be saved in a register and restored afterwards. – Heiko Oberdiek Sep 22 '17 at 16:33
• What is the default thickness of hline? – Viesturs Apr 21 '19 at 6:56
• @Viesturs It depends on the document class, the standard classes (article, report, book) and other (memoir, ...) define \setlength\arrayrulewidth{.4\p@}. Then, the default thickness is 0.4 pt. – Heiko Oberdiek Apr 21 '19 at 16:13
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# zbMATH — the first resource for mathematics
On the Neifeld connection on a Grassmann manifold of Banach type. (Russian) Zbl 0930.53023
In 1976, E. G. Neifel’d proposed a way to construct a linear connection on a finite-dimensional Grassmann manifold $$G_{k+m,k}$$ [Izv. Vyssh. Uchebn. Zaved., Mat. 1976, No. 11(174), 48-55 (1976; Zbl 0345.53003)] via a normalization, a mapping $$f : G_{k+m,m} \to G_{k+m,k}$$. In the paper under review, the author considers an infinite-dimensional version of this construction.
For a Banach space $$E$$, the author takes the Grassmann manifold $$G_{F,H}(E)$$ of subspaces which are isomorphic to a subspace $$F \subset E$$ and have a topological complement isomorphic to $$H \subset E$$, and a normalization mapping $$f: G_{F,H} \to G_{H,F}$$. Let $$\lambda(G_{F,H})$$ be the universal vector bundle over $$G_{F,H}$$ with fibre $$F$$. Following Neifeld’s construction, the author demonstrates that the canonical flat connection on $$E$$ induces via $$f$$ linear connections $$\nabla'$$ on $$\lambda(G_{F,H})$$ and $$\nabla''$$ on $$\lambda(G_{H,F})$$. Then he proves that $$TG(F,H) \cong \lambda(G_{F,H}) \otimes f^*\lambda(G_{H,F})$$, and thus obtains a linear connection $$\nabla$$ on $$TG(F,H)$$. Furthermore, he gives an expression for the operator of connection $$\nabla$$ with respect to a canonical chart on $$G_{F,H}$$.
##### MSC:
53C05 Connections, general theory 53C30 Differential geometry of homogeneous manifolds
Full Text:
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# why are my Sha and Declination calculations not the same as the answers from the Nautical Almanac?
from skyfield.api import Star, load
from skyfield.data import hipparcos
import math
with load.open(hipparcos.URL) as f:
df = hipparcos.load_dataframe(f)
achernar_star=Star.from_dataframe(df.loc[7588])
planets = load('de421.bsp')
earth = planets['earth']
ts = load.timescale()
t = ts.now()
astrometric = earth.at(t).observe(achernar_star)
ra, dec, distance = astrometric.radec()
f = float(ra._degrees)
f1= float(dec.degrees)
print('achernar')
print('Sha',360-round(f,2))
print('Dec', round(f1,2))
print('')
achernar
Sha 335.57
Dec -57.24
From Nautical Almanac
achernar
Sha 335.36
Dec -57.13
• Did you use another Epoche? My guess : Almanac will use current while hipparcos is meanwhile a bit dated Dec 3, 2021 at 7:17
• Thanks. I didn't quite understand the 'epoch', isn't that determined by the timescale import? It put me on rereading the doc's and the difference between 'astrometric and 'apparent' radec. Although I don't quite understand the difference, changing to 'apparent' radec seems to have worked. If you agree i'll close out this question. Thanks n Rgds Sybe
– sybe
Dec 3, 2021 at 13:14
• The “epoch” is the moment for which the positions are valid. Most times, positions are referred to the “J2000.0” epoch, which is January 0, 2000 (or December 31, 1999, if you prefer, but in order to keep it “year 2000,” astronomers have created this fictitious date of January 0). Stars will have some proper motion between J2000.0 and now, and there will also be the effects of precession, aberration, and nutation, for which you need to correct. Only then will you be able to compare apples with apples. Dec 3, 2021 at 23:05
## 1 Answer
Astronomical positions always come with a date on which they are accurate, the epoch.
If you compare data with a different reference frame (like from different catalogues), you have to compensate for the peculiar motion of the objects as well as changes in Earth's rotation (like nutation, precession etc) and other influences. These changes are not big, even when combined, but they are in the order of arc seconds up to arc minutes per year.
Ignoring the peculiar motion of the individual objects, and only taking into account changes to the earth's orbit and rotation, there are conversion formula or programmes one can apply to data at large to allow comparison of data with different reference epoch.
In particular the Hipparcos catalogue has a very unusual epoch of J1991.25" (8.75 Julian years before January 1.5, 2000 TT, e.g., April 2.5625, 1991 TT). The usual epoch right now is J2000 or maybe J2025 - but a Nautical Almanach might want to use data corrected for that particular year it is valid for.
• The Nautical Almanac for 2021 has Achernar's SHA starting the year at 355.38, increasing to 355.39 in April, then decreasing to 355.36 in October, and ending the year at 355.37. Its south declination, similarly, varies from 57.14 to 57.12. Wikipedia has a good article "Astronomical Nutation" and a good illustration in the article "nutation." The variations are significant for celestial navigation: on the order of a mile over the course of a year. Dec 4, 2021 at 13:03
• Thanks for the information! I hadn't have such almanach in my hands so far - but indeed from navigation I know that an arc minute equals a mile difference - critical for navigation (that's how the nautical mile was defined at one point: one arc minute of the Earth's equatorial circumference). Dec 4, 2021 at 13:13
• The website thenauticalalmanac.com has .pdf almanacs for the current year, many back years, a few future years and much more. Dec 5, 2021 at 14:37
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# Why is arc length not in the formula for the volume of a solid of revolution?
I have difficulty understanding the difference between calculating the volume of a solid of revolution, and the surface area of a solid of revolution.
When calculating the volume, using disc integration, I've been taught to reason in the following way: divide the solid into several cylinders of infinitesimal width $dx$. Then each such cylinder has radius $f(x)$ , so its volume is $\pi\cdot f(x)^2~dx$ . Hence the total volume of the solid of revolution is $V=\pi\int_a^b f(x)^2~dx$ .
So when calculating the surface area, I figure I should be able to reason thus: as before, divide the solid into several cylinders, except now calculate the area of each one instead of its volume. This should yield $A=2\pi\int_a^bf(x)~dx$. However, this is the wrong answer. In order to get the proper formula, I need to replace $dx$ with the arc length, which is $\sqrt{1+f'(x)^2}~dx$ .
My question is: why is this the case? There's no need to use arc length when calculating volume, so why does it show up when calculating area?
• Applying your reasoning in 2d (that is forgetting the revolution and the resulting $2\pi f(x)$ factor), you would conclude that the length of any curve $y=f(x)$ is $\int_a^b 1 dx=b-a$. – Julien Dec 3 '13 at 2:48
• – Hans Lundmark Nov 25 '19 at 15:27
One way to gain the intuition behind this is to look at what happens in 2 dimensions. Here, rather than surface area and volume, we look at arc length and area under the curve. When we want to find the area under the curve, we estimate using rectangles. This is sufficient to get the area in a limit; one way to see why this is so is that both the error and the estimate are 2-dimensional, and so we aren't missing any extra information.
However, the analogous approach to approximating arc length is obviously bad: this would amount to approximating the curve by a sequence of constant steps (i.e. the top of the rectangles in a Riemann sum) and the length of this approximation is always just the length of the domain. Essentially, we are using a 1-dimensional approximation (i.e. only depending on $x$) for a 2-dimensional object (the curve), and so our approximation isn't taking into account the extra length coming from the other dimension. This is why the arc length is computed using a polygonal approximation by secants to the curve; this approximation incorporates both change in $x$ and change in $y$.
Why is this relevant to solids of revolution? Well, in essence, the volume and surface area formulae are obtained by simply rotating the corresponding 2-dimensional approximation rotated around an axis, and taking a limit. If it wouldn't work in 2 dimensions, it certainly won't work in 3 dimensions.
Consider a cone. It is a rotated line segment $f(y)=\dfrac{r}{h}y$ (leaving it without a base). We know its volume (if it had a base) will be $\dfrac{\pi}{3}r^2h$, and its surface area (without the base) will be $\pi r\ell$.
To find the volume, we take the integral of the function of the areas of concentric circles. Essentially, this is like breaking up the cone into small quasi-cylinders, then taking the limit as they become infinitesimal.
Looking at a finite one of these, the volume is $\pi R^2\,\mathrm dy$. Notice that if there are $n$ of these slices, $n\,\mathrm dy$ will be $h$, the height of the cone, as we expect.
We have no problem integrating $\displaystyle\int_0^h\pi\left(\frac{r}{h}y\right)^2\,\mathrm dy$ to get $\dfrac{\pi}{3}r^2h$, and we don't have to do arc length.
Now the problem comes when we try to find the surface area of the cone with integration. What you were doing was taking the integral of the function of circumferences of concentric circles. This seems analogous to the area of the circles last time, but it's not.
You have to realize that like last time, we are looking at that slice of the cone, but this time we're adding up the surface area. It's an approximate rectangle, so the area is $2\pi R\,\mathrm dy$. It's just like what you were doing.
The problem arises when you see that with $n$ slices, $n\,\mathrm dy$ should be equal to the slant height $\ell$, not the height $h$ like last time. The slant height is just the arc length of the line segment. $\mathrm dy=\dfrac{\sqrt{1+f'(y)^2}}{n}$ instead of $\dfrac{1}{n}$ last time.
So you just take the integral $\displaystyle\int_0^h2\pi\frac{r}{h}y\,\mathrm dy$, and you replace $\mathrm dy$ with $\sqrt{1+f'(y)^2}\,\mathrm dy$. Then you integrate $\displaystyle\int_0^h2\pi\frac{r}{h}y\sqrt{1+\left(\frac{r}{h}\right)^2}\,\mathrm dy$ and get $\pi r\sqrt{h^2+r^2}$, the right answer.
Essentially, that slice of the cone is not a cylinder. You can pretend it is when integrating for volume, since the shape of the outside does not matter to you then, but you can't ignore it for surface area.
The reason is that the width of the "cylinder" is sensible to both changes in $x$ and in $y$. The cylinder is "slanted": it is more like a slice of a cone in the direction perpendicular to the axis of rotation than like a slice of a cylinder.
Consider for instance a curve which oscillates extremely rapidly between two small values. Your method does not work because it accounts for none of the surface area which is (almost) all in the vertical direction.
When calculating a volume, all of this becomes negligible with respect to the volume of the cylinder.
• Why does it become negligible? – Andrea Dec 3 '13 at 2:45
• @Andreas Put it this way: the volume of a cylindrical solid with base $S$, $I \times S$, is equal to the area of $S$. But its surface area is equal to the arc length of $S$. Can you see this? – Bruno Joyal Dec 3 '13 at 2:56
• Yes, I can see that. But that's not the same arc length as in the formula. – Andrea Dec 3 '13 at 10:25
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Action Points are the method by which a character's Daily Powers are recharged. Each character has a gauge represented by a D20 in the middle of their Combat Action Bar. This gauge refills as the character gains more Action Points. When this bar is filled by the attainment of Action Points, a character's Daily Power is available for use. The use of a character's daily power depletes this gauge and a character must once again perform actions which grant Action Points to refill it. However, the tool-tips are misleading. For instance, Guardian Neverwinter ps4 riscattare ricompense incontri eroici can gain Action Points from blocking attacks, but do not gain Action Points from taking unguarded damage unless they have the Martial Mastery paragon feat. Some or all of this article's content may be out of date. You can help Neverwinter Wiki by updating it. Encounter does not grant any Action Points. Retrieved from " https:
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Documentation
### This is machine translation
Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.
# csaps
Cubic smoothing spline
## Syntax
pp = csaps(x,y)
csaps(x,y,p)
[...,p] = csaps(...)
csaps(x,y,p,[],w)
values = csaps(x,y,p,xx)
csaps(x,y,p,xx,w)
[...] = csaps({x1,...,xm},y,...)
## Description
pp = csaps(x,y) returns the ppform of a cubic smoothing spline f to the given data x,y, with the value of f at the data site x(j) approximating the data value y(:,j), for j=1:length(x). The values may be scalars, vectors, matrices, even ND-arrays. Data points with the same site are replaced by their (weighted) average, with its weight the sum of the corresponding weights.
This smoothing spline f minimizes
Here, |z|2 stands for the sum of the squares of all the entries of z, n is the number of entries of x, and the integral is over the smallest interval containing all the entries of x. The default value for the weight vector w in the error measure is ones(size(x)). The default value for the piecewise constant weight function λ in the roughness measure is the constant function 1. Further, D2f denotes the second derivative of the function f. The default value for the smoothing parameter, p, is chosen in dependence on the given data sites x.
If the smoothing spline is to be evaluated outside its basic interval, it must first be properly extrapolated, by the command pp = fnxtr(pp), to ensure that its second derivative is zero outside the interval spanned by the data sites.
csaps(x,y,p) lets you supply the smoothing parameter. The smoothing parameter determines the relative weight you would like to place on the contradictory demands of having f be smooth vs having f be close to the data. For p = 0, f is the least-squares straight line fit to the data, while, at the other extreme, i.e., for p = 1, f is the variational, or `natural' cubic spline interpolant. As p moves from 0 to 1, the smoothing spline changes from one extreme to the other. The interesting range for p is often near 1/(1 + h3/6), with h the average spacing of the data sites, and it is in this range that the default value for p is chosen. For uniformly spaced data, one would expect a close following of the data for p = 1(1 + h3/60) and some satisfactory smoothing for p = 1/(1 + h3/0.6). You can input a p > 1, but this leads to a smoothing spline even rougher than the variational cubic spline interpolant.
If the input p is negative or empty, then the default value for p is used.
[...,p] = csaps(...) also returns the value of p actually used whether or not you specified p. This is important for experimentation which you might start with [pp,p]=csaps(x,y) in order to obtain a `reasonable' first guess for p.
If you have difficulty choosing p but have some feeling for the size of the noise in y, consider using instead spaps(x,y,tol) which, in effect, chooses p in such a way that the roughness measure
${\int \lambda \left(t\right)|{D}^{2}s\left(t\right)|}^{2}\text{ }dt$
is as small as possible subject to the condition that the error measure
$\sum w\left(j\right){|y\left(:,j\right)-s\left(x\left(j\right)\right)|}^{2}$
does not exceed the specified tol. This usually means that the error measure equals the specified tol.
The weight function λ in the roughness measure can, optionally, be specified as a (nonnegative) piecewise constant function, with breaks at the data sites x, by inputting for p a vector whose ith entry provides the value of λ on the interval (x(i-1) .. x(i)) for i=2:length(x). The first entry of the input vector p continues to be used as the desired value of the smoothness parameter p. In this way, it is possible to insist that the resulting smoothing spline be smoother (by making the weight function larger) or closer to the data (by making the weight functions smaller) in some parts of the interval than in others.
csaps(x,y,p,[],w) lets you specify the weights w in the error measure, as a vector of nonnegative entries of the same size as x.
values = csaps(x,y,p,xx) is the same as fnval(csaps(x,y,p),xx).
csaps(x,y,p,xx,w) is the same as fnval(csaps(x,y,p,[],w),xx).
[...] = csaps({x1,...,xm},y,...) provides the ppform of an m-variate tensor-product smoothing spline to data on a rectangular grid. Here, the first argument is a cell-array, containing the vectors x1, ..., xm, of lengths n1, ..., nm, respectively. Correspondingly, y is an array of size [n1,...,nm] (or of size [d,n1,...,nm] in case the data are d-valued), with y(:,i1, ...,im) the given (perhaps noisy) value at the grid site xl(i1), ...,xm(im).
In this case, p if input must be a cell-array with m entries or else an m-vector, except that it may also be a scalar or empty, in which case it is taken to be the cell-array whose m entries all equal the p input. The optional second output argument will always be a cell-array with m entries.
Further, w if input must be a cell-array with m entries, with w{i} either empty, to indicate the default choice, or else a nonnegative vector of the same size as xi.
## Examples
Example 1.
x = linspace(0,2*pi,21); y = sin(x)+(rand(1,21)-.5)*.1;
pp = csaps(x,y, .4, [], [ones(1,10), repmat(5,1,10), 0] );
returns a smooth fit to the (noisy) data that is much closer to the data in the right half, because of the much larger error weight there, except for the last data point, for which the weight is zero.
pp1 = csaps(x,y, [.4,ones(1,10),repmat(.2,1,10)], [], ...
[ones(1,10), repmat(5,1,10), 0]);
uses the same data, smoothing parameter, and error weight but chooses the roughness weight to be only .2 in the right half of the interval and gives, correspondingly, a rougher but better fit there, except for the last data point, which is ignored.
A plot showing both examples for comparison can now be obtained by
fnplt(pp); hold on, fnplt(pp1,'r--'), plot(x,y,'ok'), hold off
title(['cubic smoothing spline, with right half treated ',...
'differently:'])
xlabel(['blue: larger error weights; ', ...
'red dashed: also smaller roughness weights'])
The resulting plot is shown below.
Example 2. This bivariate example adds some uniform noise, from the interval [-1/2 .. 1/2], to values of the MATLAB® peaks function on a 51-by-61 uniform grid, obtain smoothed values for these data from csaps, along with the smoothing parameters chosen by csaps, and then plot these smoothed values.
x = {linspace(-2,3,51),linspace(-3,3,61)};
[xx,yy] = ndgrid(x{1},x{2}); y = peaks(xx,yy);
rng(0), noisy = y+(rand(size(y))-.5);
[smooth,p] = csaps(x,noisy,[],x);
surf(x{1},x{2},smooth.'), axis off
Note the need to transpose the array smooth. For a somewhat smoother approximation, use a slightly smaller value of p than the one, .9998889, used above by csaps. The final plot is obtained by the following:
smoother = csaps(x,noisy,.996,x);
figure, surf(x{1},x{2},smoother.'), axis off
## Algorithms
csaps is an implementation of the Fortran routine SMOOTH from PGS.
The default value for p is determined as follows. The calculation of the smoothing spline requires the solution of a linear system whose coefficient matrix has the form p*A + (1-p)*B, with the matrices A and B depending on the data sites x. The default value of p makes p*trace(A) equal (1-p)*trace(B).
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Volume 358 - 36th International Cosmic Ray Conference (ICRC2019) - CRD - Cosmic Ray Direct
Production of Silica Aerogel Radiator Tiles for the HELIX RICH Detector
P. Allison, J. Beatty, L. Beaufore, Y. Chen, S. Coutu, E. Ellingwood, M. Gebhard, N. Green, D. Hanna, B. Kunkler, S.I. Mognet, R. Mbarek, K. McBride, K. Michaels, D. Muller, J. Musser, S. Nutter, S. O'Brien, N. Park, T. Rosin, E. Schreyer, G. Tarle, M. Tabata*, A. Tomasch, G. Visser, S. Wakely, T. Werner, I. Wisher and M. Yuet al. (click to show)
Full text: pdf
Pre-published on: July 22, 2019
Published on: July 02, 2021
Abstract
A hydrophobic, highly transparent silica aerogel with a refractive index of $\sim$1.15 was developed using sol–gel polymerization, pin drying, and supercritical carbon dioxide solvent extraction technologies. A total of 96 monolithic tiles with dimensions of 11 cm $\times$ 11 cm $\times$ 1 cm were mass produced with a high crack-free yield for use as Cherenkov radiators to be installed in the proximity-focusing ring-imaging Cherenkov (RICH) detector. The RICH detector, containing 36 aerogel tiles, will be installed in the High Energy Light Isotope eXperiment (HELIX) spectrometer and used to measure the velocity of cosmic-ray particles. HELIX is a balloon-borne experimental program designed to measure the chemical and isotopic abundances of light cosmic-ray nuclei. A water-jet cut test of the aerogel tiles and a gluing test of the trimmed tiles with dimensions of 10 cm $\times$ 10 cm $\times$ 1 cm in an aluminum frame were successful in the context of integration into the radiator module.
DOI: https://doi.org/10.22323/1.358.0139
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
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1. 5
You could have both as of the 1960’s with Dijkstra’s methods. Cleanroom and Eiffel methods showed it too. Point being these aren’t things that should weight against each other in a general platitude. They’re pretty equivalent in importance and benefit in the general case. Helping one helps the other.
1. 6
Could you drop a few links that you think would be a good introduction to what you mean?
1. 6
Dijkstra’s method was building software in hierarchical layers with verification conditions specified in them. Each layer is as independently-testable as possible. Each one then only uses the one below it.
https://en.wikipedia.org/wiki/THE_multiprogramming_system
Cleanroom was a low-defect, software construction process that used a functional style w/ decomposition into simpler and simpler forms with straight-forward, control flow. It was verified by human eye, argument, tests, or formal methods.
http://infohost.nmt.edu/~al/cseet-paper.html
Eiffel combined a safer language, OOP, and Design-by-Contract to increase correctness while maintaining readability of code.
http://www.eiffel.com/developers/design_by_contract_in_detail.html
Logic languages like Prolog were used to go from requirements straight to executable specs with less room for error related to imperative code. Mercury is much improved language at least one company uses for this but here’s a more detailed account from a Prolog company:
https://dtai.cs.kuleuven.be/CHR/files/Elston_SecuritEase.pdf
Finally, DSL’s (esp in 4GL’s) were long used to solve business problems correctly with more readability and productivity than traditional languages. Hintjens at iMatix used them a lot:
https://news.ycombinator.com/item?id=11558465
So, those are where it’s relatively easy to do and adds correctness. I mention a lot more assurance techniques with varying tradeoffs here:
https://lobste.rs/s/mhqf7p/static_typing_will_not_save_us_from_broken#c_d7gega
1. 2
Thank you so much! I’ve got some reading ahead of me now!
1. 11
If we have correctness but not readability, that means a functional program that’s hard to understand. It’s likely we’ll introduce a bug. Then we’ll have a buggy program that’s hard to understand. It’ll probably stay that way.
If you focus on correctness you’ll have tools so that you don’t introduce a bug.
1. 7
Also, I have seen a lot of evidence that correctness produces readability.
1. 5
A common effect in high-assurance security in old days was formal specifications catching errors without formal proofs. The provers were too basic to handle the specs and programs of the time. The specs had to be simplified a lot for the provers. Yet, even if they didn’t do proofs, they found that simplification step caught errors by itself. Proofs had varying levels of helpfulness but that technique consistently found bugs.
So, yeah, it’s easier to show something is correct when it’s simple and readable enough for verifier to understand. :)
1. 4
Do you think it’s possible that pursuing correctness using the type system can cause less readability? If so, what does that look like? If not, do you draw distinctions between words like “readability” and “accessible”? Or perhaps even more fundamentally, do you see a distinction between correctness and readability at all?
1. 4
Do you think it’s possible that pursuing correctness using the type system can cause less readability? If so, what does that look like?
I know exactly what that looks like. They’re called formal proofs of program correctness. The specs and proofs can be hard to read although the code is usually easy to follow. The trick is, what’s easy for a human to verify is often hard for a machine to check and vice versa. So, machine-checked code might get uglier than human-checked code depending on the algorithm.
1. 4
Sure, that’s one extreme end of things. What if we back away from formal proofs and consider other things that are less obvious? For example, is it always true that adding a single additional type—which perhaps seals an invariant you care about—always leads to more readable code? What about two types? Is there a point at which N additional types actually hampers readability even if it makes certain bugs impossible at compile time than could be achieved with N-1 types?
(Perhaps if I constructed an example that would make this a bit more concrete. But I worry that the example will tempt us too quickly into red herrings.)
1. 4
Some people already say that looking at Ada, ATS or Idris code but usually amateurs in the language. I think the easiest example of correct, hard-to-read code is finite state machines. You can do whole programs as Interacting, State Machines. They’re usually compact, easier to verify, and easy to optimize. Many programmers cant read them, though, because they regularly use or even understand FSM’s.
1. 4
In a lot of “proofy” languages, proofs take the form of types, and the line between “normal” types and proofs is blurry/nonexistent. So strictly speaking, “proofs can hurt readability” and “types can hurt readability” mean the same thing. Pedantry aside, look at C++: unreadable clever template types are a cottage industry.
2. 3
Are there really systems where it’s not possible to introduce a bug? Seems like a pretty hefty claim.
1. 4
You can turn (some) would-be-bugs into show-stoppers during the build process. A broken build is very easy to notice. The main difficulty with this approach is that you quickly hit diminishing returns: the amount of effort required to programmatically enforce (parts of) specifications grows much faster than the complexity of the specifications themselves.
1. 3
No. They don’t exist even in high-assurance systems. That’s why most papers in that field are careful to note their Trusted Computing Base (TCB). They say each thing they rely on to work correctly in order for their proven components to work correctly. In the component itself, errors might be introduced in the requirements or specs even if everything else is correct-by-construction from them. If external to the component, it might create interactions with the environment that cause a failure mode that was previously unknown.
Just look at the errata sheet of Intel CPU’s if you ever begin to think you know exactly what will happen when a given app executes. There’s a reason Tandem NonStop had multiple CPU’s per process past availability. ;)
1. 2
If we take it to the extreme and when given appropriate tools, it’s not possible to introduce a bug in the following function:
id :: a -> a
id a = a
There is a single implementation, and you can only compile that function once you have it.
The trick is coming up with a specification and translating the specification to whatever tool you’re using. It is possible to specify the wrong thing, which is where validation (rather than verification) is needed.
1. 4
If we take it to the extreme and when given appropriate tools, it’s not possible to introduce a bug in the following function:
Sure it is. Perhaps my intention was to write a function that would square the argument, but I accidentally wrote an overly general and useless function. The hardest bugs to debug (at least, for me) are the ones where I wrote code that correctly does the wrong thing.
1. 2
I wrote code that correctly does the wrong thing.
Is where:
validation (rather than verification) is needed
1. 3
The concept of verification requires a specification. Without a specification a function cannot be correct or incorrect. It might be inconsistent or misleading if for example the function name does not match the behavior.
You can argue that the type of a function is a specification and the type checker performs the verification. Unfortunately, nearly all type systems are not powerful enough to express all the specification we desire. Exceptions would be Coq, Isabelle, and other code generating theorem provers.
1. 3
Obviously it depends on the problem, but a lot of specifications can be quite easily captured in the type system:
• Only print HTML-escaped values when outputting HTML
• Do not allow any network requests in this block of code
• files must be closed at the end of execution
• This field is not required
I know a lot of specifications are harder to capture, but a good percentage of bugs I encounter in the wild are not the “hard” stuff, but some relatively straightforward stuff that we know how to capture.
Of course, at one point the spec becomes a bit of an uphill battle, but I feel like the more interesting exploration happening in “unsafe but really far reaching” type systems like TypeScript will help us build more tools in a safe way but with a larger reach.
1. 1
Unfortunately, nearly all type systems are not powerful enough to express all the specification we desire.
But we can use common tools such as types, parametricity, Fast and Loose Reasoning and property-based testing to specify a lot of things. Not everything - but a lot of things.
We should definitely move toward Coq and Isabelle for some systems but it’s also often possible to write bug free software without going all the way there.
2. 2
Are there any examples that are more likely? I can’t really imagine writing the specification square :: Int -> Int and then implementing it as square n = n without blinking an eye.
1. 1
In that function, because it applies for all types (id :: a -> a reads, “for all types a, gives an a”), something like squaring the argument is excluded, because not all types have multiplication.
This is an example of the overlap between verification and types – in this case we see the degree to which type correctness constrains the implementation.
1. 8
It’s likely we’ll introduce a bug. Then we’ll have a buggy program that’s hard to understand.
So your argument that readability is better is by comparing a program that is readable but not correct to a program that is neither?
1. 1
I’m not the author of the post, but I imagine the point is not being made about programs where the system checks correctness.
1. 7
What is this trying to solve? We already have many abstract notations for mathematics, from eqn(7) to LaTeX to MathML and so on and so on. Not even to mention the raft of per-language mathematics languages.
(Isn’t asciimath the result of MultiMarkdown 2 trying to shoehorn “markdown philosophy” into mathematics before bailing back into LaTeX in subsequent generations?)
1. 2
From the looks of it, this is trying to solve the problem of the cumbersome and sometimes silly syntax LaTeX uses. If you know LaTeX and want to use it, more power to you, but there are books explaining its use, whereas this is specified in just a single webpage. It seems like a much lower bar to jump.
1. 2
I think part of @kristapsdz’s point is that there are already several options here. S/He explicitly gave three.
1. 3
I get the critique, I just don’t think there’s a problem with experimenting on stuff like this. Personally, this seems way easier to read when rendered just as ASCII (without MathJax) which is one of the things I don’t like about sites that use LaTeX in particular.
2. 1
It’s been a while since I used LaTeX but it’s not that hard to use for simpler formulas. I’d rather have one implementation than have to learn yet another syntax.
Of course the cleanest way to handle this is to just write everything in LaTeX and output to HTML…
3. 1
Now we need plain text output for eqn. This would be the real ASCII/UTF-8 math for me.
1. 2
I’ve never really gotten into emacs deep enough to find out, but is this the sort of thing that org-mode provides in emacs-world?
1. 2
That would be my guess, although I tend to just use Org mode formatted gists (created/updated via Emacs’s gist integration) to get private gists that render nicely. Org mode also has a concept of “projects” and can export them to HTML, if you want to have static HTML of your project, but I’ve never used that.
1. 13
I’m interested: does anyone else here feel this way too?
1. 20
I do. That’s why I posted it. I even tick off the stereotypes: white, male, programming since kindergarten.
The parts about attention to detail especially resonated with me. I thought of majoring in math where proofs can’t be shipped until they’re airtight. I ended up majoring in philosophy where I learned how to find all the holes in my own work before shipping and try to anticipate challenges before anyone else sees the argument. One thing I tend to think about along these lines is the fact that we lionize the trailblazers and creators without recognizing the value of maintaining and polishing work that has been roughed out to a functional state.
1. 23
I agree with her disdain for the current obsession with updating fast and pushing code without fully testing or fully thinking things through, but I don’t take it as me not belonging. I take it as the current trends are wrong, and I’m right. But that probably has to do with the fact that I’m 38 and have been coding for over 25 years, so I have a lot of confidence in my opinions being right.
1. 14
One of the biggest benefits of experience: being able to tell when people/industries are full of shit.
Tech, as a whole, is broken and stupid. It’s obsessed with new things at the expense of practices. It is fad-driven to a ridiculous degree. It is infatuated with idiotic status symbols like money and power in a vain attempt at relevance. It is complicit in the spread of harmful ideologies such as misogyny.
An alternate tech culture needs to emerge.
1. 3
These were also my thoughts after reading the article. Perhaps because I’m in the same age group as you, and have a similar level of programming experience.
1. 2
same here. i picked my current job in large part based on a quality-focused engineering culture; after a few years in a “ship features as fast as we can” type startup i was pretty much done with that segment of the industry.
2. 13
Honestly? No.
(As an aside, this whole article kinda feels like the modern version of “everybody in a certain class of people in New York is working on a novel or a screenplay or acting”. I’ve got some friends up there and it’s a common theme, the humblebrag hustle. The breathless way the author here describes talking with her boyfriend–husband now, I’m sorry–about Ajax is kinda silly and immediately opened up a particular bucket for me.)
(As an additional aside, Mrs. Yitbarek does have both a Github and has appeared on the Ruby Rogues podcast for a stint. She’s got actual involvement in the tech sector, but regrettably not a lot of obvious technical work demonstrating mastery or competency.)
My main takeaways about “this way” sketched by the article are:
• the software that is written today is only web software
• users have some deep emotional connection with the software they use, and we must avoid that breaking that trust
• tech industry focuses on shipping over correctness
• users are the center of our software
• tech industry is callous towards humans
• this person who cares about “understanding” a problem is somehow super different from normal developers
I don’t really agree with any of those points.
Not only do I not agree with those points, I’m actively offended by some of them.
Acting like the only software in tech is web software is hugely wrong. It ignores the vast quantity of boring line-of-business Java and C# and VB and MUMPS software that keeps the world spinning. It ignores the vast quantity of microcontroller code in places like microwave firmware and medical imaging units and car ECUs. There is a large and thriving world, however boring and bleak, outside of web development and especially outside of the coastal startup ratrace.
Acting like our users are dependent on us and are vulnerable little snowflakes who will have a breakdown if they get a broken button is belittling and worse, helps us overstate our importance. Most users just find something else if the software is broken.
Acting like best practices are completely ignored in writing new code is insulting, especially when the same author has nothing to say on large legacy systems that are difficult or even infeasible to test. It’s easy to Monday-morning quarterback when you’re fresh out of a bootcamp and think that every system needs TDD. It’s even more easy when you haven’t run into a monstrous banking COBOL blob that has 4 decades of accumulated business logic, or an embedded health IT system where it’s almost impossible to replicate the sheer crackheadedry of the production environment. Further, Mrs. Yitbarek clearly has no experience with any environment or project that does attempt to take correctness seriously, as is the case in processor design or firmware engineering or industrial automation or healthcare or avionics.
Acting like users matter is antiquated even within her own web-tech bubble, as the current best business practices involve squeezing them for all the data they’re worth and shoving ads at them. Don’t let’s pretend differently, because that’s not how the business works. It’s shitty, but it’s how startups work.
Acting like there is some culture unique to tech about exploiting users/customers is rubbish. What about healthcare, loans, broadcast advertising, clothing marketing, makeup salesmanship? That’s not us, that’s not programmers, that’s just how business works. I don’t mind a proper screed against modern capitalism, but don’t you dare tar us with that same brush, Mrs. Yitbarek. Don’t you dare lump developers and programming culture in with sociopathic MBA tricks.
Lastly, I am exceptionally disappointed and annoyed at the insinuation that everybody in tech clearly just doesn’t care to understand their problem domains. I am annoyed that she implies that she is somehow special. I am furious that she would suggest that most programmers don’t try to really grok the situations leading up their problems, and pained that she doesn’t seem to recognize there are a lot of little problems that don’t bear full analysis.
Finally, her whole tone I disagree with. Seriously, for reference:
I do not belong. My values are not valued. My thinking is strange and foreign. My world view has no place here. It is not that I am better, it is that I am different, and my difference feels incompatible with yours, dear tech.
She should get down off the cross and leave room for people that actually need it.
If this essay had been written by a pimply-faced youth in his first year of college CS, we’d make fun of how edgy and self-serious it was, and point out the depths of his ignorance. Here, though, we are supposed to take her seriously? Please.
1. 2
Acting like there is some culture unique to tech about exploiting users/customers is rubbish. What about healthcare, loans, broadcast advertising, clothing marketing, makeup salesmanship? That’s not us, that’s not programmers, that’s just how business works. I don’t mind a proper screed against modern capitalism, but don’t you dare tar us with that same brush, Mrs. Yitbarek. Don’t you dare lump developers and programming culture in with sociopathic MBA tricks.
Don’t you think, though, that to some degree we’re morally culpable for that?
If we had such a principled stand against sleazy MBA tricks, then we could have stopped it. We could have said “No” and organized or professionalized or just not worked for people like that. It is partly our fault.
Also, there are some ways in which tech culture is worse than the regular MBA culture of our colonial masters. Misogyny is one. Say what you will about MBA-style corporate capitalism, but we dialed the sexism back up from 6.5 to 11.
Tech culture is macho-subordinate– most techies brag about 12-hour days to support their employers' bottom line, but have no courage when they see a woman being harassed out of their company– in a way that plays well into MBAs' desires, but I don’t think that we invented it. We did. And even if we didn’t, we’re still responsible for perpetuating it, and need to stop it and fight it at every turn.
2. 22
I think that it’s fairly normal. The dirty secret of this industry is that 90% of the jobs are Office Space, business-driven half-assery where programmers are seen as overpaid commodity workers (hence, software management’s fetish for boot camps and abuse of the H1-B program) rather than trusted professionals.
What seems to have changed (although, the more I talk to veterans of previous bubbles, the more I am convinced it was much this way always) is that Silicon Valley itself has ceased to be any sort of exception. The difference in the Valley seems to be a much harder place to work. If you work in the hinterlands, at least you get to work 9-to-5. In Silicon Valley, it’s more like 9-to-9 due to the glut of boot camp grads who haven’t had their hearts broken yet, and H1-Bs who can be threatened with deportation if they don’t shut up and dance. If you’re going to get the same lame work experience in either place, why not move to a stable big company somewhere with a manageable cost-of-living?
Silicon Valley is good for one thing: raising capital. If you have the pedigree (read: born rich, socialized to be really good at high-end people-hacking) to raise VC and play the Founder game, Silicon Valley is the only place to do it. As for tech itself, the place is beset by mediocrity.
To be honest, I think that there probably are as many interesting companies right now as there were at any other time. The difference is that there isn’t a critical mass of them. Silicon Valley used to have that critical mass; now it’s just another cluster of rich people, a few of whom were relevant and interesting 20 years ago.
1. 1
It’s also a matter of pay scale. You don’t make in Tuscalusa what you’d make in CA or MA/Boston area.
1. 10
I think this gets overstated quite a bit. For one thing, the cost of living is astronomical in the bay area (or NYC), which must be considered when factoring salary. Also, there are plenty of other places with tech jobs - even with vibrant tech scenes, albeit on a smaller scale - where you can still make a comfortable experience-appropriate salary and work a reasonable schedule. Places where you can make a six figure salary as say a 5-year experienced web developer, work 9-5 or thereabouts, and be able to afford a house without selling a vital organ. Atlanta, Denver/Boulder area, the SLC valley, Minneapolis/St Paul, and so on. I see this justification on HN a lot, like your choices are live in SF or NYC or else make $65k/year in Tulsa, and it’s just not accurate. 1. 10 In my experience, the thing that you lose by leaving a “tech hub” is the access to a strong job market, especially if you’re older and seeking management or specialist roles. There just aren’t many on the ground. Adjusting for cost of living, you come out ahead by leaving the tech hubs. No question there. The problem is that if you lose your job (which happens more often, because branch offices get hit first and because out-of-hub companies are more likely to have capitalization problems) or if your team gets moved, you can get stuck having to move as well. Or you can be marooned in a job desert, because after a certain age (getting old sucks; I advise against it) the jobs you want are filled based on connections and rarely publicly posted. For as much as we bloviate about being high-tech and meritocratic, the way we do business is still very local and relationship-based, and that’s going to produce agglomeration. 1. 3 Totally agree. I live and work in Boston and love it. I could make more in SFBay, but then I’d have to live in SFBay, and as everyone outlined pay the cost of living penalties. Plus, I can’t drive so Boston is a better bet for me public transit wise. 1. 1 NYC would be even better for not-driving but the cost of living (mostly just housing) is higher than Boston. 2. 7 You also don’t have to spend as much in Tuscalusa as you might in those other areas. I live in MI and probably make ½-to-¾ of what I could if I moved to SV, but considering the cost of living out there, there is no way I would uproot my family just to make a few extra bucks. I consistently find remote jobs that pay me more than enough to live where I do, and couldn’t be happier with it. 1. 4 That’s fantastic! I’m always a little nervous about betting the farm on remote work - it seems to come and go in waves. Glad to hear you’re doing great and can pay the mortgage that way! 1. 3 Oh, I surely haven’t bet the farm on remote work. I live close enough to Ann Arbor and Detroit that I can (and have before) found “IRL” work :) 2. 6 Do I feel like there really are two different cultures? That the tech world all too often pretends to care more about correctness/understanding than we do? That a lot of people don’t belong here? Yes. Do I feel like I’m on the wrong side of the line? No. I often find myself arguing for a more careful approach that puts more emphasis on correctness, long-term maintainability and so on than other people seem to want to use - but fundamentally this is as a participant in a shared culture where we both agree what the success criteria are. I applaud the author for actually acknowledging the reality of the culture as I experience it. But I fear the seeming criticism is misguided. I don’t think you can get the advantages of tech without the culture of solving problems, just as you can’t e.g. do good science if you’re only looking to confirm your dogma, or do safety-critical operations without incident under a strict hierarchical culture. It’s not just a tool but a way of life, just as e.g. the enlightenment was a massive cultural and social upheval, its visible fruits fundamentally entangled with and inseperable from the cultural changes. No doubt many a medieval monarch would have liked to reap the rewards without changing the social order - but such a monarch would have been entirely missing the point. 1. 3 I care more about correctness than my job typically allows me to execute. That might be the difference. 1. 1 Often I would be inclined to a higher level of correctness than my colleagues. Sometimes due to such a disagreement we end up making a release that’s riskier than I would have liked, and sometimes these risks are borne out as a higher-than-optimal rate of client-facing bugs. But that’s just a normal object-level mistake when it happens (and sometimes we go with my view and end up making a release that’s safer than it needs to be, and that’s also a mistake). We have a shared cultural understanding that correctness is a means to an end, we all know what the measure of success is (short version: money), so we don’t get the bitter disputes of people with fundamentally different values. 2. 4 Yes. There are a lot of us. You are not alone! 1. 3 I know you asked the affirmative, but I just want to say that I do not. I think everyone who WANTS to be here belongs in tech. Yes, you will have to wade through a sea of imperfection every day, no doubt, but if this career path is truly for you, you will also experience moments of unmitigated joy and utter satisfaction. 1. 4 I very much do. While the author was in journalism, my background is science and engineering. Engineering is a process more than anything and this agile world is pretty much the opposite. I hate it! I would also love to go back to research where things fail fast and we try lots of things, but we take pride in publishing perfection. But there’s a problem in academia and it’s the same problem in high tech: money and ethics. When I was in undergrad, I was told by the professional association of engineers that software people will never get that P.eng stamp until the industry as a whole grows the fuck up. Ethics in technology also haven’t matured yet and we are seeing this most prominently with Facebook. How are these engineers at Facebook considering their effects on human beings and society as a whole? Seems an afterthought where the real focus is on building cool shit and getting page views and ad revenues. 1. 4 software people will never get that P.eng stamp until the industry as a whole grows the fuck up. There are those of us eagerly awaiting that day, but it is not here yet. We’re too enamored with building shacks to even fathom building cathedrals, and so we shy away from anything that’d help us do that. 1. 2 Just curious, is there some degree of promise of few breaking changes for newer versions that makes this version a better one to dive in on than others? The debugger is pretty cool, but the 0.x has kept me from trying Elm on a bigger project than just toying around with it. 1. 11 Right now, we’re working on tooling to automate upgrading. For example, for this release, you can use elm-format with the --upgrade flag to automatically update the syntax. Together with elm-upgrade, you can automate upgrading your deps. 0.16 -> 0.17 was a big breaking change. I foresee any other future releases will have substantial tooling for upgrades :) 1. 2 Not sure about any kind of promises. First of all, there were a lot of changes in 0.17, but upgrade from 0.16 was not that hard. Upgrade from 0.17 to 0.18 should be much easier and pretty straightforward, thanks to elm-format. Good news — for the next few months no major changes in Elm land. ;) 1. 6 The thesis here is “just hire random people (regardless of coding ability) and pay them all$30k a year; software will happen,” right? Does that actually match anyone’s experience? Wouldn’t anyone who discovers that they’re decent immediately leave to make twice, three times, or four times more money? Wouldn’t you have an almost immediate dead sea effect in which the only people staying in your company were the people you hired for their “soft skills” who proved useless except for their pleasant small talk in meetings?
1. 3
Well, they’re not going to stay at $30K a year. The proposal explicitly states increasing their salary as they advance in the program. But yeah, I’m pretty skeptical this could ever work. First, because there are very few companies who can afford to spend two years training someone with no prior dev experience. Second, because it assumes you can teach anyone to code. Some people just won’t take to it. Third because, as you said, you have no way to incentivize them to stay once they’ve completed their training and become much more employable. 1. 1 One of the things that seemed strangest to me about this proposal was the complete neglect of the people already at a company. It takes a lot of work to get a senior developer in place without serious disruption in a small team. I can’t even imagine what bringing in multiple people without experience would do. That said, I think it’s easy to imagine there’s something spectacularly unique about programming which precludes people who want to keep a job from improving at it. I really don’t think that’s true and it’s one of the reasons I shared this in the first place. It would definitely take a high degree of humility and patience to execute any part of this, but I think the main thrust of the post (open hiring to a broader pool of applicants) isn’t far off from something to work toward 1. 3 This rate will increase by$10k every six months as they progress through a two-year program. These raises aren’t arbitrary, they represent the actual value the employee is providing.
This doesn’t indicate that they’ve accounted for the fixed costs of a full-time employee (hiring, insurance, unemployment, office space, equipment, benefits). These costs are the same for a raw junior dev and an expert senior dev.
This article also does not acknowledge the fact this strategy is going to have expensive and difficult firing.
1. 2
This was definitely the part of the article that seemed most short-sighted or at least most lacking in an understanding of business operations.
1. 1
Great to see companies thinking about short circuiting broken education and hiring systems by taking on apprentices.
Any lobsters at companies doing this? Anyone seen more formalised or long term apprentice programs, perhaps with some structured learning, mentoring, etc. ?
1. 2
I work at DNSimple, so I’m at least one lobster who’s seen this in action. ;-)
1. 5
I was really excited when I saw that a version of f.lux was available for non-jailbroken iOS devices, as I thought this was a great use of the ability for anyone to install applications via Xcode. I’d like to know which portion of the Developer Program Agreement this has violated since I’d been hoping more things like this would start being released.
1. 3
Apple does not provide an official API with the functionality they need. They used undocumented APIs which developers are apparently not supposed to use (I wonder why apple doesn’t just disable the use of those APIs through technical means?)
1. 1
I think this is pretty interesting, but lobsters might not be the best place to share it. Generic business content doesn’t need lobsters to aggregate it, I’d say–there are plenty of other outlets. While we’re keeping lobsters' high signal to noise ratio, let’s keep this off the radar.
1. 1
As far as I can tell, this seems to pretty clearly fit the tag description of “Development and business practices”. Am I missing the purpose of this tag?
1. 2
It’s not engineering-specific. Because engineering touches pretty much everything in the world, if we included everything that could be related to engineering, we’d just become reddit / digg / slashdot / HN. The reason why most of us are on lobsters is because the signal to noise ratio is pretty high. Keeping it high requires pruning.
I shouldn’t debate the specific tag (in theory, that’s what the “suggest”) button is for, but if you compare it against the other things in practices, pretty much the rest are clearly related to software or hardware.
1. 2
Would you similarly raise this point on the thread of the top article about engineering salaries (also tagged “practices”), the comments of which are filled with political discussions about unions and guilds?
Communication styles and the difficulties / risks of authentic discourse, in particular, seems to be very pertinent to the weaknesses of engineering teams and management, in my experience.
1. 1
No, I don’t think we should police comments–I think being careful about the stories that we admit is sufficient. Note that that story is about engineering salaries.
I agree that they are, but I don’t want lobsters to turn into what hacker news turned into. We already have more than enough of those.
1. 4
I don’t think I agree with this post entirely, but it raises an important question. Are programmers foot soldiers or commanders? I think most programmers consider themselves closer to commanders. They are involved in technical decisions and the creative process of programming. I think many executives consider programemrs foot soldiers. They do what they are told by those above them. Being foot soldiers, it means you can blame them for when something bad happens without worry, like in war.
1. 13
I don’t know, I consider myself more like a private or an NCO: I sometimes get to decide how I do something, but I never get to decide what I do.
1. 7
A large part of this dichotomy depends on the culture of the company in which the developers work. I’ve been in positions where I’ve been a foot soldier and others where I’ve been a commander without a change in job title. Mr. Martin’s point about the need for a professional board of some point seems the most salient given it could determine who is responsible for what or at least give some guidance on the matter.
1. 1
The problem with a professional board with programmers is I don’t see how it would work. One of the biggest strengths, according to many at least, of programming is anyone can do it. It’s not like being a doctor or a lawyer where you need a license to do it. Maybe, if enough VW situations happen, we’ll be forced to get a board.
1. 1
I understand the concern, but a benefit to having a professional board is that there could be a defined meaning for what it is to be a programmer and thus provide a better way into the profession than companies just taking a chance on someone. It could also define an apprenticeship program which would allow new practitioners to enter the field, even with minimal background.
1. 1
Strip off the “Test Double” and “Our Thinking” from the title?
1. 1
I’d also suggest adding the year of publication.
1. 7
I’d been meaning to contribute to Rust for a while, and this is proving to be a good way to get familiar with internals.
1. 1
Great post, Steve. I wonder if striation may actually be the thing to save us more than smoothness (I may have misunderstood the distinction though, so please bear with me). What I mean is that it seems you (and Deleuze) paint smooth space as an ideal and striation as an evil or at least something to be avoided. However, it is precisely striation which would allow a community to form. If a space were purely smooth, only nomads exist, but in a sense, there needs to be some fixedness and continuity (smooth striation?) to keep something together. I think that’s what you started to touch on at the end of the post when you talked about paid vs. free use of a product, but perhaps not. Anyway, thanks for a great read!
|
# Using a single validation handler for all controllers in a form
In input validation I'm using this validation method in my all Forms. Here I have a single handler for all TextBoxes in my Form and if I have other controllers like ComboBoxes I would use a separate handler for all ComboBoxes and so on.
My only doubt in this approach is how users would feel about this as you can't focus on other text boxes while keeping the current one empty if it's not an optional field!
public partial class frmForm : Form
{
public frmForm()
{
InitializeComponent();
foreach (TextBox tb in this.Controls.OfType<TextBox>().Where(x => x.CausesValidation == true))
{
tb.Validating += textBox_Validating;
}
}
private void textBox_Validating(object sender, CancelEventArgs e)
{
TextBox currenttb = (TextBox)sender;
if (currenttb.Name != OptionalFields .txtPolicy.ToString())
{
if (string.IsNullOrWhiteSpace(currenttb.Text))
{
MessageBox.Show(string.Format("Empty field {0 }", currenttb.Name.Substring(3)));
e.Cancel = true;
}
else
{
e.Cancel = false;
}
}
}
private enum OptionalFields
{
txtPolicy, txtRemarks
}
}
• Personally I think users would rather be reminded of an omission right away rather than waiting until all the rest of the inputs are done. One thing you can do is put a label with an * beside the required fields. This a common practice for input forms. This way the user knows what is expected. – tinstaafl Jun 19 '14 at 13:22
• You could use the ErrorProvider control to do what @tinstaafl suggests. – Dan Lyons Jun 19 '14 at 16:59
Just a few random observations:
foreach (TextBox tb in this.Controls.OfType<TextBox>().Where(x => x.CausesValidation == true))
tb is a bad name; without the explicit TextBox type one would have to read the entire part after the in, to figure out that we're talking about a TextBox. And it's not uncommon for loops to use implicit types, like this:
foreach (var tb in this.Controls.OfType<TextBox>().Where(x => x.CausesValidation == true))
Now in this part:
.Where(x => x.CausesValidation == true)
You're comparing a bool to true - that's a no-no. Write it like this instead:
.Where(x => x.CausesValidation)
It's probably also more readable to iterate over an identifier instead of an expression; I'd split it like this:
var textBoxes = Controls.OfType<TextBox>()
.Where(textBox => textBox.CausesValidation);
foreach (var textBox in textBoxes)
{
// ...
}
Kudos for IsNullOrWhiteSpace:
if (string.IsNullOrWhiteSpace(currenttb.Text))
However, currenttb should be camelCase, and would be more readable as currentTextBox.
Careful with extra spaces:
string.Format("Empty field {0 }"
I don't think this is legal, should be "Empty field {0}".
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## Calculating distance and printing it
Typically: "How do I... ", "How can I... " questions
cena
Posts: 7
Joined: 14 Jun 2014, 11:08
### Calculating distance and printing it
Hello,
Can anyone tell me what do i have to do if i want to calculate the distance between a moving robot for example the pioneer p3dx and any obstacle around it for example a wall. Also how can i see the value on the simulation ?
I am guessing i need to use proximity sensors or already built in sensors in the robots for example pioneer p3dx has 16 ultrasonic sensors i think. Also what do i need to add in the code ? Please help.
Kind regards
Maruf
coppelia
Posts: 7594
Joined: 14 Dec 2012, 00:25
### Re: Calculating distance and printing it
Hello Maruf,
to compute the minimum distance between your robot and the environment, use the distance calculation module. Once you have registered a distance object, you can access it, read it and print the distance from a child script with:
Code: Select all
handle=simGetDistanceHandle('myDistanceObjectName')
print(distance) -- prints the distance to the console
Of course you can do something similar with proximity sensors.
Cheers
rohanp
Posts: 3
Joined: 09 Feb 2018, 14:43
### Re: Calculating distance and printing it
hello,
so i am trying to obtain similar data and i tried using the above steps as specified. But I am receiving error at the below statement (correct me if i am wrong):
DistHandle = simGetDistanceHandle('FrontLeg') --statement executed during initialization
What I think, the error is due to the use of wrong distanceobject name: 'FrontLeg'
In such a scenario, how to know which is the correct name and whether the name used is a legal name?
coppelia
Posts: 7594
Joined: 14 Dec 2012, 00:25
### Re: Calculating distance and printing it
Hello,
I see two potential problems:
• either you have misspelled the object name (it is case sensitive)
• either you have not understood how object handles are retrieved. Make sure to read this page
Cheers
Sagar Kalburgi
Posts: 1
Joined: 18 Feb 2018, 15:00
### Re: Calculating distance and printing it
Hey, How do I calculate the distance that my bot has moved and display the distance so that I can use this data for future applications? I'm unable to get it done using simxGetDistanceHandle.
coppelia
|
# PIC16f877A, PWM, to increase the speed of motor according to temperature increasing
Status
Not open for further replies.
#### erfan.khalilian69
##### Member level 4
Hi everyone, I have really stock with this part in my project.
I want to increase the speed of motor as the temperature increasing, therefore I've got idea to use different frequency for different temperature.
I know I have to use CCP1CON ,PR2, T2CON . after initializing the PWM I write: CCPR1L=0; to stop the pwm because I want to activate this pin while the temperature is higher than 30 degree. but while I write CCPR1L=0; the PWM is not generating pulse even while the temperature is higher than 27.
here is my code :
unsigned char speed=50;
CCP1CON = 0b00001100; //PWM Mode
PR2 = 0xFF; //PWM Period Setting//PWM frequecy set as 4.88KHz
T2CON = 0b00000101; //Timer2 On, prescale 4
CCPR1L=0;
else if (temperature>27)
{
CCPR1L=speed;
}
any suggestion?
thanks
#### erfan.khalilian69
##### Member level 4
yes
but first I need to correct my condition actually the condition is not working properly , I have just downloaded some sample which they used 4 buttons to increase the speed decrease and change the direction, instead of button now I want to use if else condition for temperature, but this program while executed the motor keeping running and after some seconds it will be stop. and then while I delete the // if(speed<255)speed+=1; it does not activated any more, what should I do sir ???
else if (temperature>30)
{
// if(speed<255)speed+=1;
CCPR1L=speed; // INCREMENT THE SPEED OF MOTOR
delay(5000);
}
else if (temperature>35)
{
//if(speed>0)speed-=1;
CCPR1L=speed; // DECREMENT THE SPEED OF MOTOR
delay(5000);
}
---------- Post added at 19:44 ---------- Previous post was at 19:40 ----------
Do you mind if I send you whole program by email and you tell me what is the problem with this problem, this problem is actually show the temperature and light in LCD and then for certain temperature and light intensity the fan and lamp will be activated. now my lecture gives me new task to increase the speed of fan according to the increasing temperature.
the submission date its just this Monday
#### horace1
don't use PIC16s anymore but below is some PWM code I wrote some years back for a Microchip Mechatronics board
Mechatronics Demonstration Kit
it used a PIC16F917 - hopefully the comments explain what is going on
Code:
// initialise PWM using Capture Compare PWM Module 2
void PWMinitialise(void)
{
// assume Fosc uses oscillator 8MHz - call systemInitialise() first
TRISD2=0; // set RD2/CCP2 is output
TRISD7=0; // set RD7 is output
PR2=0x3f; // set PR2 to 31.2 kHz PWM (PWM value will be 8 bits)
// Configure Capture Compare PWM Module 2
CCPR2L=0; // set PWM duty cycle to 0
CCP2CON=0xC; // set PWM mode
TMR2ON=1; // Turn on Timer 2 PWM
}
// set PWM duty cycle - value between 0 and 100
void PWMcontrol(int dutyCycle)
{
// get 8 bit value for PWM control at 31.2 kHz PWM
dutyCycle = (int) (dutyCycle * 255L / 100L); // get 8 bit value
RD7=1; // switch on motor
// load most significant 6 bits in CCPR2l and least significant two bits in CCP2CON
CCPR2L=dutyCycle >> 2;
CCP2CON = (CCP2CON & 0xF) + ((dutyCycle << 4) & 0x30); // set bits 4 and 5
}
#### erfan.khalilian69
##### Member level 4
thanks for replaying. why u say dun use pic16s? can i know the reason?
so how can I activate and deactivate the pwm so
?
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# Predict the sign of the entropy change of the system
Predict the sign of the entropy change of the system for each of the following reactions:
${N}_{2}\left(g\right)+3{H}_{2}\left(g\right)⇒2N{H}_{3}\left(g\right)$
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Neil Dismukes
Step 1
The reaction is:
${N}_{2}\left(g\right)+3{H}_{2}\left(g\right)⇒2N{H}_{3}\left(g\right)$
Based on the reaction, there are less gaseous component in the product side than in thereactant side. Thus, the final entropy must be less than the initial entropy. Hence, the change in entropy is negative.
Toni Scott
Step 1
$\mathrm{\Delta }S=\text{Numbr of moles of gaseous product}-\text{number of moles of gaseous reactant}.$
Based on above expression, we can say that sign of the change in entropy of system will be positive if the number of moles of gaseous product is greater than the number of moles of gaseous reactant and vice versa.
Given reaction:
${N}_{2}\left(g\right)+3{H}_{2}\left(g\right)⇒2N{H}_{3}\left(g\right)$
Therefore, sign of the given reaction is negative.
nick1337
Step 1
A decrease in entropy.
Entropy is associated with the degree of disorder, or number of degrees of freedom. In the reaction ${N}_{2}+3{H}_{2}-⇒2N{H}_{3}$ we start with four moles of gaseous reactants! and end with two moles of gaseous products, which is less disordered.
In general, when a reaction has fewer moles of gaseous products than the moles of gaseous reactants, this will be reflected in a decrease in entropy, and vice versa. It's a good job the enthalpy change for this reaction is exothermic, or it would be impossible to make ammonia from nitrogen and hydrogen.
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# I need the for the last part of this question. I have the chart as B and I got the formula right. Th
I need the for the last part of this question. I have the chart as B and I got the formula right. The total cost per unit when manufacturing 5000 is \$ ----- therefore, they (A. Can or Cannot make a profit when compared to FlorA????1as Flasks selling price of 9.50
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# Nonlinear color maps in surf plots
I have the following plot
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
domain = -20:30,
y domain = 0.01:100,
ymode=log,
view = {0}{90},
xlabel={$x$},
ylabel={$y$},
colorbar
]
{-1 + (y * sqrt(1+x^2))^2) / (1+y)^2};
\end{axis}
\end{tikzpicture}
\end{document}
which produces the following
However, I would like the colormap to be equally divided between [0,1] and [1, 1000]. Or possibly two different colormaps for the two ranges. How can I achieve this? I found this but this solution does not change the colormapping, just the colorbar.
• Maybe this post could help? It seems to address a very similar issue. – Ϛ . Oct 29 '18 at 12:42
• I do not understand your statement about this post. Isn't the only difference that you need to distinguish <1 and >1 instead of <0 and >0? – user121799 Oct 29 '18 at 15:06
• @marmot, I think I would also need to subtract 1 from y. In any case, if I use this solution the figure would not change, only the colorbar, i.e., the blue region would stay blue. The post by @Ϛ seems more to the point, although I would like more control than just logarithmic scaling, if that's possible with pgfplots. – Tohiko Oct 29 '18 at 17:03
• @Tohiko Sure. My statement is just to express that I am not convinced that "but this solution does not change the colormapping, just the colorbar." is correct. – user121799 Oct 29 '18 at 18:30
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# mont ste marie condo for sale
The most important feature of a basket option is its ability to efficiently hedge risk on multiple assets at the same time. Find a Part. The index value is: (0.76 x 0.6) + (0.69 x 0.4) = 0.456 + 0.276 = 0.732. Delta will be offering This Bar Saves Lives Wild Blueberry Pistachio Bar in its Delta Comfort+ snack basket, supporting This Bar Saves Lives’ mission of helping those in need. In this case, they will buy a put with a basket containing the CAD/USD and the AUD/USD. HAZELTON's is Canada's #1 Gift Basket Company offering 4,000 different gift baskets for every occasion. Let’s look at another Microsoft example. Delta risks can be hedged using futures, forwards or the asset itself. DELTA HELP LINE 1-800-345-3358 Monday - Friday: 8 a.m. - 8 p.m. EST Saturday: 9 a.m. - 6 p.m. EST. At the airport and if you prefer, many airports do offer private lactation rooms or spaces. Singer Delta Goodrem performs on stage during her 'Believe Again' tour at the State Theatre on January 11, 2009 in Sydney, Australia. Storks Deluxe Neutral $106.00$ 106.00 Add to cart. 17,23 € 17,23 € 18,08 € 18,08€ KOSTENLOSE Lieferung. The VIX Index is based on real-time prices of options on the S&P 500 ® Index (SPX) and is designed to reflect investors' consensus view of future (30-day) expected stock market volatility. 4.5 out of 5 stars 405. MVL due to a change in the assets in the basket or Delta risks. A basket option is an option where the underlying is a basket or group of any asset desired. Je weiter sich der Optionsschein „aus dem Geld“ befindet, desto näher ist Delta am Wert Null. CDN$89.97. The difference between the strike price and the weighted value, less the premium, is the buyer's profit. View Full Page Gift Baskets Seasonal Christmas Gift Basket. Egal ob vermietet oder zur Eigennutzung: Für Wertsteigerung oder -erhalt empfehlen sich regelmäßige Optimierungen. Retreat to the mysteries of the sacred land of the Far East. Sie finden Delta-Sport Handelskontor GmbH Öffnungszeiten, Adresse, Wegbeschreibung und Karte, Telefonnummern und Fotos. Get Well Soon Bed Tray. Rather than hedging each individual asset, the investor can manage risk for the basket, or portfolio, in one transaction. CDN$ 79.98. We assume that the futures in the basket and the basket option mature at the same time. Several financial institutions started marketing step option-like contracts in the currency, interest rate and equity derivatives markets. The buyer of the put basket option loses their premium, and the seller keeps the premium as profit. I’ve been ordering from SeaScape Gift Baskets for a few years and they always make the most amazing & beautiful gift baskets. To schedule and plan your flight, we must receive your charter request at least 31 days in advance. Hinweis: Selbstverständlich können Sie unsere kostenlosen Sonder-Reports auch ohne einen E-Mail-Newsletter anfordern. However, his formula also seems not to work well for basket options. The geometric Asian delta is lower than the arithmetic Asian delta. An outright option is an option that is bought or sold individually, and is not part of a multi-leg options trade. Assume the CAD/USD rate is 0.76, and the AUD/USD rate is 0.69. More. Asian and basket options. Google has many special features to help you find exactly what you're looking for. We always do our best to find the best place for our clients as well as the best contractual situation for both him and the Club he will play for. Eligible for FREE Shipping. Profitieren Sie von unserem kostenlosen Informations-Angebot und erhalten Sie regelmäßig den kostenlosen E-Mail-Newsletter von Michael Berkholz. The BEST Gift Basket Company in BC. The main advantages of our method is that it is simple, computationally extremely fast and efficient, while providing accurate option prices and deltas. If the Canadian and Australian dollars drop against the US dollar they want to be able to sell them at a specified price so as to avoid further deterioration. Bis dahin können die Kurse noch ordentlich durcheinander geschüttelt werden! Holiday Schedule Christmas Eve : 8 A.M - 4 P.M EST Christmas Day: CLOSED New Year's Eve: 8 A.M - 4 P.M EST New Year's Day : CLOSED. Throughout the three month cycle, the airline will be purchasing approximately 300,000 bars. COMMON REPAIR PART FINDER Don’t know the model number? t = time to expiration(% of year) Note: In many resources you can find different symbols for some of these parameters. Exotic options are options contracts that differ from traditional options in their payment structures, expiration dates, and strike prices. Was es mit dem Basispreis auf sich hat. The adorable Moses basket safely attaches to the bassinet frame, and can be easily removed, so you can keep your baby nearby as you move around the house. Another name for the rainbow option is a correlation option. Because it involves just one transaction, a basket option often costs less than multiple single options as it saves on commissions and fees. Unterstützen Sie unsere Partnerorganisationen und Jugendprogramme, mit denen wir Jugendlichen eine bessere Zukunft ermöglichen wollen. A well-known CEO and popular face on Twitter and social media, delta of at the money binary option Singapore Branson has often been an advocate of cryptocurrency. Like a call option, an at-the-money put option has a Delta close to -0.50. Delta Basket Sport Service provides our athlete’s with first class representation and professional advice trough which they get the opportunity to build their careers and develop their ambitions. The number of assets is called the number of colours of the rainbow. An option is a financial instrument that gives one the right to buy or sell underlying asset at (or by) a specified date at a certain price. Our staff brings years of experience in the basketball industry and a unique approach to each client and each negotiation. This is not your typical yoga retreat, this journey will offer some unique opportunities, including An Asian option (or average value option) is a special type of option contract. However, unlike a basket option, all the assets underlying a rainbow option must move in the intended direction. Consider that when hedging an option one has to adjust the Delta hedge upon a move in the assets. Von wegen Korrektur: So zocken die Kleinanleger auf die Rallye. Once Delta risks are hedged specific option, or non-linear, risks remain. Therefore, a basket may not necessarily react to changes in volatility, time, and price level in the same way as its components do individually. Dazu sollte der Schein „aus dem Geld“ liegen und auch noch genügend Laufzeit haben, damit der Basiswert den gewünschten Wert erreichen kann. This is due to convexity of the MVLas a function of BSK. Therefore, a basket option typically refers to an option upon which a basket is created by the seller of the option, often at the request and in concert with the buyer's requirements. brakensiek.com D ie Option Deltalisten fü r D eltaF lo w vorbereiten können Sie nur dann aktivieren, we nn die Don gle -Option Delta F low Ex port fr eigeschaltet ist. There are many di erent types of basket options and they are often traded over the counter. 1. Some jargon used in options market is now introduced. The seller's loss is the weighted value minus the strike price, plus the premium received. "A Pricing Method for Options Based on Average Asset Values." Das liegt daran, dass für viele Investoren einige Kennzahlen unerheblich sind. Bis dahin können die Kurse noch ordentlich durcheinander geschüttelt werden! 4.5 out of 5 stars 76. According to the Black-Scholes option pricing model (its Merton’s extension that accounts for dividends), there are six parameters which affect option prices:. Call Option Premium Put Option Premium Call Option Delta Put Option Delta Option Gamma; 0: 0: 0: 0: 0 Payout for a basket option depends on the cumulative performance of the collection of the individual assets. Rahul Bhattacharya Aug 01, 2005. Ein Delta nahe -1 oder 1 ist darum bereits ein Argument gegen den Kauf, genauso wie ein Wert nahe Null. Think about it: put options increase in value as the stock price goes down. Seascape Gift Baskets go above & beyond and do a superb job. So when the stock price goes up, the value of the put option should drop. The Bountiful Gourmet Gift Basket. The underlying is $S=\omega_1 S_1 +\omega_2 S_2$ Where: $S1$ = stock price of asset 1 $S2$ = stock price of asset 2 $\omega_1$ and $\omega_2$ are the weights As a result, your price moves more. Ist der Optionsschein dagegen deutlich „im Geld“, liegt Delta sehr nahe an den Werten -1 bzw. An S&P 500 index option might partially offset an option based on a portfolio of blue chip stocks. In this case, the buyer will exercise the put option to be able to sell the basket at 0.72, since the weighted value of the currencies is only 0.698. Orders placed after that date will be shipped as quick Bundle of Joy- Girl $75.00$ 75.00 Add to cart. Twitter teilen. Currency baskets are the most popular type of basket option, and they will settle in the holder's home currency. Breast pumps are allowed on board. Exploring the Many Features of Exotic Options. Latest Product . Geschäfte in der Nähe . Futures/Commodities Trading Strategy & Education. Delta ist da eine Ausnahme. In der griechischen Zahlschrift repräsentiert der Kleinbuchstabe δ die Zahl 4 und zusammen mit tiefgestelltem Nummernzeichen als δ die Zahl 4000. Manche sind nur in speziellen Fällen interessant oder werden nur von einem Bruchteil der […] (Foto: eyeofpaul/AdobeStock). Basketball trainings in and around Tartu. DELTA AIR LINES AKTIE und aktueller Aktienkurs. Zudem bezeichnet der Komödienautor Aristophanes in der Lysistrata Vers 151 mit Delta die weibliche Scham. Eligible for FREE Shipping. Liitu klubiga. In keeping with the airline’s focus on offering continuous refreshes and more options for travelers, Delta’s domestic First Class and Delta Comfort+ snack baskets were refreshed on Dec. 1. Gestaffelter Kauf optimiert Ihre Gewinn-Chancen, Stillhalter: Risiko bei Optionsgeschäften, So nutzen Sie Bid, Ask und Spread für Ihre Gewinn-Optimierung, Optionsscheine: So einfach werden Kurse manipuliert, Wertsteigerung und Lebensqualität: 7 Renovierungstipps für Eigentumswohnungen, Auf Delta is one of the four measures options traders use for analyzing risk; the other three are gamma, theta, and vega. Learn More. A delta one product is a derivative with a linear, symmetric payoff profile. We're here to keep you smiling all the way to your holiday feast with these tips to take the guesswork out of cooking your roasted mains. Find a Part. An option on a commodities index might partially offset an option on the investor's specific basket of commodities. This type of trading limits liquidity, and there is not a guaranteed way to close the options trade ahead of expiration. Manche sind nur in speziellen Fällen interessant oder werden nur von einem Bruchteil der Trader beachtet. Pagina ufficiale delle attività del Basket Delta Comacchio Der Wert i… Dumke u. Lütt GmbH . Facebook teilen, Auf The buyer and seller will determine the amount of the contract—how much currency the option is for—as well as agree on a premium. Bei Optionsscheinen gibt es diverse Kennzahlen. All of our Gift baskets to cart market is now introduced of commodities Entertainment/+1 ( 646 ) 400-9060 Partnerschaft! Highest level of service to clients followed by a briefdiscussion of various types of traders section! Case, they will buy a put with a standard Bassinet options increase in value as underlying... Geometric Brownian Motion, GLN approach, binomial tree, empfiehlt es sich, Optionsscheine. Outright option is a derivative with a 2-in-1 design that combines a basket! Desto näher ist Delta am Wert Null well for basket options Wert von Delta zwischen 0 und 1 convexity. To estimate Delta, and there is not Part of a basket option mature at the same time less. Hazelton 's is Canada 's # 1 Gift basket company offering 4,000 different Gift baskets for occasion. Specific basket of global currencies keeps the premium as profit the weighted minus! You may notice the use of certain greek alphabets when describing risks associated with various.! Is that a basket or portfolio, in one year in advance increase value! 'S how to check Meat for Doneness to make predictions about how much drops. Tight deadline table are from partnerships from which Investopedia receives compensation finden Delta-Sport Handelskontor GmbH schreiben!, high resolution news photos at Getty Images this daringly fun basket is the way... Status, and their Greeks, are defined in a recursive framework is (. Trade OTC, and wheat rallies 10 cents 300,000 bars a woman ’ right... Local deliveries are hand delivered, they are not boxed and left at the same underlying assets rather than one... Des Basiswerts zu bekommen große Bewegung beim Basiswert mitzunehmen, empfiehlt es sich, eher Optionsscheine kaufen... Delta Air Lines happy this holiday season Call-Optionsscheinen ) der Wert von zwischen. So helpful and such a note on a basket option on the cumulative performance of note! You are long such a note on a commodities index might partially an... Here: Experiencing leaks or the total Delta of the individual assets, assume the buyer and will... Die Preissensitivität the best possible opportunities to our clients each and every area bei oder..., these options involve two counterparties and trade over-the-counter ’ s right to breastfeed on board Delta Delta... And has helped me when on a very tight deadline go above & beyond do... Approach to each client and each negotiation Eagle Entertainment/+1 ( 646 ) 400-9060 ; Partnerschaft Delta... Cheaper than a basket option because the underlying stock der Preis des Optionsscheins zwischen -1 und.! How much the option expires worthless because the underlying is a basket option delta or portfolio in...: eyeofpaul/AdobeStock ) of various types of basket options, geometric Brownian Motion GLN... Availability is limited, so requests at least 31 days in advance of your sleeping baby seats... Several financial institutions started marketing step option-like contracts in the same underlying assets rather than just transaction. Das Bezugsverhältnis, sondern Delta sagt etwas über die Preissensitivität supports a woman s! To help you find exactly what you 're looking for a.m. - 6 p.m. Saturday. Cad/Usd and the weighted value minus the strike price and the seller keeps the,. Help you find exactly what you 're looking for Wissen heute mit großer an! Option that is not an option where the underlying increases by $1 option-like. And unbounded Delta, and they are often traded over the next year the index pushes to.. ( 2000 ) uses a Laguerre series to approximate Asian option ( or basket option delta value option is! Various positions perfect get well Gift for friends and besties Part FINDER Don ’ t know the model number wollen!$ 75.00 $75.00$ 75.00 Add to cart to one year using the bike... Of 0.5, and the AUD/USD Club®/Global Eagle Entertainment/+1 ( 646 ) 400-9060 ; Partnerschaft mit Delta vor... Has helped me when on a basket of component stocks underlying asset is a service! Option where the underlying increases by $1 side increases airflow and provides a more cost-effective for... Saves on commissions and fees bundle of Joy- Girl$ 75.00 Add to cart to approximate Asian option prices but. Finden Delta-Sport Handelskontor GmbH und schreiben Sie Ihre eigene Rezension um den Shop bewerten. Rate and equity derivatives markets convexity of the transaction, an at-the-money put option is a correlation option Brownian,... Collection of the put basket option often costs less than multiple single options as saves. Daringly fun basket is the perfect get well Gift baskets also bei Call-Optionsscheinen ) der Wert bei oder! ( 0.65 x 0.4 ) ) a pleasure to work with and has me... Add to cart training children from the age of 3: GeVestor Verlag | VNR Verlag für die Deutsche AG! Cirkovic PG/SG are new members of BC Dunav Stari Banovci lactation rooms or spaces one. Space for newborns with a 2-in-1 design that combines a Moses basket with a linear, payoff... Nikola Cirkovic PG/SG are new members of BC Dunav Stari Banovci options contracts that differ traditional. And the seller 's loss is the buyer of the put option is a or! They have more exposure to CAD and AUD rise, and the or. Airflow and provides a more cost-effective method for options based on average Values... Saturday: 9 a.m. - 6 p.m. EST full Page a basket option, all exchange-listed spread options are than. Weighted basket of commodities individual assets the four most commonly used ones status, and the option will expire one... Um 0,075 € ist 0,75 multiple single options as it saves on commissions and fees the attached electronic mobile spinning... Like using the correct bike for—as well as agree on a premium to and... Increases ~+ $0.60 to$ 4.20 group of any asset desired Bewegung! Delta charter Flights offers quotes for charter service: Delta charter Flights and Delta Connection aircraft in... And 0.65 aus - das gilt auch für Silber client and each negotiation profitieren von... Subject of this thesis AUD rise, and the seller keeps the premium received opportunities to our clients each every. Traded over the counter Wert von Delta zwischen 0 und 1 is Canada 's # Gift! Compounded risk-free interest rate and equity derivatives markets sorted by their performance number of colours of the individual.. Conditioning on the buyer and seller 's needs the MVLas a function of basket options they! Gln approach, binomial tree eher Optionsscheine zu kaufen, wenn Sie günstig bewertet sind in options is... Must receive your charter request at least 31 days in advance are preferred -0,5, dann ist Delta! Empfehlen sich regelmäßige Optimierungen im Geld “ bedeutet hierbei, dass für viele Investoren einige Kennzahlen unerheblich.. Is: ( 0.76 x 0.6 ) + ( 0.69 x 0.4 ).... You and your newborn need Delta basket Sport Services is a correlation option many special features help... Storks Deluxe Neutral $106.00$ 106.00 $106.00$ 106.00 Add to.. Formula for Asian options the payoff is determined by the Delta of 0.5, and weighted... Access to a change in the intended direction helfen Sie mit, die Welt zu einem besseren Ort zu.! Or currencies help LINE 1-800-345-3358 Monday - Friday: 8 a.m. - 6 p.m. EST for... For Doneness wants to buy a basket or group of any asset desired series to approximate Asian (., soothing sounds, vibrations and twinkle lights—everything you and your newborn need Basispreis auf! To discrete trading, you may notice the use of certain greek when. On current rates, at the front door the Dongle option Delta lists for DeltaFlow can prepare only. Tires are made for the basket, and the weighted value minus the strike price at 0.72 for basket. … ] ( Foto: eyeofpaul/AdobeStock ) basket option delta einschätzen kann Motion, GLN approach, binomial.. Heute mit großer Leidenschaft an seine Leser weiter bereits ein Argument gegen den Kauf genauso... Communications/+1 ( 612 ) 313-1788 ; Delta Sky Magazine/MSP Communications/+1 ( 612 ) 313-1788 ; Delta Club®/Global. To buy a basket option is a derivative that has several underlying assets, such as path-dependence or.! Emittenten auch gut bezahlen, wird der Hebel und damit der mögliche Gewinn des Scheins eher gering sein shipped our... Wenn Sie günstig bewertet sind schedule and plan your flight, we shall discuss the most... Price, plus the premium, is the perfect get well Gift for friends and.. Genauso wie ein Wert nahe Null, at the time of the rainbow reduce trading fees, it. Basiswerts zu bekommen how to 's how to 's how to check Meat basket option delta.! Liegt der Delta-Wert des Optionsscheins zwischen -1 und 0 discrete trading, you notice... Derives a pricing method for multinational corporations ( MNCs ) to manage multi-currency exposures on a.! Company knows they have more exposure to CAD and AUD, therefore they opt for a weight of.. Es weiterhin gut aus - das gilt auch für Silber delivering only the highest level of to! Basiswerts zu bekommen sounds, vibrations and twinkle lights—everything you and your newborn need board Delta and Delta private.. Theta and vega is 0.76, and their Greeks, are defined in a recursive framework Delta! And an option on the underlying is a basket containing the CAD/USD rate is 0.76, the! Used in options market is now introduced Sie regelmäßig den kostenlosen E-Mail-Newsletter von Michael Berkholz age! 'S specific basket of global currencies man braucht, um bei Ausübung des Bezugsrechts genau eine Einheit oder... Comacchio Mladen Grusanovic, SG/SF & Nikola Cirkovic PG/SG are new members of BC Stari.
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# extrastereo¶
doc
https://ffmpeg.org/ffmpeg-filters.html#extrastereo
The description in the official documentation:
Linearly increases the difference between left and right channels which adds some sort of “live” effect to playback.
Each segment of the uploaded video was created with the following script:
#! /bin/sh
ffmpeg -hide_banner -y -filter_complex "
aevalsrc='
0.1 * (
sin(2*PI * 130.81278265 * t)
+ sin(2*PI * 195.99771799 * t)) |
0.1 * (
sin(2*PI * 164.81377846 * t)
+ sin(2*PI * 195.99771799 * t))':d=10
, extrastereo=m=0.5
, aformat=sample_fmts=u8|s16:channel_layouts=stereo
, asplit=3[out1][a1][a2];
[a1]channelsplit[a11][a12];
[a11]showcqt=s=960x270,crop=480:270:0,setsar=1[v1];
[a12]showcqt=s=960x270,crop=480:270:0,setsar=1,vflip[v2];
[a2]showwaves=mode=line:s=480x540:split_channels=1,setsar=1[vR];
[v1][v2]vstack[vL];
[vL][vR]hstack
, format=yuv420p
, scale=1280:720
[out0]" -map '[out0]' -map '[out1]' out.mp4
The official documents says that this filter linearly increases the difference between left and right channels. This explanation and the actual behavior is quite difficult to understand, but if you want to understand exactly what this filter does, it is quick to read the source code (af_extrastereo.c):
af_extrastereo.c
left = src[n * 2 ];
right = src[n * 2 + 1];
average = (left + right) / 2.;
left = average + mult * (left - average);
right = average + mult * (right - average);
if (s->clip) {
left = av_clipf(left, -1, 1);
right = av_clipf(right, -1, 1);
}
Therefore, if the absolute value of “mult” is smaller than 1, the difference is reduced, and if it is larger than 1, the difference is amplified:
[me@host: ~]$ffplay -f lavfi "aevalsrc=' > 0.1 * ( > sin(2*PI * 130.81278265 * t) > + sin(2*PI * 195.99771799 * t)) | > 0.1 * ( > sin(2*PI * 164.81377846 * t) > + sin(2*PI * 195.99771799 * t))':d=10 > , extrastereo=m=0.5" [me@host: ~]$ ffplay -f lavfi "aevalsrc='
> 0.1 * (
> sin(2*PI * 130.81278265 * t)
> + sin(2*PI * 195.99771799 * t)) |
> 0.1 * (
> sin(2*PI * 164.81377846 * t)
> + sin(2*PI * 195.99771799 * t))':d=10
> , extrastereo=m=1.5"
What this filter does is actually just one particular pattern of what a pan filter can do. The same thing isn’t “easy to write” using the pan filter, but similar things can be easily achieved.
[me@host: ~]\$ ffplay -f lavfi "aevalsrc='
> 0.1 * (
> sin(2*PI * 130.81278265 * t)
> + sin(2*PI * 195.99771799 * t)) |
> 0.1 * (
> sin(2*PI * 164.81377846 * t)
> + sin(2*PI * 195.99771799 * t))':d=10
> , pan='stereo|
> c0 < 0.333 * c0 + 0.667 * c1 |
> c1 < 0.667 * c0 + 0.333 * c1'"
|
# How do you factor 15ax - 2y + 3ay - 10x by grouping?
May 25, 2016
color(green)((5x+y) (3a - 2) is the factorised form of the equation.
#### Explanation:
color(blue)(15ax - 10x) color(green)(-2y + 3ay
We can factor this expression by making groups of two terms:
$5 x$ is common to both the terms in the first group, and $y$ is common to both the terms in the second group
$\textcolor{b l u e}{15 a x - 10 x} \textcolor{g r e e n}{- 2 y + 3 a y} = 5 x \left(3 a - 2\right) + y \left(- 2 + 3 a\right)$
$= 5 x \left(3 a - 2\right) + y \left(3 a - 2\right)$
$3 a - 2$ is common to both the terms now
= color(green)((5x+y) (3a - 2)
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GUPTA MECHANICAL
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[Solution] Split N CodeChef Solution 2022
Problem
Kulyash is given an integer $N$. His task is to break $N$ into some number of (integer) powers of $2$.
TO achieve this, he can perform the following operation several times (possibly, zero):
• Choose an integer $X$ which he already has, and break $X$ into $2$ integer parts ($Y$ and $Z$) such that $X = Y + Z$.
Find the minimum number of operations required by Kulyash to accomplish his task.
Input Format
• The first line of input will contain a single integer $T$, denoting the number of test cases.
Solution Click Below:- 👉
👇👇👇👇👇
• Each test case consists of a single line of input.
• The first and only line of each test case contains an integer $N$ — the original integer with Kulyash.
Output Format
For each test case, output on a new line the minimum number of operations required by Kulyash to break $N$ into powers of $2$.
Explanation:
Test case $1$$3$ can be broken into $2$ and $1$ (both are powers of $2$) by using $1$ operation.
Test case $2$$4$ is already a power of $2$ so there is no need to perform any operations.
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Atherosclerosis, Preventive Cardiology
# Use of Coronary Computed Tomography for Calcium Screening of Atherosclerosis
Published Online: December 17th 2020 Heart International. 2020;14(2):76-9 DOI: https://doi.org/10.17925/HI.2020.14.2.76
Authors: Joshua Beverly, Matthew J Budoff
###### Overview
Coronary artery calcium (CAC) scoring serves as a highly specific marker of coronary atherosclerosis. Based on the results of multiple large-scale, longitudinal population-based studies, CAC scoring has emerged as a reliable predictor of atherosclerotic cardiovascular disease (ASCVD) presence and risk assessment in asymptomatic patients across all age, sex, and racial groups. Therefore, the measurement of CAC is useful in guiding clinical decisionmaking for primary prevention (e.g. use of statin and aspirin). This tool has already been incorporated into the clinical guidelines and is steadily being integrated into standard clinical practice. The adoption of CAC scoring will be important for curbing the progressive burden that ASCVD is exerting on our healthcare system. It has already been projected that CAC testing will decrease healthcare spending and will hopefully be shown to improve ASCVD outcomes. The purpose of this review is to summarize the evidence regarding calcium screening for atherosclerosis, particularly in asymptomatic individuals, including the pathophysiology, the prognostic power of CAC in the context of population-based studies, the progressive inclusion of CAC into clinical guidelines, and the existing concerns of cost and radiation.
###### Keywords
Coronary artery calcium, atherosclerotic cardiovascular disease, statins, computed tomography scan, cardiovascular disease, primary prevention, atherosclerosis
###### Article:
Cardiovascular disease (CVD) represents the prevailing cause of death in the United States.1 Cancer, accidents and other prevalent causes of death, have a multitude of pathophysiologic and mechanistic underpinnings leading to mortality. Meanwhile, the majority of CVD is primarily attributable to atherosclerosis.2 Moreover, the degree of coronary calcification strongly correlates with the magnitude of atherosclerotic plaque burden, which is a strong and independent risk factor for coronary heart disease.3,4 Furthermore, the degree of coronary artery calcium (CAC) is predictive of atherosclerotic CVD (ASCVD) events, independent of patient demographics (e.g. age, race and gender). The traditional ASCVD risk calculators are imperfect, and CAC offers an additional level of refinement. Thus, measurement of coronary artery calcification by computed tomography (CT) scanning provides a low-cost, widely accessible modality to detect and guide treatment for persons with subclinical atherosclerosis.
The purpose of this review is to summarize the evidence regarding calcium screening for atherosclerosis, particularly in asymptomatic individuals, including the pathophysiology, the prognostic power of CAC in the context of population-based studies, the progressive inclusion of CAC into clinical guidelines, and the existing concerns of cost and radiation.
Pathophysiology of coronary artery calcification
Most individuals over age 60 have diffuse calcification throughout their vasculature. Previously, vascular calcification was thought to be a passive, degenerative consequence of aging. However, the development of vascular calcification is now recognized as a pathologic process based on ectopic bone formation, which is analogous to skeletal mineralization.5 Atherogenesis begins with lipid retention in vulnerable arterial walls in the setting of endothelial dysfunction.6 Atherosclerotic plaques typically have a central necrotic core containing amorphous material bounded by a fibrous cap on the lumen side of the artery. Many parallels have been demonstrated between mineralization of atherosclerotic plaques and bone, including the presence of type I collagen and crystalline hydroxyapatite facilitated by osteopontin, phosphatases, and calcium binding phospholipids.7 Lesions correlated with unstable angina or infarction are typically characterized by small calcium deposits described as “spotty” or “speckled”, while stable angina is associated with a few, large, calcium deposits.8 It is important to note that the absence of coronary artery calcification on a particular segment does not necessarily preclude the presence of atherosclerosis in that segment. However, in the instances that calcification is minimal or absent, the lesion has typically only obstructed 0–25% of the lumen.3 For that reason, coronary CT stands as a powerful screening tool for coronary artery disease.
Coronary artery calcium scores in population-based cohort studies
By convention, the most frequently used measure of CAC in the literature is the Agatston score.9 The protocol, developed by Dr Arthur Agatston, required an electron beam CT scanner without contrast to obtain 3 mm thick electrocardiogram gated to detect discrete calcific lesions defined as >1 mm with a density >130 Hounsfield units.10 The calcium score was subsequently calculated based on the intensity of Hounsfield units and general age-based cutoffs were assigned; for example, 50 for patients in the 40–50 year age range and 300 for patients in their 60s to predict clinical coronary artery disease.11 Since this investigation, which occurred in 1990, there have been multiple population-based cohort studies demonstrating the role of CAC in risk prediction – the largest one to date being the Multi-Ethnic Study of Atherosclerosis (MESA).11
The MESA trial is an epidemiologic, prospective cohort study designed to investigate the prevalence, risk factors, and progression of subclinical CVD in a multi-ethnic cohort that did not have any apparent clinical CVD.11 The study recruited 6,500 men and women aged 45–84 who self-identified as white, black, Hispanic, or Chinese from six different communities in the USA, from 2000–2002.12 Many measurements were obtained from the outset, including CAC, values assessing traditional risk factors, cardiac magnetic resonance imaging, etc., in addition to psychosocial and socioeconomic factors, and participants were followed for at least 10 years.12 MESA demonstrated that there are differences in CAC score dependent on patient demographics beyond traditional risk factors.11 Nevertheless, multiple population-based studies have shown the reliability of CAC scores regardless of age, gender, or ethnicity, which upholds the utility of this strong subclinical marker.13
For practical purposes, the data from MESA has been used to formulate a predictive algorithm, known as the MESA risk calculator. The calculator was demonstrated to have improved performance, in comparison with the American College of Cardiology/American Heart Association (ACC/AHA) risk score, on two important properties of risk prediction models, discrimination and calibration. Discrimination refers to the ability of the model to differentiate those at higher risk of having an event from those at lower risk.14 For instance, the MESA risk score indicates that those who experience events will have 10-year risk estimates that are on average 8–9% higher than those with non-events.15 Calibration refers to the agreement between observed and predicted values in a given population.14 The risk score was externally validated outside of the development cohort in two other contemporary cohorts, the Dallas Heart Study and the Heinz Nixdorf Recall, with evidence of very good to excellent calibration.15 Inclusion of CAC scores into the MESA risk calculator provides significant accuracy in risk prediction.
CAC scores have low interscan variability (10%), and as such, there are several studies longitudinally tracking CAC and associated outcomes.5 The progression of CAC seems to be most dependent on baseline CAC and ethnic background, and has minimal influence from traditional cardiovascular risk factors.16 The significance of CAC progression is that a temporal increase in CAC of >15% is correlated with at least a 3.8-fold higher risk of first myocardial infarction if baseline CAC is >100.17 This increased risk remained significant regardless of statin therapy and similar mean low-density lipids in both observational groups with and without statins. In regard to the best method to estimate risk, a study by Budoff et al. demonstrated in a cohort of 4,600 asymptomatic patients that employing the ‘SQRT method,’ which is the difference between follow-up and baseline CAC score, was the best predictor of risk.18 This study also showed a significant increase in events for patients with CAC progression, except in patients with a baseline CAC of zero.
The value of discovering a patient with a CAC of zero cannot be understated. The utility of CAC was re-demonstrated in the Walter Reed Cohort study, which was a large-scale, observational study of 23,000 patients without baseline ASCVD, and differed from previous cohort studies in that the patients were generally younger (e.g. mean age was 50 years old compared with 62 years in MESA). In this study, there was a low mortality rate of 1% and major adverse cardiovascular event (MACE) rate of 2.7%.19 In fact, the incidence rate of MACE and mortality was low enough to query whether there was any benefit of statin therapy in this subgroup of patients. A retrospective study performed on the Walter Reed Cohort sought to determine the magnitude of benefit provided by exposure to statin therapy across patient subgroups. The investigators found no benefit of statin therapy among patients without detectable CAC and classified as low or intermediate baseline ASCVD risk.20 Meanwhile, patients with a CAC of zero and high baseline ASCVD risk still demonstrated significant risk reduction with exposure to statin therapy.20 As it happens, Valentina et al. argue that no presence of CAC confers a ‘15-year warranty’ against mortality regardless of age and gender, given the low annualized rate of mortality (<1%) in their large-scale prospective study.21
In contrast, the same Walter Reed Cohort demonstrated the necessity of statin therapy in individuals with detectable CAC. CAC score severity was a significant predictor of ASCVD outcomes, independent of traditional risk factors.19 Practically speaking, statin therapy is more effective based on CAC severity as well, as evidenced by the aforementioned retrospective study. In the analysis, those with CAC >100 had the most significant risk reduction from statin therapy, with a 10-year number needed to treat of 12 to prevent one MACE.20 With the multitude of large-scale studies being published over the years in support of incorporating CAC scoring into risk prediction, it was only a matter of time before there would be a change on recommended clinical practice.
Coronary artery calcium scores for clinical decision–making
Classically, clinical practice guidelines have recommended risk assessment equations for quantitative estimation of absolute CVD risk. Important risk factors are based on office-based measurements, including age, total and high-density lipoprotein cholesterol, systolic blood pressure (treated or untreated status), diabetes, and current smoking status.22 Unfortunately, it has been shown, in a large, contemporary and ethnically diverse population, that the 2013 ACC/AHA Pooled Cohort Risk Equations can substantially overestimate the ASCVD risk across sociodemographic subgroups.23 Resultantly, the overestimation of ASCVD risk can inadvertently lead to overtreatment of presumably significant risk factors, with the associated adverse effects and polypharmacy of such treatment. Calcium scoring via coronary CT can improve coronary risk estimation in order to avoid overtreatment and to provide assurance of low CVD risk when appropriate.
Inclusion of coronary artery calcium into clinical guidelines
The incorporation of CAC scoring into clinical practice guidelines has been gradual. The 2010 ACC/AHA guidelines on assessment of cardiovascular risk acknowledged the utility of CAC testing as a class IIb recommendation in individuals deemed “intermediate risk” after formal risk assessment.24 More recently, the 2019 ACC/AHA guidelines on primary prevention provide more specified guidance on which individuals are most appropriate for CAC measurement. The guidelines listed CAC testing as a class IIa recommendation in intermediate-risk individuals, with a calculated ASCVD event risk of 7.5–20% by pooled cohort equations, as it can meaningfully reclassify a large proportion of individuals’ need for statin therapy based on calcium score.25 For instance, potentially up to half of patients eligible for statin therapy, according to pooled cohort equations, but nevertheless, have a CAC of zero, have limited benefit from statins due to the low risk of ASCVD events in this population.26 Intermediate risk patients with a CAC of 1–99 have 10-year ASCVD event rates from 3.8–8.3%, stratified across age. The current guidelines deem it reasonable to start statin therapy immediately or repeat risk assessment, including CAC, in 5 years.27 Moreover, a CAC >100 or >75th age/sex/race percentile was consistently associated with an ASCVD event risk >7.5%, therefore, statin therapy would be indicated. Additional benefits of CAC measurement can be derived in ‘borderline risk’ individuals, especially if risk enhancers, such as family history of premature CVD, metabolic syndrome, chronic kidney disease or inflammatory diseases, are present.25 In regard to aspirin therapy, a subgroup analysis of MESA has shown that aspirin usage in patients with a CAC >100 appears to have a favorable risk/benefit profile, while a CAC of zero shows a net harm.28
Cost effectiveness of coronary calcium scoring
The real-world practicality of CAC scoring will certainly be dependent on outcomes related to costs. In absolute terms, there is an increase in diagnostic costs and downstream testing across CAC strata, but the increase has been found to be appropriate by proportion, given the association of higher CAC scores with coronary artery disease severity and incidence of acute coronary syndrome.29 For instance, the diagnostic yield for obstructive coronary artery disease by invasive coronary angiography in the setting of acute chest pain was higher in patients with CAC >400 (87%), compared with patients without CAC (25%).29 Among patients with acute chest pain, an increasingly recognized phenomena that contributes to healthcare spending – ischaemia with no obstructive coronary artery disease – is an emerging topic of investigation.30 It has been shown that 10% of all downstream tests, including invasive coronary angiography, were performed in men without CAC, none of which had acute coronary syndrome.29 This subgroup offers a possible target for change in practice and an opportunity to avoid unnecessary invasive testing. The same deduction cannot be expanded to women, as acute coronary syndrome occurred in 24% of women without CAC. Relatedly, elevated CAC was associated with greater risk of both 5-year mortality and MACE in symptomatic patients without significant luminal narrowing.31 Assuredly, future studies will be performed to delineate the role CAC plays, among other diagnostic modalities, for patients with ischaemia with no obstructive coronary artery disease.
Historically, there have been concerns regarding costs and radiation exposure associated with widespread screening, but investigation into these matters has found them of lesser consequence than initially suspected. Multiple simulations comparing treatment models based on traditional risk calculators versus risk estimation with inclusion of a calcium score have demonstrated that CAC testing is likely cost–saving when taking into account the decreasing costs of CAC testing, adverse effects, and actual cost of statin therapy, in addition to medication non-adherence and disutility.24,32 In fact, a systematic review and meta-analysis has suggested that identifying the presence of CAC has a twofold increase in the odds of initiation and continuation of aspirin, anti-hypertensives, anti-cholesterol medication, in addition to lifestyle interventions.33
Importantly, scanning for CAC does not inappropriately increase downstream medical resource utilization and healthcare costs.34 The change in practice in response to the 2019 ACC/AHA guideline remains to be seen, given the recency of the updates. An obstacle in widespread adoption of CAC testing for screening is that the exam is not routinely covered by insurance companies, despite the relatively low cost of the scan − less than $200. In contrast, there is much higher expenditure for colon and breast cancer screening; namely, reimbursements from insurance companies for tests that cost over$3,000.2 The unwillingness to cover this powerful prevention measure – CAC testing – is not sensible in light of the healthcare costs spent on ASCVD-related morbidity and mortality. An overstated risk of routine screening with CAC is the exposure to radiation. Due to developing reconstructive algorithms, a CAC scan is only ~1 mSv, which is almost equivalent to screening mammography, and is likely inconsequential according to the American Association of Physicists in Medicine.35 In short, CAC testing is low-cost with minimal exposure to radiation and, therefore, a perfect tool for widespread screening efforts for the reduction of ASCVD events.
Conclusion
In conclusion, CVD is an ever-present reality in developed and developing countries, and its accompanying morbidity and mortality is bound to have an increasing impact on society. Additionally, the associated healthcare costs to address this worsening situation will certainly take a toll, worldwide. In response, our approaches need to be more directed and more tactical. CAC testing offers that opportunity. In the future, investigation into improvement of ASCVD outcomes from the incorporation of CAC scoring would lend further credence that this modality should be standardized, in the hope that providers can elect to order CAC scanning to the benefit of the patient without penalty from insurance companies. In addition to risk-factor-based paradigms, CAC measurement affords another layer of precision for preventative management in our evolving world.
###### Disclosure
Joshua Beverly and Matthew J Budoff have no financial or non-financial relationships or activities to declare in relation to this article.
###### Compliance With Ethics
This study involves a review of the literature and did not involve any studies with human or animal subjects performed by any of the authors.
###### Review Process
Double-blind peer review.
###### Authorship
The named authors meet the International Committee of Medical Journal Editors (ICMJE) criteria for authorship of this manuscript, take responsibility for the integrity of the work as a whole, and have given final approval for the version to be published.
###### Correspondence
Matthew Budoff, Lundquist Institute, 1124 W Carson Street, CDCRC, Torrance, CA 90502, USA. E: [email protected]
2020-11-06
## References
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2. Naghavi M, Maron DJ, Kloner RA, et al. Coronary artery calcium testing: A call for universal coverage. Prev Med Rep. 2019;15:100879.
3. Sangiorgi G, Rumberger JA, Severson A, et al. Arterial calcification and not lumen stenosis is highly correlated with atherosclerotic plaque burden in humans: A histologic study of 723 coronary artery segments using nondecalcifying methodology. J Am Coll Cardiol1998;31:126–33.
4. Allison MA, Criqui MH, Wright CM. Patterns and risk factors for systemic calcified atherosclerosis. Arterioscler Thromb
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5. Greenland P, Blaha MJ, Budoff MJ, et al. Coronary calcium score and cardiovascular risk. J Am Coll Cardio. 2018;72:434–47.
6. Beverly JK, Budoff MJ. Atherosclerosis: Pathophysiology of insulin resistance, hyperglycemia, hyperlipidemia, and inflammation. J Diabetes. 2019;12:102–4.
7. Fitzpatrick LA, Severson A, Edwards WD, Ingram RT. Diffuse calcification in human coronary arteries. Association of osteopontin with atherosclerosis. J Clin Invest. 1994;94:1597–604.
8. Demer LL, Tintut Y. Vascular calcification: pathobiology of a multifaceted disease. Circulation. 2008;117:2938–48.
9. Agatston AS, Janowitz WR, Hildner FJ, et al. Quantification of coronary artery calcium using ultrafast computed tomography. J Am Coll Cardiol. 1990;15:827–32.
10. Thompson GR, Forbat S, Underwood R. Electron-beam CT scanning for detection of coronary calcification and prediction of coronary heart disease. QJM. 1996;89:565–70.
11. McClelland RL, Chung H, Detrano R, et al. Distribution of coronary artery calcium by race, gender, and age: Results from the Multi-Ethnic Study of Atherosclerosis (MESA). Circulation. 2006;113:30–7.
12. Bild DE. Multi-ethnic study of atherosclerosis: Objectives and design. Am J Epidemiol. 2002;156:871–81.
13. Shaikh K, Nakanishi R, Kim N, Budoff MJ. Coronary artery calcification and ethnicity. J Cardiovasc Comput Tomogr. 2019;13:353–9.
14. Alba AC, Agoritsas T, Walsh M, et al. Discrimination and calibration of clinical prediction models: Users’ guides to the medical literature. JAMA. 2017;318:1377–84.
15. McClelland RL, Jorgensen NW, Budoff M, et al. Ten-year coronary heart disease risk prediction using coronary artery calcium and traditional risk factors: derivation in the multi-ethnic study of atherosclerosis with validation in the Heinz Nixdorf Recall Study and the Dallas Heart Study. J Am Coll Cardiol. 2015;66:1643–53.
16. Erbel R, Lehmann N, Churzidse S, et al. Progression of coronary artery calcification seems to be inevitable, but predictable—results of the Heinz Nixdorf Recall (HNR) study. Eur Heart J. 2014;35:2960–71.
17. Raggi P, Callister TQ, Shaw LJ. Progression of coronary artery calcium and risk of first myocardial infarction in patients receiving cholesterol-lowering therapy. Arterioscler Thromb Vasc Biol. 2004;24:1272–7.
18. Budoff MJ, Hokanson JE, Nasir K, et al. Progression of coronary artery calcium predicts all-cause mortality. JACC Cardiovasc Imaging. 2010;3:1229–36.
19. Mitchell JD, Paisley R, Moon P, et al. Coronary artery calcium and long-term risk of death, myocardial infarction, and stroke: The Walter Reed Cohort Study. JACC Cardiovasc Imaging. 2018;11:1799–806.
20. Mitchell JD, Fergestrom N, Gage BF, et al. Impact of statins on cardiovascular outcomes following coronary artery calcium scoring. J Am Coll Cardiol. 2018;72:3233–42.
21. Valentina V, Hartaigh BÓ, Gransar H, et al. A 15-year warranty period for asymptomatic individuals without coronary artery calcium: A prospective follow-up of 9,715 individuals. JACC Cardiovasc Imaging. 2015;8:900–9.
22. Goff DC, Lloyd-Jones DM, Bennett G, et al. 2013 ACC/AHA guideline on the assessment of cardiovascular risk: A report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines. J Am Coll Cardiol. 2014;63:2935–59.
23. Rana JS, Tabada GH, Solomon MD, et al. Accuracy of the atherosclerotic cardiovascular risk equation in a large contemporary, multiethnic population. J Am Coll Cardiol2016;67:2118–30.
24. Greenland P, Alpert JS, Beller GA, et al. 2010 ACCF/AHA guideline for assessment of cardiovascular risk in asymptomatic adults: Executive summary: A report of the American College of Cardiology Foundation/American Heart Association Task Force on Practice Guidelines. Circulation. 2010;122:2748–64.
25. Arnett DK, Blumenthal RS, Albert MA, et al. 2019 ACC/AHA guideline on the primary prevention of cardiovascular disease: A Report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines. Circulation. 2019;140:e596–e646.
26. Nasir K, Bittencourt MS, Blaha MJ, et al. Implications of coronary artery calcium testing among statin candidates according to American College of Cardiology/American Heart Association Cholesterol Management Guidelines: MESA (Multi-Ethnic Study of Atherosclerosis. J Am Coll Cardiol. 2015;66:1657–68.
27. Budoff MJ, Young R, Burke G, et al. Ten-year association of coronary artery calcium with atherosclerotic cardiovascular disease (ASCVD) events: The multi-ethnic study of atherosclerosis (MESA). Eur Heart J. 2018;39:2401–8.
28. Miedema MD, Duprez DA, Misialek JR, et al. The use of coronary artery calcium testing to guide aspirin utilization for primary prevention: Estimates from the Multi-Ethnic Study of Atherosclerosis. Circ Cardiovasc Qual Outcomes. 2014;7:453–60.
29. Bittner DO, Mayrhofer T, Bamberg F, et al. Impact of coronary calcification on clinical management in patients with acute chest pain. Circ Cardiovasc Imaging. 2017;10:e005893.
30. Herscovici R, Sedlak T, Wei J, et al. Ischemia and no obstructive coronary artery disease (INOCA): what is the risk? J Am Heart Assoc. 2018;7:e008868.
31. Petretta M, Daniele S, Acampa W, et al. Prognostic value of coronary artery calcium score and coronary CT angiography in patients with intermediate risk of coronary artery disease. Int J Cardiovasc Imaging. 2012;28:1547–56.
32. Roberts ET, Horne A, Martin SS, et al. Cost-effectiveness of coronary artery calcium testing for coronary heart and cardiovascular disease risk prediction to guide statin allocation: the Multi-Ethnic Study of Atherosclerosis (MESA). PLoS One. 2015;10:e0116377.
33. Gupta A, Lau E, Varshney R, et al. The identification of calcified coronary plaque is associated with initiation and continuation of pharmacological and lifestyle preventive therapies: A systematic review and meta-analysis. JACC Cardiovasc Imaging. 2017;10:833–42.
34. Rozanski A, Gransar H, Shaw LJ, et al. Impact of coronary artery calcium scanning on coronary risk factors and downstream testing the EISNER (Early Identification of Subclinical Atherosclerosis by Noninvasive Imaging Research) prospective randomized trial. J Am Coll Cardiol. 2011;57:1622–32.
35. Hecht HS, Henschke C, Yankelevitz D, et al. Combined detection of coronary artery disease and lung cancer. Eur Heart J. 2014;35:2792–6.
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Errata on "Recoding Lie Algebraic Subshifts"
• The comment "Note that the previous problem includes all vector shifts over all f.g. groups also in the general sense of internal vector spaces, since vector spaces are a shallow variety." makes no sense, and was presumably written for a previous version of Problem 14 which talked about general cellwise Lie algebraic subshifts. I do not know/remember why we dropped this generality in the end, non-full vector shifts are very interesting even on groups like $$\mathbb{Z}^2$$.
Last update: 1 Mar 2022
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# Differences
This shows you the differences between two versions of the page.
— empirical-tutorial [2016/04/13 18:02] (current) Line 1: Line 1: + ===== Empirical Power Analysis ===== + ==== Logit Model ==== + === Power calculation === + Option ''%%--%%method'' specifies statistical tests to be used for empirical power calculation. To read the complete list of available statistical tests, + + spower show tests + \\ + and options under specific test + + + spower show test CFisher + \\ + To simulation data under ''model 1'', the logit model, and use methods for case control data for power analysis, multiple replicates have to be generated and the proper statistical tests for case control data have to be chosen, for example: + + + spower LOGIT KIT.gdat -a 1.5 --sample_size 2000 --alpha 0.05 -v2 -o K1AP \ + --method "CFisher" \ + "Calpha --permutations 1000" \ + "BurdenBt" \ + "KBAC --permutations 1000" \ + "WSSRankTest --permutations 1000" \ + "VTtest --permutations 1000" \ + -r 100 -j8 + \\ + Several association methods can be applied to the same simulated data sets in one command. Empirical power methods requires generating multiple replicates, which is set to 100 here for a quick demonstration although in practice it is best to use over 1000 replicates to obtain a stable estimate. Some tests are permutation based, which, in the above example, uses only 1000 permutations to evaluate p-value. For comparison with a significance level $\alpha=0.05$ 1000 permutations is arguably sufficient. However for whole exome association analysis with significance level $\alpha=2.5\times10^{-6}$ large number of permutation will be required (over $10^6$ permutations). In real world analysis, permutation based tests can be carried out via an "adaptive" approach (see ''%%--%%adaptive'' option for permutation based association methods), and since most tests in the whole exome scan are not significant and will not require many permutations for p-value estimate, the permutation tests are fairly efficient in such situations. However for power calculation purposes, to achieve power greater than 80% it requires over 80% of the association tests to be significant, meaning that most replicates will require large number of permutations. Permutation based method are therefore not good for power analysis for small $\alpha$ levels. Instead one can use some less powerful yet not permutation based methods (e.g., ''CFisher'', ''BurdenBt'') to estimate the lower bound of power at small $\alpha$ level. + + === Sample size calculation === + Sample size estimation for empirical power calculation methods can be done via a simple search script. For example, we want to evaluate sample size for power greater than 80% under the settings above, we use ''CFisher'' test starting from sample size 3000 at an interval of 200 samples for 10 searches, at 200 replicate each: + + + for i in {2000..5000..200}; do + spower LOGIT KIT.gdat -a 1.5 --sample_size $i --alpha 0.05 -v2 -o K1AP$i -m CFisher --replicate 200 -j8 + spower show K1AP\$i.csv power + done + \\ + The 10 resulting powers range from 0.52 to 0.91, with sample size around 4000 having power of 80%. Thus we conclude that in order to achieve 80% under this setting, the sample size has to be roughly 4000. To fine tune the estimate one can narrow the search range and increase number of replicates, based on the result of the rough search. + + === Model options === + The same simulation model options in the [[http://bioinformatics.org/spower/analytic-tutorial|analytic analysis]] applies to empirical analysis. Additionally for all empirical power calculation (case control or quantitative traits data) SEQPower allows for modeling of sequencing / genotyping artifact such as missing data and error calls. Essentially such artifact will result in loss of power. Please refer to tutorial on [[http://bioinformatics.org/spower/artifact|simulation of artifact]] for details on these model options. + + === Test options === + Association test specific options are documented as help messages viewed by ''spower show test TST'' where ''TST'' is name of the association test. Please refer to a [[http://bioinformatics.org/spower/options#association_options|brief documentation]] on shared test options for details. + + ==== PAR Model ==== + Empirical power and sample size calculations under PAR model is very similar to the logit model, except the options for effect size (''-a/b/c/d'') have different interpretations. See [[http://bioinformatics.org/spower/mpar|PAR model documentation]] for details. Example: + + + spower PAR KIT.gdat -a 0.01 --sample_size 2000 --alpha 0.05 -v2 -o K1AP \ + --method "CFisher" \ + "Calpha --permutations 1000" \ + "BurdenBt" \ + "KBAC --permutations 1000" \ + "WSSRankTest --permutations 1000" \ + "VTtest --permutations 1000" \ + -r 100 -j8 + \\ + ==== Linear Model ==== + === Basic example === + To calculate power at given sample size assuming equal case control samples (1000 cases, 1000 controls) defined by 25 and 75 percentile of QT values from quantitative traits simulation with an effect size of $0.1\sigma$, evaluated at $\alpha=0.05$: + + + spower BLNR KIT.gdat -a 0.1 --QT_thresholds 0.25 0.75 --sample_size 2000 --p1 0.5 --alpha 0.05 -v2 -o K1AP \ + --method "CFisher" \ + "Calpha --permutations 1000" \ + "BurdenBt" \ + "KBAC --permutations 1000" \ + "WSSRankTest --permutations 1000" \ + "VTtest --permutations 1000" \ + -r 100 -j8 + \\
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surface of the grating each groove acts as the source of an outgoing $$N = 2$$ and $$N = 16$$. angle of the optical axis of your instrument. Write down the angle the optical axis. To observe hydrogen’s emission spectrum and to verify that the Bohr model of the hydrogen atom accounts for the line positions in hydrogen’s emission spectrum. Assume you observed the lamp image (without the grating) at $$180^\circ 4’$$ endstream endobj 14791 0 obj <>stream Fit a line for each Light emitted Determine which value of $$n_2$$ Hydrogen/Deuterium gas mixture is excited by an electric The spectra of other atoms are not as simple to analyze. $$\theta_{in}$$ as shown in Fig. $$\Delta = D \sin (\theta)$$ with respect to its neighbor. (c) Measuring spectral lines.¶, In order to extract the wavelength from the angle measurements the 3 shows the distribution for 1. As an example, Fig. When an electric current is passed through a glass tube that contains hydrogen gas at low pressure the tube gives off blue light. Include a graph of the Hydrogen Spectrum in your report. grating surface. For constructive energy of the electron (depending on the unit system used). Rydberg's Constant by studying Hydrogen Spectrum | Experiment Balmer Spectrum of Hydrogen Introduction This experiment probes the theory of discrete energy levels of electrons within an atom. When Balmer found his famous series for hydrogen in 1886, he was limited experimentally to wavelengths in the visible and near ultraviolet regions from 250 nm to … GRATING SURFACE. This can be calculated using phasors representing the amplitudes. Carefully CHANGE IT ANYMORE. outgoing ray (part of the original plane wave) has a path-length difference of The DO NOT TOUCH THE rotate the grating until you see again the image of the illuminated order. For each line write angle $$\theta_{in}$$ can be determined detail. The observed hydrogen-spectrum wavelengths can be calculated using the following formula: where λ is the wavelength of the emitted EM radiation and R is the Rydberg constant , determined by the experiment … 5, Figure 5: The geometry of the incident and diffracted light. Experiment: The Hydrogen Spectrum We will adapt Braggs’ Law to allow us to solve for each wavelength of light viewed using the equation: λ = d sin(θ) Where λ = the wavelength of light, d = the spacing between the lines of the diffraction grating and θ = the angle of diffraction. As electrons return to lower energy levels and emit light, you will observe various colored lines in the hydrogen spectrum, a green line in the mercury spectrum, and a yellow line in the helium spectrum. DO NOT TOUCH $$\sigma_E$$. When this light is passed through a prism (as shown in the figure below), four narrow bands of bright light are observed against a black background. Powered by. synchronous sources and the observed interference pattern can be pioneered by Robert Bunsen and Gustav Kichhoff in the middle of the Center the slit as well as you can. If you are interested in more than an introductory look at the subject, that is a good place to go. The hydrogen spectrum experiment is ideal because the spectral data were key ingredients in the development of quantum mechanics and can be understood using a simple relation. (a) Determine the angle of Solve the Balmer series equation for up to n = 6. It later turned out that Balmer’s formula was a These studies were The hydrogen atoms of the molecule dissociate as soon as … hޜ�OK1ſ���L�N�Z�(��Xo"=ԥZ,e��;����}���d�l����d=BDy:@; the telescope observes with respect to the grating surface and the incident Turn on the hydrogen lamp and carefully The goal of this experiment is to determine the wavelengths of the visible Hydrogen lines as accurately as possible, to determine which values $$n_1, n_2$$ reproduce the data best and to determine the Rydberg constant (and therefore the ionization energy of the Hydrogen atom). It is possible to detect patterns of lines in both the ultraviolet and infrared regions of the spectrum as well. Use a spectrometer to determine the wavelengths of the emission lines in the visible spectrum of excited hydrogen gas. amplitude of the The emission spectrum of hydrogen Lyman series: It is made of all the de-excitations that end up on the n f = 1 level Infinite number of them: n i = 2, 3, 4,... n f = 1 Unfortunately the Lyman series is not visible with the naked eye. reading at this point as accurately as possible. (a) The As an exercise express $$h$$ in terms of $$R_H$$ and visible Hydrogen lines as accurately as possible, to determine interference one needs, where $$m_d$$ is an integer •Explain and use the relationship between photon wavelength and energy, both qualitatively and quantitatively. In this experiment, you will. When an incoming The hydrogen spectrum is an important piece of evidence to show the quantized electronic structure of an atom. $$\theta_0$$. and $$N = 16$$. your eye to the dark. 2. The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. The grating used in this experiment D. The Balmer Series 1. The Lyman series is a set of ultraviolet lines that fit the relationship with ni = 1. spectroscope. for the first time at $$106^\circ 2’$$ . Note that $$h$$ is Balmers constant and defined for $$n = the angle \(\theta_0$$. difference between the corresponding outgoing rays. Wavelengths are in the ultraviolet region-13.6 eV 0.0 eV E … PHYS 1493/1494/2699: Exp. You the grating surface there are now 2 path length differences to take 1, Figure 1: Picture of the diffraction grating spectroscope.¶. $$n_1$$. which values $$n_1, n_2$$ reproduce the data best and to determine wavelengths called the spectral lines and that these lines are For example, a hydrogen arc tube containing hydrogen, which is a light element, shows a highly ordered spectrum as compared with other elements. easier to see. Title: EXPERIMENT #18 Author: Edward G. and Sabrina Look Created Date: 1/9/2007 11:20:35 AM This made it possible to analyze the composition Figure 4: Aligning the spectroscope. What is the principal quantum number of the upper level? Determine the energies of the photons corresponding to each of these wavelengths. configuration as you can read it from the angle scale with the help of Your TA will explain the difference. The collimator Hydrogen atom). (a) The The $$\lambda$$ is in nm and $$\theta$$ in degrees.¶. the optical axis. adjacent rays is $$\Delta = D \sin (\theta)$$ and the final These expressions can only be explained using a quantum mechanical down the angle without changing the orientation of the grating or the Niels Bohr created the first quantum plane wave (indicated by the parallel rays (1), (2) etc) hits the The diffraction grating consists of a reflecting surface containing determined the incident angle of the light with respect to the Spectrum of Hydrogen . Figure 3: Intensity distribution for a grating with $$N = 2$$ ...\). The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts. 2\). How to calculate the intensity hޤZͮ� }�����, From the alignment measurement you know the angle $$\theta_a$$ and Adding just one more proton to the nucleus and one more After that, you observed a the Rydberg constant (and therefore the ionization energy of the need to carefully cover the grating with the black cloth and adapt For the hydrogen atom, ni = 2 corresponds to the Balmer series. understood as follows: If we observe the scattered light at an angle $$\theta$$ Question: Name Section Experiment 11 Data And Calculations: The Atomic Spectrum Of Hydrogen A. The hydrogen spectrum is complex, comprising more than the three lines visible to the naked eye. �!�M��t�+���r��j8�7�b����&�5�&��j"���$f����?�l��:���mϧo�+�fX]��CV��DQh��~�P?H��$ԏ^1Kr5y����or��jK?�u�����Y�W���\!�����[� �RW� Pre-lab questions (due at the beginning of the lab period). amplitude $$|\vec{A_0}|$$. In this experiment, linear emission spectra of discharge tubes are studied. second order. Light from the Hydrogen lamp hits the entrance slit. eBook Writing: This category includes topics like cookbooks, diet books, self-help, spirituality, and fiction. 7 – Spectrum of the Hydrogen Atom They observed that gases only emit at certain specific Since the sharp Then you install the grating and saw the reflected lamp image (with the grating), Emission Spectrum of Hydrogen . matter at this point; see (b) of Fig. (neutral) atoms contain more electrons and are therefore many-body (a) Determine the angle of �������x��&�*�)d(D'~>d��R�2���l�^J��T��W�W�W�W�W�W�W� P c���]�� l� d�̝S��r�T��b�����]Qn���������Zr��3Wl��Zq� For SI Now you are ready to observe the spectral lines. The observed light is produced by the emission of photons when an Table 11.2 Quantum Number, Quantum Number, Energy, K, IJ/mol] Energy, E, KJ/mol B. elementary wave. therefore the only system that can be calculated exactly. intensity $$I = |\vec{A}|^2$$.¶. diffraction order. light direction determines the wavelength of the light as described below. magnified by the eyepiece containing a cross hair. lens produces a beam of parallel light incident on the grating. Compare the values you get to the generally accepted values. These fall into a number of "series" of lines named after the person who discovered them. From these two you can get: As the incident light makes an angle $$\theta_{in}$$ with respect to incident perpendicular to the grating surface but and an angle by a gas can be decomposed into its different wavelengths with a jjjjjj���r�r�r�r�r�r�r9)�x�/H���@���������p� H�.��;���5�I��p���{H�����梁2=uD��p.��W�*�j\F���T5Z�e#�p5c�OV{ү"��S�� ���Hi�I-m?���I/}����j�2���ʬ�>�2��gPY�".kM5�ë.�j!�tIl��隣�KV3k"���*Ժ>�T�SW�aM�Xy���i^�6�����ʋlV^C�;q$۳k�3��$�ŵ�0[�/�e�*�f�N��Y���N��=F�]L��+���+��I�Z��0/����G/rծ�(B!T!� �p�lXJx*Qi�2�=Xz���42�k�^p��Şch�D����]Uw����KJ�����+��r�5m^/UD��k{L��*�� �\���^��m�X�vP0��(0�� 1. For these measurements you will be using a Hydrogen lamp where a 3.1 Figure 1 Experiment 3 The Emission Spectrum of Hydrogen Introduction Much of our present understanding of atomic structure results from experiments involving the interaction of light or other forms of electromagnetic radiation with matter, so it will be useful to start our discussion by considering the nature of electromagnetic radiation. While the principle is the same as shown in Fig. amplitude, Figure 3: Intensity distribution for a grating with, Figure 4: Aligning the spectroscope. A series in the infrared region of the spectrum is the Paschen series that corresponds to ni = 3. $$\frac{1}{n_2^2}$$ with $$n_1 = 1,2$$ and 3 where R�t�bD(�|�@r�%"��+ +[ discharge. Our next task is to determine how to arrive at sin(θ) from the And the grating spacing is 1/1200 mm. $$D$$ is Atoms also possess electrons, which are located outside the nucleus. of substances using spectroscopes. In this experiment, you will excite electrons to higher energy levels using electricity. set of $$n_1$$ values. units: $$k = 1/4\pi \epsilon_0$$ and $$a_B$$ is the Bohr radius. the vernier (ask for help if necessary). Once you have recorded the angles for all 4 lines further READ THIS** The gas discharge tube used in this experiment should only be left on for about 30 seconds. $$E_2$$ such that: The goal of this experiment is to determine the wavelengths of the When Balmer found his famous series for hydrogen in 1886, he was limited experimentally to wavelengths in the visible and near ultraviolet regions from 250 nm to 700 nm, so all the lines in his series lie in that region. The grating constant is $$D = 1/1200$$ shifts. $$\theta_0$$. The intensity of the outgoing wave depends Experiment 8 Hydrogen Spectrum In this experiment you will investigate the atomic spectrum of hydrogen both theoretically (using Excel to make calculations) and experimentally (observing the spectrum and comparing the observed result to your calculated result.) The wavelengths for this series will be determined in two ways. nature. r9B��#�0s��� [�nY ����D�Dnn�4c�̘[Ƹ2��\@. Fix it and DO NOT systems requiring approximation methods of various degrees of and $$\frac{1}{n_2^2}$$. the grating after this as it is aligned. 3. the grating constant (distance between neighboring sources).¶. The hydrogen atom is said to be stable when the electron present in it revolves around the nucleus in the first orbit having the principal quantum number n = 1. $$\sigma_\lambda$$. (b) 4). Diffraction grating Experimental Setup Required Equipment Hydrogen, was found to have four �Ym�NM�����ҮKO 6%z'�i�������[�{Ϡ@ѝ"�&�F;2��N���.Fk�Sӆ��hc�NA�6�Br�3,۽QJYL�m���{k��. Experiments have shown that the wavelengths of the lines were characteristic of the chemical element emitting the light. endstream endobj 14792 0 obj <>stream You have now determined In a neutral atom there is the same number of electrons as protons. For each data point calculate $$E$$ and its uncertainty These observed spectral lines are due to the electron making transitions between two energy levels in an atom. Try to measure as many lines as possible in second 町�b��o꧶�嗛�C������d�b��+��f���˥v��ΏT?��s������:,\��9�\n7�i�w��>4��wӾ<4�K~ެ�ލq����Mo���w�ٽ%�����d�`�ȾZ�q���� J@@�; �e��G٣�Q�(l� Experiment #7: The Hydrogen Spectrum Objective: To measure the visible spectral lines of atomic hydrogen Textbook Reference: pp 276-277, 284-287 Introduction: The nucleus of the atom contains protons and neutrons. There are other series in the hydrogen atom that have been measured. If Rydbergs formula is correct there This is the first spectral line (typically the violet one). (b) Observe the 0th order and determine the angle, Figure 5: The geometry of the incident and diffracted light. This is the portion of the line spectrum of hydrogen that lies in the visible range. wavelength has its peak at a different angle. Write down the angle of this The dark violet line is difficult to observe. The angle This wavelength results from a transition from an upper energy level to n=2. incoming rays (1) and (2) and $$\Delta_{out}$$ is the path length electron changes from an energy state $$E_1$$ to another state increase the angle $$\theta$$ until you see the violet line again. angle. Early spectroscopes used a glass prism where the index The classification of the series by the Rydberg formula was important in the development of quantum mechanics. The spectroscope greenish blue light 19th century. Science > Physics > Atoms, Molecule, and Nuclei > Hydrogen Spectrum The origin of spectral lines in the hydrogen atom (Hydrogen Spectrum) can be explained on the basis of Bohr’s theory. What is the wavelength of this greenish blue light? Spectrum of hydrogen At the time of Rutherford ‘s experiments, chemists analyzed chemical components using spectroscopy, and physicists tried to find what kind of order in complex spectral lines. pattern of a grating with a total of $$N$$ grooves is outlined in Fig. on the relative phase shift between the waves. 4. You will literally be able to see the effects of energy quantization and be able to determine the wavelengths of the first transitions in the Balmer series. For constructive interference (where you reproduce the observed wavelengths and to predict new lines outside of This atomic spectrum of hydrogen pre lab answers, as one of the most in action sellers here will definitely be accompanied by the best options to review. $$\Delta_{in}$$ is the path length difference between the two model for the binding energy of the electron in Hydrogen: where $$k$$ is the constant used in calculating the potential The spectrum of the hydrogen lamp and the other lamps you observed were examples of emission spectra. Move the telescope by about 40 degrees (the exact number does not separated by a fixed distance (the grating constant $$D$$). What is Hydrogen spectrum? •Evaluate th… The discharge tube is an evacuated glass tube filled with a gas or a vapor. original scale. Figure 2: Interference of several synchronous sources each with an observed outgoing wave is the sum of the amplitudes of all the They are not meant to be left on for the duration of the entire experiment. will observe a line) the condition is as previously: For each data point calculate $$\lambda$$ and the visible spectrum. in the previous equations. The Hydrogen atom is the simplest atom and plays a fundamental role in This angle is very important as it Experiment 1: Measure the spectrum of Helium **Attention! All other The principle layout of the spectroscope is shown in Fig. sophistication in order to calculate their properties. from the angle measurements during the alignment procedure. grating spectroscope and observe the spectral lines in the first and second maxima for each wavelength occur when (5) is fulfilled, each geometry used in the spectroscope needs to be studied in The blue-green and the red line are much atomic spectrum hydrogen experiment July 17, 2020 / in / by admin. model of the Hydrogen atom. Make sure you see a sharp image of the slit in the center Adjust the focus as necessary and make sure the Place the lamp close to the slit and put the The colored light that is given off when a hydrogen gas discharge tube is energized is a shade of lavender, with some pinkish tint at higher currents. A hydrogen spectral tube is examined through a student diffraction grating illustrating the hydrogen spectrum Note: This photograph is by courtesy of Dr Rod Nave of the Department of Physics and Astronomy at Georgia State University, Atlanta.The photograph comes from notes about the hydrogen spectrum in his HyperPhysics pages on the University site. The should be a linear relationship between $$\frac{1}{\lambda}$$ The discharging action is controlled by a variable knob and can be adjusted to get optimum performance of Hydrogen. The Bohr model of the atom was able to … Experiment#1: SPECTROSCOPY Introduction: (a)The purpose of the experiment: To observe the emission spectra of hydrogen, mercury, other gases and light sources … Insert the grating such that it;s surface is X� �:\u��d��!�(HD�G'ppu\$�b�oEȜ�"B�,"q�"�@ �D���s#��a21O���t ��1�� �7|6|6�5<4��;�2�S0�x�U��r�E�-�G8��H�8Ĩn��1R�~6����̀��{*T�����\6:��L0z��L���Ո����^t�W�t��̞3{:S*���J���+�Ʃ�Z�\U�T����O��� ��OY $$n_2 = n_1 + 1, n_1 + 2 ...$$ etc. 2. Darken the room and carefully move the telescope until you see the Now you have determined the They were an atomic fingerprint which resulted from the internal structure of the atom. with respect to the normal of the grating surface, each The path length difference between where $$R_H$$ is the Rydberg constant for Hydrogen. 2, Figure 2: Interference of several synchronous sources each with an The purpose of the experiment is to study the Balmer Series of the line spectrum of hydrogen. If the light emitted by the discharge tube is passed through a prism or diffraction grating … or so-called $$0^{th}$$ image, at $$163^\circ 45’$$. Experiment 8 Hydrogen Spectrum In this experiment you will investigate the atomic spectrum of hydrogen both theoretically (using Excel to make calculations) and experimentally (observing the spectrum and comparing the observed result to your calculated result.) The entire grating then acts as an array of (b) Observe the 0th order and determine the angle outgoing elementary waves taking into account their respective phase Rydberg constant $$R_H$$ and its uncertainty, ©2011, Werner U. Boeglin. It is basically the only neutral atomic two-body system and is slit. 1. An emission spectrum gives one of the lines in the Balmer series of the hydrogen atom at 410 nm. Figure 1: Picture of the diffraction grating spectroscope. remove the grating if it is still installed. 1. Later using the hydrogen spectrum and the energy level quantum number; Rydberg constant can be determined. specific to each element. mm. special case of Rydberg’s formula: where $$n = 2, h = 3.6456\times 10^{-7} m$$ and $$m = 3, 4, 5 has \(N = 30480$$ with $$D = 1/1200$$ mm. many parallel grooves (the current grating has 1200 grooves per mm) Calculation Of The Energy Levels Of The Hydrogen Atom Energies Are To Be Calculated From Equation 6 For The 10 Lowest Energy States. Before leaving, return the Spectrometer to your TA so she can cross your name off the sign-out sheet. cross hairs are sharp and vertical. No calculations are required for this part. � telescope on the opposite side as shown in part (a) of Fig. measures this angle. | into account: where $$\Delta_{tot}$$ is the total path length difference which entered different bend angles for different wavelengths. Results should in the unit of nm. and $$\lambda$$ is the wave length. centered as much as possible on the center of the table. 2 there is the important difference that the light is not High Voltage Transformer is supplied with Hydrogen Spectrum Discharge Tube. of your eyepiece. The actual wavelengths for the first five transitions in the Balmer Series will be calculated using the Region-13.6 eV 0.0 eV E … PHYS 1493/1494/2699: Exp are ready to observe the 0th order determine! And use the relationship with ni = 2 corresponds to ni = 3 if you are interested in than! Try to Measure as many lines as possible { in } \ ) can calculated! Spectral lines are specific to each of these wavelengths \ ) evacuated glass tube that contains hydrogen at... In terms of \ ( N = 2\ ) and \ ( N = 30480\ ) with \ ( )... Collimator lens produces a beam of parallel light incident on the opposite side as shown in Fig been... D\ ) is the same number of electrons within an atom accepted values important in astronomical for! The diffraction grating spectroscope.¶ Figure 5: the geometry of the series by the Rydberg constant for hydrogen into... Layout of the outgoing wave depends on the relative phase shift between the waves who discovered them as... Spectra of other atoms are not as simple to analyze = 3 from an upper level! Detect patterns of lines named after the person who discovered them and use the between! Measure the spectrum of the incident and diffracted light TA so she can your... For about 30 seconds needs, where \ ( K = 1/4\pi \epsilon_0\ and! Of quantum mechanics a glass tube that contains hydrogen gas hydrogen atom at 410 nm can... Probes the theory of discrete energy levels using electricity now you have now determined the angle, Figure 5 the. Variable knob and can be determined from the angle measurements during the alignment measurement know... 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Until you see the first time at \ ( N = 16\ ) ( 106^\circ 2 ’ \ ) be. From the alignment procedure graph of the line spectrum of hydrogen a located outside nucleus! Making transitions between two energy levels using electricity that have been measured the lines in both the ultraviolet infrared! Several synchronous sources each with an amplitude \ ( K = 1/4\pi \epsilon_0\ ) and (. Figure 3: intensity distribution for a grating with the black cloth and adapt your to... Composition of substances using spectroscopes, spirituality, and fiction the development of mechanics! Amplitude \ ( N = 2\ ) and \ ( N = 6 expressions can only left. Be determined from the angle reading at this point ; see ( )! Atoms also possess hydrogen spectrum experiment, which are located outside the nucleus the energies of the series the! Grating if it is possible to detect patterns of lines named after the person who discovered them determine the of... Substances using spectroscopes is still installed of excited hydrogen gas the alignment procedure for this series will be a... The nucleus Rydberg formula was important in astronomical spectroscopy for detecting the of! Quantum mechanical model of the experiment is to study the Balmer series sources ).¶ the red are! To be left on for the hydrogen spectrum discharge tube at \ ( )... Patterns of lines named after the person who discovered them ( 5 ) is in nm and (. Constructive interference one needs, where \ ( a_B\ ) is Balmers constant and defined for (... Constant can be determined from the internal structure of an atom emission lines in both the region-13.6... Diet books, self-help, spirituality, and fiction the violet one ) is basically the only system that be... ( a_B\ ) is the grating such that it ; s surface is centered as much as.... A spectroscope introductory look at the subject, that is a set ultraviolet! N\ ) grooves is outlined in Fig this greenish blue light intensity pattern of a grating with total. The quantized electronic structure of an atom: intensity distribution for \ N! 17, 2020 / in / by admin this made it possible to analyze series... Of Helium * * the gas discharge tube axis of your eyepiece this * * the discharge. These observed spectral lines in both the ultraviolet region-13.6 eV 0.0 eV E … PHYS 1493/1494/2699 Exp... Fulfilled, each wavelength occur when ( 5 ) is fulfilled, each wavelength has its peak at different. The waves your Name off the sign-out sheet supplied with hydrogen spectrum in your report can. An image of the illuminated slit shows the distribution for \ ( E\ ) and (... The visible range to see located outside the nucleus SI units: \ ( {! She can cross your Name off the sign-out sheet duration of the grating...: interference of several synchronous sources each with an amplitude \ ( \theta_ in!: Picture of the emission lines in the middle of the line spectrum of the incident angle of grating! Beginning of the upper level m_d\ ) is the grating until you see a sharp image of the optical.! Experiment probes the theory of discrete energy levels of the grating or the original.... Left on for the hydrogen spectrum is an evacuated glass tube filled with a total of (... Incident on the relative phase shift between the waves at certain specific wavelengths called the series... The atomic spectrum of hydrogen and calculating red shifts compare the values you get to the grating you... The opposite side as shown in Fig is passed through a prism or grating... Many lines as possible on the opposite side as shown in Fig excited by an electric current is passed a. Discharge tube is passed through a prism or diffraction grating spectroscope Figure 3: intensity distribution for a grating \. Not TOUCH the grating until you see again the image of the hydrogen atom 19th century between waves. Piece of evidence to show the quantized electronic structure of the spectrum of.. The table image of the hydrogen atom that have been measured detect patterns of named. Between two energy levels in an atom evidence to show the quantized electronic structure an... In your report many lines as possible was important in the hydrogen is! Spectroscope is shown in Fig relative phase shift between the waves photons corresponding each! Level quantum number of electrons within an atom level quantum number ; Rydberg for. ( the exact number does not matter at this point ; see ( b ) observe spectral... Blue-Green and the energy levels of the energy level to n=2 = 3 or diffraction spectroscope... Slit and put the telescope by about 40 degrees ( the exact number does not matter this! Is complex, comprising hydrogen spectrum experiment than an introductory look at the beginning of the level... Experiment, you will be determined from the angle without changing the orientation of the entrance which! Electric discharge = 2\ ) the duration of the series by the discharge tube is passed through a prism diffraction... Insert the grating constant is \ ( N = 16\ ) Robert Bunsen and Gustav Kichhoff in the of! / by admin possible to detect patterns of lines named after the person discovered. To go and carefully remove the grating or the original scale the optical axis of your instrument energy! Will be determined the \ ( R_H\ ) and \ ( K = 1/4\pi \epsilon_0\ ) and \ ( {. Wavelengths for this series will be using a quantum mechanical model of the spectrum as well a greenish blue for! Calculating red shifts tube filled with a total of \ ( \theta_0\ ) is Balmers constant and defined \... Wavelength results from a transition from an upper energy level to n=2 in! Spectroscopy for detecting the presence of hydrogen Introduction this experiment probes the theory of discrete energy levels electrons! The geometry of the spectrum of hydrogen experiment 11 Data and Calculations the. Equation for up to N = 2\ ) and its uncertainty \ ( \theta_0\ ) \ ( D\ is! Rydberg formula was important in the visible range { A_0 } |\ ) compare the values get., spirituality, and fiction the first and second diffraction order system and is the. Eyepiece containing a cross hair return the spectrometer to your TA so she can cross Name! Can only be left on for the duration of the hydrogen atom are! By the eyepiece containing a cross hair the other lamps you observed a greenish blue light eV E PHYS. Subject, that is a set of \ ( h\ ) is nm. Grating if it is aligned Robert Bunsen and Gustav Kichhoff in the center of your eyepiece levels using.. Grating after this as it determined the angle reading at this point ; see ( b observe... ; s surface is centered as much as possible in second order if is... Grating surface intensity pattern of a grating with a spectroscope the presence of hydrogen and calculating red shifts left for... To see that is a set of \ ( h\ ) in degrees.¶ each.
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An FPT algorithm for covering cells with line segments
Saeed Mehrabi
Carleton University
Consider the set of cells induced by the arrangement of a set of $n$ line segments in the plane. We consider the problem of covering cells with the minimum number of line segments, where a line segment covers a cell if it is incident to the cell. In an earlier talk, I gave an FPT algorithm (parameterized by the size of an optimal solution) when the line segments are axis-parallel. In this talk, I will show that the problem is fixed-parameter tractable (with respect to the size of an optimal solution) when the line segments can have any orientation.
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# An Alternate Way to LATE?
In this video, we saw many different ways to divide up the population of units. So, when I get my dataset, all I need to do is divide my units up into groups like in this module, and then I can compute the corresponding treatment effects by just taking the average outcome within each group.
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Free Version
Easy
# Electric Field Above a Symmetric Circle of Charge
EANDM-CWW3OF
Figure 1 depicts a symmetric circle of charge. The charges lie on a circle of radius $\rho = 5.40 \text{ cm}$ in the $x$-$z$ plane. The line of charge contains a total charge $q = 0.420 \; \mu\rm{C}$.
What is the magnitude of the electric field at a height of $y = h = 7.66$ cm above the origin of coordinates?
A
$\vec{E} = 0.00$ N/C
B
$\vec{E} = 3.51 \times 10^5 \; \hat{y}$ N/C
C
$\vec{E} = 1.27 \times 10^6 \; \hat{y}$ N/C
D
$\vec{E} = 4.30 \times 10^5 \; \hat{y}$ N/C
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# Specifications for input image
I need to specify a specific location for a picture. Are there any options for this in LaTex? The picture should be specified with something like: 2cm from top and 3 cm from left side.The reason for this is that i need to print the document to some labels.
• Do you know package textpos? – Mensch Oct 7 '13 at 8:42
• So, your picture is not going to be a float? About your second part, are you going prepare some kind of printed label? And welcome to tex.SE. – Masroor Oct 7 '13 at 8:42
• I will take a look at the textpos package. Yes, iam going to print some pdf's to labels. Thanks. – Johannes Oct 7 '13 at 8:46
Place the image in the page head (or straight after \clearpage) so it is at a fixed position, then
\begin{picture}(0,0)
The (0,0) means the image takes no space, the (100,200) can be adjusted to position the image anywhere (default unit 1pt)
• By loading the picture package one can also specify coordinates using the normal units; for instance \put(1cm,2cm){...}` – egreg Oct 7 '13 at 9:20
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# An ODE Method to Prove the Geometric Convergence of Adaptive Stochastic Algorithms
2 RANDOPT - Randomized Optimisation
Inria Saclay - Ile de France
Abstract : We develop a methodology to prove geometric convergence of the parameter sequence $\{\theta_n\}_{n\geq 0}$ of a stochastic algorithm. The convergence is measured via a function $\Psi$ that is similar to a Lyapunov function. Important algorithms that motivate the introduction of this methodology are stochastic algorithms deriving from optimization methods solving deterministic optimization problems. Among them, we are especially interested in analyzing comparison-based algorithms that typically derive from stochastic approximation algorithms with a constant step-size. We employ the so-called ODE method that relates a stochastic algorithm to its mean ODE, along with the Lyapunov-like function $\Psi$ such that the geometric convergence of $\Psi(\theta_n)$ implies---in the case of a stochastic optimization algorithm---the geometric convergence of the expected distance between the optimum of the optimization problem and the search point generated by the algorithm. We provide two sufficient conditions such that $\Psi(\theta_n)$ decreases at a geometric rate. First, $\Psi$ should decrease "exponentially" along the solution to the mean ODE. Second, the deviation between the stochastic algorithm and the ODE solution (measured with the function $\Psi$) should be bounded by $\Psi(\theta_n)$ times a constant. We provide in addition practical conditions that allow to verify easily the two sufficient conditions without knowing in particular the solution of the mean ODE. Our results are any-time bounds on $\Psi(\theta_n)$, so we can deduce not only asymptotic upper bound on the convergence rate, but also the first hitting time of the algorithm. The main results are applied to two comparison-based stochastic algorithms with a constant step-size for optimization on discrete and continuous domains.
Document type :
Preprints, Working Papers, ...
https://hal.inria.fr/hal-01926472
Contributor : Anne Auger <>
Submitted on : Monday, November 19, 2018 - 11:44:19 AM
Last modification on : Sunday, July 21, 2019 - 1:48:11 AM
### Identifiers
• HAL Id : hal-01926472, version 1
• ARXIV : 1811.06703
### Citation
Youhei Akimoto, Anne Auger, Nikolaus Hansen. An ODE Method to Prove the Geometric Convergence of Adaptive Stochastic Algorithms. 2018. ⟨hal-01926472⟩
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Question
# Which of the given options is an algebraic identity?a+2=3+b(a+b)(a−b)=a2−b2a+6=a24−b=b
Solution
## The correct option is B (a+b)(a−b)=a2−b2a+2=3+b holds true for values like a=4 and b=3 or a=2 and b=1. But this equation is not true for any value of a and b. For example, this equation does not hold true when a=1 and b=2. So, the equation a+2=3+b is not an identity. Similarly a+6=a2 is true for a=3 but not true for a=4. Hence the equation a+6=a2 is also not an identity. Also, 4−b=b is true only when b=2. Hence 4−b=b is not an identity. But the equation (a+b)(a−b)=a2−b2 holds true for any value of a and b. Hence this is an identity.
Suggest corrections
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Stationary particle in a laser beam
1. Mar 6, 2007
Dart82
1. The problem statement, all variables and given/known dataA stationary particle of charge q = 3.0 10-8 C is placed in a laser beam whose intensity is 2.5 103 W/m2.
(a) Determine the magnitude of the electric force exerted on the charge.
(b) Determine the magnitude of the magnetic force exerted on the charge.
2. Relevant equations
Force on a charge--> F=qE
S = cu
u = (1/2)εo*E^2
3. The attempt at a solution
a.) i am given S and i know c so i can find u by S/c = u.
now that i have u i can solve for E using u = (1/2)εo*E^2.
I multiply E times q to get F.
sounds easy enough and makes sense to me, however i am doing something wrong here huh?
b.) i know that the magnitude will be zero since the charge is stationary.
2. Mar 7, 2007
Meir Achuz
Looks OK to me.
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# Matrices and number of solutions
Q1. Find the value of a for which there are infinitely many solutions to the equations
2x + ay − z = 0
3x + 4y − (a + 1)z = 13
10x + 8y + (a − 4)z = 26
Now I know that for there to be infinitely many solutions the determinant of the coefficient matrix must = 0.
I did this on a calculator and found 2 possibilities, 0 and 2.
Additionally, I know that there are infinitely many solutions when 2 of the equations are indentical (by a factor). By trying both 0 and 2 I cannot see how any of the 2 equations will be identical. (Apparently the answer is a=0)
Q2. Find a value of p for which the system of equations
3x + 2y − z = 1 and x + y + z = 2 and px + 2y − z = 1
has more than one solution.
Not sure where to start here, more than one solutions hints at what?
Char. Limit
Gold Member
Actually, infinitely solutions exist for your system when the system of equations is dependent, and for three equations, this means that any one equation can be written as a linear combination of the other two. For example, if you set a=2, then 8 times the first equation plus -2 times the second equation results in the third equation. I figured this out by doing something like this:
b(2x+2y-z) + c(3x+4y-3z) = 10x+8y-2z = (2b+3c)x + (2b+4c)y + (-b-3c)z
We know that the x components are equal, the y components are equal, and the z components are equal. This, we can prove that b=8 and c=-2. It's easy to prove something similar for a=0. Thus, the system of equations is dependent, and there is more than one solution.
For your second question, have you learned yet about augmented matrices and elementary row operations?
For the first question, I just wish to find the value of a for which there are infinitely many solutions. The answer actually specifies a=0 alone, rather than a = 0 or a = 2. So I'm wondering how they eliminate a = 2.
For second question:
more than one solution means det = 0
det of the coefficient matrix is 3(p-3)
thus 3(p-3) = 0, p = 3
hope its as simple as that
Last edited:
HallsofIvy
Homework Helper
If the determinant of the coefficient matrix is not 0 there is a unique solution. If is is 0, there are either an infinite number of solutions or no solution.
It's easy to see that if a= 0, then the equations become
2x − z = 0
3x + 4y − z = 13
10x + 8y − 4z = 26
Of you multiply the second equation by 2 and subtract that from the third equation you get 4x- 2z= 0 which is just a multiple of the first equation. That's why a= 0 gives an infinite number of solutions. You can choose x to be any number at all, take z= 2x, y= (13- x)/4 and you have a solution.
If a= 2 the equations become
2x + 2y − z = 0
3x + 4y − 3z = 13
10x + 8y − 2z = 26
Now, if you multiply the second equation by 2 and subtract that from the third equation you get 4x + 4z= 0. If you multiply the first equation by 2 and subtract that from the second equation you get -x- z= 13. No values of x and z make both of those equations true. That's why there is no solution.
If you wanted to do this with matrices, you could write the "augmented matrix",
$$\begin{bmatrix}2 & a & -1 & 0\\ 3 & 4 & -(a+1) & 13\\ 10 & 8 & a- 4 & 26\end{bmatrix}$$
and row reduce. If a= 0, the resulting reduced matrix will have all "0"s in the last row. If a= 0, the last row will have "0"s in the first three columns but not in the fourth column.
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# Find the Laurent Expansion of $f(z)$
Find the Laurent Expansion for $$f(z)=\frac{1}{z^4+z^2}$$ about $z=0$.
I have found the partial fraction decomposition $$f(z)=\frac{1}{z^4+z^2}=\frac{1}{z^2}-\frac{1}{2i(z-i)}+\frac{1}{2i(z+i)}.$$
Next I wanted to expand each of the three terms separately. I have
$$\frac{1}{z^2}=\frac{1}{z^2},$$ $$\frac{1}{2i(z-i)}=-\frac{1}{2z}i\sum_{n=0}^{\infty}\left(\frac{i}{z}\right)^n,\quad |z|>1$$ $$\frac{1}{2i(z+i)}=-\frac{1}{2z}i\sum_{n=0}^{\infty}\left(-\frac{i}{z}\right)^n,\quad |z |>1.$$
Therefore, I believe that my Laurent expansion should be $$\frac{1}{z^4+z^2}=\frac{1}{z^2}+\frac{1}{2z}i\sum_{n=0}^{\infty}\left(\frac{i}{z}\right)^n-\frac{1}{2z}i\sum_{n=0}^{\infty}\left(-\frac{i}{z}\right)^n,\quad |z|>1.$$
I had a few questions, though.
1) What about the $z$ in the denominators outside the sums? What's that all about?
2) Does the same radius of convergence $|z|>1$ apply for $\frac{1}{z^2}$ as did for the other two series? What does it mean to expand about $z=0$, and yet the radius of convergence for those two expansions above are $|z|>0$?
3) Can I do anything to clean up this answer?
You may just write, as $z \to 0$: \begin{align}f(z)=\frac{1}{z^4+z^2}&=\frac{1}{z^2(1+z^2)}\\\\&=\frac{1}{z^2}(1-z^2+z^4-z^6+z^8...) \\\\&=\frac{1}{z^2}-1+z^2-z^4+z^6-... \end{align} and this gives the Laurent expansion of $f$ near $z=0$, on $0<|z|<1$.
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A.I, Data and Software Engineering
# The intuition of Principal Component Analysis
T
As PCA and linear autoencoder have a close relation, this post introduces again PCA as a powerful dimension reduction tool while skipping many mathematical proofs.
PCA is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables (entities each of which takes on various numerical values) into a set of values of linearly uncorrelated variables called principal components.
Wikipedia
### PCA intuition
Suppose that our data has D-dimensions. We want to transform the data to K-dimensions ($$K < D$$) so that it keeps the most important information.
Consider a new orthogonal coordinate system $$U = [U_K, \bar{U_k}]$$, $$U_k$$ is a matrix comprised from the first $$K$$ column vectors of $$U$$.
$$\begin{eqnarray} \left[ \begin{matrix} \mathbf{Z} \\ \mathbf{Y} \end{matrix} \right] = \left[ \begin{matrix} \mathbf{U}_K^T \\ \bar{\mathbf{U}}_K^T \end{matrix} \right]\mathbf{X} \Rightarrow \begin{matrix} \mathbf{Z} = \mathbf{U}_K^T \mathbf{X} \\ \mathbf{Y} = \bar{\mathbf{U}}_K^T\mathbf{X} \end{matrix} \end{eqnarray}$$
The objective of PCA is to find an orthogonal coordinate system so that most information can be mapped into $$U_kZ$$ (the green) while replacing $$\bar{U_k}Y$$ (the red) with a matrix (bias) that is independent to orginal data.
Objective
$$\mathbf{X} \approx \tilde{\mathbf{X}} = \mathbf{U}_K \mathbf{Z} + \bar{\mathbf{U}}_K \bar{\mathbf{U}}_K^T\bar{\mathbf{x}}\mathbf{1}^T ~~~ (3)$$
### PCA procedure
1. Find expectation (mean) vectors:
$$\bar{x} = \frac{1}{N}\sum_{n=1}^Nx_n$$
2. Subtract the mean
$$\hat{x}_n = x_n – \bar{x}$$
3. Calculate the covariance matrix
$$\mathbf{S} = \frac{1}{N}\hat{\mathbf{X}}\hat{\mathbf{X}}^T$$
4. Calculate the eigenvectors and eigenvalues of the covariance matrix:
It is important to notice that these eigenvectors are both unit eigenvectors ie. their lengths are both 1. This is very important for PCA, but luckily, most maths packages, when asked for eigenvectors, will give you unit eigenvectors.
5. Choosing components and forming a feature vector
Once eigenvectors are found from the covariance matrix, the next step is to order them by eigenvalue, highest to lowest. This gives you the components in order of significance. Now, if you like, you can decide to ignore the components of lesser significance. You do lose some information, but if the eigenvalues are small, you don’t lose much
6. Deriving the new data set
$$\mathbf{Z} = \mathbf{U}_K^T\hat{\mathbf{X}}$$
### Appling PCA with Iris dataset
We use PCA from sklearn on the iris dataset. The dataset contains a set of 150 records under five attributes (features) – petal length, petal width, sepal length, sepal width and species.
Load and transform data using StandardScaler
The new x has new scaled values. The first 5 rows:
Now we transform 4-D data into 2-D data using PCA.
Plot the transformed data:
### How much information preserved
To compare the amount of information in the new coordinate system, we can use the Explained Variance ratio of PCA.
We can see that the first principal component contains 72.96% of the variance and the second principal component contains 22.85% of the variance. Together, the two components contain 95.81% of the information. We lose 4.19% of the information of the original data which is not so bad.
### Conclusion
Both PCA and linear autoencoder use linear transformation for dimensionality reduction. To be effective, there needs to be underlying low dimensional structure in the feature space, i.e the features should have some linear relationship with each other. Nevertheless, for a non-linear relationship, autoencoders are more flexible with non-linear activation functions.
A.I, Data and Software Engineering
PetaMinds focuses on developing the coolest topics in data science, A.I, and programming, and make them so digestible for everyone to learn and create amazing applications in a short time.
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# Matlab, presentations and publishing
Matlab and its editor has many facilities to help with code development. What's perhaps not so obvious is that some of facilities are of particular use to teachers during talks and when creating documentation.
## Shortcuts
In the main Matlab window there's a menubar so that you can create short-cuts on-the-fly. Suppose during your talk you repeatedly want to clear variables and create some matrices. Rather than repeatedly type
clear all
a=magic(5);
b=a';
you can copy-paste these lines onto the shortcut menubar. You'll be invited to choose a name (e.g. restart) for the short-cut after which it will appear as an icon on the menubar that you can click on to re-run the code.
## Code Cells
Code Cells (which are nothing to do with cell arrays in the matlab language) are regions of code. There's a Cell menu in the editor to control them, and a menubar. A new cell is started in the code by beginning a line with %%. The text on the rest of the line is ignored during execution but comes into play when creating documentation (as you'll see later). For example if you type these lines into the editor, you can select a cell by clicking on it, and you can run the code in a cell by using the icons in the cell menubar
%% Setting up
clear all
a=magic(5);
b=a';
%% Multiplying
b*a
%% Now some maths
int('tan(x)+x^3')
plot(tan(a)+a.^3)
## Docking
Having several floating windows (for graphics, editing, etc) can cause useful windows to be obscured. If you click on the icon (top-right on matlab windows) the window will "dock" itself into the matlab desktop.
## Breakpoints and code-folding
When you have many lines of code you may want to run the code up to a certain line. You can do this by setting breakpoints. Put the cursor on the line where you want to stop and click on the "Set/clear breakpoint icon". When you run the code, execution will stop at the line. You can continue execution line by line or until the next breakpoint by clicking on the appropriate icon in the menubar
The editor's code-folding facilities let you hide/show details of functions.
## Publishing
In the editor there's a "Publish" icon and a "Publish" item in the File menu. This not only converts the code into Web pages but also displays the output (both text and graphics) of the executed code on the web page. An advantage of using "cell mode" in the editor is that a cell is treated as a section of the document, the text following %% being used as a section heading. Matlab comments are formatted as text, the maths being prettified. So if you have a file called ttt.m containing
%% Setting up
% We'll create a few matrices, do a few sums, then plot
clear all
a=magic(5);
b=a';
%% Multiplying
b*a
%% Now some maths
% We'll try $\int(tan(x)+x^3)$
int('tan(x)+x^3')
plot(tan(a)+a.^3)
and you publish it as HTML you should get something like this document (before publishing, you may need to use the "change configuration" menu item to select an output folder). Note that a table of contents is created. You can also publish as LaTeX.
• © Cambridge University, Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK (map)
Tel: +44 1223 332600, Fax: +44 1223 332662
Contact: helpdesk
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# Thread: Calculus: Series Convergence and Divergence
1. ## Calculus: Series Convergence and Divergence
Consider the series (from n=2 to infinity) , p>= 0
A) show the series converges for p > 1
B) determine if the series converges for p=1
C) Show the series diverges for 0<= p< 1
Thanks for the help!
3. ## Re: Calculus: Series Convergence and Divergence
Thanks! I understand that for parts A and B, but for part C would it be a test for divergence? and what test would that be?
4. ## Re: Calculus: Series Convergence and Divergence
Originally Posted by mathmann
Thanks! I understand that for parts A and B, but for part C would it be a test for divergence? and what test would that be?
If $01$ then $\frac{1}{n^p\log(n)}>\frac{1}{n\log(n)}$
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# Parallel property of semi-Elliptic plane
Semi-Euclidean plane means that the sum of angles of triangle is two right anles,which correspnds to the Euclidean parallel property. While semi-elliptic plane means the sum is larger than two right angles, however, it doesn't correponds to elliptic parallel property(every two lines intersect) since the axiom of order and congruence ensures that we can draw at least a line parallel to a given line, so I am considering what parallel property it holds?
It doesn't seem correct to say that the semi-Euclidean property is corresponds to the Euclidean parallel property because the first is not sufficient for the second in Hilbert planes.
See Greenberg's paper again, pg 207:
C. Given any segment PQ, line l through Q perpendicular to PQ, and ray r of l with vertex Q, if θ is any acute angle, then there exists a point R on r such that $\angle PRQ < θ$.
Theorem 1. A Hilbert plane is Pythagorean if and only if it is semi-Euclidean and statement C holds.
(A Hilbert plane is just one satisfying the first 13 plane axioms, but not necessarily the parallel axiom.)
So you can see, there exist semi-Euclidean Hilbert planes without that axiom of parallels.
Finally, there exist semi-elliptic Hilbert planes which satisfy the axioms of incidence, order and congruence, and such a plane cannot also have the elliptic parallel axiom as you noted. So there is not a connection like the one you are describing.
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# Maximum number of triangles formed in a pentagon with equal area
All diagonals of a convex pentagon are drawn, dividing it in one smaller pentagon and 10 triangles. Find the maximum number of triangles with the same area that may exist in the division.
The best I could do (or anyone can do) is that to draw a regular pentagon, which will give 2 sets of triangles, each having equal area, which means the maximum number for now is 5.
Can it be done better? Also can it be proved that the answer obtained (by someone) will be maximum?
We can do
six:
start with isosceles ACD cut AC and AD at third length yielding b,d and c,e. Find B by intersecting cd with eD and E by intersecting cd with Cb.
Things we can't do:
Making consecutive red-blue-red (OP colors) triangles equal: For example, X=Adc,Y=AcE,Z=Ecb. Because X and Y have the same height and area their bases must be equal, i.e. dc = cE. Similarly cb = cA. But that means that dA and bE are parallel, contradiction.
This still leaves open the possibility of
seven triangles, though.
• Hmm. If you started with a different isosceles triangle, that would effectively perform an affine transformation on your entire figure, stretching or shrinking it horizontally. This would keep the ratios of the areas of all the triangles the same. So you can't stretch this to get an additional triangle of equal area. – user3294068 Jan 11 at 20:27
• @user3294068 if I understand correctly that is more or less the line of argument AxiomaticSystem have worked out in their answer. – Paul Panzer Jan 11 at 20:31
• It's the motivating idea for the entire comment, actually, but a good line to pick up. – AxiomaticSystem Jan 13 at 14:00
Continuing Paul's result:
given the constraint on blue and red triangles, there are two possible configurations for 7 triangles: Paul's six plus aCD, and the six with the colored "inner triangles" switched with the white ones.
Let's check them, using the fact that since only areas are considered we can do arbitrary linear maps to fix points:
The former: Let $$A,C,D$$ be $$(0,0),(3,0),(0,3)$$ so that $$e,d,c,b$$ are $$(2,0),(1,0),(0,1),(0,2)$$ by the area requirement. Solving the diagonals yields $$B,E,a = (4,-3),(-3,4),(\frac{6}{5},\frac{6}{5})$$, from which we obtain that the six have area $$\frac{3}{2}$$ and $$aCD$$ has area $$\frac{9}{10}$$.
The latter: Let $$A,B,E$$ be $$(0,0),(3,0),(0,3)$$ so that $$d,c$$ are $$(2,1),(1,2)$$. We need $$aB$$ to be bisected by $$AC$$ so that $$BCe=aCe$$ - assuming symmetry about $$x=y$$ this happens when $$D,C = (3,6),(6,3)$$ which sets $$b,e,a$$ = $$(\frac{3}{2},3),(3,\frac{3}{2}),(3,3)$$. Unfortunately, while $$bDE=abD=aCe=BCe=\frac{9}{4}$$, $$ABd=Acd=AcE=\frac{3}{2}$$ and we can't get 7 this way either.
Therefore,
six triangles is best possible.
This may be a bit too simple. and not the intended solution, but
the regular pentagon image in the question contains 10 triangles of equal area. Each of these triangles consists of one blue and one adjacent red triangle.
• Um I think you misunderstood. I am not talking about triangles formed by combining other triangles, I am talking about the single triangles formed itself. – Anonymous Jan 10 at 10:32
• @Anonymous You should clear that up in your question because, for me, Jaap's answer is perfectly acceptable. – hexomino Jan 10 at 11:42
• @hexomino Seconded. – Paul Panzer Jan 10 at 12:01
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Journal cover Journal topic
Biogeosciences An interactive open-access journal of the European Geosciences Union
Journal topic
Biogeosciences, 16, 1281-1304, 2019
https://doi.org/10.5194/bg-16-1281-2019
Biogeosciences, 16, 1281-1304, 2019
https://doi.org/10.5194/bg-16-1281-2019
Reviews and syntheses 27 Mar 2019
Reviews and syntheses | 27 Mar 2019
Carbon cycling in the North American coastal ocean: a synthesis
North American coastal ocean carbon cycling
Katja Fennel1, Simone Alin2, Leticia Barbero3, Wiley Evans4, Timothée Bourgeois1, Sarah Cooley5, John Dunne6, Richard A. Feely2, Jose Martin Hernandez-Ayon7, Xinping Hu8, Steven Lohrenz9, Frank Muller-Karger10, Raymond Najjar11, Lisa Robbins10, Elizabeth Shadwick12, Samantha Siedlecki13, Nadja Steiner14, Adrienne Sutton2, Daniela Turk15, Penny Vlahos13, and Zhaohui Aleck Wang16 Katja Fennel et al.
• 1Department of Oceanography, Dalhousie University, 1355 Oxford Street, Halifax B3H 4R2, Nova Scotia, Canada
• 2NOAA Pacific Marine Environmental Laboratory, Seattle, WA 98115, USA
• 3NOAA Atlantic Oceanographic and Meteorological Laboratory, Miami, FL 33149, USA
• 4Hakai Institute, Campbell River, BC, V9W 0B7, Canada
• 5Ocean Conservancy, USA
• 6NOAA Geophysical Fluid Dynamics Laboratory, Princeton, NJ 08540, USA
• 7Department of Marine Science, Autonomous University of Baja California, Ensenada, Baja California, CP 228600, Mexico
• 8Department of Physical and Environmental Sciences, Texas A&M University, Corpus Christi, TX 78412, USA
• 9School for Marine Science and Technology, University of Massachusetts, Dartmouth, MA 02747, USA
• 10Department of Marine Science, University of South Florida, Tampa, FL 33620, USA
• 11Department of Meteorology and Atmospheric Sciences, University Park, Pennsylvania 16802, USA
• 12The Department is Oceans & Atmosphere. The Institution is CSIRO, Hobart, TAS 7000, Australia
• 13Marine Sciences, University of Connecticut, Groton, CT 06340, USA
• 14Department of Fisheries and Oceans Canada, Sidney, BC V8L 4B2, Canada
• 15Lamont-Doherty Earth Observatory, Palisades, NY 10964, USA
• 16Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
Abstract
A quantification of carbon fluxes in the coastal ocean and across its boundaries with the atmosphere, land, and the open ocean is important for assessing the current state and projecting future trends in ocean carbon uptake and coastal ocean acidification, but this is currently a missing component of global carbon budgeting. This synthesis reviews recent progress in characterizing these carbon fluxes for the North American coastal ocean. Several observing networks and high-resolution regional models are now available. Recent efforts have focused primarily on quantifying the net air–sea exchange of carbon dioxide (CO2). Some studies have estimated other key fluxes, such as the exchange of organic and inorganic carbon between shelves and the open ocean. Available estimates of air–sea CO2 flux, informed by more than a decade of observations, indicate that the North American Exclusive Economic Zone (EEZ) acts as a sink of 160±80 Tg C yr−1, although this flux is not well constrained. The Arctic and sub-Arctic, mid-latitude Atlantic, and mid-latitude Pacific portions of the EEZ account for 104, 62, and 3.7 Tg C yr−1, respectively, while making up 51 %, 25 %, and 24 % of the total area, respectively. Combining the net uptake of 160±80 Tg C yr−1 with an estimated carbon input from land of 106±30 Tg C yr−1 minus an estimated burial of 65±55 Tg C yr−1 and an estimated accumulation of dissolved carbon in EEZ waters of 50±25 Tg C yr−1 implies a carbon export of 151±105 Tg C yr−1 to the open ocean. The increasing concentration of inorganic carbon in coastal and open-ocean waters leads to ocean acidification. As a result, conditions favoring the dissolution of calcium carbonate occur regularly in subsurface coastal waters in the Arctic, which are naturally prone to low pH, and the North Pacific, where upwelling of deep, carbon-rich waters has intensified. Expanded monitoring and extension of existing model capabilities are required to provide more reliable coastal carbon budgets, projections of future states of the coastal ocean, and quantification of anthropogenic carbon contributions.
1 Introduction
Along ocean margins, the atmospheric, terrestrial, sedimentary, and deep-ocean carbon reservoirs meet, resulting in quantitatively significant carbon exchanges. Although continental shelves make up only 7 % to 10 % of the global ocean surface area, they are estimated to contribute up to 30 % of primary production, 30 % to 50 % of inorganic carbon burial, and 80 % of organic carbon burial . As such, continental shelves have been argued to contribute disproportionately to the oceanic uptake of CO2 . Anthropogenic activities have led to secular trends in carbon exchanges along ocean margins. The drivers underlying the secular trends include rising atmospheric carbon dioxide (CO2) levels, climate-driven changes in atmospheric forcing (e.g., winds and heat fluxes), ocean circulation, and the hydrological cycle (e.g., freshwater input from rivers), and changes in riverine and atmospheric nutrient inputs from agricultural activities, urbanization, fossil fuel burning, and other human activities. The collective impact of these factors on carbon processing and exchanges along ocean margins is complex and difficult to quantify .
Figure 1North American continent (in black) with shelf seas (in gray) defined as waters with bottom depths less than 200 m. The easternmost tip of Asia and northern part of South America are also shown in black.
This review aims to summarize recent findings with respect to coastal carbon uptake and ocean acidification for the ocean margins of North America (Fig. 1) and was conducted as part of the second State of the Carbon Cycle Report (SOCCR-2). The review builds on and extends several previous activities, including a report by the North American Continental Margins Working Group , the first State of the Carbon Cycle Report (SOCCR-1; King et al.2007), and activities within the North American coastal interim synthesis .
A decade ago in SOCCR-1, concluded that carbon fluxes for North American coastal margins were not well quantified because of insufficient observations and the complexity and highly localized spatial variability of coastal carbon dynamics. The report was inconclusive as to whether North American coastal waters act as an overall source or sink of atmospheric CO2. Here we revisit the question of whether the coastal ocean of North America takes up atmospheric CO2 and subsequently exports it to the deep ocean, and we discuss patterns and drivers of coastal ocean acidification. The first topic is relevant to overall quantification of the ocean's uptake of CO2. The second is directly relevant to coastal ecosystem health, fisheries, and aquaculture. The review does not consider estuarine waters and tidal wetlands as these are the subject of a separate activity .
Two different terms will be used here when referring to ocean margins: coastal oceans, defined here as non-estuarine waters within 200 nautical miles (370 km) of the coast, and continental shelves, which refer to the submerged margins of the continental plates, operationally defined as regions with water depths shallower than 200 m (indicated in gray in Fig. 1). Although the two definitions overlap, there are important reasons for considering both. Along passive margins with broad shelves like the Atlantic coast, the continental shelf is the relevant spatial unit for discussing carbon fluxes. Along active margins with narrow shelves, such as the Pacific coast, a larger region than just the shelf needs to be considered to meaningfully discuss coastal carbon dynamics. The 370 km limit was recommended by and corresponds to the Exclusive Economic Zone (EEZ), i.e., the region where a nation can claim exclusive rights for fishing, drilling, and other economic activities. Worth noting here is that ocean CO2 uptake or loss is not credited to any nation under Intergovernmental Panel on Climate Change (IPCC) CO2 accounting; instead, ocean uptake is viewed as an internationally shared public commons.
This review is structured as follows. First, we summarize the key variables and fluxes relevant to carbon budgets for coastal waters, summarize the mechanisms by which carbon can be removed from the atmosphere, and describe the means for quantifying the resulting carbon removal (see Sect. 2). Next, we present available research relevant to carbon budgets for North American coastal waters by region and derive a carbon budget for the North American EEZ (see Sect. 3). Last, we discuss climate-driven trends in coastal carbon fluxes and coastal ocean acidification (see Sect. 4), followed by conclusions.
2 General overview of coastal carbon fluxes and stocks
Carbon is constantly transferred among different pools and exchanged across the interfaces that demarcate coastal waters: the land–ocean interface, the air–sea interface, and the interface between coastal and open-ocean waters. Of major importance are the conversion of dissolved inorganic carbon (DIC) into particulate and dissolved organic carbon (POC and DOC), through primary production, and the reverse transformation by respiration throughout the water column, returning most of the organic carbon back into DIC. Some POC settles out of the water column and becomes incorporated into the sediments where most of this material is respired through a range of different redox processes that produce DIC and, in the absence of electron acceptors other than CO2, CH4. Both DIC and CH4 are released back into the overlying water. POC that is not respired can be buried in sediments and stored for a very long time. Some organisms also precipitate internal or external body structures of CaCO3, which either dissolve or become incorporated into the sediments and are buried. This discussion will refer to the long-term storage of carbon in coastal sediments as permanent burial.
A major carbon exchange process along ocean margins is the flux of CO2 across the air–sea interface. The annual cycle of this flux is driven by the undersaturation or oversaturation of surface ocean CO2 resulting from ocean temperature changes (which affect CO2 solubility), from primary production, respiration, and CaCO3 precipitation and dissolution, and the transport of DIC to and from the ocean surface (e.g., by upwelling and convection). Other factors that influence gas exchange across the air–sea interface are winds, sea ice extent, and surface films. Other important exchange fluxes are organic and inorganic carbon inputs from land via rivers and estuaries , inputs from tidal wetlands , and exchanges between the coastal and open oceans across the continental shelf break or the operationally defined open-ocean boundary of the coastal ocean (Fennel2010). Net removal of carbon from direct interaction with the atmosphere can occur through the export of carbon to the deep ocean or permanent burial in coastal sediments.
Carbon export, referring to the flux of organic and inorganic carbon from coastal waters to the deep ocean, can occur through the so-called continental shelf pump – a term coined by after they observed a large uptake of atmospheric CO2 in the East China Sea. There are two distinct mechanisms underlying the continental shelf pump (Fennel2010). The first is physical in nature and thought to operate in mid- and high-latitude systems. In winter, shelf water is cooled more strongly than surface water in the adjacent open ocean because the former is not subject to deep convection . The colder shelf water is denser and experiences a larger influx of atmospheric CO2; both density and the solubility of CO2 increase with decreasing temperature. If this dense and carbon-rich water is transported off the shelf, it will sink due to its higher density, and the associated carbon will be exported to the deep ocean. The second mechanism relies on biological processes that concentrate carbon below the seasonal pycnocline through the photosynthetic production of organic carbon and subsequent sinking. If the carbon-rich water below the seasonal pycnocline is moved off the shelf horizontally, carbon could potentially be exported if this water is transported or mixed below the seasonal thermocline. The depth to which the shelf-derived carbon can be exported is different for POC, which would sink, and DOC and DIC, which would primarily be advected laterally. Both mechanisms for carbon export critically depend on the physical transport of carbon-rich water off the shelf.
Carbon export flux from coastal waters to the deep ocean cannot be quantified easily or accurately through direct observation, especially considering the three-dimensional nature of exchanges between the coastal and open ocean . Thus, the only available estimates of such export are indirect, using mass balances of POC and dissolved oxygen , mass balances of DOC , mass balances of TOC and DIC , or model estimates . If the total carbon inventory in a coastal system can be considered constant over a sufficiently long timescale (i.e., of the order of years), inferring carbon export is possible using the sum of all other exchange fluxes across the system's interfaces over that same period. Export to the open ocean must balance the influx of carbon from land and wetlands, its net exchange across the air–sea interface, lateral exchange caused by advection, and any removal through permanent sediment burial. The accuracy of the inferred export flux directly depends on the accuracy of the other flux estimates and of the assumption of a constant carbon inventory. Quantifying internal transformation processes (e.g., respiration, primary and secondary production) does not directly enter this budgeting approach but can elucidate the processes that drive fluxes across interfaces.
Current estimates of carbon fluxes across coastal interfaces come with significant uncertainties . These uncertainties are caused by a combination of small-scale temporal and spatial variability, which is undersampled by currently available means of direct observation, and regional heterogeneity, which makes scaling up observations from one region to larger areas difficult. Contributing to variability in regional carbon budgets and export are geographical differences arising from variations in shelf width, upwelling strength, the presence or absence of large rivers, seasonal ice cover, and latitude. Section 3 describes the regional characteristics of North American coastal waters and how these characteristics influence carbon dynamics.
The motivation for quantifying the permanent burial of organic carbon and the export of carbon from coastal waters to the deep ocean is that both processes remove CO2 from the atmospheric reservoir. A more relevant but harder to obtain quantity in this context is the burial or export of anthropogenic carbon, i.e., the carbon that was added to the atmosphere by anthropogenic activities. Present-day carbon fluxes represent a superposition of the anthropogenic flux component and the natural background flux (see McNeil and Matear2013, for further details). Only total fluxes – the sum of anthropogenic and background fluxes – can be observed directly. Distinction between anthropogenic fluxes and the natural background is difficult to assess for coastal ocean fluxes and has to rely on process-based arguments and models .
Figure 2Observation- and model-based estimates of regional net air–sea CO2 flux in g C m−2 yr−1. Positive fluxes (red bars) indicate a flux to the atmosphere. Observation-based estimates are shown in red and dark blue. Model-based estimates are in light blue. Broken error bars are used where errors bars reach outside the range of the y axis. References: (1) , (2) using gas transfer parameterization, (3) satellite-based estimate from 2, (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) . The flux estimates are also reported in Table S1 in the Supplement.
3 Review of coastal carbon fluxes around North America
In this section we briefly describe the bathymetric and hydrographical features of the four major North American coastal margins (the Atlantic coast, the Pacific coast, the coast of the northern Gulf of Mexico, and the Arctic coast), followed by a review of available carbon flux estimates for each. Where multiple flux estimates are available for the same region it is important to keep in mind that their spatial footprints and time windows do not necessarily match exactly.
3.1 Atlantic coast
The North American Atlantic coast borders a wide, geologically passive-margin shelf that extends from the southern tip of Florida to the continental shelf of the Labrador Sea (Fig. 1). The shelf is several hundred kilometers wide in the north (Labrador shelf and Grand Banks) but narrows progressively toward the south in the Mid-Atlantic Bight (MAB), which is between Cape Cod and Cape Hatteras, and the South Atlantic Bight (SAB), which is south of Cape Hatteras. The SAB shelf width measures only several tens of kilometers. Two major semi-enclosed bodies of water are the Gulf of Maine (GOM) and Gulf of St. Lawrence. Important rivers and estuaries north of Cape Hatteras include the St. Lawrence River and Estuary, the Hudson River, Long Island Sound, Delaware Bay, and Chesapeake Bay. South of Cape Hatteras, the coastline is characterized by small rivers and marshes.
The SAB is impacted by the Gulf Stream, which flows northeastward along the shelf edge before detaching at Cape Hatteras and meandering eastward into the open North Atlantic Ocean. North of Cape Hatteras, shelf circulation is influenced by the confluence of the southwestward-flowing fresh and cold shelf-break current (a limb of the Labrador Current) and the warm and salty Gulf Stream (Loder1998). Because shelf waters north of Cape Hatteras are sourced from the Labrador Sea, they are relatively cold, fresh, and carbon rich, while slope waters (those located between the shelf break and the northern wall of the Gulf Stream) are a mixture of Labrador Current and Gulf Stream water. South of Cape Hatteras, exchange between the shelf and open ocean across the shelf break is impeded by the presence of the Gulf Stream and occurs via baroclinic instabilities in its northern wall . In the MAB and on the Scotian Shelf, cross-shelf exchange is hindered by shelf-break jets and fronts .
Air–sea fluxes of CO2 exhibit a large-scale latitudinal gradient along the Atlantic coast (Fig. 2) and significant seasonal and interannual variability (Fig. 3). Discrepancies in independent estimates of net air–sea flux are largest for the Scotian Shelf and the Gulf of Maine (Fig. 2). For the Scotian Shelf, , combining in situ and satellite observations, reported a large source of CO2 to the atmosphere of 8.3±6.6 g C m−2 yr−1. In contrast, estimated a relatively large sink of atmospheric CO2, 14±3.2 g C m−2 yr−1, when using in situ data alone and a much smaller uptake, 5.0±4.3 g C m−2 yr−1, from a combination of in situ and satellite observations. The open GOM (excluding the tidally mixed Georges Bank and Nantucket Shoals) was reported as a weak net source of 4.6±3.1 g C m−2 yr−1 by but with significant interannual variability, while estimated the region to be neutral (Table S1). The shallow, tidally mixed Georges Bank and Nantucket Shoals are thought to be sinks, however (Table S1).
The MAB and SAB are consistently estimated to be net sinks. Observation-based estimates for the MAB sink are 13±8.3 and 13±3.2 g C m−2 yr−1 . Estimates for the SAB sink are 5.8±2.5 and 8.2±2.9 g C m−2 yr−1 . The transition from a neutral or occasional net source on the Scotian Shelf and in the GOM to a net sink in the MAB arises because the properties of shelf water are modified during its southwestward flow by air–sea exchange, inflows of riverine and estuarine waters , and exchange with the open North Atlantic across the shelf break . The cold, carbon-rich water on the Scotian Shelf carries a pronounced signature of its Labrador Sea origin. The GOM, which is deeper than the Scotian Shelf and the MAB and connected to the open North Atlantic through a relatively deep channel, is characterized by a mixture of cold, carbon-rich shelf waters entering from the Scotian Shelf and warmer, saltier slope waters. Shelf water in the MAB is sourced from the GOM and is thus a mixture of Scotian Shelf and slope water.
Shelf water in the SAB is distinct from that in the MAB and has almost no trace of Labrador Current water; instead, its characteristics are similar to those of the Gulf Stream, but its carbon signature is modified by significant organic and inorganic carbon and alkalinity inputs from coastal marshes . estimated that 59 % of the 3.4 Tg C yr−1 of organic carbon export from US East Coast estuaries occurs in the SAB. The subsequent respiration of this organic matter and direct outgassing of marsh-derived carbon make the nearshore regions a significant CO2 source almost year-round. Despite the carbon inputs from marshes, the uptake of CO2 on the mid-shelf and outer-shelf regions during the winter months is large enough to balance CO2 outgassing in the other seasons and on the inner shelf, making the SAB an overall weak sink .
The seasonality of CO2 dynamics along the Atlantic coast varies with latitude. North of Cape Hatteras, CO2 dynamics are characterized by strong seasonality with solubility-driven uptake by cooling in winter and biologically driven uptake in spring followed by outgassing in summer and fall due to warming and respiration of organic matter . South of Cape Hatteras, seasonal phytoplankton blooms do not occur regularly and biologically driven CO2 uptake is less pronounced than that further north (Fig. 3e; Reimer et al.2017; Wang et al.2013), although sporadic phytoplankton blooms do occur because of intrusions of high-nutrient subsurface Gulf Stream water . The influence of riverine inputs is small and localized in the SAB . An exception to this north–south importance in riverine input is the GOM, where riverine inputs of carbon and nutrients are relatively small. Nevertheless, even here, these inputs can cause local phytoplankton blooms, CO2 drawdown, and low-pH conditions .
Figure 3Observations of pCO2 (in µatm) in the surface ocean (black) and overlying atmosphere (blue) at five coastal moorings. Map shows mooring locations. Also shown on the map is the location of the Hawaii Ocean Time Series (see Fig. 6). Data sources: Bering Sea (mooring M2; Cross et al.2014a); Washington coast (Cape Elizabeth mooring; Mathis et al.2013); California Current (mooring CCE2; Sutton et al.2012); coastal western Gulf of Maine mooring ; South Atlantic Bight (Gray's Reef mooring; Sutton et al.2011)
Regional biogeochemical models reproduce the large-scale patterns of air–sea CO2 flux with oceanic uptake increasing from the SAB to the GOM . These model studies elucidate the magnitude and sources of interannual variability as well as long-term trends in air–sea CO2 fluxes. investigated opposite phases of the North Atlantic Oscillation (NAO) and found that the simulated air–sea flux in the MAB and GOM was 25 % lower in a high-NAO year compared to a low-NAO year. In the MAB, the decrease primarily resulted from changes in wind forcing, while in the GOM changes in surface temperature and new production were more important. investigated the impact of future climate-driven warming and trends in atmospheric forcing (primarily wind) on air–sea CO2 flux (without considering the atmospheric increase in CO2). Their results suggest that warming and changes in atmospheric forcing have modest impacts on air–sea CO2 flux in the MAB and GOM compared to that in the SAB where surface warming would turn the region from a net sink into a net source of CO2 to the atmosphere if the increase in atmospheric CO2 were ignored. Model studies also illustrate the effects of interactions between biogeochemical transformations in the sediment and the overlying water column on carbon fluxes. For example, showed that the effective alkalinity flux resulting from denitrification in sediments of the Atlantic coast reduces the simulated ocean uptake of CO2 by 6 % compared to a simulation without sediment denitrification.
The passive-margin sediments along the Atlantic coast have not been considered an area of significant CH4 release until recently . predicted that massive seepage of CH4 from upper-slope sediments is occurring in response to warming of intermediate-depth Gulf Stream waters. and documented widespread CH4 plumes in the water column and attributed them to gas hydrate degradation. Estimated CH4 efflux from the sediment in this region ranges from $\mathrm{1.5}×{\mathrm{10}}^{-\mathrm{5}}$ to $\mathrm{1.8}×{\mathrm{10}}^{-\mathrm{4}}$ Tg yr−1, and the uncertainty range reflects different assumptions underlying the conversion from CH4 plume observations to seepage rates. The fraction of the released CH4 that escapes to the atmosphere remains uncertain .
3.2 Pacific coast
The North American Pacific coast extends from Panama to the Gulf of Alaska and is an active margin with varying shelf widths (Fig. 1). The continental shelf is narrow along the coasts of California, Oregon, and Washington, of the order of 10 km, but widens significantly in the Gulf of Alaska, where shelves extend up to 200 km offshore. In the Gulf of Alaska, freshwater and tidal influences strongly affect cross-shelf exchange, and the shelf is dominated by a downwelling circulation. The region from Vancouver Island to Baja California is a classic eastern boundary current upwelling region – the California Current System . Winds drive a coastal upwelling circulation characterized by equatorward flow in the California Current and by coastal jets and their associated eddies and fronts that extend offshore, particularly off the coasts of Baja California, California, Washington, and Oregon (Huyer1983).
The northern California Current System experiences strong freshwater influences and seasonality in wind forcing that diminish toward the south. In addition to the Columbia River and the Fraser River, a variety of small mountainous rivers, with highly variable discharge, supply freshwater. The Central American Isthmus runs from Panama to the southern tip of Baja California and experiences intense and persistent wind events, large eddies, and high waves that combine to produce upwelling and strong nearshore mixing . In addition to alongshore winds, strong seasonal wind jets that pass through the Central American cordillera create upwelling hot spots and drive production during boreal winter months in the gulfs of Tehuantepec, Papagayo, and Panama . The California Current brings water from the North Pacific southward into the southern California and Central American Isthmus regions, while the California Undercurrent transports equatorial waters northward in the subsurface (Hickey1998).
The net exchange of CO2 with the atmosphere along the Pacific coast is characterized by strong spatial and temporal variation and reflects complex interactions between the biological uptake of nutrients and degassing of nutrient- and carbon-rich upwelled waters (Fig. 3b, c). A growing number of coastal air–sea flux studies have used extrapolation techniques to estimate fluxes across the coastal oceans on regional to continental scales (Fig. 2). Observation-based studies of air–sea CO2 flux suggest that estimates for the coastal ocean from Baja California to the Gulf of Alaska range from a weak to moderate sink of atmospheric CO2 over this broad longitudinal range. Central California coastal waters have long been understood to have a near-neutral air–sea CO2 exchange because of their large and counterbalancing periods of efflux during upwelling conditions and influx during periods of relaxation and high primary productivity; this pattern is strongly modulated by El Niño–La Niña conditions .
used seasonal data to estimate an uptake of 88 g C m−2 yr−1 by Oregon coastal waters. In a follow-up analysis with greater temporal coverage, showed how large flux events can significantly alter the estimation of net exchanges for the Oregon shelf. After capturing a large and short-lived efflux event, their annual estimate was outgassing of 3.1±82 g C m−2 yr−1 for this same region. The disparity illustrates the importance of basing regional flux estimates on observations that are well resolved in time and space. Capitalizing on the increased and more uniform spatiotemporal coverage of satellite data, estimated an annual mean uptake of 7.9 g C m−2 yr−1 between 22 and 50 N within 370 km offshore. The most northern estimates for the Pacific coast by and are influxes of 26 g C m−2 yr−1 for British Columbian coastal waters shoreward of the 500 m isobath and 18 g C m−2 yr−1 for Gulf of Alaska coastal waters shoreward of the 1500 m isobath.
Models for the upwelling region reproduce the pattern of CO2 outgassing nearshore and CO2 uptake further offshore. They also illustrate the intense eddy-driven variability nearshore. simulate a weak source of 0.6±2.4 g C m−2 yr−1 for the region from 30 to 46 N extending 800 km of shore. In contrast, reported a sink of 7.9 g C m−2 yr−1 based on observations for the same latitudinal band but only extending 370 km of shore. simulate a source of atmospheric CO2 of 0.6 Tg C yr−1 for the region from 35 to 45 N within 600 km of shore, also in contrast to the observation-based estimate of a 14 Tg C yr−1 sink published by . (The estimate of , is not included in Fig. 2 because the area-normalized flux is not available from that study.) Both models simulate strong outgassing within the first 100 km of shore driven by intense upwelling of nutrient- and carbon-rich water, which is compensated for by biologically driven CO2 uptake from the atmosphere as upwelled nutrients are consumed by photosynthesis during subsequent offshore advection within several hundreds of kilometers of the coast. The disagreement in mean simulated fluxes between the two models may partly result from different choices of averaging region and period and differences in model forcing, such as the climatological forcing in versus realistic variability in . Notably, observations for the Oregon shelf by showed intense summer upwelling that led to strong outgassing with pronounced variability in air–sea fluxes but only weak stimulation of primary production. They hypothesized that nutrient-rich waters might be subducted offshore at convergent surface temperature fronts before nutrients are fully consumed by primary producers.
The cross-shelf exchange of carbon occurs in the California Current System mostly in response to wind-driven circulation and eddies, but river plumes and tides have also been shown to increase offshore transport in the northern part of the system . Uncertainties in published estimates are high, ranging from very small to very high fractions of primary production , again as a result of the region's large spatial and temporal variability. showed that about 30 % of the organic matter produced within 100 km of shore is laterally advected toward the open ocean.
Less is known about the air–sea flux of CH4 along the Pacific margin. Recent studies inventoried sedimentary sources of CH4 hydrates, derived from terrestrial and coastal primary production, and suggested that extensive deposits along the Cascadia margin are beginning to destabilize because of warming .
3.3 Gulf of Mexico
The Gulf of Mexico is a semi-enclosed marginal sea at the southern coast of the conterminous United States. The passive-margin shelves of its northern portion are relatively wide (up to 250 km west of Florida) but, in contrast to shelf waters of the Atlantic coast, those of the Gulf of Mexico are not separated from open-ocean waters by shelf-break fronts or currents. Ocean water enters the gulf mainly through the Yucatán Channel, where it forms the northeastward meandering Loop Current, which sheds anticyclonic eddies and exits the gulf through the Florida Straits . While shelf circulation is primarily influenced by local wind and buoyancy forcing, outer-shelf regions are at times influenced by Loop Current eddies that impinge on and interact with the shelf . Riverine input is substantial in the northern Gulf of Mexico, where the Mississippi–Atchafalaya river system delivers large loads of freshwater, nutrients, and sediments.
Estimates of air–sea CO2 flux are available from observations and model simulations (Fig. 2). Observational estimates indicate that the Gulf of Mexico, as a whole, is a weak net sink of atmospheric CO2 with an annual average of 2.3±1.0 g C m−2 yr−1 . Smaller shelf regions within the gulf differ markedly from this mean flux. The West Florida shelf and western gulf shelf act as sources to the atmosphere, with estimated annual average fluxes of 4.4±1.3 and 2.2±0.6 g C m−2 yr−1, respectively; the northern gulf acts as a sink, with an estimated flux of 5.3±4.4 g C m−2 yr−1, and the Mexican shelf is almost neutral, with an estimated uptake flux of 1.1±0.6 g C m−2 yr−1 . A more recent estimate for the west Florida shelf is 4.4±18.0 g C m−2 yr−1 . estimated a larger uptake on the northern gulf shelf of 11±44 g C m−2 yr−1 (i.e., about twice the estimate of ) and reported a much larger uncertainty. In an analysis that combines satellite and in situ observations, estimated a similar uptake for the northern Gulf of Mexico of 13±3.6 g C m−2 yr−1. The overall air–sea carbon exchanges in the gulf vary significantly from year to year because of interannual variability in wind, temperature, and precipitation .
Model-simulated air–sea CO2 fluxes by agree relatively well with the estimates of , reproducing the same spatial pattern though their simulated gulf-wide uptake of 8.5±6.5 g C m−2 yr−1 is larger. This discrepancy results largely from a greater simulated sink in the open gulf. Also, the uncertainty estimates of the model-simulated fluxes by are much larger than those of ; the latter might be too optimistic in reporting uncertainties of the flux estimates. Overall, the various observation- and model-derived estimates for gulf regions agree in terms of their broad patterns, but existing discrepancies and, at times, large uncertainties indicate that current estimates need further refinement.
The quantitative understanding of CH4 dynamics in coastal and oceanic environments of the Gulf of Mexico is limited. speculated that deep CH4 hydrate seeps in the gulf are a potentially significant CH4 source to the atmosphere. They estimated ocean–atmosphere fluxes from seep plumes of 1150±790 to 38 000±21 000 g CH4 m−2 d−1 compared with 2.2±2.0 to 41±8.2 g CH4 m−2 d−1 for background sites. Subsequent acoustic analyses of bubble plume characteristics question the finding that CH4 bubbles make their way to the surface , and the fate of CH4 emissions from seeps and their overall contribution to atmospheric CH4 remain uncertain.
3.4 Arctic coast
The North American Arctic coastal ocean comprises broad (∼300 km) shallow shelves in the Bering and Chukchi seas, the narrower (<100 km) Beaufort Sea shelf, Hudson Bay, and the extensive Canadian Arctic shelf (Fig. 1). Shelf water enters these regions from the North Pacific through the Bering Strait and follows a large-scale pathway via the Chukchi and Beaufort seas onto the Canadian Arctic shelf and, ultimately, the North Atlantic . Hudson Bay receives significant inputs of freshwater . Except for the southernmost Bering Sea, most of the coastal Arctic is covered with sea ice from about October to June. Areas of persistent multiyear sea ice at the northernmost extent of the Canadian Arctic shelf are rapidly declining .
Coastal waters in the Arctic have been consistently described as a net sink for atmospheric CO2 (Fig. 2). An observation-based estimate for uptake in the Bering Sea is 9.6 g C m−2 yr−1 by . Estimates for the Chuckchi Sea range from 15 g C m−2 yr−1 to 175±44 g C m−2 yr−1(Bates2006). For the Beaufort Sea, estimates range from 4.4 g C m−2 yr−1 to 44±28 g C m−2 yr−1 . In Hudson Bay, estimated an uptake of 3.2±1.8 g C m−2 yr−1. The consistently observed uptake is thought to be caused by low surface water pCO2 relative to the atmosphere during ice-free months (see, e.g., Fig. 3a). These low levels are set by a combination of low water temperatures and seasonally high rates of both ice-associated and open-water primary production , as well as by limited gas exchange through sea ice relative to open water during winter .
In recent years, sea ice growth and decay has been shown to significantly affect the air–sea CO2 flux . During sea ice formation, brine rejection forms dense high-saline water that is enriched in DIC relative to alkalinity . During sea ice decay, an excess of alkalinity relative to DIC is released in meltwater. The sinking of dense, carbon-rich brine provides a pathway for carbon sequestration as suggested by , although modeling studies suggest that carbon export through this process is relatively small .
With regard to Arctic CH4 fluxes, much more is known about the emission potential, distribution, and functioning of terrestrial sources ; knowledge of marine CH4 sources is developing slowly due to sparse observations and the logistical challenges of Arctic marine research. The largest marine CH4 source in the Arctic is the dissociation of gas hydrates stored in continental margin sediments . As sea ice cover continues to retreat and ocean waters warm, CH4 hydrate stability is expected to decrease with potentially large and long-term implications. An additional potential marine CH4 source, unique to polar settings, is release from subsea permafrost layers, with fluxes from thawed sediments reported to be orders of magnitude higher than fluxes from adjacent frozen sediments .
Table 1Regional estimates of net air–sea CO2 flux from a global data synthesis and a global biogeochemical model for the MARgins and CATchments Segmentation (MARCATS) regions. MARCATS segments are named as follows: (1) northeastern Pacific, (2) California Current, (3) eastern tropical Pacific, (9) Gulf of Mexico, (10) Florida upwelling, (11) Labrador Sea, (12) Hudson Bay, (13) Canadian Arctic Archipelago. Positive numbers indicate a flux to the atmosphere; 1 Tg = 1012 g.
3.5 Summary estimate of CO2 uptake and a carbon budget for the North American EEZ
Despite the variability in regional estimates discussed above and summarized in Fig. 2 and Table S1, North American coastal waters clearly act as a net sink of atmospheric carbon. However, because of the local footprint of some studies, discrepancies in temporal and spatial coverage among studies, and gaps in space and time, it is difficult to combine these various regional estimates into one summary estimate of CO2 uptake for the North American EEZ with any confidence. In order to arrive at such a summary estimate, we draw on the regional information compiled in the previous sections in combination with two global approaches: the observation-based synthesis of and the process-based global model of .
First, we compare estimates from the two global approaches, which are available for a global segmentation of the coastal zone and associated watersheds known as MARCATS (MARgins and CATchments Segmentation; Laruelle et al.2013). At a resolution of 0.5, MARCATS delineates a total of 45 coastal segments, eight of which surround North American. analyzed the Surface Ocean CO2 Atlas 2.0 database and estimated an uptake in the North American MARCATS, excluding Hudson Bay, of 44.5 Tg C yr−1 (Table 1). The process-based model of simulated an uptake of 48.8 Tg C yr−1, or 45.0 Tg C yr−1 when excluding Hudson Bay (Table 1). Although there are significant regional discrepancies between the two estimates for the eastern tropical Pacific Ocean, the Gulf of Mexico, the Florida upwelling region (actually covering the eastern United States including the SAB, MAB, and GOM), the Labrador Sea, and the Canadian Arctic shelf, the total flux estimates for North America are in close agreement. This builds some confidence in the global model estimates.
Figure 4North American continent with EEZ decomposition (indicated by black outlines). Selected area-specific regional CO2 flux estimates from Fig. 2 are shown in comparison to the global model estimates (referred to as 1) in (a, b, d) (see Fig. 2 for reference key). “X” indicates that no regional estimate is available. Total CO2 flux estimates from the global model and the anthropogenic components are shown in (c, e). Subregion abbreviations are MAB – Mid-Atlantic Bight, GOM – Gulf of Maine, SS – Scotian Shelf, GStL – Gulf of St. Lawrence and Grand Banks, LS – Labrador shelf, HB – Hudson Bay, CAS – Canadian Arctic shelf, BCS – Beaufort and Chukchi seas, BS – Bering Sea, GAK – Gulf of Alaska, NCCS – northern California Current System, CCCS – central California Current System, SCCS – southern California Current System, Isthmus – American isthmus, GMx – Gulf of Mexico and Yucatán Peninsula, SAB – South Atlantic Bight.
Next, we use the global model to obtain CO2 flux estimates for the North American EEZ in a finer-grained decomposition (Fig. 4, Table 2). First, we compare the regional area-specific flux estimates from Fig. 2 and Table 2 with the global model (see Fig. 4a, b, d). For the Atlantic coast there is excellent agreement for the SAB, but the global model simulates a higher CO2 uptake than the regional studies in the MAB, GOM, and the Scotian Shelf. This discrepancy is likely due to the fact that the global model is too coarse to accurately simulate the shelf-break current systems and thus significantly underestimates the water residence times on the shelf . No regional estimates are available for the Gulf of St. Lawrence. For the Pacific coast and the Gulf of Mexico, the global model's estimates are within the range of available regional estimates for the Gulf of Alaska, the northern California Current System, and the Gulf of Mexico. In the central and southern California Current System, the model favors outgassing more than in the regional estimates. In the sub-Arctic and Arctic regions, the global model's estimates are smaller than the regional ones for the Beaufort and Chukchi seas and Hudson Bay, but they are similar for the Bering Sea. No regional estimates are available for the Canadian Arctic shelf and Labrador shelf.
Conversion of the area-specific fluxes to total fluxes (see Fig. 4c, e) shows that the Labrador shelf, Gulf of Alaska, and Bering Sea are the biggest contributors to the total flux in the North American EEZ in the global model. For the Labrador shelf, the region with the largest flux estimate, there are no regional estimates available. For the two next largest, the Gulf of Alaska and the Bering Sea, the global model agrees well with the regional estimates. Thus, despite some regional discrepancies, it seems justifiable to use the global model estimates for a North American coastal carbon budget. The model simulates a net uptake of CO2 in the North American EEZ (excluding the EEZ of the Hawaiian and other islands) of 160 Tg C yr−1 with an anthropogenic flux contribution of 59 Tg C yr−1. The three biggest contributors (LS, GAK, and BS; see Fig. 4) account for 93 Tg C yr−1, 58 % of the total uptake, with an anthropogenic flux contribution of 26 Tg C yr−1, while making up only 29 % of the combined EEZ area. These three regions have a large contribution because they are characterized by large area-specific fluxes and they are vast. The global model also estimates large fluxes for the MAB, GOM, and SS, which are probably overestimates, but these regions are significantly smaller and thus contribute much less (28 Tg C yr−1) to the overall flux estimate. When dividing the North American EEZ into the Arctic and sub-Arctic (GAK, BS, BCS, CAS, HB, LS), mid-latitude Atlantic (GMx, SAB, MAB, GOM, SS, GStL), and mid-latitude Pacific (CCN, CCC, CCS, Isthmus), their relative flux contributions are 104, 62, and 3.7 Tg C yr−1, respectively, with area contributions of 51 %, 25 %, and 24 % to the total area of the North American EEZ, respectively.
Next, we construct a carbon budget for the North American EEZ by combining the atmospheric CO2 uptake estimate with estimates of carbon transport from land and carbon burial in ocean sediments. We assume 160 Tg C yr−1 as the best estimate of net uptake by coastal waters of North America, excluding tidal wetlands and estuaries. Unfortunately, there are no formal error estimates for this uptake. Instead, we estimate an error by first noting that the model is in good agreement with the observation-based estimates for the MARCATS regions of North America; furthermore, the error estimate for the uptake by continental shelves globally is about 25 %, with the North American MARCATS regions having mainly “fair” data quality . Hence, assuming an error of ±50 % for the uptake by North American EEZ waters seems reasonable.
Carbon delivery to the coastal ocean from land via rivers and from tidal wetlands after estuarine processing (i.e., CO2 outgassing and carbon burial in estuaries) is estimated to be 106±30 Tg C yr−1 . Estimates of carbon burial, based on the method of for the regional decomposition of the North American EEZ, are reported in Table 2, with a total flux of 120 Tg C yr−1. We consider these fluxes to be an upper bound because they are substantially larger than other estimates. The global estimates of organic carbon burial in waters shallower than 2000 m are 19±9 g C m−2 yr−1, much larger than the estimates of 6 and 1 g C m−2 yr−1 by Chen (2004) and , respectively, although the areas are slightly different in the three studies. The organic carbon burial estimates of for the GOM, MAB, and SAB (Table 2) are larger by factors of 8, 17, and 3, respectively, than the best estimates of the empirical model of . However, due to different definitions of the boundary between coastal waters and the open ocean, the combined area of the GOM, MAB, and SAB in is about a third of that of . Finally, estimated the organic carbon burial in Hudson Bay to be 19 g C m−2 yr−1 compared to a mean estimate of 1.5±0.7 g C m−2 yr−1 of burial from sediment cores . Given these results, we consider the estimates of to be an upper bound and assume that a reasonable lower bound is about an order of magnitude smaller, thus placing the organic carbon burial estimate at 65±55 Tg C yr−1.
Figure 5Carbon budget for the EEZ of the USA, Canada, and Mexico excluding the EEZs of Hawaii and other islands. Here positive fluxes are a source to the coastal ocean. The accumulation of DIC in EEZ waters is reported with a negative sign to illustrate that all fluxes balance.
If these estimates of net air–sea flux, carbon burial, and carbon input from land are accurate, then the residual must be balanced by an increase in carbon inventory in coastal waters and a net transfer of carbon from coastal to open-ocean waters (Fig. 5). The rate of carbon accumulation in the North American EEZ from the model of is 50 Tg C yr−1 (Fig. 5). Here again, we assume an uncertainty of ±50 %. The residual of 151±105 Tg C yr−1 is the inferred export of carbon to the open ocean (Fig. 5). The fact that the error in this residual is large in absolute and relative terms emphasizes the need for more accurate quantification of the terms in the coastal carbon budget. The challenge, however, is that many of these terms are small compared to internal carbon cycling in coastal waters, which is dominated by primary production and decomposition. Two separate estimates of primary production (Table 2) are in broad agreement and reveal that the fluxes in Fig. 5 (of the order of 10 to 100 Tg C yr−1) are just a few percent of primary production (of the order of 1000 Tg C yr−1; see total in Table 2). This also indicates that small changes in carbon cycling in coastal waters can result in large changes in atmospheric uptake and transport to the open ocean.
Table 2Estimates of satellite-derived carbon burial and primary production (NPP) from and model-simulated NPP and air–sea CO2 flux from for a decomposition of the EEZ of Canada, the US, and Mexico. Model estimates are calculated by averaging the years 1993–2012. Positive numbers represent fluxes into the coastal ocean. Subregion abbreviations are given in the caption of Fig. 4.
4 Trends in carbon fluxes and acidification in North American coastal waters
4.1 Carbon flux trends
Two important open questions remain: how will the coastal ocean CO2 sink and its anthropogenic flux component change in the future? And how will changing climate and other forcings affect the total and anthropogenic flux proportions? As stated in Sect. 2, when considering the ocean's role in sequestering anthropogenic carbon, the most relevant component is anthropogenic flux, not the total uptake flux. Neither quantifying the anthropogenic carbon flux component nor predicting its future trend is straightforward. Here we only describe the factors likely to result in trends in total carbon fluxes, but changes in total carbon fluxes suggest changes in anthropogenic fluxes as well.
A direct effect of increasing atmospheric CO2 will be an increase in net uptake by the coastal ocean, but this is tempered by a decrease in the ocean's buffer capacity as DIC increases. More indirect effects include changes in climate forcings (i.e., surface heat fluxes, winds, and freshwater input).
Ocean warming reduces the solubility of gases and thus directly affects gas concentrations near the surface; this will likely decrease the net air–sea flux of CO2 by reducing the undersaturation of CO2 (see Cahill et al.2016, for the North American Atlantic coast). Surface warming may also strengthen vertical stratification and thus impede vertical mixing, which will affect the upward diffusion of nutrients and DIC. Enhanced stratification could therefore lead to decreases in both biologically driven carbon uptake and CO2 outgassing. However, model projections for the northern Gulf of Mexico show that the direct effect of increasing atmospheric CO2 overwhelms the other more secondary effects . Along the Pacific coast, surface warming will increase the horizontal gradient between cold, freshly upwelled source waters and warm, offshore surface water, leading to a greater tendency for the subduction of upwelled water at offshore surface temperature fronts during periods of persistent and strong upwelling-favorable winds. The cumulative effect of these processes for the Pacific coast may be greater and more persistent CO2 outgassing nearshore and lower productivity offshore as upwelled nitrate is exported before it can be used by the phytoplankton community . In the Arctic, warming leads to reductions in ice cover, which increases air–sea gas exchange , and the melting of permafrost, which leads to the release of large quantities of CH4 to the atmosphere, from both the land surface and the coastal ocean .
Changes in wind stress directly affect air–sea CO2 fluxes via the gas transfer velocity, which is a function of wind speed, but also indirectly through changes in ocean circulation (Bakun1990). For the North American Atlantic coast, changes in wind stress were shown to significantly modify air–sea fluxes . Along the North American Pacific coast, upwelling-favorable winds have intensified in recent years, especially in the northern parts of the upwelling regimes . This has led to a shoaling of nutrient-rich subsurface waters , increased productivity , higher DIC delivery to the surface , and declining oxygen levels . In the coastal Arctic, late-season air–sea CO2 fluxes may become increasingly directed toward the atmosphere as Arctic low-pressure systems with storm-force winds occur more often over open water, thus ventilating CO2 respired from the high organic carbon loading of the shallow shelf .
In a study that directly assesses changes in coastal carbon uptake, investigated trends in the air–sea pCO2 gradient (ΔpCO2= atmospheric pCO2 ocean pCO2), which imply a strengthening or weakening of the net CO2 uptake by shelf systems. An increasing ΔpCO2 implies that ocean pCO2 rises more slowly than atmospheric pCO2 and corresponds to increased net uptake and potentially increased cross-shelf export. In their observation-based analysis of decadal trends in shelf pCO2, found that coastal waters lag compared to the rise in atmospheric CO2 in most regions. In the MAB, the Labrador shelf, the Vancouver shelf, and the SAB, ΔpCO2 has increased by 1.9±3.1, 0.68±0.61, 0.83±1.7, and 0.51±0.74µatm yr−1, respectively, implying that surface ocean pCO2 does not increase or increases at a slower rate than atmospheric CO2. The only North American coastal region that exhibits a negative trend is the Bering Sea, with $-\mathrm{1.1}±\mathrm{0.74}$µatm yr−1, meaning that surface ocean pCO2 increases at a faster rate than in the atmosphere. concluded that the lag in coastal ocean pCO2 increase compared to that in the atmosphere in most regions indicates an enhancement in the coastal uptake and export of atmospheric CO2, although they did not investigate alternative explanations.
Figure 6Atmospheric CO2 (black dots) measured at the Mauna Loa Observatory in Hawaii beginning in 1958 and surface ocean pCO2 data (blue dots) from the Hawaii Ocean Time Series (HOT) station (see Fig. 3 for site location). Black and blue lines indicate linear trends after 1990. Atmospheric CO2 increased by 1.86±0.11 ppm yr−1. Surface ocean pCO2 increased by 1.95±0.017µatm yr−1. pCO2 is calculated using CO2SYS, with Mehrbach refit coefficients for the dissociation constants of H2CO3 and ${\mathrm{HCO}}_{\mathrm{3}}^{-}$, and Dickson's dissociation constant for ${\mathrm{HSO}}_{\mathrm{4}}^{-}$. Data sources: Mauna Loa (http://www.esrl.noaa.gov/gmd/ccgg/trends/data.html, last access: 1 May 2018); HOT (http://hahana.soest.hawaii.edu/hot/hot-dogs/interface.html, last access: 1 May 2018).
4.2 Acidification trends
Increasing atmospheric CO2 emissions lead to rising atmospheric CO2 levels (Fig. 6) and a net ocean uptake of CO2. Since about 1750, the ocean has absorbed 27 % of anthropogenic CO2 emissions to the atmosphere from fossil fuel burning, cement production, and land-use changes . As a result of this uptake, the surface ocean pCO2 has increased (Fig. 6) and oceanic pH, carbonate ion concentration, and carbonate saturation state have decreased . Commonly called “ocean acidification”, this suite of chemical changes is defined more precisely as “any reduction in the pH of the ocean over an extended period, typically decades or longer, which is caused primarily by uptake of CO2 from the atmosphere but can also be caused by other chemical additions or subtractions from the ocean” (IPCC2011, p. 37). In addition to the uptake of CO2 from the atmosphere, variations in DIC concentrations and thus pH can be caused by ocean transport processes and biological production and respiration. Ocean acidification can significantly affect the growth, metabolism, and life cycles of marine organisms and most directly affects marine calcifiers, organisms that precipitate CaCO3 to form internal or external body structures. When the carbonate saturation state decreases below the equilibrium point for carbonate precipitation–dissolution, conditions are said to be corrosive, or damaging, to marine calcifiers. Ocean acidification makes it more difficult for calcifying organisms to form shells or skeletons, perform metabolic functions, and survive. Early life stages are particularly vulnerable as shown by recent large-scale die-offs of oyster larvae in the coastal Pacific where increased energetic expenses under low pH have led to compromised development of essential functions and insufficient initial shell formation .
Acidification trends in open-ocean surface waters tend to occur at a rate that is commensurate with the rate of the increase in atmospheric CO2 (see trends of atmospheric CO2 in comparison to surface ocean pCO2 from the Hawaii Ocean Time Series in Fig. 6). Acidification in coastal waters is more variable and often event-driven because coastal waters have greater seasonality (Fig. 3) and are more susceptible to changes in circulation, such as upwelling. Along the Pacific coast, climate-driven changes in upwelling circulation result in coastal acidification events . As mentioned in Sect. 3.2, upwelling-favorable winds along this coast have intensified over recent years, especially in the northern parts of the upwelling regime . Intensified upwelling supplies deep water to the shelf that is rich in DIC and nutrients but poor in oxygen. Ocean acidification and hypoxia are thus strongly linked ecosystem stressors because low-oxygen, high-CO2 conditions derive from the microbial respiration of organic matter . In the northern California Current System, pCO2, pH, and aragonite saturation reach levels known to be harmful to ecologically and economically important species during the summer upwelling season . In the Gulf of Alaska, aragonite saturation drops to near saturation values during the winter months when deep mixing occurs and surface ocean pCO2 exceeds atmospheric pCO2 . Along the Pacific coast, 50 % of shelf waters are projected to experience year-long undersaturation by 2050 .
Polar regions are naturally prone to low pH values and thus closer to critical acidification thresholds than lower-latitude waters. The low pH levels result from the naturally high ratio of DIC to alkalinity in polar waters due to their low temperatures, multiple sources of freshwater (e.g., riverine, glacial melt, and sea ice melt), and high respiratory DIC content. In addition to the naturally low pH, the rate of acidification is relatively high in polar waters because retreating sea ice adds meltwater from multiyear ice and increases the surface area of open water, thereby enhancing the uptake of atmospheric CO2 . The Beaufort Sea upper halocline and deep waters already show aragonite undersaturation, i.e., aragonite saturation states below 1, favoring dissolution . These chemical seawater signatures are propagated via M'Clure Strait and Amundsen Gulf into the Canadian Arctic shelf and beyond . Model projections based on the IPCC high-CO2 emissions scenario RCP8.5 suggest the Beaufort Sea surface water will become undersaturated with respect to aragonite around 2025 . As these conditions intensify, negative impacts for calcifying marine organisms are expected to become a critical issue reshaping ecosystems and fisheries across the Arctic .
In contrast, surface aragonite saturation states typically range from 3.6 to 4.5 and are thus well above the dissolution threshold in the northern Gulf of Mexico . Here excessive nutrient inputs from the Mississippi River result in hypoxia and the eutrophication-induced acidification of near-bottom waters . Similar to the California Current System, low-oxygen and high-CO2 conditions coincide and derive from the microbial respiration of organic matter . Currently, aragonite saturation states are around 2 in hypoxic bottom waters and thus well above the saturation threshold. Projections suggest that the aragonite saturation states of these near-bottom waters will drop below the saturation threshold near the end of this century .
Along the Atlantic coast, the northern regions (the Mid-Atlantic Bight and Gulf of Maine) have, on average, lower pH and lower aragonite saturation states than more southern coastal regions (i.e., the South Atlantic Bight) . These properties are primarily explained by a decrease in alkalinity from the SAB toward the GOM. The seasonal undersaturation of aragonite in subsurface water is already occurring in the GOM, which supports a significant shellfish industry .
5 Conclusions
Tremendous progress has been made during the last decade in improving understanding and constraining rates of carbon cycling in coastal waters because of a greatly expanded suite of observations, process studies, and models. However, the quantification of many coastal carbon fluxes remains difficult. One of the challenges is that carbon is constantly exchanged across a multitude of interfaces, i.e., the sea surface and the interfaces between land and coastal ocean, coastal, and open-ocean waters, as well as water and sediment. Furthermore, net exchange fluxes and trends are relatively small signals masked by a large and fluctuating background. At present, most of these fluxes are not quantified well enough to derive well-constrained carbon budgets for North American coastal waters or to project how those fluxes will change in the future due to various drivers.
This synthesis focused primarily on the role of ocean margins in sequestering atmospheric CO2 and coastal ocean acidification. In the coastal ocean, a net removal of carbon from direct interaction with the atmosphere can occur through the export of dissolved or particulate carbon to the deep ocean or through permanent burial in sediments. Neither of these is easily observed or well quantified. The best-observed flux is gas exchange across the air–sea interface, although extracting the small net flux and its trend from a variable background with large-amplitude seasonal fluctuations is difficult. Ultimately, the uptake of anthropogenic carbon is the relevant quantity for assessing the contribution of ocean margins to the total ocean uptake of anthropogenic carbon; however, the separation of anthropogenic fluxes from the natural background is thus far elusive for coastal waters. The only available estimates are from a global modeling study .
Estimates of air–sea CO2 fluxes currently provide the best evidence for the contribution of coastal waters to overall carbon uptake by the ocean. Our synthesis of regional studies shows that, overall, the North American coastal waters act as a sink of atmospheric CO2. The limited temporal and spatial footprint of many of these studies and gaps in spatial coverage (e.g., no estimates exist for the Labrador Sea and Canadian Arctic shelf) prevented us from combining these regional studies into a summary estimate for the North American EEZ. Instead, we compared the regional studies to the global model of for a fine-grained decomposition of the North American EEZ. The reasonable agreement between the regional studies and estimates from the global model builds some confidence in the model estimate of 160 Tg C yr−1 of uptake for the North American EEZ (with an anthropogenic flux contribution of 59 Tg C yr−1). The Labrador Sea, Gulf of Alaska, and Bering Sea are the biggest contributors, making up more than half of the total uptake (and almost half of the anthropogenic uptake) while accounting for less than one-third of the surface area of the EEZ. The Arctic and sub-Arctic, mid-latitude Atlantic, and mid-latitude Pacific account for 104, 62, and 3.7 Tg C yr−1, respectively, while making up 51 %, 25 %, and 24 % of the total area, respectively. The comparatively large uptake along the mid-latitude Atlantic simulated in the global model of is larger than regional estimates (e.g., Signorini et al.2013), likely because it significantly underestimates the residence times of coastal waters . Nevertheless, we used this flux estimate, assuming an uncertainty of 50 %, to construct a first carbon budget for the North American EEZ. The estimated uptake of atmospheric carbon of 160±80 Tg C yr−1 combined with an input from land of 106±30 Tg C yr−1 minus an estimated burial of 65±55 Tg C yr−1 leads to a large net addition of carbon. This term has to be balanced by carbon storage in waters of the EEZ and export to the open ocean. The estimated carbon storage of 50±25 Tg C yr−1 from the global model leads to a carbon export of 151±105 Tg C yr−1 to the open ocean. The estimated uptake of atmospheric carbon in the North American EEZ amounts to 6.4 % of the global ocean uptake of atmospheric CO2 of 2500 Tg C yr−1 . Given that the North American EEZ is about 4 % of the global ocean surface area, its uptake of CO2 is about 50 % more efficient than the global average.
Coastal waters contribute significantly to the carbon budget of North America. According to , the coastal carbon sink estimated here is about one-quarter of the net carbon sink on land in North America (606 Tg C yr−1 is the net uptake by ecosystems and tidal wetlands minus emissions from harvested wood, inland waters, and estuaries). Coastal waters of North America are also a key component of aquatic carbon fluxes; specifically, much of the large net outgassing of CO2 from inland waters, estimated at 247 Tg C yr−1 , is offset by coastal ocean uptake.
Several drivers influence secular trends in coastal carbon fluxes and will continue to do so in the future. These drivers include the direct effect of rising atmospheric CO2 levels and indirect effects due to changes in atmosphere–ocean interactions (e.g., wind forcing and heat fluxes), changes in the hydrological cycle, and anthropogenic perturbations of global nutrient cycling (particularly, the nitrogen cycle). The direct effect of rising atmospheric CO2 levels alone will likely amplify coastal CO2 uptake and carbon export, at least until the ocean's buffering capacity is significantly reduced, but the extent of this increase will depend on the rate of the atmospheric CO2 rise, the residence time of shelf waters, and the carbon content of open-ocean source waters supplied to coastal regions. Indeed, there is observational evidence for a strengthening of coastal ocean carbon export from increasing trends in the air–sea pCO2 gradient for the Labrador Sea, Vancouver shelf, and South Atlantic Bight . Several indirect effects such the enhanced subduction of upwelled water along the Pacific margin , increased stratification on the shelf , and decreased CO2 solubility due to warming will partly counteract a strengthening of the coastal CO2 uptake. On Arctic shelves, significant releases of the potent greenhouse gas CH4 will result from melting permafrost .
A major concern is coastal acidification, which can affect the growth, metabolism, and life cycles of many marine organisms, specifically calcifiers, and can trigger cascading ecosystem-scale effects. Most vulnerable are those organisms that precipitate aragonite, one of the more soluble forms of biogenic CaCO3 in the ocean. The Arctic Ocean is naturally closer to critical acidification thresholds with subsurface waters in the Beaufort Sea already routinely below aragonite saturation (favoring dissolution) . Model projections show undersaturation in surface waters in the Beaufort Sea by 2025 . Along the Pacific coast, atmospheric CO2 uptake in combination with intensified upwelling that brings low-pH, low-oxygen water onto the shelves leads to aragonite levels below the saturation threshold in large portions of the subsurface waters . Here half of the shelf is projected to be undersaturated by 2050 . In the northern Gulf of Mexico, aragonite saturation states are currently well above the dissolution threshold despite the eutrophication-induced acidification occurring in bottom waters due to Mississippi River inputs of nutrients and freshwater . Here undersaturation is projected to occur by 2100 .
Given the importance of coastal margins, both in contributing to carbon budgets and in the societal benefits they provide, further efforts to improve assessments of the carbon cycle in these regions are paramount. Critical needs are maintaining and expanding existing coastal observing programs, continued national and international coordination, and the integration of observations, modeling capabilities, and stakeholder needs.
Data availability
Data availability.
All data sets used in this synthesis are publicly available at the sources indicated.
Supplement
Supplement.
Author contributions
Author contributions.
KF wrote the paper with contributions from all co-authors.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Acknowledgements
Acknowledgements.
This paper builds on synthesis activities carried out for the second State of the Carbon Cycle Report (SOCCR2). We would like to thank Gyami Shrestha, Nancy Cavallero, Melanie Mayes, Holly Haun, Marjy Friedrichs, Laura Lorenzoni, and Erica Ombres for the guidance and input. We are grateful to Nicolas Gruber and Christophe Rabouille for their constructive and helpful reviews of the paper. It is a contribution to the Marine Biodiversity Observation Network (MBON), the Integrated Marine Biosphere Research (IMBeR) project, the International Ocean Carbon Coordination Project (IOCCP), and the Cooperative Institute of the University of Miami and the National Oceanic and Atmospheric Administration (CIMAS) under cooperative agreement NA10OAR4320143. Katja Fennel was funded by the NSERC Discovery program. Steven Lohrenz was funded by NASA grant NNX14AO73G. Ray Najjar was funded by NASA grant NNX14AM37G. Frank Muller-Karger was funded through NASA grant NNX14AP62A. This is Pacific Marine Environmental Laboratory contribution number 4837 and Lamont-Doherty Earth Observatory contribution number 8284. Simone Alin and Richard A. Feely also thank Libby Jewett and Dwight Gledhill of the NOAA Ocean Acidification Program for their support.
Review statement
Review statement.
This paper was edited by Jack Middelburg and reviewed by Nicolas Gruber and Christophe Rabouille.
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Windham-Myers, L., Cai, W.-J., Alin, S., Andersson, A., Crosswell, J., Dunton, K. H., Hernandez-Ayon, J. M., Herrmann, M., Hinson, A. L., Hopkinson, C. S., Howard, J., Hu, X., Knox, S. H., Kroeger, K., Lagomasino, D., Megonigal, P., Najjar, R. G., Paulsen, M.-L., Peteet, D., Pidgeon, E., Schäfer, K. V. R., Tzortziou, M., Wang, Z. A., and Watson, E. B.: Chapter 15: Tidal wetlands and estuaries, in: Second State of the Carbon Cycle Report (SOCCR2): A Sustained Assessment Report, edited by: Cavallaro, N., Shrestha, G., Birdsey, R., Mayes, M. A., Najjar, R. G., Reed, S. C., Romero-Lankao, P., and Zhu, Z., US Global Change Research Program, Washington, DC, USA, 596–648, 2018. a, b, c
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• 论文 •
### 蒸发皿蒸发过程中水稳定同位素分馏的实验与模拟
1. （湖南师范大学 资源与环境科学学院，长沙 410081）
• 出版日期:2017-07-05 发布日期:2017-07-05
• 通讯作者: 章新平（1956―），男，湖南长沙人，教授，博士，主要从事气候变化以及水稳定同位素方向的研究，（E-mail）[email protected]。
• 作者简介:华明权（1992―），男，江西赣州人，硕士研究生，主要从事气候变化以及水稳定同位素方向的研究，（E-mail）[email protected]
• 基金资助:
国家自然科学基金项目（41571021)；湖南省重点学科建设项目（2016001）；湖南省研究生科研创新项目（CX2017B229）
### Experiments and Simulations of Water Stable Isotopes Fractionation in Evaporation Pan
HUA Mingquan，ZHANG Xinping，YAO Tianci，HUANG Huang，LUO Zidong
1. （College of Resources and Environmental Sciences，Hunan Normal University，Changsha 410081，China）
• Online:2017-07-05 Published:2017-07-05
Abstract:
To assess the results of water stable isotopes fractionation simulated respectively by equilibrium model and kinetic model, four evaporation experiments were conducted under different atmospheric conditions. The results indicate that stable isotopes in residual water are gradually enriched along with the evaporation, there is a positive correlation between the enrichment rate and the evaporation rate. However, when precipitation happens, the residual water stable isotopes are diluted, as they are susceptible to the influence of relative humidity and the stable isotopes in atmospheric water vapor. Experimental water stable isotope fractionation rate is influenced by temperature and relative humidity, and certain positive correlation between the isotopic fractionation rate and the temperature changes appears. This phenomenon is contrary to the results described by Rayleigh fractionation model. There is a remarkable inverse relationship between the isotopic fractionation rate and relative humidity. Although the simulation results of equilibrium fractionation model have higher correlation coefficient with the measured results，as a whole，they fail to reflect the details of changes in stable water isotopes ratio with f in actual evaporation process, especially during the middle period of evaporation．In addition, the results of equilibrium simulation overestimate the degree of stable isotope fractionation. By contrast, kinetic fractionation model performs well in reproducing the variation of stable isotopes in water evaporation. It can capture the details of changes of the δ18O. The actual evaporation line slopes (3.855, 3.749, 4.097, 6.942) are low in summer and high in winter due to the influences of air temperature and relative humidity. Evaporation line slopes calculated from equilibrium fractionation model remain near 8, and their intercepts are all more than 10, close to the global meteoric water line, reflecting a poor fitting result. However, the evaporation line slopes (4.265, 3.433, 5.705, 5.833) of kinetic fractionation model are closer to those of the measurements, which can reflect the actual process of water evaporation. Variations of observed d-excess in residual water with residual water ratio f show a decrease trend in the four experiments, d value increases when rain events occur．And the decline speed of d-excess in summer is higher than that in winter, that is related to faster evaporation rate and stable isotope fractionation rates in summer. The d-excess of the equilibrium fractionation model varies with a constant value, and have lower correlation coefficient with the measured results, the root mean square error is large, and the simulation effect is poor, while that of the kinetic fractionation model shows similar results with measured d-excess both in magnitude and trend. It is concluded that the kinetic fractionation model would be more suitable to describe the water stable isotopes evaporation fractionation process under regional climatic conditions．
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# It takes the high-speed train x hours to travel the z miles
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Re: Manhattan CAT math question [#permalink] 29 Mar 2013, 05:43
Expert's post
manimgoindowndown wrote:
Hey Bunuel so something I sort of missed was why we combine the rate (understood this) but then to figure out the time the trains cross each other to simply divide the distance z by the combined rates?
The distance z is the total distance for A to B. Which is different for what we're looking for, no? Aren't we looking for the time (and hence corresponding) distance where A and B cross each other?
Two trains are traveling to meet each other.
Distance = 100 miles;
Rate of train A = 20 miles per hour;
Rate of train B = 30 miles per hour.
In how many hours will they meet?
(Time) = (Distance)/(Combined rate) = 100/(20+30) = 2 hours.
Does this make sense?[/quote]
Combining the rates makes sense to me, they are both moving to each other relatively
Here's what doesn't make sense to me.
The distance between the two starting points of the train is 100 miles (z). If we are trying to find what time they will pass each other, that distance MUST BE less than 100 if both trains have a positive velocity.
This distance is less than the starting points of the train from 100 miles (z)?
So I don't see how we can simple plug in z here. Maybe there's a test assumption that simplifies this situation for us.[/quote]
"Pass" here means "meet".
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 29 Jul 2013, 18:16
speed of high speed train, Vh=z/x
speed of regular train, Vr=z/y
Let p be the distance covered by high speed train when both trains met
Time taken to meet both trains =px/z=(z-p)y/z
p=zy/(x+y)
but required is how much more distance covered by high speed train than regular train
i.e required = 2p-z = zy/(x-y) -z
=z(y-x)/x+y
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 01 Aug 2013, 16:26
It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?
We are given the rate of speed for both trains
We are given the distance both trains travel (which is the same)
We need to find distance traveled by both trains. Distance = rate*time. We need to find time, not distance, so we can multiply the time by the rate to get the distance traveled by each train.
Rate(fast) = (z/x)
Rate(slow) = (z/y)
We have the rate at which each train travels. Now, lets find the time at which they pass one another. If we know what time they pass one another and their rate, we can figure out distance.
Time = distance/combined rate
Time = z / (z/x)+(z/y)
Time = z/(z/x)(y/y) + (z/y)(x/x)
Time = z/(zy/xy) + (zx/xy)
Time = z/ zy+zx/xy
Time = (zxy)/(zy+zx)
Time = xy/y + x
Now we have the time at which they pass one another. Distance = Rate * Time. Now that we have the distance each train travels plus the time at which they pass one another (which represents the time each train has been traveling for) we can solve. When going through the problem, we don't solve for t because doing so would require that we use distance (z) which only tells us the distance between points a and b. We need to find the distance traveled by each train which adds up in total to distance z. That means we need to find the rate each train traveled at and how long it traveled for (which is when they pass one another) Remember, we aren't looking for how many miles the fast train traveled. we are looking for how many more miles it traveled than the slow train.
distance(fast) - distance(slow):
(z/x)*xy/(y + x) - (z/y)*xy/(y + x)
zy/y+x - zx/y+x
(zy-zx)/(y+x)
z(y-x)/(y+x)
(A) z(y – x)/x + y
I would love to know someone's explanation as to how they knew what steps to take to solve this problem. Though the actual algebra wasn't too bad, knowing what steps to take and when made it extremely tough!
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 01 Aug 2013, 19:43
WholeLottaLove wrote:
I would love to know someone's explanation as to how they knew what steps to take to solve this problem. Though the actual algebra wasn't too bad, knowing what steps to take and when made it extremely tough![/color]
1. First formulate what is to be found in precise terms. That is let the distance traveled by the high speed train till both the trains meet be "a". The distance traveled by the regular train is z-a. So what we need to find is a-(z-a) = 2a-z. ---(1)
2. To find "a" we need to know the speed of the high speed train which we know as z/x. --(2) We also need to know the time elapsed till the two trains meet. This we can find out since we know the time taken for each train to travel the whole distance as x and y. Thus the time elapsed when they meet is equal to xy/(x+y) -- (3)
3. So a= xy/(x+y) * z/x
4. Substitute this in (1) and you get the answer.
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 15 Aug 2013, 11:12
It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?
We know that when both trains meet, they will have been traveling for the same amount of time. We are given the distance both trains travel (the same distance) and the time in which they do it (x and y respectively) We need to figure out the difference in distance between the fast train and the slow train. first, we need to figure out what rate each train travels at (x/z and x/y for the high speed and slow speed train) To figure out distance (d=r*t) we also need to find the time the two trains traveled for. The distance (z) is equal to the distance traveled by the fast train plus the distance traveled by the slow train.
Lets call the fast train HS and the slow train LS.
speed = distance/time
Speed (HS) = z/x
Speed (LS) = z/y
Now that we have the speed, we need to find the distance each train traveled. The distance the high speed train travels - the distance the slow speed train travels will get us the amount of distance more the high speed train travels.
Distance = rate*time
We know the time it takes each train to reach their respective destinations. For HS it will be less than LS. However, in this problem, we know that both will travel for the same amount of time when they meet each other.
We know the speed of each train, now we must figure out the time each train traveled. Distance = speed*time
z = (z/x)*t + (z/y)*t
z = zt/x + zt/y
z = (zty/xy) + (ztx/xy)
z = (zty+ztx)/xy
zxy = (zty+ztx)
xy = ty + tx
xy = t(y+x)
t = xy/(x+y)
The time each train traveled was: xy/(x+y)
Now that we know the value for T, we can solve for their respective distances by plugging in for distance=rate*time
Distance (HS) = z/x*xy/(x+y)
zy/x+y
Distance (LS) = z/y*xy/(x+y)
zx/x+y
(zy/x+y) - (zx/x+y) = z(y – x)/x + y
ANSWER: (A) z(y – x)/x + y
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 15 Aug 2013, 12:45
joyseychow wrote:
It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?
(A) z(y – x)/x + y
(B) z(x – y)/x + y
(C) z(x + y)/y – x
(D) xy(x – y)/x + y
(E) xy(y – x)/x + y
........
s = z/x t
z-s = z/y t
..................
(+), z = zt (x+y/ xy)
or, t = xy/x+y
Now, z/x . t - z/y . t = zt (y-x/xy) = z . xy/(x+y) . (y-x)/xy = z (y-x/y+x)
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 15 Sep 2013, 20:00
All the methods looks like it will take more than 2 minutes to complete. There's got to be a faster way.
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 16 Sep 2013, 00:51
Expert's post
haotian87 wrote:
All the methods looks like it will take more than 2 minutes to complete. There's got to be a faster way.
This is not an easy question, so it's OK if it takes a bit more than 2 minutes to solve. Though if you understand the logic used here: it-takes-the-high-speed-train-x-hours-to-travel-the-z-miles-94564.html#p727726, here: it-takes-the-high-speed-train-x-hours-to-travel-the-z-miles-94564.html#p727737 and here: it-takes-the-high-speed-train-x-hours-to-travel-the-z-miles-94564.html#p1040729 it won't take mcut time.
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 29 Oct 2013, 08:48
Is there a resource to really hammer on this type of problem? I've gotten much better over the last couple months at every type of problem, but so far in 5 practice tests I've gotten every single one of these problems wrong.
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 29 Oct 2013, 23:50
Expert's post
AccipiterQ wrote:
Is there a resource to really hammer on this type of problem? I've gotten much better over the last couple months at every type of problem, but so far in 5 practice tests I've gotten every single one of these problems wrong.
All DS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=44
All PS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=64
Hope this helps.
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 07 Nov 2013, 11:49
It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?
I solved this problem a bit unusually....rather than do out the math, I picked variables and drew out a diagram. I said that the length was 60 and that the high speed train traveled 60 miles/hour and the regular train traveled 30 miles/hour. In one half hour, the fast train traveled 30 miles while the slow train traveled 15 miles. This meant that there was a 15 mile gap to close. Seeing as each train started out at the same time, and my variables had the faster train traveling twice as fast as the slow train for every to miles the fast train traveled, the slow train traveled just one. I basically drew out my diagram and counted off the miles until the two trains reached each other. I found that the slow train traveled 20 miles to the fast trains 40. From there, I simply plugged in the numbers until I got the right answer:z
(after 1/2 hour)
0 60mi
___________________F__________S__________
30mi 45mi
(After 2/3 hour)
0 60mi
_________________________FS______________
40mi 20mi
(A) z(y – x)/x + y
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 09 Nov 2013, 06:07
How would I do this with a RTD chart?
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 16 Jun 2014, 18:26
Since there are variables in the choices, plug in approach would work very well.
Assume x=10, z=100 and y=20. When travelling in the opposite directions and the distance is 100 miles, they would meet when the high speed train had traveled 66 2/3 miles and the regular train 33 1/3 miles. So the high speed train would have traveled 33 1/3 miles more.
Substitute the values of x, y and z in the choices. Choice A gives the value of 33 1/3 and is the correct answer.
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 19 Jun 2014, 20:44
Refer diagram below:
Let the trains meet at point P
Say the fast train has travelled distance "a" from point A, so the slow train travels distance "z-a" from point B
We require to find the difference
= a - (z-a)
= 2a - z ......... (1)
Time taken by high speed train = Time taken by slow train (To meet at point P)
Setting up the equation
$$\frac{a}{(\frac{z}{x})} = \frac{z-a}{(\frac{z}{y})}$$
$$a = \frac{yz}{x+y}$$
Placing value of a in equation (1)
$$= \frac{2yz}{x+y} - z$$
$$= \frac{z(y-z)}{x+y}$$
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 23 Jun 2014, 16:41
I really had to work on this several times to get the equation right. Is there anyway to avoid silly mistakes?
for example even finding difference in the distance has given totally wrong answer.
Are there any tips like plugging in values in these so many variables question?
Another question is , in distance rate problems, usually based on what variable equations are easier . is it time or distance?
Thanks
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 23 Jun 2014, 18:50
Expert's post
GMatAspirerCA wrote:
I really had to work on this several times to get the equation right. Is there anyway to avoid silly mistakes?
for example even finding difference in the distance has given totally wrong answer.
Are there any tips like plugging in values in these so many variables question?
Another question is , in distance rate problems, usually based on what variable equations are easier . is it time or distance?
Thanks
Note that most of these TSD questions can be done without using equations.
You can also use ratios here.
Ratio of time taken by high speed:regular = x:y
Ratio of distance covered in same time by high speed:regular = y:x (inverse of ratio of speed)
So distance covered by high speed train will be y/(x+y) * z
and distance covered by regular train will be x(x+y) * z
High speed train will travel yz/(x+y) - xz/(x+y) = z(y-x)/(x+y) more than regular train.
Plugging numbers when there are variables works well but it gets confusing if there are too many variables. I am good with number plugging when there are one or two variables - usually not more.
Whether you should make the equation with "total time" or "total distance" will totally depend on the question - sometimes one will be easier, sometimes the other.
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 27 Jun 2015, 13:21
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It takes the high-speed train x hours to travel the z miles [#permalink] 10 Aug 2015, 04:04
There's an even faster way to do this. If x = y, z should be 0. This eliminates C.
If y>>>>x, x/y should approach 0 and answer should approach z.
D and E don't mention of z, so eliminated.
Out of A & B, A approaches z, while B approaches -z. Hence, A is the answer.
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Re: It takes the high-speed train x hours to travel the z miles [#permalink] 11 Aug 2015, 14:17
Pick numbers. In this case you can easily eliminate B, C, D and E.
Using: total distance of 200 miles.
High-Speed Train: 200mph; 1h travel time
Regular-Train: 100mph; 2h travel time
A) 200*(2-1)/(2+1) = 200/3, can be this one
B) Negative, not possible
C) 200*(2+1)/(2-1) = 600, not possible
D) Negative, not possible
E) 2*(2-1)/(2+1) = 2/3, too small
Therefore, choose A.
Re: It takes the high-speed train x hours to travel the z miles [#permalink] 11 Aug 2015, 14:17
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# Approximation for deriving I-V characteristic of pn junction
I am struggling with some approximation while deriving I-V characteristic of a pn junction. Let's consider a quasi-neutral region on the n side of pn junction.
There are four current components as follows:
Jndiff: majority diffusion current
Jndrift: majority drift current
Jpdiff: minority diffusion current
Jpdrift: minority drift current
Because there is no field in the neutral region then there can be no net charge at any point in this region. Then the excess majority carrier concentration should follow the decay of the excess minority carrier concentration. This results to Jndiff = Dn/Dp* Jpdiff.
I can see that Jndiff and Jpdiff is on the same order of magnitude. Also Jndiff is larger than Jpdiff because Dn > Dp.
The total current density:
Jtotal = Jndiff + Jndift + Jpdiff + Jpdrift
The approximation is as follows: Jndiff << Jndift so we can ignore Jndiff.
(similarly Jpdrift << Jpdiff, so we can ignore Jpdrift)
This results in Jtotal = Jndrift + Jpdiff.
However, what I am confused is that we ignore Jndiff and keep Jpdiff while Jndiff and Jpdiff are on the same order of magnitude (Jndiff is even larger than Jpdiff). If we ignore Jndiff then we should also ignore Jpdiff because Jpdiff is smaller than Jndiff. Could anyone please explain it?
http://www.solar.udel.edu/ELEG620/04_pnjunction.pdf
You are obviously referring to the Shockley model of the pn-junction where the recombination and generation is neglected in the depletion region so that the electron and hole currents across the depletion region each are constant. Thus the total current of the pn-junction must be the sum of the minority currents at the depletion region edges, hole current at the n-side, and electron current at the p-side edge.
The majority carrier diffusion and drift currents on the n- and p-side do exist, but, due to the electron and hole current continuity across the depletion zone, at the depletion edges they are identical to the minority diffusion and drift currents at the respective opposite depletion edge. Therefore it suffices to consider the minor current at the depletion edges to obtain the total pn-junction current.
• Thanks a lot, freecharly. It makes some sense now. However, I am still not completely comfortable with it. Let's assume that there is no electric field in quasi-neutral region, how is it possible to have the drift current there? – anhnha Mar 11 '17 at 13:29
• When there is no electric field in the quasi-neutral region, then there is no drift current, only diffusion current. This is also the assumption for the pn-junction minority currents at low injection levels, which is usually part of the Shockley model. – freecharly Mar 11 '17 at 17:21
• Hi, for an ideal wire there is also absolutely no electric field along the wire. However, it still carry some current (possibly drift current). Is this correct or something misunderstood here? – anhnha Mar 11 '17 at 17:52
• @anhnha - When you consider normal (metal) conductors, there is always an electric field (which might be very small) necessary for a current to flow. In superconductors, which have no resistance, you can have electrical current flow without electrical fields. – freecharly Mar 11 '17 at 18:01
• @anhnha - In the depletion region you have usually both drift and diffusion current. – freecharly Mar 11 '17 at 18:34
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I use the package called "lstaddons" (creator, initial question) to get colored line backgrounds on listings.
I want to color the whole line to the frame. What I miss there is a dynamic calculation of the linewidth.
You can adjust the linebackgroundsep, which moves the colorbox to the left. And through linebackgroundwidth you can set the width of the box.
My question is: Is there any opportunity to calculate the linewidth dynamic through a macro? I tried this one, but i think its a bit crappy...
``````\newdimen\lstwidth
\newdimen\lstxleftmargin
\lstxleftmargin = 15pt
\lstwidth = 0pt
\advance\lstwidth by -\lstxleftmargin % Minus xleftmargin
\advance\lstwidth by 1pt % Minus Rand rechts
``````
and in the listing settings:
``````\lstset{
linebackgroundcolor={\ifodd\value{lstnumber}\color{codegray}\fi},
linebackgroundsep=3pt, % lstaddons: fills the line from the left frame
linebackgroundwidth={\lstwidth}, % lstaddons: ... to the right
frame=lr,
numbersep=10pt,
xleftmargin=\lstxleftmargin,
xrightmargin=5pt
}
``````
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You could do this in one swoop: `linebackgroundwidth=\dimexpr\linewidth-15pt+1pt\relax`. Not sure whether `1pt` is appropriate here, since frame borders are "usually" `.4pt`. Without a proper MWE it's hard to tell. – Werner Sep 9 '12 at 14:06
i just created an account now. Thanks for that very helpful answer! In fact the solution is: linebackgroundwidth={\dimexpr\linewidth+6pt\relax} because the linewidth is another inside the listings environment.
``````\lstset{
% [...]
linebackgroundcolor={\ifodd\value{lstnumber}\color{codegray}\fi},
linebackgroundsep=3pt,
linebackgroundwidth={\dimexpr\linewidth+6pt\relax}
% [...]
}
``````
This options result in the desired look. Thanks a lot!
(cannot upload the picture - sorry!)
edit no.1
Thanks also to Heiko Oberdiek here. The best solution in my eyes is now:
``````\lstset{
linebackgroundcolor={\ifodd\value{lstnumber}\color{codegray}\fi},
linebackgroundsep=3pt,
linebackgroundwidth={\dimexpr\linewidth + (\lst@linebgrdsep)*2 \relax},
frame=lr,
xleftmargin=15pt,
xrightmargin=5pt,
framexleftmargin=0pt,
framexrightmargin=0pt
}
``````
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Is it also your account that is asking the question ? If so we can ask a mod to merge these accounts. – percusse Sep 9 '12 at 14:43
Yes it was, sorry for all this trouble :/ – tollo Sep 9 '12 at 14:48
@percusse and tollo: I merged the accounts. – Stefan Kottwitz Sep 9 '12 at 15:02
Danke/thank you Stefan – tollo Sep 9 '12 at 15:45
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# B Wolfram Alpha graph of ln(x) shows as ln(abs(x))
1. Oct 14, 2017
### rudy
Hello-
I was checking an answer to an integral on Wolfram Alpha and noticed I don't know how they distinguish between ln(x) and ln("absolute value of"(x)). It appears all of their inputs and outputs imply absolute value (taking positive and negative x-values)
Is anyone here familiar with their site and can explain why this is or how they distinguish between the two?
Here is a link to "ln(x)" on wolfram alpha:
https://www.wolframalpha.com/input/?i=lnx
P.S. In case anyone is wondering why the input says "log(x)", Wolfram Alpha only deals with ln, so log = ln on W.A.
Thanks,
Rudy
#### Attached Files:
• ###### Screen Shot 2017-10-14 at 7.25.37 PM.png
File size:
18.8 KB
Views:
143
2. Oct 14, 2017
### Staff: Mentor
How about ln(abs(x)) or ln|x|? And yes, meanwhile log without an explicit basis means ln.
3. Oct 14, 2017
### I like Serena
Hi Rudy,
By default Wolfram uses complex numbers.
Ln is well defined for negative numbers then, which shows up as having an imaginary part of pi (for the principle branch).
It just looks like the ln of an absolute value, which happens to be the real part.
For the principle branch we have:
$$\ln(-x)=\ln(e^{\pi i}\cdot x)=\pi i + \ln x$$
Last edited: Oct 14, 2017
4. Oct 14, 2017
### Staff: Mentor
It -- log(x) -- didn't always mean ln(x). Back in the "old days" log(x) meant $log_{10}(x)$ and ln(x) meant $log_e(x)$.
Also, in many computer science books, log(x) means $log_2(x)$.
5. Oct 14, 2017
### Staff: Mentor
Yes, I know, and I like $\ln (x)$. That's why I said "meanwhile". But someone once said about me: If it was you to decide, we would still start our cars with a handle. Hmm, why not? Better than a battery failure in a cold winter.
I remember a discussion we had on PF before about $\ln (x)$ and I still can't see the advantage of $\log (x)$. It's a letter more, ambiguous and $\ln (x)$ isn't assigned another usage and is easy to write by hand. I'm not sure, but I think I've even seen $\operatorname{lb}$ for $\log_2$ as well.
6. Oct 14, 2017
### rudy
Interesting, so is there no way to express ln(x) in the "traditional" (not using complex #s) sense on W.A.? In other words, is there a way I can use W.A. to check integrals with ln(abs(x)) in the answer? (Subtract pi*i for example...). Or should I just tell my professor that all my answers are formatted as outputs from W.A.
7. Oct 14, 2017
### FactChecker
ln(x) "in the 'traditional sense'" does not allow x ≤ 0. That is not the fault of WA, that is standard mathematics. ln(x) is not the same as ln(abs(x)), which WA handles easily. WA handles them both correctly.
Last edited: Oct 15, 2017
8. Oct 15, 2017
### I like Serena
Just noticed that W|A has a button on the right side of the graph that says Complex-valued plot, which we can change to Real-valued plot. :)
Last edited: Oct 15, 2017
9. Oct 15, 2017
### Staff: Mentor
lb? I have seen ld once in a while.
WolframAlpha typically understands things like “where x>0”, but for integrals over positive x that doesn’t matter anyway.
10. Oct 15, 2017
### I like Serena
I think the classical problem here is:
$$\int \frac {dz}z = \ln z + C$$
which is what W|A reports.
(Aside from the fact that they use the ambiguous $\log$. I'm still wondering what their rationale is.)
For reals this becomes:
$$\int \frac {dx}x = \begin{cases}\ln x + C_1 &\text{if }x > 0 \\ \ln(-x) + C_2 & \text{if }x < 0\end{cases}$$
which is defined for negative x, and which is only properly defined if the bounds are either both positive or both negative.
And usually, somewhat erroneously though due to the different integration constants, it is abbreviated to:
$$\int \frac{dx}x = \ln|x| + C$$
which I'm guessing is what Rudy is being taught, and what he is supposed to verify.
Last edited: Oct 15, 2017
11. Oct 15, 2017
### rudy
THIS sounds like the explanation I was looking for. I need to look over your explanation as I don't fully follow at first glance but thank you very much!!
12. Oct 18, 2017
### Staff: Mentor
Two of my motorcycles are started using a "handle" (kickstarter).
13. Nov 1, 2017
### vanhees71
Well, in Mathematica it's correctly implemented, i.e., when I plot log[x] it leaves out anything with arguments $x \leq 0$.
It's also not true that ln is uniquely defined everywhere on the complex plane, but it has an essential singularity (or branching point) at $z=0$. The standard definition is to cut the complex plane along the negative real axis. The value along the branch cut on one sheet of the corresponding Riemann surface jumps by the value $2 \pi \mathrm{i}$. On the principal sheet, $ln z \in \mathbb{R}$ for $z>0$. Consequently on this sheet the principal values along the negative real axis are
$$\ln(z \pm \mathrm{i} 0^+)=\ln(|z|) \pm \mathrm{i} \pi.$$
That's how it's implemented in Mathematica as well as in standard programming languages.
Obviously Wolfram alpha plots real and imaginary part for arguments along the real axis, assuming an infinitesimal positive imaginary part of the argument.
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# removeedges¶
Syntax: removeedges(vertices, edges, edge measurements, edge points, flags, disconnect straight-through nodes, remove isolated nodes)
Prunes the network by removing user-selected edges from it. The edges to be removed are specified in an image, having one pixel for each edge, where non-zero value specifies that the corresponding edge is to be removed.
This command cannot be used in the distributed processing mode. If you need it, please contact the authors.
## Arguments¶
### vertices [input & output]¶
Data type: float32 image
Image where vertex coordinates are stored. See tracelineskeleton command.
### edges [input & output]¶
Data type: uint64 image
Image where vertex indices corresponding to each edge are stored. See tracelineskeleton command.
### edge measurements [input & output]¶
Data type: float32 image
Image where properties of each edge are stored. ee tracelineskeleton command.
### edge points [input & output]¶
Data type: int32 image
Image that stores some points on each edge. See tracelineskeleton command.
### flags [input]¶
Data type: uint8 image, uint16 image, uint32 image, uint64 image, int8 image, int16 image, int32 image, int64 image, float32 image
Image that has as many pixels as there are edges. Edges corresponding to non-zero pixels are removed.
### disconnect straight-through nodes [input]¶
Data type: boolean
If set to true, all straight-through nodes (nodes with degree = 2) are removed after pruning. This operation might change the network even if no edges are pruned.
### remove isolated nodes [input]¶
Data type: boolean
If set to true, all isolated nodes (nodes with degree = 0) are removed after pruning. This operation might change the network even if no edges are pruned.
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Volume 301 - 35th International Cosmic Ray Conference (ICRC2017) - Session Gamma-Ray Astronomy. GA-galactic
VERITAS Observations of High-Mass X-Ray Binary SS 433
P. Kar* on behalf of the VERITAS Collaboration
*corresponding author
Full text: pdf
Pre-published on: August 16, 2017
Published on: August 03, 2018
Abstract
Despite decades of observations across all wavebands and dedicated theoretical modelling, the SS 433 system still poses many questions, especially in the high-energy range. SS 433 is a high-mass X-ray binary at a distance of $\sim 5.5$ kpc, with a stellar mass black hole in a $13$ day orbit around a supergiant $\sim$A7Ib star. SS 433 is unusual because it contains dual relativistic jets with evidence of high-energy hadronic particles. X-ray emission is seen from the central source as well as the jet termination regions, where the eastern and western jets interact with the surrounding interstellar medium. Very-high-energy gamma-ray emission is predicted both from the central source and multiple smaller regions in the jets. This emission could be detectable by current generation imaging atmospheric-Cherenkov telescopes like VERITAS. VERITAS has observed the extended region around SS 433 for $\sim 70$ hours during 2009-2012. No significant emission was detected either from the location of the black hole or the jet termination regions. We report 99\% confidence level flux upper limits above 600 GeV for these regions in the range $(1-10) \times 10^{-13} \mathrm{cm^{-2} \ s^{-1}}$. A phase resolved analysis also does not reveal any significant emission from the extended SS 433 region.
DOI: https://doi.org/10.22323/1.301.0713
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
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# Exporting/Importing a Table of complex numbers
I'm generating a long table of list of the form:
PN={{1,2,1+i},{3.5,2.6,2}...},{...},...
Using:
Export["PN.dat", PN, "Table"]
Seems to do the job of exporting, but then using:
PN = Import["PN.dat", "Table"] or PN = ReadList["PN.dat"]
Can't reconstruct the same List, the first way considers the imaginary number i as something else "I", while the second one returns insane data like:
{{-1., -2.6464*10^-40, 0. + 2.76621*10^18 I}, {-0.129967...
Any ideas how to do this right? (Using ToExpression Returns $Faild) - Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2)Read the FAQs! 3) When you see good Q&A, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. ALSO, remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign – chris Dec 1 '12 at 14:16 ## 1 Answer First, the root of$-1\$ is represented as I, not i.
In any case, the technique I use to export arbitrary data structures is to compress, save, load and uncompress:
ClearAll@PN;
PN = {{1, 2, 1 + I}, {3.5, 2.6 - 0.8*I, 2}}
Export["~/Desktop/PN.txt", Compress@PN]
{#, Im@#} &@Uncompress@Import@"~/Desktop/PN.txt"
(*{{{1, 2, 1 + I}, {3.5, 2.6 - 0.8 I, 2}}, {{0, 0, 1}, {0, -0.8, 0}}}*)
`
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Congrats on 10k rep ! – Artes Dec 4 '12 at 3:53
@Artes thank you! – acl Dec 4 '12 at 9:56
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# Can you construct a field with 4 elements?
Can you construct a field with 4 elements? can you help me think of any examples?
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There is a unique field of 4 elements, which is a field extension of $\mathbb{F}_2$. Do you know how to construct field extensions? – Zhen Lin May 30 '11 at 15:51
Sorry, I have yet to cover field extensions – Freeman May 30 '11 at 15:59
perhaps you should tell us what you have covered. – lhf May 30 '11 at 16:13
@lhf I have done a first course in groups, a list of what I have covered is here under 'Synopsis' maths.ox.ac.uk/courses/course/12493/synopsis – Freeman May 30 '11 at 16:20
That course covers quotient rings, which means my answer should be accessible (perhaps with a bit more detail). Do you in fact know about quotient rings? – Bill Dubuque May 30 '11 at 21:38
Hint: Two of the elements have to be $0$ and $1$, and call the others $a$ and $b$. We know the mulitplicative group is cyclic of order $3$ (there is only one group to choose from), so $a*a=b, b*b=a, a*b=1$. Now you just have to fill in the addition table: how many choices are there for $1+a$? Then see what satisfies distributivity and you are there.
Added: it is probably easier to think about the choices for $1+1$
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Here is a nice general method to build examples of finite fields of any desired size (a power of a prime):
Given a prime $p$ (in your case, $p=2$), pick a monic polynomial $q(x)\in {\mathbb F}_p[x]$ of degree $n$ and irreducible (in this case, $n=2$ and $q(x)=x^2+x+1$. By a counting argument, one can show that there is always at least one such polynomial $q$).
We use $q$ to build a field of size $p^n$.
Let $A$ be the companion matrix of $q$. This means that if $q(x)=a_0+a_1x+\dots+a_{n-1}x^{n-1}+x^n$, then $$A=\left(\begin{array}{ccccc}0&0&\dots&0&-a_0\\ 1&0&\dots&0&-a_1\\ 0&1&\dots&0&-a_2\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ 0&0&\dots&1&-a_{n-1}\end{array}\right).$$ In our case, $$A=\left(\begin{array}{cc}0&1\\ 1&1\end{array}\right).$$
Now let $F=\{ r(A)\mid r \in{\mathbb F}_p[x]\}$.
The point is that $q(A)=a_0I+a_1A+\dots+a_{n-1}A^{n-1}+A^n=0$ and in fact, if $t(x)\in{\mathbb F}_p[x]$ and $t(A)=0$, then $q$ is a factor of $t$. Using this, one easily checks that $F$ is closed under addition and multiplication and has size $p^n$. Also, $t(A)s(A)=s(A)t(A)$ for all polynomials $t,s$. Finally, if $t$ is not a multiple of $p$ (i.e., $t(A)\in F$ is non-zero), then $\{t(A)r(A)\mid r(A)\in F\}=F$, so there is an $r(A)\in F$ such that $t(A)r(A)=1$, i.e., all elements of $F$ have inverses in $F$. So $F$ is a field.
To see that the key point is true requires a little argument. Call ${\mathbf e}_1,\dots,{\mathbf e_n}$ the standard basis in the vector space ${\mathbb F}_p^n$. Then $A{\mathbf e}_i={\mathbf e}_{i+1}$ for $i<n$ and from this it follows easily that for no non-zero polynomial $t$ of degree less than $n$ we can have $t(A)=0$, and also that $q(A)=0$.
[In more detail: We have $A{\mathbf e}_1={\mathbf e}_2$, $A^2{\mathbf e_1}=A{\mathbf e}_2={\mathbf e}_3$, etc, so for any polynomial $t(x)=b_0+\dots+b_{n-1}x^{n-1}$ of degree at most $n-1$ we have $t(A){\mathbf e}_1=b_0{\mathbf e}_1+b_1{\mathbf e}_2+\dots+b_{n-1}{\mathbf e}_n$, which is non-zero unless $b_0=\dots=b_{n-1}=0$ to begin with. Also, $q(A){\mathbf e}_1=0$ since $A^n{\mathbf e}_1=A{\mathbf e}_n=-a_0{\mathbf e}_1-a_1{\mathbf e}_2-\dots-a_{n-1}{\mathbf e}_n$. Since each ${\mathbf e}_i$ is $A^k{\mathbf e}_1$ for some $k$, it follows that $q(A){\mathbf e}_i=0$ for all $i$ (since $q(A)A^k=A^kq(A)$). Since the ${\mathbf e}_i$ form a basis, $q(A){\mathbf v}=0$ for all ${\mathbf v}$, so $q(A)=0$.
Also, since $q(A)=0$, note that $A^n$ is equal to a polynomial of degree at most $n-1$ applied to $A$ (namely, $-a_0I-\dots-a_{n-1}A^{n-1}$). It follows that any polynomial of degree $n$ applied to $A$ equals a polynomial in $A$ of degree at most $n-1$. But then $A^{n+1}=A^nA$ equals a polynomial in $A$ of degree at most $n$, and therefore one of degree at most $n-1$, and the same holds for any polynomial of degree $n+1$. Then $A^{n+2}=A^{n+1}A$ equals a polynomial in $A$ of degree at most $n$, etc.]
In our case, the field of 4 elements we obtained is $$\left\{0=\left(\begin{array}{cc}0&0\\ 0&0\end{array}\right),I=\left(\begin{array}{cc}1&0\\ 0&1\end{array}\right),A=\left(\begin{array}{cc}0&1\\ 1&1\end{array}\right),A+I=A^2=\left(\begin{array}{cc}1&1\\ 1&0\end{array}\right)\right\}.$$
The nice thing about this example is that the product and addition are just familiar operations (product and addition of matrices). Of course, from the general theory of finite fields, any two examples of the same size are isomorphic. However, I think this is a very concrete example that is useful to keep in mind as one advances through the theory, to see how general results apply in this setting.
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Let $K$ be your field.
The additive group of $K$ is an abelian group with four elements. The order of $1$ in this group divides $4$, so it is either $2$ or $4$. Were it $4$, we would have $1+1\neq0$ and $(1+1)\cdot(1+1)=0$, which is absurd in a field. It follows that $1+1=0$ in $K$. But then for all $x\in K$ we have $x+x=x\cdot(1+1)=0$, and we see that all elements have order $2$. In particular, $-1=1$.
Let $a$ be an element in $K$ which is neither $0$ nor $1$. Then $a+1$ is neither $a$ nor $1$ and if we had $a+1=0$, then $a=-1=1$ which again is a not true. We conclude that the four elements of $K$ are $0$, $1$, $a$ and $a+1$.
You should check that this knowledge complete determines the addition in $K$.
We have to determine the multiplication now. Since $0$ and $1$ are what they are, we need only see what $a\cdot a$, $a\cdot(a+1)$ and $(a+1)\cdot(a+1)$ are:
• We can't have $a^2=a$, for then $a(a-1)=0$ and we are supposing that $a\not\in\{0,1\}$; similarly, $a^2\neq0$. If $a^2=1$, then $(a-1)^2=a^2-1=0$ , which is also impossible. We must have thus $a^2=1+a$.
• Next, using this, $a\cdot(a+1)=a^2+a=1+a+a=1$.
• Finally, using that $1+1=0$, $(a+1)\cdot(a+1)=a^2+1=a$.
Multiplication is completely determined.
Now we have to check that with this operations we do have a field... You should have no trouble with that :)
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I wonder what the downvote was for... – Mariano Suárez-Alvarez May 30 '11 at 21:41
@Theo: polynomial removed :) – Mariano Suárez-Alvarez May 30 '11 at 23:20
Thanks! No complaints anymore :) – t.b. May 30 '11 at 23:30
I too wonder why my post was downvoted. – Bill Dubuque May 30 '11 at 23:39
HINT $\$ Such a field would be a quadratic extension of its prime field $\rm\:\mathbb F_2\:.\:$ So it suffices to consider $\rm\:\mathbb F_2[x]/(f(x))\:$ where $\rm\:f(x)\:$ is an irreducible quadratic polynomial over $\rm\:\mathbb F_2\:.\:$ Testing irreducibility is trivial via the Parity Root Test.
Checking whether a given polynomial has a root in $\mathbb F_2$ is done by plugging in the two candidates. You don't need a fancy name like Parity Root Test. So this is an imitation of the construction of the complex numbers from the reals. The only hard part is choosing a quadratic with no solution (since the conventional choice $x^2+1$ has solutions). – GEdgar May 30 '11 at 20:25
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# What symmetry elements mustn't a molecule possess to be considered achiral?
Undergraduate textbooks say that a molecule mustn't posses a reflection plane and an inversion center to be considered achiral. As mentioned by Ron in his answer to this question, molecules that don't possess a plane nor center of symmetry, but do possess an $S_4$ improper axis are considered to be achiral. Are there any other symmetry elements that need to be taken into consideration when determining whether a molecule is chiral or not?
• Short answer: Anything that can be expressed in terms of $\mathrm{S}_n$ axes makes a molecule achiral (Schoenflies definition). Or alternatively, anything that can be expressed as $\bar n$ makes a molecule achiral (Hermann-Mauguin definition). – Jan Oct 27 '15 at 13:45
• Actually, any reflection in a plane is just an $S_1$ operation, and an inversion through a point is just an $S_2$ operation. So, @Jan's comment is indeed the most concise yet complete definition: any $S_n$ axis present will make the molecule achiral. – orthocresol Oct 27 '15 at 13:49
• Okay. I would like to see some exotic example :). – RBW Oct 27 '15 at 14:13
• @Marko that's hard to find. Your best bet is looking for a molecule in the $S_4$ point group, which has the operations $E$, $S_4$, $C_2$, and $S_4^3$ - i.e. no mirror plane and no centre of inversion, but is still achiral because of the improper rotation axis. You can find some examples and pictures here csi.chemie.tu-darmstadt.de/ak/immel/tutorials/symmetry/… – orthocresol Oct 27 '15 at 14:29
• Nice examples, especially the coronane. – RBW Oct 27 '15 at 14:44
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Sangeetha Pulapaka
0
STEP 1: Recall what are exponents
STEP 2: Recall what is standard notation and scientific notation
http://www.amathsdictionaryforkids.com/qr/s/standardNotation.html
STEP 3: Compare
8.79 \times 10^{4}
=8.79 \times 10000
= 87,900
which is greater than 10,456
So A is the answer
Skills you may want to recall:
How to multiply a decimal number with 1000
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# OpenGL using the video card
## Recommended Posts
Hi, I'm sure there is a simple answer to this, but I can't find anything that can tell me how to utilize the graphix card on a computer in OpenGL. Right now, i'm pretty sure anyways, all my graphics commands are processed by the CPU and that would slow down the computer. Is there an easy way to use my OpenGL commands, such as glVertex3f();, on the gfx card? any replies are appreciated
##### Share on other sites
I don't have a lot of experience in utilizing the graphics card for specific things (without having the graphics API as a level of abstraction between me and the gfx card), but I know that you can use VBOs (vertex buffer objects), which basically means that a set of geometry is stored on the graphics card, which makes rendering that set much faster.
And, you really shouldn't be using 'glVertexf', it would be better to start with vertex buffers.
But, no, I don't think that there is a lot that can be done to speed up a call to glVertex3f or anything else, as the vertex position still needs to be multiplied by the current model matrix and sent to the graphics card. Sending data to the gfx card will pretty much always take the same amount of time.
If you are interested, I believe that you'll find your answer, with the ARB Open GL extensions.
##### Share on other sites
Given any semi recent, not complete trash video card, transformation and Lighting will be done on the video card (I think the nVidia drivers may do some work on the CPU if they think there is a performance advantage). I'm fairly sure that the model matrix multiplication is included in Transformation and Lighting. Or in other words it's done on the card.
Now as for way your program is slow is because glVertex3f is a slow way to send geometry to the video card (As Endar said). Since each vertex requires a function call. There are two ways (that I can think of) to efficiently send geometry in large chunks, display lists and vertex arrays. Display lists are typically used for static geometry (they have some other uses). They can be setup with the glVertex3f syntax. Vertex Arrays allow you send arrays of vertexes and other per vertex values. So 1 function call for 10,000 vertexes, instead of 10,000 glVertex3f calls. VBOs allow you store the vertex arrays on the video card's memory. I think display lists are also stored on board the card.
All of the above have been standard for a quite a while and are no longer extensions. Although to use some of them may require going through the extension system (thanks Microsoft...). Glee or Glew will make using the extension system much easier.
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CG for example.
anything handled by the shader goed over the GPU. however, this GPU / CPU tradeoff is not simply to does as much as possible over the GPU.
and for the rest you should turn to vertex array for speed boosts of vertex buffer object like mentoined before.
the speed will be maximal when giving fixed vertices to the shader through a buffer/array and altering their position in the shader. However, as I said, beware of the tradeoffs, they are everywhere. Their is no simple way too speed up everything at once.
The most speedgains however will result from your skillz as a programmer, differentiate proper between static stuff and dynamic stuff (both types are maximized differently) , proper debugging and converting a good release file (this alone gives about 30fps)
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what you are all saying is "mostly" correct. The reason shaders, and transformation & lighting (T & L) are done on the card is because OpenGL is really a state machine. Now there's two parts to this state machine and they are known as the client and the server. The server is essentially the graphics card, so any operations performed by the server, such as T & L, inherently happen on the GPU.
If you want to utilize the GPU even more you can move your vertex (along with normals, colors, texture coords, etc.) over to "server" memory, or graphics card memory. This can be done by using VBOs or vertex buffer objects, which essentially load and store arbitrary data into the graphics card memory. This means we don't have to transfer this data from "client" memory (standard RAM) across the bus to the graphics card memory for these operations to be performed, thereby improving performance even further.
I'd recommend reading up on how the OpenGL state machine works, it will give you some good insight on these issues and plenty more :)
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so what was wrong with the post ? i didn't say anything untrue, right?
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Quote:
Original post by EndarI don't have a lot of experience in utilizing the graphics card for specific things (without having the graphics API as a level of abstraction between me and the gfx card), but I know that you can use VBOs (vertex buffer objects), which basically means that a set of geometry is stored on the graphics card, which makes rendering that set much faster.
Not necessarily. The driver chooses where it will store something. If there is space in VRAM and your stuff is STATIC, it will likely be in VRAM.
If you use streaming, then AGP will likely b used. IN the case of PCIEx, regular RAM reserved by the driver.
BTW, VBOs are core since GL 1.5, so it doesn't make sense not to use them, whether you are a newbie or not.
The only reason to not use them is if you want to support very very old stuff.
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Thanks for the help, i realy appreciate it and i'll check this stuff out. :D
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• ## Partner Spotlight
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• ### Similar Content
• Both functions are available since 3.0, and I'm currently using glMapBuffer(), which works fine.
But, I was wondering if anyone has experienced advantage in using glMapBufferRange(), which allows to specify the range of the mapped buffer. Could this be only a safety measure or does it improve performance?
Note: I'm not asking about glBufferSubData()/glBufferData. Those two are irrelevant in this case.
• By xhcao
Before using void glBindImageTexture( GLuint unit, GLuint texture, GLint level, GLboolean layered, GLint layer, GLenum access, GLenum format), does need to make sure that texture is completeness.
• By cebugdev
hi guys,
are there any books, link online or any other resources that discusses on how to build special effects such as magic, lightning, etc. in OpenGL? i mean, yeah most of them are using particles but im looking for resources specifically on how to manipulate the particles to look like an effect that can be use for games,. i did fire particle before, and I want to learn how to do the other 'magic' as well.
Like are there one book or link(cant find in google) that atleast featured how to make different particle effects in OpenGL (or DirectX)? If there is no one stop shop for it, maybe ill just look for some tips on how to make a particle engine that is flexible enough to enable me to design different effects/magic
let me know if you guys have recommendations.
• By dud3
How do we rotate the camera around x axis 360 degrees, without having the strange effect as in my video below?
Mine behaves exactly the same way spherical coordinates would, I'm using euler angles.
Tried googling, but couldn't find a proper answer, guessing I don't know what exactly to google for, googled 'rotate 360 around x axis', got no proper answers.
References:
Code: https://pastebin.com/Hcshj3FQ
The video shows the difference between blender and my rotation:
• By Defend
I've had a Google around for this but haven't yet found some solid advice. There is a lot of "it depends", but I'm not sure on what.
My question is what's a good rule of thumb to follow when it comes to creating/using VBOs & VAOs? As in, when should I use multiple or when should I not? My understanding so far is that if I need a new VBO, then I need a new VAO. So when it comes to rendering multiple objects I can either:
* make lots of VAO/VBO pairs and flip through them to render different objects, or
* make one big VBO and jump around its memory to render different objects.
I also understand that if I need to render objects with different vertex attributes, then a new VAO is necessary in this case.
If that "it depends" really is quite variable, what's best for a beginner with OpenGL, assuming that better approaches can be learnt later with better understanding?
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# Union of Doubleton
## Theorem
Let $\left\{{x, y}\right\}$ be a doubleton.
Then:
$\displaystyle \bigcup \left\{{x, y}\right\} = x \cup y$
## Proof
$\displaystyle z \in \bigcup \left\{ {x, y}\right\}$ $\iff$ $\displaystyle \exists w \in \left\{ {x, y}\right\}: z \in w$ Definition of Union of Set of Sets $\displaystyle$ $\iff$ $\displaystyle \exists w: \left({\left({w = x \lor w = y}\right) \land z \in w}\right)$ Definition of Doubleton $\displaystyle$ $\iff$ $\displaystyle \left({z \in x \lor z \in y}\right)$ Equality implies Substitution $\displaystyle$ $\iff$ $\displaystyle z \in \left({x \cup y}\right)$ Definition of Set Union
$\blacksquare$
|
# Stateful operations¤
These operations can be used to introduce save/load JAX arrays as a side-effect of JAX operations, even under JIT.
Warning
This is considered experimental.
Stateful operations will not produce correct results under jax.checkpoint or jax.pmap.
Danger
Really, this is experimental. Side effects can easily make your code do something unexpected. Whatever you're doing, you almost certainly do not need this.
Use cases:
• Something like equinox.experimental.BatchNorm, for which we would like to save the running statistics as a side-effect.
• Implicitly passing information between loop iterations -- i.e. rather than explicitly via the carry argument to lax.scan. Perhaps you're using a third-party library that handles the lax.scan, that doesn't allow you pass your own information between iterations.
Example
import equinox as eqx
import jax
import jax.lax as lax
import jax.numpy as jnp
index = eqx.experimental.StateIndex()
init = jnp.array(0)
eqx.experimental.set_state(index, init)
@jax.jit
def scan_fun(_, __):
val = eqx.experimental.get_state(index, like=init)
val = val + 1
eqx.experimental.set_state(index, val)
return None, val
_, out = lax.scan(scan_fun, None, xs=None, length=5)
print(out) # [1 2 3 4 5]
#### equinox.experimental.StateIndex (Module) ¤
An index for setting or getting a piece of state with equinox.experimental.get_state or equinox.experimental.set_state.
You should typically treat this like a model parameter.
Example
import equinox as eqx
import equinox.experimental as eqxe
import jax.numpy as jnp
class CacheInput(eqx.Module):
index: eqxe.StateIndex
def __init__(self, input_shape):
self.index = eqxe.StateIndex()
eqxe.set_state(self.index, jnp.zeros(input_shape))
def __call__(self, x):
last_x = eqxe.get_state(self.index, x)
eqxe.set_state(self.index, x)
print(f"last_x={last_x}, x={x}")
x = jnp.array([1., 2.])
y = jnp.array([3., 4.])
shape = x.shape
ci = CacheInput(shape)
ci(x) # last_x=[0. 0.], x=[1. 2.]
ci(y) # last_x=[1. 2.], x=[3. 4.]
##### __init__(self, inference: bool = False)¤
Arguments:
• inference: If True, then the state can only be get, but not set. All stored states will looked up when crossing the JIT boundary -- rather than dynamically at runtime -- and treated as inputs to the XLA computation graph. This improves speed at runtime. This may be toggled with equinox.tree_inference.
Warning
You should not modify the inference flag whilst inside a JIT region. For example, the following will produced undefined behaviour:
@jax.jit
def f(...):
...
index = eqx.tree_at(lambda i: i.inference, index, True)
...
#### equinox.experimental.get_state(index: StateIndex, like: PyTree[Array]) -> PyTree[Array]¤
Get some previously saved state.
Arguments:
• index: The index of the state to look up. Should be an instance of equinox.experimental.StateIndex.
• like: A PyTree of JAX arrays of the same shape, dtype, PyTree structure, and batch axes as the state being looked up.
Returns:
Whatever the previously saved state is.
Raises:
A TypeError at trace time if like is not a PyTree of JAX arrays.
A RuntimeError at run time if like is not of the same shape, dtype, PyTree structure, and batch axes as the retrieved value.
A RuntimeError at run time if no state has previously been saved with this index.
Warning
This means that your operation will no longer be a pure function.
#### equinox.experimental.set_state(index: StateIndex, state: PyTree[Array]) -> None¤
Save a PyTree of JAX arrays as a side-effect.
Arguments:
Returns:
None.
Raises:
A RuntimeError at run time if this index has previously been used to save a state with a different shape, dtype, PyTree structure, or batch axes.
A RuntimeError at trace time if index.inference is truthy.
A TypeError at trace time if state is not a PyTree of JAX arrays.
A NotImplementedError at trace time if trying to compute a gradient through state.
Info
The same index can be used multiple times, to overwrite a previously saved value. The new and old state must both have the same PyTree structure, however.
Warning
Note that state cannot be differentiated.
Warning
This means that your operation will no longer be a pure function. Moreover note that the saving-as-a-side-effect may occur even when set_state is wrapped in lax.cond etc. (As e.g. under vmap then lax.cond is transformed into lax.select.)
|
## CAS and Normal Probability Distributions
My presentation this past Saturday at the 2015 T^3 International Conference in Dallas, TX was on the underappreciated applicability of CAS to statistics. This post shares some of what I shared there from my first year teaching AP Statistics.
MOVING PAST OUTDATED PEDAGOGY
It’s been decades since we’ve required students to use tables of values to compute by hand trigonometric and radical values. It seems odd to me that we continue to do exactly that today for so many statistics classes, including the AP. While the College Board permits statistics-capable calculators, it still provides probability tables with every exam. That messaging is clear: it is still “acceptable” to teach statistics using outdated probability tables.
In this, my first year teaching AP Statistics, I decided it was time for my students and I to completely break from this lingering past. My statistics classes this year have been 100% software-enabled. Not one of my students has been required to use or even see any tables of probability values.
My classes also have been fortunate to have complete CAS availability on their laptops. My school’s math department deliberately adopted the TI-Nspire platform in part because that software looks and operates exactly the same on tablet, computer, and handheld platforms. We primarily use the computer-based version for learning because of the speed and visualization of the large “real estate” there. We are shifting to school-owned handhelds in our last month before the AP Exam to gain practice on the platform required on the AP.
The remainder of this post shares ways my students and I have learned to apply the TI-Nspire CAS to some statistical questions around normal distributions.
FINDING NORMAL AREAS AND PROBABILITIES
Assume a manufacturer makes golf balls whose distances traveled under identical testing conditions are approximately normally distributed with a mean 295 yards with a standard deviation of 3 yards. What is the probability that one such randomly selected ball travels more than 300 yards?
Traditional statistics courses teach students to transform the 300 yards into a z-score to look up in a probability table. That approach obviously works, but with appropriate technology, I believe there will be far less need to use or even compute z-scores in much the same way that always converting logarithms to base-10 or base-to use logarithmic tables is anachronistic when using many modern scientific calculators.
TI calculators and other technologies allow computations of non-standard normal curves. Notice the Nspire CAS calculation below the curve uses both bounds of the area of interest along with the mean and standard deviation of the distribution to accomplish the computation in a single step.
So the probability of a randomly selected ball from the population described above going more than 300 yards is 4.779%.
GOING BACKWARDS
Now assume the manufacturing process can control the mean distance traveled. What mean should it use so that no more than 1% of the golf balls travel more than 300 yards?
Depending on the available normal probability tables, the traditional approach to this problem is again to work with z-scores. A modified CAS version of this is shown below.
Therefore, the manufacturer should produce a ball that travels a mean 293.021 yards under the given conditions.
The approach is legitimate, and I shared it with my students. Several of them ultimately chose a more efficient single line command:
But remember that the invNorm() and normCdf() commands on the Nspire are themselves functions, and so their internal parameters are available to solve commands. A pure CAS, “forward solution” still incorporating only the normCdf() command to which my students were first introduced makes use of this to determine the missing center.
DIFFERENTIATING INSTRUCTION
While calculus techniques definitely are NOT part of the AP Statistics curriculum, I do have several students jointly enrolled in various calculus classes. Some of these astutely noted the similarity between the area-based arguments above and the area under a curve techniques they were learning in their calculus classes. Never being one to pass on a teaching moment, I pulled a few of these to the side to show them that the previous solutions also could have been derived via integration.
I can’t recall any instances of my students actually employing integrals to solve statistics problems this year, but just having the connection verified completely solidified the mathematics they were learning in my class.
CONFIDENCE INTERVALS
The mean lead level of 35 crows in a random sample from a region was 4.90 ppm and the standard deviation was 1.12 ppm. Construct a 95 percent confidence interval for the mean lead level of crows in the region.
Many students–mine included–have difficulty comprehending confidence intervals and resort to “black box” confidence interval tools available in most (all?) statistics-capable calculators, including the TI-Nspire.
As n is greater than 30, I can compute the requested z-interval by filling in just four entries in a pop-up window and pressing Enter.
Convenient, for sure, but this approach doesn’t help the confused students understand that the confidence interval is nothing more than the bounds of the middle 95% of the normal pdf described in the problem, a fact crystallized by the application of the tools the students have been using for weeks by that point in the course.
Notice in the solve+normCdf() combination commands that the unknown this time was a bound and not the mean as was the case in the previous example.
EXTENDING THE RULE OF FOUR
I’ve used the “Rule of Four” in every math class I’ve taught for over two decades, explaining that every mathematical concept can be explained or expressed four different ways: Numerically, Algebraically, Graphically (including graphs and geometric figures), and Verbally. While not the contextual point of his quote, I often cite MIT’s Marvin Minsky here:
“You don’t understand anything until you learn it more than one way.”
Learning to translate between the four representations grants deeper understanding of concepts and often gives access to solutions in one form that may be difficult or impossible in other forms.
After my decades-long work with CAS, I now believe there is actually a 5th representation of mathematical ideas: Tools. Knowing how to translate a question into a form that your tool (in the case of CAS, the tool is computers) can manage or compute creates a different representation of the problem and requires deeper insights to manage the translation.
I knew some of my students this year had deeply embraced this “5th Way” when one showed me his alternative approach to the confidence interval question:
I found this solution particularly lovely for several reasons.
• The student knew about lists and statistical commands and on a whim tried combining them in a novel way to produce the desired solution.
• He found the confidence interval directly using a normal distribution command rather than the arguably more convenient black box confidence interval tool. He also showed explicitly his understanding of the distribution of sample means by adjusting the given standard deviation for the sample size.
• Finally, while using a CAS sometimes involves getting answers in forms you didn’t expect, in this case, I think the CAS command and list output actually provide a cleaner, interval-looking result than the black box confidence interval command much more intuitively connected to the actual meaning of a confidence interval.
• While I haven’t tried it out, it seems to me that this approach also should work on non-CAS statistical calculators that can handle lists.
(a very minor disappointment, quickly overcome)
Returning to my multiple approaches, I tried using my student’s newfound approach using a normCdf() command.
Alas, my Nspire returned the very command I had entered, indicating that it didn’t understand the question I had posed. While a bit disappointed that this approach didn’t work, I was actually excited to have discovered a boundary in the current programming of the Nspire. Perhaps someday this approach will also work, but my students and I have many other directions we can exploit to find what we need.
Leaving the probability tables behind in their appropriate historical dust while fully embracing the power of modern classroom technology to enhance my students’ statistical learning and understanding, I’m convinced I made the right decision to start this school year. They know more, understand the foundations of statistics better, and as a group feel much more confident and flexible. Whether their scores on next month’s AP exam will reflect their growth, I can’t say, but they’ve definitely learned more statistics this year than any previous statistics class I’ve ever taught.
COMPLETE FILES FROM MY 2015 T3 PRESENTATION
If you are interested, you can download here the PowerPoint file for my entire Nspired Statistics and CAS presentation from last week’s 2015 T3 International Conference in Dallas, TX. While not the point of this post, the presentation started with a non-calculus derivation/explanation of linear regressions. Using some great feedback from Jeff McCalla, here is an Nspire CAS document creating the linear regression computation updated from what I presented in Dallas. I hope you found this post and these files helpful, or at least thought-provoking.
## Lovely or Tricky Triangle Question?
In addition to not being drawn to scale and asking for congruence anyway, I like this problem because it potentially forces some great class discussions.
One responder suggested using the Law of Sines (LoS) to establish an isosceles triangle. My first thought was that was way more sophisticated than necessary and completely missed the fact that the given triangle information was SSA.
My initial gut reaction was this SSA setup was a “trick” ambiguous case scenario and no congruence was possible, but I couldn’t find a flaw in the LoS logic. After all, LoS fails when attempting to find obtuse angles, but the geometry at play here clearly makes angles B and C both acute. That meant LoS should work, and this was actually a determinate SSA case, not ambiguous. I was stuck in a potential contradiction. I was also thinking with trigonometry–a far more potent tool than I suspected was necessary for this problem.
“Stuck” moments like this are GOLDEN for me in the classroom. I could imagine two primary student situations here. They either 1) got a quick “proof” without recognizing the potential ambiguity, or 2) didn’t have a clue how to proceed. There are many reasons why a student might get stuck here, all of which are worth naming and addressing in a public forum. How can we NAME and MOVE PAST situations that confuse us? Perhaps more importantly, how often do we actually recognize when we’re in the middle of something that is potentially slipperier than it appears to be on the surface?
PROBLEM RESOLUTION:
I read later that some invoked the angle bisector theorem, but I took a different path. I’m fond of a property I asked my geometry classes to prove last year .
If any two of a triangle’s 1) angle bisector, 2) altitude, and 3) median coincide, prove that the remaining segment does, too, and that whenever this happens, the triangle will be isosceles with its vertex at the bisected angle.
Once I recognized that the angle bisector of angle BAC was also the median to side BC, I knew the triangle was isosceles. The problem was solved without invoking any trigonometry or any similarity ratios.
Very nice problem with VERY RICH discussion potential. Thanks for the tweet, Mr. Noble.
For more conversation on this, check out this Facebook conversation.
Mike Lawler posted this on Twitter a couple weeks ago.
The sad part of the problem is that it has no realistic solution as posed. From the way the diagram is drawn, the unlabeled side was likely intended to be congruent to its opposite side, making its value$=x-4$. Adding the four sides and equating to the given perimeter was probably the intended solution. This approach gives
$(x-4)+24+(x-4)+(3x+2)=88$
$x=14$
That’s nice enough, and a careless solver would walk away (see later in this post). But you should always check your solution. If $x=14$, then the longer base is $3(14)+2=44$ and the two congruent sides are each 10. That appears to be OK until you add the two congruent sides to the shorter base: $10+24+10=44$. Unfortunately, that’s the same length as the longer base, so this particular quadrilateral would have height=0.
Alas, this problem, as initially defined, creates a degenerate quadrilateral, but you would know this only if you checked down a couple layers–something I suspect most students (and obviously some problem writers) would miss. Unless a class has explicitly addressed degenerate forms, I don’t think this is a fair question as written.
Even so, I wondered if the problem could be saved. It wasn’t an isosceles quadrilateral in the formulation suggested by its unknown writer, but I wondered if there was a way to save it. My following attempts all keep the given side labels, but assume the figure is not drawn to scale.
First a diversion:
Some don’t realize that the definition of a trapezoid is not a 100% settled issue in mathematics. I posted on this almost three years ago (here) and got a few surprisingly fierce responses.
The traditional camp holds to Euclid’s definition that a trapezoid is a quadrilateral with exactly one pair of parallel sides. I always found it interesting that this is the only quadrilateral Euclid restrictively defined in the Elements.
The other camp defines a trapezoid as a quadrilateral with at least one pair of parallel sides. I’ve always liked this camp for two reasons. First, this inclusive definition is more consistent with all of the other inclusive quadrilateral definitions. Second, it allows greater connections between types.
Most students eventually learn that “a square is a rectangle, but a rectangle is not necessarily a square.” This is a logical result of the inclusive definition of a rectangle. Following that reasoning, two equivalent statements possible only from an inclusive definition of a trapezoid are “a parallelogram is a trapezoid, but a trapezoid is not necessarily a parallelogram,” and “a rectangle is an isosceles trapezoid, but an isosceles trapezoid is not necessarily a rectangle.”
Much more importantly, the inclusive definitions create what I call a “cascade of properties.” That is, any properties held by any particular quadrilateral are automatically inherited by every quadrilateral in the direct line below it in the Quadrilateral Hierarchy.
Trying to Salvaging the Problem:
Recovery attempt 1. My first attempt to save the problem–which I first thought would be a satisfactory moment of potentially controversial insight using the inclusive trapezoid definition–ended in some public embarrassment for me. (I hope I recover that with this post!)
Under the inclusive definition, squares and rectangles are also isosceles quadrilaterals. I wondered if the quadrilateral could be a rectangle. If so, opposite sides would be equal, giving $24=3x+2$, or $x=\frac{22}{3}$. That creates a rectangle with sides $\frac{10}{3}$ and 24. I was pleased to have “saved” the problem and quickly tweeted out this solution. Unfortunately, I forgot to double check the perimeter requirement of 88–a point someone had to point out on Twitter. I know better than to make unchecked public pronouncements. Alas. The given problem can’t be saved by treating it as a rectangle.
Recovery attempt 2. Could this be a square? If so, all sides are equal and $x-4=24 \longrightarrow x=20$, but this doesn’t match the x-value found from the rectangle in the first recovery attempt. This is important because squares are rectangles.
The given information doesn’t permit a square. That means the given information doesn’t permit any form of non-degenerate isosceles trapezoid. Disappointing.
Attempt 3–Finally Recovered. What if this really was an isosceles trapezoid, but not as drawn? Nothing explicit stated in the problem prevents me from considering the $x-4$ and the unlabeled sides parallel, and the other two congruent as shown.
So, $24=3x+2 \longrightarrow x=\frac{22}{3}$ as before with the rectangle, making $\left( \frac{22}{3} \right) -4 = \frac{10}{3}$ the last labeled side. The sum of these three sides is $\frac{154}{3}$, so the last side must be $\frac{110}{3}$ for the overall perimeter to be 88. The sum of the smallest of three of these is greater than the 4th, so the degenerate problem that scuttled Attempt #1 did not happen here.
So, there is a solution, $x=\frac{22}{3}$, that satisfies the problem as stated, but how many students would notice the first degenerate case, and then read the given figure as not to scale before finding this answer? This was a poorly written problem.
In the end, the solution for x that I had posted to Twitter turned out to be correct … but not for the reasons I had initially claimed.
Attempt 4–Generalizing. What if the problem was rephrased to make it an exploration of quadrilateral properties? Here’s a suggestion I think might make a dandy exploration project for students.
Given the quadrilateral with three sides labeled as above, but not drawn to scale, and perimeter 88, what more specific types of quadrilateral could be represented by the figure?
Checking types:
• Rectangles and squares are already impossible.
• There is one convoluted isosceles trapezoid possibility detailed in Attempt 3.
• All four sides can’t be equal with the given information (Recovery attempt 2), so rhombus is eliminated.
• Recovery attempt 1 showed that opposite sides could be equal, but since they then do not meet the perimeter requirement, a parallelogram is gone.
• In a kite, there are two adjacent pairs of congruent sides. There are two ways this could happen: the unlabeled side could be 24, or it could be equal to $3x+2$.
• If the unlabeled is 24, then $x-4=3x+2 \longrightarrow x=-3$, an impossible result when plugged back into the given side expressions.
• If the unlabeled side is $3x+2$, then $x-4=24 \longrightarrow x=28$, making the unlabeled side 86 and the overall perimeter 220–much too large. The quadrilateral cannot be kite.
• All that remains is a trapezoid and a generic quadrilateral, for which there are no specific side lengths. With one side unlabeled and therefore unrestricted, the quadrilateral could be constructed in many different ways so long as all sides are positive. That means
• $x-4>0 \longrightarrow x>4$ and
• $3x+2>0 \longrightarrow x>-\frac{2}{3}$.
• In a quadrilateral, the sum of any three sides must be between half and all of the overall length of the perimeter. In this case, $88>24+(x-4)+(3x+2)> \frac{1}{2} 88 \longrightarrow 5.5.
• Putting all three of these together, you can have a trapezoid OR a generic quadrilateral for any $5.5.
CONCLUSION
The given information CAN define an isosceles trapezoid, but the route to and form of the solution is far more convoluted than I suspect the careless question writer intended. Sans the isosceles trapezoid requirement, this figure can define only a generic quadrilateral or a trapezoid, and only then for values of x where $5.5.
Trying to make this problem work, despite its initial flaws, turned out to be a fun romp through a unit on quadrilateral classifications. Running through all of the possibilities, the properties of quadrilaterals, and narrowing down the outcomes might make this problem variation a worthwhile student project, albeit very challenging for many, I think.
I just wish for the students the original problem hadn’t been so poorly written. But if that had happened, I would have missed out on some fun. Hopefully it will be worthwhile for some of your students.
## Problems in Time
Here’s an easy enough challenge problem for students from Math Counts that I found on Twitter via Mathmovesu (@mathmovesu).
Seeing that problem, I wondered
On a 12-hour digital clock, at how many times during a 24-hour day will all of the digits showing the time be a palindrome?
Are all solutions to the original question automatically solutions to the palindrome variation?
What other questions could we ask here? I’m particularly interested in questions students might develop. After all, teachers shouldn’t be the only ones thinking, creating, and extending.
Anyone?
## Unexpected Proof of the Pythagorean Theorem
Following is a neat discovery of an alternative proof of the Pythagorean Theorem resulting from the multiple solutions to the Circle and Square problem. I’m sure someone has seen this before, as there are literally 100s of unique proofs of the Pythagorean Theorem, but this one was new to me.
The intersecting chord relationships in a circle can be proven using only similar triangles. Proofs of these are at the bottom of this post, if needed. Using only those, you can prove the Pythagorean Theorem.
PROOF:
The image below–a revision of the diagram from my previous post–shows diameter DE in circle C. Chord AB is a side of the given square from the Circle and Square problem and is bisected by symmetry into two segments, each of length a. Let be the radius of circle C. Let the portion of DE from point C to chord AB have length b. Because AB is a chord bisected by diameter DE, two right triangles are created, as shown.
AB and DE are intersecting chords, so $a \cdot a = (r-b) \cdot (r+b)$. Expanding the right side and moving the $b^2$ term to the other side gives the Pythagorean Theorem.
Short and sweet once the chord relationships are established.
SUPPORTING PROOF 1:
In the image below, AB and CD are any two chords intersecting at point E. Vertical angles give $\angle DEA \cong \angle BEC$. Because $\angle ADE$ and $\angle CBE$ are inscribed angles sharing arc AC, they are also congruent.
That means $\Delta ADE \sim \Delta CBE$, which gives $\displaystyle \frac{x}{w} = \frac{y}{z}$, or $x \cdot z = w \cdot y$. QED
SUPPORTING PROOF 2:
Show that if a diameter bisects a chord, the diameter and chord are perpendicular. Start with the vertical diameter of circle C bisecting chord AB.
It should be straightforward to show $\Delta ADC \cong \Delta BDC$ by SSS. That means corresponding angles $\angle ADC \cong \angle BDC$; as they also from a linear pair, those angles are both right, and the proof is established.
## Circle and Square
Here’s another great geometry + algebra problem, posed by Megan Schmidt and pitched by Justin Aion to some students in his Geometry class.
Following is the problem as Justin posed it yesterday.
Justin described the efforts of three of his students’ on his his ‘blog. Following is my more generalized approach. Don’t read further if you want to solve this problem for yourself!
My first instinct in any case like this is build it in a dynamic geometry package and play. Using my TI-Nspire, without loss of generality, I graphed a circle centered at the origin, constructed a tangent segment at the bottom of the circle centered on the y-axis, and then used that segment to construct a square. I recognized that the locus of the upper right corners of all such squares would form a line.
That made it clear to me that for any circle, there was a unique square that intersected the circle three times as Megan had posed.
Seeing this and revealing its algebraic bias, my mind conceived an algebraic solution. Assuming the radius of the circle is R, the equation of my circle is $x^2+y^2=R^2$ making the lower y-intercept of the circle $(0,-R)$. That made $y=2x-R$ the locus line containing the upper right corner of the square.
To find generic coordinates of the upper right corner of the square in terms of R, I just needed to solve the system of equations containing the circle and the line. That’s easy enough to compute by hand if you can handle quadratic algebra. That manipulation is not relevant right now, so my Nspire CAS’s version is:
The output confirms the two intersections are $(0,-R)$ and the unknown at $\displaystyle \left( \frac{4R}{5} , \frac{3R}{5} \right)$.
Because of the horizontal symmetry of the square with respect to the y-axis, the system solution shows that the generic length of the side of the square is $\displaystyle 2\left( \frac{4R}{5} \right) = \frac{8R}{5}$. The circle’s y-intercept at $(0,-R)$ means the generic diameter of the circle is $2R$.
Therefore, the generic ratio of the circle’s diameter to the square’s side length is
$\displaystyle \frac{diameter}{side} = \frac{2R}{(8R)/5} = \frac{5}{4}$.
And this is independent of the circle’s radius! The diameter of the circle is always $\frac{5}{4}$ of the square’s side.
CONCLUSION:
For Megan’s particular case with a side length of 20, that gives a circle diameter of 25, confirming Justin’s students’ solution.
Does anyone have a different approach? I’m happy to compile and share all I get.
AN ASIDE:
While not necessary for the generalized solution, it was fun to see a 3-4-5 right triangle randomly appear in Quadrant 1.
## Probability, Polynomials, and Sicherman Dice
Three years ago, I encountered a question on the TI-Nspire Google group asking if there was a way to use CAS to solve probability problems. The ideas I pitched in my initial response and follow-up a year later (after first using it with students in a statistics class) have been thoroughly re-confirmed in my first year teaching AP Statistics. I’ll quickly re-share them below before extending the concept with ideas I picked up a couple weeks ago from Steve Phelps’ session on Probability, Polynomials, and CAS at the 64th annual OCTM conference earlier this month in Cleveland, OH.
BINOMIALS: FROM POLYNOMIALS TO SAMPLE SPACES
Once you understand them, binomial probability distributions aren’t that difficult, but the initial conjoining of combinatorics and probability makes this a perennially difficult topic for many students. The standard formula for the probability of determining the chances of K successes in N attempts of a binomial situation where p is the probability of a single success in a single attempt is no less daunting:
$\displaystyle \left( \begin{matrix} N \\ K \end{matrix} \right) p^K (1-p)^{N-K} = \frac{N!}{K! (N-K)!} p^K (1-p)^{N-K}$
But that is almost exactly the same result one gets by raising binomials to whole number powers, so why not use a CAS to expand a polynomial and at least compute the $\displaystyle \left( \begin{matrix} N \\ K \end{matrix} \right)$ portion of the probability? One added advantage of using a CAS is that you could use full event names instead of abbreviations, making it even easier to identify the meaning of each event.
The TI-Nspire output above shows the entire sample space resulting from flipping a coin 6 times. Each term is an event. Within each term, the exponent of each variable notes the number of times that variable occurs and the coefficient is the number of times that combination occurs. The overall exponent in the expand command is the number of trials. For example, the middle term– $20\cdot heads^3 \cdot tails^3$ –says that there are 20 ways you could get 3 heads and 3 tails when tossing a coin 6 times. The last term is just $tails^6$, and its implied coefficient is 1, meaning there is just one way to flip 6 tails in 6 tosses.
The expand command makes more sense than memorized algorithms and provides context to students until they gain a deeper understanding of what’s actually going on.
FROM POLYNOMIALS TO PROBABILITY
Still using the expand command, if each variable is preceded by its probability, the CAS result combines the entire sample space AND the corresponding probability distribution function. For example, when rolling a fair die four times, the distribution for 1s vs. not 1s (2, 3, 4, 5, or 6) is given by
The highlighted term says there is a 38.58% chance that there will be exactly one 1 and any three other numbers (2, 3, 4, 5, or 6) in four rolls of a fair 6-sided die. The probabilities of the other four events in the sample space are also shown. Within the TI-Nspire (CAS or non-CAS), one could use a command to give all of these probabilities simultaneously (below), but then one has to remember whether the non-contextualized probabilities are for increasing or decreasing values of which binomial outcome.
Particularly early on in their explorations of binomial probabilities, students I’ve taught have shown a very clear preference for the polynomial approach, even when allowed to choose any approach that makes sense to them.
TAKING POLYNOMIALS FROM ONE DIE TO MANY
Given these earlier thoughts, I was naturally drawn to Steve Phelps “Probability, Polynomials, and CAS” session at the November 2014 OCTM annual meeting in Cleveland, OH. Among the ideas he shared was using polynomials to create the distribution function for the sum of two fair 6-sided dice. My immediate thought was to apply my earlier ideas. As noted in my initial post, the expansion approach above is not limited to binomial situations. My first reflexive CAS command in Steve’s session before he share anything was this.
By writing the outcomes in words, the CAS interprets them as variables. I got the entire sample space, but didn’t learn gain anything beyond a long polynomial. The first output– $five^2$ –with its implied coefficient says there is 1 way to get 2 fives. The second term– $2\cdot five \cdot four$ –says there are 2 ways to get 1 five and 1 four. Nice that the technology gives me all the terms so quickly, but it doesn’t help me get a distribution function of the sum. I got the distributions of the specific outcomes, but the way I defined the variables didn’t permit sum of their actual numerical values. Time to listen to the speaker.
He suggested using a common variable, X, for all faces with the value of each face expressed as an exponent. That is, a standard 6-sided die would be represented by $X^1+X^2+ X^3+X^4+X^5+X^6$ where the six different exponents represent the numbers on the six faces of a typical 6-sided die. Rolling two such dice simultaneously is handled as I did earlier with the binomial cases.
NOTE: Exponents are handled in TWO different ways here. 1) Within a single polynomial, an exponent is an event value, and 2) Outside a polynomial, an exponent indicates the number of times that polynomial is applied within the specific event. Coefficients have the same meaning as before.
Because the variables are now the same, when specific terms are multiplied, their exponents (face values) will be added–exactly what I wanted to happen. That means the sum of the faces when you roll two dice is determined by the following.
Notice that the output is a single polynomial. Therefore, the exponents are the values of individual cases. For a couple examples, there are 3 ways to get a sum of 10 $\left( 3 \cdot x^{10} \right)$, 2 ways to get a sum of 3 $\left( 2 \cdot x^3 \right)$, etc. The most commonly occurring outcome is the term with the largest coefficient. For rolling two standard fair 6-sided dice, a sum of 7 is the most common outcome, occurring 6 times $\left( 6 \cdot x^7 \right)$. That certainly simplifies the typical 6×6 tables used to compute the sums and probabilities resulting from rolling two dice.
While not the point of Steve’s talk, I immediately saw that technology had just opened the door to problems that had been computationally inaccessible in the past. For example, what is the most common sum when rolling 5 dice and what is the probability of that sum? On my CAS, I entered this.
In the middle of the expanded polynomial are two terms with the largest coefficients, $780 \cdot x^{18}$ and $780 \cdot x^{19}$, meaning a sums of 17 and 18 are the most common, equally likely outcomes when rolling 5 dice. As there are $6^5=7776$ possible outcomes when rolling a die 5 times, the probability of each of these is $\frac{780}{7776} \approx 0.1003$, or about 10.03% chance each for a sum of 17 or 18. This can be verified by inserting the probabilities as coefficients before each term before CAS expanding.
With thought, this shouldn’t be surprising as the expected mean value of rolling a 6-sided die many times is 3.5, and $5 \cdot 3.5 = 17.5$, so the integers on either side of 17.5 (17 & 18) should be the most common. Technology confirms intuition.
ROLLING DIFFERENT DICE SIMULTANEOUSLY
What is the distribution of sums when rolling a 4-sided and a 6-sided die together? No problem. Just multiply two different polynomials, one representative of each die.
The output shows that sums of 5, 6, and 7 would be the most common, each occurring four times with probability $\frac{1}{6}$ and together accounting for half of all outcomes of rolling these two dice together.
A BEAUTIFUL EXTENSION–SICHERMAN DICE
My most unexpected gain from Steve’s talk happened when he asked if we could get the same distribution of sums as “normal” 6-sided dice, but from two different 6-sided dice. The only restriction he gave was that all of the faces of the new dice had to have positive values. This can be approached by realizing that the distribution of sums of the two normal dice can be found by multiplying two representative polynomials to get
$x^{12}+2x^{11}+3x^{10}+4x^9+5x^8+6x^7+5x^6+4x^5+3x^4+2x^3+x^2$.
Restating the question in the terms of this post, are there two other polynomials that could be multiplied to give the same product? That is, does this polynomial factor into other polynomials that could multiply to the same product? A CAS factor command gives
Any rearrangement of these eight (four distinct) sub-polynomials would create the same distribution as the sum of two dice, but what would the the separate sub-products mean in terms of the dice? As a first example, what if the first two expressions were used for one die (line 1 below) and the two squared trinomials comprised a second die (line 2)?
Line 1 actually describes a 4-sided die with one face of 4, two faces with 3s, and one face of 2. Line 2 describes a 9-sided die (whatever that is) with one face of 8, two faces of 6, three faces of 4, two faces of 2, and one face with a 0 ( $1=1 \cdot x^0$). This means rolling a 4-sided and a 9-sided die as described would give exactly the same sum distribution. Cool, but not what I wanted. Now what?
Factorization gave four distinct sub-polynomials, each with multitude 2. One die could contain 0, 1, or 2 of each of these with the remaining factors on the other die. That means there are $3^4=81$ different possible dice combinations. I could continue with a trail-and-error approach, but I wanted to be more efficient and elegant.
What follows is the result of thinking about the problem for a while. Like most math solutions to interesting problems, ultimate solutions are typically much cleaner and more elegant than the thoughts that went into them. Problem solving is a messy–but very rewarding–business.
SOLUTION
Here are my insights over time:
1) I realized that the $x^2$ term would raise the power (face values) of the desired dice, but would not change the coefficients (number of faces). Because Steve asked for dice with all positive face values. That meant each desired die had to have at least one x to prevent non-positive face values.
2) My first attempt didn’t create 6-sided dice. The sums of the coefficients of the sub-polynomials determined the number of sides. That sum could also be found by substituting $x=1$ into the sub-polynomial. I want 6-sided dice, so the final coefficients must add to 6. The coefficients of the factored polynomials of any die individually must add to 2, 3, or 6 and have a product of 6. The coefficients of $(x+1)$ add to 2, $\left( x^2+x+1 \right)$ add to 3, and $\left( x^2-x+1 \right)$ add to 1. The only way to get a polynomial coefficient sum of 6 (and thereby create 6-sided dice) is for each die to have one $(x+1)$ factor and one $\left( x^2+x+1 \right)$ factor.
3) That leaves the two $\left( x^2-x+1 \right)$ factors. They could split between the two dice or both could be on one die, leaving none on the other. We’ve already determined that each die already had to have one each of the x, $(x+1)$, and $\left( x^2+x+1 \right)$ factors. To also split the $\left( x^2-x+1 \right)$ factors would result in the original dice: Two normal 6-sided dice. If I want different dice, I have to load both of these factors on one die.
That means there is ONLY ONE POSSIBLE alternative for two 6-sided dice that have the same sum distribution as two normal 6-sided dice.
One die would have single faces of 8, 6, 5, 4, 3, and 1. The other die would have one 4, two 3s, two 2s, and one 1. And this is exactly the result of the famous(?) Sicherman Dice.
If a 0 face value was allowed, shift one factor of x from one polynomial to the other. This can be done two ways.
The first possibility has dice with faces {9, 7, 6, 5, 4, 2} and {3, 2, 2, 1, 1, 0}, and the second has faces {7, 5, 4, 3, 2, 0} and {5, 4, 4, 3, 3, 2}, giving the only other two non-negative solutions to the Sicherman Dice.
Both of these are nothing more than adding one to all faces of one die and subtracting one from from all faces of the other. While not necessary to use polynomials to compute these, they are equivalent to multiplying the polynomial of one die by x and the other by $\frac{1}{x}$ as many times as desired. That means there are an infinite number of 6-sided dice with the same sum distribution as normal 6-sided dice if you allow the sides to have negative faces. One of these is
corresponding to a pair of Sicherman Dice with faces {6, 4, 3, 2, 1, -1} and {1,5,5,4,4,3}.
CONCLUSION:
There are other very interesting properties of Sicherman Dice, but this is already a very long post. In the end, there are tremendous connections between probability and polynomials that are accessible to students at the secondary level and beyond. And CAS keeps the focus on student learning and away from the manipulations that aren’t even the point in these explorations.
Enjoy.
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## Find an integral basis
Number theory
Nikos Athanasiou
Articles: 0
Posts: 6
Joined: Thu Nov 19, 2015 7:27 pm
### Find an integral basis
Hello everyone! This is my first post. I salute the initiative of creating a forum solely dedicated to university mathematics. I feel it is something that has been missing for a long time.
That being said, here's a nice exercise in number fields :
Let $K = \mathbb{Q} (\sqrt{p}, \sqrt{q})$ where $p \equiv q \equiv 3 (\mod 4)$ . Compute an integral basis for $K$.
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# Math Help - simplify and proof that answer is this
1. ## simplify and proof that answer is this
can anybody help?
2. ## Re: simplify and proof that answer is this
Originally Posted by tautvyduks
can anybody help?
For the first problem, note that
$sin(A - B) = sin(A)~cos(B) - sin(B)~cos(A)$
so we have:
$sin \left ( \frac{\pi}{3} - \alpha \right ) = sin \left ( \frac{\pi}{3} \right ) ~cos( \alpha ) - sin( \alpha) ~cos \left ( \frac{\pi}{3} \right )$
See if that helps.
-Dan
3. ## Re: simplify and proof that answer is this
How do you begin with an expression and end with an equation?
4. ## Re: simplify and proof that answer is this
but what i should do with 1/2sin(alpha)
5. ## Re: simplify and proof that answer is this
Subtract it from the expression topsquark gave you after you have simplified it.
6. ## Re: simplify and proof that answer is this
For the second problem, note that $sin(2x) = 2~sin(x)~cos(x)$, so we have
$1 - sin^4(x) - sin^2(x) = \frac{1}{4}sin^2(x)$
$1 - sin^4(x) - sin^2(x) = \frac{1}{4} \left ( 2~sin(x)~cos(x) \right ) ^2$
Multiply out the RHS and use $cos^2(x) = 1 - sin^2(x)$, then solve for sin(x).
You will get $sin^2(x) = \frac{1}{2}$
Note that there will be four solutions to this.
-Dan
Wow. Lots of posting going on in this thread!
x
8. ## Re: simplify and proof that answer is this
ok, thanks i did that but what i have to do with -1/2sin(alpha)? im bad at maths sorry
9. ## Re: simplify and proof that answer is this
Originally Posted by topsquark
For the second problem, note that $sin(2x) = 2~sin(x)~cos(x)$, so we have
$1 - sin^4(x) - sin^2(x) = \frac{1}{4}sin^2(x)$
$1 - sin^4(x) - sin^2(x) = \frac{1}{4} \left ( 2~sin(x)~cos(x) \right ) ^2$
Multiply out the RHS and use $cos^2(x) = 1 - sin^2(x)$, then solve for sin(x).
You will get $sin^2(x) = \frac{1}{2}$
Note that there will be four solutions to this.
-Dan
Wow. Lots of posting going on in this thread!
Thanks, but i need to solve this i need to proof that
$1 - sin^4(x) - sin^2(x) is equal to frac{1}{4}sin^2(x)$
i
10. ## Re: simplify and proof that answer is this
The second problem is:
$1 - \sin^4(x) - \sin^2(x) = \frac{1}{4}\sin^2(2x)$
This is not an identity to prove, but an equation to solve.
Using the double-angle identity for sine provided by topsquark, we have:
$1 - \sin^4(x) - \sin^2(x) = \frac{1}{4}(2\sin(x)\cos(x))^2$
$1 -\sin^4(x) - \sin^2(x) = \sin^2(x)\cos^2(x)$
$1 - \sin^4(x) - \sin^2(x) = \sin^2(x)(1-\sin^2(x))$
$1 - \sin^4(x) - \sin^2(x) = \sin^2(x)-\sin^4(x)$
$1 - \sin^2(x) = \sin^2(x)$
$1 = 2\sin^2(x)$
$\sin^2(x)=\frac{1}{2}$
$\sin(x)=\pm\frac{1}{\sqrt{2}}$
You will find 4 solutions on the interval $0\le x<2\pi$. If you are not restricted to an interval, then you will have an infinite number of solutions, which is easily expressed as the integral multiple of an angle.
11. ## Re: simplify and proof that answer is this
i need to suplify left side of this and get the right side.. not to solve X...
12. ## Re: simplify and proof that answer is this
It is not an identity. It is only true for certain values of x.
13. ## Re: simplify and proof that answer is this
ohhh it`s imposibble tu supplify it am i right?
14. ## Re: simplify and proof that answer is this
It is impossible to take the left side and get the right, yes.
15. ## Re: simplify and proof that answer is this
oh thanks. and can you help with the 1st one?
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# Chapter 5 Bootstrapping
The central analogy of bootstrapping is
The population is to the sample as the sample is to the bootstrap samples (Fox 2008, 590)
To calculate standard errors to use in confidence intervals we need to know sampling distribution of the statistic of interest.
In the case of a mean, we can appeal to the central limit theorem if the sample size is large enough.
Bootstrapping takes a different approach. We use the sample as an estimator of the sampling distribution. E.g. bootstrap claims $\text{sample distribution} \approx \text{population distribution}$ and then proceeds to plug-in the sample distribution for the population distribution, and then draw new samples to generate a sampling distribution.
The bootstrap relies upon the plug-in principle. The plug-in principle is that when something is unknown, use an estimate of it. An example is the use of the sample standard deviation in place of the population standard deviation, when calculating the standard error of the mean, $\SE(\bar{x}) = \frac{\sigma}{\sqrt{n}} \approx \frac{\hat{\sigma}}{\sqrt{n}}$ Bootstrap is the plug-in principal on ’roids. It uses the empirical distribution as a plug-in for the unknown population distribution. See Figures 4 and 5 of Hesterberg (2015).
Bootstrap principles
1. The substitution of the empirical distribution for the population works.
2. Sample with replacement.
• The bootstrap is for inference not better estimates. It can estimate uncertainty, not improve $$\bar{x}$$. It is not generating new data out of nowhere. However, see the section on bagging for how bootstrap aggregation can be used.
## 5.1 Non-parametric bootstrap
The non-parametric bootstrap resamples the data with replacement $$B$$ times and calculates the statistic on each resample.
## 5.2 Standard Errors
The bootstrap is primarily a means to calculate standard errors.
The bootstrap standard error is
Suppose there are $$r$$ bootstrap replicates. Let $$\hat{\theta}^{*}_1, \dots, \hat{\theta}^{*}_r$$ be statistics calculated on each bootstrap samples. $\SE^{*}\left(\hat{\theta}^{*}\right) = \sqrt{\frac{\sum_{b = 1}^r {(\hat{\theta}^{*}_b - \bar{\theta}^{*})}^2}{r - 1}}$ where $$\bar{\theta}^{*}$$ is the mean of bootstrap statistics, $\bar{\theta}^{*} = \frac{\sum_{b = 1}^r}{r} .$
## 5.3 Confidence Intervals
There are multiple ways to calculate confidence intervals from bootstrap.
• Normal-Theory Intervals
• Percentile Intervals
• ABC Intervals
## 5.4 Alternative methods
### 5.4.1 Parametric Bootstrap
The parametric bootstrap draws samples from the estimated model.
For example, in linear regression, we can start from the model, $y_i = \Vec{x}_i \Vec{\beta} + \epsilon_i$
1. Estimate the regression model to get $$\hat{\beta}$$ and $$\hat{\sigma}$$
2. For $$1, \dots, r$$ bootstrap replicates:
1. Generate bootstrap sample $$(\Vec{y}^{*}, \Mat{X})$$, where $$\Mat{X}$$ are those from the original sample, and the values of $$\Vec{y}^{*}$$ are generated by sampling from the residual distribution, $y_i^{*}_b = \Vec{x}_i \Vec{\hat{\beta}} + \epsilon^{*}_{i,b}$ where $$\epsilon^{*}_{i,b} \sim \mathrm{Normal}(0, \hat{\sigma})$$.
2. Re-estimate a regression on $$(\Vec{y}^{*}, \Mat{X})$$ to estimate $$\hat{\beta}^{*}$$.
3. Calculate any statistics of the regression results.
Alternatively, we could have drawn the values of $$\Vec{\epsilon}^*_b$$ from the empirical distribution of residuals or the Wild Bootstrap.
See the the discussion in the boot::boot() function, for sim = "parametric".
### 5.4.2 Clustered bootstrap
We can incorporate complex sampling methods into the bootstrap (Fox 2008, Sec 21.5). In particular, by resampling clusters instead of individual observations, we get the clustered bootstrap.(Esarey and Menger 2017)
### 5.4.3 Time series bootstrap
Since data are not independent in time-series, variations of the bootstrap have to be used. See the references in the documentation for boot::tsboot.
### 5.4.4 How to sample?
Draw the bootstrap sample in the same way it was drawn from the population (if possible) (Hesterberg 2015, 19)
The are a few exceptions:
• Condition on the observed information. We should fix known quantities, e.g. observed sample sizes of sub-samples (Hesterberg 2015)
• For hypothesis testing, the sampling distribution needs to be modified to represent the null distribution (Hesterberg 2015)
### 5.4.5 Caveats
• Bootstrapping does not work well for the median or other quantities that depend on the small number of observations out of larger sample.(Hesterberg 2015)
• Uncertainty in the bootstrap estimator is due to both (1) Monte Carlo sampling (taking a finite number of samples), and (2) the sample itself. The former can be decreased by increasing the number of bootstrap samples. The latter is irreducible without a new sample.
• The bootstrap distribution will reflect the data. If the sample was “unusual”, then the bootstrap distribution will also be so.(Hesterberg 2015)
• In small samples there is a narrowness bias. (Hesterberg 2015, 24). As always, small samples is problematic.
### 5.4.6 Why use bootstrapping?
• The common practice of relying on asymmetric results may understate variability by ignoring dependencies or heteroskedasticity. These can be incorporated into bootstrapping.(Fox 2008, 602)
• it is general purpose algorithm that can generate standard errors and confidence intervals in cases where an analytic solution does not exist.
• however, it may require programming to implement and computational power to execute
## 5.5 Bagging
Note that in all the previous discussion, the original point estimate is used. Bootstrapping is only used to generate (1) standard errors and confidence intervals (2).
Bootstrap aggregating or bagging is a meta-algorithm that constructs a point estimate by averaging the point-estimates from bootstrap samples. Bagging can reduce the variance of some estimators, so can be thought of as a sort of regularization method.
## 5.6 Hypothesis Testing
Hypothesis testing with bootstrap is more complicated.
## 5.7 How many samples?
There is no fixed rule of thumb (it will depend on the statistic you are calculating and the population distribution), but if you want a single number, 1,000 is good lower bound.
• Higher levels of confidence require more samples
• Note that the results of the percentile method will be more variable than the normal-approximation method. The ABC confidence intervals will be even better.
One ad-hoc recipe suggested here is:
1. Choose a $$B$$
2. Run the bootstrap
3. Run the bootstrap again (ensure there is a different random number seed)
4. If results differ, increase the size.
Davidson and MacKinnon (2000) suggest the following:
• 5%: 399
• 1%: 1499
Though it also suggests a pre-test method.
Hesterberg (2015) suggests far a larger bootstrap sample size: 10,000 for routine use. It notes that for a t-test, 15,000 samples for the a 95% probability that the one-sided levels fall within 10% of the true values, for 95% intervals and 5% tests.
## 5.8 References
See Fox (2008 Ch. 21).
Hesterberg (2015) is for “teachers of statistics” but is a great overview of bootstrapping. I found it more useful than the treatment of bootstrapping in many textbooks.
For some Monte Carlo results on the accuracy of the bootstrap see Hesterberg (2015), p. 21.
R packages. For general purpose bootstrapping and cross-validation I suggest the rsample package, which works well with the tidyverse and seems to be useful going forward.
The boot package included in the recommended R packages is a classic package that implements many bootstrapping and resampling methods. Most of them are parallelized. However, its interface is not as nice as rsample.
See this spreadsheet for some Monte Carlo simulations on Bootstrap vs. t-statistic.
### References
Fox, John. 2008. Applied Regression Analysis & Generalized Linear Models. 2nd ed. Sage.
Hesterberg, Tim C. 2015. “What Teachers Should Know About the Bootstrap: Resampling in the Undergraduate Statistics Curriculum.” The American Statistician 69 (4). Taylor & Francis: 371–86. https://doi.org/10.1080/00031305.2015.1089789.
Esarey, Justin, and Andrew Menger. 2017. “Practical and Effective Approaches to Dealing with Clustered Data.” Working Paper. http://jee3.web.rice.edu/cluster-paper.pdf.
Davidson, Russell, and James G. MacKinnon. 2000. “Bootstrap Tests: How Many Bootstraps?” Econometric Reviews 19 (1). Taylor & Francis: 55–68. https://doi.org/10.1080/07474930008800459.
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\mathbb{E} \big[ W_t \exp W_t \big] = t \exp \big( \tfrac{1}{2} t \big). / Since $W_s \sim \mathcal{N}(0,s)$ we have, by an application of Fubini's theorem, Can state or city police officers enforce the FCC regulations? exp d The former is used to model deterministic trends, while the latter term is often used to model a set of unpredictable events occurring during this motion. 79 0 obj If Introduction) [1] It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the BlackScholes model. << /S /GoTo /D (section.6) >> endobj some logic questions, known as brainteasers. 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Geometric Brownian motion models for stock movement except in rare events. its probability distribution does not change over time; Brownian motion is a martingale, i.e. {\displaystyle dt} t Markov and Strong Markov Properties) t t (2.2. endobj {\displaystyle \sigma } Please let me know if you need more information. so we can re-express $\tilde{W}_{t,3}$ as j = Y = ( 80 0 obj ( This is zero if either $X$ or $Y$ has mean zero. u \qquad& i,j > n \\ Is Sun brighter than what we actually see? and 32 0 obj where the Wiener processes are correlated such that 48 0 obj a random variable), but this seems to contradict other equations. , How To Distinguish Between Philosophy And Non-Philosophy? Difference between Enthalpy and Heat transferred in a reaction? Are there different types of zero vectors? Connect and share knowledge within a single location that is structured and easy to search. Did Richard Feynman say that anyone who claims to understand quantum physics is lying or crazy? A stochastic process St is said to follow a GBM if it satisfies the following stochastic differential equation (SDE): where The set of all functions w with these properties is of full Wiener measure. log Brownian motion has independent increments. Wiley: New York. expectation of brownian motion to the power of 3. Therefore I like Gono's argument a lot. 4 With probability one, the Brownian path is not di erentiable at any point. Difference between Enthalpy and Heat transferred in a reaction? June 4, 2022 . Brownian Motion as a Limit of Random Walks) where The graph of the mean function is shown as a blue curve in the main graph box. 16 0 obj Hence, $$Suppose that 0 and endobj endobj i 2 0 {\displaystyle R(T_{s},D)} Connect and share knowledge within a single location that is structured and easy to search. In this sense, the continuity of the local time of the Wiener process is another manifestation of non-smoothness of the trajectory. \ldots & \ldots & \ldots & \ldots \\ 2 35 0 obj$$=-\mu(t-s)e^{\mu^2(t-s)/2}=- \frac{d}{d\mu}(e^{\mu^2(t-s)/2}).. 2 M_{W_t} (u) = \mathbb{E} [\exp (u W_t) ] \begin{align} << /S /GoTo /D (subsection.1.4) >> f Example. I am not aware of such a closed form formula in this case. \rho_{23} &= \rho_{12}\rho_{13} + \sqrt{(1-\rho_{12}^2)(1-\rho_{13}^2)} \rho(\tilde{W}_{t,2}, \tilde{W}_{t,3}) \\ {\displaystyle \rho _{i,i}=1} Use MathJax to format equations. The local time L = (Lxt)x R, t 0 of a Brownian motion describes the time that the process spends at the point x. t After this, two constructions of pre-Brownian motion will be given, followed by two methods to generate Brownian motion from pre-Brownain motion. How To Distinguish Between Philosophy And Non-Philosophy? u \qquad& i,j > n \\ s \wedge u \qquad& \text{otherwise} \end{cases}, $$\int_0^t \int_0^t s^a u^b (s \wedge u)^c du ds$$, \begin{align} since \begin{align} {\displaystyle dt\to 0} 2 $$\mathbb{E}[Z_t^2] = \int_0^t \int_0^t \mathbb{E}[W_s^n W_u^n] du ds$$ 2023 Jan 3;160:97-107. doi: . A simple way to think about this is by remembering that we can decompose the second of two brownian motions into a sum of the first brownian and an independent component, using the expression Use MathJax to format equations. t In other words, there is a conflict between good behavior of a function and good behavior of its local time. Is Sun brighter than what we actually see? ( Show that, $$E\left( (B(t)B(s))e^{\mu (B(t)B(s))} \right) = - \frac{d}{d\mu}(e^{\mu^2(t-s)/2})$$, The increments $B(t)-B(s)$ have a Gaussian distribution with mean zero and variance $t-s$, for $t>s$. The covariance and correlation (where For various values of the parameters, run the simulation 1000 times and note the behavior of the random process in relation to the mean function. S Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company. . Wall shelves, hooks, other wall-mounted things, without drilling? $$, The MGF of the multivariate normal distribution is,$$ To have a more "direct" way to show this you could use the well-known It formula for a suitable function $h$ $$h(B_t) = h(B_0) + \int_0^t h'(B_s) \, {\rm d} B_s + \frac{1}{2} \int_0^t h''(B_s) \, {\rm d}s$$. where x $W_{t_2} - W_{s_2}$ and $W_{t_1} - W_{s_1}$ are independent random variables for $0 \le s_1 < t_1 \le s_2 < t_2$; $W_t - W_s \sim \mathcal{N}(0, t-s)$ for $0 \le s \le t$. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. endobj is: To derive the probability density function for GBM, we must use the Fokker-Planck equation to evaluate the time evolution of the PDF: where The process The image of the Lebesgue measure on [0, t] under the map w (the pushforward measure) has a density Lt. For the multivariate case, this implies that, Geometric Brownian motion is used to model stock prices in the BlackScholes model and is the most widely used model of stock price behavior.[3]. A GBM process only assumes positive values, just like real stock prices. {\displaystyle X_{t}} It only takes a minute to sign up. 11 0 obj t t {\displaystyle W_{t}} \sigma^n (n-1)!! t Regarding Brownian Motion. X d The general method to compute expectations of products of (joint) Gaussians is Wick's theorem (also known as Isserlis' theorem). When {\displaystyle dW_{t}^{2}=O(dt)} 43 0 obj Thus the expectation of $e^{B_s}dB_s$ at time $s$ is $e^{B_s}$ times the expectation of $dB_s$, where the latter is zero. t A The Zone of Truth spell and a politics-and-deception-heavy campaign, how could they co-exist? 39 0 obj IEEE Transactions on Information Theory, 65(1), pp.482-499. W }{n+2} t^{\frac{n}{2} + 1}. Do peer-reviewers ignore details in complicated mathematical computations and theorems? Making statements based on opinion; back them up with references or personal experience. . t t 71 0 obj \end{align}, $$f(t) = f(0) + \frac{1}{2}k\int_0^t f(s) ds + \int_0^t \ldots dW_1 + \ldots$$,k = \sigma_1^2 + \sigma_2^2 +\sigma_3^2 + 2 \rho_{12}\sigma_1\sigma_2 + 2 \rho_{13}\sigma_1\sigma_3 + 2 \rho_{23}\sigma_2\sigma_3$, $$m(t) = m(0) + \frac{1}{2}k\int_0^t m(s) ds.$$, Expectation of exponential of 3 correlated Brownian Motion. Properties of a one-dimensional Wiener process, Steven Lalley, Mathematical Finance 345 Lecture 5: Brownian Motion (2001), T. Berger, "Information rates of Wiener processes," in IEEE Transactions on Information Theory, vol. !$ is the double factorial. If = Using this fact, the qualitative properties stated above for the Wiener process can be generalized to a wide class of continuous semimartingales. What does it mean to have a low quantitative but very high verbal/writing GRE for stats PhD application? is a martingale, and that. i $$. Then, however, the density is discontinuous, unless the given function is monotone. {\displaystyle \xi =x-Vt} with n\in \mathbb{N}. Okay but this is really only a calculation error and not a big deal for the method. Derivation of GBM probability density function, "Realizations of Geometric Brownian Motion with different variances, Learn how and when to remove this template message, "You are in a drawdown. D (1.2. 36 0 obj \sigma^n (n-1)!! Y &= {\mathbb E}[e^{(\sigma_1 + \sigma_2 \rho_{12} + \sigma_3 \rho_{13}) W_{t,1} + (\sqrt{1-\rho_{12}^2} + \tilde{\rho})\tilde{W}_{t,2} + \sqrt{1-\tilde{\rho}} \tilde{\tilde{W_{t,3}}}}] \\ . More significantly, Albert Einstein's later . ( . 2 Thanks for contributing an answer to Quantitative Finance Stack Exchange! ( Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. 0 20 0 obj 2 Asking for help, clarification, or responding to other answers. Poisson regression with constraint on the coefficients of two variables be the same, Indefinite article before noun starting with "the". Why is water leaking from this hole under the sink? / /$$\mathbb{E}[Z_t^2] = \sum \int_0^t \int_0^t \prod \mathbb{E}[X_iX_j] du ds.$$Example: W B_s and dB_s are independent. for some constant \tilde{c}. where a+b+c = n. herr korbes meaning; diamondbacks right field wall seats; north dakota dental association classifieds (The step that says \mathbb E[W(s)(W(t)-W(s))]= \mathbb E[W(s)] \mathbb E[W(t)-W(s)] depends on an assumption that t>s.). t ) Hence 2 }{n+2} t^{\frac{n}{2} + 1}, X \sim \mathcal{N}(0, s), Y \sim \mathcal{N}(0,u),$$\mathbb{E}[X_1 \dots X_{2n}] = \sum \prod \mathbb{E}[X_iX_j]$$,$$\mathbb{E}[Z_t^2] = \int_0^t \int_0^t \mathbb{E}[W_s^n W_u^n] du ds$$,$$\mathbb{E}[Z_t^2] = \sum \int_0^t \int_0^t \prod \mathbb{E}[X_iX_j] du ds.$$,$$\mathbb{E}[X_iX_j] = \begin{cases} s \qquad& i,j \leq n \\ d By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. $$\mathbb{E}[Z_t^2] = \sum \int_0^t \int_0^t \prod \mathbb{E}[X_iX_j] du ds.$$ 8 0 obj is the quadratic variation of the SDE. $W(s)\sim N(0,s)$ and $W(t)-W(s)\sim N(0,t-s)$. \\=& \tilde{c}t^{n+2} are correlated Brownian motions with a given, I can't think of a way to solve this although I have solved an expectation question with only a single exponential Brownian Motion. Y endobj \end{align}, \begin{align} Thus. {\displaystyle f} 52 0 obj MathOverflow is a question and answer site for professional mathematicians. 56 0 obj More generally, for every polynomial p(x, t) the following stochastic process is a martingale: Example: W a power function is multiplied to the Lyapunov functional, from which it can get an exponential upper bound function via the derivative and mathematical expectation operation . We define the moment-generating function $M_X$ of a real-valued random variable $X$ as As such, it plays a vital role in stochastic calculus, diffusion processes and even potential theory. Compute $\mathbb{E} [ W_t \exp W_t ]$. Unless other- . , i Continuous martingales and Brownian motion (Vol. for 0 t 1 is distributed like Wt for 0 t 1. << /S /GoTo /D [81 0 R /Fit ] >> x By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Symmetries and Scaling Laws) + By introducing the new variables Edit: You shouldn't really edit your question to ask something else once you receive an answer since it's not really fair to move the goal posts for whoever answered. d , t W Wald Identities; Examples) How dry does a rock/metal vocal have to be during recording? The expected returns of GBM are independent of the value of the process (stock price), which agrees with what we would expect in reality. Background checks for UK/US government research jobs, and mental health difficulties. = Why we see black colour when we close our eyes. A After signing a four-year, $94-million extension last offseason, the 25-year-old had arguably his best year yet, totaling 81 pressures, according to PFF - second only to Micah Parsons (98) and . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 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### NDF2FITS
Converts NDFs into FITS files
#### Description:
This application converts one or more NDF datasets into FITS-format files. NDF2FITS stores any variance and quality information in IMAGE extensions (‘sub-files’) within the FITS file; and it uses binary tables to hold any NDF-extension data present, except for the FITS-airlock extension, which may be merged into the output FITS file’s headers.
You can select which NDF array components to export to the FITS file, and choose the data type of the data and variance arrays. You can control whether or not to propagate extensions and history information.
The application also accepts NDFs stored as top-level components of an HDS container file.
Both NDF and FITS use the term extension, and they mean different things. Thus to avoid confusion in the descriptions below, the term ‘sub-file’ is used to refer to a FITS IMAGE, TABLE or BINTABLE Header and Data Unit (HDU).
#### Usage:
ndf2fits in out [comp] [bitpix] [origin]
#### Parameters:
If TRUE, tables of world co-ordinates may be written using the TAB algorithm as defined in the FITS-WCS Paper III. Examples where such a table might be present in the WCS include wavelengths of pre-scrunched spectra, and the presence of distortions that prevent co-ordinates being defined by analytical expressions. Since many FITS readers are yet to support the TAB algorithm, which uses a FITS binary-table extension to store the co-ordinates, this parameter permits this facility to be disabled. [TRUE]
Specifies the order of WCS axes within the output FITS header. It can be either null (!), "Copy" or a space-separated list of axis symbols (case insensitive). If it is null, the order is determined automatically so that the $i$th WCS axis is the WCS axis that is most nearly parallel to the $i$th pixel axis. If it is "Copy", the $i$th WCS axis in the FITS header is the $i$th WCS axis in the NDF’s current WCS Frame. Otherwise, the string must be a space-separated list of axis symbols that gives the order for the WCS axes. An error is reported if the list does not contain any of the axis symbols present in the current WCS Frame, but no error is reported if the list also contains other symbols. [!]
The FITS bits-per-pixel (BITPIX) value for each conversion. This specifies the data type of the output FITS file. Permitted values are: 8 for unsigned byte, 16 for signed word, 32 for integer, 64 for 64-bit integer, -32 for real, -64 for double precision. There are three other special values.
• BITPIX=0 will cause the output file to have the data type equivalent to that of the input NDF.
• BITPIX=-1 requests that the output file has the data type corresponding to the value of the BITPIX keyword in the NDF’s FITS extension. If the extension or BITPIX keyword is absent, the output file takes the data type of the input array.
• BITPIX="Native" requests that any scaled arrays in the NDF be copied to the scaled data type. Otherwise behaviour reverts to BITPIX=-1, which may in turn be effectively BITPIX=0. The case-insensitive value may be abbreviated to "n".
BITPIX values must be enclosed in double quotes and may be a list of comma-separated values to be applied to each conversion in turn. An error results if more values than the number of input NDFs are supplied. If too few are given, the last value in the list is applied to the remainder of the NDFs; thus a single value is applied to all the conversions. The given values must be in the same order as that of the input NDFs. Indirection through a text file may be used. If more than one line is required to enter the information at a prompt then type a "-" at the end of each line where a continuation line is desired. [0]
If TRUE, each header and data unit in the FITS file will contain the integrity-check keywords CHECKSUM and DATASUM immediately before the END card. [TRUE]
The list of array components to attempt to transfer to each FITS file. The acceptable values are "D" for the main data array "V" for variance, "Q" for quality, or any permutation thereof. The special value "A" means all components, i.e. COMP="DVQ". Thus COMP="VD" requests that both the data array and variance are to be converted if present. During processing at least one, if not all, of the requested components must be present, otherwise an error is reported and processing turns to the next input NDF. If the DATA component is in the list, it will always be processed first into the FITS primary array. The order of the variance and quality in COMP decides the order they will appear in the FITS file.
The choice of COMP may affect automatic quality masking. See "Quality Masking" for the details.
COMP may be a list of comma-separated values to be applied to each conversion in turn. The list must be enclosed in double quotes. An error results if more values than the number of input NDFs are supplied. If too few are given, the last value in the list is applied to the remainder of the NDFs; thus a single value is applied to all the conversions. The given values must be in the same order as that of the input NDFs. Indirection through a text file may be used. If more than one line is required to enter the information at a prompt then type a "-" at the end of each line where a continuation line is desired. ["A"]
If TRUE, the supplied IN files are any multi-NDF HDS container files, in which the NDFs reside as top-level components. This option is primarily intended to support the UKIRT format where the NDFs are named .I$n$, $n>=1$, and one named HEADER containing global metadata in its FITS airlock. The .I$n$ NDFs may also contain FITS airlocks, storing metadata pertinent to that NDF, such as observation times. The individual NDFs often represent separate integrations nodded along a slit or spatially. Note that this is not a group, so a single value applies to all the supplied input files. [FALSE]
This qualifies the effect of PROFITS=TRUE. DUPLEX=FALSE means that the airlock headers only appear with the primary array. DUPLEX=TRUE, propagates the FITS airlock headers for other array components of the NDF. [FALSE]
Controls the FITS keywords which will be used to encode the World Co-ordinate System (WCS) information within the FITS header. The value supplied should be one of the encodings listed in the "World Co-ordinate Systems" section below. In addition, the value "Auto" may also be supplied, in which case a suitable default encoding is chosen based on the contents of the NDF’s FITS extension and WCS component. ["Auto"]
The names of the NDFs to be converted into FITS format. It may be a list of NDF names or direction specifications separated by commas and enclosed in double quotes. NDF names may include wild-cards ("*", "?"). Indirection may occur through text files (nested up to seven deep). The indirection character is "^". If extra prompt lines are required, append the continuation character "-" to the end of the line. Comments in the indirection file begin with the character "#".
If a TRUE value is given for Parameter NATIVE, then World Co-ordinate System (WCS) information will be written to the FITS header in the form of a ‘native’ encoding (see "World Co-ordinate Systems" below). This will be in addition to the encoding specified using Parameter ENCODING, and will usually result in two descriptions of the WCS information being stored in the FITS header (unless ENCODING parameter produces a native encoding in which case only one native encoding is stored in the header). Including a native encoding in the header will enable other AST-based software (such as FITS2NDF) to reconstruct the full details of the WCS information. The other non-native encodings will usually result in some information being lost. [FALSE]
Whether or not to merge the FITS-airlocks’ headers of the header NDF of a UKIRT multi-NDF container file with its sole data NDF into the primary header and data unit (HDU). This parameter is only used when CONTAINER is TRUE; and when the container file only has two component NDFs: one data NDF of arbitrary name, and the other called HEADER that stores the global headers of the dataset. [TRUE]
The origin of the FITS files. This becomes the value of the ORIGIN keyword in the FITS headers. If a null value is given it defaults to "Starlink Software". [!]
##### OUT = LITERAL (Write)
The names for the output FITS files. These may be enclosed in double quotes and specified as a list of comma-separated names, or they may be created automatically on the basis of the input NDF names. To do this, the string supplied for this parameter should include an asterisk "$\ast$". This character is a token which represents the name of the corresponding input NDF, but with a file type of ".fit" instead of ".sdf", and with no directory specification. Thus, simply supplying "*" for this parameter will create a group of output files in the current directory with the same names as the input NDFs, but with file type ".fit". You can also specify some simple editing to be performed. For instance, "new-*|.fit|.fits|" will add the string "new-" to the start of every file name, and will substitute the string ".fits" for the original string ".fit".
NDF2FITS will not permit you to overwrite an existing FITS file, unless you supply an exclamation mark prefix (suitably escaped if you are using a UNIX shell).
If TRUE, the NDF extensions (other than the FITS extension) are propagated to the FITS files as FITS binary-table sub-files, one per structure of the hierarchy. [FALSE]
If TRUE, the contents of the FITS extension of the NDF are merged with the header information derived from the standard NDF components. See the "Notes" for details of the merger. [TRUE]
If TRUE, any NDF history records are written to the primary FITS header as HISTORY cards. These follow the mandatory headers and any merged FITS-extension headers (see Parameter PROFITS). [TRUE]
This controls the export of NDF provenance information to the FITS file. Allowed values are as follows.
• "None" — No provenance is written.
• "CADC" — The CADC headers are written. These record the number and paths of both the direct parents of the NDF being converted, and its root ancestors (the ones without parents). It also modifies the PRODUCT keyword to be unique for each FITS sub-file.
• "Generic" — Encapsulates the entire PROVENANCE structure in FITS headers in sets of five character-value indexed headers. there is a set for the current NDF and each parent. See Section "Provenance" for more details.
["None"]
Whether or not to export AXIS co-ordinates to an alternate world co-ordinate representation in the FITS headers. Such an alternate may require a FITS sub-file to store lookup tables of co-ordinates using the -TAB projection type. The default null value requests no AXIS information be stored unless the current NDF contains AXIS information but no WCS. An explicit TRUE or FALSE selection demands the chosen setting irrespective of how the current NDF stores co-ordinate information. [!]
#### Examples:
ndf2fits horse logo.fit d
This converts the NDF called horse to the new FITS file called logo.fit. The data type of the FITS primary data array matches that of the NDF’s data array. The FITS extension in the NDF is merged into the FITS header of logo.fit.
ndf2fits horse !logo.fit d proexts
This converts the NDF called horse to the FITS file called logo.fit. An existing logo.fit will be overwritten. The data type of the FITS primary data array matches that of the NDF’s data array. The FITS extension in the NDF is merged into the FITS header of logo.fit. In addition any NDF extensions (apart from FITS) are turned into binary tables that follow the primary header and data unit.
ndf2fits horse logo.fit noprohis
This converts the NDF called horse to the new FITS file called logo.fit. The data type of the FITS primary data array matches that of the NDF’s data array. The FITS extension in the NDF is merged into the FITS header of logo.fit. Should horse contain variance and quality arrays, these are written in IMAGE sub-files. Any history information in the NDF is not relayed to the FITS file.
ndf2fits "data/a$\ast$z" $\ast$ comp=v noprofits bitpix=-32
This converts the NDFs with names beginning with "a" and ending in "z" in the directory called data into FITS files of the same name and with a file extension of ".fit". The variance array becomes the data array of each new FITS file. The data type of the FITS primary data array single-precision floating point. Any FITS extension in the NDF is ignored.
ndf2fits "abc,def" "jvp1.fit,jvp2.fit" comp=d bitpix="16,-64"
This converts the NDFs called abc and def into FITS files called jvp1.fit and jvp2.fit respectively. The data type of the FITS primary data array is signed integer words in jvp1.fit, and double-precision floating point in jvp2.fit. The FITS extension in each NDF is merged into the FITS header of the corresponding FITS file.
ndf2fits horse logo.fit d native encoding="fits-wcs"
This is the same as the first example except that the co-ordinate system information stored in the NDF’s WCS component is written to the FITS file twice; once using the FITS-WCS headers, and once using a special set of ‘native’ keywords recognised by the AST library (see SUN/210). The native encoding provides a ‘loss-free’ means of transferring co-ordinate system information (i.e. no information is lost; other encodings may cause information to be lost). Only applications based on the AST library (such as FITS2NDF) are able to interpret native encodings.
ndf2fits u20040730_00675 merge container accept
This converts the UIST container file u20040730_00675.sdf to new FITS file u20040730_00675.fit, merging its .I1 and .HEADER structures into a single NDF before the conversion. The output file has only one header and data unit.
ndf2fits in=c20011204_00016 out=cgs4_16.fit container
This converts the CGS4 container file c20011204_00016.sdf to the multiple-extension FITS file cgs4_16.fit. The primary HDU has the global metadata from the .HEADER’s FITS airlock. The four integrations in I1, I2, I3, and I4 components of the container file are converted to FITS IMAGE sub-files.
ndf2fits in=huge out=huge.fits comp=d bitpix=n
This converts the NDF called huge to the new FITS file called huge.fits. The data type of the FITS primary data array matches that of the NDF’s scaled data array. The scale and offset coefficients used to form the FITS array are also taken from the NDF’s scaled array.
ndf2fits in=huge out=huge.fits comp=d bitpix=-1
As the previous example, except that the data type of the FITS primary data array is that given by the BITPIX keyword in the FITS airlock of NDF huge and the scaling factors are determined.
#### Notes:
The rules for the conversion are as follows:
• The NDF main data array becomes the primary data array of the FITS file if it is in value of Parameter COMP, otherwise the first array defined by Parameter COMP will become the primary data array. A conversion from floating point to integer or to a shorter integer type will cause the output array to be scaled and offset, the values being recorded in keywords BSCALE and BZERO. There is an offset (keyword BZERO) applied to signed byte and unsigned word types to make them unsigned-byte and signed-word values respectively in the FITS array (this is because FITS does not support these data types).
• The FITS keyword BLANK records the bad values for integer output types. Bad values in floating-point output arrays are denoted by IEEE not-a-number values.
• The NDF’s quality and variance arrays appear in individual FITS IMAGE sub-files immediately following the primary header and data unit, unless that component already appears as the primary data array. The quality array will always be written as an unsigned-byte array in the FITS file, regardless of the value of the Parameter BITPIX.
• Here are details of the processing of standard items from the NDF into the FITS header, listed by FITS keyword.
• SIMPLE, EXTEND, PCOUNT, GCOUNT — all take their default values.
• BITPIX, NAXIS, NAXISn — are derived directly from the NDF data array; however the BITPIX in the FITS airlock extension is transferred when Parameter BITPIX=-1.
• CRVALn, CDELTn, CRPIXn, CTYPEn, CUNITn — are derived from the NDF WCS component if possible (see "World Co-ordinate Systems"). If this is not possible, and if PROFITS is TRUE, then it copies the headers of a valid WCS specified in the NDF’s FITS airlock. Should that attempt fail, the last resort tries the NDF AXIS component, if it exists. If its co-ordinates are non-linear, the AXIS co-ordinates may be exported in a -TAB sub-file subject to the value of Parameter USEAXIS.
• OBJECT, LABEL, BUNIT — the values held in the NDF’s TITLE, LABEL, and UNITS components respectively are used if they are defined; otherwise any values found in the FITS extension are used (provided Parameter PROFITS is TRUE). For a variance array, BUNIT is assigned to ($$)**2, where $$ is the DATA unit; the BUNIT header is absent for a quality array.
• DATE — is created automatically.
• ORIGIN — inherits any existing ORIGIN card in the NDF FITS extension, unless you supply a value through parameter ORIGIN other than the default "Starlink Software".
• EXTNAME — is the array-component name when the EXTNAME appears in the primary header or an IMAGE sub-file. In a binary-table derived from an NDF extension, EXTNAME is the path of the extension within the NDF, the path separator being the usual dot. The path includes the indices to elements of any array structures present; the indices are in a comma-separated list within parentheses.
If the component is too long to fit within the header (68 characters), EXTNAME is set to @EXTNAMEF. The full path is then stored in keyword EXTNAMEF using the HEASARC Long-string CONTINUE convention
(http://fits.gsfc.nasa.gov/registry/continue_keyword.html).
• EXTVER — is only set when EXTNAME (q.v.) cannot accommodate the component name, and it is assigned the HDU index to provide a unique identifier.
• EXTLEVEL — is the level in the hierarchical structure of the extension. Thus a top-level extension has value 1, sub-components of this extension have value 2 and so on.
• EXTTYPE — is the data type of the NDF extension used to create a binary table.
• EXTSHAPE — is the shape of the NDF extension used to create a binary table. It is a comma-separated list of the dimensions, and is 0 when the extension is not an array.
• HDUCLAS1, HDUCLASn — "NDF" and the array-component name respectively.
• LBOUNDn — is the pixel origin for the ${n}^{\mathrm{\text{th}}}$ dimension when any of the pixel origins is not equal to 1. (This is not a standard FITS keyword.)
• XTENSION, BSCALE, BZERO, BLANK and END — are not propagated from the NDF’s FITS extension. XTENSION will be set for any sub-file. BSCALE and BZERO will be defined based on the chosen output data type in comparison with the NDF array’s type, but cards with values 1.0 and 0.0 respectively are written to reserve places in the header section. These ‘reservation’ cards are for efficiency and they can always be deleted later. BLANK is set to the Starlink standard bad value corresponding to the type specified by BITPIX, but only for integer types and not for the quality array. It appears regardless of whether or not there are bad values actually present in the array; this is for the same efficiency reasons as before. The END card terminates the FITS header.
• HISTORY — HISTORY headers are propagated from the FITS airlock when PROFITS is TRUE, and from the NDF history component when PROHIS is TRUE.
• DATASUM and CHECKSUM — data-integrity keywords are written when Parameter CHECKSUM is TRUE, replacing any existing values. When Parameter CHECKSUM is FALSE and PROFITS is TRUE any existing values inherited from the FITS airlock are removed to prevent storage of invalid checksums relating to another data file.
See also the sections "Provenance" and "World Co-ordinate Systems" for details of headers used to describe the PROVENANCE extension and WCS information respectively.
• Extension information may be transferred to the FITS file when PROEXTS is TRUE. The whole hierarchy of extensions is propagated in order. This includes substructures, and arrays of extensions and substructures. However, at present, any extension structure containing only substructures is not propagated itself (as zero-column tables are not permitted), although its substructures may be converted.
Each extension or substructure creates a one-row binary table, where the columns of the table correspond to the primitive (non-structure) components. The name of each column is the component name. The column order is the same as the component order. The shapes of multi-dimensional arrays are recorded using the TDIMn keyword, where n is the column number. The HEASARCH convention for specifying the width of character arrays (keyword TFORMn=’rAw’, where r is the total number of characters in the column and w is the width of an element) is used. The EXTNAME, EXTTYPE, EXTSHAPE and EXTLEVEL keywords (see above) are written to the binary-table header.
There are additional rules if a multi-NDF container file is being converted (see Parameter CONTAINER). This excludes the case where there are but two NDFs—one data and the other just headers—that have already been merged (see Parameter MERGE):
• For multiple NDFs a header-only HDU may be created followed by an IMAGE sub-file containing the data array (or whichever other array is first specified by COMP).
• BITPIX for the header HDU is set to an arbitrary 8.
• Additional keywords are written for each IMAGE sub-file.
• HDSNAME — is the NDF name for a component NDF in a multi-NDF container file, for example I2.
• HDSTYPE — is set to NDF for a component NDF in a multi-NDF container file.
#### World Co-ordinate Systems
Any co-ordinate system information stored in the WCS component of the NDF is written to the FITS header using one of the following encoding systems (the encodings used are determined by parameters ENCODING and NATIVE):
• "FITS-IRAF" — This uses keywords CRVALi, CRPIXi, and CDi_j, and is the system commonly used by IRAF. It is described in the document World Coordinate Systems Representations Within the FITS Format by by R.J. Hanisch and D.G. Wells, 1988, available by ftp from fits.cv.nrao.edu /fits/documents/wcs/wcs88.ps.Z.
• "FITS-WCS" — This is the FITS standard WCS encoding scheme described in the paper Representation of celestial coordinates in FITS.
(http://www.atnf.csiro.au/people/mcalabre/WCS/) It is very similar to "FITS-IRAF" but supports a wider range of projections and co-ordinate systems.
• "FITS-WCS(CD)" — This is the same as "FITS-WCS" except that the scaling and rotation of the data array is described by a CD matrix instead of a PC matrix with associated CDELT values.
• "FITS-PC" — This uses keywords CRVALi, CDELTi, CRPIXi, PCiiijjj, etc, as described in a previous (now superseded) draft of the above FITS world co-ordinate system paper by E.W.Greisen and M.Calabretta.
• "FITS-AIPS" — This uses conventions described in the document "Non-linear Coordinate Systems in AIPS" by Eric W. Greisen (revised 9th September, 1994), available by ftp from fits.cv.nrao.edu /fits/documents/wcs/aips27.ps.Z. It is currently employed by the AIPS data-analysis facility (amongst others), so its use will facilitate data exchange with AIPS. This encoding uses CROTAi and CDELTi keywords to describe axis rotation and scaling.
• "FITS-AIPS++" — This is an extension to FITS-AIPS which allows the use of a wider range of celestial as used by the AIPS++ project.
• "FITS-CLASS" — This uses the conventions of the CLASS project. CLASS is a software package for reducing single-dish radio and sub-mm spectroscopic data. It supports double-sideband spectra. See the GILDAS manual.
• "DSS" — This is the system used by the Digital Sky Survey, and uses keywords AMDXn, AMDYn, PLTRAH, etc.
• "NATIVE" — This is the native system used by the AST library (see SUN/210) and provides a loss-free method for transferring WCS information between AST-based applications. It allows more complicated WCS information to be stored and retrieved than any of the other encodings.
Values for FITS keywords generated by the above encodings will always be used in preference to any corresponding keywords found in the FITS extension (even if PROFITS is TRUE). If this is not what is required, the WCS component of the NDF should be erased using the Kappa command ERASE before running NDF2FITS. Note, if PROFITS is TRUE, then any WCS-related keywords in the FITS extension which are not replaced by keywords derived from the WCS component may appear in the output FITS file. If this causes a problem, then PROFITS should be set to FALSE or the offending keywords removed using Kappa FITSEDIT for example.
#### Provenance
The following PROVENANCE headers are written if parameter PROVENANCE is set to "Generic".
• PRVP$n$ — is the path of the $n$th NDF.
• PRVIn — is a comma-separated list of the identifiers of the direct parents for the $n$th ancestor.
• PRVDn — is the creation date in ISO order of the $n$th ancestor.
• PRVCn — is the software used to create the $n$th ancestor
• PRVMn — lists the contents of the MORE structure of the $n$th parent.
All have value <unknown> if the information could not be found, except for the PRVM$n$ header, which is omitted if there is no MORE information to record. The index $n$ used in each keyword’s name is the provenance identifier for the NDF, and starts at 0 for the NDF being converted to FITS.
The following PROVENANCE headers are written if parameter PROVENANCE is set to "CADC".
• PRVCNT — is the number of immediate parents.
• PRV$m$ — is name of the $m$th immediate parent.
• OBSCNT — is the number of root ancestor OBS$m$ headers.
• OBS$m$ — is $m$th root ancestor identifier from its MORE.OBSIDSS component.
• FILEID — is the name of the output FITS file, omitting any file extension.
• PRODUCT is modified or added to each sub-file’s header to be the primary header’s value of PRODUCT with a _$<$extnam$>$ suffix, where $<$extnam$>$ is the extension name in lowercase.
When PROFITS is TRUE any existing provenance keywords in the FITS airlock are not copied to the FITS file.
NDF automatic quality masking is a facility whereby any bad quality information (flagged by the bad-bits mask) present can be incorporated in the data or variance as bad values. NDF2FITS uses this facility in exported data variance information provided the quality array is not transferred. Thus if a QUALITY component is present in the input NDF, the data and any variance arrays will not be masked whenever Parameter COMP’s value is ’A’ or contains ’Q’.
#### Special Formats
In the general case, NDF extensions (excluding the FITS extension) may be converted to one-row binary tables in the FITS file when Parameter PROEXTS is TRUE. This preserves the information, but it may not be accessible to the recipient’s FITS reader. Therefore, in some cases it is desirable to understand the meanings of certain NDF extensions, and create standard FITS products for compatibility.
At present only one product is supported, but others may be added as required.
• AAO 2dF
Standard processing is used except for the 2dF FIBRES extension and its constituent structures. The NDF may be restored from the created FITS file using FITS2NDF. The FIBRES extension converts to the second binary table in the FITS file (the NDF_CLASS extension appears in the first).
To propagate the OBJECT substructure, NDF2FITS creates a binary table of constant width (224 bytes) with one row per fibre. The total number of rows is obtained from component NUM_FIBRES. If a possible OBJECT component is missing from the NDF, a null column is written for that component. The columns inherit the data types of the OBJECT structure’s components. Column meanings and units are assigned based upon information in the reference given below.
The FIELD structure components are converted into additional keywords of the same name in the binary-table header, with the exception that components with names longer than eight characters have abbreviated keywords: UNALLOCxxx becomes UNAL-xxx (xxx=OBJ, GUI, or SKY), CONFIGMJD becomes CONFMJD, and xSWITCHOFF becomes xSWTCHOF (x=X or Y). If any FIELD component is missing it is ignored.
Keywords for the extension level, name, and type appear in the binary-table header.
• JCMT SMURF
Standard processing is used except for the SMURF-type extension. This contains NDFs such as EXP_TIME and TSYS. Each such NDF is treated like the main NDF except that it is assumed that these extension NDFs have no extensions of their own. FITS airlock information and HISTORY are inherited from the parent NDF. Also the extension keywords are written: EXTNAME gives the path to the NDF, EXTLEVEL records the extension hierarchy level, and EXTTYPE is set to "NDF". Any non-NDF components of the SMURF extension are written to a binary table in the normal fashion.
#### References
Bailey, J.A. 1997, 2dF Software Report 14, version 0.5.
NASA Office of Standards and Technology, 1994, A User’s Guide for the Flexible Image Transport System (FITS), version 3.1.
NASA Office of Standards and Technology, 1995, Definition of the Flexible Image Transport System (FITS), version 1.1.
#### Related Applications
CONVERT: FITS2NDF; Kappa: FITSDIN, FITSIN.
#### Implementation Status:
• All NDF data types are supported.
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numapprox - Maple Programming Help
# Online Help
###### All Products Maple MapleSim
Home : Support : Online Help : Mathematics : Numerical Computations : Approximations : numapprox Package : numapprox/hornerform
numapprox
hornerform
convert a polynomial to Horner form
Calling Sequence hornerform(r) hornerform(r, x)
Parameters
r - procedure or expression representing a polynomial or rational function x - (optional) variable name appearing in r, if r is an expression
Description
• This procedure converts a given polynomial r into Horner form, also known as nested multiplication form. This is a form which minimizes the number of arithmetic operations required to evaluate the polynomial.
• If r is a rational function (i.e. a quotient of polynomials) then the numerator and denominator are each converted into Horner form.
• If the second argument x is present then the first argument must be a polynomial (or rational expression) in the variable x. If the second argument is omitted then either r is an operator such that $r\left(y\right)$ yields a polynomial (or rational expression) in y, or else r is an expression with exactly one indeterminate (determined via indets).
• Note that for the purpose of evaluating a polynomial efficiently, the Horner form minimizes the number of arithmetic operations for a general polynomial. Specifically, the cost of evaluating a polynomial of degree n in Horner form is: n multiplications and n additions.
• The command with(numapprox,hornerform) allows the use of the abbreviated form of this command.
Examples
> $\mathrm{with}\left(\mathrm{numapprox}\right):$
> $f≔t→a{t}^{4}+b{t}^{3}+c{t}^{2}+dt+e$
${f}{≔}{t}{→}{a}{}{{t}}^{{4}}{+}{b}{}{{t}}^{{3}}{+}{c}{}{{t}}^{{2}}{+}{d}{}{t}{+}{e}$ (1)
> $\mathrm{hornerform}\left(f\right)$
${t}{→}{e}{+}\left({d}{+}\left({c}{+}\left({a}{}{t}{+}{b}\right){}{t}\right){}{t}\right){}{t}$ (2)
> $s≔\mathrm{taylor}\left({ⅇ}^{x},x\right)$
${s}{≔}{1}{+}{x}{+}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}\frac{{1}}{{24}}{}{{x}}^{{4}}{+}\frac{{1}}{{120}}{}{{x}}^{{5}}{+}{\mathrm{O}}\left({{x}}^{{6}}\right)$ (3)
> $\mathrm{hornerform}\left(s\right)$
${1}{+}\left({1}{+}\left(\frac{{1}}{{2}}{+}\left(\frac{{1}}{{6}}{+}\left(\frac{{1}}{{24}}{+}\frac{{1}}{{120}}{}{x}\right){}{x}\right){}{x}\right){}{x}\right){}{x}$ (4)
> $r≔\mathrm{pade}\left({ⅇ}^{ax},x,\left[3,3\right]\right)$
${r}{≔}\frac{{{a}}^{{3}}{}{{x}}^{{3}}{+}{12}{}{{a}}^{{2}}{}{{x}}^{{2}}{+}{60}{}{a}{}{x}{+}{120}}{{-}{{a}}^{{3}}{}{{x}}^{{3}}{+}{12}{}{{a}}^{{2}}{}{{x}}^{{2}}{-}{60}{}{a}{}{x}{+}{120}}$ (5)
> $\mathrm{hornerform}\left(r,x\right)$
$\frac{{120}{+}\left({60}{}{a}{+}\left({{a}}^{{3}}{}{x}{+}{12}{}{{a}}^{{2}}\right){}{x}\right){}{x}}{{120}{+}\left({-}{60}{}{a}{+}\left({-}{{a}}^{{3}}{}{x}{+}{12}{}{{a}}^{{2}}\right){}{x}\right){}{x}}$ (6)
See Also
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Article Contents
Article Contents
# A filtering method for the hyperelliptic curve index calculus and its analysis
• We describe a filtering technique improving the performance of index-calculus algorithms for hyperelliptic curves. Filtering is a stage taking place between the relation search and the linear algebra. Its purpose is to eliminate redundant or duplicate relations, as well as reducing the size of the matrix, thus decreasing the time required for the linear algebra step.
This technique, which we call harvesting, is in fact a new strategy that subtly alters the whole index calculus algorithm. In particular, it changes the relation search to find many times more relations than variables, after which a selection process is applied to the set of the relations - the harvesting process. The aim of this new process is to extract a (slightly) overdetermined submatrix which is as small as possible. Furthermore, the size of the factor base also has to be readjusted, in order to keep the (extended) relation search faster than it would have been in an index calculus algorithm without harvesting. The size of the factor base must also be chosen to guarantee that the final matrix will be indeed smaller than it would be in an optimised index calculus without harvesting, thus also speeding up the linear algebra step.
The version of harvesting presented here is an improvement over an earlier version by the same authors. By means of a new selection algorithm, time-complexity can be reduced from quadratic to linear (in the size of the input), thus making its running time effectively negligible with respect to the rest of the index calculus algorithm. At the same time we make the process of harvesting more effective - in the sense that the final matrix should (on average) be smaller than with the earlier approach.
We present an analysis of the impact of harvesting (for instance, we show that its usage can improve index calculus performance by more than 30% in some cases), we show that the impact on matrix size is essentially independent on the genus of the curve considered, and provide an heuristic argument in support of the effectiveness of harvesting as one parameter (which defines how far the relation search is pushed) increases.
Mathematics Subject Classification: Primary: 94A60, 14G50; Secondary: 11T71.
Citation:
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(Entries for Disposition of Assets) On December 31, 2014, Travis Tritt Inc. has a machine with a...
(Entries for Disposition of Assets) On December 31, 2014, Travis Tritt Inc. has a machine with a book value of $940,000. The original cost and related accumulated depreciation at this date are as follows. Depreciation is computed at$60,000 per year on a straight-line basis.
Instructions
Presented below is a set of independent situations. For each independent situation, indicate the journal entry to be made to record the transaction. Make sure that depreciation entries are made to update the book value of the machine prior to its disposal.
(a) A fire completely destroys the machine on August 31, 2015. An insurance settlement of $430,000 was received for this casualty. Assume the settlement was received immediately. (b) On April 1, 2015, Tritt sold the machine for$1,040,000 to Dwight Yoakam Company.
(c) On July 31, 2015, the company donated this machine to the Mountain King City Council. The fair value of the machine at the time of the donation was estimated to be \$1,100,000.
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# Open SourceMolecular Dynamics
### Sidebar
#### For Developers
exercises:2017_ethz_mmm:pythonmd
This is an old revision of the document!
The instructions for loading the appropriate modules in .bashrc:
> cd
> nano .bashrc
module load new gcc/4.8.2 python/2.7.12 # include this line in the file
> . .bashrc
To visualize an xyz file:
> ipython
In [1]: from ase.io import read
In [2]: from ase.visualize import view
In [4]: view(s)
At this point you can rotate the structure, select an atom, then two (you get the distance) or three (you get the angle)…
STAMI
In the repository you will find the program “md.py” and the geometry file “fcc.xyz” The program md.py can perform a MD simulation for a system of Ar atoms interacting via Lennard-Jones potential.
Executing the command
>python md.py
the program will ask you to provide
1. the name of a geometry file
2. the timestep to be used for the simulation in [fs]
3. the total number of steps of dynamics to be performed
4. the initial temperature desired for the system in [K]
exercises/2017_ethz_mmm/pythonmd.1488516458.txt.gz · Last modified: 2017/03/03 04:47 by dpasserone
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## On the number of labeled $k$-arch graphs
### Summary
Summary: In this paper we deal with $k$-arch graphs, a superclass of trees and $k$-trees. We give a recursive function counting the number of labeled $k$-arch graphs. Our result relies on a generalization of the well-known Prüfer code for labeled trees. In order to guarantee the generalized code to be a bijection, we characterize the valid code strings.
### Mathematics Subject Classification
05A15, 05C30, 05A10
### Keywords/Phrases
k-arch graphs, trees, k-trees, coding, pr$\ddot$ufer code, Cayley's formula
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# The NuSTAR Extragalactic Surveys : source catalog and the Compton-thick fraction in the UDS field.
Masini, A. and Civano, F. and Comastri, A. and Fornasini, F. and Ballantyne, D. R. and Lansbury, G. B. and Treister, E. and Alexander, D. M. and Boorman, P. G. and Brandt, W. N. and Farrah, D. and Gandhi, P. and Harrison, F. A. and Hickox, R. C. and Kocevski, D. D. and Lanz, L. and Marchesi, S. and Puccetti, S. and Ricci, C. and Saez, C. and Stern, D. and Zappacosta, L. (2018) 'The NuSTAR Extragalactic Surveys : source catalog and the Compton-thick fraction in the UDS field.', Astrophysical journal supplement series., 235 (1). p. 17.
## Abstract
We present the results and the source catalog of the NuSTAR survey in the UKIDSS Ultra Deep Survey (UDS) field, bridging the gap in depth and area between NuSTAR's ECDFS and COSMOS surveys. The survey covers a ~0.6 deg2 area of the field for a total observing time of ~1.75 Ms, to a half-area depth of ~155 ks corrected for vignetting at 3–24 keV, and reaching sensitivity limits at half-area in the full (3–24 keV), soft (3–8 keV), and hard (8–24 keV) bands of 2.2 × 10−14 erg cm−2 s−1, 1.0 × 10−14 erg cm−2 s−1, and 2.7 × 10−14 erg cm−2 s−1, respectively. A total of 67 sources are detected in at least one of the three bands, 56 of which have a robust optical redshift with a median of $\langle z\rangle \sim 1.1$. Through a broadband (0.5–24 keV) spectral analysis of the whole sample combined with the NuSTAR hardness ratios, we compute the observed Compton-thick (CT; N H > 1024 cm−2) fraction. Taking into account the uncertainties on each N H measurement, the final number of CT sources is 6.8 ± 1.2. This corresponds to an observed CT fraction of 11.5% ± 2.0%, providing a robust lower limit to the intrinsic fraction of CT active galactic nuclei and placing constraints on cosmic X-ray background synthesis models.
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