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https://www.gradesaver.com/textbooks/science/physics/fundamentals-of-physics-extended-10th-edition/chapter-2-motion-along-a-straight-line-problems-page-33/13c	## Fundamentals of Physics Extended (10th Edition) We found that the average speeds of the trip were 73km/h and 68km/h (average speed for each direction of the trip). The average of the whole trip is just the average of the two speeds.---73+68=141 141$\div$2= 70.5	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9843255877494812, "perplexity": 1612.25471689186}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578765115.93/warc/CC-MAIN-20190426093516-20190426115516-00181.warc.gz"}
https://arrayfire.org/arrayfire-rust/arrayfire/fn.gradient.html	pub fn gradient<T>(input: &Array<T>) -> (Array<T>, Array<T>) where T: HasAfEnum + FloatingPoint, The gradients along the first and second dimensions are calculated simultaneously. # Parameters • input is the input Array # Return Values A tuple of Arrays. The first Array is dx which is the gradient along the 1st dimension. The second Array is dy which is the gradient along the 2nd dimension.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42005640268325806, "perplexity": 8159.069559867445}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304134.13/warc/CC-MAIN-20220123045449-20220123075449-00422.warc.gz"}
http://cstheory.stackexchange.com/questions/11722/a-lottery-that-you-can-be-convinced-that-it-is-fair	# A lottery that you can be convinced that it is fair (Sorry if this is well known.) I would like to give some item to one of $k$ agents, so that agent $j$ will get the item with probability $p_i$. Is there a cryptographic (or other) tool so that every agent (and even every observer) will be able to be convinced that the random drawing was indeed fair? - Are the agents allowed to know $p_0$..$p_k$? – Mike Samuel Jun 21 '12 at 18:53 Have you seen this? ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4232861 – dspyz Feb 13 '14 at 16:57 If I am understanding the problem correctly, it would seem to amount to public flipping a $k$-sided coin. There seem to be lots of ways to do this if you assume bit commitment. One example would be having each party generate a random integer between 0 and $k-1$, using bit commitment to publicly commit to that bit string. Then once each agent has committed, they all publicly reveal their secret integer. The winning agent is then the one indexed by the sum of the integers modulo $k$. If even one agent is honest, then the flip must be random. Of course one problem with this is that it requires bit commitment. Information theoretic schemes for bit commitment are impossible for both classical and quantum computing (though Adrian Kent recently proposed a scheme exploiting relativity). However, secure bit commitment can be achieved with computational assumptions. - My problem with this approach is that if you want to convince a lot of outside observers from fairness, then each of them has to commit a bit and you must be sure that each of them will reveal the proof of their commitment. You can't just ignore the bit of an observer that does not reveal their proof because then the last observer to reveal could manipulate the lottery result by deciding whether or not to reveal his proof. – Zsbán Ambrus Jun 15 '12 at 19:22 @user8067: I don't believe it is possible without interaction or trusting that at least one party is honest. The reason I say this is that if the initial randomness is actually predetermined through a conspiracy of everyone participating at that point, then the entire process is deterministic and not random. However the problem requires the process be random, so this seems to be the best you can do. – Joe Fitzsimons Jun 15 '12 at 19:27 I'm not convinced that is possible. – Joe Fitzsimons Jun 15 '12 at 20:23 @RickyDemer: There's not enough information in the question to tell what adversary model is applicable here. If Gil told us exactly what it's for, then it would be easier to prove whether or not a specific scheme meets his requirements. But that said, I have no doubt Gil is more than capable of checking whether or not our answers meet his needs. – Joe Fitzsimons Jun 16 '12 at 20:25 @RickyDemer: It's not at all clear to me what the obvious model is for this case. It strongly depends the setup, and it's not obvious what the default assumptions should be. It's a little much to downvote and start acting like both my answer and Lev's are wrong. They don't explicitly include the caveat pointed out in Adam's answer. Note that I am -not- editing my answer, because without more information from Gil, I don't see it making sense to guess about the adversary model, and so I am leaving it as general as possible (not specifying whether or not the bit commitment need be non-maliable). – Joe Fitzsimons Jun 16 '12 at 21:30 As other users have hinted at, this is a well-studied problem in cryptography. It is called "coin-flipping" and is a special case of multiparty computation. What protocol does the job actually depends on the context quite a lot. • In the "standalone" setting, the protocol will be run in isolation, without players being involved in other protocols (or indeed, any interaction with the outside world) at the same time. There is a wonderfully thorough treatment of this in Oded Goldreich's textbook "Foundations of Cryptography" (Volume 2, I think). Just to give an idea of how subtle it is, the "everybody commits to random values" protocol suggested by another responder is insecure if the commitment scheme you use is malleable. Nonmalleable commitment schemes do give you a secure protocol, but they are a bit complicated to design. • In settings where participants are involved in other concurrent protocols, you want a protocol that is composable. There are various notions of composability, but the strongest one, called universal composability, requires some additional set-up assumptions (for example, a PKI or a common random string visible to all parties but controllable by none of them). I don't know of an accessible treatment of this topic, unfortunately. But looking at a recent paper on either universal composability or nonmalleable commitment would be a good place to start. - “a common random string visible to all parties but controllable by none of them” is exactly what we want to generate. – Zsbán Ambrus Jun 16 '12 at 11:53 and after somehow solving that problem once, one can universally composably $\hspace{1 in}$ solve it again (arbitrarily many times). $\:$ – Ricky Demer Jun 16 '12 at 17:37 I think UC commitment is known for Registered Public Key setup (which is a stronger assumption than PKI) and multi-string setup (which is a weaker assumption than common random string). – Ricky Demer Jun 16 '12 at 20:55 Welcome to the site, Adam! – Gil Kalai Jun 16 '12 at 23:08 I don't know much crypto, but perhaps the following would work. Assuming the $p_j$'s are publicly known, all that's needed to determine the winner is to select a random number from [0,1]. Here's the process: Each agent selects a random vector in $\{0,1\}^b$, where $b$ is the number of bits of precision that are needed for the process. Then they all cryptography commit to their vectors using known protocols. Finally, once all the vectors are committed to, all their vectors are revealed (and checked) and XORed and the result is the random number to be used. Namely the resulting vector is the binary representation of digits past the decimal point. Any agent can be sure the chosen random number came uniformly at random by choosing his own vector uniformly at random. For any observer to be convinced, they have to trust that at least one agent followed the protocol, but if none did, I guess nobody really wanted a fair lottery to begin with. - Sorry Lev, I've just noticed your answer. When I started writing an answer there was nothing here, but we both seem to have come up with very similar answers. – Joe Fitzsimons Jun 15 '12 at 18:35 No worries! Seems we're on the right track, then. – Lev Reyzin Jun 15 '12 at 19:36 Yes, actually I think there are a lot of papers on this in the context of coin flipping, but I don't really know that literature well enough to give a proper answer based on it. – Joe Fitzsimons Jun 15 '12 at 19:40 The earliest reference I know is: M. Blum. Coin Flipping By Telephone. CRYPTO 1981: 11-15. Can be downloaded at dm.ing.unibs.it/giuzzi/corsi/Support/papers-cryptography/… – Ryan Williams Jun 16 '12 at 1:23 There's a standard attack, if you use standard bit commitment schemes (e.g., hashing). Let's consider the case with two parties, Alice and Bob, where Alice goes first. After Alice broadcasts her commitment, Bob can copy it. After Alice opens her commitment, Bob can open his the same now. Now their random vectors are equal, so they xor to zero -- Bob was able to force the final value to zero, a contradiction of the requirement for fairness. – D.W. Feb 28 '13 at 2:18 Passive observers can't verify that the drawing wasn't staged. Inputs into pseudorandom process can be chosen to give desired result. However if the observer can supply a random number that he knows is random AND make sure that other agents won't change their inputs afterwards (because they could compensate his effect with their inputs), then he can be sure that the result was indeed random. This requires commitment scheme which we don't know any that is mathematically proven to be secure but in practice can be realized using secure hash (such as SHA3). Consider this example: I've made an example implementation. You can see it live here: https://mrogalski.eu/cl/ or check sources on GitHub. - This is already noted in Joe's answer. – Kaveh Feb 12 '14 at 14:43 The graphic illustration is very nice! – Gil Kalai Feb 12 '14 at 15:16 The graphics are very pretty but your answer contains nothing that isn't in the existing answers. – David Richerby Feb 12 '14 at 15:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8042916655540466, "perplexity": 723.5121432639612}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398471436.90/warc/CC-MAIN-20151124205431-00176-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.math.snu.ac.kr/board/index.php?mid=colloquia&document_srl=813561&l=en&sort_index=speaker&order_type=desc	※ 줌(zoom) 병행 Zoom: https://snu-ac-kr.zoom.us/j/86561055957?pwd=UGEvajVpK3BGenNaZFpGUmtuTVFBUT09 회의 ID: 865 6105 5957 암호: 716477 The volume of p-adic manifolds appears in many branches of number theory such as Weil conjecture on Tamagawa number 1, Kudla-Rapoport conjecture, Fundamental lemma, and so on. In this talk, we will explain a description of the volume in terms of algebraic geometry, and then explain recent results in this context.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9480145573616028, "perplexity": 1178.6234849888879}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363006.60/warc/CC-MAIN-20211204185021-20211204215021-00425.warc.gz"}
http://brianhamrick.com/blog/devils-chessboard	29 June 2016 During my stream today, one of my viewers asked me if I had heard of the Devil's Chessboard problem. I hadn't, but it led to some quite interesting questions. The basic question is as follows: The devil has captured two people and is playing a game with them for their freedom. Person A will be presented with a chessboard with a penny in each square (64 total), with each penny either heads up or tails up randomly. The devil will choose a particular square and point it out to Person A. Person A then chooses a single square, and flips the penny in that square. Afterward, Person A is sent away and Person B is brought forward. Based on the new state of the board, Person B must point out the same square that the devil did in order to win. The two people can devise a strategy beforehand, but cannot communicate once the game starts. How can they win? If you haven't heard the problem before, I'd recommend thinking about it for a while first. Despite looking like a typical "gotcha" brainteaser, the idea behind the solution is actually widely applicable to various situations. We'll also consider generalizations to the Devil's Chessboard where the number of coins changes from 64 to a different number $$n$$. The 64 coin solution Number the coins from 0 to 63, and define the value of a board as the bitwise xor of the coins that are showing heads. So for example, if coins 3, 5, 12, 14, and 57 are heads and the rest are tails, the value of the board is 61: 3 = 000011 5 = 000101 12 = 001100 14 = 001110 57 = 111001 ----------- 61 = 111101 Person A wants to find a coin to flip that will cause the value of the resulting board to be the index of the square that the devil pointed out. This will always be possible, and person A can determine which coin to flip by taking the devil's pointed out square and xoring it with the current value of the board. This works because $$x \oplus y \oplus y = x$$ (where $$\oplus$$ denotes xor), so flipping coin $$i$$ changes the value of the board by xoring it with $$i$$, regardless of whether the coin is flipped from heads to tails or from tails to heads. Now let's consider the question of whether it is possible to win the $$n$$ coin version of this game. Again, I recommend spending some time to think about the question for yourself before reading on. When is the game winnable? For this question, it helps to recast the problem in a different light. We can associate an arrangment of $$n$$ coins as a string in $$\{0, 1\}^n$$, which is just a compact way of denoting an n-bit string. So for example, $$\{0, 1\}^3 = \{000, 001, 010, 011, 100, 101, 110, 111\}$$. Now, we'll construct a graph where the vertex set is $$\{0, 1\}^n$$ and two vertices are connected by an edge if they differ in exactly one bit. In the context of the game, when person A is presented with the initial board, they will pick one of its $$n$$ neighbors to present to person B. This graph is exactly the hypercube graph $$Q_n$$. Each vertex corresponds to an arrangement of coins, so we'll assign each vertex a value which is the square that person B will point to if presented with that arrangement. An assignment of values will correspond to a winning strategy whenever every vertex's neighbor set contains all $$n$$ possible values. Now we can use a counting argument. Look at any particular arrangement. In a winning strategy, It will have exactly one neighbor with value 0. So we count $$2^n$$ 0s, but each 0 got counted $$n$$ times, because every arrangement has $$n$$ neighbors. That means that there is a total of $$\frac{2^n}{n}$$ 0s. But the number of 0s needs to be an integer, so $$n$$ must divide $$2^n$$, which occurs exactly when $$n$$ is a power of 2. Furthermore, the solution from earlier generalizes straightforwardly to any number of coins that is a power of 2, so we have our answer: the game is winnable exactly when $$n$$ is a power of 2. Are there other solutions? Now that we've established that $$n$$ has to be a power of 2, it seems like there's something special about being able to index the coins with bit-strings in the way that we did earlier. We built our solution on the structure of xor, but maybe there is another type of structure that also leads to a solution. So let's think about how many different solutions we can get out of the xor idea. It certainly doesn't matter what ordering we assign to the pennies, and furthermore once we've done the xoring, we can apply any bijective function to the result and not ruin the coloring property. So we have valid assignments of the form $$f(\bigoplus x_i)$$ where $$f: \{0, \ldots, n-1\} \to \{0, \ldots, n-1\}$$ is a bijection, the $$x_i$$ are a permutation of $$\{0, \ldots, n-1\}$$, and the xor ranges over all $$i$$ where the $$i$$th coin shows heads. But we can actually go further than that. Let's go back to the graph coloring idea. Instead of considering the graph $$Q_n$$, let's consider the graph $$Q_n^2$$ -- the graph with length $$n$$ bitstrings as vertices, and an edge between two vertices if the corresponding bitstrings differ in exactly two places. In a winning solution, no two adjacent vertices in this graph will have the same value, because they have a common neighbor in $$Q_n$$. Conversely, any proper $$n$$-coloring of $$Q_n^2$$ leads to a winning strategy. To see that, notice that for any arrangement, all of its neighbors in $$Q_n$$ differ from each other in exactly two spots, so they are adjacent in $$Q_n^2$$. As a result, in such a coloring, any arrangement has $$n$$ neighbors that all have different values, so every value in $$\{0, \ldots, n-1 \}$$ must be present, meaning that this corresponds to a winning strategy. The bijective function $$f$$ that we applied earlier just corresponds to permuting the colors in a proper $$n$$-coloring to get another proper $$n$$-coloring. But notice that $$Q_n^2$$ has two connected components: one where the bitstrings have an even number of 1s, and one where the bitstrings have an odd number of 1s. So we were actually too strict before. The bijection can be different depending on the parity of the number of 1s. So now our solutions are of the form $$f_b(\bigoplus x_i)$$, where $$b$$ is 0 when there are an even number of heads and 1 when there are an odd number, $$x_i$$ are a permutation of $$\{ 0, \ldots, n-1 \}$$, and $$f_0, f_1 : \{ 0, \ldots, n-1 \} \to \{ 0, \ldots, n-1 \}$$ are bijections. At this point, it looks like we've covered all the "obvious" fudging that turns one solution into an equivalent one. But we don't know whether there's another solution still. For 2 and 4 coins, there's nothing else. For 2 coins, $$Q_2$$ is just a square, and it's easy to verify that the only assignments that are winning are two adjacent 0s and two adjacent 1s and that these are all captured by the form of solution that we already know about. The 4 coin problem is much more interesting. We're looking at the hypercube $$Q_4$$. But again, it'll be more useful to instead look at $$Q_4^2$$. The odd component of $$Q_4^2$$ consists of the strings 0001, 0010, 0100, 1000, 0111, 1011, 1101, and 1110. In that set, all of the strings with a single 1 are adjacent to each other, and similarly for the strings with three 1s. Between those two sets, most of the pairs are adjacent as well, with the exception that a string is not adjacent to its complement. So 0001 is adjacent to every string except for 1110, and similarly for the others. So between 0001, 0010, 0100, and 1000, all 4 values are represented, and 1110 is adjacent to all of them except for 0001. Therefore, 1110's value must be the same as 0001's value, and similarly for the other pairs of complements. Therefore, a 4-coloring of the odd component of $$Q_4^2$$ is just any bijection between $$\{0, 1, 2, 3\}$$ and $$\{0001, 0010, 0100, 1000\}$$, with the other values being determined from those. This freedom is captured in our general form by the choice of $$f_1$$. Now let's look at our even component. For any bitstring, say 0000, it will not be adjacent to its complement, in this case 1111, but it will be adjacent to all of the other six bitstrings. Therefore, whatever value is assigned to 0000, the other values are all present in the middle layer, so the value of 1111 must be the same as the value of 0000. Similarly, the value of 1100 must be the same as that of 0011, and so on. So a 4-coloring of the even component corresponds to a bijection between $$\{0, 1, 2, 3\}$$ and $$\{0000, 1001, 1010, 1100\}$$, which is captured in our general form by the choice of $$f_0$$. Unfortunately, 4 coins is too small to really see the pattern as we go to 8 coins, 16 coins, and beyond. Does more freedom show up at some point? I do not know the answer. My guess is that the general form that I've given here really does include all of the possibilities, but that's really just a guess and it would not be surprising at all to find out that my guess is wrong. Can you figure it out?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7985692024230957, "perplexity": 166.75293175514048}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547584519757.94/warc/CC-MAIN-20190124080411-20190124102411-00617.warc.gz"}
https://workfamilyhealthnetwork.org/publications/author/24701/Brockwood%2C%20K	# Publications by Author: Brockwood, K 2017 Kossek EE, Wipfli B, Thompson RA, Brockwood K. The Work, Family, and Health Network Organizational Intervention: Core Elements and Customization for Diverse Occupational Health Contexts. In: Occupational Health Disparities: Improving the Well-Being of Ethnic and Racial Minority Workers. Washington, DC: American Psychological Association ; 2017. pp. 181-215. Publisher's Version 2013 Barbosa C, Bray JW, Brockwood K, Reeves D. Costs of a Work-Family Intervention: Evidence From the Work, Family, and Health Network. Am J Health Promot. [Internet]. 2013;Aug 23 :[Epub ahead of print]. Publisher's VersionAbstract Purpose . To estimate the cost to the workplace of implementing initiatives to reduce work-family conflict. Design . Prospective cost analysis conducted alongside a group-randomized multisite controlled experimental study, using a microcosting approach. Setting . An information technology firm. Subjects . Employees (n = 1004) and managers (n = 141) randomized to the intervention arm. Intervention . STAR (Start. Transform. Achieve. Results.) to enhance employees' control over their work time, increase supervisor support for employees to manage work and family responsibilities, and reorient the culture toward results. Measures . A taxonomy of activities related to customization, start-up, and implementation was developed. Resource use and unit costs were estimated for each activity, excluding research-related activities. Analysis . Economic costing approach (accounting and opportunity costs). Sensitivity analyses on intervention costs. Results . The total cost of STAR was $709,654, of which$389,717 was labor costs and $319,937 nonlabor costs (including$313,877 for intervention contract). The cost per employee participation in the intervention was $340 (95% confidence interval:$330-$351);$597 ($561-$634) for managers and $300 ($292-\$308) for other employees (2011 prices). Conclusion . A detailed activity costing approach allows for more accurate cost estimates and identifies key drivers of cost. The key cost driver was employees' time spent on receiving the intervention. Ignoring this cost, which is usual in studies that cost workplace interventions, would seriously underestimate the cost of a workplace initiative.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19656087458133698, "perplexity": 22973.40625354777}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439740733.1/warc/CC-MAIN-20200815065105-20200815095105-00323.warc.gz"}
https://planetmath.org/axiomofcountablechoice	axiom of countable choice The Axiom of Countable Choice (CC) is a weak form of the Axiom of Choice (http://planetmath.org/AxiomOfChoice). It states that every countable set of nonempty sets has a choice function. (that is, the Zermelo-Fraenkel axioms together with the Axiom of Countable Choice) suffices to prove that the union of countably many countable sets is countable. It also suffices to prove that every infinite set has a countably infinite subset, and that a set $X$ is infinite if and only if there is a bijection between $X$ and a proper subset of $X$. Title axiom of countable choice AxiomOfCountableChoice 2013-03-22 14:46:23 2013-03-22 14:46:23 yark (2760) yark (2760) 14 yark (2760) Definition msc 03E25 countable axiom of choice countable AC countable choice	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 3, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9995307922363281, "perplexity": 215.22860148148925}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038862159.64/warc/CC-MAIN-20210418224306-20210419014306-00620.warc.gz"}
https://mathspace.co/textbooks/syllabuses/Syllabus-408/topics/Topic-7228/subtopics/Subtopic-96603/?activeTab=theory	NZ Level 5 Divide by decimals Lesson Remember! When we divide a number by a decimal that's less than one, our number will get bigger. ## Change the Divisor to a Whole Number You've already learnt how to divide decimal numbers by whole numbers so this can be a really useful strategy. Let's look at an example to explain how this strategy works. #### Examples ##### Question 1 Evaluate$5.6\div0.8$5.6÷0.8 Think: We can change $0.8$0.8 to a whole number ($8$8) by multiplying in by $10$10. Remember we need to multiply both numbers in our equation by the same value to keep our equation balanced. We could now write our equation as $56\div8$56÷8, which is $7$7. Do: $5.6\div0.8=7$5.6÷0.8=7 Make sense? Let's do another example to make sure. ##### question 2 Evaluate$5.23\div0.4$5.23÷0.4 ThinkWe can change $0.4$0.4 to a whole number ($4$4) by multiplying it by $10$10. So we need to multiply both numbers in our equation by $10$10. Our equation becomes $52.3\div4$52.3÷4, which would be $13.075$13.075. Do$5.23\div0.4=13.075$5.23÷0.4=13.075 ##### QUESTION 3 Evaluate $43\div8$43÷8. ##### QUESTION 4 Evaluate $\frac{3.44}{8}$3.448. ##### QUESTION 5 Evaluate $251.439\div3$251.439÷3 ##### QUESTION 6 Evaluate $\frac{0.247}{0.019}$0.2470.019 ### Outcomes #### NA5-3 Understand operations on fractions, decimals, percentages, and integers	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7998450994491577, "perplexity": 3102.4906489529853}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058589.72/warc/CC-MAIN-20210928002254-20210928032254-00677.warc.gz"}
http://lucatrevisan.wordpress.com/latex-to-wordpress/using-latex2wp/	The distribution contains the following files: • latex2wp.py: the conversion program • latex2wpstyle.py: specifies typesetting options, and environments and macros recognized during the conversion • readme.txt: some basic information on how to use LaTeX2WP • terrystyle.py: sets the typesetting options in the style of Terry Tao’s blog. • macrosblog.tex: defines LaTeX commands recognized by LaTeX2WP for typsetting colors, links to URLs, and images, so that LaTeX files containing such commands can be typeset and previewed offline • example.tex: a sample post showing how to use the main functionalities recognized by LaTeX2WP • post-template.tex: a starting point for writing a post in LaTeX; it imports various packages and macros so that pictures, hyperlinks etc. can be seen in the preview the same way they will appear in the post. • knuth.png: a picture (from xkcd, Copyright Randall Munroe) required to preview example.tex • gpl.txt: the text of the GNU General Public License • changelog.txt: a list of changes from previous versions. By looking at example.tex, it should be easy to see how to get started. Indeed, just starting to write LaTeX, and seeing what happens with the conversion should be fine. Your mathematical posts do not have to look like mine. A number of stylistic changes can be made by editing latex2wpstyle.py (make a copy before editing it); comparing it to terrystyle.py, and reading the comments in the code, should help understand how to make such changes. It is possible to add your own LaTeX macros, if they do not involve passing of parameters. It wouldn’t be too hard to add support for arbitrary LaTeX macros and environments, but right now I have run out of energy (maybe during the Summer). Another limitation is that there is no support for footnotes, and no support for bibliographic references. I will definitely work on this during the Summer. When LaTeX2WP cannot do what you want, you can always put HTML code in the scope of a \ifblog . . . \fi. The conversion will output such HTML code verbatim, and it will be ignored in the LaTeX preview. Conversely, anything in the scope of \iftex . . . \fi is compiled in the LaTeX preview but skipped in the conversion.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9206945300102234, "perplexity": 1940.3602600286215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368702652631/warc/CC-MAIN-20130516111052-00083-ip-10-60-113-184.ec2.internal.warc.gz"}
https://www.sas1946.com/main/index.php?topic=47097.0	• December 09, 2022, 02:14:40 AM • Welcome, Guest Pages: [1] Go Down ### AuthorTopic: DBW QMB extracted Method? (Read 1324 times) 0 Members and 1 Guest are viewing this topic. #### Benny • member • Offline • Posts: 157 ##### DBW QMB extracted Method? « on: July 09, 2015, 04:59:25 PM » Does the method where you extract all the maps from DBW into 4.12 Modact [By extracting the map SFS files into the SFS_AUTO folder and putting the contents of DBW's QMBPro into Modact's QMBPro] work with the three C.U.P. modules? Logged Bf-109's are incredible. #### benitomuso • SAS Team • member • Offline • Posts: 2584 • P.A.L. ##### Re: DBW QMB extracted Method? « Reply #1 on: July 09, 2015, 09:02:33 PM » Does the method where you extract all the maps from DBW into 4.12 Modact [By extracting the map SFS files into the SFS_AUTO folder and putting the contents of DBW's QMBPro into Modact's QMBPro] work with the three C.U.P. modules? Your question is not clearly understandable. The SFS contents of the C.U.P. SFSs were packed with a tool made by me, and as any SFS can easily be extracted even with the TotalMODder V3, the SFSExtractor, the Kegetys dinput.dll dumper or eventually some old Java methods of content dumping. Regards, Pablo Logged #### Benny • member • Offline • Posts: 157 ##### Re: DBW QMB extracted Method? « Reply #2 on: July 10, 2015, 11:44:02 AM » Does the method where you extract all the maps from DBW into 4.12 Modact [By extracting the map SFS files into the SFS_AUTO folder and putting the contents of DBW's QMBPro into Modact's QMBPro] work with the three C.U.P. modules? Your question is not clearly understandable. The SFS contents of the C.U.P. SFSs were packed with a tool made by me, and as any SFS can easily be extracted even with the TotalMODder V3, the SFSExtractor, the Kegetys dinput.dll dumper or eventually some old Java methods of content dumping. Regards, Pablo I guess what I should say is, if I install the DBW QMB maps into CUP, they will all work? Logged Bf-109's are incredible. #### benitomuso • SAS Team • member • Offline • Posts: 2584 • P.A.L. ##### Re: DBW QMB extracted Method? « Reply #3 on: July 10, 2015, 09:21:01 PM » Does the method where you extract all the maps from DBW into 4.12 Modact [By extracting the map SFS files into the SFS_AUTO folder and putting the contents of DBW's QMBPro into Modact's QMBPro] work with the three C.U.P. modules? Your question is not clearly understandable. The SFS contents of the C.U.P. SFSs were packed with a tool made by me, and as any SFS can easily be extracted even with the TotalMODder V3, the SFSExtractor, the Kegetys dinput.dll dumper or eventually some old Java methods of content dumping.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8493143916130066, "perplexity": 25096.669432877978}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711394.73/warc/CC-MAIN-20221209080025-20221209110025-00714.warc.gz"}
https://rd.springer.com/article/10.1007%2FPL00022715	Computational Statistics , Volume 15, Issue 4, pp 463–484 # Parallel MARS Algorithm Based on B-splines • Sergey Bakin • Markus Hegland • Michael R. Osborne Article ## Summary We investigate one of the possible ways for improving Friedman’s Multivariate Adaptive Regression Splines (MARS) algorithm designed for flexible modelling of high-dimensional data. In our version of MARS called BMARS we use B-splines instead of truncated power basis functions. The fact that B-splines have compact support allows us to introduce the notion of a “scale” of a basis function. The algorithm starts building up models by using large-scale basis functions and switches over to a smaller scale after the fitting ability of the large scale splines has been exhausted. The process is repeated until the prespecified number of basis functions has been produced. In addition, we discuss a parallelisation of BMARS as well as an application of the algorithm to processing of a large commercial data set. The results demonstrate the computational efficiency of our algorithm and its ability to generate models competitive with those of the original MARS. ## Keywords MARS B-splines Data Mining Parallel Algorithms ## Notes ### 8 Acknowledgements We are most grateful to Prof J.H. Friedman for suggesting the idea of the experiment involving the synthetic data set and to Dr B. Turlach for very fruitful discussions. Our thanks are also due to the anonymous referees for their constructive comments which greatly helped to improve the quality of this paper. The research of S. Bakin was supported by the Australian Government (Overseas Postgraduate Research Scholarship), by the Australian National University (ANU PhD Scholarship) and, also, by the Advanced Computational Systems CRC (ACSys), Australia. ## References 1. Breiman, L., Friedman, J.H., Olshen, R.A. & Stone, C.J. (1984), Classification and Regression Trees, Wadsworth, Belmont, California. 2. Chen, Z. (1990), Beyond additive models: interactions by smoothing spline methods, Technical Report SMS-009-90, The Australian National University.Google Scholar 3. Cox, M.G. (1981), Practical spline approximation, Topics in Numerical Analysis, Lancaster, 79–112.Google Scholar 4. Fayyad, U., Piatetsky-Shapiro, G. & Smyth, P. (1996), From Data Mining to Knowledge Discovery: An Overview, in ‘Advances in Knowledge Discovery and Data Mining’, pp. 1–36.Google Scholar 5. Friedman, J.H. (1991), ‘Multivariate Adaptive Regression Splines’, The Annals of Statistics, 19(1), 1–141. 6. Friedman, J.H. (1981), Estimating functions of mixed ordinal and categorical variables, Technical Report 108, Stanford University.Google Scholar 7. Friedman, J.H. & Stuetzle, W. (1981), ‘Projection Pursuit Regression’, Journal of the American Statistical Association, 76, 817–823. 8. Geist, A., Beguelin, A., Dongarra, J., Jiang, W., Manchek, R. & Sunderam, V. (1994), PVM: Parallel Virtual Machine, MIT Press.Google Scholar 9. George, E.I. & McCulloch, R.E. (1993), ‘Variable selection via Gibbs sampling’, Journal of the American Statistical Association, 88, 881–889. 10. Luenberger, D.G. (1984), Linear and Nonlinear Programming, Reading, Massachusetts. 11. McCullagh, P. & Neider, J.A. (1983), Generalized Linear Models, Chapman and Hall.Google Scholar 12. Miller, A.J. (1990), Subset Selection in Regression, Chapman and Hall.Google Scholar 13. Stone, G. (1997), Analysis of Motor Vehicle Claims Data using Statistical Data Mining, CMIS Confidential Report CMIS-97/73, CSIRO, Australia.Google Scholar 14. Wahba, G. (1990), Spline Models for Observational Data, SIAM, Philadelphia. ## Authors and Affiliations • Sergey Bakin • 1 • Markus Hegland • 2 • Michael R. Osborne • 1 1. 1.School of Mathematical SciencesThe Australian National UniversityCanberraAustralia 2. 2.Computer Sciences LaboratoryThe Australian National UniversityCanberraAustralia	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8180072903633118, "perplexity": 6351.939627616313}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540528490.48/warc/CC-MAIN-20191210180555-20191210204555-00202.warc.gz"}
https://wiki.cs.byu.edu/cs-236/homework-6	## Objectives • Express problems using predicate calculus and propositional logic • Use inference for sound reasoning over premises in propositional logic and predicate calculus to conclude properties • Proof by contradiction in Datalog using resolution ## Problems For the International version of the book, change “Section 1.6” to “Section 1.5”. For each of the problems (except Section 1.6 question 24), you will need to provide a proof in addition to what the question is asking (unless the conclusion you are asked to prove is incorrect; instead you will need to explain why it is incorrect). For the problems involving Section 1.6 question 10, you don't need to explain what rules of inference are used as long as you provide a proof. 1. (6 points) Section 1.6 Problem 6 2. (2 points) Section 1.6 Problem 8 3. (6 points) Section 1.6 Problem 10 part a 4. (8 points) Section 1.6 Problem 10 part b (use resolution) 5. (3 points) Section 1.6 Problem 16 part b 6. (3 points) Section 1.6 Problem 16 part d 7. (2 points) Section 1.6 Problem 24 8. (4 points) Section 1.6 Problem 34 part a (use resolution) 9. (6 points) Use resolution to answer the query in a.dl below 10. (6 points) Use resolution to answer the query in b.dl below 11. (6 points) Use resolution to answer the query in c.dl below ### a.dl Schemes: C(X) P(X) W(X) Facts: C('d') Rules: P(X) :- C(X). W(X) :- P(X). Queries: W(X)? ### b.dl Schemes: J(X) C(X) P(X) R(X) Facts: J('d') C('d') Rules: P(X) :- J(X). R(X) :- C(X), P(X). Queries: R(X)? ### c.dl Schemes: P(X,Y) Q(X,Y,Z) R(X,Z) Facts: P('a','a') P('a','b') P('a','c') Q('a','b','c') Rules: R(X,Z) :- P(X,Z), Q(X,Y,Z) Queries: R('a',X)?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8430066108703613, "perplexity": 2051.7377697093475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488517048.78/warc/CC-MAIN-20210622093910-20210622123910-00631.warc.gz"}
https://portlandpress.com/clinsci/article-abstract/66/5/525/73497/Radionuclide-Demonstration-of-Ventilatory?redirectedFrom=fulltext	1. The distribution of 5 μm 99mTc aerosol particles deposited in the lungs was compared with that of 81mKr gas in 20 asthmatic subjects (FEV1.0≥75% predicted) whose asthma was mild or in remission. Sixteen normal non-smokers and 14 ‘normal’ cigarette smokers were studied as control subjects. 2. Radioaerosol lung penetration in the ‘normal’ smokers was the same as in the normal non-smokers but was reduced in the asthmatic subjects. 3. Radioaerosol penetrated better than 81mKr to the lung apices of normal non-smokers and asthmatic subjects; it penetrated better than 81mKr to the lung bases of the asthmatic subjects. 4. Uneven distribution of aerosol relative to 81mKr related strongly to maximal mid-expiratory flow rate (MMFR) in the asthmatic subjects. 5. Aerosol deposition abnormalities in symptom-free asthmatic subjects may reflect basal airways closure at functional residual capacity and abnormal patterns of lung filling. This content is only available as a PDF.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8322131633758545, "perplexity": 19195.7008295605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541288287.53/warc/CC-MAIN-20191214174719-20191214202719-00058.warc.gz"}
https://fr.maplesoft.com/support/help/Maple/view.aspx?path=MathApps%2FDirectionFields	Direction Fields - Maple Help Home : Support : Online Help : Math Apps : Calculus : Differential : Direction Fields Direction Fields Main Concept A differential equation (DE) is a mathematical equation which relates an unknown function and one or more of its derivatives. DEs are an important tool in many areas of pure and applied mathematics, as well as other subjects such as physics, engineering, economics, and biology. The order of a DE is the order of the highest derivative of the dependent variable with respect to the independent variable appearing in the equation. The focus of this app is on first-order differential equations, which only include the first derivative and the function itself. These DEs often have the form where x is the independent variable, y is the dependent variable, and so , also written, is the derivative of the function $y\left(x\right)$ with respect to x. Although there are many techniques for solving first-order DEs, it can be very difficult or even impossible to solve them explicitly in some cases, and so there is need for a way to visualize and numerically approximate the solution curves. This is where direction fields become useful. A direction field (or slope field) is a graphical representation of the solutions of a first-order differential equation achieved without solving the DE explicitly. At each point (x,y) in the plane, you plot the direction vector $\left[\begin{array}{c}1\\ f\left(x,y\right)\end{array}\right]$, which is tangent to (has the same slope as) the solution curve through that point. These vectors are often normalized to be of consistent length to emphasize their direction rather than magnitude. You can then approximate the solution curves by following the direction vectors. Often, you are also given an initial condition, . This allows you to illustrate a specific curve in the family of solutions by ensuring that the curve you sketch passes through the point while still following in the directions of the vectors. Choose a first-order differential equation from the list or enter your own in the text box below the list to plot its direction field. Enter values for ${x}_{0}$ and ${y}_{0}$ in the text boxes below the plot to set an initial condition, then select Add a Solution Curve to add the solution curve which satisfies this initial condition. Click the plot twice to define the opposite corners of a rectangular viewing area into which you would like to zoom. To zoom out from this region, click Zoom Out, or click Default Zoom to return to the viewing window you started with. Warning: Due to the numerical methods being used to approximate the solution curve, the curve may end abruptly when approaching an asymptote. = yxx+yx^2 - 3x +1cos(x)1/(1 + exp(-x))xsin(y)(y^2)*xsin(x + y)Custom DE Initial Condition: $y($	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8809496760368347, "perplexity": 492.99874043633775}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335424.32/warc/CC-MAIN-20220930020521-20220930050521-00252.warc.gz"}
http://spjohnston.com/wikiredia.php?topic=Hypersonic_flight	4766 words Hypersonic flight - Wikipedia # Hypersonic flight Hypersonic flight is flight through the atmosphere below about 90 kilometres at speeds above Mach 5, a speed where dissociation of air begins to become significant and high heat loads exist. ## History The first manufactured object to achieve hypersonic flight was the two-stage Bumper rocket, consisting of a WAC Corporal second stage set on top of a V-2 first stage. In February 1949, at White Sands, the rocket reached a speed of 8288.12 kilometres/h (5150 mph), or approximately Mach 6.7.[1] The vehicle, however, burned on atmospheric re-entry, and only charred remnants were found. In April 1961, Russian Major Yuri Gagarin became the first human to travel at hypersonic speed, during the world's first piloted orbital flight. Soon after, in May 1961, Alan Shepard became the first American and second person to achieve hypersonic flight when his capsule reentered the atmosphere at a speed above Mach 5 at the end of his suborbital flight over the Atlantic Ocean. In November 1961, Air Force Major Robert White flew the X-15 research airplane at speeds over Mach 6.[2][3] On 2 October 1967, in California, X-15 reached Mach 6.7, but by the time the vehicle approached Edwards Air Force Base, intense heating associated with shock waves around the vehicle had partially melted the pylon that attached the ramjet engine to the fuselage. The reentry problem of a space vehicle was extensively studied.[4] The NASA X-43A flew on scramjet for 10 seconds, and then glided for 10 minutes on its last flight in 2004. The Boeing X-51 Waverider flew on scramjet for 210 seconds in 2013, finally reaching Mach 5.1 on its fourth flight test. The hypersonic regime has since become the subject for further study during the 20-1th century, and strategic competition between China, Russia, and the U.S. ## Physics The stagnation point of air flowing around a body is a point where its local velocity is zero.[4] At this point the air flows around this location. A shock wave forms, which deflects the air from the stagnation point and insulates the flight body from the atmosphere.[4] This can affect the lifting ability of a flight surface to counteract its drag and subsequent free fall.[5] Ning describes a method for interrelating Reynolds number with Mach number.[6] In order to maneuver in the atmosphere at faster speeds than supersonic, the forms of propulsion can still be airbreathing systems, but a ramjet no longer suffices for a system to attain Mach 5, as a ramjet slows down the airflow to subsonic.[7] Some systems (waveriders) use a first stage rocket to boost a body into the hypersonic regime. Other systems (boost-glide vehicles) use scramjets after their initial boost, in which the speed of the air passing through the scramjet remains supersonic. Other systems (munitions) use a cannon for their initial boost. ### High Temperature Effect Hypersonic flow is a high energy flow.[8] The ratio of kinetic energy to the internal energy of the gas increases as the square of the Mach number. When this flow enters a boundary layer, there are high viscous effects due to the friction between air and the high-speed object. In this case, the high kinetic energy is converted in part to internal energy and gas energy is proportional to the internal energy. Therefore, hypersonic boundary layers are high temperature regions due to the viscous dissipation of the flow's kinetic energy. Another region of high temperature flow is the shock layer behind the strong bow shock wave. In the case of the shock layer, the flows velocity decreases discontinuously as it passes through the shock wave. This results in a loss of kinetic energy and a gain of internal energy behind the shock wave. Due to high temperatures behind the shock wave, dissociation of molecules in the air becomes thermally active. For example, for air at T > 2000 Kelvin, dissociation of diatomic oxygen into oxygen radicals is active: O2 → 2O For T > 4000 Kelvin, dissociation of diatomic nitrogen into N radicals is active: N2 → 2N Consequently, in this temperature range, molecular dissociation followed by recombination of oxygen and nitrogen radicals produces nitric oxide: N2 + O2 → 2NO, which then dissociates and recombines to form ions: N + O → NO+ + e ### Low Density Flow At standard sea-level condition for air, the mean free path of air molecules is about ${\displaystyle \lambda =68\mathrm {nm} }$ . Low density air is much thinner. At an altitude of 104 kilometres (342000 feet) the mean free path is ${\displaystyle \lambda =1\,ft=0.305\,m}$ . Because of this large free mean path aerodynamic concepts, equations, and results based on the assumption of a continuum begin to break down, therefore aerodynamics must be considered from kinetic theory. This regime of aerodynamics is called low-density flow. For a given aerodynamic condition low-density effects depends on the value of a nondimensional parameter called the Knudsen number ${\displaystyle K_{n}}$ , defined as ${\displaystyle K_{n}={\frac {\lambda }{l}}}$ where ${\displaystyle l}$ is the typical length scale of the object considered. The value of the Knudsen number based on nose radius, ${\displaystyle K_{n}={\frac {\lambda }{R}}}$ , can be near one. Hypersonic vehicles frequently fly at very high altitudes and therefore encounter low-density conditions. Hence, the design and analysis of hypersonic vehicles sometimes require consideration of low-density flow. New generations of hypersonic airplanes may spend a considerable portion of their mission at high altitudes, and for these vehicles, low-density effects will become more significant.[8] ### Thin Shock Layer The flow field between the shock wave and the body surface is called the shock layer. As the Mach number M increases, the angle of the resulting shock wave decreases. This Mach angle is described by the equation ${\displaystyle \mu =\sin ^{-1}(a/v)}$ where a is the speed of the sound wave and v is the flow velocity. Since M=v/a, the equation becomes ${\displaystyle \mu =\sin ^{-1}(1/M)}$ . Higher Mach numbers position the shock wave closer to the body surface, thus at hypersonic speeds, the shock wave lies extremely close to the body surface, resulting in a thin shock layer. At low Reynolds number, the boundary layer grows quite thick and merges with the shock wave, leading to a fully viscous shock layer.[9] ### Viscous Interaction The compressible flow boundary layer increases proportionately to the square of the Mach number, and inversely to the square root of the Reynolds number. At hypersonic speeds, this effect becomes much more pronounced, due to the exponential reliance on the Mach number. Since the boundary layer becomes so large, it interacts more viscously with the surrounding flow. The overall effect of this interaction is to create a much higher skin friction than normal, causing greater surface heat flow. Additionally, the surface pressure spikes, which results in a much larger aerodynamic drag coefficient. This effect is extreme at the leading edge and decreases as a function of length along the surface.[8] ### Entropy Layer The entropy layer is a region of large velocity gradients caused by the strong curvature of the shock wave. The entropy layer begins at the nose of the aircraft and extends downstream close to the body surface. Downstream of the nose, the entropy layer interacts with the boundary layer which causes an increase in aerodynamic heating at the body surface. Although the shock wave at the nose at supersonic speeds is also curved, the entropy layer is only observed at hypersonic speeds because the magnitude of the curve is far greater at hypersonic speeds.[8] ## Hypersonic weapons development In the last year, China has tested more hypersonic weapons than we have in a decade. We've got to fix that. — Michael Griffin, US Undersecretary of Defense for Research and Engineering, Flightglobal (2018)[10] Two main types of hypersonic weapons are hypersonic cruise missiles and hypersonic glide vehicles.[11] Hypersonic weapons, by definition, travel five or more times the speed of sound. Hypersonic cruise missiles, which are powered by scramjet, are restricted below 100000 feet; hypersonic glide vehicles can travel higher. Compared to a ballistic (parabolic) trajectory, a hypersonic vehicle would be capable of large-angle deviations from a parabolic trajectory.[7] According to CNBC, Russia and China lead in hypersonic weapon development, trailed by the United States.[12] France, India, and Australia may also be pursuing the technology.[7] Japan is acquiring both scramjet (Hypersonic Cruise Missile), and boost-glide weapons (Hyper Velocity Gliding Projectile).[13] Waverider hypersonic weapons delivery is an avenue of development. China's XingKong-2 (星空二号, Starry-sky-2), a waverider, had its first flight 3 August 2018.[14][15][16] In 2016, Russia is believed to have conducted two successful tests of Avangard, a hypersonic glide vehicle. The third known test, in 2017, failed.[17] In 2018, an Avangard was launched at the Dombarovskiy missile base, reaching its target at the Kura shooting range, a distance of 3700 miles (5955 kilometres). [18] Avangard uses a scramjet engine.[19] Avangard uses new composite materials which are to withstand temperatures of up to 2000 degrees Celsius (3632 degrees Fahrenheit).[20] The Avangard's environment at hypersonic speeds reaches such temperatures.[20] Russia considered its carbon fiber solution to be unreliable,[21] and replaced it with composite materials.[20] Two Avangard hypersonic glide vehicles (HGVs)[22] will first be mounted on SS-19 ICBMs; on 27 December 2019 the weapon was first fielded to the Yasnensky Missile Division, a unit in the Orenburg Oblast.[23] In an earlier report, Franz-Stefan Gady named the unit as the thirteenth Regiment/Dombarovskiy Division (Strategic Missile Force).[22] These tests have prompted US responses in weapons development[24][25][26][27] per John Hyten's USSTRATCOM statement 05:03, 8 August 2018 (UTC).[28] At least one vendor is developing ceramics to handle the temperatures of hypersonics systems.[19] There are over a dozen US hypersonics projects as of 2018, notes the commander of USSTRATCOM;[28][29][30] from which a future hypersonic cruise missile is sought, perhaps by Q4 FY2021.[31] There are also privately developed hypersonic systems.[32] DoD tested a Common Hypersonic Glide Body (C-HGB) in 2020.[33][34][35] According to Air Force chief scientist, Dr. Greg Zacharias, the US anticipates having hypersonic weapons by the 2020s,[36] hypersonic drones by the 2030s, and recoverable hypersonic drone aircraft by the 2040s.[37] The focus of DoD development will be on air-breathing boost-glide hypersonics systems.[38] Countering hypersonic weapons during their cruise phase will require radar with longer range, as well as space-based sensors, and systems for tracking and fire control.[38][39][40][41] Rand Corporation (28 September 2017) estimates there is less than a decade to prevent Hypersonic Missile proliferation.[42] In the same way that anti-ballistic missiles were developed as countermeasures to ballistic missiles, counter-countermeasures to hypersonics systems were not yet in development, as of 2019.[7][43][21][44] But by 2019, 157.4 million dollars was allocated in the FY2020 Pentagon budget for hypersonic defense, out of 2.6 billion dollars for all hypersonic-related research.[45] Both the US and Russia withdrew from the Intermediate-Range Nuclear Forces (INF) Treaty in February 2019. This will spur arms development, including hypersonic weapons.[46][47] ## References 1. ^ Winter, Frank (3 August 2000). "V-2 missile". Smithsonian National Air and Space Museum. airandspace.si.edu. Retrieved 16 August 2018. 2. ^ White, Robert. "Across the Hypersonic Divide". HistoryNet. HistoryNet LLC. Retrieved 11 October 2015. 3. ^ "Hypersonic plane passes latest test". ABC News (Australian Broadcasting Corporation). 22 March 2010. Retrieved 18 February 2014. 4. ^ a b c Alfred J. Eggers, H. Julian Allen, Stanford Neice (10 December 1954), "A comparative analysis of the performance of long-range hypervelocity vehicles", NACA report 1382, pp. 1141–1160 5. ^ 6. ^ 7. ^ a b c d 8. ^ a b c d Anderson, John (2016). Introduction to Flight (Eighth ed.) McGraw-Hill Education 9. ^ "Mach Angle". Glenn Research Center, NASA. 6 April 2018. 10. ^ Reim2018-12-14T18:43:02+00:00, Garrett. "Counter hypersonic weapon possible by mid-2020s: DoD". Flight Global. 11. ^ "fas.org" (PDF). 12. ^ Miller, Jeff Morganteen,Andrea (26 September 2019). "Hypersonic weapons are the center of a new arms race between China, the US and Russia". CNBC. 13. ^ Yeo, Mike (13 March 2020). "Japan unveils its hypersonic weapons plans". Defense News. 14. ^ 15. ^ 16. ^ 17. ^ Macias, Amanda (26 December 2018). "The Kremlin says it conducted another successful test of a hypersonic weapon". CNBC. Retrieved 27 December 2018. 18. ^ "Putin crows as he oversees Russian hypersonic weapons test", ABC News, 26 December 2018 19. ^ a b Nick Stockton (27 December 2018), "Rotating Detonation Engines Could Propel Hypersonic Flight", Wired 20. ^ a b c "Putin Says 'Invulnerable' New Hypersonic Nuclear Missile Is Ready For Deployment", The Huffington Post, 27 December 2018 21. ^ a b Amanda Macias (12 October 2018), "Russia hits a snag in developing a hypersonic weapon after Putin said it was already in production", CNBC 22. ^ a b Franz-Stefan Gady (14 November 2019) Russia: Avangard Hypersonic Warhead to Enter Service in Coming Weeks: "The Russian Strategic Missile Force will receive the first two ICBMs fitted with the Avangard warhead in late November or early December." The Avangard HGV was codenamed Yu-71, under Project 4202. "In late November – early December, two UR-100N UTTKh missiles equipped with the hypersonic glide vehicles from the first regiment of Avangard systems will assume experimental combat duty in the Dombarovsky division of the Strategic Missile Force,"—Tass, 13 November. The "13th regiment will reportedly be the first unit to receive the two retrofitted SS-19 ICBMs. The regiment is part of the Dombarovskiy (Red Banner) missile division". Eventually 4 more SS-19s fitted with Avangard HGVs will join the thirteenth Regiment; a second regiment with six Avangard / SS-19s will be stood up by 2027. 23. ^ Vladimir Isachenkov (27 December 2019) "New Russian weapon can travel 27 times the speed of sound", Associated Press. —Avangard has been fielded to the Yasnensky Missile Division, a unit in the Orenburg Oblast"The first regiment with the 'Avangard' took up combat duty" На боевое дежурство заступил первый полк с "Авангардами" (in Russian). Interfax. 27 December 2019. 24. ^ a b 25. ^ Joseph Trevithick (6 September 2018), "DARPA Starts Work On 'Glide Breaker' Hypersonic Weapons Defense Project", The Drive 26. ^ 27. ^ 28. ^ a b USSTRATCOM, CNBC 29. ^ Sydney Freedberg (13 March 2019), "Hypersonics Won't Repeat Mistakes Of F-35 inches, Breaking Defense 30. ^ Joseph Trevithic (6 August 2019), "Air Force Reveals Tests Of Supposed Record-Setting Scramjet Engine From Northrop Grumman" 31. ^ Garrett Reim (29 Apr 2020 ) US Air Force launches study of another hypersonic cruise missile 32. ^ Colin Clark (19 June 2019), "Raytheon, Northrop Will 'Soon' Fly Hypersonic Cruise Missile", Breaking Defense, Paris Air Show, new additive-process materials to build the combustor of a scramjet; potential integration among members of an intercommunicating swarm of hypersonics systems. 33. ^ Sydney J. Freedberg Jr. (20 Mar 2020) Hypersonics: Army, Navy Test Common Glide Body "The U.S. Navy and U.S. Army jointly executed the launch of a common hypersonic glide body (C-HGB), which flew at hypersonic speed to a designated impact point" 34. ^ "Pentagon to TestFly New Hypersonic Weapon This Year". www.nationaldefensemagazine.org. 35. ^ Bryan Clark (21 April 2020) DoD Is Running the Wrong Way in the Hypersonics Race 500 pound payload; maneuverability at Mach 5 is an issue; possible red herring for funding 36. ^ Sean Kimmons (31 May 2019), "Joint hypersonic weapon tests to start next year", Army News Service 37. ^ Osborn, Kris (12 August 2017). "Get Ready, Russia and China: America's Next Fighter Jet Will Dominate the Skies". The National Interest. Retrieved 2 March 2018. 38. ^ a b David Vergun (14 December 2018), "DOD scaling up effort to develop hypersonics", U.S. Army 39. ^ Loren Thompson (30 July 2019) "Defense Against Hypersonic Attack Is Becoming The Biggest Military Challenge Of The Trump Era" 40. ^ John L. Dolan, Richard K. Gallagher & David L. Mann (23 April 2019) "Hypersonic Weapons – A Threat to National Security" Hypersonic and Ballistic Tracking Space Sensor (HBTSS) 41. ^ Paul McLeary (18 December 2019), "MDA Kickstarts New Way To Kill Hypersonic Missiles" MDA's Hypersonic Defense Weapon System - 4 Interceptors 42. ^ "Hypersonic Missile Nonproliferation", Rand Corporation, 28 September 2017, via YouTube 43. ^ a b "Putin unveils new nuclear missile, says 'listen to us now'". nbcnews.com. Retrieved 2 March 2018. 44. ^ Sydney Freedberg (1 February 2019) "Pentagon Studies Post-INF Weapons, Shooting Down Hypersonics", Breaking Defense 45. ^ a b c d Kelley M. Sayler (11 July 2019), "Hypersonic Weapons: Background and Issues for Congress", Congressional Research Service 46. ^ Linda Givetash (2 February 2019), "Putin says Russia also suspending key nuclear arms treaty after U.S. move to withdraw", NBC News, Reuters 47. ^ Rebecca Kheel and Morgan Chalfant (31 July 2019) "Landmark US-Russia arms control treaty poised for final blow", The Hill 48. ^ "THE Aerojet X-8 inches. www.456fis.org. 49. ^ Gibbs, Yvonne (13 August 2015). "NASA Dryden Fact Sheets - X-15 Hypersonic Research Program". NASA. 50. ^ "Lockheed X-17 inches. www.designation-systems.net. 51. ^ "X-51A Waverider". U.S. Air Force. 52. ^ China unveils Dongfeng-17 conventional missiles in military parade, 1 October 2019, via YouTube. See minute 0:05 to 0:49 for 16 Hypersonic Glide Vehicles (white-tipped contrast atop their DF-17 fuselages mounted on booster rockets. 53. ^ Ankit Panda (7 October 2019) "Hypersonic Hype: Just How Big of a Deal Is China's DF-17 Missile?", The Diplomat. A conventional-weapons-only boost-glide HGV mounted on endo-atmospheric fuselage (DF-17). 54. ^ 55. ^ Peri, Dinakar (12 June 2019). "DRDO conducts maiden test of hypersonic technology demonstrator". The Hindu. 56. ^ April 2015, Elizabeth Howell 21. "Buran: The Soviet Space Shuttle". Space.com. 57. ^ "RLV-TD - ISRO". www.isro.gov.in. 58. ^ Ba (Nyse) (1 January 2020). "Autonomous Systems - X-37B". Boeing. Retrieved 18 March 2020. 59. ^ "Project 863-706 Shenlong ("Divine Dragon")". www.globalsecurity.org. 60. ^ 61. ^ "BOR-4 inches. space.skyrocket.de. 62. ^ "The Martin Marietta X-23 Prime". www.456fis.org. 63. ^ "X-24 inches. www.astronautix.com. 64. ^ "Asset". www.astronautix.com. 65. ^ "JAXA \| Hypersonic Flight Experiment "HYFLEX"". JAXA \| Japan Aerospace Exploration Agency. 66. ^ Drye, Paul (10 July 2012). "Sänger-Bredt Silbervogel: The Nazi Space Plane". 67. ^ "Keldysh Bomber". www.astronautix.com. 68. ^ "Tu-2000 inches. www.astronautix.com. 69. ^ Mark Wade. "Tsien Spaceplane 1949 inches. astronautix.com. 70. ^ "HOPE". www.astronautix.com. 71. ^ Conner, Monroe (30 March 2016). "Lockheed Martin X-33 inches. NASA. 72. ^ "Hermes". www.astronautix.com. 73. ^ 74. ^ "Mustard". www.astronautix.com. 75. ^ "Kliper". www.astronautix.com. 76. ^ "Valier "Raketenschiff" (1929): Classic Rocketship Series #6 inches. The Virtual Museum of Flying Wonders. Fantastic Plastic Models. 77. ^ "Rockwell C-1057 "Breadbox" Space Shuttle (1972)". The Virtual Museum of Flying Wonders. Fantastic Plastic Models. 78. ^ Cui, et. al. (February 2019) Hypersonic I-shaped aerodynamic configurations Science China Physics, Mechanics & Astronomy 61:024722 Wind tunnel proposal 79. ^ "ISRO's AVATAR – making India proud again". www.spsmai.com. 80. ^ 81. ^ January 2020, Mike Wall 23. "DARPA scraps XS-1 military space plane project after Boeing drops out". Space.com. 82. ^ "Dream Chaser® - America's Spaceplane™ \| Sierra Nevada Corporation". www.sncorp.com. 83. ^ "NASA X-43 inches. Aerospace Technology. 84. ^ Conner, Monroe (4 April 2016). "X-43A (Hyper-X)". NASA. 85. ^ "HyperSoar - Military Aircraft". fas.org. 86. ^ 87. ^ "Falcon HTV-2 inches. www.darpa.mil. 88. ^ "Boeing Unveils Hypersonic Airliner Concept". Aviation Week. 26 June 2018. 89. ^ Joe Pappalardo (26 June 2018). "How Boeing's Hypersonic Passenger Plane Concept Works". Popular Mechanics. 90. ^ "SR-72 Hypersonic Demonstrator Aircraft". Airforce Technology. 91. ^ Dan Goure (20 June 2019) "Hypersonic Weapons Are Almost Here (And They Will Change War Forever)" Lockheed-Martin vs Raytheon-Northrup 92. ^ Steve Trimble (29 July 2019), "Raytheon Tactical Boost Glide Baseline Review Completed", Aviation Week 93. ^ Dr. Peter Erbland, Lt. Col. Joshua Stults () "Tactical Boost Glide" 94. ^ "Saenger II". www.astronautix.com. 95. ^ "Hytex". www.astronautix.com. 96. ^ "Horus". www.astronautix.com. 97. ^ February 2013, Markus Hammonds 20. "Skylon Space Plane: The Spacecraft of Tomorrow". Space.com. 98. ^ D. Preller; P. M. Smart. "Abstract: SPARTAN: Scramjet Powered Accelerator for Reusable Technology AdvaNcement" (PDF). 2014 ReinventingSpace Conference (Rispace 2014). 99. ^ "High-Speed Experimental Fly Vehicles - INTernational". European Space Agency. 100. ^ Ros, Miquel. "Space tech meets aviation: The hypersonic revolution". CNN. 101. ^ "Advanced Hypersonic Weapon (AHW)". Army Technology. 102. ^ a b c 103. ^ Chris Martin (17 December 2019) "Lockheed awards $81.5M contract for hypersonic missile motor", Defense News, HCSW$81.5M, ARRW 104. ^ a b Theresa Hitchens (27 February 2020) Lockheed Martin, Air Force Press Ahead On Air-Launched Hypersonic Missile =HSW-ab; ARRW funding is augmented; 105. ^ Joseph Trevithick (18 June 2019), "Northrop And Raytheon Have Been Secretly Working On Scramjet Powered Hypersonic Missile", The Drive 106. ^ a b Kris Osborn (1 October 2019), "Air Force arms B1-B bomber with hypersonic weapons", Fox News 107. ^ a b Jr, Sydney J. Freedberg. "Hypersonic Missiles: Plethora Of Boost-Glide & Cruise". 108. ^ John A. Tirpak (10 Feb 2020) Air Force Cancels HCSW Hypersonic Missile in Favor of ARRW 109. ^ Kyle Mizokami (18 September 2019) "The Air Force Is Working on 'Hacksaw,' a Mach 5 Missile", Popular Mechanics 110. ^ 111. ^	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 8, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4378279447555542, "perplexity": 18432.28365010175}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655896169.35/warc/CC-MAIN-20200708000016-20200708030016-00226.warc.gz"}
https://www.clutchprep.com/physics/practice-problems/38930/the-impedance-of-a-series-rlc-circuit-at-resonance-is-described-by-which-of-the-	Resonance in Series LRC Circuits Video Lessons Concept # Problem: The impedance of a series RLC circuit at resonance is described by which of the following? A) less than R B) impossible to determine C) equal to R D) larger than R 81% (71 ratings) ###### Problem Details The impedance of a series RLC circuit at resonance is described by which of the following? A) less than R B) impossible to determine C) equal to R D) larger than R	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9420353770256042, "perplexity": 2444.328230012285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141195069.35/warc/CC-MAIN-20201128040731-20201128070731-00207.warc.gz"}
https://proceedings.neurips.cc/paper/2018/hash/c60d870eaad6a3946ab3e8734466e532-Abstract.html	#### Authors Xiaowei Chen, Weiran Huang, Wei Chen, John C. S. Lui #### Abstract <p>We introduce the community exploration problem that has various real-world applications such as online advertising. In the problem, an explorer allocates limited budget to explore communities so as to maximize the number of members he could meet. We provide a systematic study of the community exploration problem, from offline optimization to online learning. For the offline setting where the sizes of communities are known, we prove that the greedy methods for both of non-adaptive exploration and adaptive exploration are optimal. For the online setting where the sizes of communities are not known and need to be learned from the multi-round explorations, we propose an upper confidence'' like algorithm that achieves the logarithmic regret bounds. By combining the feedback from different rounds, we can achieve a constant regret bound.</p>	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8970956206321716, "perplexity": 1007.420334398039}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178367183.21/warc/CC-MAIN-20210303165500-20210303195500-00530.warc.gz"}
https://dwwiki.mooo.com/w/index.php?title=Description_line_(item)&diff=prev&oldid=19892	# Difference between revisions of "Description line (item)" An item's description is made up of several lines. ## Main description This is a description of what the item looks like. ## Name (if deluded) If an item is deluded, there will be a line saying what it is, of the form: <Deluded Name> is a <normal short name of item>. ## Holyness Certain holy items--holy symbols, holy amulets, holy relics, prayer books, and prayer beads--have a line indicating which deity they're consecrated to. • Pishe: The <item> radiates a reassuring cyan glow like the sun after rain. • Gufnork: The <item> gently radiates a fuzzy white glow. • Gapp: The <item> stylishly radiates a pristine golden light. • Sandelfon: The <item> indifferently radiates a harsh grey light. • Fish: The <item> slowly pulsates, washing from a deep blue to a light aquamarine. • Hat: The <item> sheds an irritating orange glow that makes you feel that someone is creeping up on you. • Sek: The <item> beats regularly with blood-red pulses of light. ## Consumed Some items can be consumed or used up in some way, and have a line indicating how much of them has been used. (Note that food that has been partially eaten has lines after other effects showing this.) ### Books of cigarette papers A book of cigarette papers has a line showing how many papers are left in it: There are <number> papers left in it. ### Burnable items A candle or block of incense has this line, which also shows whether it's lit. It is <lit\|not currently lit>. It is <stage>. These are the stages of regular non-scented candles: • It is new. • It is almost new. • It is not yet halfway burnt. • It is more than halfway burnt. • It is almost burnt to a stub. • It is burnt to a stub. Various scented candles have slightly different stages: • It is brand new. • It is almost new. • It is not yet halfway burnt. • It is more than halfway burnt. • It is almost burnt to the bottom. • It is burnt down to a small lumpy disk of wax. A coarse waxen candle has a slightly different set of stages: • It looks brand new. • It looks almost new. • It is not yet halfway burnt. • It is more than halfway burnt. • It is almost burnt to a stub. • It is burnt to a stub. Blocks of incense have this set of stages: • It is unmarred and unburned. • It is slightly scorched. • Half of it has burnt away. • It is nearly completely burnt. • It is burnt to a stub. Lanterns have two lines. One shows whether it's lit, and the other shows the fuel left. The first line is one of: • The lantern is not lit. • The wick flickers inside spreading a dull glow. The stages of fuel left are: • ? • It is almost completely out of fuel. • ? Torches do not have an extra line showing how much of them is left or whether they're lit--rather, their entire description changes. ## Special corpse statuses A corpse can have pieces of it cut off with a knife. If this has been done to it, there's a line that looks like this: It appears to be missing its <body part(s)>. A corpse that is going to turn into a vampire has this line added to it: It seems to be twitching slightly, almost as if it's still alive. You probably shouldn't get too close. NPC priests in Djelibeybi can do something to a corpse that gives it the following line: It seems to glow from within with golden light. A corpse with this line may eventually disappear in a special way instead of decaying normally. ## Other effects There are various other effects that can be applied to an item. They show up in the order they were applied in--for example, if you perform Light on something, then ward it, the Light line will be before the ward line until the Light ritual runs out. If you perform Light on it again after the first one runs out, the line will then be after the ward line. Appearance Type Source It is glowing brilliantly <colour>. ritual Light It is dusted with <type(s) of powder>. item powdered rock It has a colourful aura, with flickers of <colour> and <colour>. ritual warded It is bathed in a <colour> aura. ritual warded ## Corpse inventory A corpse will have the same inventory and purse lines as the living thing it used to be. ## Eaten Food (including fluff) that has been partially eaten has a line showing how much is left: It is about <amount> gone. ## Decayed Most food has a line showing how fresh or decayed it is. The stages are: • It looks nice and fresh. • It looks a bit rotten. • It is half rotten. • It is mostly rotten. • It is almost completely rotten. If you pickle it, the line becomes: It seems to have been pickled. ## Octarine These lines, in octarine, are visible only to wizards and witches naturally. Others can see them by using Detect Magic on the item or zapping a short wand at it. ### Enchantment First, if the item is enchanted, there will be a line showing the level. The normal levels are: • 1-10%: 'It occasionally pulses with octarine light' • 11-20%: 'It emits a slight octarine glow' • 21-30%: 'It softly pulses in dull octarine shades' • 31-40%: 'It gives off a steady but dull octarine glow' • 41-50%: 'It gives off a steady octarine glow' • 51-60%: 'It glows an intense octarine' • 61-70%: 'It emits a bright octarine colour' • 71-80%: 'It brightly pulses octarine' • 81-90%: 'It glows brilliant octarine shades' • 91-100%: 'It radiates pure octarine brilliance' ### Delusion or talismanhood Next, if it is a talisman or proto-talisman, there will be a line showing its level. The levels are: • It has a faint octarine shadow about it that disappears if you look at it squarely. • It has an octarine shadow about it that flickers occasionally out of the corner of your eye. • It has a flickering octarine haze about it. • It has the hazy octarine sparkle of a magical talisman. The last one indicates a full talisman. ## Pockets Some clothing has pockets. It has a line indicating this: The <item> has <pocket or pockets>. If there's anything in it, and it's not closed, there's an additional line showing what's in it. It is <fullness> with: <item or items>. There's also a line saying whether it's open or closed. Either: It is open. Or: You cannot see inside it. It is closed. ## Writing If the item has something written on it, you'll see this line: It appears to have something written on it. ## Condition Most items have a line showing their condition: It is in <condition> condition. Not all items have this line, but not having the line doesn't necessarily mean it has no condition and can't be broken (for example, musical instruments can break if held when fighting or, sometimes, in containers). ## Contents Some containers (possibly non-clothing containers) have a line or two after the condition describing the contents. For dry containers, it looks like this: The <item> is <fullness> with <item(s)>. For vessels, it looks like this: The cup is about one-quarter full with two ounces of green tea. It is about one-quarter full. In either case, the line or lines are only there if the container is open and not empty. ## Open/closed Some containers have the line saying whether it's open or closed here. It looks like either: It is open. Or: It is closed. Books also have this line, but the "open" version looks like: It is open at page <number>.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43286511301994324, "perplexity": 7494.412350570807}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711221.94/warc/CC-MAIN-20221207221727-20221208011727-00612.warc.gz"}
http://www.databaseforum.info/2/566899.aspx	Setup projects: "variables" in registry values? Author Message Posted: Visual C# General, Setup projects: "variables" in registry values? Top My question is probably best posed as a scenario:During install, I want to add a registry string that contains the full path of where I was installed to. For example, if the user elects to install to "c:\program files\MyProg", then as part of the setup process I want to add a registry value under HKLM\Software\\InstallPath = "c:\program files\MyProg".It looks as though the VS 2005 Setup project only allows "fixed" values added to the registry. I'm hoping I'm wrong.Brad. Visual C#1 fperugini Posted: Visual C# General, Setup projects: "variables" in registry values? Top Brad, Did you find a solution to this problem I want to do the exact same thing. I already tried [Application Folder] as the Value property and it did not seem to work. -Frank joeycalisay Posted: Visual C# General, Setup projects: "variables" in registry values? Top have you guys tried a value of [TARGETDIR], see this post. fperugini Posted: Visual C# General, Setup projects: "variables" in registry values? Top Thanks! That was it. The reference article was helpful too. -Frank	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8225762844085693, "perplexity": 6786.141868456503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997858892.28/warc/CC-MAIN-20140722025738-00119-ip-10-33-131-23.ec2.internal.warc.gz"}
https://studyqas.com/what-is-the-quotient-1-3-divided-by-1-3/	# What is the quotient 1/3 divided by (-1/3) What is the quotient 1/3 divided by (-1/3) ## This Post Has 7 Comments 1. pearfam98 says: divided became multiplication 1/3 x 5/3 1 x 5=5 3 x 3=9 answer is 5/9 2. volocibel says: To divide a fraction, you turn the numerator and denominator around, and multiply by the number you originally would divide it by. so you go 3/1 times by 5. so it is 15/1 so 15. 3. dbag1162 says: Did you just assume my gender? Step-by-step explanation: 4. kirstenb278 says: Since 1/3 and -1/3 have the exact same denominators and numerators they will divide into 1. But since one of the number are negative, that means your answer switches to be negative 1 Step-by-step explanation: 5. mhwalters says: 5 ÷ ( 1 / 3 ) = 5 × ( 3 / 1 ) = 15 / 1 = 15 ; 6. cxttiemsp021 says: -1 Step-by-step explanation: 7. CoolDudeTrist says: I think the answer is 5/9	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9808217287063599, "perplexity": 2525.586378864805}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499946.80/warc/CC-MAIN-20230201144459-20230201174459-00604.warc.gz"}
https://rdrr.io/cran/ProbYX/man/rp.html	# rp: Signed log-likelihood ratio statistic In ProbYX: Inference for the Stress-Strength Model R = P(Y<X) ## Description Compute the signed log-likelihood ratio statistic (r_p) for a given value of the stress strength R = P(Y<X), that is the parameter of interest, under given parametric model assumptions. ## Usage 1 rp(ydat, xdat, psi, distr = "exp") ## Arguments ydat data vector of the sample measurements from Y. xdat data vector of the sample measurements from X. psi scalar for the parameter of interest. It is the value of R, treated as a parameter under the parametric model construction. distr character string specifying the type of distribution assumed for Y and X. Possible choices for distr are "exp" (default) for the one-parameter exponential, "norm_EV" and "norm_DV" for the Gaussian distribution with, respectively, equal or unequal variances assumed for the two random variables. ## Details The two independent random variables Y and X with given distribution distr are measurements of the diagnostic marker on the diseased and non-diseased subjects, respectively. For the relationship of the parameter of interest (R) and nuisance parameters with the original parameters of distr, look at the details in loglik. ## Value Value of the signed log-likelihood ratio statistic r_p. ## Note The r_p values can be also used for testing statistical hypotheses on the probability R. Giuliana Cortese ## References Cortese G., Ventura L. (2013). Accurate higher-order likelihood inference on P(Y<X). Computational Statistics, 28:1035-1059. Severini TA. (2000). Likelihood Methods in Statistics. Oxford University Press, New York. Brazzale AR., Davison AC., Reid N. (2007). Applied Asymptotics. Case-Studies in Small Sample Statistics. Cambridge University Press, Cambridge.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9082325100898743, "perplexity": 3770.930001573604}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549427749.61/warc/CC-MAIN-20170727062229-20170727082229-00593.warc.gz"}
https://www.giancolianswers.com/giancoli-physics-7th-edition-solutions/chapter-3/problem-7	## You are here Hi joseotilio25, this is a personal preference. I choose to make every vector subtraction problem an addition problem. When subtraction comes along, as in part b) here, I choose to make it an addition problem by adding the second vector in the opposite direction. This technique has the advantage that every vector problem, including subtraction, involves putting the tail of the second vector on the head of the first. To illustrate why this works, consider $3 - 2 = 1$. This can also be written as an addition problem by adding the opposite of the second number. The second number is $2$, so adding it's opposite means adding $-2$. It looks like $3 + (-2) = 1$. It works out to the same answer, as it should, and with arithmetic there's no advantage to making subtraction into an "adding the opposite" question, whereas with vectors, changing subtraction to "adding the opposite" has the advantage that you can keep on using the "head to tail" method. In the end, it's an issue of personal preference. You could instead learn a "head to head" method, and create the resultant by connecting the remaining tails if you want a different technique.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47954699397087097, "perplexity": 407.5366936428018}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540543252.46/warc/CC-MAIN-20191212102302-20191212130302-00450.warc.gz"}
https://zenodo.org/record/3479347/export/csl	Project deliverable Open Access # Europeanisation of national policy dialogues on energy pathways Aze, François; Dallamaggiore, Eve; Salel, Mathieu; Boo, Eva; Dunphy, Niall; Lennon, Breffní; Gaffney, Christine; Revez, Alexandra; Axon, Stephen; Otal, Josep; Chichinato, Orsetta; Melchiorre, Tiziana; Costantini, Valeria ### Citation Style Language JSON Export { "publisher": "Zenodo", "DOI": "10.5281/zenodo.3479347", "language": "eng", "title": "Europeanisation of national policy dialogues on energy pathways", "issued": { "date-parts": [ [ 2016, 10, 31 ] ] }, "abstract": "<p>The principal objective of the ENTRUST project is to develop an understanding of the “human factor” in the energy system in order to utilise derived knowledge to foster the transition towards a sustainable energy paradigm. To develop this understanding, it is necessary to assess the policy landscape that influences energy consumption, the progress of the energy transition, and the public discourse on, and engagement with the energy transition – this work forms the basis of Work Package 4. Within this WP, T4.2 entitled “Assessment of Europeanisation in national policy dialogue” operates on the premise that “Europe’s energy systems are deeply integrated” assesses the extent to which this is reflected in national policy dialogues.<br>\nDespite all the efforts to date to shape the European project including the energy dimension, complete integration of energy infrastructures and markets has not been achieved (Auverlot et al., 2014). In order to address the existing problems that result from this non-integration it is necessary to develop a meaningful, coherent, and comprehensive EU energy policy. Such an EU energy policy is vital to deal with global issues:</p>\n\n<ul>\n\t<li>Tackling climate change requires not only a shared commitment but also a common means;</li>\n\t<li>Building a coherent and comprehensive climate policy could strengthen the leading role of Europe in the international climate negotiations;</li>\n\t<li>Energy security issues must be considered in a comprehensive and inclusive manner on a EU-wide basis, rather than solely on the national scale, in order to tackle common problems and further protect European interests;</li>\n\t<li>Ensure the competitiveness of European companies;</li>\n\t<li>Inspire the European project which is losing momentum.</li>\n</ul>\n\n<p>This deliverable, D4.2, analyses the development of such a European energy policy, the different Europeanisation processes influencing this development, and to what extent this EU vision is transcribed into the national policy dialogues.<br>\nThe Europeanisation topic has been widely studied over the past two decades. While some authors describe Europeanisation as the emergence of exclusively European governance structures, the majority agree that Europeanisation describes a transfer process between the European institutions and the member States (MS). Integration of energy strategies, policy and legal systems (implementation of laws) plus the resulting effects on the energy system constitutes the concept of Europeanisation that supports this analysis. Thus, Europeanisation may be conceived as a dynamic process of policy transfer under the influence of several actors: European Commission, European Parliament, European Council, the MS and the lobbyists.<br>\nThe methodology of this study was developed to analyse, respectively, the top-down, bottom-up, and horizontal Europeanisation that have been implemented in order to decrypt the strategies at stake in six EU countries – namely France, Germany, Ireland, Italy, Spain and the UK. For each country, the analysis has involved: a review of policy making processes – the national contribution to EU policy making, the transposition of EU directives, and national policy making; a review of the evolution of the Policy and Legal System (PLS) over the period 2005-2016; and ascertaining to what extent the European energy vision is transferred to the national level.<br>\nMeasuring the gap between the energy vision promoted by the European Commission and the reality of the existing energy system provides interesting insights that can facilitate the design of effective policy recommendations that serve the European project. Finally, the study of the horizontal Europeanisation is relevant insofar as it identifies the most interesting policies that, potentially, should be replicated. </p>", "author": [ { "family": "Aze, Fran\u00e7ois" }, { "family": "Dallamaggiore, Eve" }, { "family": "Salel, Mathieu" }, { "family": "Boo, Eva" }, { "family": "Dunphy, Niall" }, { "family": "Lennon, Breffn\u00ed" }, { "family": "Gaffney, Christine" }, { "family": "Revez, Alexandra" }, { "family": "Axon, Stephen" }, { "family": "Otal, Josep" }, { "family": "Chichinato, Orsetta" }, { "family": "Melchiorre, Tiziana" }, { "family": "Costantini, Valeria" } ], "type": "report", "id": "3479347" } 34 32 views	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15239116549491882, "perplexity": 6645.130826405973}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154126.73/warc/CC-MAIN-20210731203400-20210731233400-00073.warc.gz"}
https://mozart.github.io/mozart-v1/doc-1.4.0/cpitut/node23.html	## 3.3 The Linear Programming Model Tackling a multi-knapsack problem with a LP solver amounts to implementing a branch & bound solver to obtain integral solutions. The idea is to compute a continuous solution and to branch over the problem variables with continuous solutions. This is done until only integral problem variables are left. This is what the procedure `DistributeKnapSackLP` does. `declare proc {DistributeKnapSackLP Vs ObjFn Constraints MaxProfit} choice DupVs = {DuplicateRIs Vs} DupMaxProfit V DupV in DupMaxProfit = {RI.var.bounds {RI.getLowerBound MaxProfit} {RI.getUpperBound MaxProfit}} {LP.solve DupVs ObjFn Constraints DupMaxProfit optimal} V#DupV = {SelectVar Vs#DupVs} case {IsDet V} then DupMaxProfit = MaxProfit DupVs = Vs else choice {RI.lessEq {Ceil DupV} V} [] {RI.lessEq V {Floor DupV}} end {DistributeKnapSackLP Vs ObjFn Constraints MaxProfit} end end end ` It first duplicates the problem variables (note this is possible due to stability) and invokes the LP solver on them to compute a (possibly continuous) solution. Then it selects the first duplicated continuous problem variable `DupV` by `SelectVar` (see below). If continuous variables are left (see the `else` branch of the `case` statement), it creates two choices on the corresponding original problem variable `V`: and calls `DistributeKnapSackLP` recursively. In case no continuous variables are left, an integral solution is found and the original problem variables are unified with duplicated ones. For completeness sake the auxiliary functions `SelectVar` and `DuplicateRIs` are presented here. `declare fun {SelectVar VsPair} case VsPair of nil#nil then unit#unit [] (VH\|VT)#(RVH\|RVT) then % check for integrality case RVH == {Round RVH} then {SelectVar VT#RVT} else VH#RVH end else unit end end ` `declare fun {DuplicateRIs Vs} {Map Vs fun {\$ V} {RI.var.bounds {RI.getLowerBound V} {RI.getUpperBound V}} end}end ` The procedure `KnapsackLP` return the script which creates the appropriate parameters for the LP solver and eventually calls `DistributeKnapSackLP`. `declare fun {KnapsackLP Problem} NumProducts = {Length Problem.profit} Resources = Problem.resourcesin proc {\$ Sol} sol(maxprofit: MaxProfit = {RI.var.decl} products: Products = {MakeList NumProducts}) = Sol ObjFn Constraints in {ForAll Products proc {\$ V} {RI.var.bounds 0.0 RI.sup V} end} ObjFn = objfn(row: {Map Problem.profit IntToFloat} opt: max) Constraints = {Map {Arity Resources} fun {\$ ResourceName} Resource = Resources.ResourceName in constr(row: {Map Resource.npp IntToFloat} type: '=<' rhs: {IntToFloat Resource.ta}) end} {DistributeKnapSackLP Products ObjFn Constraints MaxProfit} end end ` Feeding `{ExploreBest {KnapsackLP Problem} proc {\$ O N} {RI.lessEq O.maxprofit+1.0 N.maxprofit} end}` produces the following search tree. Tobias Müller Version 1.4.0 (20080702)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8518862724304199, "perplexity": 1089.7488644803575}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948596051.82/warc/CC-MAIN-20171217132751-20171217154751-00044.warc.gz"}
https://teachingcalculus.com/2013/02/04/painting-a-point/?shared=email&msg=fail	# Painting a Point Accumulation 7: An application (of paint) Suppose you started with a point, the origin to be specific, and painted it. You put on layers and layers of paint until your point grows to a sphere with radius r. Let’s stop and admire your work part way through the job; at this point the radius is ${{x}_{i}}$ and $0\le {{x}_{i}}\le r$. How much paint will you need for the next layer? Easy: you need an amount equal to the surface area of the sphere, $4\pi {{x}_{i}}^{2}$, times the thickness of the paint. As everyone knows paint is thin, specifically $\Delta x$ thin. So we add an amount of paint to the sphere equal to $4\pi {{x}^{2}}\left( \Delta x \right)$. The volume of the final sphere must be the same as the total amount of paint. The total amount of paint must be the (Riemann) sum of all the layers or $\displaystyle \sum\limits_{i=1}^{n}{4\pi {{x}_{i}}^{2}\left( \Delta x \right)}$. As usual $\Delta x$ is very thin, tending to zero as a matter of fact, so the amount of paint must be $\displaystyle \underset{\Delta x\to 0}{\mathop{\lim }}\,\sum\limits_{i=1}^{n}{4\pi {{x}_{i}}^{2}\left( \Delta x \right)=\int_{0}^{r}{4\pi {{x}^{2}}}dx=\left. \tfrac{4}{3}\pi {{x}^{3}} \right\|_{0}^{r}=\tfrac{4}{3}\pi {{r}^{3}}}$. A standard related rate problem is to show that the rate of change of the volume of a sphere is proportional to its surface area – the constant of proportionality is dr/dt. So it should not be a surprise that the integral of this rate of change of the surface area is the volume. The integral of a rate of change is the amount of change. Interestingly this approach works other places as long as you properly define “radius:” • A circle centered at the origin with radius x and perimeter of $2\pi x$, gains area at a rate equal to its perimeter times the “thickness of the edge” $\Delta x$: $\displaystyle A=\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{k=1}^{n}{2\pi x\Delta x}=\int_{0}^{r}{2\pi x\,dx=\pi {{r}^{2}}}$ • A square centered at the origin with “radius” x with sides whose length are s =2 x, gains area at a rate equal to its perimeter (8x) times the “thickness of the edge” $\Delta x$: $\displaystyle A=\underset{n\to \infty }{\mathop{\text{lim}}}\,\sum\limits_{k=1}^{n}{8x\Delta x=\int_{0}^{x}{8x\,dx}}=4{{x}^{2}}={{(2x)}^{2}}={{s}^{2}}$ • A cube centered at the origin with “radius” x and edges of length 2x, gains volume at a rate equal to its surface area, $6(4{{x}^{2}})$, times the “thickness of the face” $\Delta x$ – think paint again: $V=\underset{n\to \infty }{\mathop{\text{lim}}}\,\sum\limits_{k=1}^{n}{\text{6(4}{{\text{x}}^{2}})\Delta x}=\int_{0}^{x}{24{{x}^{2}}dx}=8{{x}^{3}}={{(2x)}^{3}}={{s}^{3}}$ This site uses Akismet to reduce spam. Learn how your comment data is processed.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 16, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9234445095062256, "perplexity": 416.1776273836084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058589.72/warc/CC-MAIN-20210928002254-20210928032254-00009.warc.gz"}
http://eprints.adm.unipi.it/1839/	# Large-n Critical Behavior of O(n)xO(m) Spin Models Pelissetto, Andrea and Rossi, Paolo and Vicari, Ettore (2001) Large-n Critical Behavior of O(n)xO(m) Spin Models. Nuclear Physics B, 607 . p. 605. ISSN 1873-1562 Full text not available from this repository. ## Abstract We consider the Landau-Ginzburg-Wilson Hamiltonian with O(n)x O(m) symmetry and compute the critical exponents at all fixed points to O(n^{-2}) and to O(\epsilon^3) in a \epsilon=4-d expansion. We also consider the corresponding non-linear sigma model and determine the fixed points and the critical exponents to O(\tilde{\epsilon}^2) in the \tilde{\epsilon}=d-2 expansion. Using these results, we draw quite general conclusions on the fixed-point structure of models with O(n)xO(m) symmetry for n large and all 2 < d < 4. Item Type: Article Imported from arXiv Area02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici Dipartimenti (until 2012) > DIPARTIMENTO DI FISICA " E. FERMI" dott.ssa Sandra Faita 09 Apr 2015 16:00 09 Apr 2015 16:00 http://eprints.adm.unipi.it/id/eprint/1839 ### Repository staff only actions View Item	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9377576112747192, "perplexity": 9897.931265324409}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540518337.65/warc/CC-MAIN-20191209065626-20191209093626-00043.warc.gz"}
http://html.rhhz.net/ieee-jas/html/2018-3-670.htm	IEEE/CAA Journal of Automatica Sinica 2018, Vol. 5 Issue(3): 670-682 PDF A Mode-Switching Motion Control System for Reactive Interaction and Surface Following Using Industrial Robots Danial Nakhaeinia, Pierre Payeur, Robert Laganière School of Electrical Engineering and Computer Science, University of Ottawa, Ontario K1N6N5, Canada Abstract: This work proposes a sensor-based control system for fully automated object detection and exploration (surface following) with a redundant industrial robot. The control system utilizes both offline and online trajectory planning for reactive interaction with objects of different shapes and color using RGBD vision and proximity/contact sensors feedback where no prior knowledge of the objects is available. The RGB-D sensor is used to collect raw 3D information of the environment. The data is then processed to segment an object of interest in the scene. In order to completely explore the object, a coverage path planning technique is proposed using a dynamic 3D occupancy grid method to generate a primary (offline) trajectory. However, RGB-D sensors are very sensitive to lighting and provide only limited accuracy on the depth measurements. Therefore, the coverage path planning is then further assisted by a real-time adaptive path planning using a fuzzy self-tuning proportional integral derivative (PID) controller. The latter allows the robot to dynamically update the 3D model by a specially designed instrumented compliant wrist and adapt to the surfaces it approaches or touches. A modeswitching scheme is also proposed to efficiently integrate and smoothly switch between the interaction modes under certain conditions. Experimental results using a CRS-F3 manipulator equipped with a custom-built compliant wrist demonstrate the feasibility and performance of the proposed method. Key words: Adaptive control fuzzy-PID controller manipulator control motion planning surface following Ⅰ. INTRODUCTION Sensor-based control in robotics can contribute to the ever growing industrial demand to improve speed and precision, especially in an uncalibrated working environment. But beside the kinematic capabilities of common industrial robots, the sensing abilities are still underdeveloped. Force sensors are mainly used in the context of the classical constrained hybrid force/position control [1]-[3] where force control is added for tasks that involve dealing with contact on surfaces. Tactile sensors determine different physical properties of objects and allow the assessment of object properties such as deformation, shape, surface normal, curvature measurement, and slip detection through their contact with the world [4], [5]. However, these sensors are only applicable where prior knowledge of the environment is available and there is a physical interaction between the robot and objects. In addition, the execution speed of the task is limited due to the limited bandwidth of the sensors, and to prevent loss of contact and information some planned trajectories must be prescribed [6]. Using vision sensors in order to control a robot is commonly called visual servoing where visual features such as points, lines and regions are used in various object manipulation tasks such as alignment of a robot manipulator with an object [7]. In contrast to force/tactile control, vision-based control systems require no contact with the object, allow non-contact measurement of the environment and do not need geometric models. The vision measurement is usually combined with force/tactile measurement as hybrid visual/force control [8], [9] for further manipulation. 3D profiling cameras, scanners, sonars or combinations of them have been used for manipulation of objects, which often result in lengthy acquisition and slow processing of massive amounts of information [10]. An alternative to obtain 3D data is replacing the high-cost sensors by an affordable Kinect sensor [11], [12]. The Kinect technology is used to rapidly acquire RGB-D data over the surface of objects. Beyond selecting proper sensors, reliable interaction control strategy and reactive planning algorithms are required to direct the robot motion under consideration of the kinematic constraints and environment uncertainties [13]. Although conventional proportional derivative/proportional integral derivative (PD/PID) controllers are the most applicable controller for robot manipulators, they are not suitable for nonlinear systems and lack robustness to disturbances and uncertainties. A general solution to this problem is to design and develop adaptive controllers where adaptive laws are devised based on the kinematics and dynamic models of the robot systems [14]. Furthermore, to achieve a better performance and smoothly switch between different motion modes, switched control systems were proposed [15] to dictate switching law and determine which motion mode(s) should be active. Aiming at bringing dexterous manipulation at a higher level of performance, dexterity and operational capabilities, this work proposes a unique mode-switching motion control system. It details the development of a dexterous manipulation framework and algorithms using a specially designed compliant wrist for complete exploration and live surface following of objects with arbitrary surface shapes endowed with adaptive motion planning and control approach coupled with vision, proximity and contact sensing. In order to enable industrial robots to interact with the environment smoothly and flexibly, adaptable compliance should be incorporated to industrial robots. A review of the traditional and recent robotics technologies shows that in many cases the modifications are technically challenging, not feasible and require hardware modifications, retrofitting, and new components which result in high costs. In this work, the flexibility problem is addressed by using a low cost specially designed compliant wrist mounted on the robot end-effector to increase the robot mechanical compliance and reduce the risk of damages. In contrast to other works, the adaptive controllers solve the force control problem in form of a position control problem where infrared sensors provide the required information for the interaction instead of touch sensors (force/torque, tactile and haptic). The proposed adaptive controllers require no learning procedure, no precise mathematical model of the robot and the environment and do not rely on force/torque calculation. As such the controllers enable the robot to interact with objects with and without contact. The paper is organized as follows: Section Ⅱ gives an overview of the control system design. Section Ⅲ presents the offline trajectory planning, and Section Ⅳ details the design of the online proximity and contact path planning. Section Ⅴ describes the proposed switching scheme. Experimental results are presented in Section Ⅵ, and a final discussion concludes the paper in Section Ⅶ. Ⅱ. MODE-SWITCHING MOTION CONTROL SYSTEM OVERVIEW The robotic interaction with objects or surface following problem consists of a complete exploration and alignment of a robot's end-effector with a surface while accommodating its location and curvature. This work proposes a switched control approach for fast and accurate interaction with objects of different shapes and colors. In order to guide the robot's end-effector towards the surface, and then control its motion to execute the desired interaction with the surface, the problem is divided into 3 stages of free, proximity and contact motion. Each of the three control modes uses a specific sensory information to guide the robot in different regions of the workspace. The main components and interconnections, as well as how they interact with each other are shown in Fig. 1. Download: larger image Fig. 1 Block diagram of the proposed mode switching control system The first step to achieve interaction with an object is the detection and localization of that object in the robot workspace. For that matter, a Kinect sensor is used for rapidly acquiring color and 3D data of the environment and to generate a primary (offline) trajectory as a general guidance for navigation and interaction with the object (free motion mode). The proximity control and contact control modes are also designed and integrated to the system. They dynamically update the 3D model through using a specially designed instrumented compliant wrist and modify the position and orientation of the robot based on the online sensory information when it is in close proximity (proximity interaction) and in contact with the object (contact interaction). The following sections detail the design and implementation of the system and its main components. Ⅲ. OFFLINE (FREE MOTION) TRAJECTORY PLANNING In the free motion phase, which refers to the robot movement in an unconstrained workspace, a 3D model of the object of interest is constructed using 3D data collected by a Kinect sensor. For that matter, the Kinect sensor is positioned behind the robot with its viewing axis pointing towards the surface of the object for collecting data over the object as shown in Fig. 2. Based on the surface shape acquired by this peripheral vision stage, a unique coverage path planning (CPP) strategy is developed using a dynamic 3D occupancy grid to plan a global trajectory and support the early robotic exploration stage of the object's surface. Download: larger image Fig. 2 The RGB-D sensor positioning A. Object Detection and Segmentation In order to efficiently navigate a robotic manipulator and interact with objects of various shapes, identification and localization of the object of interest in the robot workspace must first be achieved. For that matter, a Kinect sensor is used to acquire RGB images of the workspace along with depth information. When multiple objects are present in the working environment, objects of interest must be identified and discriminated from the scene. Three filters are used to extract and segment an object of interest from the workspace: a depth filter, a color filter and a distance filter. The data acquired by the Kinect sensor contains an RGB image and a collection of vertices ($PointCloud$ ). Each point, $p_i$ , with ($x, y, z$ ) coordinates is defined with respect to the Kinect ($K$ ) reference frame and supports corresponding ($r, g, b$ ) color values, defined as follows: $\begin{eqnarray} PointCloud=P^K=\bigcup\limits_{i=0}^{\nu-1}p_i \\ \end{eqnarray}$ $p_i=[p_{ix}, p_{iy}, p_{iz}, p_{ir}, p_{ig}, p_{ib}]$ (1) where $v$ is the number of vertices in the point cloud. The depth of field covered by the Kinect sensor is typically between 0.5 m to 6 m and the error in depth considerably rises with the distance [16]. Therefore, the noisy background is discarded and the maximum depth range is limited to that of the robot workspace. To filter out the vertices that are not in the desired depth range (Dz), a thresholding filter is applied (see Algorithm 1) which eliminates all the vertices with a depth value (Z-coordinate) over a pre-set desired range (Fig. 3). Algorithm 1: Object of Interest Segmentation 1: Inputs: $PointCloud= [p_0, p_1, \ldots, p_{v-1}], ~ObjRGB = [\alpha_k, \beta_k, \gamma_k], ~ObjCoordinate = [X_k, Y_k, Z_k], k\in[0, \mu-1]$ 2: Output: $ObjCloud^{\rm Robot}$ 3: Parameters: $\nu, \mu, \mathit{￡}_\max, \lambda$ 4: for $(k=0, \ldots, \mu-1)$ 5: for $(i=0, \ldots, \nu-1)$ 6: $\Delta Z_k$ =$Dz-p_{iz}$ 7: $\Delta E_i$ =$\sqrt{(\alpha_k-p_{ir})^2+(\beta_k-p_{ig})^2+(\gamma_k-p_{ib})^2}$ 8: $\mathit{￡}_k$ =$\sqrt{(X_k-p_{ix})^2+(Y_k-p_{iy})^2+(Z_k-p_{iz})^2}$ 9: if $(\Delta Z_k\geq 0\;\&\;\Delta E_i \leq \lambda\;\&\;\mathit{￡}_k \leq \mathit{￡}_{\rm max})$ then 10: $O^K [i]= p_i$ 11: end if 12: end for 13: end for 14: $O^R=T_K^R\cdot O^K$ 15: return $ObjCloud^{\rm Robot}=O^R$ Download: larger image Fig. 3 Depth filter: (a) original data from Kinect, (b) after applying the depth filter In order to optimize the robot movement, the desired object information should be extracted from the RGB-D data using color and distance segmentation. After acquiring the data, the RGB image (Fig. 4(a)) is presented to the operator. A mouse event callback function waits for the operator to click on any points of the desired object and returns the RGB-D values of the corresponding pixels. The RGB values of the points selected over the desired object (Fig. 4(b)) are used as a filter for the color segmentation. To increase the accuracy of the color segmentation, the operator can choose a number of points ($\mu$ ) over the object surface according to the object's size and shape. The RGB values of the operator selected points of interest (2) are used to define a range of color for the object of interest. The vertices in the RGB image that are within the same color range and for which the Euclidean color distance ($\Delta E$ ) is less than a specific pre-set threshold ($\lambda$ ) are extracted from the point cloud, while the other vertices are eliminated. $ObjectRGB = [\alpha_k, \beta_k, \gamma_k], \;\; k\in[0, \mu-1]$ (2) $ObjectCoordinate = [X_k, Y_k, Z_k], \;\; k\in[0, \mu-1].$ (3) Download: larger image Fig. 4 (a) RGB image of the working environment, and (b) RGB values related to the selected points over the object of interest (the white square board) The color segmentation allows to group parts of similar color. However, if there are multiple objects of similar color in the scene, a single object of interest cannot be identified only using color segmentation. Therefore, a distance filter is also applied on the point cloud to extract only the object of interest. Since each pixel in the RGB image corresponds to a particular point in the RGB-D point cloud, a primary estimate of the object of interest's position (3) in the workspace is extracted from the vertices corresponding to the points selected by the operator. By clicking on points respectively close to the corners and to the center of the object of interest, the maximum distance ($\mathit{￡}_\max$ ) between the center and the corners is calculated by (4). Then, the distance between each vertex in the point cloud and the center point ($\mathit{￡}$ ) selected by the user is compared with the maximum distance ($\mathit{￡}_\max$ ) and the vertices for which that distance is higher than $\mathit{￡}_\max$ are dropped. \begin{align} \mathit{￡}_\max&= {\rm max}\sqrt{(X_c-p_{kx})^2+(Y_c-p_{ky})^2+(Z_c-p_{kz})^2}\\ &~~~~~~~~~~~~~~~~~~~k=0, \ldots, \mu-1 \end{align} (4) where $[X_c, Y_c, Z_c]$ are the coordinates of the object center and $\mu$ is the number of selected points by the operator. This filter ensures that objects sharing similar color will be segmented individually, unless they overlap in space. Eventually, the remaining set of $m$ vertices ($O_i$ ) forms the object of interest RGB-D point cloud (5). However, the vertices are defined with respect to the Kinect reference frame and must be transformed to the robot's ($R$ ) base frame (6) $\begin{eqnarray} ObjCloud^{\rm Kinect}=O^{K}=\bigcup\limits_{i=0}^{m-1}O_i \end{eqnarray}$ (5) where $O_i=[o_{ix}, o_{iy}, o_{iz}, o_{ir}, o_{ig}, o_{ib}]$ , and $\begin{eqnarray} ObjCloud^{\rm Robot}=O^R=T_K^R\cdot O^R \end{eqnarray}$ (6) where $T_K^R$ is the homogeneous transformation matrix of the Kinect frame with respect to the robot base frame. The transformation matrix is estimated using the method proposed in [17]. B. Coverage Path Planning The key task of coverage path planning (CPP) is to guide the robot over the object surface and guarantee a complete coverage using the preprocessed RGB-D data. The proposed CPP is developed using the dynamic 3D occupancy grid method. The occupancy grid is constant when the environment (object) is static. In most of the previously proposed methods, the occupancy grid is built in an offline phase and it is not updated during operation, which requires very accurate localization. However, in the proposed method the occupancy grid is initially formed using the information provided by the Kinect sensor and it is dynamically refined during interaction using the data acquired by proximity sensors embedded in the compliant wrist mounted on the robot. 1) Occupancy Grid As shown in Fig. 5(a), once the object of interest is identified and modeled in 3D, the object surface is discretized to a set of uniform cubic cells (7). The resolution of the occupancy grid is adapted according to the volume of the object of interest: $(Z_\max-Z_\min){\rm mm}\times(X_\max-X_\min){\rm mm}\times(Y_\max-Y_\min){\rm mm}$ Download: larger image Fig. 5 (a) Object of interest 3D model, and (b) object discretized to a set of uniform cubic cells where $Y_\min$ , $Y_\max$ , $X_\min$ , $X_\max$ , $Z_\min$ and $Z_\max$ correspond respectively to the minimum and maximum values of the $Y, X$ and $Z$ coordinates in the point cloud of the object of interest. Size of the cells can be selected based on the end-effector size or the desired resolution of the grid for a particular application. Therefore, initially the object of interest is mapped into an occupancy grid with cube cells of the same size as the robot's tool plate size, in the present case 130 mm $\times$ 130 mm $\times$ 130 mm. The major issue arises when cells are partially occupied. That usually happens where the object has acute edges and also near the borders of the object of interest. $\begin{eqnarray} Obj=\bigcup\limits_{I=0}^{H-1}\bigcup\limits_{J=0}^{V-1}\bigcup\limits_{K=0}^{P-1}C_{I, J, K} \end{eqnarray}$ (7) where $C_{I, J, K}$ represents a cell in the object model and $\begin{eqnarray} P= \|\|(X_\max - X_\min)/130\|\|\\ H= \|\|(Y_\max - Y_\min)/130\|\|\\ V= \|\|(Z_\max - Z_\min)/130\|\|. \end{eqnarray}$ (8) In order to solve the problem, the grid resolution is increased and two different cells (larger and smaller) sizes are used (Fig. 5(b)). The smaller cells ($C^s$ ) are cubes with size of 65 mm $\times$ 65 mm $\times$ 65 mm with each larger cell ($C^B$ ) containing 8 smaller cells in two layers of four (Fig. 6(a)). Another problem with 3D occupancy grids is that they require large memory space, especially when fine resolution is required [18]. Considering that the RGB-D sensor is perceiving the scene from a point of view that is perpendicular to the surface of the object, the regions in the back are essentially occluded. Therefore, to achieve computational efficiency and decrease complexity and the number of cells, the front and back layers of the larger cells are merged into one layer and the smaller cells are replaced with cuboid cells of size 65 mm $\times$ 65 mm $\times$ 130 mm (Fig. 6(b)), leading to a 2.5D occupancy grid model. The occupancy grid is formed by determining the state of each cell. The smaller cells ($C_{i, j, k}^s$ ) are classified with two states as occupied or free. A cell is called occupied if there exist at least some vertices in the cell. If the smaller cell is occupied, the cell value is 1, otherwise it is 0. The state variables associated with the larger cells ($C_{I, J, K}^B$ ) are: occupied, unknown and free which are identified based on the smaller cell's value. If more than two smaller cells of a larger cell are occupied, the value of the associated larger cell is 1, else if one or two of the small cells are occupied the value is 0.5, and if all the small cells are free then it is 0 (9). The occupancy grid corresponding to the larger cells is represented by a $H \times V \times P$ matrix (10). Initially all cells are considered as unknown. Therefore, the occupancy matrix, $OccMatrix$ is initialized with a value equal to 0.5 where $C_{I, J, K}^B$ contains occupancy information associated with the larger cell ($I, J, K$ ) and cell (0, 0, 0) is located in the upper left corner of the grid. $\begin{eqnarray} &C_{i, j, k}^s=S (0={\rm free}; 1={\rm occupied})~~~~~~~~~\\ &C_{I, J, K}^B=S (0={\rm free}; 0.5={\rm unknown}; 1={\rm occupied}) \end{eqnarray}$ (9) $\begin{eqnarray} &OccMatrix \\[2mm] &=\!\!\left[\!\!\!\begin{array}{cccccccc}C_{0, 0, 0}^B &\!\! C_{0, 1, 0}^B &\!\! \ldots &\!\! C_{0, V-1, 0}^B &\!\! C_{0, V, 0}^B\\[3mm] C_{1, 0, 0}^B &\!\! C_{1, 1, 0}^B&\!\!\ldots &\!\!C_{1, V-1, 0}^B&\!\!C_{1, V, 0}^B\\ \vdots &\!\! \vdots &\!\! \ddots &\!\! \vdots &\!\!\vdots\\ C_{H-1, 0, 0}^B&\!\!C_{H-1, 1, 0}^B&\!\!\ldots&\!\!C_{H-1, V-1, 0}^B&\!\!C_{H-1, V, 0}^B\\[3mm] C_{H, 0, 0}^B&\!\!C_{H, 1, 0}^B&\!\!\ldots&\!\!C_{H, V-1, 0}^B &\!\! C_{H, V, 0}^B \end{array}\!\!\!\right]\!\!\!. \end{eqnarray}$ (10) Download: larger image Fig. 6 (a) Smaller cell and larger cell representation, and (b) merging smaller cell to reduce data volume The occupancy matrix provides the required information to plan an offline trajectory to explore the object surface. Therefore, in the next step the occupancy matrix is used for global path planning. In addition, to preserve the dynamic characteristic of the occupancy grid and achieve a more accurate and efficient exploration, the occupancy grid will be updated using extra sensory information when the robot is in close proximity of the object. 2) Global Trajectory Generation In order to explore the object completely and optimize the trajectory, the robot should explore all the occupied cells and avoid the free ones. The robot's end-effector pose at each time step is defined by a set of points: $\begin{eqnarray} P_G [k]=(pos_G [k], R_G^{\it \Phi} [k], dir_G [k]) \end{eqnarray}$ (11) where $pos_G=[p_G^x, p_G^y, p_G^z], R_G^{\it \Phi}=[r_k^{\theta}, r_k^{\varphi}, r_k^{\psi}]$ and $dir_G$ determine the robot position, orientation and direction of motion respectively. The concatenation over iterations, $k$ , of the set of points generates a global trajectory for the robot. $Trajectory_{\rm Global} \\ =P_G [0]\frown P_G [1] \frown P_G [2] \frown \cdots \frown P_G [occ]$ (12) where $occ$ is the number of occupied cells in the occupancy grid. In this work, the start point is always the first occupied cell on the front upper row of the occupancy grid and the initial moving direction is horizontal. The robot position at each moving step ($pos_G [k]$ ) is defined by extracting the closest point in the object point cloud ($ObjCloud^{\rm Robot}$ ) to the center of the occupied larger cell ($centre(C_{I, J, K}^B)$ ) in the robot moving direction. However, if the larger cell is not completely occupied ($C_{I, J, K}^B=0.5$ ) the $pos_G (k)$ is determined based on the new measurements from the proximity sensors (detailed in Section IV-B). As shown in Fig. 7(a), the robot can move in 5 directions [horizontally (left/right), vertically down, and diagonally (left/right) down] and it must move through all the points to cover the target area. The target area is covered using a zigzag (Fig. 7(b)) pattern which is also called Seed Spreader motion [19]. The robot begins from a start point and moves horizontally to the right towards the center of the next occupied cell. If there is no occupied cell on the right, the motion direction is changed and the robot moves vertically (diagonally) down to the next point. Then, the robot again moves horizontally but in the opposite direction until it reaches the last occupied cell on the other side of the object. The process continues until the robot has explored the entire area. Download: larger image Fig. 7 (a) Accessible directions of motion, (b) global trajectory planning to ensure coverage, and (c) vertex normal calculation at the center of a larger cell The set of points forming a path for the robot defined in the previous step determines the positions for the end-effector in Cartesian coordinates over the object surface. In addition to the robot position, to ensure proper alignment of the end-effector with the surface, it is required to estimate the surface normal and calculate the end-effector orientation at each point. The local normal at each point is calculated using the neighbor cells (Fig. 7(c)). Given that there are four smaller cells forming a larger cell, five points situated in the center of each cell in three dimensions are obtained. Each set of the three points forms a triangle for a total of four triangles that can be generated. First, the normal to each triangle ($N_i$ ) is calculated and normalized. The normal of each triangle is computed as the cross product between the vectors representing two sides of the triangle. The following equations define the normal vector, $N$ , calculated from a set of three vertices, $E$ , $F$ , $G$ , point coordinates: $\begin{eqnarray} N_x=(E_y-G_y\cdot E_z-F_z)-(E_z-G_z\cdot E_y-F_y) \end{eqnarray}$ (13) $\begin{eqnarray} N_y=(E_z-G_z\cdot E_x-F_x)-(E_x-G_x\cdot E_z-F_z) \end{eqnarray}$ (14) $\begin{eqnarray} N_z=(E_x-G_x\cdot E_y-F_y)-(E_y-G_y\cdot E_x-F_x). \end{eqnarray}$ (15) The resulting normals are then normalized such that the length of the edges does not come into account. The normalized vector $N_{\rm norm}$ is computed as: $\begin{eqnarray} norm= \sqrt{N_x^2+N_y^2+N_z^2} \end{eqnarray}$ (16) $\begin{eqnarray} N_{\rm norm}=[N_{nx}~~~N_{ny}~~~N_{nz}] \end{eqnarray}$ (17) where $N_{nx}\!=\!N_{x}/norm, N_{ny}\!=\!N_{y}/norm, N_{nz}\!=\!N_{z}/norm$ . Then, taking the average of the four triangle normals provides the estimated object's surface normal at the center of the larger occupied cell and the object's surface orientation is deduced from the normal vector to the surface (Fig. 7(c)). Ⅳ. ONLINE (PROXIMITY/CONTACT) PATH PLANNING The acquisition speed of the Kinect and its low cost have been major selection criteria for this sensor to be used for 3D modelling. However, the information from a Kinect sensor is not sufficient and accurate enough for developing a full reactive surface following approach which also requires close and physical interaction with an object [20]. Furthermore, the object may move or deform under the influence of the physical interaction. Therefore, to compensate for errors in the rough 2.5D profile of the surface provided by the RGB-D sensor and to further refine the path planning, a model-free adaptive fuzzy self-tuning PID position controller and an orientation controller are developed using real-time proximity and contact sensory information provided by a custom designed compliant wrist [21] attached to the end-effector of the robot, as shown in Fig. 8(a). The compliant wrist provides a means of detecting objects both in contact and proximity to the end-effector, as well as adding a degree of compliance to the end-effector which enables the latter to slide on the object without damaging it and to adapt to its surface changes when contact happens. As shown in Fig. 8(b), the compliant wrist is equipped with eight infrared distance measurement sensors. The infrared sensors are arranged in two arrays of four sensors each: an external array and an internal array. The external sensor array allows to measure distances at multiple points between the wrist and the object located in front of the end-effector. The internal sensor array is situated between the base of the compliant wrist structure and a moveable plate, as shown in Fig. 8(a), which allows the device to determine surface orientation and distance to an object when the robot is contacting with it. The sensing layers estimate an object pose in the form of a 3D homogeneous transformation matrix. The rotation and translation parameters are obtained using the distance measurements from either array of four infrared (IR) sensors. Equation (18) shows how the transformation matrix is calculated using distances provided by the internal sensors (contact sensing layer). A similar calculation can be made from the external sensors using values $A'$ , $B'$ , $C'$ and $D'$ measured by external sensors (Fig. 8(c)). The transformation matrix determines the object pose with respect to the compliant wrist frame, which is transferred to the robot's base frame (19). Download: larger image Fig. 8 (a) Compliant wrist, (b) internal and external sensors arrangement, and (c) distance measurements from internal and external sensors $\begin{eqnarray} &\!\!\!\!\!\!\!\!\!\!\!\!\!Q_{\rm endeff/object}~~~~\\ &\!\!\!\!\!=\!\! \left[\!\!\begin{array}{cccccccc} {\rm cos} \alpha &\!\! 0 &\!\! {\rm sin} \alpha &\!\! 0\\ {\rm sin} \beta {\rm sin} \alpha &\!\! {\rm cos} \beta &\!\! {\rm -sin} \beta {\rm cos} \alpha &\!\! 0\\ {\rm-cos} \beta {\rm sin} \alpha &\!\! {\rm sin} \beta &\!\! {\rm cos} \beta {\rm cos} \alpha &\!\! \dfrac{A\!\!+\!\!B\!\!+\!\!C\!\!+\!\!D}{4}\\ 0&\!\!0&\!\!0&\!\!1 \end{array}\!\!\right] \end{eqnarray}$ (18) where $\beta={\rm atan}2((D-B)/W)$ , $\alpha={\rm atan}2((A-C)/W)$ $\begin{eqnarray} Q_{\rm base/object}=Q_{\rm base/wrist}\cdot Q_{\rm endeff/object}. \end{eqnarray}$ (19) A. Adaptive Position/Orientation Control The surface following and tracking of the objects can be accomplished either with contact (for applications such as polishing, welding, or cleaning) or without contact (for applications like painting and inspection). In order to guide the robot under consideration of kinematic motion constraints, an adaptive on-line trajectory generation is proposed to generate continuous command variables and modify the position and orientation of the robot based on the online sensory information when the robot end-effector is in close proximity of (proximity control mode) or in contact with (contact control mode) an object. The robot position over the object's surface is controlled using a fuzzy self-tuning PID controller and its orientation is corrected whenever there is an error between the surface orientation estimated via proximity/contact sensors and the end-effector's orientation to make the system adaptive to the working environment (Fig. 9). Download: larger image Fig. 9 Block diagram of the real-time position and orientation controller 1) Adaptive Position Control The typical PID controller has been widely used in industry because of its simplicity and performance to reduce the error and enhance the system response. To design a PID controller it is required to select the PID gains $K_P$ , $K_I$ , and $K_D$ properly (20). However, the PID controller with fixed parameters is inefficient to control systems with uncertain models and parameter variations. $\begin{eqnarray} U_k=K_P\cdot E_k+K_I \sum\limits_{i=0}^k E_k +K_D (E_k-E_{k-1}) \end{eqnarray}$ (20) where $E_k$ is defined in (21). Fuzzy control is ideal to deal with nonlinear systems where there is a wide range of operating conditions, an inexact model exists and accurate information is not required. It has a better performance in dealing with uncertainty and change in environment than a PID controller but PID has a faster response and it minimizes the error better than fuzzy control. Therefore, to take advantage of both controllers, a fuzzy self-tuning PID controller is designed to control the robot's movement and to smoothly follow an object's surface from a specific distance or alternatively while maintaining contact. The fuzzy self-tuning PID controller's output is a real-time adjustment value (Æ) of the position based on the error ($E$ ) between the current robot distance from the object ($D$ ) and the desired distance to the object $d\breve{z}$ (this value is zero when contact with the object is required). $D$ is obtained by proximity sensors or by contact sensors on the compliant wrist when the robot is in close proximity of or in contact with the object respectively. The PID gains are tuned using the fuzzy system rather than the traditional approaches. The Æ is then sent to the robot controller to eliminate the error and make the system adaptive to the changes in the working environment. The fuzzy controller input variables are the distance error ($E_k$ ) and change of error ($\Delta E_k$ ), and the outputs are the PID controller parameters. The standard triangular membership functions and Mamdani type inference are adopted for the fuzzification due to their less computation, which enhances speed of the system reaction $\begin{eqnarray} E_k = D_{k}-d\breve{z}, \;\;\;\;\;\; \Delta E_k = E_k - E_{k-1}. \end{eqnarray}$ (21) The error ($E_k$ ) in distance is represented by five linguistic terms: large negative (LN), small negative (SN), zero (Z), small positive (SP), and large positive (LP). Similarly, the fuzzy set of change of error ($\Delta E$ ) is expressed by negative big (NB), negative (N), zero (Z), positive (P), and positive big (PB), both defined over the interval from -50 mm to 50 mm. When the robot is in close proximity of the object, it can move backward, forward or not change depending on the robot distance to the surface. The output linguistic terms for each PID gain $k_p'$ , $k_i'$ and $k_d'$ are (Fig. (10)): large forward (LF), forward (F), no change (NC), backward (B), large backward (LB) over the interval [-1, 1]. Tables Ⅰ- define the fuzzy rules for the $k_p'$ , $k_i'$ and $k_d'$ gains. The center of gravity (COG) method is used to defuzzify the output variable (22). $\begin{eqnarray} COG= \dfrac{\sum\limits_{i=1}^m \mu(f_i)\cdot f_i}{\sum\limits_{i=1}^m \mu(f_i)}. \end{eqnarray}$ (22) Download: larger image Fig. 10 Fuzzy membership functions for: (a) error, (b) change of error, and (c) PID gains estimates $k'_p$ , $k'_i$ and $k'_d$ Table Ⅰ FUZZY RULE BASE OF k'p Table Ⅱ FUZZY RULE BASE OF k'i Table Ⅲ FUZZY RULE BASE OF k'd In order to obtain feasible and optimum value for the PID parameters, the actual gains are computed using the range of each parameter determined experimentally (23) from the outputs of the fuzzy inference system. $\begin{eqnarray} &k_p'=\dfrac{K_P-K_{P_\min}}{K_{P_\max}-K_{P_\min}}= \dfrac{K_P}{K_{P_\max}-K_{P_\min}}\\ &K_p=k_p'\\ &k_i'=\dfrac{K_I-K_{I_\min}}{K_{I_\max}-K_{I_\min}}=\dfrac{K_I-0.01}{0.1-0.01}\\ &K_I=0.99k_i'+0.01\\ &k_d'=\dfrac{K_D-K_{D_\min}}{K_{D_\max}-K_{D_\min}}= \dfrac{K_D-0.003}{0.01-0.003}\\ &K_D=0.007k_d'+0.003 \end{eqnarray}$ (23) where $K_P\in[0, 1], K_I\in[0.01, 0.1], K_D\in[0.003, 0.01]$ . 2) Adaptive Orientation Control When the robot is in close proximity of (or in contact with) the object, the orientation of the object surface is estimated by proximity/contact sensors in terms of the pitch ($r_S^{\varphi}$ ) and yaw($r_S^{\psi}$ ) with respect to the wrist plane. Let the rotation matrix of the surface generic orientation, $r_S^{\phi}$ , be denoted with $R_S^{\phi}$ with respect to the wrist plane, and the rotation of the end-effector obtained from the initial global trajectory, be described by $R_G^{\phi}$ , the desired rotation of the end-effector, $R_R^{\phi}$ to align the end-effector with the surface can be determined by (24) $\begin{eqnarray} R_R^{\phi} [K]=R_G^{\phi} [K]R_S^{\phi} [K] \end{eqnarray}$ (24) where $r_G^{\phi}=[r_G^{\theta}, r_G^{\varphi}, r_G^{\psi}], r_S^{\phi}=[0, r_S^{\varphi}, r_S^{\psi}], r_R^{\phi}=[r_r^{\theta}, r_r^{\varphi}, r_r^{\psi}].$ In a surface following task, the $R_S^{\phi}$ is the orientation to be tracked by the robot. However, in order to obtain a smooth orientation, it is not directly sent to the controller. Instead, the orientation of the end-effector is updated using an adaptive orientation signal ($R_A^{\phi}$ ) at each moving step to compensate for the orientation error between the end-effector and the surface. The error decreases exponentially to eliminate the orientation error (adjust $r_S^{\phi}$ to zero) rapidly. $\begin{eqnarray} R_R^{\phi} [k]=R_G^{\phi} [k]R_A^{\phi} [k] \end{eqnarray}$ (25) $\begin{eqnarray} R_A^{\phi} [k]=\eta *R_S^{\phi} [k]~~~~~~ \end{eqnarray}$ (26) where $\eta$ is a proportional gain to decrease the error and minimize the convergence time. A large gain value reduces the convergence time but may lead to tracking loss or task failure due to fast motion, while a small gain value increases the convergence time. Therefore, in order to increase the convergence time, reduce oscillation near equilibrium point and preserve the system stability, the gain value is varied according to the orientation error value (27). The gain value is small initially ($\eta_0$ ) while the error is larger, and the error is reduced exponentially until it reaches a specific threshold ($\partial$ ) near the equilibrium point ($r_S^{\phi}$ = 0). Then, as the orientation error got smaller, the gain switches to a larger gain value ($\eta_0 < \eta_1$ ) to eliminate the remaining orientation error as fast as possible [22]. By using the adaptive orientation signal, the robot end-effector orientation angles are calculated by (28). $\begin{eqnarray} \eta=\left\{\begin{array}{llllll} \eta_0=\dfrac{r_S^{\phi}}{\|\|r_S^{\phi} \|\|},&\|\|r_S^{\phi}\|\|\geq \partial\\[7mm] \eta_1=\dfrac{1}{\partial} r_S^{\phi},&\|\|r_S^{\phi}\|\| < {\partial} \end{array}\right. \end{eqnarray}$ (27) $\begin{eqnarray} r_R^{\phi} [k]=\left\{\begin{array}{llllll} r_R^{\theta} (k)=r_G^{\theta}(k)\\ r_R^{\varphi} (k)=r_G^{\varphi} (k)+r_A^{\varphi} (k)\\ r_R^{\psi} (k)=r_G^{\psi} (k)+r_A^{\psi} (k). \end{array}\right. \end{eqnarray}$ (28) B. Updating the Occupancy Grid The object of interest might not be acquired with sufficient accuracy by the Kinect sensor alone due to its limited depth resolution or not be segmented completely from the point cloud. In order to update the occupancy grid previously described, the compliant wrist provides closer and higher accuracy feedback about the object's location. As shown in Fig. 11, the compliant plate is able to cover four smaller cells (one largest cell), given the selected initial resolution of the occupancy grid. The external sensors, which are protruding on the four sides of the compliant plate, can provide real-time look-ahead information while the robot is moving. As the robot moves along the global trajectory to its new pose, the existing occupancy map is updated using the new measurements. For example when the robot is moving to the right, the sensor situated on the right side will allow an update of the state of the two cells located ahead on the right, especially when the next cell value is 0.5 (unknown cell). If the sensor detects the object, the cell value changes to 1 (occupied), else it will change to zero (empty). The robot keeps moving in the previous direction if the next cell is occupied, else it stops there and moves to the next pose along the global trajectory. Download: larger image Fig. 11 Cells coverage by the wrist embedded sensors Ⅴ. SWITCHING CONTROL SCHEME To achieve a seamless and efficient integration of vision and real-time sensory information and smoothly switch between different interaction modes, a mode switching scheme is also proposed as it provides the manipulator with the capability to operate independently in each of the 3 stages (free motion, proximity, and contact) or in transition in between stages to perform more complicated tasks as required by different applications. Since this work focuses on the task space control, a discrete-time switching system is proposed in order to switch smoothly between global trajectory following and sensor-based motion control. The proposed switched-control system consists of continuously working subsystems and a discrete system that supervise the switching between the subsystems [23]. The proposed switching control system is modeled as follows: $\begin{eqnarray} E_{(k+1)}=f_{{\delta}(e)} (E_{k}, D_k), \quad\quad \delta\in\{F, P, {\rm and}~ C\}. \end{eqnarray}$ (29) The value $\delta$ determines which function $f_{{\delta}(e)} (E_{k}, D_k)$ controls the system behavior at each moving step ($k$ ) and $f_F, f_P, f_C$ correspond to free motion, proximity and contact control modes respectively. The switching signal $\delta$ (30) is determined based on the distance error (values are in mm). The error values shown in (30) are estimated experimentally based on the extensive compliant wrist sensor's performance analysis detailed in [21]. For a compliant wrist equipped with different IR sensors, or other robot-mounted distance measurement devices, re-calibration of (30) would be necessary, but the general framework would remain valid as such: $\begin{eqnarray} \delta(e)=\left\{\begin{array}{llllll} C,&E_k < -20\\ P,&-20 \leq E_k \leq 40\\ F,&E_k > 40. \end{array}\right. \end{eqnarray}$ (30) In the free motion phase, which refers to the robot movement in an unconstrained workspace, the 3D model of the object is used to plan a global trajectory (detailed in Section Ⅲ) and guide the robot from an initial position towards the object where the robot pose is given by (31) $\begin{eqnarray} f_F=\left\{\begin{array}{llllll} pos_R [k]=pos_G [k]=[p_G^x, p_G^y, p_G^z]\\[2mm] r_R^{\phi} [k]= r_G^{\phi} [k]=[r_G^{\theta}, r_G^{\varphi}, r_G^{\psi}]. \end{array}\right. \end{eqnarray}$ (31) The proximity phase enables the robot to refine the reference (global) trajectory using the proximity sensing information to track the desired trajectory within a specific distance without contact or adjust the robot pose before contact happens (transition) to damp the system and align the robot with surface. It also enables the robot to update the cell of the occupancy grid while moving along the global trajectory. $\begin{eqnarray} f_P=\left\{\begin{array}{llllll} pos_R [k]=pos_G [k]+ {Æ}_P [k]\\[2mm] r_R^{\phi} [k]= r_G^{\varphi} [k]+r_{AP}^{\varphi} [k] \end{array}\right. \end{eqnarray}$ (32) where ÆP is position control signal generated by the self-tuning fuzzy PID controller and $r_{AP}^{\varphi}$ is adaptive orientation control signal obtained using proximity sensors. The contact with surface is triggered by the internal sensors where the contact plate is deflected under externally applied forces. The contact motion mode enables the robot to more precisely adapt to the changes and forces generated by the surfaces with which it comes into contact. When the contact is detected, the internal sensors provide the fuzzy inputs (error and change of error) instead of external sensors to make sure that the robot remains in contact with the object and prevent the robot from being pushed too much into the object. $\begin{eqnarray} f_c=\left\{\begin{array}{llllll} pos_R [k]=pos_G [k]+ {Æ}_C [k]\\[3mm] r_R^{\phi} [k]= r_G^{\varphi} [k]+r_{AC}^{\varphi} [k] \end{array}\right. \end{eqnarray}$ (33) where ${Æ}_{PC}$ and $r_{AC}^{\varphi}$ are adaptive position and orientation signals obtained from contact sensory information. Ⅵ. EXPERIMENTAL RESULTS To validate the feasibility and assess the accuracy of the proposed method, experiments are carried out with a 7-DOF CRS F3 manipulator which consists of a 6-DOF robot arm mounted on a linear track. The algorithms used for this work were developed in C++ and run on a computer with an Intel core i7 CPU and Windows 7. A. Object Segmentation Table Ⅳ shows the efficiency of the proposed segmentation algorithm in extracting the object of interest from the scene shown in Fig. 3 where there are four objects of different shapes and colors. The original point cloud provided by the Kinect sensor after applying the depth filter includes 41 204 points from which over 99 % of those corresponding to the objects of interest have been successfully recovered from the point cloud. Table Ⅳ OBJECT SEGMENTATION RESULTS B. Contact Interaction In this experiment, it is desired to closely follow the surface of a real automotive door panel (Fig. 12) while maintaining contact and accommodating its curvature. As shown in Fig. 12(a), the Kinect sensor is located facing the door panel and the robot moves on a two-meter linear track to fully reach the surface. The Kinect collects raw 3D information on the environment. The RGB image captured by the Kinect (Fig. 12(b)) is presented to the operator. The operator selects the object of interest and its point cloud is automatically extracted from the scene, except for the window area since glass is not imaged well with Kinect sensor technology and also the window area is beyond the robot workspace. A global trajectory is then generated using the proposed coverage path planning method (Section Ⅲ-B) to completely explore and scan the object of interest's surface (Fig. 13(a)). Download: larger image Fig. 12 (a) Automotive door panel set up with respect to the robot and the Kinect sensor, and (b) front view of real automotive door panel Download: larger image Fig. 13 (a) Trajectory planning to ensure full coverage over the region of interest. (b) Global trajectory. (c) Fuzzy self-tuning PID controller performance. (d) Internal sensors dataset Fig. 13(a) shows the global (offline) trajectory generated using the proposed coverage path planning method, which consists of a set of 3D points (Fig. 13(b)). Once the global trajectory is generated, the free motion mode is initially activated to guide the robot towards the start point. When the robot is in close proximity of the object, the proximity (external) sensors detect the object, the motion control mode is switched to the proximity mode, where the adaptive pose controllers adjust the robot position and orientation using the external sensors in preparation for a safe contact with the object. When the initial contact happens the control mode switches to contact mode, and the adaptive pose controllers generate the depth and orientation control signals to maintain contact with the object. The fuzzy inputs and the depth control signal are shown in Fig. 13(c). The position control signal (${Æ}$ ) is varying from -20 mm to 25 mm, which shows the smooth and stable motion of the robot over the object surface. The ${Æ}$ signal changes according to the error ($E$ ) and change of error ($\Delta E$ ). When the robot moves horizontally the change of the ${Æ}$ signal is small but when the robot moves vertically on the object surface, the $E$ and $\Delta E$ are changed more substantially (due to change of the door curvature). As a result, the ${Æ}$ signal is larger to compensate the error as desired (Fig. 13(c)). The internal sensors detect the contact when the compliant wrist is deflected. In order to make sure that the robot is perfectly in contact with the object and detects the contact by the internal sensors, the desired distance to the object is set to $d\breve{z}=-$ 3 mm. Therefore, the average distance obtained from sensors in each moving step ($k$ ) should be around -3 mm to eliminate the error ($E_k = D_k-d\breve{z}$ ). The average distance measurement of the internal sensors (Fig. 13(d)) from the object during the surface following process was about -3.42 mm, which shows that the robot maintained contact during the interaction (Fig. (14)). The robot orientation error is compensated using the adaptive orientation signal ($r_{AC}^{\varphi}$ ). The robot moves to the next pose defined by the global trajectory and the same process as above repeats for each moving step until the robot has explored the entire surface. Fig. 15 shows the system performance in refining the position and orientation of the robot during contact interaction. The depth adjustment over the object surface using the adaptive position controllers (depicted in red) is shown in Fig. 15(a), and compared with the depth measurements estimated from the RGB-D data (depicted in blue). The orientation correction is represented in Fig. 15(b), the global object surface orientation with respect to the robot base frame around the $y$ -axis (in blue) and $z$ -axis (in red) estimated as part of the offline path planning process are also updated locally using the online sensory information (in green and purple) from the compliant wrist. Download: larger image Fig. 14 Robot performance at following the door panel's curved surface Download: larger image Fig. 15 System performance in refining the robot pose in contact mode C. Proximity Interaction In this experiment, it is desired to scan and follow the object's surface (Fig. 12(b)) at a fixed distance from it. Fig. 16(a) shows the adaptive self-tuning fuzzy-PID performance in controlling the robot movement over the surface of the object while maintaining a desired distance (50 mm) from the object but still accommodating its curvature (Figs. 16(c) and (d)). In Fig. 16(c), the blue curve represents the pre-planned trajectory which is locally refined (orange curve) using the sensory information provided by the external sensors. The global trajectory is also refined locally in orientation (Fig. 16(d)). The average of the distance measurements (Fig. 16(b)) from the surface was 56.8 mm, which verifies that the robot remains within the desired distance from the object during the surface following. Download: larger image Fig. 16 The system performance in refining the robot pose in proximity interaction Ⅶ. CONCLUSION This work presented the design and implementation of a switching motion control system for automated and efficient proximity/contact interaction and surface following of objects of arbitrary shape. The proposed control architecture enables the robot to detect and follow the surface of an object of interest, with or without contact, using the information provided by a Kinect sensor and augmented locally using a specially designed instrumented compliant wrist. A tri-modal discrete switching control scheme is proposed to supervise the robot motion continuously and switch between different control modes and related controllers when it finds the robot within certain regions of the workspace relative to the object surface. The proposed method was implemented and validated through experimental results with a 7-DOF robotic manipulator. The experimental results demonstrated that the robot can successfully scan an entire region of an object of interest while closely following the curved surface of the object with or without contact. The adaptive controllers and the switching control scheme can be improved in future work. This includes designing new adaptive controllers that are less sensitive and have faster but smoother response to changes in the environment, and using a hybrid switched control system to allow actual data fusion from multiple sensing sources which would result in smoother switching between the interaction modes. ACKNOWLEDGMENTS The authors wish to acknowledge the contribution of Mr. Pascal Laferrière to this research through the development of the instrumented compliant wrist device. REFERENCES	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37623339891433716, "perplexity": 852.9034310889085}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247479101.30/warc/CC-MAIN-20190215183319-20190215205319-00038.warc.gz"}
https://www.math.bgu.ac.il/en/teaching/fall2021/courses/workshop-in-analysis	## Dr. Yair Hartman #### Time and Place: יום ג 10:00 - 08:00 בבניין כתות לימוד [35] חדר 115 ## Abstract The goal of the workshop is to examine and provide complimentary material for the course “Geometric Calculus 1” 201.1.1031 (as well as the course “Introduction to Analysis” 201.1.1051). The workshop is given in parallel with Geometric Calculus 1, and the workshop content follows the courses. Part of the main goals of the workshop, especially due to the Corona pandemic, is to improve the student’s teamwork skills. During the workshop, the students will work in small groups and will practice their “mathematical conversation” skills: how to think together, how to find the essence of an idea and how to present a mathematical idea to others. ## Course topics This course is meant to discuss problems and provide examples in the following topics. Close coordination with the parallel course Geometric Calculus 1 is recommended. 1. Topology of $\mathbb{R}^n$: open, closed, compact and connected sets. 2. Continuity and differentiability of functions from $\mathbb{R}^m$ to $\mathbb{R}^n$, including the basic geometric properties of directional derivatives and the gradient. Curves in $\mathbb{R}^n$. 3. Implicit and inverse function theorems 4. Taylor’s theorem for multivariable functions and the Hessian 5. Extrema for multivariable functions, with and without constraints 6. Fubini’s theorem and the change of variables formula	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7385097742080688, "perplexity": 1501.663597491322}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499819.32/warc/CC-MAIN-20230130133622-20230130163622-00467.warc.gz"}
https://opengeomechanics.centre-mersenne.org/item/OGEO_2019__1__A1_0/	Editorial Open Geomechanics, Volume 1 (2019) , article no. 1, 2 p. This Editorial is the first publication from the journal Open Geomechanics, a radically open-access scientific journal for Geomechanics Research, edited by Geomechanics researchers for Geomechanics researchers. We believe that the results of scientific research should be available to all. For this reason, this journal is committed to publishing high quality work within the remit of diamond open access — free to publish and read. Our aim is to become a recognised journal in the field of geomechanics, and a launchpad for new ideas for the dissemination of research in this field. Research manuscripts (in any geomechanics related topics such as analytical, numerical or experimental studies) or case studies, negative results, as well as replicability or reproducibility studies are welcome. Accepted: Published online: DOI: https://doi.org/10.5802/ogeo.0 @article{OGEO_2019__1__A1_0, author = {And\o, Edward and Dijkstra, Jelke and Frost, David and Herle, Ivo and Hurley, Ryan and Marks, Benjy and Muir Wood, David and Tamagnini, Claudio and Viggiani, Cino}, title = {Editorial}, journal = {Open Geomechanics}, eid = {1}, } Andò, Edward; Dijkstra, Jelke; Frost, David; Herle, Ivo; Hurley, Ryan; Marks, Benjy; Muir Wood, David; Tamagnini, Claudio; Viggiani, Cino. Editorial. Open Geomechanics, Volume 1 (2019) , article no. 1, 2 p. doi : 10.5802/ogeo.0. https://opengeomechanics.centre-mersenne.org/item/OGEO_2019__1__A1_0/`	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21202602982521057, "perplexity": 15550.30428409828}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038067400.24/warc/CC-MAIN-20210412113508-20210412143508-00392.warc.gz"}
https://hal.archives-ouvertes.fr/hal-01544861	# On the Komlós, Major and Tusnády strong approximation for some classes of random iterates Abstract : The famous results of Komlós, Major and Tusnády (see [15] and [17]) state that it is possible to approximate almost surely the partial sums of size n of i.i.d. centered random variables in L p (p > 2) by a Wiener process with an error term of order o(n 1/p). Very recently, Berkes, Liu and Wu [3] extended this famous result to partial sums associated with functions of an i.i.d. sequence, provided a condition on a functional dependence measure in L p is satisfied. In this paper, we adapt the method of Berkes, Liu and Wu to partial sums of functions of random iterates. Taking advantage of the Markovian setting, we shall give new dependent conditions, expressed in terms of a natural coupling (in L ∞ or in L 1), under which the strong approximation result holds with rate o(n 1/p). As we shall see our conditions are well adapted to a large variety of models, including left random walks on GL d (R), contracting iterated random functions, autoregressive Lipschitz processes, and some ergodic Markov chains. We also provide some examples showing that our L 1-coupling condition is in some sense optimal. Type de document : Pré-publication, Document de travail MAP5 2017-24. 2017 Domaine : Littérature citée [24 références] https://hal.archives-ouvertes.fr/hal-01544861 Contributeur : Jérôme Dedecker <> Soumis le : jeudi 22 juin 2017 - 11:18:14 Dernière modification le : jeudi 31 mai 2018 - 09:12:02 Document(s) archivé(s) le : samedi 16 décembre 2017 - 02:42:41 ### Fichiers KMT-submitted-revised.pdf Fichiers produits par l'(les) auteur(s) ### Identifiants • HAL Id : hal-01544861, version 1 • ARXIV : 1706.08282 ### Citation Christophe Cuny, Jérôme Dedecker, Florence Merlevède. On the Komlós, Major and Tusnády strong approximation for some classes of random iterates. MAP5 2017-24. 2017. 〈hal-01544861〉 ### Métriques Consultations de la notice ## 157 Téléchargements de fichiers	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8682437539100647, "perplexity": 3581.474716949266}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511703.70/warc/CC-MAIN-20181018042951-20181018064451-00196.warc.gz"}
https://infoscience.epfl.ch/record/196113	Infoscience Journal article # Probing the origin of cosmic rays with extremely high energy neutrinos using the IceCube Observatory We have searched for extremely high energy neutrinos using data taken with the IceCube detector between May 2010 and May 2012. Two neutrino-induced particle shower events with energies around 1 PeV were observed, as reported previously. In this work, we investigate whether these events could originate from cosmogenic neutrinos produced in the interactions of ultrahigh energy cosmic rays with ambient photons while propagating through intergalactic space. Exploiting IceCube's large exposure for extremely high energy neutrinos and the lack of observed events above 100 PeV, we can rule out the corresponding models at more than 90% confidence level. The model-independent quasidifferential 90% C. L. upper limit, which amounts to E-2 phi(nu e)+(nu mu)+(nu tau) = 1.2 x 10(-7) GeV cm(-2) s(-1) sr(-1) at 1 EeV, provides the most stringent constraint in the energy range from 10 PeV to 10 EeV. Our observation disfavors strong cosmological evolution of the highest energy cosmic-ray sources such as the Fanaroff-Riley type II class of radio galaxies.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8860697746276855, "perplexity": 2335.906445499645}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424909.50/warc/CC-MAIN-20170724182233-20170724202233-00446.warc.gz"}
https://chengjunwang.com/publication/tracing-attention/	# Tracing the Attention of Moving Citizens ### Abstract With the widespread use of mobile computing devices in contemporary society, our trajectories in the physical space and virtual world are increasingly closely connected. Using the anonymous smartphone data of $1 × 10^5$ users in a major city of China, we study the interplay between online and offline human behaviors by constructing the mobility network (offline) and the attention network (online). Using the network renormalization technique, we find that they belong to two different classes: the mobility network is small-world, whereas the attention network is fractal. We then divide the city into different areas based on the features of the mobility network discovered under renormalization. Interestingly, this spatial division manifests the location-based online behaviors, for example shopping, dating, and taxi-requesting. Finally, we offer a geometric network model to help us understand the relationship between small-world and fractal networks. Type Publication Scientific Reports, 6, 33103. doi: 10.1038/srep33103 More detail can easily be written here using Markdown and $\rm \LaTeX$ math code.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7115377187728882, "perplexity": 2098.8630421778016}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038083007.51/warc/CC-MAIN-20210415035637-20210415065637-00254.warc.gz"}
http://www.decarpentier.nl/game-theory	## Game theory: Leader strategies in repeated games May 13, 2011 AI Using game theory to analyse and optimize and balance strategies in complex computer games is still a very long stretch. But you can use it to analyse seamingly trivial games to find far from trivial strategies. In the following document from 2006 called "Leader Strategies in Repeated Games. An investigation of advantages, weaknesses and improvements", Richard Noorlandt and I investigate and extend existing techniques to find best response strategies for games like Prisoner's dilemma. Note that this article might be a little too dry for the taste of the average game developer, as it's mainly aimed at game theorists. On the other hand, it might just give developers some interesting insights into how a theoretical framework can be applied to the field of games. In the Downloads section, you'll find a paper-formatted version of this document and a presentation containing a summary, as well as more detailed results from the different experiments. ### Abstract Against an unchanging opponent, best response strategies can provide a robust and natural means for maximizing an agent’s payoff in simple repeated multi-agent games. Best response agents learn from previous experience in order to determine the optimal equilibrium against this opponent’s fixed behavior. However, letting two best response agents play against each other may result in suboptimal performance. Littman and Stone [1] suggest an asymmetric solution to this problem. In their paper, best response strategies, called ‘followers’, play against ‘leader’ strategies. These leader strategies carefully plan the follower’s experience, indirectly influencing the follower’s best response reaction. By making use of this responsive behavior, leaders are able to maximize their own payoff. In this paper we extend and improve the strategies proposed by Littman and Stone, while trying to get more insight in the behavior of leading strategies. ### 1. Introduction Multi-agents systems have found many uses in recent years [2], [3], [4]. However, guaranteeing strategy optimality for complex environments is hard or even impossible. Studying smaller and simpler multi-agent problems has proven to be more promising. Some non-trivial classes of multi-agent problems can be described using repeated bimatrix games. For these problems, general-sum bimatrix games are powerful enough to describe different game types that present various difficult challenges for simultaneous agent learning and planning. For a short discussion of bimatrix games, we would like to refer to [5]. A standard approach to learning in games is to apply a general-purpose adaptive strategy like Q-learning [6], which is a form of reinforcement learning [7]. Q-learner agents base their strategy on their previous experience to optimize a best-response model. These agents are guaranteed to be optimal against fixed strategies [1], but when paired with other best response learners, suboptimal strategies can occur. Like Littman and Stone discuss in their paper “Leading Best-Response Strategies in Repeated Games” [1], we examine the approach of pairing best response agents with leaders. Leaders selectively plan their own actions, factoring in the best response behavior of the opponent. This makes it possible for leader agents to exploit the opponent’s predictability, maximizing their own payoff on the long run. Littman and Stone introduced two leader strategies. The Godfather leader strategy is based on the reciprocity of choosing an action that is beneficial for the other, retaliating the best response opponent when the implicit offer is turned down. The Bully leader strategy determines the best-response reaction to each of its own choices, and chooses the action that is most beneficial to itself. Although these proposed leader strategies look promising and can be very successful, they have several weaknesses. These weaknesses will be presented and explored in this paper. Also, suggestions are made to improve the performance of these leader strategies. The exact strategies mentioned by Littman and Stone, together with our suggested extensions, were implemented and tested against each other to get a detailed view on the achieved performance. In section 2 we present a brief overview of the strategies introduced by Littman and Stone, describe their shortcomings and introduce our suggested improvements. In section 3 we present and explain the results from our experiments. ### 2. Strategies The behavior of a single agent in a multi-agent environment is determined by a strategy. This strategy decides on the agent’s action to be taken at every stage, given a limited view on its environment. The expected payoff of a strategy is highly dependent of the environment and the rich interaction between strategies of agents. Hence, no single strategy is optimal, but rather, the collection of strategies must be a Nash equilibrium [8]. Finding this Nash equilibrium for complex games where each agent uses only incomplete information has been proved to be very challenging. One approach is ‘best response’. A best response strategy tries to maximize its payoff by exploiting any observed patterns in its previous experience. The complexity of the patterns that a best response agent is able to recognize depends on the amount of information it observes at each stage and the size and complexity of its memory. Using only its own history of actions, simple but stable agents, called independent learners, can be trained. Using more information allows more complex behavior of an agent, but might result in slower convergence or even instability. At the other extreme, if an agent is able to fully observe the rules of the system and have complete information on the strategies of all other agents, complex solvers and/or heuristics might maximize its own expected payoff. However, this may be impractical or even impossible for larger systems and more complex opponents. Like Littman and Stone, we only examine two player games in the form of bimatrix games. Generalization can probably be made for larger systems, but this is outside the scope of this paper. Best response independent learners (ILs) adapt to their environment by modeling the expected payoff for choosing an action, given a limited history of their previous choices. Used often in research due to its simplicity, Littman and Stone implemented two best response IL variants as Q-learners. These ILs are an example of what Littman and Stone call ‘follower’ strategies because of their adaptive nature. In contrast, joint action learners (JALs) use more advanced reinforcement learning techniques to learn from their own choices together with the choices made by opposing agents. Although strictly not the same, the leader strategies proposed by Littman and Stone could be classified as JALs, since they coordinate their choices given the opponent’s behavior. Pairing a follower with a leader creates an asymmetric relationship in which the leader can guide the follower into conditioned behavior, maximizing the expected payoff for the leader. This asymmetric relation causes typical symmetric IL-IL game instability to be resolved. ### 2.1 Q-Learning A simple, well-understood algorithm for single agent learning is Q-learning [6]. Q-values, Q(x, i), provide an estimate of the value of performing action x when in state i. These Q-values are updated through explorative sampling to build an estimate over multiple steps. Different formulations of the update rule are found in literature, but we follow the notation used by Littman and Stone. $Q(x, i) = \alpha \,(r + \gamma\,\underset{i'}{max}\,Q(y, i'))\,+\,(1 - \alpha) \,Q(x,i)$ These estimates can be used to exploitatively choose the action with the highest expected payoff. Deciding when to explore either exploitive or non-exploitive depends on the learning policy. Together with the learning rate and the state space size, this policy influences the convergence speed. #### 2.1.1 ε-greedy policy The ε-greedy policy for Q-learning either chooses a random action with probability ε or chooses the action with the highest Q-value in the current state otherwise. In other words, the exploration-exploitation ratio is defined by ε / (1 - ε). This ratio is kept fixed throughout the experiment. Choosing a larger ε will result in faster obtainment of more accurate estimations, and with it, faster convergence, but has the disadvantage of having a higher probability of choosing suboptimal actions after being converged. Choosing ε too small might cause the Q-value estimation to take more steps before it becomes accurate, having a negative effect on convergence. An advantage of this policy is that in dynamically changing multi-agent environments, agents implementing the ε-greedy policy will remain adaptive to their surroundings. This policy was chosen by Littman and Stone because it is simple, easy to understand and slow to converge, making it ideal to study it in detail. We implemented their Q0 and Q1 agents. Q0 is a stateless Q-learner. Q1 has its own previous action as its state. #### 2.1.2 Boltzmann policy A popular policy is the Boltzmann policy or Boltzmann exploration [9]. Simulating the process of annealing, action x is chosen with probability $P(x) = \frac{exp \,(\frac{Q(x)}{T})}{\sum\limits_{i \in X} exp \,(\frac{Q(i)}{T})}$ The temperature parameter T starts off high and decreases over time, so that the initial explorative nature of an agent using this policy will slowly change into exploitive behavior. This ensures fast convergence of the Q-values at its start-up time, after which the Q-values are used more and more exploitive. However, some care must be taken not to decrease T too rapid, since this might cause the explorative phase of the agent to become too short to acquire accurate estimations of the Q-values. In practice, this policy can be used robustly in many situation, while converging much faster than when using a conservative ε-greedy policy. One disadvantage of this policy in ever changing environments is that after the explorative phase, adapting to new opponent strategies becomes increasingly difficult. Its fast convergence makes it useful for many practical purposes, but also makes it more difficult to study in detail. For the purpose of comparison, this policy has been included in our experiments too. These Q-learning agents are called B0 and B1 and are otherwise identical to the Q0 and Q1. #### 2.1.3 Parameter settings Figure 1: Q-learning, the effect of parameters and policy As mentioned before, the performance of a Q-learning agent is for one part determined by the exploration policy. However, this is not the only factor that influences the learning rate and accuracy. The formula that is used to update the Q-values has a few parameters that determine the speed in which the Q-values are updated, namely α and γ. Both of these parameters should have a value between 0 and 1. A higher value of a results in the table with Q-values being updated more rapid. The value of γ determines the role of future interactions on the Q-value: the higher the value of γ, the more weight is assigned to results of future choices while determining the Q-values. That the used parameters and policy indeed have a large impact on the convergence and performance of a Q-learner can be seen in figure 1. This graph shows some performance characteristics of a Q1 (ε-greedy) and B1 (Boltzmann) learner when playing against a Godfather in the assurance game. On the y-axis we have plotted the average payoff against the number of iterations on the x-axis for a variety of a (rate) values. For the ε-greedy policy we have also included various ε (random) values. The value of γ is kept constant on 0.9. What the graph shows is that the learning rate and exploration settings have a big impact on the convergence speed. For example, an increased ε value will let the agent do more exploring, which leads to finding its optimum faster, but at the cost of the average payoff after convergence. It also becomes very clear that the Boltzmann policy converges even many times faster than a ε-greedy policy. ### 2.2 Bully The Bully strategy is one of the two leader strategies introduced by Littman and Stone. This strategy assumes that the opponent will eventually play best response when the Bully consistently chooses the same action at every step. In order to maximize its own payoff, the Bully needs to know the payoff matrix of its opponent to determine what the best response choice for the opponent will be for each of its own actions. By pairing its own choice with the expected choice of its opponent, a Bully is able to figure out what its own expected payoff will be for each of its own actions. The payoff is maximized by consistently choosing for the action with the highest expected payoff. The success of this strategy depends heavily on a game’s payoff matrix structure and doesn’t necessarily converge to an optimal combined strategy. Since the Bully limits itself to a subset of action-pairs, other action pairs that might be more promising are left unconsidered. This is exemplified in section 3.3 by the Prisoner’s Dilemma. ### 2.3 Godfather The other leader strategy proposed by Littman and Stone is the Godfather strategy. Like Bully, it chooses an action pair to play for and assumes that the opponent uses a best response strategy. However, instead of acting passively like the Bully strategy, Godfather uses active reciprocity to punish the opponent if it deviated from a certain appreciated action in the previous step. This action appreciated by the Godfather is part of an action pair, called the targetable pair. To determine this pair, the security levels of the Godfather and its opponent are determined first [1]. The action that forces the opponent to play for its security level payoff is the Godfather’s way to punish its opponent. Then, the Godfather’s half of the targetable pair must be the choice that allows the opponent to play for a higher payoff than its security level, or else punishment would be meaningless. Lastly, the opponent’s half of this pair is determined by the Godfather to be the action that will result in the highest expected payoff for the Godfather, given the Godfather’s half. The successfulness of this strategy depends on the learning capabilities of the opponent. If an opponent is unable to comprehend the effects of being punished one step after choosing the ‘wrong’ action, the Godfather might be unable to condition its opponent in playing the targetable pair. In the case of a Q-learning opponent, this means that at stateless Q-learners will result in suboptimal behavior. ### 2.4 Extending Godfather In this paper, we present two extensions to the Godfather strategy. The first extension is based on the observation that for some game matrices, passive Bully-like behavior might suffice to get a best response opponent to play its half of the targetable pair. The second extension attempts to use opponent prediction to punish the opponent in the same step it is most likely to make a wrong choice. By punishing the opponent in the step that a wrong choice is made instead of one step later, even stateless opponents are able to learn this lesson. #### 2.4.1 Best response exploit Some types of games, like the Chicken game and Prisoner’s dilemma need Godfather’s punishment in order to make the opponent choose an action that wouldn’t be chosen if the opponent would go for its own maximal payoff. However, it isn’t always necessary to punish if the opponent chooses the wrong action. In the case of the Assurance and Deadlock game, the opponent will eventually choose for its half of the targetable pair if the Godfather plays its own half, even if punishment isn’t executed when the best response opponent explores its other options. This will be true for any game for which the best response opponent will have a higher expected payoff when choosing to play its half of the targetable pair. By not executing opponent punishment in games for which best response opponents tend to play their half of the targetable pair anyway (albeit without knowing it), the opponents have an easier lesson to learn. This means even simpler best response agents, that are unable to comprehend punishment, will be able to perform well in these games. Also, agents that are able to perform well against the standard Godfather, are likely to convergence in less steps. #### 2.4.2 Response prediction For games in which there is no benefit from the best response exploit, another extension is presented here. A standard Godfather can be privately fitted with a ‘predictor’ of a simple best response strategy that would be unable to learn from punishment. This predictor is updated every step, exactly like an opponent with an identical best response strategy would be. When this best response strategy is implemented using a sufficiently simple Q-learning strategy where the Q-values would converge to the same numbers for each run, the response of the predictor and such an opponent are guaranteed to converge over time. This allows the Godfather to predict the action to be chosen by an opponent that implemented the identical strategy, after the predictor has been trained sufficiently. If this is the case, a Godfather is able to punish the opponent in the current step when a wrong choice is predicted, instead of punishing it one step after it actually happened. This early punishment is an easier lesson to comprehend and can even be used against stateless Q-learners. The disadvantage of this technique is that not only the payoff matrix of the opponent needs to be known, but also the precise implementational details of the opponent that the Godfather is attempting to predict. However, if this limitation isn’t problematic for a certain multi-agent environment, considerable performance gains can be achieved by this extension. To determine whether the Godfather’s opponent is an opponent using the same strategy as the predictor, an assessment of the predictor’s accuracy needs to be made. We implemented two different policies for comparison. The first policy used a running average of predictor correctness Ri to get a measure between 0 and 1. This measure was then used to calculate the probability Pi = Max(0, 2(Ri - .5)) for acting reciprocally to the predicted action instead of the standard Godfather’s behavior of acting to the opponent’s previous choice. This relation has the characteristic of having zero probability for an average accuracy that is equal or less than what a random strategy would achieve. The second policy bases its decision on whether or not the predictor made a correct prediction in the previous step. If it predicted the action of the opponent correctly in the previous step, the Godfather assumes the predictor will be correct for the current step and will act accordingly. However, if the predictor did not correctly predict the opponent’s choice in the previous step, the Godfather will assume the strategy of the predictor is either not identical to the opponent’s strategy, or the predictor is not trained enough. In either case, it chooses to go for the standard Godfather behavior for the current step. #### 2.4.3 Combining extensions Response prediction might help improve the performance if the opponent is a best response agent. Moreover, response prediction can be used for every game type. On the other hand, the best response exploit can only be used for certain game types, but is advantageous for more types of opponents. To get the most out of our proposed extensions, the Godfather can check whether or not the game matrix is suitable for the best response exploit. If it is suitable, the best response exploit is used. Otherwise, the response predictor is used. ### 3 Results In order to test the effectiveness of our extensions to the Godfather strategy we implemented a framework that runs a large number of simulations of the games being played by different agent combinations. Because the new strategies are based on the ones that are introduced by Littman and Stone, we decided to run the tests and compute the results in a similar way as described in their paper [1]. However, we did implement and test more agent types and ran more trials to get more accurate averages. The results, as given in the following sections, were computed by running experiments that placed two agents against each other in a certain game. Each experiment consisted of 30,000 iterations. That is, each experiment is a repeated game where each agent takes 30,000 turns. For each experiment, the average payoff of the last 5,000 iterations was computed. We ran each experiment 100,000 times and measured the mean and standard deviation of this averaged payoff, as opposed to the 100 test runs used by Littman and Stone. It is worth noting that the reported results only represent the scores after the scores had time to stabilize, due to the fact that the average payoff is calculated only over the last 5,000 iterations of each experiment. We therefore only analyzed performance after the strategies of the agent pairs had stabilized, ignoring initial performance. For the Q0 and Q1 learners we used identical parameters as Littman and Stone: γ = 0.9, α = 0.1, and ε = 0.1 for the greedy policy. These same settings were used for the reinforcement learners that used the Boltzmann strategy, but with T(i) = 16 * .99i as its temperature at iteration i. For consistency, we will call action 0 “cooperate” and action 1 “defect” in the same way as in the Littman and Stone paper. We ran tests for all possible agent combinations of implemented agents, including competing leader strategies. For comparison, we also added an agent type that acts randomly. Although the main goal is to see how well leaders perform against followers, it is interesting to see how leaders perform against each other as these numbers can give some insight on the overall performance and stability in the case where no assumptions can be made on the type of opponent. General results in the form of the average payoff for each game are shown in tables 1-4. For brevity, the exact values of the standard deviations are omitted. However, high standard deviations, most likely due to instable solutions, are color-coded. In the tables, the following abbreviations and color codes are used: Q0: Q0 learner Q1: Q1 learner Bu: Bully Gf: Godfather Ra: Random Gb: Godfather with best response exploit Gp: Godfather with Q0 predictor, policy 2 Gn: Godfather with Q0 predictor, policy 1 Gu: Combination of Gb and Gp B0: Q0 with Boltzmann policy B1: Q1 with Boltzmann policy Also, the following color coding is applied throughout this document: Mutual defection Sucker Tempted Mutual cooperation Unstable Bad performance ### 3.1 Deadlock The deadlock game is a simple game, consisting of the following matrices: $M_1 = \begin{bmatrix} 3 & & 2 \\ \\ 0 & & 1 \end{bmatrix} \, , \, M_2 = \begin{bmatrix} 3 & & 0 \\ \\ 2 & & 1 \end{bmatrix}$ As mentioned by Littman and Stone, in this game both agents perform best if they both cooperate. A best response strategy will do this automatically, guaranteeing solid performance for most agents. As we can see in table 1, almost all combinations of agents come quite close to the maximum achievable score of 3. Player Q0 Q1 Bu Gf Ra Gb Gp Gn Gu B0 B1 Opponent Q0 2,805 2,805 2,950 2,805 1,993 2,950 2,681 2,793 2,950 2,950 2,950 Q1 2,805 2,805 2,950 2,805 1,993 2,950 2,681 2,793 2,950 2,950 2,950 Bu 2,850 2,850 3,000 3,000 2,010 3,000 2,858 2,858 3,000 3,000 3,000 Gf 2,805 2,805 3,000 3,000 1,898 3,000 1,048 2,756 3,000 3,000 3,000 Ra 2,553 2,553 2,670 1,898 1,898 2,670 1,860 2,279 2,670 2,670 2,670 Gb 2,850 2,850 3,000 3,000 2,010 3,000 2,857 2,858 3,000 3,000 3,000 Gp 2,766 2,766 2,953 1,048 1,892 2,952 1,090 2,671 2,952 2,953 2,953 Gn 2,801 2,801 2,953 2,756 1,953 2,953 2,590 2,781 2,952 2,952 2,952 Gu 2,850 2,850 3,000 3,000 2,010 3,000 2,857 2,857 3,000 3,000 3,000 B0 2,850 2,850 3,000 3,000 2,010 3,000 2,858 2,857 3,000 3,000 3,000 B1 2,850 2,850 3,000 3,000 2,010 3,000 2,858 2,857 3,000 3,000 3,000 Table 1: Deadlock There are, however, some interesting combinations of agents that result in one of the agents performing poorly. It is very clear that the random strategy overall performs a lot worse than other strategies. Also, when Gp plays against another Gp or Gf agent, both agents perform extremely poor. Further analyzing the results, we can see that the Bully strategy is hard to beat on the long run. This is easily explained by the fact that the opponent’s best response always results in cooperation. Thus, both the Bully and it’s opponent have a tendency to mutual cooperation. The opponent’s random exploration is the only factor that prevents both agents from reaching truly optimal results. The Gb and Gu strategies perform as well as Bully. Because Gb will never need to execute punishment for this game, it will always play its half of the targetable pair. Random exploration by the opponent results in self punishment and explains the suboptimal performance against agents with a stochastic element. Likewise, Gu will never need to execute punishment either and effectively becomes like Gb. Other solid performers are the Boltzmann strategies. This is due to the fact that these learners converge very quickly, after which their choices become fixed on cooperating. Only random exploration on the opponent’s side can have a small negative effect on the result. This is reflected by the somewhat lower scores when playing against stochastic strategies. ### 3.2 Assurance Although its matrices are the transpose of the deadlock game, the assurance game has more complex characteristics. Optimal results can be achieved when both agents cooperate, but when one of the agents chooses to defect, it’s important for the other agent to defect too. When both agents choose the same option they will always get the same payoff. If they both choose a different option, on the other hand, one of the agents will get a payoff of 0. $M_1 = \begin{bmatrix} 3 & & 0 \\ \\ 2 & & 1 \end{bmatrix} \, , \, M_2 = \begin{bmatrix} 3 & & 2 \\ \\ 0 & & 1 \end{bmatrix}$ The fact that this game is more difficult than deadlock can easily be seen from our test results, which show more variance than with deadlock. It’s easy to see that Bu, Gb, Gu and the Boltzmann strategies are the best overall performers. Just like in Deadlock, this is the result from the fact that both agents are best off always cooperating, with deviations from an optimal score being the result of random explorations. Player Q0 Q1 Bu Gf Ra Gb Gp Gn Gu B0 B1 Opponent Q0 1,561 1,683 2,850 1,343 2,239 2,850 2,711 2,109 2,850 1,940 1,927 Q1 1,683 1,952 2,850 2,805 2,017 2,850 2,765 2,401 2,850 1,850 1,916 Bu 2,950 2,950 3,000 3,000 2,670 3,000 2,952 2,953 3,000 3,000 3,000 Gf 1,343 2,805 3,000 3,000 1,898 3,000 1,048 2,732 3,000 3,000 3,000 Ra 1,947 1,915 2,010 1,898 1,898 2,010 1,888 1,925 2,010 2,000 2,000 Gb 2,950 2,950 3,000 3,000 2,670 3,000 2,952 2,952 3,000 3,000 3,000 Gp 2,635 2,676 2,857 1,048 1,828 2,857 1,117 2,538 2,857 2,858 2,857 Gn 2,107 2,374 2,858 2,732 2,084 2,857 2,617 2,683 2,858 2,857 2,790 Gu 2,950 2,950 3,000 3,000 2,670 3,000 2,952 2,953 3,000 3,000 3,000 B0 1,940 1,840 3,000 3,000 2,601 3,000 2,953 2,952 3,000 3,000 2,663 B1 1,924 1,915 2,993 3,000 2,448 2,993 2,952 2,876 2,993 2,553 2,292 Table 2: Assurance What is different, however, is the occurrence of many unstable results when at least one of the agents uses a stochastic strategy. Especially when Q0 or Gn are involved, the results show a very large standard deviation: Q0 Q1 Gn Q0 1.561 (0.821) 1.683 (0.860) 2.109 (0.865) Q1 1.683 (0.861) 1.952 (0.875) 2.401 (0.686) Gn 2.107 (0.857) 2.374 (0.669) 2.683 (0.238) In the table, the standard deviation of the results is shown in parenthesis. It is obvious that the standard deviation for the shown player combinations is quite large. Where most measured results have a variance far below 0.01, these combinations are several orders of magnitude higher. This is due to the involvement of multiple random factors, whose interaction has a large influence on the outcome of the game. On one hand, mispredictions made by Gn’s internal predictor can destabilize the other agent’s Q-values, while on the other hand, random exploration by the reinforcement learners affect performance in a negative way. Since bad decisions made by either agent are reflected in the Q-values of both agents (in the case of Gn inside the internal predictor), prediction errors can propagate indirectly between agents and influence future results. It is due to this interaction that eventual average payoffs may vary greatly. An explanation for this behavior can be given by the fact that when one agent cooperates while the other defects, the cooperating agent gets a very low payoff of 0. Thus, asymmetric choices have a large impact on the results. When one of the agents uses a form of random exploration or punishment based on a stochastic predictor, these occasional asymmetric choices will immediately have a large impact on the Q-value of a Q-learning based agent. This is illustrated by figure 2, which is a plot of a Q1-Learner’s Q-values during the first 8,000 iterations in a game played against Gn. Figure 2: Q-values for Gn-Q1 The Q1 agent’s Q-values show an unstable pattern. This is due to ε-greedy exploration on the Q1 learner’s side and false predictions on Gn’s side. These two factors result in the agents making opposite choices, resulting in a low payoff for one of the agents. When this happens, the Q-value will drop immediately, as can be seen from the figure. Recovery from these low scores is fairly rapid, since Q1 realizes that cooperating remains the best option. Other combinations of agents that show striking results are Gp-Gf and Gp- Gp. These opponents get extremely poor results for reasons that are not immediately obvious. The explanation for this phenomenon lies in the fact that both strategies can get in a continuous cycle of mutual punishment. The problem lies in Gp’s internal Q0-based predictor. Gp assumes that its prediction will be correct when the last prediction was. At some point in time, it will happen that the prediction will be inaccurate due to the predictor’s stochastic element. In time it will occur that the predictor’s Q-value reaches the point where it suggests that defecting will improve the payoff (due to the memoryless characteristics of Q0). If the previous prediction was correct, Gp will unjustly punish its opponent based on this false prediction. As a reaction, the Godfather opponent will punish Gn due to its betrayal. In the next turn, Gn will again predict that its opponent will defect, and since the last prediction was assumed to be correct, it will punish Gf again in return and keep the cycle alive until a new misprediction will be made and propagated. ### 3.3 Prisoner’s Dilemma The prisoner’s dilemma is a problem in game theory. It is defined by the following matrices: $M_1 = \begin{bmatrix} 3 & & 0 \\ \\ 5 & & 1 \end{bmatrix} \, , \, M_2 = \begin{bmatrix} 3 & & 5 \\ \\ 0 & & 1 \end{bmatrix}$ The main issue with the prisoner’s dilemma is that although both agents are best off by always cooperating, defecting is a very attractive strategy. From the results below we can see a great difference in scores among the agent combinations. It is especially notable that the Bully strategy as proposed by Littman and Stone performs extremely poor against all agents (except Random). This is a result from Bully’s assumption that its opponent will always play best response, which is defecting by default. Based on this assumption, the Bully will also choose to defect, resulting in a payoff of 1 for both agents. Player Q0 Q1 Bu Gf Ra Gb Gp Gn Gu B0 B1 Opponent Q0 1,181 1,158 1,200 1,355 0,536 1,355 2,757 2,805 2,757 1,200 1,200 Q1 1,175 1,205 1,200 2,948 0,583 2,947 2,982 3,073 2,982 1,200 1,200 Bu 0,950 0,950 1,000 1,000 0,330 1,000 0,953 0,953 0,952 1,000 1,000 Gf 1,355 2,948 1,000 3,000 2,561 3,000 2,491 1,300 2,491 3,000 3,000 Ra 3,577 3,553 3,680 2,561 2,561 2,561 2,588 2,886 2,588 3,679 3,526 Gb 1,355 2,947 1,000 3,000 2,561 3,000 2,491 1,301 2,491 3,000 3,000 Gp 2,726 2,786 1,190 2,491 2,508 2,491 2,473 2,068 2,473 2,857 2,854 Gn 2,792 2,573 1,190 1,300 1,913 1,301 1,903 1,477 1,903 2,858 2,786 Gu 2,726 2,786 1,190 2,491 2,508 2,491 2,473 2,068 2,473 2,857 2,858 B0 0,950 0,950 1,000 3,000 0,331 3,000 3,095 3,095 3,095 3,000 2,413 B1 0,950 0,950 1,000 3,000 0,636 3,000 3,089 3,089 3,089 1,783 1,646 Table 3: Prisoner's Dilemma From the results we can see that there is no obvious best strategy for the prisoner’s dilemma, which is in line with prior research on the game. It is interesting to note that although the game has very complex dynamics, the simple reinforcement learners perform relatively well against all but Q-learners and Bully strategies. Another interesting phenomenon which is related to learning speeds can be observed by comparing Gp and Gn. As Axelrod notes in [10], “The speed of response depends upon the time required to detect a given choice by the other player. The shorter this time is, the more stable cooperation can be.” When we look at the predicting extensions to Godfather, it can easily be seen that Gp will be more predictable and transparent to an opponent than Gn. Since Gp bases its decision on whether or not to use its prediction only on the accuracy of last turn’s prediction. This behavior can be observed relatively quick by an opponent, giving it a chance to react in a timely manner. Gn, on the other hand, bases its decisions on a much slower and more gradually changing parameter: the running average of the predictor’s performance. This behavior is very obscure and difficult to detect for an opposing agent, limiting the opponent’s reaction time in return. According to Axelrod, Gp should thus give it’s opponents a better chance to achieve cooperation than Gn. Our results indeed seem to confirm this, as Gn’s performance is much more unstable than Gp. ### 3.4 Chicken Chicken represents the game where two cars are approaching each other on a highway. If none of the agents changes it’s course, both will crash on each other giving a low score for both. On the other hand, if only one of the agents changes course, the one that is changing lanes gets a low payoff, and the other gets a high payoff. Essentially, both agents must try to choose the opposite action of their opponent to maximize their own performance. The matrices are given below: $M_1 = \begin{bmatrix} 3.0 & & 1.5 \\ \\ 3.5 & & 1.0 \end{bmatrix} \, , \, M_2 = \begin{bmatrix} 3.0 & & 3.5 \\ \\ 1.5 & & 1.0 \end{bmatrix}$ When analyzing our results, we can see that the Bully as proposed by Littman and Stone performs extremely well against reinforcement learners, but can’t handle other leading strategies. This again is a result from the deterministic nature of the Bully which essentially always chooses to defect, thereby limiting the other agent’s payoff to a maximum of 1.5 while enforcing its own payoff to be 3.5. While playing against other leader strategies the score is disastrous due to constant mutual defection (be it because of another Bully whose standard choice is to defect, or due to punishment executed by a Godfather-like strategy). Player Q0 Q1 Bu Gf Ra Gb Gp Gn Gu B0 B1 Opponent Q0 2,432 2,479 3,375 2,850 1,871 2,850 2,909 2,907 2,909 2,217 2,187 Q1 2,440 2,867 3,375 2,948 2,004 2,948 2,966 2,978 2,966 2,777 2,246 Bu 1,475 1,475 1,000 1,000 1,335 1,000 1,024 1,024 1,024 1,500 1,500 Gf 2,850 2,948 1,000 3,000 2,561 3,000 2,492 2,821 2,492 3,000 3,000 Ra 2,625 2,613 2,675 2,561 2,561 2,561 2,562 2,573 2,562 2,628 2,560 Gb 2,850 2,948 1,000 3,000 2,561 3,000 2,492 2,821 2,492 3,000 3,000 Gp 2,845 2,881 1,119 2,492 2,551 2,492 2,498 2,737 2,498 2,929 2,929 Gn 2,900 2,805 1,119 2,821 2,428 2,821 2,780 2,840 2,780 2,929 2,929 Gu 2,845 2,881 1,119 2,492 2,551 2,492 2,498 2,737 2,498 2,929 2,929 B0 2,762 2,695 3,500 3,000 1,842 3,000 3,024 3,024 3,024 2,701 2,511 B1 2,791 2,697 3,488 3,000 2,581 3,000 3,021 3,024 3,024 2,892 2,806 Table 4: Chicken The Godfather and our extensions to it perform quite well against most agents except the Bully. Their good performance is due to their continuous choice for the targetable pair. The reinforcement learners quickly learn their lessons, while other Godfathers will always cooperate by also choosing their part of the targetable pair. ### 4 Conclusions We have extended the Godfather strategy with many different features to improve its performance. In the paper by Littman and Stone, the only combination of agents that always settles on mutual cooperation is Gf-Q1. In other combinations, good performance could not be guaranteed. As our results have shown, the Godfather strategy can be made more robust to perform more consistently to other types of agents. The best response exploit helps Godfather to perform better or equal against Q0 agents in all games but the prisoner’s dilemma. Because of the lack of memory, a Q0 learner is not capable to learn in the prisoner’s dilemma and thereby continuously chooses to defect. Due to Q0’s tendency to defect without the effect of selfpunishment, Gb will very often have to execute punishment. Almost continuous mutual defection is the result. Another extension that tries to make Godfather perform better against Q0 agents is the use of an internal Q0 predictor. This approach improves performance slightly in the prisoner’s dilemma and chicken games. Performance is improved significantly in assurance, but here the extension cannot prevent the results from having a high variance and thus being unstable. In the deadlock game, performance against Q0 and Q1 is slightly decreased due to mispredictions in Godfather’s internal learner. This phenomenon is also visible while playing against other leading strategies where the use of a Q0 predictor is greatly misplaced. The trend seems to be that stochastic strategies decrease performance while playing against a deterministic agent. When combining the best response exploit with a Q0 predictor we get the best of both worlds. Comparing the results of Gu with Gb and Gp we can see that the score that Gu obtains is actually max(Gb, Gp), thereby indicating that combining strategies can work well in most cases. It should be noted though that every Godfather based strategy is unable to handle consistently noncooperating agents in games where defecting can increase an agent’s performance. This indeed is in line with previous research showing that an always-defect strategy is evolutionary stable in the prisoner’s dilemma, making it impossible for another strategy to invade on the long term. See [11]. One big advantage of the Godfather based strategies is that they tend to perform relatively well against other cooperating leaders. This is due to the fact that in such a situation both agents keep aiming for the targetable pair, resulting in frequent mutual cooperation. The more deterministic the involved strategies are, the better the overall performance in this case. Since the basic strategy on which these agents rely is deterministic in nature, using stochastic elements only tends to disrupt the trend of mutual cooperation for a short time. Furthermore, we have seen that all Godfather variants tend to lead reinforcement learners well. As long as an opponent is willing to adapt itself to the leading strategy the overall performance will generally be good. In these cases the stability of the follower has the most impact on the average payoff of both agents. This indeed explains why the Boltzmann strategy works better than the ε-greedy strategy: Boltzmann quickly converges to mutual cooperation, where ε-greedy occasionally keeps exploring with negative effect. We have shown that extending the Godfather strategy can improve performance in many situations. It however remains a fact that a strategy which aims at mutual cooperation does not work well in every game/agent combination. To further improve the agents it will be necessary to implement heuristics to discover if an opponent is playing with an aggressive non-cooperative strategy, and adapt its playing style to handle this kind of situation. ### 5. References [1] M. L. Littman and P. Stone. “Leading Best-Response Strategies in Repeated Games”. AT&T Labs Research. 2001 [2] B. Burmeister, A. Haddadi, G.Matylis. Application of Multi-Agent Systems in Traffic and Transportation. IEE Proceedings, Vol 144, Issue 1. p. 51-60. 1997 [3] J. Ferber. Multi-Agent System: An Introduction to Distributed Artificial Intelligence. Harlow: Addison Wesley Longman. ISBN 0-201-36048-9. 1999 [4] N. R. Jennings and M. J. Wooldridge. Agent Technology: Foundations, Applications, and Markets. Springer-Verlag New York, Inc. ISBN: 3-540-63591-2. 1998 [5] K. Fukuda. Bimatrix Games. [6] C. J. C. H. Watkins and P. Dayan. “Technical Note on Q-learning”. Machine Learning 8, p 279-292. 1992 [7] C. Claus and Craig Boutilier. “The Dynamics of Reinforcement Learning in Cooperative Multiagent Systems”. Department of Computer Science, University of British Colombia. 1998 [8] J. Nash. Equilibrium Points in N-Person Games. Proceedings of NAS. 1950 [9] M. Mundhe and S. Sen. “Evaluating concurrent reinforcement learners”. Department of Mathematical & Computer Sciences, University of Tulsa. [10] R. Axelrod. The Evolution of Cooperation. ISBN 0465021212. 1984 [11] R. Axelrod. “The Evolution of Cooperation”. Science, 211, p. 1390-1396. 1981 ### Comments (1) Ade October 21, 2012 Taking the ovrvieew, this post is first class	{"extraction_info": {"found_math": true, "script_math_tex": 6, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6118525266647339, "perplexity": 862.0981689760662}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315750.62/warc/CC-MAIN-20190821022901-20190821044901-00109.warc.gz"}
http://physics.stackexchange.com/users/8225/haatschii	Haatschii less info reputation 6 bio website haatschii.de location Berlin, Germany age 27 member for 3 years seen Nov 19 '14 at 17:36 profile views 12 Bloub 2 Questions 4 How to prove that the symmetrisation Operator is hermitian? 1 Ideal gas with two kinds of particles, Grand canonical partition function 128 Reputation +5 Ideal gas with two kinds of particles, Grand canonical partition function +20 How to prove that the symmetrisation Operator is hermitian? This user has not answered any questions 6 Tags 0 homework-and-exercises × 2 0 thermodynamics 0 mathematical-physics 0 quantum-mechanics 0 statistical-mechanics 0 operators 8 Accounts Stack Overflow 2,559 rep 21852 Mathematics 337 rep 216 TeX - LaTeX 300 rep 110 Physics 128 rep 6 Meta Stack Exchange 111 rep 3	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8834101557731628, "perplexity": 6024.397164600226}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131298177.21/warc/CC-MAIN-20150323172138-00262-ip-10-168-14-71.ec2.internal.warc.gz"}
http://crypto.stackexchange.com/users/452/poncho?tab=activity	poncho Reputation 40,988 99/100 score 1d comment Calculating the average key search time of DES @TalenKylon: well, the most significant bits contribute to the key value (it's the lsbits that are ignored), and so that would reduce the key space to 48 bits. Also, when someone says "ASCII character", they often mean "printable ASCII character", that is, a value between 0x20 and 0x7e; that would reduce the keyspace somewhat more. 1d answered Calculating the average key search time of DES 1d comment Is it possible to apply hill-climbing algorithm to Diffie–Hellman? Actually, it's quite easy to give them a metric with the actual solution as a local maximum. What's difficult is to give a metric that gives a useful indication of "you're close" 1d comment RSA 1024 bit recover private exponent from many signatures Attempting to recover $d$ is a deadend. Instead, you should attempt to figure out how to deduce a signature without knowing $d$. Hint: the relation $a^d \times b^d = (ab)^d \pmod N$ is useful. 1d comment RSA 1024 bit recover private exponent from many signatures There is no known way to recover $d = 3^{-1} \bmod lcm(P-1, Q-1)$ given access to an oracle that computes $f(x) = x^d \bmod N$. Are you sure that your teacher didn't ask you to compute the signature for another message that you haven't been given the signature to? 1d comment Byte size of Diffie-Hellman public values @thotheolh: the obvious way to represent A and B are in arrays of 256 bytes. 1d answered Byte size of Diffie-Hellman public values 2d comment Cipher that XORs each character with another in the string, using character parity to control the offset I rather doubt anything this goofy has a formal name... 2d answered How is RSA able to prevent brute forcing using the public key? Oct 3 comment Why not to use curve over field of $p^m$ with $p > 2$ for ECDSA? "Arithmetic gets more involved for $GF(p^m), m>1$..."; actually, the fastest known curve with circa 128 bit security is FourQ; it has $m=2$ (and $p= 2^{127}-1$) Oct 2 awarded Necromancer Oct 1 comment Combining md5 collisions to create more collisions Short answer: yes. As for how, see: iacr.org/archive/crypto2004/31520306/multicollisions.pdf . With this technique, a billion-way collision is quite feasible. Oct 1 revised Encrypting a 160-bit plaintext into a 160 bit ciphertext with a 128-bit Block Cipher edited tags Oct 1 comment Is it possible to add error propagation to OTP? @RichieFrame: nit, $GF(2^{8})$ multiplication wouldn't work, as a 0 in the pad would kill things. However, $GF(257)$ multiplication (with the convention that the 0x00 byte stands for the value 256) would work. Oct 1 comment Why does GnuPG save an array of remainders when generating prime numbers? @ZachDziura: the general formula is: if bit $i$ corresponds to the integer $ai+b$, then if $b % p = 0$, then set bits $kp$ (for integers $k$ in range), else if $a % p = 0$, then don't set any bits, else set bits $kp + p - (b a^{-1} \bmod p)$. Actually, if both $a % p = 0$ and $b % p = 0$, then no primes will be in range (as $ai + b$ will always be a multiple of $p$; presumably that'll never happen, as $a$ and $b$ must be relatively prime. Oct 1 comment Why does GnuPG save an array of remainders when generating prime numbers? @ZachDziura: actually, you would typically add twice the iteration (as there is little value even numbers. And, you don't divide each of the those numbers by each small prime (that's what you're trying to avoid); instead for each small prime $p$, you compute the initial candidate $prime % p$, and from that deduce which $prime+step$'s would be multiple of $p$. For example, if $p=3$ and $prime % p = 1$, then you know that $prime+2$, $prime+6$, $prime+10$, etc are multiples of 3; you can set those bits in the sieve Oct 1 answered Why does GnuPG save an array of remainders when generating prime numbers? Sep 30 awarded Enlightened Sep 30 awarded Nice Answer Sep 30 reviewed No Action Needed How can cryptographic signatures be somehow linked to a physical signature?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7154010534286499, "perplexity": 1275.7622750072228}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443736679756.40/warc/CC-MAIN-20151001215759-00003-ip-10-137-6-227.ec2.internal.warc.gz"}
https://www.nature.com/articles/s41467-020-16072-4?utm_campaign=MultipleJournals_USG_ECOEVO&utm_source=Nature_community&utm_medium=Community_sites&utm_content=BenJoh-Nature-MultipleJournals-Evolutionary_Biology-Global&error=cookies_not_supported&code=bdd2feb0-174b-4f7d-8a05-57102988c78d	# A mechanistic explanation of the transition to simple multicellularity in fungi ## Abstract Development of multicellularity was one of the major transitions in evolution and occurred independently multiple times in algae, plants, animals, and fungi. However recent comparative genome analyses suggest that fungi followed a different route to other eukaryotic lineages. To understand the driving forces behind the transition from unicellular fungi to hyphal forms of growth, we develop a comparative model of osmotrophic resource acquisition. This predicts that whenever the local resource is immobile, hard-to-digest, and nutrient poor, hyphal osmotrophs outcompete motile or autolytic unicellular osmotrophs. This hyphal advantage arises because transporting nutrients via a contiguous cytoplasm enables continued exploitation of remaining resources after local depletion of essential nutrients, and more efficient use of costly exoenzymes. The model provides a mechanistic explanation for the origins of multicellular hyphal organisms, and explains why fungi, rather than unicellular bacteria, evolved to dominate decay of recalcitrant, nutrient poor substrates such as leaf litter or wood. ## Introduction There is a well-established trend over evolutionary time for organisms to increase in size and complexity1,2, with multicellular lineages emerging independently from unicellular ancestors multiple times in algae, plants, animals, and fungi3,4,5,6,7,8. Plausible mechanistic explanations for the transition to multicellularity have focussed on the potential benefits arising from the division of labour, particularly germ-line and soma9, predator escape10, enhanced stress resistance11, or circumventing diffusion limits for nutrient acquisition or distribution12,13,14. In most eukaryotic lineages, the transition to multicellularity is thought to involve co-option and expansion of gene families for adhesion, signalling, and cell–cell transport12,15, whilst division of labour and differentiation are typically associated with innovation and expansion of new transcription factor families12,15. However, recent comparative genome analyses of fungal lineages do not show a marked increase in gene duplications or the typical proliferation of kinases, receptors, or adhesion protein families expected within this general framework8,16,17. Rather, these studies highlight the importance of co-option and modification of existing gene families, particularly those governing endomembrane complexity, cytoskeletal transport, cell-wall biogenesis, septal pore gating, and osmotrophy8,17,18. The evolution of multicellular fungi was a critical event in the emergence of terrestrial ecosystems19,20,21,22. Extant fungi now account for the second largest fraction of biomass in terrestrial ecosystems after plants23, and they are critically involved in soil formation, wood decomposition, and nutrient cycling24,25,26. Genetic evidence indicates that all fungi are descended from a motile aquatic ancestor27, with subsequent loss of flagella and the development of multicellular hyphal growth linked to adaptation to land environments8,20,21,22,28. Whilst the genomic basis underpinning the transition from a unicellular to a multicellular hyphal state, and subsequent development of complex multi-cellular fruiting bodies is beginning to emerge8,16,17,29, the drivers behind these changes and mechanistic explanations of their success are currently lacking. Many fungi are osmotrophic30 and acquire carbon (C), nitrogen (N), and phosphate (P) from the environment by uptake of low-molecular-weight compounds directly, through solubilisation of mineral phosphate31, or following extracellular digestion using exoenzymes to breakdown high-molecular-weight carbohydrates, organic phosphates, protein, or other recalcitrant polymers such as pectins, chitin, and lignin20,24,26. Indeed, genetic evidence suggests that the production of exoenzymes to digest plant or algal cell walls is an ancestral trait, found in unicellular chytrids28 that predate the earliest forms of hyphal multicellularity, or adaptation to terrestrial environments20,21. Terrestrial mycelial fungi grow by apical extension and branching of hyphae, with coenocytic cell compartments in primitive species, or partitioned by septa in basidiomycetes and ascomycetes, where cytoplasmic continuity is maintained through septal pores32,33,34. The polarised growth and fractal-like branching of mycelial fungi constitute an efficient space-searching strategy35, and large interconnected mycelial networks can span soil gaps and patches of nutrients24,32,36. These distinctive features of fungal growth are evolutionarily adaptive, but they do not explain why fungi and, to a lesser extent, hyphal actinomycetes, rather than unicellular bacteria, evolved to dominate the decay of hard to digest, nutrient-poor substrates. The amount of C, N, and P available depends on the resource environment37, and many environments have a C:N:P ratio that is very different from the optimal ratio for growth. Typical internal C:N and N:P molar ratios for bacteria and fungi themselves also span a wide range from 5-200:1 and 4-20:1, respectively38,39,40. Growth also requires additional acquisition of C to fuel respiration, and carbon use efficiencies (CUE) of 0.5 or less are typical41,42. Cells can survive if they are only supplied with a source of energy (C), but they cannot grow and divide unless they also have a supply of N, P, and other micro-nutrients. It follows that nutrient supply has a critical impact on growth rates. Colonisation of land presents additional challenges as net movement of soluble nutrients is reduced in terrestrial compared to aquatic environments, as the soil pore tortuosity significantly increases the path length for diffusion. Furthermore, the requirement to breakdown C-rich polymers produces even greater spatial inhomogeneities in nutrient concentration as these do not diffuse at all. Here, we develop a modelling framework to compare the predicted growth of hyphal organisms in comparison with immobile, autolytic, or motile unicellular osmotrophs in a wide range of resource environments which differ in the C:N:P ratio and the recalcitrance of the substrate. We show that hyphal osmotrophs outperform unicellular osmotrophs whenever the local resource is immobile, hard-to-digest, and nutrient-poor. This hyphal advantage arises because transporting nutrients via a contiguous cytoplasm enables continued exploitation of remaining resources after local depletion of essential nutrients, so in hyphal organisms, each exoenzyme is of benefit for longer, providing greater total benefit for the same cost. The model provides a mechanistic explanation for the origins of multicellular hyphal organisms, and explains why fungi, rather than unicellular bacteria, evolved to dominate decay of recalcitrant, nutrient-poor substrates such as leaf litter or wood. The model also suggests that multicellular fungi were pre-adapted to form mycorrhizal associations. ## Results ### Nutrient availability limits colony growth Due to the relatively low level of mixing in terrestrial habitats, we note that there are two distinct ways in which the growth of a terrestrial osmotroph may be nutrient-limited. The supply rate can be limiting (too little nutrient obtained for each unit time), or the total local supply may be limiting (only a small amount of nutrient is locally available, however rapidly it is extracted). The contiguous cytoplasm of fungi32,34 or hyphal actinomycetes43,44 enables internal transport, and here we argue that internal transport is evolutionarily adaptive if the growth of the colony is limited by the exhaustion of local nutrient supplies. In particular, we note that when a hyphal organism encounters enough resource to grow exponentially, it can sustain a digestive strategy whereby all nutrients in the substrate are digested, yet over each window of time, the resource acquired by the whole colony has a much better C:N ratio than the substrate (see Fig. 1). This beneficial mismatch in C:N ratios is akin to a biological Ponzi scheme, which can only be sustained as long as the colony has an exponentially expanding feeding surface, with newly grown regions prioritising the acquisition of growth-limiting nutrients. The advantage conferred by a hyphal morphology can be clarified by a simple toy model comparing an established colony of unicellular organisms and an established fungal colony (Fig. 1). Each colony grows through an initially homogeneous environment, consuming the local supply of C and N at a constant rate until the local supply is exhausted. If the substrate has a molar C:N ratio 100:1, but cells only require 10 C atoms for every N atom to match internal demand and respiration, 90% of the carbon in the substrate will be undigested by the time the local supply of N has been exhausted. Once the local supply of N is exhausted unicellular organisms can no longer grow, even though they contain the synthetic machinery needed for growth, and are surrounded by exoenzymes that continue to release a supply of reduced C. In contrast, the N depleted region in a fungal colony can continue to access C, digesting it completely and supplying C to the growing margin by transport through the cytoplasmic continuity of the interconnected network. If the local supply of N becomes exhausted after time T, then at time $$t$$, the volume of territory with an exhausted supply of N is the volume grown at time $$t - T$$. If the growth is exponential with a specific growth rate $$\mu$$, it follows that the fraction of territory with an exhausted supply of N is $$\frac{{e^{\mu (t - T)}}}{{e^{\mu t}}} = e^{ - \mu T}$$. In the extreme case where the time taken to exhaust the local supply of N is equal to the doubling time of the colony ($$T = \frac{{\mathrm{log}(2)}}{\mu }$$), half the colony will have exhausted the local supply of N. If, where both kinds of resource are available, a fungus takes up 10 C atoms for every N atom, the time taken to exhaust the local supply of C will be $$10T$$, only a fraction $$e^{ - 10\mathrm{log}(2)} = 0.1\%$$ of the colony will have exhausted the local supply of C, and the fungal colony will receive almost half its C from the N depleted region. If the fungus digests N at the same rate as unicells, it only has to digest C at half the rate to receive the same overall amount of C and N as the growing part of a colony of unicells, so the fungus requires a much smaller investment in C digesting exoenzymes. Whether the fungal colony receives more carbon for each unit volume, or invests less heavily in C digesting exoenzymes, it obtains an advantage over unicellular competitors, provided that the additional costs of internal transport are covered. ### Nutrient supply and demand depend on strategy for growth To quantify the scale of the advantage conferred by a hyphal morphology in various resource environments, we compare the growth of four categories of osmotrophic organism: immobile cells that occupy new territory solely by growth and division (Fig. 2a); autolytic cells that recycle material from redundant cells once nutrients are exhausted, with the most likely beneficiaries being neighbouring kin45,46 (Fig. 2b); motile cells that are able to migrate to find a new resource (Fig. 2c); and hyphal organisms that grow into new territory but remain connected through the hyphal network (Fig. 2d). Our focus is the competition to capture resource, so we model the early stages of colonisation, before crowding effects limit growth. As a simplifying assumption, we suppose that all organisms, and all generations, capture the same quantity of resource for each unit volume of growth. Thus we assume that each category of model organism grows exponentially on encountering a new resource (Fig. 2). Growth under crowded conditions where organisms overlap makes the model more complex but does not change the overall conclusions (Supplementary Note 8). The rate of substrate digestion depends on the quantity of exoenzymes that have been secreted, and we assume that for each key resource (C, N, P) the local rate of digestion is proportional to the mass of exoenzymes released for each unit volume of organism. Rates of digestion are also inversely proportional to the recalcitrance of the substrate, $$\tau$$, which we define as the time taken for each type of exoenzyme to supply the organism with a mass of nutrients (C, N, or P) equal to the total mass required to synthesise the exoenzyme in question, including the C required for respiration (see Supplementary Table 1 for a description of all model parameters). The time scale $$\tau$$ depends on abiotic factors such as temperature and pH, as well as the efficiency of the exoenzymes, the carbon cost of protein synthesis, and the physical accessibility and chemical composition of the substrate. For the sake of simplicity, we assume that all exoenzymes generate a constant supply of C, N, or P until the local resource is exhausted, at which point the local supply rate is set to zero. We believe this is a reasonable approximation for processive enzymes that break down polymers. However, as N-rich polymers tend to be embedded in a C-rich matrix, a certain amount of C digestion may be required to access the other resources. We consider the consequences of such physical shielding, set by the parameter $$\delta$$, in Supplementary Note 9. Immobile cells grow until they have exhausted the local supply of either C, N, or P, at which point they are no longer able to make any contribution to the growth of the colony (Fig. 2a). Data suggests that when nutritionally stressed cells recycle their nutrient contents through autolysis, the growth rate of neighbouring cells is increased47. In our model, we assume that when autolytic cells (Fig. 2b) exhaust the local resource, they release a fraction $$\varepsilon$$ of the cell’s contents, making that resource freely available to the remaining cells45,46, although any resource used to synthesise the exoenzymes cannot be recouped. The fraction $$\varepsilon$$ is set to 50% here, but this parameter is tunable, and even 100% recovery does not affect the model conclusions (see Supplementary Fig. 1). Motile cells are modelled as switching between two states (Fig. 2c). In state 1 they grow like other cells, but they stop growing when they exhaust the local supply of P, or when there is just enough C and N remaining to synthesise the exoenzymes they will need when they migrate to a new location. In state 2 motile cells synthesise and store those additional exoenzymes, then migrate to a new location, releasing the stored exoenzymes and returning to state 1. For fungi (Fig. 2d), exoenzymes that are initially secreted at the hyphal tip continue to release nutrients as the colony grows. These nutrients can be taken up and transported through the mycelium to the growing margin until they are locally exhausted, allowing complete exploitation of the available resource, even if it comprises a mismatched C:N:P ratio. The total amount of C, N, and P in the environment are set by the model parameters CE, NE, and PE (see Fig. 3) which are varied across a wide range of values spanning the different resource environments found in nature24,38. The density of C, N, and P within immobile cells (CI, NI, PI) are also specified as model parameters (Supplementary Note 1). Since organisms lose C through respiration, growing a unit volume of immobile cell requires a total mass of carbon CT > CI, and this total carbon cost of growing a unit volume is specified by including the CUE as a model parameter. Synthesising motile apparatus requires additional C and N, set to be 2% of the cost of synthesising a cell48, and represented by the parameter $$\alpha$$ (see Fig. 3b). Fungi also incur additional costs as exoenzymes and other materials needed at the tips need to be transported, and, while those materials are in transit, they are not yet helping liberate new food resource. The additional costs associated with internal transport are unknown, but are represented by a tunable parameter $$\beta = 0.1$$, i.e., 10% of the total C and N budget of the cell (see Fig. 3c). The fraction $$\beta$$ can be visualised as the fraction of C and N that is contained in exoenzymes or cell wall material moving within transport vesicles, although in modelling terms, the transported material could equally well be precursors moving cytoplasmically. The critical point is that they are transported over distance. Note that our choice of $$\beta$$ is such that the cost of internal transport is at least 5 times higher than cost of motility, which ‘penalises’ early evolutionary development of a hyphal morphology in comparison with other strategies. We present results for a range of values for $$\beta$$ in Supplementary Figs. 2 and 3. We assume all categories of organism can obtain low molecular weight molecules following digestion by diffusion over an external length scale $$\kappa$$ times greater than the cell radius (see Fig. 3a). The mass of C, N, and P digesting exoenzymes for each unit volume of organism are treated as variables, and in any given case we can calculate the demand for C, N, and P for each unit volume of growth, and the supply rate of C, N, and P for each unit volume of the colony. Thus for each category of organism, and each density of exoenzymes, we can calculate the maximum growth rate, given the mass required for each unit volume of growth, and given that C, N, and P cannot be used more rapidly that they are digested. The maximum growth rate is also constrained by the rates of transcription and translation, so we assume that for any category of organism, the total rate of resource use for each unit volume cannot exceed $$\lambda$$ = 0.3 g ml−1 h−1, as this ensures that the smallest doubling time for any organism in any resource environment is 51 min, which is below the typical shortest doubling time for either prokaryotic or eukaryotic cells expected in the wild49,50,51. In our model, the volume colonised for each unit time will increase in proportion to the size of the colony, and we define the apparent growth rate of a colony as the volume of resource that is colonised for each unit time, for each unit volume that has already been colonised. As our model specifies all the relevant quantities, for any given density of exoenzymes, we can calculate the apparent growth rate of the colony, and thereby find the optimal density of exoenzymes and the maximal rate of colonisation for any given category of organism. The full set of equations describing maximal colony growth for each category of organism are given in Supplementary Notes 2–5. ### Maximal colonisation rates differ between types of organism We compare the relative performance of each class of organism for a wide range of environmental C:N:P ratios and levels of substrate recalcitrance, $$\tau$$. In general, the absolute growth rate of all classes of organism declines as the recalcitrance of the substrate increases, or N or P becomes limiting (Supplementary Fig. 1). However, the relative growth rate, expressed as a ratio, emphasises which organism will perform best in each substrate regime (Fig. 4). The colour coding is presented on a cyan–yellow–magenta scale, and the hue indicates the environments where motile, autolytic, and fungal organisms dominate, respectively, according to the inset colour triangle. We find that for a specific, but broad, set of substrates, fungi can colonise resource significantly faster than motile or autolytic cells (magenta to purple regions in Fig. 4). There is a significant, physiologically relevant region of parameter space where fungi outperform motile and autolytic cells. In general, large C:N ratios, large C:P ratios and highly recalcitrant substrates strongly favour hyphal morphology (Fig. 4), and for C:N:P ratios typical of wood or leaf litter, the apparent growth rate of a fungal colony is significantly higher than the growth rate of any other kind of colony, provided there is sufficient total resource available (Fig. 5e, f). The dominance of fungi in these substrate niches is maintained even if unicells are allowed extremely favourable treatment by relaxing the cost to synthesising motile apparatus ($$\alpha = 0$$), or autolysis is allowed to recoup 100% of the cost of synthesising cells (i.e., $$\varepsilon = 1$$, Supplementary Fig. 2). Furthermore, fungi still compete effectively over a reasonable substrate range even when the cost of transport ($$\beta$$) is increased to 20% of the total (Supplementary Fig. 3). Indeed, in some environments, fungi can grow more than twice as fast as colonies of unicells when 50% of resources are allocated to transport (Supplementary Fig. 4). However, when a unit volume captures less resource than is needed to grow a unit volume (low values of $$\kappa$$, Fig. 5), capturing resource by growth alone is a losing proposition. Under those conditions, motile cells are predicted to dominate (cyan regions in Fig. 4), as they are able to move to multiple sites to access the nutrients needed for duplication, provided that the resource is sufficiently water saturated to enable cell migration52. When the substrate is easy to digest, but the local supply of resource is only just large enough to enable duplication, motile cells and fungi grow equally well, as both strategies can offset their costs and efficiently exploit the substrate, whilst autolytic or immobile cells grow much more slowly (blue regions in Fig. 4). However, when the local supply of resource is large enough to enable multiple cell divisions, colony growth is only slightly limited by the exhaustion of local supplies. Under those circumstances, all organisms can grow close to their maximal rate, but immobile or autolytic cells grow marginally more rapidly as they are not burdened by the additional costs imposed on motile or hyphal organisms (green regions in Fig. 4). Maximal rates of colonisation, and the optimal densities of exoenzymes, vary significantly over different resource environments, with different optima for each category of organism (Fig. 5). In general, there is a minimum amount of total resource required for each type of organism to grow, so the digestion radius $$\kappa$$ must be above some minimum (Fig. 5), where that minimum depends on the C:N:P ratio and density of the available resource. However, motile cells do not have a minimal value of $$\kappa$$, as they can acquire sufficient resources to duplicate by migrating to multiple sites. Above this threshold, growth rates increase with resource availability until the maximum growth rate possible for a given recalcitrance is reached (Supplementary Fig. 1). The digestion rate and rate of colonisation for each environment and type of organism also depend on the amount of exoenzymes secreted. Increasing the density of exoenzymes increases the digestion and supply rate of resource, which enables individual cells to grow more rapidly. However, when growth is limited by C or N, further increasing the density of exoenzymes will reduce the number of daughter cells that can be synthesised using the fixed amount of local resource, and this reduces the overall rate of colonisation (Supplementary Note 2). Hence the optimal density of exoenzymes, and optimal rate of digestion, is generally not the density that enables individual cells to grow as rapidly as possible. Because of their ability to transport nutrients, hyphal organisms reap a greater total benefit from exoenzymes that digest non-rate limiting resource. Hence our model predicts that in most environments, the optimal density of exoenzymes, and optimal rate of digestion, will be higher for hyphal organisms than for colonies of any unicellular organism (Fig. 5). Nevertheless, as the quality and quantity of available resource increases, the additional costs of internal transport reduce the hyphal advantage, and in rich media, such as malt agar, unicellular organisms are predicted to grow faster (Fig. 5d, h). In the early stages of colonisation, none of the cells will have exhausted the local supply of resources. However, we can also consider the case where the resources available to daughter cells are diminished due to overlap with parental cells. In this case, there is a more complex time-dependent decline in the apparent growth rate for each class of organisms, depending on the total supply of resource available (Supplementary Fig. 5). However, as the fraction of the colony that has exhausted some, but not all, essential nutrients is the part that hyphal architecture is able to exploit more effectively, the apparent growth rate of fungi declines to a lesser extent and the hyphal advantage is increased (Supplementary Note 8). The final challenge we consider is the consequence of reduced substrate accessibility, set by the model parameter $$\delta$$, whereby a certain amount of C has to be digested to access N embedded with the wall polymers (Supplementary Note 9). Imposing a constraint on the ratio between the rate of C and N digestion results in fungi generating a greater proportion of excess carbon, compared to other organisms (Supplementary Fig. 7). As we have not modelled any of the potential benefits of obtaining excess C, reduced substrate accessibility inhibits fungal growth more than other classes of organism. Nevertheless, we find that fungi continue to dominate in a similar region of parameter space under this accessibility condition (Supplementary Fig. 8). ## Discussion Our model suggests that when there is a small, exhaustible local supply of some essential nutrient, and a larger supply of other nutrients, it is evolutionarily adaptive for cells to grow as an interconnected network with a common cytoplasmic pool. As growing hyphal organisms contain an expanding volume of cytoplasm, they can only maintain a constant nuclear density by containing multiple nuclei. Hence a transition to hyphal morphologies also entails a transition to either coenocytic, or fully multicellular, modes of life. A mismatch in resource quality versus internal demand is common in many natural environments40,41, but fungi are particularly efficient at exploiting recalcitrant high C:N or N:P resources24,25,42 (Figs. 4 and 5). In general, the exoenzymes of unicellular organisms can contribute to growth for at most time $$T$$ (that is, the time to exhaust the most growth-limiting resource), but by forming an interconnected network that enables the transport of assimilated materials, multicellular fungi effectively extend the useful lifespan of any exoenzyme that digests a non-growth-limiting resource. Hyphal colonies are distinctively able to exploit the region where some but not all nutrients are depleted, and the scale of the benefit associated with a hyphal morphology depends on the relative size of this region (see Fig. 2d). This fraction of the colony will be relatively small if either nutrients in the substrate are plentiful, allowing multiple cell divisions before any part of the colony is nutrient-depleted, or if all nutrients are locally exhausted over a similar time-scale. We also note that if the substrate is easy to digest, and the cost of synthesising exoenzymes is a trivial fraction of the total cost of growth, organisms obtain little benefit from extending the effective life-span of exoenzymes. Thus we argue that a hyphal morphology is evolutionarily adaptive because it enables relatively rapid growth on recalcitrant substrates that require a significant investment in exoenzymes, in which there is a mismatch in nutrient ratios such that some essential nutrient becomes locally exhausted after a small number of cell divisions, while other nutrients remain abundant. This is reflected in the increased investment in exoenzymes (Fig. 5a, b) and relative growth (Fig. 5e, f) for fungi in recalcitrant resources, such as wood and leaf litter, but poor performance in more nutrient-rich substrates, where the additional costs of transport outweigh the benefits (Fig. 5d, h). This explains why in soil, low-quality resources favour fungi, while high-quality resources favour bacteria42. Changes in nutrient quality and availability over the course of decomposition may also explain commonly observed temporal shifts in fungal:bacterial ratios41. Our argument may also explain why some algae that need to search for substrate resources have evolved a siphonous body plan, with multiple nuclei in a common cytoplasmic pool, and a capacity for indeterminate growth in size53. We also note that in liquid niches, where the supply of nutrients to an individual cell does not come from a local, exhaustible, microscopic patch, several fungal lineages, such as yeasts, have streamlined their genomes54 and reverted to a primarily unicellular lifestyle. The advantage of a hyphal morphology is remarkably robust to changes in model parameters, most notably reducing the costs associated with motility ($$\alpha$$, Supplementary Fig. 2), increasing the benefit for autolytic cells ($$\varepsilon$$, Supplementary Fig. 2), increasing the costs of transport ($$\beta$$, Supplementary Figs. 3 and 4), imposing time-varying restrictions on resource availability due to crowding (Supplementary Figs. 5 and 6), or increasing the requirement to digest C to render N accessible ($$\delta$$, Supplementary Figs. 7 and 8). To obtain the hyphal advantage, organisms must be able to transport nutrients across the colony. Both fungi and actinomycetes can transport materials by diffusion and growth-induced mass-flow55,56, but as fungi are eukaryotic, they can also use internal vesicles, the cytoskeleton and motor proteins, which enables greater control over the internal distribution of macromolecules33,34. Expansion in these gene families is associated with the development of multicellularity in fungi8. Thus fungi are able to use C to fuel growth even when the source of C is located millimetres or even metres from the source of other essential nutrients. Our analysis strongly suggests that whenever hyphal colonies emerge, the mature parts will be a source of non-rate limiting resource (C), while the growing margin obtains growth-limiting resource (N or P). This metabolic division of labour may have pre-adapted fungi to develop the mycorrhizal associations found in 85% of extant plant species, whereby N and P acquired by the fungus are traded for C fixed by the plant57. This symbiosis is ancient and can be traced back to the earliest land colonisers19,58, and our model clarifies why filamentous fungi were ideally placed to become nutrient foragers in a symbiotic partnership, once both parties evolved the ability to exchange sugars for P and N. Such exchanges require long-distance bidirectional transport59, which does not yet have a firm, mechanical basis. Nevertheless, bidirectional transport has been observed at both the colony level60,61 and in individual hyphae of both mycorrhizal59 and saprotrophic fungi62. Bidirectional movement by diffusion can also occur at a sub-cellular level within vacuolar networks over short distances63. Although we have not explicitly considered heterogeneous environments containing multiple substrates with differing levels of recalcitrance36, our observations also explain why fungi break down lignin. For unicellular organisms, sources of C can only fuel growth and division for as long as it takes to exhaust the local supply of other essential nutrients. If cells can obtain the C they require by consuming the more readily digestible components of wood, there is no benefit from evolving mechanisms for the breakdown of the most recalcitrant forms of carbon, as the local N will already be exhausted. Conversely, when fungi release enzymes that break down lignin, the growing parts of the colony remain connected to the resulting slow but steady supply of C, and this supply reduces the need to synthesise other C digesting exoenzymes. Our model compares the rate of colonisation of competing osmotrophs, not fitness directly, which is challenging to define for fungi64. Nevertheless, all organisms require a source of C to power metabolism, and we follow Van Valen65,66 in treating competition to capture resource (energy) as a key driver of evolutionary dynamics. In this framework the expansive energy available for growth and reproduction is a good approximation for fitness65,66,67, and circumvents the problem of needing to define and count individuals and their reproductive output central to other fitness measures, which is both conceptually and practically challenging for indeterminate or colonial organisms64,67. Furthermore, the impact of competition for other resources can also be accommodated in the extent that they constrain control of trophic energy65,66. It is argued that natural selection locally maximises the amount of expansive energy for the unit under consideration at a given time scale65,66. Previously we have shown that when the time to reproduce via spores is large compared to the doubling time of a fungal colony, the total energy available for reproduction is maximised when growth rates are (almost) as large as possible68. It follows that when osmotrophs compete for the same resource, the competitor that can grow most rapidly initially is likely to be the most fit in terms of control of C supply. Overall, we suggest that the emergence of hyphal organisms is best explained by changes in the available opportunities for metabolic activity69, instead of viewing hyphal morphology as an evolutionary transition in individuality3,4. The absence of a major transition in individuality is not surprising, as clonal hyphal organisms, in a similar manner to siphonous coenocytic organisms53, have minimal cell–cell conflict and essentially bypass the alignment of fitness stage16, whilst the benefits of long-distance transport of nutrients through the connected cytoplasm directly leads to export-of-fitness at the level of the mycelial network53,70. ## Methods ### Overview of the modelling framework The model has two interacting components, a common resource environment and a representation of each class of organism. The resource environment is defined by five parameters that can be independently varied. The density of C, N, and P in the environment are given by CE, NE, and PE in g ml−1. In practice, these are set by the C:N and N:P ratio of the resource, to allow easy comparison with literature values, and the total resource density in g ml−1. To accommodate different levels of substrate digestibility, each substrate also has a level of recalcitrance, $$\tau$$ (h), which represents the time required for an exoenzyme to supply a mass of C, N, or P equal to the total mass required to synthesise the exoenzyme in question. Finally, the amount of resource available to each unit volume of organism is determined by the relative digestion radius $$\kappa$$. Full details of the parameters and set of equations used in the model are given in the Supplementary Note 1. We assume that the metabolic core of each class of organism has the same density of C, N, and P, which remain fixed in the simulations shown here (CI = 0.165 g ml−1, NI = 0.032 g ml−1, and PI = 0.005 g ml−1). All organisms also have a fixed carbon use efficiency (CUE) of 0.5, defined as the ratio between the C contained in an organism and its exoenzymes, compared to the total C consumed, including the C lost in respiration. The final common parameter is the maximum rate of resource use, $$\lambda$$, set at 0.3 g ml−1 h−1 for all organisms, which constrains the maximal mass of resource any cell can use for each unit time and volume to a reasonable biological limit. Each class of organism, apart from immobile unicells, has one additional parameter that is specific to their characteristic mode of capturing resource. Thus, autolytic cells have a recycling efficiency $$\varepsilon = 0.5$$ which sets the fraction of C, N, and P that is recouped by autolysis. Motile cells include the cost of motility $$\alpha = 0.02$$, which is the mass of C and N required to synthesise motile apparatus, relative to core demand for C and N. Fungal osmotrophs include a transport cost $$\beta = 0.1$$, defined as the mass of C and N being transported (and therefore not active), relative to the total C and N in exoenzymes and the fungal core. To optimise the rate of growth in any given resource environment, immobile cells can only modulate the relative mass of exoenzymes secreted by each unit volume of organism, represented by the variable $$x$$. For any given set of model parameters, and any given value of $$x$$, we can calculate both the mass of resource required to grow a unit volume of organism, and the supply rate of resource for each unit volume of organism. We can therefore calculate the maximal specific growth rate $$\eta$$ for individual growing immobile cells (Supplementary Note 2). However, if only a fraction of the cells in the colony have access to the nutrients needed for growth, the apparent growth rate of the whole colony $$\mu$$ will be significantly smaller than the specific growth rate of individual growing cells $$\eta$$. For any given set of model parameters, we can computationally identify the value of $$x$$ that maximises the apparent growth rate $$\mu$$ (Supplementary Note 3). We follow the same approach for colonies of autolytic cells (Supplementary Note 4), motile cells (Supplementary Note 5), and fungal hyphae (Supplementary Note 6), to identify which class of organism can most rapidly colonise any given resource. The value of the organism-specific parameters can be varied, and we discuss the most appropriate values in Supplementary Note 7. Our main focus is the initial competition to capture resource, so we model the early stages of colonisation when colonies undergo exponential growth, before crowding effects limit growth. Nevertheless, we consider the impact of crowding in Supplementary Note 8, when apparent growth rates become time-varying. We also consider the impact of resource accessibility (Supplementary Note 9), by imposing an additional environmental parameter $$\delta$$. The resource accessibility, $$\delta$$, is the minimum fraction of available C that must be digested in order to access the available N, to reflect that N may be embedded within C-rich polymers. Finally, we comment on our original assumption that all organisms can be modelled with the same CI, NI, and PI, and CUE in Supplementary Note 10. The consequence of varying any of these parameters can be explored using the MATLAB GUI interface or MATLAB scripts that are provided in Supplementary Software 1. ### Reporting summary Further information on research design is available in the Nature Research Reporting Summary linked to this article. ## Data availability The authors confirm that all relevant data are included and fully referenced in the paper and the Supplementary Information files. ## Code availability All programs were written in MATLAB (2019b, The MathWorks, Natick, MA) and are provided as a MATLAB app or a Windows standalone executable program, along with an instruction manual, from the Supplementary Software 1 as a ZIP file or available for download from https://github.com/markfricker/Fungal_multicellularity. ## References 1. 1. Bonner, J. T. The origins of multicellularity. Integr. Biol. 1, 27–36 (1998). 2. 2. Bonner, J. T. Size and Cycle: An Essay on the Structure of Biology, Vol. 2087 (Princeton University Press, 2015). 3. 3. Szathmáry, E. & Smith, J. M. The major evolutionary transitions. Nature 374, 227–232 (1995). 4. 4. Szathmáry, E. Toward major evolutionary transitions theory 2.0. Proc. Natl Acad. Sci. USA 112, 10104–10111 (2015). 5. 5. West, S. A., Fisher, R. M., Gardner, A. & Kiers, E. T. Major evolutionary transitions in individuality. Proc. Natl Acad. Sci. USA 112, 10112–10119 (2015). 6. 6. Niklas, K. J. & Newman, S. A. The origins of multicellular organisms. Evol. Dev. 15, 41–52 (2013). 7. 7. Grosberg, R. K. & Strathmann, R. R. The evolution of multicellularity: a minor major transition? Annu. Rev. Ecol. Evol. Syst. 38, 621–654 (2007). 8. 8. Kiss, E. et al. Comparative genomics reveals the origin of fungal hyphae and multicellularity. Nat. Commun. 10, 4080 (2019). 9. 9. Simpson, C. The evolutionary history of division of labour. Proc. R. Soc. B 279, 116–121 (2012). 10. 10. Boraas, M., Seale, D. & Boxhorn, J. Phagotrophy by a flagellate selects for colonial prey: a possible origin of multicellularity. Evolut. Ecol. 12, 153–164 (1998). 11. 11. Lyons, N. A. & Kolter, R. On the evolution of bacterial multicellularity. Curr. Opin. Microbiol. 24, 21–28 (2015). 12. 12. Knoll, A. H. The multiple origins of complex multicellularity. Annu. Rev. Earth Planet. Sci. 39, 217–239 (2011). 13. 13. Knoll, A. H. & Hewitt, D. Phylogenetic, Functional and Geological Perspectives on Complex Multicellularity 251–270 (MIT Press, Cambridge, 2011). 14. 14. Beaumont, N. Modelling the transport of nutrients in early animals. Evolut. Biol. 36, 256–266 (2009). 15. 15. Rokas, A. The molecular origins of multicellular transitions. Curr. Opin. Genet. Dev. 18, 472–478 (2008). 16. 16. Nagy, L. G., Kovács, G. M. & Krizsán, K. Complex multicellularity in fungi: evolutionary convergence, single origin, or both? Biol. Rev. 93, 1778–1794 (2018). 17. 17. Nguyen, T. A. et al. Innovation and constraint leading to complex multicellularity in the ascomycota. Nat. Commun. 8, 14444 (2017). 18. 18. Jedd, G. Fungal evo-devo: organelles and multicellular complexity. Trends Cell Biol. 21, 12–19 (2011). 19. 19. Heckman, D. S. et al. Molecular evidence for the early colonization of land by fungi and plants. Science 293, 1129–1133 (2001). 20. 20. Lange, L. et al. Origin of fungal biomass degrading enzymes: evolution, diversity and function of enzymes of early lineage fungi. Fungal Biol. Rev. https://doi.org/10.1016/j.fbr.2018.09.001 (2018). 21. 21. Naranjo‐Ortiz, M. A. & Gabaldón, T. Fungal evolution: major ecological adaptations and evolutionary transitions. Biol. Rev. 94, 1443–1476 (2019). 22. 22. Berbee, M. L., James, T. Y. & Strullu-Derrien, C. Early diverging fungi: diversity and impact at the dawn of terrestrial life. Annu. Rev. Microbiol. 71, 41–60 (2017). 23. 23. Bar-On, Y. M., Phillips, R. & Milo, R. The biomass distribution on earth. Proc. Natl Acad. Sci. USA 115, 6506–6511 (2018). 24. 24. Boddy, L. & Watkinson, S. C. Wood decomposition, higher fungi, and their role in nutrient redistribution. Can. J. Bot. 73, S1377–S1383 (1995). 25. 25. Gadd, G. Fungi in Biogeochemical Cycles (Cambridge University Press, Cambridge, 2006). 26. 26. van der Wal, A., Geydan, T. D., Kuyper, T. W. & de Boer, W. A thready affair: linking fungal diversity and community dynamics to terrestrial decomposition processes. FEMS Microbiol. Rev. 37, 477–494 (2013). 27. 27. Liu, Y. J., Hodson, M. C. & Hall, B. D. Loss of the flagellum happened only once in the fungal lineage: phylogenetic structure of kingdom fungi inferred from RNA polymerase II subunit genes. BMC Evol. Biol. 6, 74 (2006). 28. 28. Chang, Y. et al. Phylogenomic analyses indicate that early fungi evolved digesting cell walls of algal ancestors of land plants. Genome Biol. Evol. 7, 1590–1601 (2015). 29. 29. Krizsán, K. et al. Transcriptomic atlas of mushroom development reveals conserved genes behind complex multicellularity in fungi. Proc. Natl Acad. Sci. USA 116, 7409–7418 (2019). 30. 30. Richards, T. A. & Talbot, N. J. Osmotrophy. Curr. Biol. 28, R1179–R1180 (2018). 31. 31. Ceci, A., Pinzari, F., Russo, F., Maggi, O. & Persiani, A. M. Saprotrophic soil fungi to improve phosphorus solubilisation and release: in vitro abilities of several species. Ambio 47, 30–40 (2018). 32. 32. Fricker, M. D., Heaton, L. L., Jones, N. S. & Boddy, L. The mycelium as a network. Microbiol. Spectrum https://doi.org/10.1128/microbiolspec.FUNK-0033-2017 (2017). 33. 33. Riquelme, M. et al. Fungal morphogenesis, from the polarized growth of hyphae to complex reproduction and infection structures. Microbiol. Mol. Biol. Rev. 82, e00068-17 (2018). 34. 34. Roper, M., Lee, C., Hickey, P. C. & Gladfelter, A. S. Life as a moving fluid: fate of cytoplasmic macromolecules in dynamic fungal syncytia. Curr. Opin. Microbiol. 26, 116–122 (2015). 35. 35. Hanson, K. et al. Fungi use efficient algorithms for the exploration of microfluidic networks. Small 2, 1212–1220 (2006). 36. 36. Boddy, L. Saprotrophic cord-forming fungi: meeting the challenge of heterogeneous environments. Mycologia 91, 13–32 (1999). 37. 37. Xu, X., Thornton, P. E. & Post, W. M. A global analysis of soil microbial biomass carbon, nitrogen and phosphorus in terrestrial ecosystems. Glob. Ecol. Biogeogr. 22, 737–749 (2013). 38. 38. Cleveland, C. C. & Liptzin, D. C:N:P stoichiometry in soil: is there a Redfield ratio for the microbial biomass? Biogeochemistry 85, 235–252 (2007). 39. 39. Zhang, J. & Elser, J. J. Carbon: nitrogen: phosphorus stoichiometry in fungi: a meta-analysis. Front. Microbiol. 8, 1281 (2017). 40. 40. Mouginot, C. et al. Elemental stoichiometry of fungi and bacteria strains from grassland leaf litter. Soil Biol. Biochem. 76, 278–285 (2014). 41. 41. Manzoni, S., Jackson, R. B., Trofymow, J. A. & Porporato, A. The global stoichiometry of litter nitrogen mineralization. Science 321, 684–686 (2008). 42. 42. Soares, M. & Rousk, J. Microbial growth and carbon use efficiency in soil: links to fungal-bacterial dominance, SOC-quality and stoichiometry. Soil Biol. Biochem. 131, 195–205 (2019). 43. 43. Claessen, D., Rozen, D. E., Kuipers, O. P., Søgaard-Andersen, L. & van Wezel, G. P. Bacterial solutions to multicellularity: a tale of biofilms, filaments and fruiting bodies. Nat. Rev. Microbiol. 12, 115–124 (2014). 44. 44. Lewin, G. R. et al. Evolution and ecology of actinobacteria and their bioenergy applications. Annu. Rev. Microbiol. 70, 235–254 (2016). 45. 45. Vostinar, A. E., Goldsby, H. J. & Ofria, C. Suicidal selection: programmed cell death can evolve in unicellular organisms due solely to kin selection. Ecol. Evol. 9, 9129–9136 (2019). 46. 46. Durand, P. M., Sym, S. & Michod, R. E. Programmed cell death and complexity in microbial systems. Curr. Biol. 26, R587–R593 (2016). 47. 47. Benomar, S. et al. Nutritional stress induces exchange of cell material and energetic coupling between bacterial species. Nat. Commun. 6, 6283 (2015). 48. 48. Macnab, R. Escherichia coli and Salmonella: cellular and molecular biology. In Flagella and Motility 123–145 (ASM Press, Washington, D.C., 1996). 49. 49. Gibson, B., Wilson, D. J., Feil, E. & Eyre-Walker, A. The distribution of bacterial doubling times in the wild. Proc. R. Soc. B 285, 20180789 (2018). 50. 50. Zakhartsev, M. & Reuss, M. Cell size and morphological properties of yeast Saccharomyces cerevisiae in relation to growth temperature. FEMS Yeast Res. 18, foy052 (2018). 51. 51. Rousk, J. & Bååth, E. Growth of saprotrophic fungi and bacteria in soil. FEMS Microbiol. Ecol. 78, 17–30 (2011). 52. 52. Dechesne, A., Wang, G., Glez, G., Or, D. & Smets, B. F. Hydration-controlled bacterial motility and dispersal on surfaces. Proc. Natl Acad. Sci. USA 107, 14369–14372 (2010). 53. 53. Niklas, K. J., Cobb, E. D. & Crawford, D. R. The evo-devo of multinucleate cells, tissues, and organisms, and an alternative route to multicellularity. Evol. Dev. 15, 466–474 (2013). 54. 54. Nagy, L. G. et al. Latent homology and convergent regulatory evolution underlies the repeated emergence of yeasts. Nat. Commun. 5, 4471 (2014). 55. 55. Heaton, L., López, E., Maini, P. K., Fricker, M. D. & Jones, N. S. Growth-induced mass flows in fungal networks. Proc. R. Soc. B 277, 3265–3274 (2010). 56. 56. Heaton, L. L., Lopez, E., Maini, P. K., Fricker, M. D. & Jones, N. S. Advection, diffusion, and delivery over a network. Phys. Rev. E 86, 021905 (2012). 57. 57. Field, K. J. & Pressel, S. Unity in diversity: structural and functional insights into the ancient partnerships between plants and fungi. New Phytol. 220, 996–1011 (2018). 58. 58. Hibbett, D. S., Gilbert, L.-B. & Donoghue, M. J. Evolutionary instability of ectomycorrhizal symbioses in basidiomycetes. Nature 407, 506 (2000). 59. 59. Whiteside, M. D. et al. Mycorrhizal fungi respond to resource inequality by moving phosphorus from rich to poor patches across networks. Curr. Biol. 29, 2043–2050 (2019). 60. 60. Frey, S. D., Six, J. & Elliott, E. T. Reciprocal transfer of carbon and nitrogen by decomposer fungi at the soil-litter interface. Soil Biol. Biochem. 35, 1001–1004 (2003). 61. 61. Lindahl, B., Finlay, R. & Olsson, S. Simultaneous, bidirectional translocation of 32P and 33P between wood blocks connected by mycelial cords of Hypholoma fasciculare. New Phytol. 150, 189–194 (2001). 62. 62. Schmieder, S. S. et al. Bidirectional propagation of signals and nutrients in fungal networks via specialized hyphae. Curr. Biol. 29, 217–228 (2019). 63. 63. Darrah, P. R., Tlalka, M., Ashford, A., Watkinson, S. C. & Fricker, M. D. The vacuole system is a significant intracellular pathway for longitudinal solute transport in basidiomycete fungi. Eukaryot. Cell 5, 1111–1125 (2006). 64. 64. Pringle, A. & Taylor, J. W. The fitness of filamentous fungi. Trends Microbiol. 10, 474–481 (2002). 65. 65. Van Valen, L. Evolution as a zero-sum game for energy. Evolut. Theory 4, 289–300 (1980). 66. 66. Van Valen, L. Energy and evolution. Evolut. Theory 1, 179–229 (1976). 67. 67. Simpson, C. The major transitions in evolution revisited. In How Many Levels are There? How Insights from Evolutionary Transitions in Individuality Help Measure the Hierarchical Complexity of Life 19–34 (MIT Press, Cambridge, 2011). 68. 68. Heaton, L. L., Jones, N. S. & Fricker, M. D. Energetic constraints on fungal growth. Am. Nat. 187, E27–E40 (2016). 69. 69. OMalley, M. A. & Powell, R. Major problems in evolutionary transitions: how a metabolic perspective can enrich our understanding of macroevolution. Biol. Philos. 31, 159–189 (2016). 70. 70. Knoll, A. & Lahr, D. Fossils, feeding, and the evolution of complex multicellularity. In The Vienna Series in Theoretical Biology 1–16 (MIT Press, Boston, 2016). ## Acknowledgements This work was supported by the Human Frontier Science Program (RGP0053/2012) and the Leverhulme Trust (RPG-2015-437). The authors would also like to thank Lynne Boddy, Stuart West, Alistair Green, Ferdinando Insalata, and Ashleigh Griffin for their helpful comments. ## Author information Authors ### Contributions All authors contributed to the conception and interpretation of the model. All authors wrote and revised the manuscript. L.L.M.H. developed the model code and M.D.F. developed the GUI. ### Corresponding author Correspondence to Mark D. Fricker. ## Ethics declarations ### Competing interests The authors declare no competing interests. Peer review information Nature Communications thanks László Nagy, Karl Niklas and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ## Rights and permissions Reprints and Permissions Heaton, L.L.M., Jones, N.S. & Fricker, M.D. A mechanistic explanation of the transition to simple multicellularity in fungi. Nat Commun 11, 2594 (2020). https://doi.org/10.1038/s41467-020-16072-4 • Accepted: • Published: • ### Syncytia in Fungi • Alexander P. Mela • & N. Louise Glass Cells (2020) • ### Fungi took a unique evolutionary route to multicellularity: Seven key challenges for fungal multicellular life • László G. Nagy • , Torda Varga • , Árpád Csernetics • & Máté Virágh Fungal Biology Reviews (2020) • ### Mosaic fungal individuals have the potential to evolve within a single generation • Maura G. Tyrrell • , Diane C. Peabody • , Robert B. Peabody • , Magdalena James-Pederson • , Rachel G. Hirst • , Elisha Allan-Perkins • , Heather Bickford • , Amy Shafrir • , Robert J. Doiron • , Amber C. Churchill • , Juan Carlos Ramirez-Tapia • , Benjamin Seidel • , Lynes Torres • , Kathryn Fallavollita • , Thomas Hernon • , Lindsay Wiswell • , Sarah Wilson • , Erica Mondo • , Kathleen Salisbury • , Carrie Peabody • , Patrick Cabral • , Lauren Presti • , Kelsey McKenna-Hoffman • , Michele Flannery • , Kaitlin Daly • , Darius Haghighat • & Daniel Lukason Scientific Reports (2020)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8287975788116455, "perplexity": 4923.503498477283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141189030.27/warc/CC-MAIN-20201126230216-20201127020216-00105.warc.gz"}
http://psjd.icm.edu.pl/psjd/element/bwmeta1.element.bwnjournal-article-appv96z301kz	PL EN Preferences Language enabled [disable] Abstract Number of results Journal ## Acta Physica Polonica A 1999 \| 96 \| 3-4 \| 327-331 Article title ### Simplified Solving Procedure for the One-Dimensional Schrodinger Equation with Asymmetrical Boundary Conditions Authors Content Title variants Languages of publication EN Abstracts EN We propose a new simplified procedure for finding the analytical solutions of the stationary one-dimensional Schrodinger equation, with asymmetric boundary conditions imposed on the equation. The essence of the method consists in expressing the general solution explicitly in terms of the boundary parameters in a form which, by itself, satisfies one of the boundary conditions involved; then, the other boundary condition gives straightforwardly the characteristic equation. This method may turn out to be beneficial with regard to the recently growing interest in one-dimensional quantum systems. Keywords EN Discipline Publisher Journal Year Volume Issue Pages 327-331 Physical description Dates published 1999-09	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8534877300262451, "perplexity": 944.646424333648}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141681209.60/warc/CC-MAIN-20201201170219-20201201200219-00003.warc.gz"}
https://uk.mathworks.com/help/physmod/sdl/ref/beltdrive.html	# Belt Drive Power transmission system with taut belt connecting two pulleys • Library: • Simscape / Driveline / Couplings & Drives ## Description The Belt Drive block represents a pair of pulleys connected with a flexible ideal, flat, or V-shaped belt. The ideal belt does not slip relative to the pulley surfaces. The model accounts for friction between the flexible belt and the pulley periphery. If the friction force is not sufficient to drive the load, the model allows slip. The relationship between the tensions in the tight and loose branches conforms to the Euler equation. The model accounts for centrifugal loading in the flexible belt, pulley inertia, and bearing friction. The Belt Drive block is a structural component based on the Simscape™ Driveline™ Belt Pulley block and Simscape Translational Spring and Translational Damper blocks. The Translational Spring and Translational Damper blocks model the compliance of the belt. For the equations governing the contact dynamics between the belt and the pulley, see the Belt Pulley block. The figure shows the block diagram for the Belt Drive block. ### Equations The diagrams show the open and crossed belt drive configurations. In the open belt configuration, both pulleys tend to rotate in the same direction and the larger pulley has a larger belt wrap angle. In the crossed belt configuration, the pulleys tend to rotate in opposite directions and have the same wrap angle. Belt Drive Diagrams In the open configuration, the wrap angle of the belt around each pulley is given by the expressions: `$\begin{array}{l}{\theta }_{A}=\pi +2\ast {\mathrm{sin}}^{-1}\frac{{R}_{A}-{R}_{B}}{C},\\ {\theta }_{B}=\pi -2\ast {\mathrm{sin}}^{-1}\frac{{R}_{A}-{R}_{B}}{C}\end{array}$` where: • θA is the wrap angle of pulley A. • θB is the wrap angle of pulley B. • RA is the effective radius of pulley A. • RB is the effective radius of pulley B. • C is the distance between the centers of pulleys A and B. The diagram shows the open-configuration wrap angles and parameters. In the crossed configuration, the two wrap angles are equal and the wrap angle of the belt around each pulley is `${\theta }_{A}={\theta }_{B}=\pi +2\ast {\mathrm{sin}}^{-1}\frac{{R}_{A}+{R}_{B}}{C}$` The diagram shows the closed-configuration wrap angles and parameters. ## Assumptions and Limitations • The pulleys do not translate. • The friction coefficient and friction velocity threshold between the belt and each of the pulleys is the same. ## Ports ### Conserving expand all Rotational conserving port associated with the shaft of pulley A. Rotational conserving port associated with the shaft of pulley B. ## Parameters expand all ### Belt Belt model: • `Ideal - No slip` — Model an ideal belt, which does not slip relative to the pulley. • `Flat belt` — Model a belt with a rectangular cross-section. • `V-belt`— Model a belt with a V-shaped cross-section. #### Dependencies This parameter affects the visibility of related belt parameters and the Contact settings. Compliance model. • ```No compliance - Suitable for HIL simulation``` — Model a noncompliant belt, which does not yield elastically when subjected to a force. To prioritize performance, select this model. • `Specify stiffness and damping` — Model a compliant belt, which does yield elastically when subjected to a force. To prioritize fidelity, select this model. #### Dependencies This parameter is visible only if Belt type is set to `Ideal - No slip`. This parameter affects the visibility of related belt parameters. Sheave angle of the V-belt. #### Dependencies This parameter is visible only when Belt type is set to `V-belt`. Number of V-belts. Noninteger values are rounded to the nearest integer. Increasing the number of belts increases the friction force, effective mass per unit length, and maximum allowable tension. #### Dependencies This parameter is visible only when Belt type is set to `V-belt`. Centrifugal force model. If included, centrifugal force saturates to approximately 90 percent of the value of the force on each belt end. #### Dependencies This parameter is visible only if Belt type is set to `Flat belt` or `V-belt`. If this parameter is set to `Model centrifugal force`, the Belt mass per unit length parameter is exposed. Centrifugal force contribution in terms of linear density expressed as mass per unit length. #### Dependencies Selecting `Model centrifugal force` for the Centrifugal force parameter exposes this parameter. Effective stiffness of the belt. #### Dependencies This parameter not visible if Belt type is set to `Ideal - No slip` and Compliance is set to ```No compliance - Suitable for HIL simulation```. Effective damping of the belt. #### Dependencies This parameter not visible if Belt type is set to `Ideal - No slip` and Compliance is set to ```No compliance - Suitable for HIL simulation```. Tension in the belt when the belt and pulleys are at rest. The value must be positive. #### Dependencies This parameter not visible if Belt type is set to `Ideal - No slip` and Compliance is set to ```No compliance - Suitable for HIL simulation```. Tension threshold model. If ```Specify maximum tension``` is selected and the belt tension on either end of the belt meets or exceeds the value that you specify for Belt maximum tension, the simulation stops and generates an assertion error. #### Dependencies This parameter not visible if Belt type is set to `Ideal - No slip` and Compliance is set to ```No compliance - Suitable for HIL simulation```. For all three belt types, selecting ```Specify maximum tension``` exposes the Belt maximum tension parameter. Maximum allowable tension for each belt. When the tension on either end of the belt meets or exceeds this value, the simulation stops and generates an assertion error. #### Dependencies This parameter not visible if Belt type is set to `Ideal - No slip` and Compliance is set to ```No compliance - Suitable for HIL simulation```. For all three belt types, the Belt maximum tension parameter is visible only when the Maximum tension parameter is set to `Specify maximum tension`. ### Pulley A Viscous friction associated with the bearings that hold the axis of the pulley. Rotational inertia model. #### Dependencies Selecting ```Specify inertia and initial velocity``` exposes the Pulley inertia and Pulley initial velocity parameters. Rotational inertia of the pulley. #### Dependencies Selecting ```Specify inertia and initial velocity``` for the Inertia parameter exposes this parameter. Initial rotational velocity of the pulley. #### Dependencies Selecting ```Specify inertia and initial velocity``` for the Inertia parameter exposes this parameter. ### Pulley B Viscous friction associated with the bearings that hold the axis of the pulley. ```Specify inertia and initial velocity```— To models rotational inertia. Exposes the Pulley inertia and Pulley initial velocity parameters. #### Dependencies Selecting ```Specify inertia and initial velocity``` exposes the Pulley inertia and Pulley initial velocity parameters. Rotational inertia of the pulley. #### Dependencies Selecting ```Specify inertia and initial velocity``` for the Inertia parameter exposes this parameter. Initial rotational velocity of the pulley. #### Dependencies Selecting ```Specify inertia and initial velocity``` for the Inertia parameter exposes this parameter. ### Contact Coulomb friction coefficient between the belt and the pulley surface. Default is `0.5`. Whether the block calculates the wrap angle of the belt on the pulleys using the pulley radii, center separation, and drive type or if the wrap angles are specified directly. Options are: • ```Specify pulley center separation``` — The block calculates the wrap angle of the belt on the pulleys using the pulley radii, center separation, and drive type. Exposes the Pulley center separation parameter. • `Specify wrap angles` — The block uses the wrap angles that you specify. #### Dependencies Selecting ```Specify pulley center separation``` exposes the Pulley center separation parameter. Selecting `Specify wrap angles` exposes the Pulley A wrap angle and Pulley B wrap angle parameters. Distance between the centers of the pulleys. #### Dependencies The Pulley center separation parameter is visible only when the Wrap angle calculation parameter is ```Specify pulley center separation```. Angle of contact between the belt and pulley attached to port A. #### Dependencies The Pulley A wrap angle parameter is visible only when the Wrap angle calculation parameter is `Specify wrap angles`. Angle of contact between the belt and pulley attached to port B. The Pulley B wrap angle parameter is visible only when the Wrap angle calculation parameter is `Specify wrap angles`. Relative velocity required for peak kinetic friction in the contact. The friction velocity threshold improves the numerical stability of the simulation by ensuring that the force is continuous when the direction of the velocity changes. expand all	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7066826820373535, "perplexity": 3374.0202071407793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243990419.12/warc/CC-MAIN-20210511214444-20210512004444-00365.warc.gz"}
https://brilliant.org/discussions/thread/oh-yfracm_0c2sqrt1-v2c2ah/	× # OH Y$$\frac{m_0c^2}{\sqrt{1-v^2/c^2}}$$AH! :D 1 year, 11 months ago Sort by: Next step: Fields Medal :D · 1 year, 11 months ago Reminds me of a Good Will Hunting scene ^.^ Anyway thank you and everyone else! I shared this exclusively on Brilliant because I knew there are people who truly care and understand. Like, why are rock and ruler the best friend? Because And you are both ;) · 1 year, 11 months ago $\huge CONGRATULATIONS \ ! \$ · 1 year, 11 months ago Didn't want to make a separate note on this, but check this out: "Just a theory." "Simply exploded." This is what they call science "education." Makes me cringe. · 1 year, 11 months ago This reads like something being taught in certain schools that don't want its kids to accept the Big Bang theory. In other words, it seems intended to induce a lot of eye-rolling. · 1 year, 10 months ago They should start every science class explaining why Theory > Fact. But then try teach Big Bang and Evolution in some schools and... uh-oh. You better have Richard Dawkins somewhere in proximity. Or me ^.^ · 1 year, 10 months ago "Just a Theory". And so, "Electromagnetic Theory", "Special Theory of Relativity", "Quantum Field Theory", "Information Theory", even "Theory of Gravity" are all "just theories", i.e. it's just a guess, nothing proven here, nothing to see, move on please. "Oh, you know! It's just a theory, we don't know yet if it's true!" I used to watch science fiction movies about dystopian futures where science is dismissed, laughed at, and even made criminal. Sometimes science fiction movies can be prophetic. You think "science being made criminal" is too far fetched? In some southern states of America, it's now a criminal offense for scientists and engineers working for states to even discuss or write about rising ocean levels because of global warming. They can now be prosecuted for that. · 1 year, 10 months ago The United States?? PROSECUTED?! What states?? · 1 year, 10 months ago Read this as just one example: Scientific American A number of other states have passed similar with varying degrees of enforcement/penalties. It's basically a gag law. It's not much different from what happens if you agree to abide by certain conditions when you're hired to work for a corporation, including confidentiality, and then you violate that agreement. · 1 year, 10 months ago Ah I see. Basically they prohibit scientists from releasing any studies that inform about global warming. Why am I not surprised. No wonder I didn't do well in the Harvard Model Congress this year. I am a scientist who tried to do politics. You can imagine how that went. · 1 year, 10 months ago Wait... WHAT?! · 1 year, 10 months ago I seem to recall that Florida has passed a even stiffer gag law, and somebody lost his state job because of it. Stories like this keep cropping up, I can't remember all of them. The Catastrophe That Must Not Be Named · 1 year, 10 months ago Yea I've read an article written by a conservative the other day, asserting global warming is a "religion," not a fact. It ended with "God bless America." Oh the irony. · 1 year, 10 months ago This is why I go for the Steady State Theory instead · 1 year, 10 months ago I could make out what the first para wants to convey regarding the relation between data and theory. "simply exploded" thing...might depend on the audience being targeted. · 1 year, 11 months ago Alright... seriously... what, at all, does that GIF have to do with what I said or what you said?! · 1 year, 11 months ago umm...forget the gif...i find that face funny :D that's all.... · 1 year, 11 months ago Wow! Congrats John :) · 1 year, 11 months ago I think you're the only one to find crazier gif's than I. And ty :) · 1 year, 11 months ago Now that's my Prize : · 1 year, 11 months ago "The Ralph A. Rodriguez Memorial Award is presented to a graduating senior who has demonstrated both love of and aptitude in the area of Mathematical Science" is a thing, at the top of a list of 36 items approved by the Hoboken High School Board of Education. Hey, that's pretty good. · 1 year, 11 months ago How do you know what school I go to?? · 1 year, 11 months ago It's right on the plaque? But, true, maybe your reputation is so far and wide that the Hoboken Board of Education has decided to make this award to you even though you're attending Miami High School. · 1 year, 11 months ago Ooh... no I think from your unintentional mistake you unintentionally guessed the name of my high school - which is literally Hoboken High School. Well now it's Hoboken Junior/Senior High School now that they brought in the 7th graders but noone really calls it that ;p It's Hoboken Board of Education - not Hoboken High School Board of Education - they aren't separate. But honestly I hope I don't get THAT famous. Ugh... "CAN I HAVE YOUR AUTOGRAPH!!!" Lol. · 1 year, 11 months ago In any case, "Hoboken High" sounds like something out of the Harry Potter books. I can't keep track of either. · 1 year, 11 months ago Did you see the Go Noobs Weekly, by the way? It is in fact considered by many to be the hardest puzzle OF ALL TIME. Took a group of [educated] students over 1000 hours to solve. Now obviously it ain't the hardest - we still gotta solve the Riemann Hypothesis - but you get the case. It's hard. So if you ever need to fit a hard [doable] problem on a small paper, just print this :D And I really wonder who went around disliking all these comments. Haters, haters everywhere. But · 1 year, 11 months ago I see it now, the Go game puzzle. · 1 year, 11 months ago You deserve it! :D · 1 year, 11 months ago Great Congrats! Sir.The speed of light(c) can never defeat you :) · 1 year, 11 months ago My heartfelt Congratulations to you , Sir! · 1 year, 11 months ago	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21680690348148346, "perplexity": 4784.056229795339}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607242.32/warc/CC-MAIN-20170522230356-20170523010356-00114.warc.gz"}
https://downloads.haskell.org/ghc/latest/docs/libraries/base-4.17.0.0/GHC-MVar.html	base-4.17.0.0: Basic libraries GHC.MVar Contents Description The MVar type Synopsis # MVars data MVar a Source # An MVar (pronounced "em-var") is a synchronising variable, used for communication between concurrent threads. It can be thought of as a box, which may be empty or full. Constructors MVar (MVar# RealWorld a) #### Instances Instances details Eq (MVar a) Source # Since: base-4.1.0.0 Instance detailsDefined in GHC.MVar Methods(==) :: MVar a -> MVar a -> Bool Source #(/=) :: MVar a -> MVar a -> Bool Source # newMVar :: a -> IO (MVar a) Source # Create an MVar which contains the supplied value. Create an MVar which is initially empty. takeMVar :: MVar a -> IO a Source # Return the contents of the MVar. If the MVar is currently empty, takeMVar will wait until it is full. After a takeMVar, the MVar is left empty. There are two further important properties of takeMVar: • takeMVar is single-wakeup. That is, if there are multiple threads blocked in takeMVar, and the MVar becomes full, only one thread will be woken up. The runtime guarantees that the woken thread completes its takeMVar operation. • When multiple threads are blocked on an MVar, they are woken up in FIFO order. This is useful for providing fairness properties of abstractions built using MVars. readMVar :: MVar a -> IO a Source # Atomically read the contents of an MVar. If the MVar is currently empty, readMVar will wait until it is full. readMVar is guaranteed to receive the next putMVar. readMVar is multiple-wakeup, so when multiple readers are blocked on an MVar, all of them are woken up at the same time. Compatibility note: Prior to base 4.7, readMVar was a combination of takeMVar and putMVar. This mean that in the presence of other threads attempting to putMVar, readMVar could block. Furthermore, readMVar would not receive the next putMVar if there was already a pending thread blocked on takeMVar. The old behavior can be recovered by implementing 'readMVar as follows: readMVar :: MVar a -> IO a a <- takeMVar m putMVar m a return a putMVar :: MVar a -> a -> IO () Source # Put a value into an MVar. If the MVar is currently full, putMVar will wait until it becomes empty. There are two further important properties of putMVar: • putMVar is single-wakeup. That is, if there are multiple threads blocked in putMVar, and the MVar becomes empty, only one thread will be woken up. The runtime guarantees that the woken thread completes its putMVar operation. • When multiple threads are blocked on an MVar, they are woken up in FIFO order. This is useful for providing fairness properties of abstractions built using MVars. tryTakeMVar :: MVar a -> IO (Maybe a) Source # A non-blocking version of takeMVar. The tryTakeMVar function returns immediately, with Nothing if the MVar was empty, or Just a if the MVar was full with contents a. After tryTakeMVar, the MVar is left empty. tryPutMVar :: MVar a -> a -> IO Bool Source # A non-blocking version of putMVar. The tryPutMVar function attempts to put the value a into the MVar, returning True if it was successful, or False otherwise. tryReadMVar :: MVar a -> IO (Maybe a) Source # A non-blocking version of readMVar. The tryReadMVar function returns immediately, with Nothing if the MVar was empty, or Just a if the MVar was full with contents a. Since: base-4.7.0.0 Check whether a given MVar is empty. Notice that the boolean value returned is just a snapshot of the state of the MVar. By the time you get to react on its result, the MVar may have been filled (or emptied) - so be extremely careful when using this operation. Use tryTakeMVar instead if possible. addMVarFinalizer :: MVar a -> IO () -> IO () Source # Add a finalizer to an MVar (GHC only). See Foreign.ForeignPtr and System.Mem.Weak for more about finalizers.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29422643780708313, "perplexity": 7569.51101456155}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499713.50/warc/CC-MAIN-20230129112153-20230129142153-00030.warc.gz"}
http://math.stackexchange.com/users/3711/ghshtalt?tab=activity&sort=posts	ghshtalt Reputation 1,063 Top tag Next privilege 2,000 Rep. Sep 22 asked Why exactly can you take the absolute value of one side of this inequality and assume it is still true? Sep 20 asked Why is it that $\left\|b_n - b \right\| < \frac{\left\|b \right\|}{2} \Rightarrow \left\| b_n \right\| > \frac{\left\|b \right\|}{2}$? Sep 7 asked What is the explanation for the elements of this set? Aug 19 asked What are the explanations for certain steps in these proofs for the irrationality/rationality of certain numbers? Jul 5 asked For which $k \in \mathbb{R}$ will this be a euclidean vector space? Jul 3 asked Help understanding this example of a linear operator which rotates each vector $v$ about the z-axis by an angle $\theta$ Jun 30 asked Understanding this partial derivative problem Jun 4 asked Does this equality always hold? May 14 asked Are bounded sequences always strictly less than some fixed number $M$? May 6 asked Who was the mathematician who thought “god” was out to get him? Apr 26 asked How is it shown that a Hermitian matrix will be positive definite? Apr 23 asked What is the difference between finding a basis for a complex and a real space? Apr 17 asked How to show certain things related to scalar products Apr 17 asked Subtraction and division with integers modulo 3 Apr 16 asked How do you show this property of a differentiable function given information about the derivative? Apr 10 asked What is the best way to show that no positive powers of this matrix will be the identity matrix? Mar 29 asked Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$? Mar 13 asked Proving elementary inverse image consequence Mar 7 asked Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$ Feb 12 asked Why is the 'change-of-basis matrix' called such?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5278238654136658, "perplexity": 433.4159567440896}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860114649.41/warc/CC-MAIN-20160428161514-00079-ip-10-239-7-51.ec2.internal.warc.gz"}
http://mathonline.wikidot.com/series-convergence-and-divergence-practice-examples-2	Series Convergence and Divergence Practice Examples 2 # Series Convergence and Divergence Practice Examples 2 We will now look at some more examples of applying the various convergence/divergence tests we have looked at so far to some series without being given what test to apply specifically. More examples of evaluating series can be found on the following page: ## Example 1 Does the series $\sum_{n=1}^{\infty} \frac{100^n}{n!}$ converge or diverge? Our first though is to apply the ratio test, that is: (1) \begin{align} \quad \lim_{n \to \infty} \frac{\frac{100^{n+1}}{(n+1)!}}{\frac{100^n}{n!}} = \lim_{n \to \infty} \frac{100^{n+1}n!}{100^n (n+1)!} = \lim_{n \to \infty} \frac{100}{n+1} = 0 = L \end{align} Since $0 ≤ L < 1$, we have that $\sum_{n=1}^{\infty} \frac{100^n}{n!}$ converges by the ratio test. ## Example 2 Does the series $\sum_{n=1}^{\infty} \frac{1+n}{2+n}$ converge or diverge? Notice that $\lim_{n \to \infty} \frac{1+n}{2+n} = \lim_{n \to \infty} \frac{\frac{1}{n} + 1}{\frac{2}{n} + 1} = 1$, so $\sum_{n=1}^{\infty} \frac{1+n}{2+n}$ diverges by the divergence test. ## Example 3 Does the series $\sum_{n=1}^{\infty} \frac{1 + \sin n}{n^3}$ converge or diverge? We note that $0 ≤ 1 + \sin n ≤ 2$ for all $n \in \mathbb{N}$. So we have that $\frac{1 + \sin n}{n^3} ≤ \frac{2}{n^3}$. By the comparison test, we know that $\sum_{n=1}^{\infty} \frac{2}{n^3}$ is convergent, and since $\sum_{n=1}^{\infty} \frac{1 + \sin n}{n^3} ≤ \sum_{n=1}^{\infty} \frac{2}{n^3}$, then $\sum_{n=1}^{\infty} \frac{1 + \sin n}{n^3}$ is also convergent. ## Example 4 Does the series $\sum_{n=1}^{\infty} \frac{1}{2^n(n+1)}$ converge or diverge? Applying the ratio test we get that: (2) \begin{align} \quad \lim_{n \to \infty} \frac{\frac{1}{2^{n+1}(n+2)}}{\frac{1}{2^n(n+1)}} = \lim_{n \to \infty} \frac{2^n(n+1)}{2^{n+1}(n+2)} = \lim_{n \to \infty} \frac{n+1}{2n + 4} = \lim_{n \to \infty} \frac{1 + \frac{1}{n}}{2 + \frac{4}{n}} = \frac{1}{2} = L \end{align} Since $0 ≤ L < 1$, by the ratio test we get that $\sum_{n=1}^{\infty} \frac{1}{2^n(n+1)}$ converges. Note that we could have also applied the root test as follows (omitting to show that $\lim_{n \to \infty} (1 + n)^{1/n} = 1$): (3) \begin{align} \quad \lim_{n \to \infty} \biggr \rvert \frac{1}{2^n(n+1)} \biggr \rvert^{1/n} = \lim_{n \to \infty} \left ( \frac{1}{2^n(n+1)} \right)^{1/n} = \lim_{n \to \infty} \frac{1}{2(n+1)^{1/n}} = \frac{1}{2} \cdot \frac{1}{\lim_{n \to \infty} (n+1)^{1/n}} = \frac{1}{2} \cdot 1 = \frac{1}{2} = L \end{align} Once again since $0 ≤ L < 1$, by the root test we get that $\sum_{n=1}^{\infty} \frac{1}{2^n(n+1)}$ converges. ## Example 5 Does the series $\sum_{n=1}^{\infty} \frac{1}{\pi^n + 5}$ converge or diverge? We note that $\frac{1}{\pi^n + 5} < \frac{1}{\pi^n} = \left ( \frac{1}{\pi} \right)^n$. We note that $\sum_{n=1}^{\infty} \left ( \frac{1}{\pi} \right)^n$ is a convergent geometric series since the common ratio $\mid r \mid = \biggr \rvert \frac{1}{\pi} \biggr \rvert < 1$, and so by the comparison test since $\sum_{n=1}^{\infty} \frac{1}{\pi^n + 5} < \sum_{n=1}^{\infty} \left ( \frac{1}{\pi} \right)^n$ we have that $\sum_{n=1}^{\infty} \frac{1}{\pi^n + 5}$ converges. Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9998176693916321, "perplexity": 402.4700526285754}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578711882.85/warc/CC-MAIN-20190425074144-20190425100144-00474.warc.gz"}
https://grindskills.com/tag/biopotential/	## Alternative definitions of potential? I hope this question is simple and can be quickly cleared up. In a 1D conservative dynamical system, I’ve always been taught that the potential function is the function V(x) such that: F=−dVdx That makes sense to me, simply derived from the definitions of work and conservation of energy. However, just reading through the book … Read more ## Why is the zero of electric potential taken to be r=∞r = \infty, rather than r=0?r = 0? Wouldn’t it make more sense if it was taken to be zero at r=0? This seems to imply that with a negative test charge at r=0 from a positive point charge, V=−∞, which I have trouble conceptualizing properly. Is that accurate? Is there a better way to look at it? Answer You evidently understand that … Read more ## Why is voltage described as potential energy per charge? Voltage is often called an electromotive force since it causes a flow of charge. However, it is described in terms of Joules per Coulomb or Potential Energy per Charge. Question: How does the potential energy associated with charge contribute to its effect on the flow of charge? High voltage, or high electromotive force, causes high … Read more ## From Poisson’s equation to Laplace’s equation [closed] Closed. This question needs details or clarity. It is not currently accepting answers. Want to improve this question? Add details and clarify the problem by editing this post. Closed 2 years ago. Improve this question I want to understand how exactly ∇2V=−ρϵ0 turns into ∇2V=0. Of course it is by setting ρ equal to 0 … Read more ## Is the vector potential component AϕA_\phi for a dipole necessarily 0 due to symmetry about the zz-axis? Consider an electric dipole (+q(t), –q(t)) [where say q(t)=q0cosωt] is placed along the ˆz axis. In the spherical polar coordinates, its vector potential →A=Arˆr+Aθˆθ+Aϕˆϕ at any point M said to only be a function of r (radial distance) and θ. However, from here my professor directly concluded that the component along ˆϕ i.e., Aϕ should … Read more ## Why does the potential across the terminals of battery increase on moving from negative terminal to positive terminal? I really want to know that how does battery create a potential difference across the circuit. When we cross the battery from its negative terminal to positive terminal the potential rises by the voltage mentioned on the battery . So what exactly happens between the terminals so that the potential rises ?I know that the … Read more ## Laplace’s equation: Why is ℓ\ell to be a non-negative integer? I have got some mathematical difficulties in the following exercise: Calculate the potential of the polarized sphere along the z-axis. There are no free charges. For this, we need to solve Laplace’s equation, by using the method of separation of variables. ϕ(r,θ,ϕ)=R(r)Θ(θ) We obtain a partial differential equation on r and θ: 1R∂∂rr2∂∂rR=ℓ(ℓ+1) 1Θ1sinθ∂∂θsinθ∂∂θΘ=−ℓ(ℓ+1). My … Read more ## Point charge potential (sign problem) I’m a bit embarrassed, but I’m not able to compute the electric potential at point P (at a distance R from the origin) generated by a positive unitary point charge in the origin with the right sign. Simply use the definition V(P)=−∫P∞→E⋅d→l, forgetting the constant and choosing a straight line to integrate from infinity (so … Read more ## Electric potential vs potential difference What is the difference between electric potential and potential difference? In our course book, they are given as separate topics but their definition is given the same. Answer What is the difference between “electric potential” and “potential difference”? What is the difference between age and age difference? If age(person) is the function so that age(you) … Read more ## Is voltage electric potential or electric potential difference? On Wikipedia, voltage is defined to be the electric potential difference. However, I am still not certain as to whether voltage is the electric potential (PE/q) or electric potential change (ΔPE/q). My confusion partially comes from talking about circuits and defining the amount of volts a point in a circuit has. So, is voltage electric … Read more	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8856040835380554, "perplexity": 588.1097879412675}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337339.70/warc/CC-MAIN-20221002181356-20221002211356-00238.warc.gz"}
http://www.markleweeklydigest.org/2013/01/does-peer-production-represent-radical.html	## Thursday, January 3, 2013 ### Does Peer Production Represent a Radical Break with Capitalism? From the article: “While practically and empirically the P2P mode of production is still under the sway of capitalism and to a great extent dependent on it (buying computers and other materials and services from it and using its infrastructure), its logic radically contradicts that of capital. I described briefly above major aspects of P2P that accord to Marx’s understanding of communism. All these aspects contradict the logic of capital. Here I will show how the logic of P2P profoundly contradicts the capitalist division of labour, because division of labour is the key component of any mode of production. Let me emphasize that in P2P we have a distribution of labour and not a division of labour (Weber, 2004). The P2P modes of cooperation and the distribution of products make micro (within separate production units) and macro (among different units) capitalist divisions of labor superfluous.” Read more	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8642237186431885, "perplexity": 3630.4125377476553}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487608702.10/warc/CC-MAIN-20210613100830-20210613130830-00348.warc.gz"}
https://tex.stackexchange.com/questions/207908/change-font-size-in-chapter-title-without-affecting-running-headers-book-class/207910	# Change Font Size in Chapter Title without affecting Running Headers (Book Class) Actually, I'm using the bookest class but it inherits book class commands. The documentation is sparse, unfortunately, and CTAN's book class manual seems to be misfiled (downloading the documentation from the book class reveals a pdf about writing classes in general). I would like to change the font size of the chapter title without affecting the size of the running headers. There has to be a simple way of doing this. For: \chapter{THIS CHAPTER TITLE IS TOO LONG} substituting: \chapter{\huge THIS CHAPTER TITLE IS TOO LONG} affected the running headers. Or with the package titlesec. This allows to change the format in a way more flexible. \documentclass{book} \usepackage{titlesec} \titleformat{\chapter}[display]{\bfseries\huge}{\chaptertitlename\space\thechapter}{20pt}{\huge}{} \begin{document} \chapter{THIS CHAPTER TITLE IS TOO LONG} Text \chapter{THIS CHAPTER TITLE IS OTHER TOO LONG} Text\newpage Text \end{document} The chapter font is already \Huge in book class. Do you really want to change it? There are few ways. One is to use sectsty \documentclass{book} \usepackage{lipsum} \usepackage{sectsty} \chapterfont{\huge} \begin{document} \chapter{THIS CHAPTER TITLE IS TOO LONG} \lipsum \chapter{Some Chapter} \lipsum \end{document} Another one is to use the optional argument to \chapter \chapter[THIS CHAPTER TITLE IS TOO LONG]{\huge THIS CHAPTER TITLE IS TOO LONG} hence it is used for running headings, toc etc.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8669701218605042, "perplexity": 2817.8800928434766}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668561.61/warc/CC-MAIN-20191115015509-20191115043509-00225.warc.gz"}
https://cran.microsoft.com/snapshot/2020-12-01/web/packages/MoMPCA/vignettes/MoMPCA.html	set.seed(42) library(MoMPCA) library(aricode) ## Description MMPCA is a package to perform clustering of count data based on the mixture of multinomial PCA model. It integrates a dimension reduction aspect by factorizing the multinomial parameters in a latent space, like Latent Dirichlet Allocation of Blei et. al. It specially conceived for low sample high-dimensional data. Due to the intensive nature of the greedy algorithm, it is not suited for large sample size. ## Dataset The package contains attached data in BBCmsg. It consists in 4 text document already preprocessed with the tm package. It is mostly useful for the simulate_BBC() function. data("BBCmsg") ## Demonstration for document clustering Start by generating data from the MMPCA model with a particular $$\theta^\star$$ and $$\beta^\star$$. For more detail, check experimental section of the paper. N = 200 L = 250 simu <- simulate_BBC(N, L, epsilon = 0, lambda = 1) Ytruth <- simu$Ytruth Then perform clustering t0 <- system.time(res <- mmpca_clust(simu$dtm.full, Q = 6, K = 4, Yinit = 'random', method = 'BBCVEM', max.epochs = 7, keep = 1, verbose = 2, nruns = 2, mc.cores = 2) ) print(t0) #> user system elapsed #> 0.032 0.008 73.242 ### Results analysis tab <- knitr::kable(table(res@clustering, Ytruth), format = 'markdown') print(tab) #> #> #> \| 1\| 2\| 3\| 4\| 5\| 6\| #> \|--:\|--:\|--:\|--:\|--:\|--:\| #> \| 0\| 0\| 0\| 0\| 32\| 0\| #> \| 0\| 33\| 0\| 0\| 0\| 3\| #> \| 0\| 0\| 26\| 0\| 0\| 0\| #> \| 35\| 0\| 0\| 0\| 0\| 0\| #> \| 0\| 0\| 0\| 36\| 0\| 34\| #> \| 1\| 0\| 0\| 0\| 0\| 0\| cat('Final ARI is ', aricode::ARI(res@clustering, Ytruth)) #> Final ARI is 0.767059 Other visualization are also accessible from the plot function. Which takes several arguments ggtopics <- plot(res, type = 'topics') print(ggtopics) ggbound <- plot(res, type = 'bound') print(ggbound) ## Model selection The package contains a convenient wrapper around mmpca_clust() which performs model selection over a grid of values for $$(K,Q)$$. Here is the results for Qs = 5:7 and Ks = 3:5. t1 <- system.time(res <- mmpca_clust_modelselect(simu$dtm.full, Qs = 5:7, Ks = 3:5, Yinit = 'kmeans_lda', init.beta = 'lda', method = 'BBCVEM', max.epochs = 7, nruns = 3, verbose = 1) ) print(t1) best_model = res$models print(best_model)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8210456967353821, "perplexity": 5456.349703111124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949701.0/warc/CC-MAIN-20230401032604-20230401062604-00515.warc.gz"}
https://dlennon.org/page/20210201_censor	× ### Dustin Lennon ##### Applied Scientistdlennon.org (206) 291-8893 censored data likelihood distribution derivation event data Doubly and Randomly Censored Data A derivation of the density functions and likelihood expression associated with doubly and randomly censored data. Dustin Lennon February 2021 https://dlennon.org/20210201_censor February 2021 Abstract #### Abstract Censored data is an artifact of partial or incomplete measurements. A typical scenario would be a survival analysis of time to event data. For example, a study may end before a final measurement is available (right censoring). Another situation might occur when batch processing log file data: the reported timestamp might reflect the time of processing and not the true event time (left censoring). This post derives the density equations for censored data. Given a parameterization $\theta$, this leads naturally to a log likelihood formulation. As the censoring mechanism is, in general, random, we further allow for the possibility that this too depends on $\theta$. Doubly Censored Data #### Doubly Censored Data ##### Notation Let $\rvz$ be the uncensored random variable; $\rvl$ and $\rvr$, the left and right censoring thresholds respectively; $\rvd$, an observed random variable denoting whether $\rvz$ was uncensored(0), censored only on the left (1), censored only on the right (2), or censored on both left and right (3). Let $\rvy$ be the observed value associated with each value of $\rvd$. We define this accordingly: $\rvy = \begin{cases} \rvz & \rvd = 0 \\ \rvl & \rvd = 1 \\ \rvr & \rvd = 2 \\ (\rvl, \rvr) & \rvd = 3 \end{cases}$ The last case addresses the scenario where a non-negative random variable has limited precision: for example, when measurements are only accurate above some threshold, it may be more sensible to proceed as though we know only that these values fall below the threshold. ##### Density Calculations We assume that $\rvl, \rvr, \rvz$ are independent with distributions $G_L, G_R, F$, respectively. Then, ###### Uncensored, $\rvd = 0$: $\prob{ \rvl < \rvz < \rvr } = \int f(u) G_L(u) (1 - G_R(u)) \,du$ ###### Only left censored, $\rvd = 1$: $\prob { \left(\rvz \leq \rvl\right) \cap \left(\rvz < \rvr \right)} = \int g_L(u) \underbrace{ \int_{-\infty}^u f(v) (1-G_R(v)) \, dv }_{ I_1(u) } \, du$ ###### Only right censored, $\rvd = 2$: $\prob { \left(\rvl < \rvz \right) \cap \left(\rvr \leq \rvz \right)} = \int g_R(u) \underbrace{ \int_u^{\infty} f(v) G_L(v) \, dv }_{ I_2(u) } \, du$ ###### Left and right censored, $\rvd = 3$: $\prob { \left(\rvz \leq \rvl \right) \cap \left(\rvr \leq \rvz \right)} = \iint 1_{\left\{ v < u\right\}}(u,v) g_L(u) g_R(v) (F(u) - F(v)) \,du \,dv$ Note that the events above are a partition of the underlying probability space. A Simple Example #### A Simple Example We consider the following model, taking $\mu = 1$ and assuming known variances: $\begin{gather} \rvz \sim N\left(\mu, 1.0^2 \right), \\ \rvl \sim N\left(\frac{\mu}{2}, 0.25^2\right), \\ \rvr \sim N\left(2 \mu, 1.0^2\right). \end{gather}$ We implement this in Python as such: """ Define the random variables """ import numpy as np import pandas as pd import scipy.stats mu = 1.0 Z = scipy.stats.norm(loc=mu, scale=1.0) Yl = scipy.stats.norm(loc=0.5mu, scale=0.25) Yr = scipy.stats.norm(loc=2.0mu, scale=1.0) (F,f) = (Z.cdf, Z.pdf) (Gl,gl) = (Yl.cdf,Yl.pdf) (Gr,gr) = (Yr.cdf, Yr.pdf) ##### Simluated Maximum Likelihood Estimates We treat the events above as a multinomial random variable and compute the standard ML estimators below. """ Simulated ML estimates """ rng = np.random.default_rng(seed=42) n = int(1e6) rZ = Z.rvs(size=n, random_state = rng) rYl = Yl.rvs(size=n, random_state = rng) rYr = Yr.rvs(size=n, random_state = rng) d0_idx = ((rYl < rZ) & (rZ < rYr)) d1_idx = ((rYl >= rZ) & (rZ < rYr)) d2_idx = ((rYl < rZ) & (rZ >= rYr)) d3_idx = ((rZ < rYl) & (rZ > rYr)) p0 = d0_idx.sum() / n p1 = d1_idx.sum() / n p2 = d2_idx.sum() / n p3 = d3_idx.sum() / n ps = [p0,p1,p2,p3] ##### Direct Numerical Integration While slow, we may also evaluate the above probabilities directly via numerical integration. These are computed as follows. """ Direct numerical integration """ fn0 = lambda u: Gl(u) * f(u) * (1-Gr(u)) q0, _ = quad(fn0, -np.inf, np.inf) fn1 = lambda v,u: gl(u) * f(v) * (1-Gr(v)) q1, _ = dblquad(fn1, -np.inf, np.inf, gfun = lambda v: -np.inf, hfun = lambda u: u) fn2 = lambda v,u: gr(u) * f(v) * Gl(v) q2, _ = dblquad(fn2, -np.inf, np.inf, gfun = lambda u: u, hfun = lambda u: np.inf) fn3 = lambda v,u: gl(u) * gr(v) * (F(u) -F(v)) q3, _ = dblquad(fn3, -np.inf, np.inf, gfun = lambda u: -np.inf, hfun = lambda u: u) qs = [q0,q1,q2,q3] """ Comparing simulated estimates and direct calculations """ df = pd.DataFrame({ 'MLE' : ps, 'Direct' : qs }) df.index.name ='D' df MLE Direct D 0 0.456583 0.456117 1 0.304057 0.304133 2 0.229668 0.230070 3 0.009692 0.009680 ##### Loglikelihood The loglikelihood can be read off directly from the densitity equations above. The only complication that arises is to efficiently evaluate the inner integrals, $I_1(u)$ and $I_2(u)$. """ Loglikelihood calculation """ rdf = pd.DataFrame({ 'Yl' : rYl, 'Z' : rZ, 'Yr' : rYr } ) u = rdf.loc[d0_idx,'Z'] ll0 = Z.logpdf(u) + Yl.logcdf(u) + np.log( 1 - Yr.cdf(u) ) u = rdf.loc[d1_idx,'Yl'] ll1 = Yl.logpdf(u) + np.log(I1(u)) u = rdf.loc[d2_idx,'Yr'] ll2 = Yr.logpdf(u) + np.log(I2(u)) u = rdf.loc[d3_idx,'Yl'] v = rdf.loc[d3_idx,'Yr'] ll3 = Yl.logpdf(u) + Yr.logpdf(v) + np.log( Z.cdf(u) - Z.cdf(v) ) ll = ll0.sum() + ll1.sum() + ll2.sum() + ll3.sum() ll -1747157.5396823618	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.817575216293335, "perplexity": 11041.094504901985}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00534.warc.gz"}
http://math.stackexchange.com/questions/463483/circle-formula-given-two-points-and-a-manipulable-radius/463737	# Circle formula given two points and a manipulable radius I need to find the formula for a specific circle. I know two points that is on the circle: (1,2) and (10,16) I need to be able to manipulate the radius, so that I can find the formula that I am looking for. i.e: I will put this formula in excel, and then see what are the y values of x being 2 to 9 if I have a radius of 10 or 15 or 18 or 200. Hope my question makes sense, I appreciate any help. - What do you want to get from the formula? The center of the circle? – bubba Aug 9 '13 at 10:26 The center of the circle can move along the line (perpendicular bisector) which is orthogonal to the connection between $(1;2)$ and $(10;16)$. The general equation of a circle is: $$(X - M_x)^2 + (Y - M_y)^2 = r^2$$ $$(1 - M_x)^2 + (2 - M_y)^2 = r^2$$ $$(10 - M_x)^2 + (16 - M_y)^2 = r^2$$ or \begin{align}1 - 2M_x + M_x^2 + 4 - 4M_y + M_y^2 & = r^2\\ 100 - 20M_x + M_x^2 + 256 - 32M_y + M_y^2 & = r^2\end{align} Subtracting the second equation from the first: $$-99 + 18M_x - 252 +28M_y = 0$$ Hence, we get linear expression for $M_y$ you could use in Excel: $$M_y = - \frac{18}{28}M_x + \frac{351}{28}$$ Squared radius $r^2$ can be determined from the circle equation: $$r^2 = (1 - M_x)^2 + (1 - M_y)^2$$ For $r = 10, 15, 18, 200$ the squared radius would be $100, 225, 324, 4000$. \begin{aligned} r^2 & = (1 - M_x)^2 + (- \frac{323}{28} + \frac{18}{28}M_x)^2 \\ & = 1 - 2M_x + M_x^2 + \frac{104329}{784} - \frac{11808}{784}M_x + \frac{324}{784}M_x^2\\ & = \frac{324}{784}M_x^2 - \frac{11024}{784}M_x + \frac{105113}{784} \end{aligned} This allows us to derive $M_x$ from $r^2$. Note that two solutions exist as the center of the circle can bei either on the right or on the left of $(9.5; 9)$. Asking WolframAlpha reveals another formula suitable for Excel: $$M_x = \frac{14\sqrt{1108r^2-93025} + 3299}{554}$$ To finally compute the $Y_i$ values corresponding to your $X_i$ values: $$Y_i = M_y \pm \sqrt{r^2 - (X_i - M_x)^2}$$ -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9263923764228821, "perplexity": 385.17433564553085}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657138980.37/warc/CC-MAIN-20140914011218-00246-ip-10-234-18-248.ec2.internal.warc.gz"}
https://arxiv-export-lb.library.cornell.edu/abs/2205.11301	math.FA (what is this?) # Title: $\clw$-hypercontractions and their model Abstract: We revisit the study of $\omega$-hypercontractions corresponding to a single weight sequence $\omega=\{\omega_k\}_{k\geq0}$ introduced by Olofsson in \cite{O} and find an analogue of Nagy-Foias characteristic function in this setting. Explicit construction of characteristic functions is obtained and it is shown to be a complete unitary invariant. By considering a multi-weight sequence $\clw$ and $\clw$-hypercontractions we extend Olofsson's work \cite{O} in the multi-variable setting. Model for $\clw$-hypercontractions is obtained by finding their dilations on certain weighted Bergman spaces over the polydisc corresponding to the multi-weight sequence $\clw$. This recovers and provides a different proof of the earlier work of Curto and Vasilescu \cite{CVPoly, CV} for $\gamma$-contractive multi-operators through a particular choice of multi-weight sequence. Comments: 31 pages, updated version, comments are welcome Subjects: Functional Analysis (math.FA) MSC classes: 47A13, 47A20, 47A45, 47A56, 46E22, 47B32 Cite as: arXiv:2205.11301 [math.FA] (or arXiv:2205.11301v2 [math.FA] for this version) ## Submission history From: Monojit Bhattacharjee [view email] [v1] Mon, 23 May 2022 13:40:52 GMT (42kb) [v2] Wed, 25 May 2022 08:37:24 GMT (42kb) Link back to: arXiv, form interface, contact.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4088801145553589, "perplexity": 4716.754748895381}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710870.69/warc/CC-MAIN-20221201221914-20221202011914-00541.warc.gz"}
https://talkstats.com/threads/reg-ex-question.76203/	# Reg ex Question #### jamesmartinn ##### Member Hi! I have a string, that follows a predictable format, and I'm looking to replace certain characters in it. Please see below. Any help is appreciated. Code: > have <- "_a _a_1 _a_2 _a_3" > have [1] "_a _a_1 _a_2 _a_3" What I need to do is remove the initial underscore in each space delimited chunk, while keeping any underscores in the string. E.g. Code: > want <- "a a_1 a_2 a_3" > want [1] "a a_1 a_2 a_3" I have a list of 4-5 patterns that I've solved using {stringr} and / or gsub() and this is the only one I can't get. I realized I could break the string up into space delimited bits and use substr to cleave off the first character, but I'm wondering if there is a more elegant way? Any help is appreciated! #### Dason In regular expressions \b matches the beginning and end of a word i.e. space, tab or newline, or the beginning or end of a string. So in R we just need to escape that and then add the underscore and replace all of that with nothing. Code: x <- "_a _a_1 _a_2 _a_3" gsub("\\b_", "", x) #[1] "a a_1 a_2 a_3" #### jamesmartinn ##### Member In regular expressions \b matches the beginning and end of a word i.e. space, tab or newline, or the beginning or end of a string. So in R we just need to escape that and then add the underscore and replace all of that with nothing. Code: x <- "_a _a_1 _a_2 _a_3" gsub("\\b_", "", x) #[1] "a a_1 a_2 a_3" Thank you for the quick reply, Dason! You have no idea how much you've simplified my day... (after a very long and exhausting work week)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6066802740097046, "perplexity": 3179.250595337746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991378.48/warc/CC-MAIN-20210515070344-20210515100344-00479.warc.gz"}
https://seniorwopolu.pl/event-created/year	p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 p w ś c p s n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9298791289329529, "perplexity": 7070.390644145578}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104585887.84/warc/CC-MAIN-20220705144321-20220705174321-00700.warc.gz"}
http://math.stackexchange.com/questions/264221/non-discrete-locally-compact-group	Non-discrete locally compact group Why every non-discrete locally compact group contains a nontrivial convergent sequence? - Please only use $\LaTeX$ to format mathematics. – Arthur Fischer Dec 23 '12 at 18:39 in myresearch i got it – Wreza Shafaghi Dec 23 '12 at 19:16 This seems like the sort of question whose answer might be found in the first couple of chapters of Differential Geometry, Lie Groups, and Symmetric Spaces by Helgason. (I don't have a copy with me or else I'd have checked.) – Neal Dec 23 '12 at 20:50 It seems that non-discreteness implies that any neighborhood of identity contains infinitely many distinct elements, and compactness allows you to choose a convergent sequence out of them... – user53153 Dec 23 '12 at 21:58 @PavelM No, as compact does not imply sequentially compact in general. – Henno Brandsma Dec 23 '12 at 21:58 This is true. The difficulty is the case in which the group is not metrizable: Pavel M (and Henno Brandsma) noted that if $G$ is a metrizable locally compact group without isolated points then every neighborhood $U$ of the neutral element is infinite, so it suffices to choose an infinite sequence in a compact $U$ and extract a convergent subsequence. In the general case, I doubt that there is a simple proof, although I think the following argument is far from optimal. 1. Let $G$ be a locally compact group and let $U$ be a compact symmetric neighborhood of the identity. Then $H = \bigcup_{n=1}^\infty U^n$ is a $\sigma$-compact clopen subgroup of $G$. If $H$ is metrizable then $U$ must be metrizable Pavel M's observation does the job. If $H$ is not metrizable, then it contains a compact normal subgroup $K$ such that $H/K$ is metrizable. See Hewitt-Ross, Abstract Harmonic analysis I, Theorem 8.7. Note that $K$ can't be finite (or even metrizable) because otherwise $H$ would have to be metrizable. Therefore $K$ has no isolated points. 2. Kuz'minov proved the remarkable fact that a compact group $K$ is a dyadic space, i.e., a continuous image of the Cantor cube $\{0,1\}^\kappa$ for some $\kappa$. See Chapter III of Stevo Todorcevic, Topics in topology for a proof. 3. Katetov and Efimov independently proved that in a dyadic space every non-isolated point is the limit of a non-trivial sequence. See Cor. 2 on page 301 of Engelking, Cartesian products and dyadic spaces, Fund. Math. 57 (1964), 287-304. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9688732624053955, "perplexity": 155.15725641297362}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398451648.66/warc/CC-MAIN-20151124205411-00329-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.dpmms.cam.ac.uk/person/jg900	# Department of Pure Mathematics and Mathematical Statistics Research Interests: ## Publications Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction J Guerand, M Koumaiha – Numerische Mathematik (2019) 142, 525 C1.14 01223 765886	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.935364305973053, "perplexity": 7304.807387910275}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250598217.23/warc/CC-MAIN-20200120081337-20200120105337-00492.warc.gz"}
https://arxiv.org/list/math.MG/1911	# Metric Geometry ## Authors and titles for math.MG in Nov 2019 [ total of 58 entries: 1-25 \| 26-50 \| 51-58 ] [ showing 25 entries per page: fewer \| more \| all ] [1] Title: A Hyperbolic View of the Seven Circles Theorem Subjects: Metric Geometry (math.MG); History and Overview (math.HO) [2] Title: Traces of Newton-Sobolev, Hajlasz-Sobolev and BV functions on metric spaces Subjects: Metric Geometry (math.MG); Analysis of PDEs (math.AP); Functional Analysis (math.FA) [3] Title: Metric thickenings and group actions Subjects: Metric Geometry (math.MG); Algebraic Topology (math.AT); Geometric Topology (math.GT) [4] Title: Pythagorean Theorem & curvature with lower or upper bound Subjects: Metric Geometry (math.MG) [5] Title: On the systole growth in congruence quaternionic hyperbolic manifolds Subjects: Metric Geometry (math.MG); Geometric Topology (math.GT) [6] Title: On equicontinuity of families of mappings with a fixed point of a domain Subjects: Metric Geometry (math.MG); Complex Variables (math.CV) [7] Title: Diophantine approximations, large intersections and geodesics in negative curvature Subjects: Metric Geometry (math.MG) [8] Title: Sequences of three dimensional manifolds with positive scalar curvature Comments: 27 pages , 6 figures Subjects: Metric Geometry (math.MG); General Relativity and Quantum Cosmology (gr-qc); Differential Geometry (math.DG) [9] Title: New Multivalued Contractions and the Fixed-Circle Problem Subjects: Metric Geometry (math.MG) [10] Title: Discrete variants of Brunn-Minkowski type inequalities Subjects: Metric Geometry (math.MG); Probability (math.PR) [11] Title: Optimal monohedral tilings of hyperbolic surfaces Comments: 23 pages, 9 figures. arXiv admin note: text overlap with arXiv:1910.12966 Subjects: Metric Geometry (math.MG) [12] Title: Relating Notions of Convergence in Geometric Analysis Subjects: Metric Geometry (math.MG); Differential Geometry (math.DG) [13] Title: Iterations of curvature images Subjects: Metric Geometry (math.MG); Analysis of PDEs (math.AP); Differential Geometry (math.DG) [14] Title: Morse Quasiflats Comments: Preliminary Version. 98 pages Subjects: Metric Geometry (math.MG); Differential Geometry (math.DG); Group Theory (math.GR); Geometric Topology (math.GT) [15] Title: Duality of moduli in regular metric spaces Subjects: Metric Geometry (math.MG) [16] Title: Assouad dimension influences the box and packing dimensions of orthogonal projections Subjects: Metric Geometry (math.MG) [17] Title: Inscribed rectangles in a smooth Jordan curve attain at least one third of all aspect ratios Authors: Cole Hugelmeyer Subjects: Metric Geometry (math.MG); Geometric Topology (math.GT) [18] Title: On the Assouad dimension and convergence of metric spaces Authors: Yoshito Ishiki Subjects: Metric Geometry (math.MG) [19] Title: Convexity of sets in metric Abelian groups Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA) [20] Title: Dual quadrangles in the plane Comments: 9 pages, 9 figures Subjects: Metric Geometry (math.MG) [21] Title: Volume product and Lipschitz-free spaces Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA) [22] Title: A characterization of metric subspaces of full Assouad dimension Authors: Yoshito Ishiki Subjects: Metric Geometry (math.MG) [23] Title: Estimation of the distance between two bodies inside an $n$-dimensional ball of unit volume Comments: 6 pages, in Russian, The work was carried out with the help of the Russian Science Foundation Grant N 17-11-01377 Subjects: Metric Geometry (math.MG); Combinatorics (math.CO) [24] Title: Integral geometry of pairs of hyperplanes or lines Subjects: Metric Geometry (math.MG) [25] Title: Vertical quasi-isometries and branched quasisymmetries Comments: 50 pages, 1 figure Subjects: Metric Geometry (math.MG); Complex Variables (math.CV) [ total of 58 entries: 1-25 \| 26-50 \| 51-58 ] [ showing 25 entries per page: fewer \| more \| all ] Disable MathJax (What is MathJax?) Links to: arXiv, form interface, find, math, 1912, contact, help (Access key information)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.743126630783081, "perplexity": 14933.370704106168}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541297626.61/warc/CC-MAIN-20191214230830-20191215014830-00435.warc.gz"}
http://math.stackexchange.com/questions/50394/what-to-call-the-initial-members-of-an-ordered-set	# What to call the initial members of an ordered set? If I have an ordered set X = {a, b, c} and another ordered set Y = {a, b}, I know that that Y is a subset of X but I also want to convey that Y is the prefix of X if that makes sense. Is there a name for that? - Y would usually be called an initial segment of X. – Miha Habič Jul 8 '11 at 20:38 @Miha: "Initial segment" is very common for well-ordered sets, less so for partially ordered sets (or for totally ordered sets that don't have a least element). – Arturo Magidin Jul 8 '11 at 20:43 If $(X,\leq)$ is a partially ordered set, then a subset $Y\subseteq X$ is a downward closed subset of $X$ if and only if for all $y\in Y$, if $x\in X$ and $x\leq y$, then $x\in Y$. When $X$ is well-ordered (so that every nonempty subset has a first element), then such a set is usually called an initial segment rather than merely a downward closed set. This is sometimes also used for totally ordered sets with a least element, but not so much for sets that don't have a minimum, since 'initial segment' carries the connotation of a "beginning". Thanks to JDH for pointing out my error of statement here; initial segment is common for any linear order, not only well orders or linear orders with least element.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9276076555252075, "perplexity": 210.18303878137303}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398460519.28/warc/CC-MAIN-20151124205420-00301-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/vector-integration-in-nd.856815/	# Vector Integration in ND 1. Feb 11, 2016 ### Hornbein In N D I want to do an integral of the flux through an N-1 D surface. The usual vector calculus integration theorems say I can integrate around the perimeter of the surface. OK, but that perimeter is now N-2 D. In 4D it could be a cube or a 2-sphere. I can't use Gauss' theorem because the surface isn't closed. Now what? 2. Feb 12, 2016 ### HallsofIvy Staff Emeritus The surface doesn't have to be closed. The boundary of the surface is closed. 3. Feb 12, 2016 ### zinq (If you're not familiar with differential forms, this is a good opportunity to learn about them, since they are exactly the appropriate objects to use in the answer to your question. This may seem a bit technical, but once you are familiar with differential forms, it should make perfect sense.) Let's say we're talking about a volume-preserving flow, generated by a vector field V on Euclidean space n. Let ω denote the volume form. That V preserves ω means that the Lie derivative LVω = 0. In other words, d(ιVω) + ιV(dω) = 0, where ιV denotes the contraction of a differential form by V. Since ω is already an n-dimensional form on n, we have dω = 0 automatically, which means that d(ιVω) = 0 Now the flux form τ, i.e., the (n-1)-form that must be integrated over an (n-1)-dimensional manifold M to get the flux of V through M, is given by just contracting ω by V: τ = ιVω and so from the previous equation, the exterior derivative of the flux form vanishes everywhere: dτ = 0. In Euclidean space (and other spaces with sufficiently simple topology), when the exterior derivative d of any differential form σ vanishes everywhere, this implies by the de Rham theorem that σ itself is the exterior derivative of some form of one lower dimension. Hence we have that there exists an (n-2)-dimensional form μ such that τ = dμ. Now, the general version of Stokes's theorem that works in any dimension states that for a compact manifold M and a differential form ρ of dimension = dim(M) - 1, we have M dρ = ∫∂M ρ. (In fact, all the "usual vector calculus integration theorems" you refer to can be shown to be special cases of this general Stokes's theorem for differential forms.) Applying this Stokes's theorem to the flux form τ with τ = dμ, we have M τ = ∫M dμ and so we get flux through M = ∫M τ = ∫∂M μ. This is exactly what you asked about: How to calculate the flux through an (n-1)-dimensional manifold by integrating something else over its boundary. 4. Feb 12, 2016 ### Hornbein Golly! Thanks for going to all this effort for lil' ole me. 5. Feb 12, 2016 ### MandyStephens thanks for sharing even I was in need of this equation.. 6. Feb 13, 2016 ### lavinia One thing to underscore in zinq's post is that if you start with an arbitrary vector field then its divergence may not be zero. In this case it is not possible to find an N-2 form such that τ = dμ This is true even in three dimensions. zinq's point is that if you can solve this equation, then the flow must be volume preserving. The physical term for a volume preserving flow is that it is "incompressible". A formal way to look at this is to use the identity d(dμ)=0 which is actually true for any differential form, then one has dτ = d(dμ) = 0. Last edited: Feb 13, 2016 7. Feb 13, 2016 ### Hornbein Are you thinking of Stokes' Theorem? For Gauss' Theorem " the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence over the region inside the surface." -- Wikipedia 8. Feb 13, 2016 ### lavinia I think closed manifold here means a manifold without boundary. An N-1 manifold with boundary - as you assumed - is not closed but its boundary is. For instance, a disk in 3 space is a 2 - manifold with boundary a circle. So it is not a closed manifold. But its boundary, the circle, is closed. In general, the boundary of a boundary is empty Gauss's Theorem would apply if the N-1 manifold did not have a boundary and itself was the boundary of an N-dimensional volume. So for instance, it would apply if instead of a disk, the surface was a sphere. Last edited: Feb 13, 2016 9. Feb 15, 2016 ### WWGD Can you think of a case when it is not? I think in any chain complex you have $\partial^2 =0$, for a general boundary operator. So a counter would come from somewhere else. 10. Feb 17, 2016 ### lavinia Good question. Don't know of any. Similar Discussions: Vector Integration in ND	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9782899022102356, "perplexity": 808.0419463112465}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948588072.75/warc/CC-MAIN-20171216123525-20171216145525-00297.warc.gz"}
https://nrich.maths.org/416	Fitting In The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second wall. At what height do the ladders cross? From All Corners Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square. Look Before You Leap Stage: 4 Challenge Level: The diagonals of a square meet at $O$. The bisector of angle $OAB$ meets $BO$ and $BC$ at $N$ and $P$ respectively. The length of $NO$ is $24$. How long is $PC$?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7626543045043945, "perplexity": 289.0303914230389}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398447043.45/warc/CC-MAIN-20151124205407-00110-ip-10-71-132-137.ec2.internal.warc.gz"}
http://eprints.iisc.ernet.in/8874/	# Methodological issues in developing a community forestry greenhouse gas emissions mitigation project in Mancherial forest division of Andhra Pradesh, India Murthy, IK and Hegde, GT and Sudha, P and Ravindranath, NH (2006) Methodological issues in developing a community forestry greenhouse gas emissions mitigation project in Mancherial forest division of Andhra Pradesh, India. In: Environmental Science and Policy, 9 (6). pp. 525-537. PDF Methodological_issues_in_developing_a_community_forestry.pdf Restricted to Registered users only Download (452Kb) \| Request a copy ## Abstract There are several contentious issues related to forestry mitigation projects. The special report of the IPCC and literature published so far have shown that permanence, leakage, baseline establishment, measurement, monitoring, etc., could be addressed satisfactorily using existing scientific methods and accounting rules. To understand the methodological issues of developing community forestry projects, a case study was conducted in Mancherial forest division of Adilabad district in Andhra Pradesh, India. This paper addresses: the setting of project boundaries, baseline selection, establishment of additionality and the calculation of carbon sequestration as a result of the project, prior to project implementation. The steps involved in development of the project and the different methods used for establishing baseline, estimating leakage and transaction cost of developing a community forestry project are presented. The stock is projected to increase by $1480\times 10^3$ t C during 2000–2012 over the baseline scenario under the modeling approach and the cost of establishing a baseline and project formulation for a project extending over 32,956 ha is estimated to be US\1.25 ha^{-1}$and US\$ 4 t $C^{-1}$. Item Type: Journal Article Copyright of this article belongs to Elsevier. Baseline;Leakage;Transaction cost;Modeling;Carbon sequestration;Forestry projects Division of Mechanical Sciences > Centre for Sustainable Technologies (formerly ASTRA)Division of Biological Sciences > Centre for Ecological Sciences 21 Nov 2006 19 Sep 2010 04:32 http://eprints.iisc.ernet.in/id/eprint/8874	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19529351592063904, "perplexity": 8332.642456284659}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400379466.35/warc/CC-MAIN-20141119123259-00232-ip-10-235-23-156.ec2.internal.warc.gz"}
http://luc.lino-framework.org/blog/2013/0405.html	# 20130405 (Friday, 05 April 2013)¶ The docs below /admin need a serious redesign and most of them are currently obsolete. While working on them I noticed that the first argument to djangosite.Site.__init__() was a useless requirement: if a file passes its globals() dictionary, there is no need to also ask for the value of the __file__ key of that same dictionary! I’ll use the freedom I have as long as the only known production servers are maintained by myself and do a backwards incompatbile change in the /ref/settings: ## Adapt your settings.py files!¶ Lino until now required to write in your settings.py file: SITE = Site(__file__,globals(),...) Now you just write: SITE = Site(globals(),...) ## Moving towards a pluggable user interface¶ I am working on moving towards a pluggable user interface. One benefit of this will be docs/tickets/16. The lino.ui.base.Handle.__init__() no longer takes the ui as argument.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22434251010417938, "perplexity": 3195.2201467558803}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823565.27/warc/CC-MAIN-20181211040413-20181211061913-00393.warc.gz"}
https://quantumcomputing.stackexchange.com/questions/1899/quantum-chemistry-and-quantum-computing	# Quantum Chemistry and Quantum Computing Predicting the energy of molecules to high accuracy during the course of a chemical reaction, which in turn allows us to predict reaction rates, equilibrium geometries, transition states among others is a Quantum Chemical problem. Quantum Computing could help Quantum Chemistry by solving the Schrodinger equation for large systems. An example of a problem that is intractable but has applications to Quantum Chemistry is the Hartree-Fock method, a method to approximate the wave function and energy of a quantum many-body system (in stationary state). This problem is known to be NP-complete (see On the NP-completeness of the Hartree-Fock method for translationally invariant systems). Other examples of Quantum Computation to Quantum chemistry are 2-local-Hamiltonians (QMA-complete), Fermionic Local Hamiltonian (QMA-hard). Quantum Computing could give yes/no answers to questions to specific problems such as showing certain molecules have dipole moment. Also, NMR, Trapped Ions, and Superconducting qubits could be used to to simulate such chemical systems too. Noise being, a factor approaches such as NISQ could play a part in simulating quantum chemical systems. What Quantum Computing approaches have been successful to solving Quantum chemistry problems such as predicting reaction rates, transition rates (or even show promise)?	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8355803489685059, "perplexity": 598.4036991087711}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780053918.46/warc/CC-MAIN-20210916234514-20210917024514-00385.warc.gz"}
https://moodle.org/mod/forum/discuss.php?d=58028	## General help ### Hiding teachers in 1.7 This discussion has been locked because a year has elapsed since the last post. Please start a new discussion topic. Hiding teachers in 1.7 Hi apologies if this has already been answered or I'm just being dim but having upgraded an installation to 1.7 I can't find where to hide the teachers so they don't show in the list of courses. This was straightforward in 1.6 and the same facility doesn't appear to be available in 1.7 but perhaps I'm missing something? Average of ratings: - Re: Hiding teachers in 1.7 "I can't find where to hide the teachers so they don't show in the list of courses." Me neither, Ron. I've looked everywhere I can think of including the Tracker. Possibly needs a feature request. Average of ratings: - Re: Hiding teachers in 1.7 Ray, thanks for your report in the tracker - MDL-7544 and Yu, thanks for fixing it in 1.8. Average of ratings: - Re: Hiding teachers in 1.7 While we wait for a stable 1.8 to appear with Yu's fix (thank you, Yu) to the hidden roles bug in 1.7, has anyone come up a work-around for hiding roles when listing courses? Or a hack, perhaps? Or pointer to where in the 1.7 file system a hack might be needed? Thanks. Average of ratings: - Re: Hiding teachers in 1.7 I have a solution for part of the problem- I didn't want non-teaching course creating staff to be listed with each course, but I did want to have course creators. The patch I have made simply means that the role "Course creator" is not listed. You could of course create a new role with "name" and change the patch to omit "name" roles. Edit /course/lib.php (v 1.446.2.7 2007/01/08) insert line 1563 If ($role->name != "Course creator"){ insert line 1567 } so that the foreach loop now looks like: foreach ($teachers as $teacher) { if (!$teacher->hidden \|\| $canseehidden) {$roles = get_user_roles($context,$teacher->id, true, 'r.sortorder ASC'); $role = array_shift($roles); // First one mtrace($role->name); If ($role->name != "Course creator"){ $fullname = fullname($teacher, has_capability('moodle/site:viewfullnames', $context));$namesarray[] = format_string($role->name).': <a href="'.$CFG->wwwroot.'/user/view.php?id='. $teacher->id.'&course='.SITEID.'">'.$fullname.'</a>'; } } } Now you can asign course creators at the site level and they don't get listed with the courses If anyone knows what the '$teacher->hidden ' parameter is supposed to do, would be nice toknow... Average of ratings: - Re: Hiding teachers in 1.7 This is creating the biggest problem in our site which is not public. I'm not sure that I can hack the code in a commercial server that host my site. Any other way to fix this problem. I need to hide the teachers as I did in all previous versions. Help, please! Average of ratings: - Re: Hiding teachers in 1.7 Can you ftp into your site? You'll need log, password etc. And and ftp client. Average of ratings: - Re: Hiding teachers in 1.7 Hi, thanks for the hack, unfortunately it doesn't work for me... This is my code: foreach ($teachers as $teacher) { if (!$teacher->hidden \|\| $canseehidden) {$roles = get_user_roles($context,$teacher->id, true, 'r.sortorder ASC'); $role = array_shift($roles); // First one mtrace($role->name); If ($role->name != "Course creator"){ $fullname = fullname($teacher, has_capability('moodle/site:viewfullnames', $context));$namesarray[] = format_string($role->name).': wwwroot.'/user/view.php?id='.$teacher->id.'&course='.SITEID.'">'.$fullname.' '; } } } I think it looks the same, am I wrong? Do in need to do anything to initiate the change? Thanks! Average of ratings: - Re: Hiding teachers in 1.7 Hi Russell. Do you get any ouput? I've just noticed the call to mtrace is still in the code. Once everything is working it should be deleted. But while it is there you should see every listed teacher's role twice. If your not, perhaps your modifying a file that's not active? I notice that your teacher link is not a hyperlink - but I don't see why that should make any difference. Regards Chris Average of ratings: - Re: Hiding teachers in 1.7 Thanks Chris, I'm not sure I know what you mean by output? I'm also not sure what you mean when you say "should see every listed teachers role twice" I still only see the teachers listed once in each course. I have tried it with and without the mtrace. I'm sure I'm modifying the correct moodle site, am I modifying the wrong file within the site? any other thoughts?? Thanks, Rusty Average of ratings: - Re: Hiding teachers in 1.7 Russell, The file is course/lib.php. I have created some courses in Miscellaneous, when i click on the miscellaneous catagory the courses are listed on my screen, each course in a separate box. The teacher/creators are listed in each box. With the mtrace call in as shown you should see the role of the person listed just before each box - so you see the role twice. If in doubt insert something like mtrace("line number xxx "); You should see this on your screen when the codse is executed. If you don't then you are editing the wrong bit of code (imho). Rgds Chris Average of ratings: - Re: Hiding teachers in 1.7 a temporary solution can be found at http://moodle.org/mod/forum/discuss.php?d=63569 Average of ratings: - Re: Hiding teachers in 1.7 There's a similar problem with hiding administrators in 1.7. Although I understand that it's been fixed in 1.8, it would be VERY nice to have a patch with clear instructions for integration for 1.7 users (who just upgraded less than two months ago). Average of ratings: - Re: Hiding teachers in 1.7 Did you try changing "Course creator" to Administrator" Before: foreach ($teachers as $teacher) { if (!$teacher->hidden \|\| $canseehidden) {$roles = get_user_roles($context,$teacher->id, true, 'r.sortorder ASC'); $role = array_shift($roles); // First one If ($role->name != "Course creator"){$fullname = fullname($teacher, has_capability('moodle/site:viewfullnames',$context)); $namesarray[] = format_string($role->name).': '.$fullname.''; } } } After: foreach ($teachers as $teacher) { if (!$teacher->hidden \|\| $canseehidden) {$roles = get_user_roles($context,$teacher->id, true, 'r.sortorder ASC'); $role = array_shift($roles); // First one If ($role->name != "Administrator"){$fullname = fullname($teacher, has_capability('moodle/site:viewfullnames',$context)); $namesarray[] = format_string($role->name).': '.$fullname.''; } } } Don't know if that will help you, I don't know much about moodle code. It doesn't work for me though. Good Luck! Average of ratings: - Re: Hiding teachers in 1.7 Really the problem, I think, is due to the language used in the installation. If you look in the data-base table "mdl_role" you can see the real name assigned to each role. In italian we have "Creatori di corsi" not "Course creators". Anyway the best thing to do is to look at the number of the role we want to skip in the list, in my case I want to skip the Course creators (usually id=2) and a new role I creted (id=7). The code is now: foreach ($teachers as $teacher) { If ($teacher->id != 7 && $teacher->id != 2){ if (!$teacher->hidden \|\| $canseehidden) {$roles = get_user_roles($context,$teacher->id, true, 'r.sortorder ASC'); $role = array_shift($roles); // First one $fullname = fullname($teacher, has_capability('moodle/site:viewfullnames', $context));$namesarray[] = format_string($role->name).': <a href="'.$CFG->wwwroot.'/user/view.php?id='. $teacher->id.'&course='.SITEID.'">'.$fullname.'</a>'; } } } Good luck! Average of ratings: - Re: Hiding teachers in 1.7 Hi I am sure this is out of context but we are using moodle 1.7+. We have created a few courses and we would like to use one of the courses in a different format and hence we would like to hide them from general enrollment but make it available via a drop down on the homepage. Is there a way to avoid making it enrollable/available on the All courses list? We tried hiding it but what happened was that it was not available to students completely. To clarify we are using the same course in a new format but with lesser number of items. Also on the course there is a number displayed for each section is there a way I can hide this auto number? Regards Uday Average of ratings: -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1834932565689087, "perplexity": 5234.5704942154825}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818696182.97/warc/CC-MAIN-20170926141625-20170926161625-00385.warc.gz"}
http://link.springer.com/article/10.1007%2Fs00894-012-1658-y	Journal of Molecular Modeling , Volume 19, Issue 5, pp 2091–2095 # Simulation of laser radiation effects on low dimensionality structures • Iliana María Ramírez • Jorge Iván Usma • Francisco Eugenio López Original Paper DOI: 10.1007/s00894-012-1658-y Ramírez, I.M., Usma, J.I. & López, F.E. J Mol Model (2013) 19: 2091. doi:10.1007/s00894-012-1658-y ## Abstract This paper presents a study on a system comprised of a low-dimensional structure (Ga1-xAlxAs and GaAs quantum well wire), an intense laser field and an applied magnetic field in axial direction, resulting in a modified structure by interaction with the laser field. A variation of the concentration of aluminum is considered. So, the characteristics of the semiconductor such as the effective mass and width of the forbidden band vary due to the aluminum concentration. The electronic Landé factor control by changing of both intensity and frequency of a laser field on cylindrical quantum well wire was also reported. We use the laser dressed approximation for the treated “quantum wire + laser” system as quantum wire in the absence of radiation but with parameter (electronic barrier height and electronic effective mass) renormalized by laser effects. We consider a magnetic field applied in the parallel direction of symmetric axis of the quantum well wire. We take into account non-parabolicity and anisotropy effects on the conduction band by Ogg-McCombe Hamiltonian. ### Keywords Landé FactorLaser dressingMagnetic fieldQuantum well wireSemiconductors	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.849532425403595, "perplexity": 1993.4959858213542}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738661905.96/warc/CC-MAIN-20160924173741-00093-ip-10-143-35-109.ec2.internal.warc.gz"}
https://socratic.org/questions/57bc8fe0b72cff4e5b59ef0b	Chemistry Topics Question 9ef0b Aug 23, 2016 M = .085 ${V}_{1} \times {M}_{1} = {V}_{2} \times {M}_{2}$ Explanation: The volume times the molarity of acid $\left\{{H}^{+}\right\}$ equals the volume times the molarity of base $\left\{O {H}^{-}\right\}$ Li OH is a mono hydroxide base. so the molarity of LiOH equals the molarity of the base $\left\{O {H}^{-}\right)$ ${H}_{2} C {O}_{3}$ is a bi hydrogen acid. so the molarity of the acid ${H}^{+}$ equals $2 \times M$ the molarity of ${H}_{2} C {O}_{3}$ ${V}_{1} \times M \left(H +\right) = {V}_{2} \times M \left(O {H}^{-}\right)$ $47 m l \times 2 M \left({H}^{+}\right) = 37.5 m l \times 0.215$ M = $37.5 \times \frac{0.215}{47.0 \times 2}$ M = .0858 Aug 23, 2016 sf(0.085color(white)(l)"mol/l"# Explanation: $\textsf{{H}_{2} C {O}_{3 \left(a q\right)} + 2 L i O {H}_{\left(a q\right)} \rightarrow L {i}_{2} C {O}_{3 \left(a q\right)} + + {H}_{2} {O}_{\left(l\right)}}$ This tells us that 1 mole of $\textsf{{H}_{2} C {O}_{3}}$ will be neutralised by 2 moles of $\textsf{L i O H}$. To find the number of moles of $\textsf{L i O H}$ we can say that: $\textsf{c = \frac{n}{v}}$ $\therefore$$\textsf{{n}_{L i O H} = c \times v = 0.215 \times \frac{37.5}{1000} = 0.008}$ From the equation we can say that: $\textsf{{n}_{{H}_{2} C {O}_{3}} = \frac{0.008}{2} = 0.004}$ $\therefore$$\textsf{{c}_{{H}_{2} C {O}_{3}} = {n}_{{H}_{2} C {O}_{3}} / v = \frac{0.004}{\frac{47.0}{1000}} = 0.085 \textcolor{w h i t e}{l} \text{mol/l}}$ Impact of this question 389 views around the world	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 22, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8803132772445679, "perplexity": 5152.178282091205}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402088830.87/warc/CC-MAIN-20200929190110-20200929220110-00106.warc.gz"}
https://oneclass.com/study-guides/ca/utsg/mat/mat-224h1/1139-summary-notes-1.en.html	Study Guides (258,859) CA (125,024) UTSG (8,541) MAT (562) MAT224H1 (51) Sean Uppal (45) Final # Summary notes 1 17 Pages 419 Views Department Mathematics Course Code MAT224H1 Professor Sean Uppal This preview shows pages 1-3. Sign up to view the full 17 pages of the document. MAT224H1a.doc Page 1 of 17 Complex n-Space Cn, Complex Matrices, Spectral Theorem COMPLEX NUMBERS Definition i=1 is the imaginary unit. Definition R + babia,, is a complex number (C). a is the real part, b is the imaginary part. Properties of a Complex Number 1) ( ) ( ) ibabia + = + iff aa = and bb = . 2) ( ) ( ) ( ) ( ) ibbaaibabia + + + = + + + . 3) ( ) ( ) ( ) ( ) ibbaaibabia + = + + . 4) ( ) ( ) ( ) ( ) iabbabbaaibabia + + = + + . 5) ( ) ( ) ( ) ( ) ( ) ( ) i ba baba ba bbaa iba bia 2222 + + + + = + +. 6) ( ) bia + is a real number iff 0 = b ( C R ). Definition Let us denote biaz + = . The conjugate of z is biaz = . The absolute value of z is 22 baz+. Geometric Interpretation of a Complex Number ( ) babiaz, 2 R+= The absolute value 22 baz+= is just the distance from ( ) ba, to the origin. 21 zz is the distance from ibaz111 + = to ibaz222 + = . Polar Coordinates ( ) ( ) θ θθθθ θ θ i eririrrbiaz rb ra=+=+=+= = =sincossincos sin cos. Note: 22 bazr +== . Note: a b arctan= θ the argument of z. Definition ( ) iei θθ θ sincos+= . (a, b) real imaginary www.notesolution.com MAT224H1a.doc Page 2 of 17 Example Write iz22 + = in polar form. Let θ i rez=. ( ) ( ) 22822 22 ==+=r. ( ) 4 3 1arctan 2 2 arctan π θ == = . So 4 3 2222 π i eiz=+= . Theorem: Multiplication In Polar Coordinates If 1 11 θ i erz = and 21 22 θ i erz = are complex numbers in polar form, then 21 2121 ϑθ + =i errzz . Proof: ( ) ( ) 2121 212121 θθθθ iiii eerrererzz == . Want: 2121 θθθθ + =iii eee . ( ) ( ) ( ) ( ) ( ) ( ) ( ) 21 21 2121 21212121 2211 sincos sincoscossinsinsincoscos sincossincos θθ θθ θθθθ θθθθθθθθ θθθθ + = +++= ++= ++= i ii e i i iiee . Theorem: De Moivres Theorem If θ is any angle, then ( ) ( ) θθ ni n iee = holds for all integers n. Proof (sketch): If 0 n, use induction. If 0 < n, then 0 > n. So ( ) ( ) n i n iee =1 θθ . Since ( ) ( ) ( ) ( ) θ θ θθθθθ θθ θθ θθ =+== + == i i ieii i i i e esincossincos sincos sincos sincos 11 1, so ( ) ( ) ( ) 0,<= nee n i n i θθ . Example Find ( ) 3 31 i+. Let 3 2 231 π θ i ierei==+. ( ) ( ) 231 2 2=+=r. ( ) 3 2 3arctan π θ == . www.notesolution.com MAT224H1a.doc Page 3 of 17 So ( ) 88231 2 3 3 2 3== =+ π π i i eei. Theorem: The nth Root of Unity If 1 n is an integer, the nth root of unity (the complex numbers z such that 1 = n z ) are given by 1,,1,0, 2== nkezn k i π . Proof: Let us denote θ i rez=. We want r and θ such that ( ) ( )( ) ( ) ( ) == === =+= n k nr rrnr ninrern nn ninn π θθ θ θθ θ 2 0sin 111cos 1sincos1. When 0 = k, 0 = θ , and when nk = , 02 = = π θ . So 1,,0 = nk. POLYNOMIALS Notice that the roots of cbxax++ 2 are i a bac a b x2 4 2 2 1 + = and i a bac a b x2 4 2 2 2 =. x2 is the conjugate of x1, that is 12 xx =. Complex Polynomials Let us take ( ) C++= wuwuxxxp,, 2 a quadratic polynomial. Let us assume u1, u2 are the roots of ( ) xp. Then: 1 u may not be equal to 2 u. uuu = + 21 . wuu = 21 . Theorem: Fundamental Theorem of Algebra Every complex polynomial ( ) xp of degree 1 n has the form ( ) ( ) ( ) n uxuxuxp = 1, where u, u1,, un are complex numbers (0 i u). The numbers u1,, un are the roots of ( ) xp. u is the coefficient of xn. Corollary Every polynomial ( ) xp of positive degree with real coefficients can be factored as a product of linear and irreducible quadratic factors (in real numbers). Example ( ) ( ) ( ) == ++= 1 1 2 1 m j jj m i icbxaxxp. Using previous theorem, ( ) ( ) ( ) ( ) === = 11 111 m j j m j j m i idxdxaxxp. www.notesolution.com #### Loved by over 2.2 million students Over 90% improved by at least one letter grade. OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A! Leah — University of Toronto Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be. Saarim — University of Michigan As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes. Jenna — University of Wisconsin OneClass has allowed me to catch up with my most difficult course! #lifesaver Anne — University of California Description MAT224H1a.doc n Complex n-Space C , Complex Matrices, Spectral Theorem C OMPLEX N UMBERS Definition 1 = i is the imaginary unit. Definition a +bi,a,bR is a complex number (C). a is the real part, b is the imaginary part. Properties of a Complex Number 1) (a +bi = a +b i ) iff a = a and b = b. 2) (a +bi + a +b i = a + a + b+b i ) . 3) (a +bi a +b i = a a + b b i ) . 4) (a +bi a +b i = aa bb + ab +ba i ) . a bi aa + bb) (a b ab ) 5) a +b i = 2 2 + 2 2 i. a )+ b ( )( a )+ b ( ) 6) (a+bi ) is a real number iff b = 0 (R C ). Definition Let us denote z = a+bi . The conjugate of z is z = abi. The absolute value of z is z a +b . 2 Geometric Interpretation of a Complex Number z = a +bi R 2(a,b 2 2 The absolute value z = a +b is just the distance from imaginary (a,b to the origin. (a, b) z1 z2 is the distance from z1= a1 + b1i to z 2= a 2+ b2i . real Polar Coordinates a = rcos i b = rsin =z+ a bi = r cos + r sin i=)r cos(+ isin = r e . Note: r = z = a2 +b 2 . b Note: = arctan the argument of z. a Definition ei = cos + (sin)i . Page 1 of 17 www.notesolution.com MAT224H1a.doc Example Write z = 2 2i in polar form. z =re i Let . r = ( 2 2)+ 2 2( ) 8 = 2 2 . = arctan 2 =arctan = 3 2 4 . i3 z = 2+ 2i= 2 2 e 4 So . Theorem: Multiplication In Polar Coordinates i i i + If z1 = r1e 1 and z 2= r2e 21 are complex numbers in polar form, then z z1 2 = 1 2 e 1 2 . Proof: z z = r e i1 (r ei2 )= r r ei1e i2 . 1 2 1 2 1 2 Want: e i1ei2 = ei 1 +2 . ei1ei2= (cos 1+ isin 1)cos 2 + isin 2) = (cos 1cos 2 sin1 sin 2 + sin 1c) ( 2+ cos 1sin 2 i. ) = cos ( + +i)in + ( ) 1 2 1 2 = e (1+2 ) Theorem: De Moivres Theorem i n i n) If is any angle, then (e) = e holds for all integers n. Proof (sketch): If n 0 , use induction. n i n i If n < 0 , then n > 0 . So (e =) e ( . Since i 1 1 1 cos i sin i ) (e) = i = = cos isin = cos + )i sin (= e ) , so e cos +isin cos isin i n i )n (e) ( = e ) ,n < 0 . Example 3 Find ( + 3i . 2 i i3 Let 1 3i = re = 2 . 2 2 r = (1 )+ ( 3 = 2 . 2 = arctan() 3 = 3 . Page 2 of 17 www.notesolution.com More Less Only pages 1-3 are available for preview. Some parts have been intentionally blurred. Unlock Document Unlock to view full version Unlock Document Notes Practice Earn Me OR Don't have an account? Join OneClass Access over 10 million pages of study documents for 1.3 million courses. Join to view OR By registering, I agree to the Terms and Privacy Policies Just a few more details So we can recommend you notes for your school.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8472597002983093, "perplexity": 4978.785161706303}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221215858.81/warc/CC-MAIN-20180820062343-20180820082343-00124.warc.gz"}
http://moire.be/haskell/projects/bitcoin-hs/dist/doc/html/bitcoin-hs/Bitcoin-Crypto-EC-DiffieHellman.html	bitcoin-hs-0.0.1: Partial implementation of the Bitcoin protocol (as of 2013) Bitcoin.Crypto.EC.DiffieHellman Description Diffie-Hellman key exchange Synopsis # Documentation newtype SharedSecret Source # Constructors SharedSecret [Word8] Instances Source # Methods Source # Methods Source # MethodsshowList :: [SharedSecret] -> ShowS # Source # Methods Given your private key and somebody else's public key, this compute a (256 bit) shared secret. This is actually very simple: since pubkey = G * privkey, the shared secret will be simply G * privkey1 * privkey2. This can fail if for example an invalid pubkey is given, and in some other special circumstances.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1840505748987198, "perplexity": 11908.966279048005}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590051.20/warc/CC-MAIN-20180718041450-20180718061450-00286.warc.gz"}
https://ejercicios-fyq.com/-Material-systems-	# Material systems Problems and exercises about the matter, properties of matter, density, the Kinetic Molecular Theory, changes os state, and the gases laws. • (#4883) Seleccionar Mass of a volume of ethanol, expressed by pounds The density of ethanol is 0.79 g/mL. Calculate the mass, expressed in pounds, of 17.4 mL of ethanol, knowing that one pound is equal to 0.45 kg. Express the result using scientific notation. • (#4882) Seleccionar Will do float silver over mercury? Imagine that you heat a system with upper temperatures than the fusion points of silver and mercury. If you put in contact both substances, will do silver float over mercury? Look for the information that you need on the Internet and explain your answer. • (#4881) Seleccionar Volume occupied by a known mass of mercury The density of mercury is 13.6 g/mL. What will be the volume of 25 000 g of mercury? • (#4880) Seleccionar Mass of a piece of marble knowing its density and volume What will be the mass of a piece of marble that occupies volume, if its density is ?	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8678869605064392, "perplexity": 4375.939154568164}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369512.68/warc/CC-MAIN-20210304174506-20210304204506-00283.warc.gz"}
http://openmetric.org/til/physics/dimension-analysis-and-pythagorean-theorem/	# Today I Learned ## Dimension Analysis and Pythagorean Theorem We can derive Pythagorean theorem using simple dimension analysis. The first step is to construct the formula for areas. By dimension, we know that area should be length squared. On the other hand, we also know that the area of a triangle is determined given the hypotenuse and an angle. Here we use the example of triangle ABC, whose area should be written as where $f(\cdot)$ is a dimensionless function and $C$ is a contant. Then we write down the area for triangle ABC, triangle ABD, triangle BCD. We also know that which becomes By OctoMiao Last updated	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.853786289691925, "perplexity": 534.3593947123027}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825174.90/warc/CC-MAIN-20171022094207-20171022114207-00458.warc.gz"}
https://deltinu.wordpress.com/2012/12/03/ex-post-01-law/	# The ex post probability is either 0 or 1 The things you think of while doing the dishes. At the Maths Faculty in Cambridge, there are cunningly no dishwashers. Allegedly there are showers, a proven idea-generating tool. But I think they are there for other reasons. Intuitively, it feels as if “after the fact” the probability of any event should either be 0 or 1. Either it happened or it didn’t. Well, except if your last name is Clinton. Framing this in terms of rigorous axiomatic probability theory: consider the filtered probability space $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t\in I},\mathbb{P})$. Consider real-valued random variables on this space and use the notion of conditional expectations. Define conditional probability in terms of conditional expectation as follows: for $A \in \mathcal{F}$ and $\mathcal{G} \subseteq \mathcal{F}$ a sub-$\sigma$-algebra we have $\mathbb{P}(A \| \mathcal{G}) := \mathbb{E}(\mathbf{1}_A \| \mathcal{G})$. Now take $A \in \mathcal{F}_t$ – we are thinking of $t$ as being the current time, and we are looking at the event $A$ which occurred at or before the current time. Since $A$ is $\mathcal{F}_t$-measurable, $\mathbf{1}_A$ is an $\mathcal{F}_t$-measurable random variable. Thus we can “take out what is known”: $\mathbb{P}(A \| \mathcal{F}_t) = \mathbb{E}(\mathbf{1}_A \| \mathcal{F}_t) = \mathbf{1}_A$. But indicator functions are always either 0 or 1. Hence the result. This is a (very, very simple) 01 law. And you don’t really need maths for it.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 13, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9790832996368408, "perplexity": 352.5576716856928}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187826642.70/warc/CC-MAIN-20171023202120-20171023222120-00774.warc.gz"}
https://homework.cpm.org/category/ACC/textbook/acc7/chapter/8%20Unit%209/lesson/CC3:%208.3.1/problem/8-132	### Home > ACC7 > Chapter 8 Unit 9 > Lesson CC3: 8.3.1 > Problem8-132 8-132. A candy store’s specialty is taffy. Customers can fill a bag with taffy, and the price is based on how much the candy weighs. The store charges $2$ for $10$ ounces (oz) of taffy. 1. Copy the table below and fill in the missing values. Add three more entries. Amount of Taffy (oz) Amount of Taffy (oz) column 1 $2$ Amount of Taffy (oz) column 2 $5$ Amount of Taffy (oz) column 3 $10$ Amount of Taffy (oz) column 4 $12$ Amount of Taffy (oz) column 5 $15$ Amount of Taffy (oz) column 6 $20$ Price ($) Price ($) column 1 is blank. Price ($) column 2 is blank. Price ($) column 3 $2$ Price ($) column 4 is blank. Price ($) column 5 is blank. Price (\$) column 6 $4$ • Here are two of the answers: $\left(5, 1\right)$ and $\left(12, 2.40\right)$. Fill in the rest of the table, and add three more entries. You may find using proportions to be helpful in finding more answers. 1. Graph the values in the table. Let $x$ represent the number of ounces and $y$ represent the price in dollars. 2. Is this situation proportional? Explain your reasoning. Does the data make a straight line through $\left(0,0\right)$? 3. What is the slope of the line you graphed? What information does the slope tell you? $\text{Find the slope using }\frac{\text{rise}}{\text{run}}.$ Find the price for $1$ ounce of taffy. What do you notice? 4. Write the equation that represents the candy store’s pricing. • Use the equation $y = mx+b$, where: $m =$ slope $b =$ y-intercept Complete the table in the eTool below to graph the values. Click the link at right for the full version of the eTool:	{"extraction_info": {"found_math": true, "script_math_tex": 20, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39138975739479065, "perplexity": 3248.5094915061213}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487626122.27/warc/CC-MAIN-20210616220531-20210617010531-00135.warc.gz"}
https://codereview.stackexchange.com/questions/24165/is-this-correct-usage-of-the-decorator-pattern	Is this correct usage of the “Decorator” Pattern? I have a model class Product that gets populated from a service DTO object (using AutoMapper). The service is used to power many different applications and for each one the Product Model might need to behave a bit differently. After a bit of research I decided the 'Decorator' pattern might be a good choice to accompany these differences. Here is how I currently have implemented it. These classes are part of a library that gets included in each of the applications public class Product { public virtual string ProductName { get; set; } public virtual Decimal Price { get; set; } public virtual string ImageUrl { get; set; } public virtual string GetImageUrl(){ return ImageUrl; } } public abstract class ProductDecorator : Product { private Product decoratedProduct; // the product being decorated protected ProductDecorator(Product decoratedProduct) { this.decoratedProduct = decoratedProduct; } public override string ProductName { get { return decoratedProduct.ProductName; } set { decoratedProduct.ProductName = value; } } public override decimal Price { get { return decoratedProduct.Price; } set { decoratedProduct.Price= value; } } public override string ImageUrl { get { return decoratedProduct.ImageUrl; } set { decoratedProduct.ImageUrl= value; } } } In each application there may be need to slightly change the model. public class FooProduct : Model.ProductDecorator { public FooProduct (Model.Product product) :base(product){} //we want to serve the image through a cdn public override string GetImageUrl() { return string.Format("cnd.network.com?url={0}", HttpUtility.HtmlEncode(ImageUrl)); } } Usage would be something like this: FooProduct prod = new FooProduct(productClient.GetProduct(23213)); Response.Write(prod.GetImageUrl()); This is my first time using this pattern and I'm not sure if I've got it quite right or if it really applies to this scenario. Are there any foreseeable issues with this solution? Update I think I need to explain a little more how I got here. I created a class library to encapsulate an wcf service. The library takes the DTO's returned by the service and using AutoMapper, maps the DTO to the Product class. The issue is that the product model needs to be a bit different for each of the applications consuming the service. Just using simple inheritance not quite right because a FooProduct needs to pretty much be exactly the same as a Product but just handle the data a bit differently. // this returns a Product, but for this site I need a FooProduct var product = Client.GetProduct(232); This problem is probably a result of bad design in lower layers and from the use of AutoMapper in Client Library. • This doesn't look right; you're creating an abstract class which cannot be instantiated, and inheriting from a class that can. In addition, when I think of "decoration," I think of adding attributes to classes, not class inheritance. – Robert Harvey Mar 20 '13 at 17:48 • @RobertHarvey thanks for moving it here. I wasn't aware of this site! – NSjonas Mar 20 '13 at 18:51 • It's a way to use the decorator pattern. :) Whether it's a good candidate for it is another question. I'd keep image base urls in some config instead and have a helper generate the full urls somewhere in the client project. Hence no need for FooProduct. BUT, if you have more "business-related" things you need to decorate a product with, I'd move the decoration into the service. Use some kind of reflection or IoC to find the relevant decorator(s) and do it before the UI/client code gets it. It can continue using it as a Product. – Lars-Erik Mar 21 '13 at 12:52 I think you've misunderstood what decorator pattern is. As described in Wikipedia "In object-oriented programming, the decorator pattern is a design pattern that allows behavior to be added to an individual object, either statically or dynamically, without affecting the behavior of other objects from the same class." What you are doing is simple inheritance. You can do this with an interface, but you don't have too. You have to ask yourself the question "Do I need to use the Product class?" If you do, then leave it as is, if you don't, make it an interface, or mark it abstract. I'm going to assume you need it. Your class definition looks the same: public class Product { public virtual string ProductName { get; set; } public virtual Decimal Price { get; set; } public virtual string ImageUrl { get; set; } public virtual string GetImageUrl() { return ImageUrl; } } You would then inherit from this class for any other class you need: public class FooProduct : Product { //we want to serve the image through a cdn public override string GetImageUrl() { return string.Format("cnd.network.com?url={0}", HttpUtility.HtmlEncode(ImageUrl)); } } You can now use either class as required: var productInstance = new Product(); var fooProductInstance = new FooProduct(); The nice part is, you can now pass FooProduct in anywhere a Product is expected: public void DoSomethingWithProduct(Product product) { // Do some processing } Can be called: processor.DoSomethingWithProduct(product); or processor.DoSomethingWithProduct(fooProduct); • The issue with this design is that I don't have control on the Product instantiation since its coming from a Client Library using Automapper to go from my DTO's to the Product class. I guess I was trying to use the Decorator pattern so developers don't have to write mapping code every time they extend the Product. (essentially I'm an looking for some way to cast from a parent class to a derived class). Since these models will be passed into controls they will never build additional logic but instead just override methods – NSjonas Mar 20 '13 at 18:48 • How do you differentiate between Product and FooProduct then? – Jeff Vanzella Mar 20 '13 at 18:55 • Not quite sure what you mean by differentaite... Also I can still pass FooProduct anywhere that product is expected with the code in my answer. This solution probably arose from other issues in lower layers of the design. – NSjonas Mar 20 '13 at 18:59 • From reading that Wiki it appears the OP has done exactly what it has said. The Window example they gave is essentially exactly the implementation here. What would be different from the Wiki Window example (apart from the fact Window is abstract) to the OP example?? – dreza Mar 20 '13 at 19:10 • Gotcha! From what I understood from your original question, I thought you were just trying to inherit Product into a FooProduct. I don't think there is much you can do if you need the different classes, but can't get them from the lower level. Is the imdateurl the only property that can be changed in the Product class, or is this just an example? – Jeff Vanzella Mar 20 '13 at 19:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20434117317199707, "perplexity": 1814.6881444864698}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488528979.69/warc/CC-MAIN-20210623011557-20210623041557-00244.warc.gz"}
https://www.rockbox.org/tracker/task/10979	# Rockbox ## FS#10979 - Manual: Have all keymap actions defined in one place for each platform Attached to Project: Rockbox Opened by Tomer Shalev (tomers) - Sunday, 07 February 2010, 21:47 GMT Last edited by Tomer Shalev (tomers) - Tuesday, 09 February 2010, 07:18 GMT Task Type Patches Manual New Tomer Shalev (tomers) All players Low Normal Daily build (which?) Undecided Undecided 0 No ### Details This patch tries to avoid the \opt / \nopt hell in manual's tex files, by concentrating all different action definitions together in the platforms keymap file. Current patch contains changes only to the jpegviewer plugin, in order to demonstrate functionality. Please provide feedback before I spend a lot of time converting all other locations in the manual to this proposed form. I think this way of organizing keymap assignments is better because it is neater, and each platform has its button assignment all in one place. Adding new platform is much easier this way. The patch also use one keymap file to all ipod brands, because they are similar to each other (the ipod4g adds some keymappings, but it doesn't matter if they are defined in other ipod brands). Comment by Alexander Levin (fml2) - Monday, 08 February 2010, 23:12 GMT Here is my feedback after briefly looking at the task: 2. The task category is chosen wrong 3. I think that if we were to provide keymap files for plugins then it should be different files than the files with the core keymaps. I.e. those files should be in the "plugin" subdirectory of the manual. 4. IMO we do not need these files. Just define all the macros in the beginning of the .tex file for that plugin and then use them in text. The LaTeX code will be neat and everything will be in one place. Comment by Tomer Shalev (tomers) - Tuesday, 09 February 2010, 07:29 GMT 2. The task category is chosen wrong > I don't know how I overlooked that. I was probably too tired :-) Thanks for noticing. 3. I think that if we were to provide keymap files for plugins then it should be different files than the files with the core keymaps. I.e. those files should be in the "plugin" subdirectory of the manual. 4. IMO we do not need these files. Just define all the macros in the beginning of the .tex file for that plugin and then use them in text. The LaTeX code will be neat and everything will be in one place. > Sounds reasonable, and it is probably better than having it all in one place. But it will still have \opt and \nopt mess in each file, and when adding a new platform (which is an extremely rare event) you will have to change many files instead of copying from one platform to the new one and modifying the keymaps. I will post an updated patch in the near future according to your suggestion. Thanks. Comment by Alexander Levin (fml2) - Tuesday, 09 February 2010, 10:14 GMT One more question: do I understand correctly that you also replaced many ipod keymap files with just one? I think that this, if at all, should be done in a separate patch. Comment by Dominik Riebeling (bluebrother) - Tuesday, 09 February 2010, 18:11 GMT > One more question: do I understand correctly that you also replaced many ipod keymap files with just one? As far as I can see from the patch this is the case. And I absolutely agree that (if merging does make sense at all, haven't checked yet) it should be done in a separate patch. IMO it's fine to make this patch rely on a different patch that does the merging.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8824862241744995, "perplexity": 2083.31566496004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607811.15/warc/CC-MAIN-20170524093528-20170524113528-00324.warc.gz"}
https://lkpy.lenskit.org/en/latest/batch.html	Batch-Running Recommenders¶ The functions in lenskit.batch enable you to generate many recommendations or predictions at the same time, useful for evaluations and experiments. The batch functions can parallelize over users with the optional n_jobs parameter, or the LK_NUM_PROCS environment variable. Note Scripts calling the batch recommendation or prediction facilites must be protected; that is, they should not directly perform their work when run, but should define functions and call a main function when run as a script, with a block like this at the end of the file: def main(): # do the actual work if __name__ == '__main__': main() If you are using the batch functions from a Jupyter notbook, you should be fine - the Jupyter programs are appropriately protected. Recommendation¶ lenskit.batch.recommend(algo, users, n, candidates=None, , n_jobs=None, kwargs) Batch-recommend for multiple users. The provided algorithm should be a algorithms.Recommender. Parameters • algo – the algorithm • users (array-like) – the users to recommend for • n (int) – the number of recommendations to generate (None for unlimited) • candidates – the users’ candidate sets. This can be a function, in which case it will be passed each user ID; it can also be a dictionary, in which case user IDs will be looked up in it. Pass None to use the recommender’s built-in candidate selector (usually recommended). • n_jobs (int) – The number of processes to use for parallel recommendations. Passed to lenskit.util.parallel.invoker(). Returns A frame with at least the columns user, rank, and item; possibly also score, and any other columns returned by the recommender. Rating Prediction¶ lenskit.batch.predict(algo, pairs, , n_jobs=None, *kwargs) Generate predictions for user-item pairs. The provided algorithm should be a algorithms.Predictor or a function of two arguments: the user ID and a list of item IDs. It should return a dictionary or a pandas.Series mapping item IDs to predictions. To use this function, provide a pre-fit algorithm: >>> from lenskit.algorithms.bias import Bias >>> from lenskit.metrics.predict import rmse >>> from lenskit import datasets >>> ratings = datasets.MovieLens('data/ml-latest-small').ratings >>> bias = Bias() >>> bias.fit(ratings[:-1000]) <lenskit.algorithms.bias.Bias object at ...> >>> preds = predict(bias, ratings[-1000:]) user item rating timestamp prediction 99004 664 8361 3.0 1393891425 3.288286 99005 664 8528 3.5 1393891047 3.559119 99006 664 8529 4.0 1393891173 3.573008 99007 664 8636 4.0 1393891175 3.846268 99008 664 8641 4.5 1393890852 3.710635 >>> rmse(preds['prediction'], preds['rating']) 0.8326992222... Parameters • algo (lenskit.algorithms.Predictor) – A rating predictor function or algorithm. • pairs (pandas.DataFrame) – A data frame of (user, item) pairs to predict for. If this frame also contains a rating column, it will be included in the result. • n_jobs (int) – The number of processes to use for parallel batch prediction. Passed to lenskit.util.parallel.invoker(). Returns a frame with columns user, item, and prediction containing the prediction results. If pairs contains a rating column, this result will also contain a rating column. Return type pandas.DataFrame Isolated Training¶ This function isn’t a batch function per se, as it doesn’t perform multiple operations, but it is primarily useful with batch operations. The train_isolated() function trains an algorithm in a subprocess, so all temporary resources are released by virtue of the training process exiting. It returns a shared memory serialization of the trained model, which can be passed directly to recommend() or predict() in lieu of an algorithm object, to reduce the total memory consumption. Example usage: algo = BiasedMF(50) algo = batch.train_isolated(algo, train_ratings) preds = batch.predict(algo, test_ratings) lenskit.batch.train_isolated(algo, ratings, , file=None, *kwargs) Train an algorithm in a subprocess to isolate the training process. This function spawns a subprocess (in the same way that LensKit’s multiprocessing support does), calls lenskit.algorithms.Algorithm.fit() on it, and serializes the result for shared-memory use. Training the algorithm in a single-purpose subprocess makes sure that any training resources, such as TensorFlow sessions, are cleaned up by virtue of the process terminating when model training is completed. It can also reduce memory use, because the original trained model and the shared memory version are not in memory at the same time. While the batch functions use shared memory to reduce memory overhead for parallel processing, naive use of these functions will still have 2 copies of the model in memory, the shared one and the original, because the sharing process does not tear down the original model. Training in a subprocess solves this problem elegantly. Parameters • algo (lenskit.algorithms.Algorithm) – The algorithm to train. • ratings (pandas.DataFrame) – The rating data. • file (str or pathlib.Path or None) – The file in which to save the trained model. If None, uses a default file path or shared memory. • kwargs (dict) – Additional named parameters to lenskit.algorithms.Algorithm.fit(). Returns The saved model object. This is the owner, so it needs to be closed when finished to free resources. Return type lenskit.sharing.PersistedObject Scripting Evaluation¶ The MultiEval class is useful to build scripts that evaluate multiple algorithms or algorithm variants, simultaneously, across multiple data sets. It can extract parameters from algorithms and include them in the output, useful for hyperparameter search. For example: from lenskit.batch import MultiEval from lenskit.crossfold import partition_users, SampleN from lenskit.algorithms import basic, als from lenskit.datasets import MovieLens from lenskit import topn import pandas as pd ml = MovieLens('ml-latest-small') eval = MultiEval('my-eval', recommend=20) eval.add_algorithms([als.BiasedMF(f) for f in [20, 30, 40, 50]], attrs=['features'], name='ALS') eval.run() The my-eval/runs.csv file will then contain the results of running these algorithms on this data set. A more complete example is available in the MultiEval notebook. class lenskit.batch.MultiEval(path, , predict=True, recommend=100, candidates=None, save_models=False, eval_n_jobs=None, combine=True, kwargs) Bases: object A runner for carrying out multiple evaluations, such as parameter sweeps. Parameters • path (str or pathlib.Path) – the working directory for this evaluation. It will be created if it does not exist. • predict (bool) – whether to generate rating predictions. • recommend (int) – the number of recommendations to generate per user. Any false-y value (None, False, 0) will disable top-n. The literal value True will generate recommendation lists of unlimited size. • candidates (function) – the default candidate set generator for recommendations. It should take the training data and return a candidate generator, itself a function mapping user IDs to candidate sets. Pass None to use the default candidate set configured for each algorithm (recommended). • save_models (bool or str) – save individual estimated models to disk. If True, models are pickled to .pkl files; if 'gzip', they are pickled to gzip-compressed .pkl.gz files. • eval_n_jobs (int or None) – Value to pass to the n_jobs parameter in lenskit.batch.predict() and lenskit.batch.recommend(). • combine (bool) – whether to combine output; if False, output will be left in separate files, if True, it will be in a single set of files (runs, recommendations, and predictions). add_algorithms(algos, attrs=[], kwargs) Add one or more algorithms to the run. Parameters • algos (algorithm or list) – the algorithm(s) to add. • attrs (list of str) – a list of attributes to extract from the algorithm objects and include in the run descriptions. • kwargs – additional attributes to include in the run descriptions. add_datasets(data, name=None, candidates=None, *kwargs) Add one or more datasets to the run. Parameters • data The input data set(s) to run. Can be one of the following: • A tuple of (train, test) data. • An iterable of (train, test) pairs, in which case the iterable is not consumed until it is needed. • A function yielding either of the above, to defer data load until it is needed. Data can be either data frames or paths; paths are loaded after detection using util.read_df_detect(). • kwargs – additional attributes pertaining to these data sets. persist_data() Persist the data for an experiment, replacing in-memory data sets with file names. Once this has been called, the sweep can be pickled. run_count() Get the number of runs in this evaluation. run(runs=None, , progress=None) Run the evaluation. Parameters • runs (int or set-like) – If provided, a specific set of runs to run. Useful for splitting an experiment into individual runs. This is a set of 1-based run IDs, not 0-based indexes. • progress – A tqdm.tqdm()-compatible progress function. collect_results() Collect the results from non-combined runs into combined output files.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19535435736179352, "perplexity": 5981.36901665204}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141486017.50/warc/CC-MAIN-20201130192020-20201130222020-00248.warc.gz"}
https://sizespectrum.org/mizer/reference/validSpeciesParams.html	Check validity of species parameters and set defaults for missing but required parameters ## Usage validSpeciesParams(species_params) ## Arguments species_params The user-supplied species parameter data frame ## Value A valid species parameter data frame This function throws an error if • the species column does not exist or contains duplicates • the w_inf column does not exist or contains NAs or is not numeric It sets default values if any of the following are missing or NA • w_mat is set to w_inf/4 • w_min is set to 0.001 • alpha is set to 0.6 • interaction_resource is set to 1 Any w_mat that is given that is not smaller than w_inf is set to w_inf / 4. Any w_mat25 that is given that is not smaller than w_mat is set to w_mat * 3^(-0.1). The row names of the returned data frame will be the species names. If species_params was provided as a tibble it is converted back to an ordinary data frame.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18412615358829498, "perplexity": 6018.869371093821}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711552.8/warc/CC-MAIN-20221209213503-20221210003503-00388.warc.gz"}
http://www.mathworks.com/help/comm/ref/comm.awgnchannel-class.html?nocookie=true	Accelerating the pace of engineering and science # comm.AWGNChannel System object Package: comm Add white Gaussian noise to input signal ## Description The AWGNChannel object adds white Gaussian noise to a real or complex input signal. When the input uses a real-valued signal, this object adds real Gaussian noise and produces a real output signal. When the input uses a complex signal, this object adds complex Gaussian noise and produces a complex output signal. When the inputs to the object have a variable number of channels, the EbNo, EsNo, SNR, BitsPerSymbol, SignalPower, SamplesPerSymbol, and Variance properties must be scalars, when applicable. To add white Gaussian noise to an input signal: 1. Define and set up your additive white Gaussian noise channel object. See Construction. 2. Call step to add white Gaussian noise to the input signal according to the properties of comm.AWGNChannel. The behavior of step is specific to each object in the toolbox. ## Construction H = comm.AWGNChannel creates an additive white Gaussian noise (AWGN) channel System object™, H. This object then adds white Gaussian noise to a real or complex input signal. H = comm.AWGNChannel(Name,Value) creates an AWGN channel object, H, with each specified property set to the specified value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN). ## Properties NoiseMethod Method to specify noise level Select the method to specify the noise level as one of Signal to noise ratio (Eb/No) \| Signal to noise ratio (Es/No)\| Signal to noise ratio (SNR) \| Variance. The default is Signal to noise ratio (Eb/No). EbNo Energy per bit to noise power spectral density ratio (Eb/No) Specify the Eb/No ratio in decibels. You can set this property to a numeric, real scalar or row vector with a length equal to the number of channels. This property applies when you set the NoiseMethod property to Signal to noise ratio (Eb/No). The default is 10. This property is tunable. EsNo Energy per symbol to noise power spectral density ratio (Es/No) Specify the Es/No ratio in decibels. You can set this property to a numeric, real scalar or row vector with a length equal to the number of channels. This property applies when you set the NoiseMethod property to Signal to noise ratio (Es/No). The default is 10. This property is tunable. SNR Signal to noise ratio (SNR) Specify the SNR value in decibels. You can set this property to a numeric, real scalar or row vector with a length equal to the number of channels. This property applies when you set the NoiseMethod property to Signal to noise ratio (SNR). The default is 10. This property is tunable. BitsPerSymbol Number of bits in one symbol Specify the number of bits in each input symbol. You can set this property to a numeric, positive, integer scalar or row vector with a length equal to the number of channels. This property applies when you set the NoiseMethod property to Signal to noise ratio (Eb/No). The default is 1 bit. SignalPower Input signal power in Watts Specify the mean square power of the input signal in Watts. You can set this property to a numeric, positive, real scalar or row vector with a length equal to the number of channels. This property applies when you set the NoiseMethod property to Signal to noise ratio (Eb/No), Signal to noise ratio (Es/No), or Signal to noise ratio (SNR). The default is 1. The object assumes a nominal impedance of 1 Ω. This property is tunable. SamplesPerSymbol Number of samples per symbol Specify the number of samples per symbol. You can set this property to a numeric, positive, integer scalar or row vector with a length equal to the number of channels. This property applies when you set the NoiseMethod property to Signal to noise ratio (Eb/No) or Signal to noise ratio (Es/No). The default is 1. VarianceSource Source of noise variance Specify the source of the noise variance as one of Property \| Input port. The default is Property. Set this property to Input port to specify the noise variance value using an input to the step method. Set this property to Property to specify the noise variance value using the Variance property. This property applies when you set the NoiseMethod property to Variance. Variance Noise variance Specify the variance of the white Gaussian noise. You can set this property to a numeric, positive, real scalar or row vector with a length equal to the number of channels. This property applies when you set the NoiseMethod property to Variance and the VarianceSource property to Property. The default is 1. This property is tunable. RandomStream Source of random number stream Specify the source of random number stream as one of Global stream \| mt19937ar with seed. The default value of this property is Global stream. When you set this property to Global stream, the object uses the current global random number stream for normally distributed random number generation. When you set this property to mt19937ar with seed, the object uses the mt19937ar algorithm for normally distributed random number generation. In this scenario, when you call the reset method, the object re-initializes the random number stream to the value of the Seed property. Seed Initial seed of mt19937ar random number stream Specify the initial seed of a mt19937ar random number generator algorithm as a double-precision, real, nonnegative integer scalar. The default value of this property is 67. This property applies when you set the RandomStream property to mt19937ar with seed. For each call to the reset method, the object re-initialize the mt19937ar random number stream to the Seed value. ## Methods clone Create AWGN channel object with same property values getNumInputs Number of expected inputs to step method getNumOutputs Number of outputs from step method isLocked Locked status for input attributes and nontunable properties release Allow property value and input characteristics changes reset Reset states of the AWGNChannel System object step Add white Gaussian noise to input signal ## Examples expand all ### Add White Gaussian Noise to An 8-PSK Signal Modulate an 8-PSK signal, add white Gaussian noise, and plot the signal to observe the effects of noise. Create a PSK Modulator System object™. The default modulation order for the PSK modulator object is 8. ```hMod = comm.PSKModulator; ``` Modulate the signal by calling the step function of the PSK modulator. ```modData = step(hMod,randi([0 7],2000,1)); ``` Add white Gaussian noise to the modulated signal by passing the signal through an AWGN channel. ```hAWGN = comm.AWGNChannel('EbNo',20,'BitsPerSymbol',3); ``` Transmit the signal through the AWGN channel by calling the step function of the AWGN channel. ```channelOutput = step(hAWGN,modData); ``` Plot the noiseless and noisy data using scatter plots to observe the effects of noise. ```scatterplot(modData) scatterplot(channelOutput) ``` Change the EbNo property to 10 dB to increase the noise. ```hAWGN.EbNo = 10; ``` Pass the modulated data through the AWGN channel by calling its step method. ```channelOutput = step(hAWGN,modData); ``` Plot the channel output. You can see the effects of increased noise. ```scatterplot(channelOutput) ``` ### Process Signals When the Number of Channels is Changed Pass a single and multichannel signal through an AWGN channel System object™. Create an AWGN channel System object with the Eb/No ratio set for a single channel input. In this case, the EbNo property is specified as a scalar. ```h = comm.AWGNChannel('EbNo',15); ``` Generate random data and apply QPSK modulation. ```data = randi([0 3],1000,1); modData = pskmod(data,4,pi/4); ``` Pass the modulated data through the AWGN channel object using the step function. ```rxSig = step(h,modData); ``` Plot the noisy constellation. ```scatterplot(rxSig) ``` Generate two-channel input data and apply QPSK modulation. ```data = randi([0 3],2000,2); modData = pskmod(data,4,pi/4); ``` Pass the modulated data through the AWGN channel object using the step function. ```rxSig = step(h,modData); ``` Plot the noisy constellations. Each channel is represented as a single column in rxSig. The plots are nearly identical since the same Eb/No value is applied to both channels. ```scatterplot(rxSig(:,1)) title('First Channel') scatterplot(rxSig(:,2)) title('Second Channel') ``` Modify the AWGN channel object to apply a different Eb/No value to each channel. This is done by setting the EbNo property to a 1-by-2 vector. ```h.EbNo = [10 20]; ``` Release the AWGN channel object. This is necessary because the EbNo property must be a scalar if the number of input channels is changed. ```release(h) ``` Pass the data through the AWGN channel. ```rxSig = step(h,modData); ``` Plot the noisy constellations. There is significantly more noise on the first channel due to its lower Eb/No value. ```scatterplot(rxSig(:,1)) title('First Channel') scatterplot(rxSig(:,2)) title('Second Channel') ``` ### Add AWGN Using Noise Variance Input Port This example shows the noise variance input as a scalar or a row vector, with a length equal to the number of channels of the current signal input. Create an AWGN Channel System object™ with the NoiseMethod property set to Variance and the VarianceSource property set to Input port. ```h = comm.AWGNChannel('NoiseMethod','Variance', ... 'VarianceSource','Input port'); ``` Generate random data for two channels and apply 16-QAM modulation. ```data = randi([0 15],10000,2); txSig = qammod(data,16); ``` Pass the modulated data through the AWGN channel by calling the step function. The AWGN channel object processes data from two channels. The variance input is a 1-by-2 vector. ```rxSig = step(h,txSig,[0.01 0.1]); ``` Plot the constellation diagrams for the two channels. The second signal is noisier as its variance is ten times larger. ```scatterplot(rxSig(:,1)) scatterplot(rxSig(:,2)) ``` Repeat the process where the noise variance input is a scalar. The same variance is applied to both channels. Observe that the constellation diagrams are nearly identical. ```rxSig = step(h,txSig,0.2); scatterplot(rxSig(:,1)) scatterplot(rxSig(:,2)) ``` ### Set Random Number Seed for Repeatability This example shows how to produce the same outputs when using a random stream in which you specify the seed. Create an AWGN Channel System object™. Set the NoiseMethod property to Variance, the RandomStream property to mt19937ar with seed, and the Seed property to 99. ```h = comm.AWGNChannel( ... 'NoiseMethod','Variance', ... 'RandomStream','mt19937ar with seed', ... 'Seed',99); ``` Pass data through the AWGN channel by calling the step function. ```y1 = step(h,zeros(8,1)); ``` Reset the AWGN channel object by calling the reset method. This resets the random data stream to the initial seed of 99. ```reset(h); ``` Process the same data by calling the step function. ```y2 = step(h,zeros(8,1)); ``` Compare the two signals. ```[y1 y2] ``` ```ans = 0.6762 0.6762 -0.0536 -0.0536 1.2949 1.2949 -1.7988 -1.7988 0.6081 0.6081 0.4131 0.4131 -0.6775 -0.6775 -1.4166 -1.4166 ``` ## Algorithms This object implements the algorithm, inputs, and outputs described on the AWGN Channel block reference page. The object properties correspond to the block parameters, except for: • The block uses a random number generator based on the V5 RANDN (Ziggurat) algorithm and an initial seed, set with the Initial seed parameter to initialize the random number generator. Every time the system that contains the block is run, the block generates the same sequence of random numbers. Similarly, on the object, when you set the RandomStream property to mt19937ar with seed, you can generate reproducible numbers by resetting the object. When you set the RandomStream property to Global stream, this object uses the MATLAB® default random stream to generate random numbers. To generate reproducible numbers using this object, you can reset the MATLAB default random stream using the following code. `reset(RandStream.getGlobalStream)` • Sometimes, the input to the step method is complex. In such cases, if you try to match the block and object's random generator and seed by setting the random stream of MATLAB, the random numbers do not appear in the same order. The object creates the random data as follows: noise = randn(lengthInput,1) + 1i$×$randn(lengthInput,1) The block creates random data as follows: randData = randn(2$×$lengthInput,1) noise = randData(1:2:end) + 1i$×$randData(2:2:end) • The Symbol period block parameter corresponds to the SamplesPerSymbol property. • The Variance from mask and Variance from port block parameter options of the Mode parameter correspond to the VarianceSource property.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6182344555854797, "perplexity": 1243.1849660343207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119645898.42/warc/CC-MAIN-20141024030045-00210-ip-10-16-133-185.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/ricci-tensor-of-frw.591732/	# Ricci Tensor of FRW 1. ### psimeson 19 I am trying to understand FRW universe. To do so I am following the link below: http://www.phys.washington.edu/users/dbkaplan/555/lecture_04.pdf I am confused at equation 74. I got R00 but for Rij part I am always getting a$\ddot{a}$. I am trying to solve it for k =0. Can some please expand the Rij calculation from basics? 2. ### Mentz114 4,110 Did you do the calculation by hand ? It's hard to point out an error without seeing the working. You could list the Christoffel symbols you got. 939 4. ### psimeson 19 I did by hand and the significant Christoffel symbols here are: $\Gamma^{t}_{xx}$ = a$\ddot{a}$ $\Gamma^{x}_{tx}$ = $\frac{\dot{a}}{a}$ I am following Sean's note too. I don't know when I try to calculate R$_{xx}$ i.e. R$^{t}_{xtx}$. I am not getting the correct answer 5. ### Mentz114 4,110 Are you using this ? $$R^r_{mqs}=\Gamma ^{r}_{mq,s}-\Gamma ^{r}_{ms,q}+\Gamma ^{r}_{ns}\Gamma ^{n}_{mq}-\Gamma ^{r}_{nq}\Gamma ^{n}_{ms}$$ 6. ### psimeson 19 Yes, I used the above mentioned formula. where, r = q = t and m=s= x 7. ### Mentz114 4,110 OK, so you've got $$R^t_{xtx}=\Gamma ^{t}_{xt,x}-\Gamma ^{t}_{xx,t}+\Gamma ^{t}_{nx}\Gamma ^{n}_{xt}-\Gamma ^{t}_{nt}\Gamma ^{n}_{xx}$$ Are you doing the summation over n ? 8. ### clamtrox 939 Hang on, Christoffel symbols only contain first derivatives, what is the double dot doing there? 4,110 Good point. 10. ### psimeson 19 Sorry that's a typo, it's "a$\dot{a}$" only Last edited: Mar 30, 2012 11. ### psimeson 19 My formula is actually: $$R^t_{xtx}=\Gamma ^{t}_{xx,t}-\Gamma ^{t}_{xt,x}+\Gamma ^{n}_{xx}\Gamma ^{t}_{nt}-\Gamma ^{n}_{xt}\Gamma ^{t}_{nx}$$ 12. ### pervect 7,878 Staff Emeritus Are you calculating the Ricci in a coordinate basis, or in an orthonormal frame? And it'd be helpful to get the line element (for the former) or the set of basis vectors (for the later) that you're using - IIRC there are a couple of (equivalent) ways of writing the metric for k=0. 13. ### psimeson 19 Here's my line element: ds2 = -dt2 + a2(t) (dx2 + dy2 + dz2) Can someone please show couple of steps here? Last edited: Mar 31, 2012 14. ### clamtrox 939 $R^t_{rtr} = \partial_t \Gamma^t_{rr} - \partial_r \Gamma^t_{rt} + \Gamma^t_{t \lambda} \Gamma^{\lambda}_{rr} - \Gamma^t_{r \lambda} \Gamma^{\lambda}_{tr} = \frac{\dot{a}^2+ a \ddot{a}}{1-kr^2} - 0 + 0 - \Gamma^t_{r r} \Gamma^{r}_{tr} = \frac{\dot{a}^2+ a \ddot{a}}{1-kr^2} - \frac{\dot{a}^2}{1-kr^2} = \frac{a \ddot{a}}{1-kr^2}$ ... hopefully that's right, it's hard to get all the terms when doing calculations in latex... atleast a quick check gave the correct value for $R_{rr}$ so maybe it's right. Last edited: Mar 31, 2012 15. ### psimeson 19 if k = 0 then you get only a$\ddot{a}$ But according to the notes, we should get a$\ddot{a}$ + 2$\dot{a}$2 16. ### clamtrox 939 I think you're talking about the Ricci tensor: $R_{rr} = R^{\mu}_{r \mu r} = \frac{a \ddot{a} + 2 \dot{a}^2 + 2k}{1-kr^2}$ 17. ### psimeson 19 isn't it same as as $R_{rr} = R^{t}_{r t r}$ I am confused here. I am talking about (74) i.e Rij from: http://www.phys.washington.edu/users/dbkaplan/555/lecture_04.pdf Last edited: Mar 31, 2012 18. ### clamtrox 939 No, you sum over ALL the indices! 19. ### psimeson 19 i.e t= μ and t = $\nu$ How the does Ricci tensor equation looks like then? $R_{rr} = R^{\mu}_{r\mu r} + R^{\nu}_{r\nu r}$ Since $R^{\mu}_{r\mu r} = a\ddot{a}$ and $R^{\nu}_{r\nu r} = a\ddot{a}$ $R_{rr} = 2 a\ddot{a}$ that's not correct. I don't know I am getting confused. I am not seeing how we get $\dot{a}$2 Last edited: Mar 31, 2012 20. ### clamtrox 939 no no no, Ricci tensor is the trace of Riemann tensor, so $R^{\mu}_{r\mu r} = R^{t}_{rtr} +R^{r}_{rrr} + R^{\theta}_{r \theta r} + R^{\phi}_{r \phi r}$ Similar discussions for: Ricci Tensor of FRW	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9306098222732544, "perplexity": 2945.9181607402215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936461848.26/warc/CC-MAIN-20150226074101-00032-ip-10-28-5-156.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/interference-youngs-experiment-and-an-adhesive-tape.510404/	# Interference (Young's experiment) and an adhesive tape 1. ### zimo 45 1. The problem statement, all variables and given/known data At a young's experiment arrangement, there is a 500nm light beam, a distance of 1m from the slits to the screen and a 0.25mm between the two slits In what way the interference pattern will change if an adhesive tape is being taped to one of the slits with a 1mm thickness and an index of 1.5 (diffraction can be left out of the calculation) 2. Relevant equations Xmax = nD[Lambda]/d 3. The attempt at a solution The problem is presented in a general way, I can't find out what is the point of the adhesive tape addition to the problem. Can anyone please give a clarification and a possible direction? 2. ### ideasrule 2,322 Interference depends on the optical path length difference between two paths. Optical path length depends on the index of refraction of the material that the light is passing through, so adding tape increases this path length for one path but not the other. This changes the interference pattern.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8691384792327881, "perplexity": 416.319624771187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207932182.13/warc/CC-MAIN-20150521113212-00312-ip-10-180-206-219.ec2.internal.warc.gz"}
https://www.crypto.ethz.ch/publications/abstract.html?label=AgMaSh11	Publications: Abstract # The Equivalence of Strong RSA and Factoring in the Generic Ring Model of Computation. ## Divesh Aggarwal and Ueli Maurer and Igor Shparlinski Let $N$ be the result of an RSA modulus generation, i.e., a random variable distributed according to some appropriate distribution over the set of products of two primes, such that factoring $N$ is believed to be hard. The Strong RSA assumption states that, given an $x$ chosen uniformly at random from $\Z_N$, it is computationally infeasible to compute a $y\in \Z_N$ and an $e \in \N \setminus \{1\}$ such that $y^e \equiv x \pmod N$. This assumption is important in cryptography and has been used to construct several cryptosystems. Due to the lack of complexity-theoretic lower bound proofs for cryptographic problems in a general model of computation, it is a common practice in cryptography to give proofs of computational security in meaningful restricted models of computation. Some examples of restricted models that are interesting in cryptography are the generic group model for proving lower bounds for the discrete logarithm problem and related problems, and the random oracle model for proving the soundness of protocols or hash function constructions. A generic model captures that an algorithm does not exploit the bit representation of the elements other than for testing equality. The security of the RSA public-key cryptosystem can be analyzed in the generic ring model. In this paper, we prove that for almost all possible distributions of $N$, the problem of factoring $N$ can be efficiently reduced to solving the Strong RSA problem on $\Z_N$ in the generic ring model of computation, where an algorithm can perform ring operations, inverse ring operations, and test equality.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8831418752670288, "perplexity": 232.5809814239473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202303.66/warc/CC-MAIN-20190320064940-20190320090940-00533.warc.gz"}
https://www.techwhiff.com/issue/in-a-hospital-there-are-56-tb-patients-the-patients--79174	# In a hospital there are 56 TB patients. The patients are grouped with respect to their ages. Class Boundaries Frequency 5-10 8 10-15 9 15-20 15 20-25 10 25-30 8 30-35 6 Find the average (mean) age of the TB patients. ###### Question: In a hospital there are 56 TB patients. The patients are grouped with respect to their ages. Class Boundaries Frequency 5-10 8 10-15 9 15-20 15 20-25 10 25-30 8 30-35 6 Find the average (mean) age of the TB patients. ### Solve this quadratic equation using the quadratic formula. (3 - y)(y + 4) = 3y - 5 Solve this quadratic equation using the quadratic formula. (3 - y)(y + 4) = 3y - 5... ### How might a more diverse Supreme Court be important to a nation? How might a more diverse Supreme Court be important to a nation?... ### Correct the sentence fragment by rewriting the sentence in the paragraph box below. To manage a hospital. You should have many skills. 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A) Eumaeus B) ... ### I don’t know 676767 93939030930 I don’t know 676767 93939030930... ### 3 times a number x, subtracted from 18, is less than−90. 3 times a number x, subtracted from 18, is less than−90.... ### How did the fact that women worked in factories later lead to feminist movement? how did the fact that women worked in factories later lead to feminist movement?... ### While making an appointment to discuss Medicare Advantage (MA) and Part D plans with a potential enrollee, you are asked to describe other types of insurance products that your client might wish to purchase. What additional types of insurance can you present during the MA and Part D marketing appointment? While making an appointment to discuss Medicare Advantage (MA) and Part D plans with a potential enrollee, you are asked to describe other types of insurance products that your client might wish to purchase. 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They are rules about how Muslims should treat others.... ### Read the passage below and answer the question.⬇️ Great estates may venture more, But little boats should keep near shore This passage is an example of Franklin's use of to express a deeper truth. Select all that apply. A Imagery B rhyme C alliteration D metaphor Read the passage below and answer the question.⬇️ Great estates may venture more, But little boats should keep near shore This passage is an example of Franklin's use of to express a deeper truth. Select all that apply. A Imagery B rhyme C alliteration D metaphor... ### Did humans actually come from monkeys? Did humans actually come from monkeys?... ### Fill in the Blank 96 inches = _ _ feet Fill in the Blank 96 inches = _ _ feet... ### An ionic compound contains 2 potassium cations for every 1 oxygen anion. What is the chemical formula of the compound? An ionic compound contains 2 potassium cations for every 1 oxygen anion. What is the chemical formula of the compound?...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15726859867572784, "perplexity": 5704.887054291091}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570767.11/warc/CC-MAIN-20220808061828-20220808091828-00494.warc.gz"}
https://rd.springer.com/article/10.1007%2Fs12046-020-1278-7	Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research \| View latest news \| Sign up for updates # In-situ stress partition and its implication on coalbed methane occurrence in the basin–mountain transition zone: a case study of the Pingdingshan coalfield, China ## Abstract The basin–mountain transition zone presents complex geologic structures and non-uniformly distributed in-situ stress. Studying the spatial distribution laws of in-situ stress and their influences on coalbed methane (CBM) occurrence in coal seams plays a significant role in CBM extraction and prevention of coalmine disasters. Based on the actual measured in-situ stress data, CBM content and gas pressure data in the Pingdingshan coalfield, located in the basin–mountain transition zone in the south of the late Palaeozoic basins in the North China block, this research investigated the distribution characteristics of geologic structures and partition of in-situ stress as well as the effects of in-situ stresses on CBM occurrence in the research area using evolution theories of geologic structure and a statistical analysis method. The research results show that geologic structure and in-situ stress distribution in the research area have obvious partition characteristics. The research area is divided into three tectonic zonations. In-situ stress distribution is controlled by tectonic types and tectonic stress field evolution of different tectonic zonations, which are divided into high tectonic stress zonation, tectonic stress zonation and vertical stress zonation from east to west. Also, the research results reveal the characteristics of each stress zonation and the relationship between CBM occurrence and in-situ stress in this research area. This is a preview of subscription content, log in to check access. ## Abbreviations $$C_{\varphi }$$ : The pore compressibility of coal (MPa−1) H : The burial depth of coal seams (m) K : Absolute permeabilities under certain stresses (μm2) K 0 : Absolute permeabilities under no stress (μm2) R : The linear correlation coefficient $$\Delta \sigma$$ : The change rate of stresses (MPa) $$\sigma_{H}$$ : The maximum horizontal principal stress (MPa) $$\sigma_{h}$$ : The minimum horizontal principal stress (MPa) $$\sigma_{v}$$ : The vertical principal stress (MPa) ## References 1. 1 Yu B F 1985 Relationship between coal–gas outburst and in-situ stress. Industrial Safety and Environmental Protection 3: 2–6 2. 2 Zhu X S and Xu Y F 1994 The controlling effects of tectonic stress field and its evolution on coal and gas outburst. Journal of China Coal Society 19: 304–313 3. 3 Liu C R 2011 Distribution laws of in-situ stress in deep underground coalmines. Procedia Engineering 26: 909–917 4. 4 Cheng Y P, Zhang X L and Wang L 2013 Controlling effects of ground stress on gas pressure and outburst disaster. Journal of Mining & Safety Engineering 30: 408–414 5. 5 Han J, Zhang H W, Zhu Z M and Song J C 2007 Controlling of tectonic stress field evolution for coal and gas outburst in Fuxin basin. Journal of China Coal Society 32: 934–938 6. 6 Wang G L, Ju Y W, Zheng M Z, Cao D Y, Qin Y and Zhu Y M 2007 Tectonics of energy resource basins in Northern China. Xuzhou: China University of Mining and Technology Press 7. 7 Jia T R, Wang W, Zhang Z M, Tan Z H and Zhang Y J 2013 Influence of fault strike on gas outburst under modern tectonic stress field. Journal of Mining & Safety Engineering 30: 930–934 8. 8 Li W, Ren T W, Busch A, Den H S A M, Chen Y P and Wei Q 2018 Architecture, stress state and permeability of a fault zone in Jiulishan coal mine, China: implication for coal and gas outbursts. International Journal of Coal Geology 198: 1–13 9. 9 Mark C 2018 Coal bursts that occur during development: a rock mechanics enigma. International Journal of Mining Science and Technology 28: 35–42 10. 10 Xu H J, Sang S X, Yi T S, Zhao X, Liu H H, Li L, Zhao Z G and Xie Y 2014 Characteristics of in-situ stress field and its tectonic origin in Western Guizhou. Journal of Central South University (Science and Technology) 45: 1960–1966 11. 11 Bell J S 2006 In-situ stress and coal bed methane potential in Western Canada. Bulletin of Canadian Petroleum Geology 54: 197–220 12. 12 Bell J S and Bachu S 2003 In-situ stress magnitude and orientation estimates for Cretaceous coal-bearing strata beneath the plains area of central and southern Alberta. Bulletin of Canadian Petroleum Geology 51: 1–28 13. 13 Chen S, Tang D Z, Tao S, Xu H, Li S, Zhao J L, Ren P F and Fu H J 2017 In-situ stress measurements and stress distribution characteristics of coal reservoirs in major coalfields in China: implication for coalbed methane (CBM) development. International Journal of Coal Geology 182: 66–84 14. 14 Gentzis T 2009 Stability analysis of horizontal coalbed methane well in the Rocky Mountain Pront Ranges of southeast British Columbia, Canada. International Journal of Coal Geology 77: 328–337 15. 15 Ju W, Yang Z B, Qin Y, Yi T S and Zhang Z G 2018 Characteristics of in-situ stress state and prediction of the permeability in the upper Permian coalbed methane reservoir, western Guizhou region, SW China. Journal of Petroleum Science and Engineering 165: 199–211 16. 16 Li Y, Tang D Z, Xu H and Yu T X 2014 In-situ stress distribution and its implication on coalbed methane development in Liulin area, eastern Ordos basin, China. Journal of Petroleum Science and Engineering 122: 488–496 17. 17 Meng Z, Tian Y and Li G 2010 Characteristics of in-situ stress field in Southern Qinshui Basin and its research significance. Journal of China Coal Geology 35: 975–981 18. 18 Sang S X, Xu H J, Fang L C, Li G J and Huang H Z 2010 Stress relief coalbed methane drainage by surface vertical wells in China. International Journal of Coal Geology 82: 196–203 19. 19 Shi J Q and Durucan S 2005 A model for changes coalbed permeability during primary and enhanced and enhanced methane recovery. SPE Reservoir Evaluation & Engineering 8: 291–299 20. 20 Tyler R, Scott A R and Kaiser W R 1997 Defining coalbed gas exploration fairways in low permeability, hydrocarbon overpressured basins: an example from the Piceance basin, northwest Colorado. In: Proceedings of the 1997 International Coalbed Methane Symposium, pp. 527–533 21. 21 Jia T R, Feng Z D, Wei G Y and Ju Y W 2018 Shear deformation of fold structures in coal measure strata and coal–gas outbursts: constraint and mechanism. Energy Exploration & Exploitation 36: 185–203 22. 22 Li T, Zhang H W, Han J, Lv Y C and Lan T W 2011 Controlling effect of tectonic stress field on coal and gas outburst. Journal of Xi’an University of Science and Technology 31: 715–718 23. 23 Xu F Y, Zhu X S and Wang G L 1995 Quantitative research on the paleotectonic stress field and its control to coal and gas outburst. Scientia Geologica Sinica 30: 71–94 24. 24 Cai M F, Qiao L and Li C H 2000 Results of in situ stress measurement and their application to mining design at five metal mines. International Journal of Rock Mechanics and Mining Sciences 37: 509 25. 25 Coggan J, Gao F Q, Stead D and Elmo D 2012 Numerical modelling of the effects of weak immediate roof lithology on coal mine roadway stability. International Journal of Coal Geology 90–91: 100–109 26. 26 He M C, Xie H P, Peng S P and Jiang Y D 2005 Study on rock mechanics in deep mining engineering. Chinese Journal of Rock Mechanics and Engineering 24: 2803–2813 27. 27 Martin C D, Kaiser P K and Christiansson R 2003 Stress, instability and design of underground excavations. International Journal of Rock Mechanics and Mining Sciences 40: 1027–1047 28. 28 Hoek G and Brown G T 1980 Underground excavations in rock. London: The Institution of Mining and Metallurgy 29. 29 Karacan C O, Ulery J P and Goodman G V R 2008 A numerical evaluation on the effects of impermeable faults on degasification efficiency and methane emissions during underground coal mining. International Journal of Coal Geology 75: 195–203 30. 30 Wu Q, Wang M Y and Wu X 2004 Investigations of groundwater bursting into coal mine seam floors from fault zones. International Journal of Rock Mechanics and Mining Sciences 41: 557–571 31. 31 Martinez-Diaz J J 2002 Stress field variation related to fault interaction in a reverse oblique-slip fault: the Alhama de Murcia fault, Betic Cordillera, Spain. Tectonophysics 356: 291–305 32. 32 Kang H P, Zhang X, Si L B, Wu Y Z and Gao F Q 2010 In-situ stress measurements and stress distribution characteristics in underground coal mines in China. Engineering Geology 116: 333–345 33. 33 Zoback M L 1992 First- and second-order patterns of stress in the lithosphere: the World Stress Map Project. Journal of Geophysical Research 97: 11703–11728 34. 34 Han J, Zhang H W, Liang B, Rong H, Lan T W, Liu Y Z and Ren T 2016 Influence of large syncline on in situ stress field: a case study of the Kaiping coalfield, China. Rock Mechanics and Rock Engineering 49: 4423–4440 35. 35 Roman D C, Moran S C, Power J A and Cashman K V 2004 Temporal and spatial variation of local stress fields before and after the 1992 eruptions of Crater Peak vent, Mount Spurr volcano, Alaska. Bulletin of the Seismological Society of America 94: 2366–2379 36. 36 Tamagawa T and Pollard D D 2008 Failure permeability created by perturbed stress fields around active faults in a fractured basement reservoir. Bulletin of the American Association of Petroleum Geologists 92: 743–764 37. 37 Zoback M L and Zoback M D 1989 Global patterns of tectonic stress. Nature 341(6240): 291–298 38. 38 Gudmundsson A 2006 How local stresses control magma-chamber ruptures, dyke injections, and eruptions in composite volcanoes. Earth-Science Reviews 79: 1–31 39. 39 Tan W H, Kulatilake P and Sun H B 2014 Influence of an inclined rock stratum on in situ stress state in an open-pit mine. Geo-technical and Geological Engineering 32: 31–42 40. 40 Haimson B C 2010 The effect of lithology, inhomogeneity, topography, and faults, on in situ stress measurements by hydraulic fracturing, and the importance of correct data interpretation and independent evidence in support of results. In: Xie F (Ed.) Rock stress and earthquakes. Boca Raton: CRC Press Inc, pp. 11–14 41. 41 Hudson J A and Cooling C M 1988 In situ rock stresses and their measurement in the UK—part I: the current state of knowledge. International Journal of Rock Mechanics and Mining Sciences Abstracts 25: 363–370 42. 42 Matsuki K, Nakama S and Sato T 2009 Estimation of regional stress by FEM for a heterogeneous rock mass with a large fault. International Journal of Rock Mechanics and Mining Sciences 46: 31–50 43. 43 Hardebeck J L and Hauksson E 2001 Crustal stress field in southern California and its implications for fault mechanics. Journal of Geophysical Research 106: 21859–21882 44. 44 Martin C D and Chandler N A 1993 Stress heterogeneity and geological structures. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 30: 993–999 45. 45 Pollard D D and Segall P 1987 Theoretical displacements and stresses near fractures in rock: with applications to faults, joints, veins, dikes, and solution surfaces. In: Atkinson B K (Ed.) Fracture mechanics of rock. London: Academic Press, pp. 277–359 46. 46 Carlsson A and Christiansson R 1987 Geology and tectonics at Forsmark. Swedish State Power Board, Vattenfall 47. 47 Rebaï S, Philip H and Taboada A 1992 Modern tectonic stress field in the Mediterranean region: evidence for variation in stress directions at different scales. Geophysical Journal International 110: 106–140 48. 48 Martin C D 2007 Quantifying in situ stress magnitudes and orientations for Forsmark: Forsmark stage 2.2. Swedish Nuclear Fuel and Waste Management Co 49. 49 Homand F, Souley M, Gaviglio P and Mamane I 1997 Modelling natural stresses in the arc syncline and comparison with in situ measurements. International Journal of Rock Mechanics and Mining Sciences 34: 1091–1107 50. 50 Zhang G W, Zhang B R, Yuan X C and Xiao Q H 2001 Qingling orogenic belt and continental dynamics. Beijing: Science Press 51. 51 Yan J W, Zhang Y Z and Wang W 2015 Characteristics of gas occurrence under stepwise tectonic control in Pingdingshan mining area. Coal Geology & Exploration 43: 18–23 52. 52 Zhang Z M 2009. Gas geology. Xuzhou: China University of Mining and Technology Press 53. 53 Guo Q F and Ji D 2012 Study on measuring and test technology of ground stress field in No. 10 mine of Pingdingshan Coal Mining Group. Coal Science and Technology 40: 12–14 54. 54 Liu H B, Liu Y L, Ren F H and Miao S J 2009 Distribution regularities of in-situ stresses for eighth mine of Pingdingshan coal mining cooperation. Journal of Xi’an University of Science and Technology 2009-02: 144–148 55. 55 Zhang Y X, Cai M F and Wang K Z 2004 Study on distribution characteristics of in-situ stress for Pingdingshan No. 1 mine. Chinese Journal of Rock Mechanics and Engineering 23(23): 4033–4037 56. 56 Wan T F 2004 Outline of China’s tectonics. Beijing: Geological Publishing House 57. 57 He M X, Wang M, Qiu R H and Yang D Q 2012 Multi-stage composite superimposed basins and hydrocarbons in Southern North China. Beijing: Geological Publishing House 58. 58 GB/T 23250-2009 2009 The direct method of determining coalbed gas content. General Administration of Quality Supervision and Inspection of China, Standardization Administration of China 59. 59 AQ/T 1047-2007 2007 The direct measuring method of the coal seam gas pressure in mine. Administration of Work Safety Supervision and Administration of China 60. 60 Ye J P, Shi B S and Zhang C C 1999 Coal reservoir permeability and its controlled factors in China. Journal of China Coal Society 24: 118–122 ## Acknowledgements The study was financially supported by the National Science and Technology Major Project of China (Grant Nos. 2016ZX05066003 and 2016ZX05066006), Plan of the National Natural Science Foundation of China (41530315), Production-Study-Research Cooperation of Henan Province (16210700040), Project funded by China Postdoctoral Science Foundation (2017M622343), Key Science and Technology Program of Henan Province (152102210105), Project supported by Henan Postdoctoral Foundation (001703047), Doctoral Foundation of Henan Polytechnic University (B2016-03, B2017-04), Program for Innovative Research Team in University of Ministry of Education of China (IRT_16R22) and National Coal Field Engineering Research Center for Gas Geology and Gas Control. ## Author information Correspondence to Tianrang Jia or Guoying Wei. ## Rights and permissions Reprints and Permissions Yan, J., Jia, T., Wei, G. et al. In-situ stress partition and its implication on coalbed methane occurrence in the basin–mountain transition zone: a case study of the Pingdingshan coalfield, China. Sādhanā 45, 47 (2020). https://doi.org/10.1007/s12046-020-1278-7 • Revised: • Accepted: • Published: ### Keywords • Partition of in-situ stress • control of geological structure • coalbed methane occurrence • basin–mountain transition zone • geologic structure evolution • coalfield	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.510243833065033, "perplexity": 20621.227751640192}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875148375.36/warc/CC-MAIN-20200229022458-20200229052458-00503.warc.gz"}
http://math.ecnu.edu.cn/RCFOA/seminar_template.php?id=210	Variations on the theme of amenability Jianchao Wu (University of Muenster) 9:30 am to 10:30 am, Mar 10th, 2015 A1510, Science Building Abstract: We introduce and compare a few notions that generalize amenability for groups --- coarse amenability, algebraic amenability, and the Folner property for $C^*$-algebras. Connections between them are highlighted with the help of uniform Roe algebras. We also discuss aspects such as the dichotomy between amenability and paradoxical decomposition, and the relation between amenability and proper amenability. This is joint work with Pere Ara, Kang Li and Fernando Lledo.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4725257456302643, "perplexity": 2586.741811567645}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608648.25/warc/CC-MAIN-20170526071051-20170526091051-00188.warc.gz"}
https://www.science.gov/topicpages/f/fnal+collider+experiment.html	#### Sample records for fnal collider experiment 1. FNAL Booster intensity, extraction, and synchronization control for collider operation SciTech Connect Ducar, R.J.; Lackey, J.R.; Tawzer, S.R. 1987-03-01 Booster operation for collider physics is considerably different than for fixed target operation. Various scenarios for collider physics, machine studies, and P-Bar targeting may require that the intensity vary from 5E10 PPP to 3E12 PPP at a 15 Hertz machine cycle rate. In addition to the normal Booster single turn extraction mode, collider operations require that the Booster inject into the Main Ring a small number of beam bunches for coalescing into a single high intensity bunch. These bunches must be synchronized such that the center bunch arrives in the RF bucket which corresponds to the zero phase of the coalescing cavity. The system implemented has the ability to deliver a precise fraction of the available 84 Booster beam bunches to Main Ring or to the P-Bar Debuncher via the newly installed AP-4 beam line for tune-up and studies. It is required that all of the various intensity and extraction scenarios be accommodated with minimal operator intervention. 2. Status of FNAL SciBooNE experiment SciTech Connect Nakajima, Yasuhiro; /Kyoto U. 2007-12-01 SciBooNE is a new experiment at FNAL which will make precision neutrino-nucleus cross section measurements in the one GeV region. These measurements are essential for the future neutrino oscillation experiments. We started data taking in the antineutrino mode on June 8, 2007, and collected 5.19 x 10{sup 19} protons on target (POT) before the accelerator shutdown in August. The first data from SciBooNE are reported in this article. 3. The FNAL e938 Experiment: The Mexican Contribution to the MINER{nu}A Collaboration SciTech Connect Felix, J.; Castorena, J.; Higuera, A.; Gutierrez, M. R.; Moreno, G.; Reyes, M. A.; Urrutia, Z.; Zavala, G.; Morfin, J. G. 2009-04-20 The MINER{nu}A (Main INjector ExpeRiment for {nu}A) collaboration (http://minerva.fnal.gov//) is a neutrino scattering experiment which uses the NuMI beam-line at Fermilab. It seeks to measure low energy neutrino interactions both to support neutrino oscillation experiments and to study the strong dynamics of the nucleon and nucleus that affect these interactions. It is currently in its final prototyping stage and is preparing for full-scale construction. The first detector module was completed in early 2006 and it is planned to begin taking data in 2009. We present an overview of this experiment, emphasizing the Mexican contribution, and giving the potential physics results that this collaboration can contribute to the physics of neutrino. 4. Data Plots from FNAL-E907: Main Injector Particle Production Experiment (MIPP) DOE Data Explorer The Main Injector Particle Production Experiment (FNAL E-907, MIPP), situated in the Meson Center beamline at Fermilab, took data during the first half of 2005. MIPP was designed primarily as an experiment to measure and study in detail the dynamics associated with non-perturbative strong interactions. The primary physics motivation behind MIPP was to restart the study of non-perturbative QCD interactions, which constitute over 99% of the strong interaction cross section. The available data of that time were of poor quality and old and were not in easily accessible form. The Time Projection Chamber (TPC) [6] that was at the heart of the MIPP experiment represented the electronic equivalent of the bubble chamber with vastly superior data acquisition rates. It also digitized the charged tracks in three dimensions, obviating the need for track matching across stereo views. Coupled with the particle identification capability of MIPP, the data from MIPP was intended to add significantly to the knowledge base of non-perturbative QCD. One of the primary goals of MIPP was to verify a general scaling law of inclusive particle production that states that the ratio of a semi-inclusive cross section to an inclusive cross section involving the same particles is a function only of the missing mass squared (M2) of the system and not of the other two Mandelstam variables s and t, the center of mass energy squared and the momentum transfer squared, respectively. [Copied and edited from the following publication: The Main Injector Particle Production Experiment (MIPP) at Fermilab, Rajendran Raja, Institute of Physics (IOP) Publishing, Journal of Physics: Conference Series 9 (2005) 303 û 308, doi:10.1088/1742-6596/9/1/058 at www.iop.org/EJ/article/1742-6596/9/1/058/jpconf5_9_058.pdf] There are approximately 40 data plots available to the public from E907. A proposal to upgrade the MIPP experiment (E-P-960) has been deferred. See the MIPP homepage at http://ppd.fnal.gov/experiments 5. A Photon Collider Experiment based on SLC SciTech Connect Gronberg, J 2003-11-01 Technology for a photon collider experiment at a future TeV-scale linear collider has been under development for many years. The laser and optics technology has reached the point where a GeV-scale photon collider experiment is now feasible. We report on the photon-photon luminosities that would be achievable at a photon collider experiment based on a refurbished Stanford Linear Collider. 6. COLLIDE: Collisions into Dust Experiment NASA Technical Reports Server (NTRS) Colwell, Joshua E. 1999-01-01 The Collisions Into Dust Experiment (COLLIDE) was completed and flew on STS-90 in April and May of 1998. After the experiment was returned to Earth, the data and experiment were analyzed. Some anomalies occurred during the flight which prevented a complete set of data from being obtained. However, the experiment did meet its criteria for scientific success and returned surprising results on the outcomes of very low energy collisions into powder. The attached publication, "Low Velocity Microgravity Impact Experiments into Simulated Regolith," describes in detail the scientific background, engineering, and scientific results of COLLIDE. Our scientific conclusions, along with a summary of the anomalies which occurred during flight, are contained in that publication. We offer it as our final report on this grant. 7. Precision electroweak physics at future collider experiments SciTech Connect Baur, U.; Demarteau, M. 1996-11-01 We present an overview of the present status and prospects for progress in electroweak measurements at future collider experiments leading to precision tests of the Standard Model of Electroweak Interactions. Special attention is paid to the measurement of the {ital W} mass, the effective weak mixing angle, and the determination of the top quark mass. Their constraints on the Higgs boson mass are discussed. 8. COLLIDE-2: Collisions Into Dust Experiment-2 NASA Technical Reports Server (NTRS) Colwell, Joshua E. 2002-01-01 The Collisions Into Dust Experimental (COLLIDE-2) was the second flight of the COLLIDE payload. The payload performs six low-velocity impact experiments to study the collisions that are prevalent in planetary ring systems and in the early stages of planet formation. Each impact experiment is into a target of granular material, and the impacts occur at speeds between 1 and 100 cm/s in microgravity and in a vacuum. The experiments are recorded on digital videotape which is later analyzed. During the period of performance a plan was developed to address some of the technical issues that prevented the first flight of COLLIDE from being a complete success, and also to maximize the scientific return based on the science results from the first flight. The experiment was modified following a series of reviews of the design plan, and underwent extensive testing. The data from the experiment show that the primary goal of identifying transition regimes for low-velocity impacts based on cratering versus accretion was achieved. Following a brief period of storage, the experiment flew regimes for low-velocity impacts based on cratering versus accretion was achieved. as a Hitchhiker payload on the MACH-1 Hitchhiker bridge on STS-108 in December 2001. These data have been analyzed and submitted for publication. That manuscript is attached to this report. The experiment was retrieved in January 2002, and all six impact experiments functioned nominally. Preliminary results were reported at the Lunar and Planetary Science Conference. 9. Aerogel Cherenkov detectors in colliding beam experiments Danilyuk, A. F.; Kononov, S. A.; Kravchenko, E. A.; Onuchin, A. P. 2015-05-01 This review discusses the application of aerogel Cherenkov detectors in colliding beam experiments. Such detectors are used for charged particle identification at velocities at which other methods are ineffective. The paper examines aerogel production technology and how the aerogel optical parameters are measured. Data on threshold Cherenkov counters with direct light collection and on those using wavelength shifters are evaluated. Also presented are data on Ring Image Cherenkov detectors with single and multilayer focusing aerogel radiators. 10. FNAL system patching design SciTech Connect Schmidt, Jack; Lilianstrom, Al; Romero, Andy; Dawson, Troy; Sieh, Connie; /Fermilab 2004-01-01 FNAL has over 5000 PCs running either Linux or Windows software. Protecting these systems efficiently against the latest vulnerabilities that arise has prompted FNAL to take a more central approach to patching systems. Due to different levels of existing support infrastructures, the patching solution for linux systems differs from that of windows systems. In either case, systems are checked for vulnerabilities by Computer Security using the Nessus tool. 11. GLADE Global Liquid Argon Detector Experiment: a letter of intent to FNAL SciTech Connect Thomas, Jennifer 2012-05-13 The recent measurements of the {theta}{sub 13} mixing angle, which controls the observable size of any CP violation effects, open a window of opportunity to take advantage of the world's most powerful existing neutrino beam together with recent successes in development of the ultimate detector technology for the detection of electron neutrinos : a liquid argon (LAr) time projection chamber. During this proposed project a 5kt LAr detector (GLADE) will be developed by European groups to be put in a cryostat in the NuMI neutrino beam at Fermi National Accelerator Laboratory in the US and will start taking data in 3-5 years time to address the neutrino mass ordering. The successful fruition of this project, along with nominal exposure at NO{nu}A and T2K, together with information from double beta decay experiments could ascertain that neutrinos are Dirac particles in the next decade. 12. Recent experience in the fabrication and brazing of ceramic beam tubes for kicker magnets at FNAL SciTech Connect Ader, C.R.; Jensen, C.; Reilly, R.; Snee, D.; Wilson, J.H.; /Fermilab 2008-06-01 Ceramic beam tubes are utilized in numerous kicker magnets in different accelerator rings at Fermi National Accelerator Laboratory. Kovar flanges are brazed onto each beam tube end, since kovar and high alumina ceramic have similar expansion curves. The tube, kovar flange, end piece, and braze foil (titanium/incusil) alloy brazing material are stacked in the furnace and then brazed in the furnace at 1000 C. The ceramic specified is 99.8% Alumina, Al{sub 2}O{sub 3}, a strong recrystallized high-alumina fabricated by slip casting. Recent experience at Fermilab with the fabrication and brazing of these tubes has brought to light numerous problems including tube breakage and cracking and also the difficulty of brazing the tube to produce a leak-tight joint. These problems may be due to the ceramic quality, voids in the ceramic, thinness of the wall, and micro-cracks in the ends which make it difficult to braze because it cannot fill tiny surface cracks which are caused by grain pullout during the cutting process. Solutions which are being investigated include lapping the ends of the tubes before brazing to eliminate the micro-cracks and also metallization of the tubes. 13. Cooling of electronics in collider experiments SciTech Connect Richard P. Stanek et al. 2003-11-07 Proper cooling of detector electronics is critical to the successful operation of high-energy physics experiments. Collider experiments offer unique challenges based on their physical layouts and hermetic design. Cooling systems can be categorized by the type of detector with which they are associated, their primary mode of heat transfer, the choice of active cooling fluid, their heat removal capacity and the minimum temperature required. One of the more critical detector subsystems to require cooling is the silicon vertex detector, either pixel or strip sensors. A general design philosophy is presented along with a review of the important steps to include in the design process. Factors affecting the detector and cooling system design are categorized. A brief review of some existing and proposed cooling systems for silicon detectors is presented to help set the scale for the range of system designs. Fermilab operates two collider experiments, CDF & D0, both of which have silicon systems embedded in their detectors. A review of the existing silicon cooling system designs and operating experience is presented along with a list of lessons learned. 14. High luminosity muon scattering at FNAL SciTech Connect Bazizi, K. ); Conrad, J.; Fang, G. ); Erdmann, M. ); Geesaman, D.; Jackson, H. ); Guyot, C.; Virchaux, M. ); Holmgren, H. ); Malensek, A.; Melanson, H.; Morfin 1990-02-01 The charge of this group was to evaluate the physics that can be done with a high luminosity {mu} scattering experiment at FNAL using the upgraded Tevatron muon beam, and consider the apparatus required. In this report, the physics that can be accomplished with a high luminosity {mu} scattering experiment is evaluated. The CERN and FNAL {mu} beams are compared in the context of such an experiment. The expected muon flux with the upgraded machine is estimated. Two possible detectors are compared: the air-core toroid experiment proposed by Guyot et al., and an upgraded version of the E665 double-diode apparatus now in place at FNAL. The relative costs of the detectors are considered. A list of detailed questions that need to be answered regarding the double-diode experiment has be compiled. 2 refs., 10 figs., 2 tabs. 15. First Results from the Phobos Experiment at the RHIC Collider Katzy, Judith; Back, B. B.; Baker, M. D.; Barton, D. S.; Betts, R. R.; Bindel, R.; Budzanowski, A.; Busza, W.; Carroll, A.; Decowski, M. P.; Garcia, E.; George, N.; Gulbrandsen, K.; Gushue, S.; Halliwell, C.; Heintzelman, G. A.; Henderson, C.; Holyński, R.; Hofman, D.; Holzman, B.; Johnson, E.; Kane, J.; Katzy, J.; Kulinich, P.; Kucewicz, W.; Lin, W. T.; McLeod, D.; Manly, S.; Michalowski, J.; Mignerey, A.; Muelmenstaedt, J.; Nouicer, R.; Olszewski, A.; Pak, R.; Park, I. C.; Pernegger, H.; Reed, C.; Remsberg, L. P.; Reuter, M.; Roland, C.; Roland, G.; Rosenberg, L.; Sarin, P.; Sawicki, P.; Skulski, W.; Steadman, S. G.; Stephans, G. S. F.; Steinberg, P.; Stodulski, M.; Sukhanov, A.; Tang, J.-L.; Teng, R.; Trzupek, A.; Vale, C.; van Nieuwenhuizen, G. J.; Verdier, R.; Wadsworth, B.; Wolfs, F. L. H.; Wosiek, B.; Woźniak, K.; Wuosmaa, A. H.; Wysłouch, B. PHOBOS is one of the four experiments at the Relativistic Heavy Ion Collider that started colliding gold nuclei at a center of mass energy of √sNN = 56 and 130 GeV per pair of colliding nucleons in June 2000. The pseudorapidity density of primary charged particles in central collisions has been measured near mid-rapidity. 16. Low energy [bar p] physics at FNAL SciTech Connect Hsueh, S.Y. 1992-12-01 The charmonium formation experiment is the only low energy [bar p] experiment at FNAL. This paper describes the performance of the Fermilab [bar p] Accumulator during fixed target run for the experiment and the planned upgrades. We also discuss the proposal for the direct CP violation search in [bar p] + p [yields] [bar [Lambda 17. FNAL central email systems SciTech Connect Schmidt, Jack; Lilianstrom, Al; Pasetes, Ray; Hill, Kevin; /Fermilab 2004-10-01 The FNAL Email System is the primary point of entry for email destined for an employee or user at Fermilab. This centrally supported system is designed for reliability and availability. It uses multiple layers of protection to help ensure that: (1) SPAM messages are tagged properly; (2) All mail is inspected for viruses; and (3) Valid mail gets delivered. This system employs numerous redundant subsystems to accomplish these tasks. 18. Laser ion source for isobaric heavy ion collider experiment Kanesue, T.; Kumaki, M.; Ikeda, S.; Okamura, M. 2016-02-01 Heavy-ion collider experiment in isobaric system is under investigation at Relativistic Heavy Ion Collider. For this experiment, ion source is required to maximize the abundance of the intended isotope. The candidate of the experiment is 96Ru + 96Zr. Since the natural abundance of particular isotope is low and composition of isotope from ion source depends on the composites of the target, an isotope enriched material may be needed as a target. We studied the performance of the laser ion source required for the experiment for Zr ions. 19. Laser ion source for isobaric heavy ion collider experiment. PubMed Kanesue, T; Kumaki, M; Ikeda, S; Okamura, M 2016-02-01 Heavy-ion collider experiment in isobaric system is under investigation at Relativistic Heavy Ion Collider. For this experiment, ion source is required to maximize the abundance of the intended isotope. The candidate of the experiment is (96)Ru + (96)Zr. Since the natural abundance of particular isotope is low and composition of isotope from ion source depends on the composites of the target, an isotope enriched material may be needed as a target. We studied the performance of the laser ion source required for the experiment for Zr ions. PMID:26931981 20. Beam dump experiment at future electron-positron colliders Kanemura, Shinya; Moroi, Takeo; Tanabe, Tomohiko 2015-12-01 We propose a new beam dump experiment at future colliders with electron (e-) and positron (e+) beams, BDee, which will provide a new possibility to search for hidden particles, like hidden photon. If a particle detector is installed behind the beam dump, it can detect the signal of in-flight decay of the hidden particles produced by the scatterings of e± beams off materials for dumping. We show that, compared to past experiments, BDee (in particular BDee at e+e- linear collider) significantly enlarges the parameter region where the signal of the hidden particle can be discovered. 1. Cross section measurements in the main injector particle production (FNAL-E907) experiment at 58 GeV energy SciTech Connect Gunaydin, Yusuf Oguzhan 2009-12-01 Cross-sections are presented for 58 GeV π, K, and p on a wide range of nuclear targets. These cross-sections are essential for determining the neutrino flux in measurements of neutrino cross-sections and oscillations. The E907 Main Injector Particle Production (MIPP) experiment at Fermilab is a fixed target experiment for measuring hadronic particle production using primary 120 GeV/c protons and secondary π, K, and p beams. The particle identification is made by dE/dx in a time projection chamber, and by time-of-flight, differential Cherenkov and ring imaging Cherenkov detectors, which together cover a wide range of momentum from 0.1 GeV/c up to 120 GeV/c. MIPP targets span the periodic table, from hydrogen to uranium, including beryllium and carbon. The MIPP has collected ~ 0.26 x 106 events of 58 GeV/c secondary particles produced by protons from the main injector striking a carbon target. SciTech Connect Beznosko, D.; Bross, A.; Dyshkant, A.; Pla-Dalmau, A.; Rykalin, V.; /Northern Illinois U. 2005-09-01 The possibility to produce a scintillator that satisfies the demands of physicists from different science areas has emerged with the installation of an extrusion line at Fermi National Accelerator Laboratory (FNAL). The extruder is the product of the fruitful collaboration between FNAL and Northern Illinois Center for Accelerator and Detector Development (NICADD) at Northern Illinois University (NIU). The results from the light output, light attenuation length and mechanical tolerance indicate that FNAL-NICADD scintillator is of high quality. Improvements in the extrusion die will yield better scintillator profiles and decrease the time needed for initial tuning. This paper will present the characteristics of the FNAL-NICADD scintillator based on the measurements performed. They include the response to MIPs from cosmic rays for individual extruded strips and irradiation studies where extruded samples were irradiated up to 1 Mrad. We will also discuss the results achieved with a new die design. The attractive perspective of using the extruded scintillator with MRS (Metal Resistive Semiconductor) photodetector readout will also be shown. 3. Physics of leptoquarks in precision experiments and at particle colliders Doršner, I.; Fajfer, S.; Greljo, A.; Kamenik, J. F.; Košnik, N. 2016-06-01 We present a comprehensive review of physics effects generated by leptoquarks (LQs), i.e., hypothetical particles that can turn quarks into leptons and vice versa, of either scalar or vector nature. These considerations include discussion of possible completions of the Standard Model that contain LQ fields. The main focus of the review is on those LQ scenarios that are not problematic with regard to proton stability. We accordingly concentrate on the phenomenology of light leptoquarks that is relevant for precision experiments and particle colliders. Important constraints on LQ interactions with matter are derived from precision low-energy observables such as electric dipole moments, (g - 2) of charged leptons, atomic parity violation, neutral meson mixing, Kaon, B, and D meson decays, etc. We provide a general analysis of indirect constraints on the strength of LQ interactions with the quarks and leptons to make statements that are as model independent as possible. We address complementary constraints that originate from electroweak precision measurements, top, and Higgs physics. The Higgs physics analysis we present covers not only the most recent but also expected results from the Large Hadron Collider (LHC). We finally discuss direct LQ searches. Current experimental situation is summarized and self-consistency of assumptions that go into existing accelerator-based searches is discussed. A progress in making next-to-leading order predictions for both pair and single LQ productions at colliders is also outlined. 4. The FNAL Injector Upgrade Status SciTech Connect Tan, C.Y.; Bollinger, D.S.; Duel, K.L.; Karns, P.R.; Lackey, J.R.; Pellico, W.A; Scarpine, V.E.; Tomlin, R.E.; /Fermilab 2012-05-14 The new FNAL H{sup -} injector upgrade is currently being tested before installation in the Spring 2012 shutdown of the accelerator complex. This line consists of an H{sup -} source, low energy beam transport (LEBT), 200 MHz RFQ and medium energy beam transport (MEBT). Beam measurements have been performed to validate the design before installation. The results of the beam measurements are presented in this paper. 5. Electropolishing at ANL/FNAL. SciTech Connect Kelly, M. P.; Gerbick, S. M.; Wu, G.; Bice, D.; Physics; FNAL 2009-01-01 A system for electropolishing of 1.3 GHz elliptical single- and nine-cell cavities is in operation at the joint ANL/FNAL cavity processing facility located at Argonne. The system is one peice of a larger 200 m2 complete single cavity processing and assembly facility which also includes clean rooms and high-pressure rinsing. Recently, the electropolishing system has been used to process a series of single and nine-cell cavities. For single cell cavities a good set of EP parameters has been demonstrated based on more than a half dozen complete processing and cold test cycles at ANL/FNAL. The lastest six single cell cavities each exceed EACC=35 MV/m and, at this gradient, have Q in the range 6 10{sup 9} - 1 10{sup 10}. The first nine cell cavities electropolished at ANL have not yet reached similar fields ({approx}23 MV/m-26 MV/m) and ongoing activities are focussed on demonstrating >30 MV/m in these cavities. Suitable nine cell EP parameters using the ANL/FNAL EP system including acid/water temperatures, flow rates, current, voltage, air flow etc. are all substantially different than for single-cell cavities and are discussed here. 6. Fast timing and trigger Cherenkov detector for collider experiments Grigoryev, V. A.; Kaplin, V. A.; Karavicheva, T. L.; Konevskikh, A. S.; Kurepin, A. B.; Loginov, V. A.; Melikyan, Yu A.; Morozov, I. V.; Reshetin, A. I.; Serebryakov, D. V.; Shabanov, A. I.; Slupecki, M.; Trzaska, W. H.; Tykmanov, E. M. 2016-02-01 Analysis of fast timing and trigger Cherenkov detector's design for its use in collider experiments is presented. Several specific requirements are taken into account - necessity of the radiator's placement as close to the beam pipe as possible along with the requirement of gapless (solid) radiator's design. Characteristics of the Cherenkov detector's laboratory prototype obtained using a pion beam at the CERN Proton Synchrotron are also presented, showing the possibility of obtaining sufficiently high geometrical efficiency along with good enough time resolution (50 ps sigma). 7. Flavour physics and the Large Hadron Collider beauty experiment. PubMed Gibson, Valerie 2012-02-28 An exciting new era in flavour physics has just begun with the start of the Large Hadron Collider (LHC). The LHCb (where b stands for beauty) experiment, designed specifically to search for new phenomena in quantum loop processes and to provide a deeper understanding of matter-antimatter asymmetries at the most fundamental level, is producing many new and exciting results. It gives me great pleasure to describe a selected few of the results here-in particular, the search for rare B(0)(s)-->μ+ μ- decays and the measurement of the B(0)(s) charge-conjugation parity-violating phase, both of which offer high potential for the discovery of new physics at and beyond the LHC energy frontier in the very near future. PMID:22253243 8. Optical injection using colliding laser pulses: experiments at LBNL Leemans, W. P.; Geddes, C. G. R.; Toth, C.; Faure, J.; van Tilborg, J.; Marcelis, B.; Esarey, E.; Schroeder, C. B.; Fubiani, G.; Shadwick, B. A.; Dugan, G.; Cary, J.; Giacone, R. 2002-11-01 Laser driven acceleration in plasmas has succeeded in producing electron beams containing multi-nC's of charge, with some fraction of the electrons having energies in excess of 10's of MeV's but 100 % energy spread. One of the current challenges is to produce electron beams with much reduced energy spread. We report on experimental progress in the laser triggered injection of electrons in a laser wakefield accelerator using the colliding pulse method (E. Esarey et al., Phys. Rev. Lett. 79, 2682 (1997).), (C.B. Schroeder et al., Phys. Rev. E 59, 6037 (1999).). The experiments use the l'OASIS multi-beam 10 Hz high power Ti:Al_2O3 laser system (W.P. Leemans et al., Phys. Plasmas 8, 2510 (2001).). In the present experiments, two counter propagating beams (30^rc angle) are focused onto a high density gas jet. Preliminary results indicate that electron beam properties are affected by the second beam. Details of the experiments will be shown as well as comparisons with simulations. 9. The Multi-Purpose Detector (MPD) of the collider experiment Golovatyuk, V.; Kekelidze, V.; Kolesnikov, V.; Rogachevsky, O.; Sorin, A. 2016-08-01 The project NICA (Nuclotron-based Ion Collider fAcility) is aimed to study dense baryonic matter in heavy-ion collisions in the energy range up to √{s_{NN}} = 11 GeV with average luminosity of L = 1027 cm-2s-1 (for 197Au79). The experimental program at the NICA collider will be performed with the Multi-Purpose Detector (MPD). We report on the main physics objectives of the NICA heavy-ion program and present the main detector components. 10. GARLIC: GAmma Reconstruction at a LInear Collider experiment Jeans, D.; Brient, J.-C.; Reinhard, M. 2012-06-01 The precise measurement of hadronic jet energy is crucial to maximise the physics reach of a future Linear Collider. An important ingredient required to achieve this is the efficient identification of photons within hadronic showers. One configuration of the ILD detector concept employs a highly granular silicon-tungsten sampling calorimeter to identify and measure photons, and the GARLIC algorithm described in this paper has been developed to identify photons in such a calorimeter. We describe the algorithm and characterise its performance using events fully simulated in a model of the ILD detector. 11. Electron density and plasma dynamics of a colliding plasma experiment Wiechula, J.; Schönlein, A.; Iberler, M.; Hock, C.; Manegold, T.; Bohlender, B.; Jacoby, J. 2016-07-01 We present experimental results of two head-on colliding plasma sheaths accelerated by pulsed-power-driven coaxial plasma accelerators. The measurements have been performed in a small vacuum chamber with a neutral-gas prefill of ArH2 at gas pressures between 17 Pa and 400 Pa and load voltages between 4 kV and 9 kV. As the plasma sheaths collide, the electron density is significantly increased. The electron density reaches maximum values of ≈8 ṡ 1015 cm-3 for a single accelerated plasma and a maximum value of ≈2.6 ṡ 1016 cm-3 for the plasma collision. Overall a raise of the plasma density by a factor of 1.3 to 3.8 has been achieved. A scaling behavior has been derived from the values of the electron density which shows a disproportionately high increase of the electron density of the collisional case for higher applied voltages in comparison to a single accelerated plasma. Sequences of the plasma collision have been taken, using a fast framing camera to study the plasma dynamics. These sequences indicate a maximum collision velocity of 34 km/s. 12. Linear polarization of gluons and photons in unpolarized collider experiments SciTech Connect Pisano, Cristian; Boer, Daniël; Brodsky, Stanley J.; Buffing, Maarten G. A.; Mulders, Piet J. 2013-10-01 We study azimuthal asymmetries in heavy quark pair production in unpolarized electron-proton and proton-proton collisions, where the asymmetries originate from the linear polarization of gluons inside unpolarized hadrons. We provide cross section expressions and study the maximal asymmetries allowed by positivity, for both charm and bottom quark pair production. The upper bounds on the asymmetries are shown to be very large depending on the transverse momentum of the heavy quarks, which is promising especially for their measurements at a possible future Electron-Ion Collider or a Large Hadron electron Collider. We also study the analogous processes and asymmetries in muon pair production as a means to probe linearly polarized photons inside unpolarized protons. For increasing invariant mass of the muon pair the asymmetries become very similar to the heavy quark pair ones. Finally, we discuss the process dependence of the results that arises due to differences in color flow and address the problem with factorization in case of proton-proton collisions. 13. An overview of the new test stand for H⁻ ion sources at FNAL. PubMed Sosa, A; Bollinger, D S; Duel, K; Karns, P R; Pellico, W; Tan, C Y 2016-02-01 A new test stand at Fermi National Accelerator Laboratory (FNAL) is being constructed to carry out experiments to develop and upgrade the present magnetron-type sources of H(-) ions of up to 80 mA at 35 keV in the context of the Proton Improvement Plan. The aim of this plan is to provide high-power proton beams for the experiments at FNAL. The technical details of the construction and layout of this test stand are presented, along with a prospective set of diagnostics to monitor the sources. PMID:26931987 14. The Next Linear Collider: NLC2001 SciTech Connect D. Burke et al. 2002-01-14 Recent studies in elementary particle physics have made the need for an e{sup +}e{sup -} linear collider able to reach energies of 500 GeV and above with high luminosity more compelling than ever [1]. Observations and measurements completed in the last five years at the SLC (SLAC), LEP (CERN), and the Tevatron (FNAL) can be explained only by the existence of at least one particle or interaction that has not yet been directly observed in experiment. The Higgs boson of the Standard Model could be that particle. The data point strongly to a mass for the Higgs boson that is just beyond the reach of existing colliders. This brings great urgency and excitement to the potential for discovery at the upgraded Tevatron early in this decade, and almost assures that later experiments at the LHC will find new physics. But the next generation of experiments to be mounted by the world-wide particle physics community must not only find this new physics, they must find out what it is. These experiments must also define the next important threshold in energy. The need is to understand physics at the TeV energy scale as well as the physics at the 100-GeV energy scale is now understood. This will require both the LHC and a companion linear electron-positron collider. A first Zeroth-Order Design Report (ZDR) [2] for a second-generation electron-positron linear collider, the Next Linear Collider (NLC), was published five years ago. The NLC design is based on a high-frequency room-temperature rf accelerator. Its goal is exploration of elementary particle physics at the TeV center-of-mass energy, while learning how to design and build colliders at still higher energies. Many advances in accelerator technologies and improvements in the design of the NLC have been made since 1996. This Report is a brief update of the ZDR. 15. Effect of 3D Polarization profiles on polarization measurements and colliding beam experiments SciTech Connect Fischer, W.; Bazilevsky, A. 2011-08-18 The development of polarization profiles are the primary reason for the loss of average polarization. Polarization profiles have been parametrized with a Gaussian distribution. We derive the effect of 3-dimensional polarization profiles on the measured polarization in polarimeters, as well as the observed polarization and the figure of merit in single and double spin experiments. Examples from RHIC are provided. The Relativistic Heavy Ion Collider (RHIC) is the only collider of spin polarized protons. During beam acceleration and storage profiles of the polarization P develop, which affect the polarization measured in a polarimeter, and the polarization and figure of merit (FOM) in colliding beam experiments. We calculate these for profiles in all dimensions, and give examples for RHIC. Like in RHIC we call the two colliding beams Blue and Yellow. We use the overbar to designate intensity-weighted averages in polarimeters (e.g. {bar P}), and angle brackets to designate luminosity-weighted averages in colliding beam experiments (e.g. ). 16. 2001 Report on the Next Linear Collider SciTech Connect Gronnberg, J; Breidenbach; Burke, D; Corlett, J; Dombeck, T; Markiewicz, T 2001-08-28 Recent studies in elementary particle physics have made the need for an e{sup +}e{sup -} linear collider able to reach energies of 500 GeV and above with high luminosity more compelling than ever [1]. Observations and measurements completed in the last five years at the SLC (SLAC), LEP (CERN), and the Tevatron (FNAL) can be explained only by the existence of at least one particle or interaction that has not yet been directly observed in experiment. The Higgs boson of the Standard Model could be that particle. The data point strongly to a mass for the Higgs boson that is just beyond the reach of existing colliders. This brings great urgency and excitement to the potential for discovery at the upgraded Tevatron early in this decade, and almost assures that later experiments at the LHC will find new physics. But the next generation of experiments to be mounted by the world-wide particle physics community must not only find this new physics, they must find out what it is. These experiments must also define the next important threshold in energy. The need is to understand physics at the TeV energy scale as well as the physics at the 100-GeV energy scale is now understood. This will require both the LHC and a companion linear electron-positron collider. 17. Fourth workshop on Experiments and Detectors for a Relativistic Heavy Ion Collider NASA Technical Reports Server (NTRS) Fatyga, M. (Editor); Moskowitz, B. (Editor) 1992-01-01 We present a description of an experiment which can be used to search for effects of strong electromagnetic fields on the production of e(sup +) e(sup -) pairs in the elastic scattering of two heavy ions at the Relativistic Heavy Ion Collider (RHIC). A very brief discussion of other possible studies of electromagnetic phenomena at RHIC is also presented. 18. Overview of results from the Fermilab fixed target and collider experiments SciTech Connect Montgomery, H.E. 1997-06-01 In this paper we present a review of recent QCD related results from Fermilab fixed target and collider experiments. Topics covered range from structure functions through W/Z production, heavy quark production and jet angular distributions. We also include the current state of knowledge about leptoquark pair production in hadronic collisions. 19. SNiPER: an offline software framework for non-collider physics experiments Zou, J. H.; Huang, X. T.; Li, W. D.; Lin, T.; Li, T.; Zhang, K.; Deng, Z. Y.; Cao, G. F. 2015-12-01 SNiPER (Software for Non-collider Physics ExpeRiments) has been developed based on common requirements from both nuclear reactor neutrino and cosmic ray experiments. The design and implementation of SNiPER is described in this proceeding. Compared to the existing offline software frameworks in the high energy physics domain, the design of SNiPER is more focused on execution efficiency and flexibility. SNiPER has an open structure. User applications are executed as plug-ins based on it. The framework contains a compact kernel for software components management, event execution control, job configuration, common services, etc. Some specific features are attractive to non-collider physics experiments. 20. Transition Radiation Detector in the D0 colliding beam experiment at Fermilab SciTech Connect Piekarz, H. 1995-04-01 The construction, operation and response of the Transition Radiation Detector (TRD) at DO colliding beam experiment at Fermilab are presented. The use of the TRD signal to enhance electron identification and hadronic rejection in the multiparticle background characteristic for the antiproton-proton interactions at the center-of-mass energy of 1.8 TeV is also described and results are discussed. 1. Numerical modeling of laser-driven experiments of colliding jets: Turbulent amplification of seed magnetic fields Tzeferacos, Petros; Fatenejad, Milad; Flocke, Norbert; Graziani, Carlo; Gregori, Gianluca; Lamb, Donald; Lee, Dongwook; Meinecke, Jena; Scopatz, Anthony; Weide, Klaus 2014-10-01 In this study we present high-resolution numerical simulations of laboratory experiments that study the turbulent amplification of magnetic fields generated by laser-driven colliding jets. The radiative magneto-hydrodynamic (MHD) simulations discussed here were performed with the FLASH code and have assisted in the analysis of the experimental results obtained from the Vulcan laser facility. In these experiments, a pair of thin Carbon foils is placed in an Argon-filled chamber and is illuminated to create counter-propagating jets. The jets carry magnetic fields generated by the Biermann battery mechanism and collide to form a highly turbulent region. The interaction is probed using a wealth of diagnostics, including induction coils that are capable of providing the field strength and directionality at a specific point in space. The latter have revealed a significant increase in the field's strength due to turbulent amplification. Our FLASH simulations have allowed us to reproduce the experimental findings and to disentangle the complex processes and dynamics involved in the colliding flows. This work was supported in part at the University of Chicago by DOE NNSA ASC. 2. Laboratory Magnetic Reconnection Experiments with Colliding, Magnetized Laser-Produced Plasma Plumes Fox, W. R., II; Bhattacharjee, A.; Deng, W.; Moissard, C.; Germaschewski, K.; Fiksel, G.; Barnak, D.; Chang, P. Y.; Hu, S.; Nilson, P. 2014-12-01 We present results from experiments and simulations of magnetic reconnection between colliding plumes of laser-produced plasma. In the experiments, which open up a new experimental regime for reconnection study, bubbles of high-temperature, high-density plasma are created by focusing lasers down to sub-millimeter-scale spots on a plastic or metal foil, ionizing the foil into hemispherical bubbles that expand supersonically off the surface of the foil. If multiple bubbles are created at small separation, the bubbles expand into one another, and the embedded magnetic fields (either self-generated or externally imposed) are squeezed together and reconnect. We will review recent experiments, which have observed magnetic field annihilation, outflow jets, particle energization, and the formation of elongated current sheets. We compare the results against experiments with unmagnetized plumes, which observe the Weibel instability as the two plumes collide and interact. Particle-in-cell simulations of the strongly driven reconnection in these experiments show fast reconnection due to two-fluid effects, flux pile-up, and plasmoid formation, and show particle energization by reconnection. 3. Laboratory experiments on cluster/aerosol formation by colliding ablation plumes Hirooka, Y.; Tanaka, K. A.; Sato, H.; Ishihara, K.; Sunahara, A. 2010-08-01 First-of-a-kind experiments on cluster/aerosol formation by colliding ablation plumes have been conducted, radiating Al, Cu and C with 3ω-YAG laser at power densities between 2~30 J/cm2/pulse. Visible spectroscopy indicates that the excitation light intensities of Cu and Al plumes are not necessarily be doubled in collision, but can rather be weakened due to atomic and molecular reactions. For colliding C plumes, Swan band radiation has been observed, indicative of C2 and/or C2+ formation, and ion mass spectrometry has identified Cn+-clusters, including C+, C2+, C3+, C4+ and C5+. From ICCD camera observations, C plumes generated at power densities above ~15 J/cm2/pulse tend to split into two components with respective velocities, only the slow component of which appears to be interactive to form clusters. Nano structures like CNT have been identified in deposits from colliding C plumes. 4. Nucleon Decay and Neutrino Experiments, Experiments at High Energy Hadron Colliders, and String Theor SciTech Connect Jung, Chang Kee; Douglas, Michaek; Hobbs, John; McGrew, Clark; Rijssenbeek, Michael 2013-07-29 This is the final report of the DOE grant DEFG0292ER40697 that supported the research activities of the Stony Brook High Energy Physics Group from November 15, 1991 to April 30, 2013. During the grant period, the grant supported the research of three Stony Brook particle physics research groups: The Nucleon Decay and Neutrino group, the Hadron Collider Group, and the Theory Group. 5. A new micro-strip tracker for the new generation of experiments at hadron colliders SciTech Connect Dinardo, Mauro E 2005-12-01 This thesis concerns the development and characterization of a prototype Silicon micro-strip detector that can be used in the forward (high rapidity) region of a hadron collider. These detectors must operate in a high radiation environment without any important degradation of their performance. The innovative feature of these detectors is the readout electronics, which, being completely data-driven, allows for the direct use of the detector information at the lowest level of the trigger. All the particle hits on the detector can be readout in real-time without any external trigger and any particular limitation due to dead-time. In this way, all the detector information is available to elaborate a very selective trigger decision based on a fast reconstruction of tracks and vertex topology. These detectors, together with the new approach to the trigger, have been developed in the context of the BTeV R&D program; our aim was to define the features and the design parameters of an optimal experiment for heavy flavour physics at hadron colliders. Application of these detectors goes well beyond the BTeV project and, in particular, involves the future upgrades of experiments at hadron colliders, such as Atlas, CMS and LHCb. These experiments, indeed, are already considering for their future high-intensity runs a new trigger strategy a la BTeV. Their aim is to select directly at trigger level events containing Bhadrons, which, on several cases, come from the decay of Higgs bosons, Z{sup o}'s or W{sup {+-}}'s; the track information can also help on improving the performance of the electron and muon selection at the trigger level. For this reason, they are going to develop new detectors with practically the same characteristics as those of BTeV. To this extent, the work accomplished in this thesis could serve as guide-line for those upgrades. 6. DELPHES 3: a modular framework for fast simulation of a generic collider experiment de Favereau, J.; Delaere, C.; Demin, P.; Giammanco, A.; Lemaître, V.; Mertens, A.; Selvaggi, M. 2014-02-01 The version 3.0 of the Delphes fast-simulation is presented. The goal of Delphes is to allow the simulation of a multipurpose detector for phenomenological studies. The simulation includes a track propagation system embedded in a magnetic field, electromagnetic and hadron calorimeters, and a muon identification system. Physics objects that can be used for data analysis are then reconstructed from the simulated detector response. These include tracks and calorimeter deposits and high level objects such as isolated electrons, jets, taus, and missing energy. The new modular approach allows for greater flexibility in the design of the simulation and reconstruction sequence. New features such as the particle-flow reconstruction approach, crucial in the first years of the LHC, and pile-up simulation and mitigation, which is needed for the simulation of the LHC detectors in the near future, have also been implemented. The Delphes framework is not meant to be used for advanced detector studies, for which more accurate tools are needed. Although some aspects of Delphes are hadron collider specific, it is flexible enough to be adapted to the needs of electron-positron collider experiments. [Figure not available: see fulltext. 7. Ion colliders SciTech Connect Fischer, W. 2011-12-01 Ion colliders are research tools for high-energy nuclear physics, and are used to test the theory of Quantum Chromo Dynamics (QCD). The collisions of fully stripped high-energy ions create matter of a temperature and density that existed only microseconds after the Big Bang. Ion colliders can reach higher densities and temperatures than fixed target experiments although at a much lower luminosity. The first ion collider was the CERN Intersecting Storage Ring (ISR), which collided light ions [77Asb1, 81Bou1]. The BNL Relativistic Heavy Ion Collider (RHIC) is in operation since 2000 and has collided a number of species at numerous energies. The CERN Large Hadron Collider (LHC) started the heavy ion program in 2010. Table 1 shows all previous and the currently planned running modes for ISR, RHIC, and LHC. All three machines also collide protons, which are spin-polarized in RHIC. Ion colliders differ from proton or antiproton colliders in a number of ways: the preparation of the ions in the source and the pre-injector chain is limited by other effects than for protons; frequent changes in the collision energy and particle species, including asymmetric species, are typical; and the interaction of ions with each other and accelerator components is different from protons, which has implications for collision products, collimation, the beam dump, and intercepting instrumentation devices such a profile monitors. In the preparation for the collider use the charge state Z of the ions is successively increased to minimize the effects of space charge, intrabeam scattering (IBS), charge change effects (electron capture and stripping), and ion-impact desorption after beam loss. Low charge states reduce space charge, intrabeam scattering, and electron capture effects. High charge states reduce electron stripping, and make bending and acceleration more effective. Electron stripping at higher energies is generally more efficient. Table 2 shows the charge states and energies in the 8. Colliding pulse injection experiments in non-collinear geometryfor controlled laser plasma wakefield acceleration of electrons SciTech Connect Toth, Carl B.; Esarey, Eric H.; Geddes, Cameron G.R.; Leemans,Wim P.; Nakamura, Kei; Panasenko, Dmitriy; Schroeder, Carl B.; Bruhwiler,D.; Cary, J.R. 2007-06-25 An optical injection scheme for a laser-plasma basedaccelerator which employs a non-collinear counter-propagating laser beamto push background electrons in the focusing and acceleration phase viaponderomotive beat with the trailing part of the wakefield driver pulseis discussed. Preliminary experiments were performed using a drive beamof a_0 = 2.6 and colliding beam of a_1 = 0.8 both focused on the middleof a 200 mu m slit jet backed with 20 bar, which provided ~; 260 mu mlong gas plume. The enhancement in the total charge by the collidingpulse was observed with sharp dependence on the delay time of thecolliding beam. Enhancement of the neutron yield was also measured, whichsuggests a generation of electrons above 10 MeV. 9. Capture cavity II results at FNAL SciTech Connect Branlard, Julien; Chase, Brian; Cancelo, G.; Carcagno, R.; Edwards, H.; Fliller, R.; Hanna, B.; Harms, Elvan; Hocker, A.; Koeth, T.; Kucera, M.; /Fermilab 2007-06-01 As part of the research and development towards the International Linear Collider (ILC), several test facilities have been developed at Fermilab. This paper presents the latest Low Level RF (LLRF) results obtained with Capture Cavity II (CCII) at the ILC Test Accelerator (ILCTA) test facility. The main focus will be on controls and RF operations using the SIMCON based LLRF system developed in DESY [1]. Details about hardware upgrades and future work will be discussed. 10. Recent results from the CDF (Collider Detector at Fermilab) experiment at the Tevatron proton-antiproton collider SciTech Connect Geer, S. . High Energy Physics Lab.) 1989-09-01 Recent results from the CDF experiment are described. The Standard Model gives a good description of jet production, and W/Z production and decay. There is no evidence yet for the top quark, for fourth generation quarks, or for deviations from the Standard Model ascribable to quark substructure, supersymmetric particles, or heavy additional W-like or Z-like bosons. Limits are given where applicable. A search for a light Higgs Boson is also described. 11 refs., 24 figs. 11. Development of a forward calorimeter system for the STAR experiment Tsai, O. D.; Aschenauer, E.; Christie, W.; Dunkelberger, L. E.; Fazio, S.; Gagliardi, C. A.; Heppelmann, S.; Huang, H. Z.; Jacobs, W. W.; Igo, G.; Kisilev, A.; Landry, K.; Liu, X.; Mondal, M. M.; Pan, Y. X.; Sergeeva, M.; Shah, N.; Sichtermann, E.; Trentalange, S.; Visser, G.; Wissink, S. 2015-02-01 We present results of an R&D program to develop a forward calorimeter system (FCS) for the STAR experiment at the Relativistic Heavy Ion Collider at BNL. The FCS is a very compact, compensated, finely granulated, high resolution calorimeter system being developed for p+p and p+A program at RHIC. The FCS prototype consists of both electromagnetic and hadron calorimeters. The electromagnetic portion of the detector is constructed with W powder and scintillation fibers. The hadronic calorimeter is a traditional Pb/Sc-plate sandwich design. Both calorimeters were readout with Hamamatsu MPPCs. A full- scale prototype of the FCS was tested with a beam at FNAL in March 2014. We present details of the design, construction technique and performance of the FCS prototype during the test run at FNAL. 12. Issues and experience with controlling beam loss at the Tevatron collider SciTech Connect Annala, Gerald; /Fermilab 2007-07-01 Controlling beam loss in the Tevatron collider is of great importance because of the delicate nature of the cryogenic magnet system and the collider detectors. Maximizing the physics potential requires optimized performance as well as protection of all equipment. The operating history of the Tevatron has significantly influenced the way losses are managed. The development of beam loss management in the Tevatron will be presented. 13. OPERATIONS ELECTRONIC LOGBOOK EXPERIENCE AT BNL. SciTech Connect SATOGATA,T.; CAMPBELL,I.; MARR,G.; SAMPSON,P. 2002-06-02 A web-based system for electronic logbooks, ''elog'', developed at Fermilab (FNAL), has been adopted for use by AGS and RHIC operations and physicists at BNL for the 2001-2 fixed target and collider runs. This paper describes the main functional and technical issues encountered in the first year of electronic logbook use, including security, search and indexing, sequencer integration, archival, and graphics management. We also comment on organizational experience and planned changes for the next facility run starting in September 2002. 14. Experimental characterization of a coaxial plasma accelerator for a colliding plasma experiment Wiechula, J.; Hock, C.; Iberler, M.; Manegold, T.; Schönlein, A.; Jacoby, J. 2015-04-01 We report experimental results of a single coaxial plasma accelerator in preparation for a colliding plasma experiment. The utilized device consisted of a coaxial pair of electrodes, accelerating the plasma due to J ×B forces. A pulse forming network, composed of three capacitors connected in parallel, with a total capacitance of 27 μF was set up. A thyratron allowed to switch the maximum applied voltage of 9 kV. Under these conditions, the pulsed currents reached peak values of about 103 kA. The measurements were performed in a small vacuum chamber with a neutral-gas prefill at gas pressures between 10 Pa and 14 000 Pa. A gas mixture of ArH2 with 2.8% H2 served as the discharge medium. H2 was chosen in order to observe the broadening of the Hβ emission line and thus estimate the electron density. The electron density for a single plasma accelerator reached peak values on the order of 1016 cm-3 . Electrical parameters, inter alia inductance and resistance, were determined for the LCR circuit during the plasma acceleration as well as in a short circuit case. Depending on the applied voltage, the inductance and resistance reached values ranging from 194 nH to 216 nH and 13 mΩ to 23 mΩ, respectively. Furthermore, the plasma velocity was measured using a fast CCD camera. Plasma velocities of 2 km/s up to 17 km/s were observed, the magnitude being highly correlated with gas pressure and applied voltage. 15. Experimental characterization of a coaxial plasma accelerator for a colliding plasma experiment SciTech Connect Wiechula, J.; Hock, C.; Iberler, M.; Manegold, T.; Schönlein, A.; Jacoby, J. 2015-04-15 We report experimental results of a single coaxial plasma accelerator in preparation for a colliding plasma experiment. The utilized device consisted of a coaxial pair of electrodes, accelerating the plasma due to J×B forces. A pulse forming network, composed of three capacitors connected in parallel, with a total capacitance of 27 μF was set up. A thyratron allowed to switch the maximum applied voltage of 9 kV. Under these conditions, the pulsed currents reached peak values of about 103 kA. The measurements were performed in a small vacuum chamber with a neutral-gas prefill at gas pressures between 10 Pa and 14 000 Pa. A gas mixture of ArH{sub 2} with 2.8% H{sub 2} served as the discharge medium. H{sub 2} was chosen in order to observe the broadening of the H{sub β} emission line and thus estimate the electron density. The electron density for a single plasma accelerator reached peak values on the order of 10{sup 16} cm{sup −3}. Electrical parameters, inter alia inductance and resistance, were determined for the LCR circuit during the plasma acceleration as well as in a short circuit case. Depending on the applied voltage, the inductance and resistance reached values ranging from 194 nH to 216 nH and 13 mΩ to 23 mΩ, respectively. Furthermore, the plasma velocity was measured using a fast CCD camera. Plasma velocities of 2 km/s up to 17 km/s were observed, the magnitude being highly correlated with gas pressure and applied voltage. 16. Control system for BCP processing facility at FNAL SciTech Connect Cristian Boffo et al. 2003-09-11 The surface processing is one of the key elements of superconducting RF cavity fabrication. Safety and reliability are the main requirements for the chemical surface treatment facility being developed at FNAL. Accepting the Buffered Chemical Polishing (BCP) as the baseline process, a ''gravity feed and open etching tank'' approach has been chosen at this stage. This choice resulted in the introduction of a control system with a strong automation since the number of elements to be controlled at different steps of the process is rather big. In order to allow for maximum flexibility, two operational modes were defined within the control system: semi-automatic, which requires an operator's decision to move from one stage to another, and manual. This paper describes the main features of the control system for the BCP facility that is under development at FNAL. 17. Beam dynamics studies of the 8 GeV Linac at FNAL SciTech Connect Ostroumov, P.N.; Mustapha, B.; Carneiro, J.-P.; /Fermilab 2008-11-01 The proposed 8-GeV proton driver (PD) linac at FNAL includes a front end up to {approx}420 MeV operating at 325 MHz and a high energy section at 1300 MHz. A normal conducting RFQ and short CH type resonators are being developed for the initial acceleration of the H-minus or proton beam up to 10 MeV. From 10 MeV to {approx}420 MeV, the voltage gain is provided by superconducting (SC) spoke-loaded cavities. In the high-energy section, the acceleration will be provided by the International Linear Collider (ILC)-style SC elliptical cell cavities. To employ existing, readily available klystrons, an RF power fan out from high-power klystrons to multiple cavities is being developed. The beam dynamics simulation code TRACK, available in both serial and parallel versions, has been updated to include all known H-minus stripping mechanisms to predict the exact location of beam losses. An iterative simulation procedure is being developed to interact with a transient beam loading model taking into account RF feedback and feedforward systems. 18. K (transverse) jet algorithms in hadron colliders: The D0 experience SciTech Connect V. Daniel Elvira 2002-12-05 D0 has implemented and studied a k{sub {perpendicular}} jet algorithm for the first time in a hadron collider. The authors have submitted two physics results for publication: the subjet multiplicity in quark and gluon jets and the central inclusive jet cross section measurements. A third result, a measurement of thrust distributions in jet events, is underway. A combination of measurements using several types of algorithms and samples taken at different center-of-mass energies is desirable to understand and distinguish with higher accuracy between instrumentation and physics effects. 19. An AGS experiment to test bunching for the proton driver of the muon collider. SciTech Connect Norem, J. 1998-04-27 The proton driver for the muon collider must produce short pulses of protons in order to facilitate muon cooling and operation with polarized beams. In order to test methods of producing these bunches they have operated the AGS near transition and studied procedures which involved moving the transition energy {gamma} to the beam energy. They were able to produce stable bunches with RMS widths of {sigma} = 2.2-2.7 ns for longitudinal bunch areas of {minus}1.5 V-s, in addition to making measurements of the lowest two orders of the momentum compaction factor. 20. Operation of the DC current transformer intensity monitors at FNAL during run II SciTech Connect Crisp, J.; Fellenz, B.; Heikkinen, D.; Ibrahim, M.A.; Meyer, T.; Vogel, G.; /Fermilab 2012-01-01 Circulating beam intensity measurements at FNAL are provided by five DC current transformers (DCCT), one per machine. With the exception of the DCCT in the Recycler, all DCCT systems were designed and built at FNAL. This paper presents an overview of both DCCT systems, including the sensor, the electronics, and the front-end instrumentation software, as well as their performance during Run II. 1. 15 Years of R&D on High Field Accelerator Magnets at FNAL SciTech Connect Barzi, Emanuela; Zlobin, Alexander V. 2015-12-10 The High Field Magnet (HFM) Program at Fermi National Accelerator Laboratory (FNAL) has been developing Nb3Sn superconducting magnets, materials and technologies for present and future particle accelerators since the late 1990s. This paper summarizes the main results of the Nb3Sn accelerator magnet and superconductor R&D at FNAL and outlines the Program next steps. 2. 15 Years of R&D on high field accelerator magnets at FNAL DOE PAGESBeta Barzi, Emanuela; Zlobin, Alexander V. 2016-07-01 The High Field Magnet (HFM) Program at Fermi National Accelerator Laboratory (FNAL) has been developing Nb3Sn superconducting magnets, materials and technologies for present and future particle accelerators since the late 1990s. This paper summarizes the main results of the Nb3Sn accelerator magnet and superconductor R&D at FNAL and outlines the Program next steps. 3. Exotic colliders SciTech Connect 1994-11-01 The motivation, feasibility and potential for two unconventional collider concepts - the Gamma-Gamma Collider and the Muon Collider - are described. The importance of the development of associated technologies such as high average power, high repetition rate lasers and ultrafast phase-space techniques are outlined. 4. Photon Colliders SciTech Connect Gronberg, J 2002-10-07 A photon collider interaction region has the possibility of expanding the physics reach of a future TeV scale electron-positron collider. A survey of ongoing efforts to design the required lasers and optics to create a photon collider is presented in this paper. 5. A new solid state extractor pulser for the FNAL magnetron ion source SciTech Connect Bollinger, D. S.; Lackey, J.; Larson, J.; Triplett, K. 2015-10-05 A new solid state extractor pulser has been installed on the Fermi National Accelerator Laboratory (FNAL) magnetron ion source, replacing a vacuum tube style pulser that was used for over 40 years. The required ion source extraction voltage is 35 kV for injection into the radio frequency quadrupole. At this voltage, the old pulser had a rise time of over 150 μs due to the current limit of the vacuum tube. The new solid state pulsers are capable of 50 kV, 100 A peak current pulses and have a rise time of 9 μs when installed in the operational system. This paper will discuss the pulser design and operational experience to date. 6. A new solid state extractor pulser for the FNAL magnetron ion source Bollinger, D. S.; Lackey, J.; Larson, J.; Triplett, K. 2016-02-01 A new solid state extractor pulser has been installed on the Fermi National Accelerator Laboratory (FNAL) magnetron ion source, replacing a vacuum tube style pulser that was used for over 40 years. The required ion source extraction voltage is 35 kV for injection into the radio frequency quadrupole. At this voltage, the old pulser had a rise time of over 150 μs due to the current limit of the vacuum tube. The new solid state pulsers are capable of 50 kV, 100 A peak current pulses and have a rise time of 9 μs when installed in the operational system. This paper will discuss the pulser design and operational experience to date. 7. A New Chicane Experiment In PEP-II to Test Mitigations of the Electron Cloud Effect for Linear Colliders SciTech Connect Pivi, M.T.F.; Ng, J.S.T.; Arnett, D.; Cooper, F.; Kharakh, D.; King, F.K.; Kirby, R.E.; Kuekan, B.; Lipari, J.J.; Munro, M.; Olszewski, J.; Raubenheimer, T.O.; Seeman, J.; Smith, B.; Spencer, C.M.; Wang, L.; Wittmer, W.; Celata, C.M.; Furman, M.A.; /SLAC /LBL, Berkeley 2008-07-03 Beam instability caused by the electron cloud has been observed in positron and proton storage rings, and it is expected to be a limiting factor in the performance of future colliders [1-3]. The effect is expected to be particularly severe in magnetic field regions. To test possible mitigation methods in magnetic fields, we have installed a new 4-dipole chicane experiment in the PEP-II Low Energy Ring (LER) at SLAC with both bare and TiN-coated aluminum chambers. In particular, we have observed a large variation of the electron flux at the chamber wall as a function of the chicane dipole field. We infer this is a new high order resonance effect where the energy gained by the electrons in the positron beam depends on the phase of the electron cyclotron motion with respect to the bunch crossing, leading to a modulation of the secondary electron production. Presumably the cloud density is modulated as well and this resonance effect could be used to reduce its magnitude in future colliders. We present the experimental results obtained during January 2008 until the April final shut-down of the PEP-II machine. 8. A New Chicane Experiment in PEP-II to Test Mitigations of the Electron Cloud Effect for Linear Colliders SciTech Connect Pivi, M. T.; Pivi, M.T.F.; Ng, J.S.T.; Arnett, D.; Cooper, F.; Kharakh, D.; King, F.K.; Kirby, R.E.; Kuekan, B.; Lipari, J.J.; Munro, M.; Olszewski, J.; Raubenheimer, T.O.; Seeman, J.; Spencer, C.M.; Wang, L.; Wittmer, W.; Celata, C.M.; Furman, M.A.; Smith, B. 2008-06-11 Beam instability caused by the electron cloud has been observed in positron and proton storage rings, and it is expected to be a limiting factor in the performance of future colliders [1-3]. The effect is expected to be particularly severe in magnetic field regions. To test possible mitigation methods in magnetic fields, we have installed a new 4-dipole chicane experiment in the PEP-II Low Energy Ring (LER) at SLAC with both bare and TiN-coated aluminum chambers. In particular, we have observed a large variation of the electron flux at the chamber wall as a function of the chicane dipole field. We infer this is a new high order resonance effect where the energy gained by the electrons in the positron beam depends on the phase of the electron cyclotron motion with respect to the bunch crossing, leading to a modulation of the secondary electron production. Presumably the cloud density is modulated as well and this resonance effect could be used to reduce its magnitude in future colliders. We present the experimental results obtained during January 2008 until the April final shut-down of the PEP-II machine. 9. Muon collider progress SciTech Connect Noble, Robert J. FNAL 1998-08-01 Recent progress in the study of muon colliders is presented. An international collaboration consisting of over 100 individuals is involved in calculations and experiments to demonstrate the feasibility of this new type of lepton collider. Theoretical efforts are now concentrated on low-energy colliders in the 100 to 500 GeV center-of-mass energy range. Credible machine designs are emerging for much of a hypothetical complex from proton source to the final collider. Ionization cooling has been the most difficult part of the concept, and more powerful simulation tools are now in place to develop workable schemes. A collaboration proposal for a muon cooling experiment has been presented to the Fermilab Physics Advisory Committee, and a proposal for a targetry and pion collection channel experiment at Brookhaven National Laboratory is in preparation. Initial proton bunching and space-charge compensation experiments at existing hadron facilities have occurred to demonstrate proton driver feasibility. 10. High-performance DIRC detector for the future Electron Ion Collider experiment Kalicy, G.; Allison, L.; Cao, T.; Dzhygadlo, R.; Horn, T.; Hyde, C.; Ilieva, Y.; Nadel-Turonski, P.; Park, K.; Peters, K.; Schwarz, C.; Schwiening, J.; Stevens, J.; Xi, W.; Zorn, C. 2016-07-01 A radially-compact subsystem providing particle identification (e/π, π/K, K/p) over a wide momentum range is an essential requirement for the central detector of an Electron-Ion Collider (EIC). With a radial size of only a few cm, a detector based on Detection of Internally Reflected Cherenkov light (DIRC) principle is a very attractive solution. The R&D undertaken by the EIC PID consortium achieved the goal of showing feasibility of a high-performance DIRC that would extend the momentum coverage well beyond state-of-the-art allowing 3σ separation of π/K up to 6 GeV/c, e/K up to 1.8 GeV/c and p/K up to 10 GeV/c. A key component to reach such a performance is a special 3-layer spherical compound lens. This article describes the status of the design and R&D for the DIRC at EIC detector, with a focus on the detailed Monte Carlo simulation results for the high-performance DIRC. 11. Development of Large Area Gas Electron Multiplier Detector and Its Application to a Digital Hadron Calorimeter for Future Collider Experiments SciTech Connect Yu, Jaehoon; White, Andrew 2014-09-25 The UTA High Energy Physics Group conducted generic detector development based on large area, very thin and high sensitivity gas detector using gas electron multiplier (GEM) technology. This is in preparation for a use as a sensitive medium for sampling calorimeters in future collider experiments at the Energy Frontier as well as part of the tracking detector in Intensity Frontier experiments. We also have been monitoring the long term behavior of one of the prototype detectors (30cmx30cm) read out by the SLAC-developed 13-bit KPiX analog chip over three years and have made presentations of results at various APS meetings. While the important next step was the development of large area (1m x 1m) GEM planes, we also have looked into opportunities of applying this technology to precision tracking detectors to significantly improve the performance of the Range Stack detector for CP violation experiments and to provide an amplification layer for the liquid Argon Time Projection Chamber in the LBNE experiment. We have jointly developed 33cmx100cm large GEM foils with the CERN gas detector development group to construct 33cm x100cm unit chambers. Three of these unit chambers will be put together to form a 1m x 1m detector plane. Following characterization of one 33cmx100cm unit chamber prototype, a total of five 1m x 1m planes will be constructed and inserted into an existing 1m3 RPC DHCAL stack to test the performance of the new GEM DHCAL in particle beams. The large area GEM detector we planned to develop in this proposal not only gives an important option to DHCAL for future collider experiments but also the potential to expand its use to Intensity Frontier and Cosmic Frontier experiments as high efficiency, high amplification anode planes for liquid Argon time projection chambers. Finally, thanks to its sensitivity to X-rays and other neutral radiations and its light-weight characteristics, the large area GEM has a great potential for the use in medical imaging and 12. Design Concept and Parameters of a 15 T $Nb_{3}Sn$ Dipole Demonstrator for a 100 TEV Hadron Collider SciTech Connect Zlobin, A. V.; Andreev, N.; Barzi, E.; Kashikhin, V. V.; Novitski, I. 2015-06-01 FNAL has started the development of a 15 T $Nb_{3}Sn$ dipole demonstrator for a 100 TeV scale hadron collider. This paper describes the design concept and parameters of the 15 T $Nb_{3}Sn$ dipole demonstrator. The dipole magnetic, mechanical and quench protection concept and parameters are presented and discussed. 13. Muon colliders SciTech Connect Palmer, R.B. \|; Sessler, A.; Skrinsky, A. 1996-01-01 Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should thus be regarded as complementary. Parameters are given of 4 TeV and 0.5 TeV high luminosity {micro}{sup +}{micro}{sup {minus}}colliders, and of a 0.5 TeV lower luminosity demonstration machine. We discuss the various systems in such muon colliders, starting from the proton accelerator needed to generate the muons and proceeding through muon cooling, acceleration and storage in a collider ring. Problems of detector background are also discussed. 14. When Rubrics Collide: One Undergraduate Writing Tutor's Experience Negotiating Faculty and Institutional Assessments ERIC Educational Resources Information Center Martin, Kelli 2013-01-01 This article recounts one undergraduate writing tutor's experience helping a fellow peer navigate an institutional assessment rubric that seemed to contrast the assessment criteria provided by the student's instructor. This article presents a reflection on that experience, framed by Hutchings, Huber, and Ciccone's (2011) work on… 15. A search for B_S0 oscillations at the Tevatron collider experiment D0 SciTech Connect Krop, Dan N.; /Indiana U. 2007-04-01 We present a search for B{sub S}{sup 0} oscillations using semileptonic B{sub S} {yields} D{sub s}{mu}X (D{sub S} {yields} K{sub S}{sup 0}K). The data were collected using the D0 detector from events produced in {radical}s = 1.96 TeV proton-antiproton collisions at the Fermilab Tevatron. The Tevatron is currently the only place in the world that produces B{sub S}{sup 0} mesons and will be until early 2008 when the Large Hadron Collider begins operating at CERN. One of the vital ingredients for the search for B s oscillations is the determination of the flavor of the B{sub S}{sup 0} candidate (B{sub S}{sup 0} or {bar B}{sub S}{sup 0} ) at the time of its production, called initial state flavor tagging. We develop an likelihood based initial state flavor tagger that uses objects on the side of the event opposite to the reconstructed B meson candidate. To improve the performance of this flavor tagger, we have made it multidimensional so that it takes correlations between discriminants into account. This tagging is then certified by applying it to sample of semimuonic B{sup (0,+)} decays and measuring the well-known oscillation frequency {delta}m{sub d}. We obtain {delta}m{sub d} = 0.486 {+-} 0.021 ps{sup -1}, consistent with the world average. The tagging performance is characterized by the effective efficiency, {epsilon}D{sup 2} = (1.90 {+-} 0.41)%. We then turn to the search for B{sub S}{sup 0} oscillations in the above-named channel. A special two-dimensional mass fitting procedure is developed to separate kinematic reflections from signal events. Using this mass fitting procedure in an unbinned likelihood framework, we obtain a 95% C.L. of {Delta}m{sub s} > 1.10 ps{sup -1} and a sensitivity of 1.92 ps-1. This result is combined with other analyzed B{sub S}{sup 0} decay channels at D0 to obtain a combined 95% C.L. of {Delta}m{sub s} > 14.9 ps-1 and a sensitivity of 16.5 ps-1. The corresponding log likelihood scan has a preferred value of {Delta}m{sub s} = 19 ps-1 16. When Worlds Collide: Identity, Culture and the Lived Experiences of Research When "Teaching-Led" ERIC Educational Resources Information Center Sharp, John G.; Hemmings, Brian; Kay, Russell; Callinan, Carol 2015-01-01 This article presents detailed findings from the qualitative or interpretive phase of a mixed-methods case study focusing on the professional identities and lived experiences of research among six lecturers working in different capacities across the field of education in a "teaching-led" higher education institution. Building upon the… 17. PHENIX Conceptual Design Report. An experiment to be performed at the Brookhaven National Laboratory Relativistic Heavy Ion Collider SciTech Connect Nagamiya, Shoji; Aronson, Samuel H.; Young, Glenn R.; Paffrath, Leo 1993-01-29 The PHENIX Conceptual Design Report (CDR) describes the detector design of the PHENIX experiment for Day-1 operation at the Relativistic Heavy Ion Collider (RHIC). The CDR presents the physics capabilities, technical details, cost estimate, construction schedule, funding profile, management structure, and possible upgrade paths of the PHENIX experiment. The primary goals of the PHENIX experiment are to detect the quark-gluon plasma (QGP) and to measure its properties. Many of the potential signatures for the QGP are measured as a function of a well-defined common variable to see if any or all of these signatures show a simultaneous anomaly due to the formation of the QGP. In addition, basic quantum chromodynamics phenomena, collision dynamics, and thermodynamic features of the initial states of the collision are studied. To achieve these goals, the PHENIX experiment measures lepton pairs (dielectrons and dimuons) to study various properties of vector mesons, such as the mass, the width, and the degree of yield suppression due to the formation of the QGP. The effect of thermal radiation on the continuum is studied in different regions of rapidity and mass. The e{mu} coincidence is measured to study charm production, and aids in understanding the shape of the continuum dilepton spectrum. Photons are measured to study direct emission of single photons and to study {pi}{sup 0} and {eta} production. Charged hadrons are identified to study the spectrum shape, production of antinuclei, the {phi} meson (via K{sup +}K{sup {minus}} decay), jets, and two-boson correlations. The measurements are made down to small cross sections to allow the study of high p{sub T} spectra, and J/{psi} and {Upsilon} production. The PHENIX collaboration consists of over 300 scientists, engineers, and graduate students from 43 institutions in 10 countries. This large international collaboration is supported by US resources and significant foreign resources. 18. The Pixel Detector of the ATLAS experiment for Run 2 of the Large Hadron Collider Oide, H. 2014-12-01 The Pixel Detector of the ATLAS experiment has shown excellent performance during the whole Run 1 of the LHC. Taking advantage of the long shutdown, the detector was extracted from the experiment and brought to surface in order to equip it with new service quarter panels, to repair modules, and to ease installation of the Insertable B-Layer (IBL). The IBL is the fourth layer of the Run 2 Pixel Detector, and it was installed at a radius of 3.3 cm in May 2014 between the existing Pixel Detector and the new smaller-radius beam pipe. To cope with the high radiation and pixel occupancy due to the proximity to the interaction point, a new read-out chip and two different silicon sensor technologies (planar and 3D) have been developed. Furthermore, the physics performance is expected to improve through the reduction of pixel size. As well, targeting for a low material budget, a new mechanical support using lightweight staves and a CO2 based cooling system were adopted. An overview of the IBL project as well as the experience in its construction is presented, focusing on adopted technologies, module and staves production, qualification of assembly procedure, integration of staves around the beam pipe, and commissioning of the detector. 19. Fourth workshop on experiments and detectors for a relativistic heavy ion collider SciTech Connect Fatyga, M.; Moskowitz, B. 1990-01-01 This report contains papers on the following topics: physics at RHIC; flavor flow from quark-gluon plasma; space-time quark-gluon cascade; jets in relativistic heavy ion collisions; parton distributions in hard nuclear collisions; experimental working groups, two-arm electron/photon spectrometer collaboration; total and elastic pp cross sections; a 4{pi} tracking TPC magnetic spectrometer; hadron spectroscopy; efficiency and background simulations for J/{psi} detection in the RHIC dimuon experiment; the collision regions beam crossing geometries; Monte Carlo simulations of interactions and detectors; proton-nucleus interactions; the physics of strong electromagnetic fields in collisions of relativistic heavy ions; a real time expert system for experimental high energy/nuclear physics; the development of silicon multiplicity detectors; a pad readout detector for CRID/tracking; RHIC TPC R D progress and goals; development of analog memories for RHIC detector front-end electronic systems; calorimeter/absorber optimization for a RHIC dimuon experiment; construction of a highly segmented high resolution TOF system; progress report on a fast, particle-identifying trigger based on ring-imaging and highly integrated electronics for a TPC detector. 20. Characterising dark matter searches at colliders and direct detection experiments: Vector mediators SciTech Connect Buchmueller, Oliver; Dolan, Matthew J.; Malik, Sarah A.; McCabe, Christopher 2015-01-09 We introduce a Minimal Simplified Dark Matter (MSDM) framework to quantitatively characterise dark matter (DM) searches at the LHC. We study two MSDM models where the DM is a Dirac fermion which interacts with a vector and axial-vector mediator. The models are characterised by four parameters: mDM, Mmed , gDM and gq, the DM and mediator masses, and the mediator couplings to DM and quarks respectively. The MSDM models accurately capture the full event kinematics, and the dependence on all masses and couplings can be systematically studied. The interpretation of mono-jet searches in this framework can be used to establish an equal-footing comparison with direct detection experiments. For theories with a vector mediator, LHC mono-jet searches possess better sensitivity than direct detection searches for light DM masses (≲5 GeV). For axial-vector mediators, LHC and direct detection searches generally probe orthogonal directions in the parameter space. We explore the projected limits of these searches from the ultimate reach of the LHC and multi-ton xenon direct detection experiments, and find that the complementarity of the searches remains. In conclusion, we provide a comparison of limits in the MSDM and effective field theory (EFT) frameworks to highlight the deficiencies of the EFT framework, particularly when exploring the complementarity of mono-jet and direct detection searches. 1. Results from colliding magnetized plasma jet experiments executed at the Trident laser facility Manuel, M. J.-E.; Rasmus, A. M.; Kurnaz, C. C.; Klein, S. R.; Davis, J. S.; Drake, R. P.; Montgomery, D. S.; Hsu, S. C.; Adams, C. S.; Pollock, B. B. 2015-11-01 The interaction of high-velocity plasma flows in a background magnetic field has applications in pulsed-power and fusion schemes, as well as astrophysical environments, such as accretion systems and stellar mass ejections into the magnetosphere. Experiments recently executed at the Trident Laser Facility at the Los Alamos National Laboratory investigated the effects of an expanding aluminum plasma flow into a uniform 4.5-Tesla magnetic field created using a solenoid designed and manufactured at the University of Michigan. Opposing-target experiments demonstrate interesting collisional behavior between the two magnetized flows. Preliminary interferometry and Faraday rotation measurements will be presented and discussed. This work is funded by the U.S Department of Energy, through the NNSA-DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, grant number DE-NA0001840. Support for this work was provided by NASA through Einstein Postdoctoral Fellowship grant number PF3-140111 awarded by the Chandra X-ray Center, which is operated by the Astrophysical Observatory for NASA under contract NAS8-03060. 2. Characterising dark matter searches at colliders and direct detection experiments: Vector mediators DOE PAGESBeta Buchmueller, Oliver; Dolan, Matthew J.; Malik, Sarah A.; McCabe, Christopher 2015-01-09 We introduce a Minimal Simplified Dark Matter (MSDM) framework to quantitatively characterise dark matter (DM) searches at the LHC. We study two MSDM models where the DM is a Dirac fermion which interacts with a vector and axial-vector mediator. The models are characterised by four parameters: mDM, Mmed , gDM and gq, the DM and mediator masses, and the mediator couplings to DM and quarks respectively. The MSDM models accurately capture the full event kinematics, and the dependence on all masses and couplings can be systematically studied. The interpretation of mono-jet searches in this framework can be used to establishmore » an equal-footing comparison with direct detection experiments. For theories with a vector mediator, LHC mono-jet searches possess better sensitivity than direct detection searches for light DM masses (≲5 GeV). For axial-vector mediators, LHC and direct detection searches generally probe orthogonal directions in the parameter space. We explore the projected limits of these searches from the ultimate reach of the LHC and multi-ton xenon direct detection experiments, and find that the complementarity of the searches remains. In conclusion, we provide a comparison of limits in the MSDM and effective field theory (EFT) frameworks to highlight the deficiencies of the EFT framework, particularly when exploring the complementarity of mono-jet and direct detection searches.« less 3. Improvement of Digital Filter for the FNAL Booster Transverse Dampers SciTech Connect Zolkin, Timofey; Eddy, N.; Lebedev, V. 2013-09-26 Fermilab Booster has two transverse dampers which independently suppress beam instabilities in the horizontal and vertical planes. A suppression of the common mode signal is achieved by digital notch filter which is based on subtracting beam positions for two consecutive turns. Such system operates well if the orbit position changes sufficiently slow. Unfortunately it is not the case for FNAL Booster where the entire accelerating cycle consists of about 20000 turns, and successful transition crossing requires the orbit drifts up to about 10 μm/turn, resulting in excessive power, power amplifier saturation and loss of stability. To suppress this effect we suggest an improvement of the digital filter which can take into account fast orbit changes by using bunch positions of a few previous turns. To take into account the orbit change up toN-th order polynomial in time the system requires (N + 3) turns of “prehistory”. In the case of sufficiently small gain the damping rate and the optimal digital filter coefficients are obtained analytically. Numerical simulations verify analytical theory for the small gain and predict a system performance with gain increase. 4. Galactic scale gas flows in colliding galaxies: 3-dimensional, N-body/hydrodynamics experiments NASA Technical Reports Server (NTRS) Lamb, Susan A.; Gerber, Richard A.; Balsara, Dinshaw S. 1994-01-01 We present some results from three dimensional computer simulations of collisions between models of equal mass galaxies, one of which is a rotating, disk galaxy containing both gas and stars and the other is an elliptical containing stars only. We use fully self consistent models in which the halo mass is 2.5 times that of the disk. In the experiments we have varied the impact parameter between zero (head on) and 0.9R (where R is the radius of the disk), for impacts perpendicular to the disk plane. The calculations were performed on a Cray 2 computer using a combined N-body/smooth particle hydrodynamics (SPH) program. The results show the development of complicated flows and shock structures in the direction perpendicular to the plane of the disk and the propagation outwards of a density wave in both the stars and the gas. The collisional nature of the gas results in a sharper ring than obtained for the star particles, and the development of high volume densities and shocks. 5. Physics at hadron colliders: Experimental view SciTech Connect Siegrist, J.L. 1987-08-01 The physics of the hadron-hadron collider experiment is considered from an experimental point of view. The problems encountered in determination of how well the standard model describes collider results are discussed. 53 refs., 58 figs. 6. Search for the Production of Gluinos and Squarks with the CDF II Experiment at the Tevatron Collider SciTech Connect De Lorenzo, Gianluca 2010-05-19 sbottom decays exclusively as $\\tilde{b}$1 → b$\\tilde{x}$10. The expected signal for direct sbottom pair production is characterized by the presence of two jets of hadrons from the hadronization of the bottom quarks and E=T from the two LSPs in the final state. The events are selected with large ET and two energetic jets in the final state, and at least one jet is required to be associated with a b quark. The measurements are in good agreement with SM predictions for backgrounds. The results are translated into 95% CL exclusion limits on production cross sections and sbottom and neutralino masses in the given MSSM scenario. Cross sections down to 0.1 pb are excluded for the sbottom mass range considered. Sbottom masses up to 230 GeV/c2 are excluded at 95% CL for neutralino masses below 70 GeV/c2. This analysis increases the previous CDF limit by more than 40 GeV/c2. The sensitivity of both the inclusive and the exclusive search is dominated by systematic effects and the results of the two analyses can be considered as conclusive for CDF Run II. With the new energy frontier of the newly commissioned Large Hadron Collider in Geneva, the experience from Tevatron will be of crucial importance in the developing of effective strategies to search for SUSY in the next era of particle physics experiments. 7. Muon Collider SciTech Connect Palmer, R. 2009-10-19 Parameters are given of muon colliders with center of mass energies of 1.5 and 3 TeV. Pion production is from protons on a mercury target. Capture, decay, and phase rotation yields bunch trains of both muon signs. Six dimensional cooling reduces the emittances until the trains are merged into single bunches, one of each sign. Further cooling in 6 dimensions is then applied, followed by final transverse cooling in 50 T solenoids. After acceleration the muons enter the collider ring. Ongoing R&D is discussed. 8. The Effect of Wedge Angle on the Evolution of a Stagnation Layer in a Colliding Plasma Experiment Fallon, C.; Hayden, P.; Walsh, N.; Kennedy, E. T.; Costello, J. T. 2014-11-01 Colliding plasmas are steadily gaining significance in hohlraum studies, pulsed laser deposition and laser-induced breakdown spectroscopy for a number of reasons, not least the levels of control they o.er over the properties of the slab of plasma that accumulates at the collision front, i.e. the stagnation layer. We present here some results of a time and space resolved optical-spectroscopic study of colliding plasmas formed at the front surfaces of flat and inclined Cu slab targets as a function of the wedge angle between them for angles ranging from 100° to 180° (i.e., laterally colliding plasmas). Presented here are the kinetics of atomic/ionic spatial distributions throughout the stagnation layers, both of which have been found to vary significantly with wedge angle. 9. HIGH ENERGY PHYSICS POTENTIAL AT MUON COLLIDERS SciTech Connect PARSA,Z. 2000-04-07 In this paper, high energy physics possibilities and future colliders are discussed. The {mu}{sup +} {mu}{sup {minus}} collider and experiments with high intensity muon beams as the stepping phase towards building Higher Energy Muon Colliders (HEMC) are briefly reviewed and encouraged. 10. Colliding pulse injection experiments in non-collinear geometry for controlled laser plasma wakefield acceleration of electrons Toth, Csaba; Nakamura, K.; Geddes, C.; Michel, P.; Schroeder, C.; Esarey, E.; Leemans, W. 2006-10-01 A method for controlled injection of electrons into a plasma wakefield relying on colliding laser pulses [1] has been proposed a decade ago to produce high quality relativistic electron beams with energy spread below 1% and normalized emittances < 1 micron from a laser wakefield accelerator (LWFA). The original idea uses three pulses in which one pulse excites the plasma wake and a trailing laser pulse collides with a counterpropagating one to form a beat pattern that boosts background electrons to catch the plasma wave. Another, two-beam off-axis injection method [2] with crossing angles varying from 180 to 90 degrees avoids having optical elements on the path of the electron beam and has been studied at the LOASIS facility of LBNL as a viable method for laser triggered injection. It allows low dark current operation with controllable final beam energy and low energy spread. Here, we report on progress of electron optical injection via the two-beam non-collinear colliding pulse scheme using multi-terawatt Ti:Sapphire laser beams (45 fs, 100s of mJ) focused onto a Hydrogen gas plume. Experimental results indicate that electron beam properties are affected by the second beam. This work is supported by DoE under contract DE-AC02-05CH11231. [1] E. Esarey, et al, Phys. Rev. Lett 79, 2682 (1997) [2] G. Fubiani, Phys. Rev. E 70, 016402 (2004) 11. Deducing the nature of dark matter from direct and indirect detection experiments in the absence of collider signatures of new physics SciTech Connect Beltran, Maria; Hooper, Dan; Kolb, Edward W.; Krusberg, Zosia A. C. 2009-08-15 Despite compelling arguments that significant discoveries of physics beyond the standard model are likely to be made at the Large Hadron Collider, it remains possible that this machine will make no such discoveries, or will make no discoveries directly relevant to the dark matter problem. In this article, we study the ability of astrophysical experiments to deduce the nature of dark matter in such a scenario. In most dark matter studies, the relic abundance and detection prospects are evaluated within the context of some specific particle physics model or models (e.g., supersymmetry). Here, assuming a single weakly interacting massive particle constitutes the Universe's dark matter, we attempt to develop a model-independent approach toward the phenomenology of such particles in the absence of any discoveries at the Large Hadron Collider. In particular, we consider generic fermionic or scalar dark matter particles with a variety of interaction forms, and calculate the corresponding constraints from and sensitivity of direct and indirect detection experiments. The results may provide some guidance in disentangling information from future direct and indirect detection experiments. 12. Kaonic 3He and 4He measurements in the SIDDHARTA experiment at the DAΦNE collider Tatsuno, H.; Bazzi, M.; Beer, G.; Bombelli, L.; Bragadireanu, A. M.; Cargnelli, M.; Curceanu (Petrascu), C.; d'Uffizi, A.; Fiorini, C.; Frizzi, T.; Ghio, F.; Guaraldo, C.; Hayano, R. S.; Iliescu, M.; Ishiwatari, T.; Iwasaki, M.; Kienle, P.; Levi Sandri, P.; Longoni, A.; Marton, J.; Okada, S.; Pietreanu, D.; Ponta, T.; Rizzo, A.; Romero Vidal, A.; Sbardella, E.; Scordo, A.; Shi, H.; Sirghi, D. L.; Sirghi, F.; Tudorache, A.; Tudorache, V.; Vazquez Doce, O.; Widmann, E.; Wünschek, B.; Zmeskal, J. 2012-12-01 The SIDDHARTA collaboration measured kaonic 3He and 4He 3d → 2p X-rays with gaseous targets at the DAΦNE e+e- collider. The 2p-state strong-interaction shifts and widths were precisely determined by using 144 high-resolution silicon drift detectors. The shift of K-4He is in good agreement with theoretical calculations and consistent with the recent experimental result of KEK-PS E570. The shift of K-3He is also determined for the first time. The newly determined widths are in agreement with optical model calculations. 13. Unlocking the secrets of the kaon-nucleon/nuclei interactions at low-energies: The SIDDHARTA(-2) and the AMADEUS experiments at the DAΦNE collider Curceanu, C.; Bazzi, M.; Beer, G.; Berucci, C.; Bombelli, L.; Bragadireanu, A. M.; Cargnelli, M.; Clozza, A.; d'Uffizi, A.; Fiorini, C.; Frizzi, T.; Ghio, F.; Guaraldo, C.; Hayano, R. S.; Iliescu, M.; Ishiwatari, T.; Iwasaki, M.; Kienle, P.; Levi Sandri, P.; Longoni, A.; Marton, J.; Okada, S.; Pietreanu, D.; Piscicchia, K.; Poli Lener, M.; Ponta, T.; Romero Vidal, A.; Sbardella, E.; Scordo, A.; Shi, H.; Sirghi, D. L.; Sirghi, F.; Tatsuno, H.; Tudorache, A.; Tudorache, V.; Vazquez Doce, O.; Widmann, E.; Wünschek, B.; Zmeskal, J. 2013-09-01 The DAΦNE electron-positron collider at the Laboratori Nazionali di Frascati of INFN has made available a unique quality low-energy negative kaons “beam”, which is being used to unlock the secrets of the kaon-nucleon/nuclei interactions at low energies by the SIDDHARTA(-2) and the AMADEUS experiments. SIDDHARTA has already performed unprecedented precision measurements of kaonic atoms, and is being presently upgraded, as SIDDHARTA-2, to approach new frontiers. The AMADEUS experiment already started a data taking with a dedicated carbon target, plans to perform in the coming years precision measurements on kaon-nuclei interactions at low-energies, in particular to study the possible formation of kaonic nuclei and the Λ(1405). The two experiments are briefly presented in this paper. 14. Stable massive particles at colliders SciTech Connect Fairbairn, M.; Kraan, A.C.; Milstead, D.A.; Sjostrand, T.; Skands, P.; Sloan, T.; /Lancaster U. 2006-11-01 We review the theoretical motivations and experimental status of searches for stable massive particles (SMPs) which could be sufficiently long-lived as to be directly detected at collider experiments. The discovery of such particles would address a number of important questions in modern physics including the origin and composition of dark matter in the universe and the unification of the fundamental forces. This review describes the techniques used in SMP-searches at collider experiments and the limits so far obtained on the production of SMPs which possess various colour, electric and magnetic charge quantum numbers. We also describe theoretical scenarios which predict SMPs, the phenomenology needed to model their production at colliders and interactions with matter. In addition, the interplay between collider searches and open questions in cosmology such as dark matter composition are addressed. 15. Neutrino physics at muon colliders SciTech Connect King, B.J. 1998-03-01 An overview is given of the neutrino physics potential of future muon storage rings that use muon collider technology to produce, accelerate and store large currents of muons. After a general characterization of the neutrino beam and its interactions, some crude quantitative estimates are given for the physics performance of a muon ring neutrino experiment (MURINE) consisting of a high rate, high performance neutrino detector at a 250 GeV muon collider storage ring. 16. B physics at hadron colliders SciTech Connect Butler, J.N.; /Fermilab 2005-09-01 This paper discusses the physics opportunity and challenges for doing high precision B physics experiments at hadron colliders. It describes how these challenges have been addressed by the two currently operating experiments, CDF and D0, and how they are addressed by three experiments, ATLAS, CMS, and LHCb, at the LHC. 17. Effects of momentum conservation and flow on angular correlations observed in experiments at the BNL Relativistic Heavy Ion Collider SciTech Connect Pratt, Scott; Schlichting, Soeren; Gavin, Sean 2011-08-15 Correlations of azimuthal angles observed at the Relativistic Heavy Ion Collider have gained great attention due to the prospect of identifying fluctuations of parity-odd regions in the field sector of QCD. Whereas the observable of interest related to parity fluctuations involves subtracting opposite-sign from same-sign correlations, the STAR collaboration reported the same-sign and opposite-sign correlations separately. It is shown here how momentum conservation combined with collective elliptic flow contributes significantly to this class of correlations, although not to the difference between the opposite- and same-sign observables. The effects are modeled with a crude simulation of a pion gas. Although the simulation reproduces the scale of the correlation, the centrality dependence is found to be sufficiently different in character to suggest additional considerations beyond those present in the pion gas simulation presented here. 18. Material Procurement Report for the FNAL pp Forward Detector's Toroids and Cos8 Dipole Magnets SciTech Connect Cline, D.; Morse, R.; Orosz, I.; Thomas, L.C. 1980-10-27 We outline the possibilities of starting construction of the {bar p}p forward detector toroids and cos{theta} dipole magnets described in CDP Note 64 as soon as possible using material that already exists on the FNAL site. Personal inspection of the steel supplies indicates that as much as 2000 tons of steel or over 50% of all the steel needed for the toroids is now available at the FNAL boneyard. Copper inventories indicate that there is enough copper on the FNAL site to construct both the toroid magnets and the cos{theta} dipole magnets. A construction schedule of one toroid in FY81, two toroids in FY82, and the final toroid in FY83 is shown to be feasible. Floor space and loading requirements for the IR Hall housing the forward detector are examined and finally, budgets for the initial FY8l phase and the completed project are given. The FY81 costs are $393K and to-completion costs are$1506K. 19. Search for electroweak single top-quark production with the CDF II experiment SciTech Connect Richter, Svenja 2007-11-02 Understanding the world -- This aim drives humankind since the beginning of conscious thinking. Especially the nature of matter has been of major interest. Nowadays, we have a complex image of the constitution of matter. Atoms consist of electrons and nucleons. But even nucleons are not elementary. Their basic constituents are called quarks. Physicists developed a model describing the elementary components of matter as well as the forces between them: the standard model of elementary particle physics. The substructure of matter is only visible in scattering experiments. In high energy physics, these experiments are done at particle accelerators. The world's highest energetic collider, the Tevatron, is hosted by the Fermi National Accelerator Laboratory (FNAL), also called Fermilab, in the vicinity of Chicago. The proton-antiproton collisions with a center-of-mass energy of {radical}s = 1.96 TeV are recorded by two multipurpose detectors, namely D0 and CDF II. 20. Update to Proposal for an Experiment to Measure Mixing, CP Violation and rare Decays in Charm and Beauty Particle Decays at the Fermilac Collider - BTeV SciTech Connect Butler, Joel; Stone, Sheldon 2002-03-01 We have been requested to submit an update of the BTe V plan to the Fermilab Physics Advisory Committee, where to save money the detector has only one arm and there is no new interaction region magnet construction planned. These are to come from a currently running collider experiment at the appropriate time. The "Physics Case" section is complete and updated with the section on the "New Physics" capabilites of BTe V greatly expanded. We show that precise measurments of rare flavor-changing neutral current processes and CP violation are and will be complementary to the Tevatron and LHC to unraveling the electroweak breaking puzzle. We include a revised summary of the physics sensitivities for the one-arm detector, which are not simply taking our proposal numbers and dividing by two, because of additional improvements. One important change resulted from an improved understanding of just how important the RJCH detector is to muon and electron identification, that we can indeed separate electrons from pions and muons from pions, especially at relatively large angles beyond the physical appature of the EM calorimeter or the Muon Detector. This is documented in the "Physics Sensitivities" section. The section on the detector includes the motivation for doing band c physics at a hadron collider, and shows the changes in the detector since the proposal based on our ongoing R&D program. We do not here include a detailed description of the entire detector. That is available in the May, 2000 proposal.2 We include a summary of our R&D activities for the entire experiment. Finally, we also include a fully updated cost estimate for the one-arm system. 1. High Energy Colliders Palmer, R. B.; Gallardo, J. C. INTRODUCTION PHYSICS CONSIDERATIONS GENERAL REQUIRED LUMINOSITY FOR LEPTON COLLIDERS THE EFFECTIVE PHYSICS ENERGIES OF HADRON COLLIDERS HADRON-HADRON MACHINES LUMINOSITY SIZE AND COST CIRCULAR e^{+}e^- MACHINES LUMINOSITY SIZE AND COST e^{+}e^- LINEAR COLLIDERS LUMINOSITY CONVENTIONAL RF SUPERCONDUCTING RF AT HIGHER ENERGIES γ - γ COLLIDERS μ ^{+} μ^- COLLIDERS ADVANTAGES AND DISADVANTAGES DESIGN STUDIES STATUS AND REQUIRED R AND D COMPARISION OF MACHINES CONCLUSIONS DISCUSSION 2. Tau physics at p[bar p] colliders SciTech Connect Konigsberg, J. . High Energy Physics Lab.) 1993-01-01 Tau detection techniques in hadron colliders are discussed together with the measurements and searches performed so far. We also underline the importance tau physics has in present and future collider experiments. 3. Tau physics at p{bar p} colliders SciTech Connect Konigsberg, J. 1993-01-01 Tau detection techniques in hadron colliders are discussed together with the measurements and searches performed so far. We also underline the importance tau physics has in present and future collider experiments. 4. Experimental Study of W Z Intermediate Bosons Associated Production with the CDF Experiment at the Tevatron Collider SciTech Connect Pozzobon, Nicola; /Pisa U. 2007-09-01 Studying WZ associated production at the Fermilab Tevatron Collider is of great importance for two main reasons. On the one hand, this process would be sensitive to anomalies in the triple gauge couplings such that any deviation from the value predicted by the Standard Model would be indicative of new physics. In addition, by choosing to focus on the final state where the Z boson decays to b{bar b} pairs, the event topology would be the same as expected for associated production of a W and a Standard Model light Higgs boson (m{sub H} {approx}< 135 GeV) which decays into b{bar b} pairs most of times. The process WH {yields} W b{bar b} has an expected {sigma} {center_dot} B about five times lower than WZ {yields} Wb{bar b} for m{sub H} {approx_equal} 120 GeV. Therefore, observing this process would be a benchmark for an even more difficult search aiming at discovering the light Higgs in the WH {yields} Wb{bar b} process. After so many years of Tevatron operation only a weak WZ signal was recently observed in the full leptonic decay channel, which suffers from much less competition from background. Searching for the Z in the b{bar b} decay channel in this process is clearly a very challenging endeavour. In the work described in this thesis, WZ production is searched for in a final state where the W decays leptonically to an electron-neutrino pair or a muon-neutrino pair, with associated production of a jet pair consistent with Z decays. A set of candidate events is obtained by applying appropriate cuts to the parameters of events collected by wide acceptance leptonic triggers. To improve the signal fraction of the selected events, an algorithm was used to tag b-flavored jets by means of their content of long lived b-hadrons and corrections were developed to the jet algorithm to improve the b-jet energy resolution for a better reconstruction of the Z mass. In order to sense the presence of a signal one needs to estimate the amount of background. The relative content of 5. Overview and Performance of the Fnal Ktev Daq System Nakaya, T.; O'Dell, V.; Hazumi, M.; Yamanaka, T. KTeV is a new fixed target experiment at Permilab designed to study CP violation in the neutral kaon system. The KTeV Data Acquisition System (DAQ) is one of the highest performance DAQ's in the field of high energy physics. The sustained data throughput of the KTeV DAQ reaches 160 Mbytes/sec, and the available online level 3 processing power is 3600 Mips. In order to handle such high data throughput, the KTeV DAQ is designed around a memory matrix core where the data flow is divided and parallelized. In this paper, we present the architecture and test results of the KTeV DAQ system. 6. Observation of transverse instabilities in the FNAL 200 MeV Linac SciTech Connect McCrory, E.; Lee, G.; Webber, R.C. 1988-10-01 Using newly installed Beam Position Monitors in the downstream half of the FNAL Linac, we have observed significant transverse beam instabilities within the 30 ..mu..s beam pulse. We can affect the instability so that the peak-to-peak amplitude is as small as 0.5 mm or as large as 8 mm. The effect is largely due to a beam-plasma instability in the ten-meter 750-keV transport line. Other causes are being investigated. Using these instabilities as an analysis tool, the betatron amplitude of the beam has been reduced. 7 refs., 4 figs. 7. Status of LCLS - II QA Systems Collaboration for Cyromodule Construction at TJNAF and FNAL SciTech Connect McEwen, E. A.; Leung, J.; Bookwalter, V.; Blowers, J.; Szal, J. 2015-09-25 At the Thomas Jefferson National Accelerator Facility (Jefferson Lab), we are supporting the LCLS-II Project at SLAC. The plan is to build thirty-five 1.3 GHz continuous wave cryomodules, production to be split between JLab and FNAL (Fermilab). This has required a close collaboration between the partner labs, including enhancing our existing quality systems to include this collaboration. This overview describes the current status of the Quality System development as of August 2015, when the partner labs start the assembly of the prototype cryomodules. 8. Simulation of Multipacting in SC Low Beta Cavities at FNAL SciTech Connect Romanov, Gennady; Berrutti, Paolo; Khabiboulline, Timergali 2015-06-01 Proton Improvement Plan-II at Fermilab is a plan for improvements to the accelerator complex aimed at providing a beam power capability of at least 1 MW on target at the initiation of LBNE (Long Base Neutrino Experiment) operations. The central element of the PIP-II is a new 800 MeV superconducting linac, injecting into the existing Booster. Multipacting affects superconducting RF cavities in the entire range from high energy elliptical cavities to coaxial resonators for low-beta applications. This work is focused on multipacting study in the low-beta 325 MHz spoke cavities; namely SSR1 and SSR2, which are especially susceptible to the phenomena. The extensive simulations of multipacting in the cavities with updated material properties and comparison of the results with experimental data helped us to improve overall reliability and accuracy of these simulations. Our practical approach to the simulations is described in details. For SSR2, which has a high multipacting barrier right at the operating power level, some changes of the cavity shape to mitigate this harmful phenomenon are proposed. 9. CERN's Large Hadron Collider project Fearnley, Tom A. 1997-03-01 The paper gives a brief overview of CERN's Large Hadron Collider (LHC) project. After an outline of the physics motivation, we describe the LHC machine, interaction rates, experimental challenges, and some important physics channels to be studied. Finally we discuss the four experiments planned at the LHC: ATLAS, CMS, ALICE and LHC-B. 10. The Insertable B-Layer of the ATLAS experiment for the Run-2 at the Large Hadron Collider Guescini, Francesco 2015-10-01 The Pixel Detector of the ATLAS experiment has shown excellent performance during the whole Run-1 of LHC. Taking advantage of the long shutdown, the detector was extracted from the experiment and brought to surface, to equip it with new Service Quarter Panels, to repair modules and to ease installation of the Insertable B-Layer (IBL). IBL is a fourth layer of pixel detectors and has been installed in May 2014 between the existing Pixel Detector and a new smaller radius beam pipe at a radial distance of 3.3 cm from the beam axis. The realization of the IBL required the development of several new technologies and solutions in order to overcome the challenges introduced by the extreme environment and working conditions, such as the high radiation levels, the high pixel occupancy and the need of an exceptionally low material budget. Two silicon sensor technologies have been adopted for the IBL modules: planar and 3D. Both of these are connected via bump-bonding to the new FE-I4 front-end read-out chip. Furthermore, the physics performance will be improved through the reduction of pixel size while, targeting for a low material budget, a new mechanical support using lightweight staves and a CO2 based cooling system have been adopted. An overview of the IBL project as well as the experience in its construction is presented, focusing on adopted technologies, modules and staves production, qualification of assembly procedure, integration of staves around the beam pipe and commissioning of the detector. 11. When hope and fear collide: Expectations and experiences of first-year doctoral students in the natural sciences Robinson, C. Sean Although there is a significant body of research on the process of undergraduate education and retention, much less research exists as it relates to the doctoral experience, which is intended to be transformational in nature. At each stage of the process students are presented with a unique set of challenges and experiences that must be negotiated and mastered. However, we know very little about entering students' expectations, beliefs, goals, and identities, and how these may or may not change over time within a doctoral program. Utilizing a framework built upon socialization theory and cognitive-ecological theory, this dissertation examines the expectations that incoming doctoral students have about their programs as well as the actual experiences that these students have during their first year. Interviews were conducted with twelve students from the departments of Botany, Chemistry, and Physics prior to matriculation into their respective doctoral programs. These initial interviews provided information about students' expectations. Interviews were then conducted approximately every six to eight weeks to assess students' perceptions about their actual experiences throughout their first year. The findings of this study showed that new doctoral students tend to have uninformed and naive expectations about their programs. In addition, many of the specific policies or procedures necessary for navigation through a doctoral program were unknown to the students. While few differences existed in terms of students' expectations based on gender or discipline, there were significant differences in how international students described their expectations compared to American students. The two primary differences between American and international students revolved around the role of faculty members and the language barrier. It is clear that the first year of doctoral study is indeed a year of transition. The nature and clarity of the expectations associated with the role of 12. Photon collider Higgs factories Telnov, V. I. 2014-09-01 The discovery of the Higgs boson (and still nothing else) have triggered appearance of many proposals of Higgs factories for precision measurement of the Higgs properties. Among them there are several projects of photon colliders (PC) without e+e- in addition to PLC based on e+e- linear colliders ILC and CLIC. In this paper, following a brief discussion of Higgs factories physics program I give an overview of photon colliders based on linear colliders ILC and CLIC, and of the recently proposed photon-collider Higgs factories with no e+e- collision option based on recirculation linacs in ring tunnels. 13. THERMAL SHOCK INDUCED BY A 24 GEV PROTON BEAM IN THE TEST WINDOWS OF THE MUON COLLIDER EXPERIMENT E951 - TEST RESULTS AND THEORETICAL PREDICTIONS. SciTech Connect SIMOS,N.; KIRK,H.; FINFROCK,C.; PRIGL,R.; BROWN,K.; KAHN,S.; LUDEWIG,H.; MCDONALDK.; CATES,M.; TSAI,J.; BESHEARS,D.; RIEMER,B. 2001-11-11 The need for intense muon beams for muon colliders and neutrino factories has lead to a concept of a high performance target station in which a 1-4 MW proton beam of 6-24 GeV impinges on a target inside a high field solenoid channel. While novel technical issues exist regarding the survivability of the target itself, the need to pass the tightly focused proton beam through beam windows poses additional concerns. In this paper, issues associated with the interaction of a proton beam with window structures designed for the muon targetry experiment E951 at BNL are explored. Specifically, a 24 GeV proton beam up to 16 x 10{sup 12} per pulse and a pulse length of approximately 100 ns is expected to be tightly focused (to 0.5 mm rms one sigma radius) on an experimental target. Such beam will induce very high thermal, quasi-static and shock stresses in the window structure that exceed the strength of most common materials. In this effort, a detailed assessment of the thermal/shock response of beam windows is attempted with a goal of identifying the best window material candidate. Further, experimental strain results and comparison with the predicted values are presented and discussed. 14. PHENIX CDR update: An experiment to be performed at the Brookhaven National Laboratory relativistic heavy ion collider. Revision SciTech Connect Not Available 1994-11-01 The PHENIX Conceptual Design Report Update (CDR Update) is intended for use together with the Conceptual Design Report (CDR). The CDR Update is a companion document to the CDR, and it describes the collaborations progress since the CDR was submitted in January 1993. Therefore, this document concentrates on changes, refinements, and decisions that have been made over the past year. These documents together define the baseline PHENIX detector that the collaboration intends to build for operation at RHIC startup. In this chapter the current status of the detector and its motivation are briefly described. In Chapters 2 and 3 the detector and the physics performance are more fully developed. In Chapters 4 through 13 the details of the present design status, the technology choices, and the construction costs and schedules are presented. The physics goals of PHENIX collaboration have remained exactly as they were described in the CDR. Primary among these is the detection of a new phase of matter, the quark-gluon plasma (QGP), and the measurement of its properties. The PHENIX experiment will measure many of the best potential QGP signatures to see if any or all of these physics variables show anomalies simultaneously due to the formation of the QGP. 15. Muon Collider Task Force Report SciTech Connect Ankenbrandt, C.; Alexahin, Y.; Balbekov, V.; Barzi, E.; Bhat, C.; Broemmelsiek, D.; Bross, A.; Burov, A.; Drozhdin, A.; Finley, D.; Geer, S.; /Fermilab /Argonne /Brookhaven /Jefferson Lab /LBL, Berkeley /MUONS Inc., Batavia /UCLA /UC, Riverside /Mississippi U. 2007-12-01 Muon Colliders offer a possible long term path to lepton-lepton collisions at center-of-mass energies {radical}s {ge} 1 TeV. In October 2006 the Muon Collider Task Force (MCTF) proposed a program of advanced accelerator R&D aimed at developing the Muon Collider concept. The proposed R&D program was motivated by progress on Muon Collider design in general, and in particular, by new ideas that have emerged on muon cooling channel design. The scope of the proposed MCTF R&D program includes muon collider design studies, helical cooling channel design and simulation, high temperature superconducting solenoid studies, an experimental program using beams to test cooling channel RF cavities and a 6D cooling demonstration channel. The first year of MCTF activities are summarized in this report together with a brief description of the anticipated FY08 R&D activities. In its first year the MCTF has made progress on (1) Muon Collider ring studies, (2) 6D cooling channel design and simulation studies with an emphasis on the HCC scheme, (3) beam preparations for the first HPRF cavity beam test, (4) preparations for an HCC four-coil test, (5) further development of the MANX experiment ideas and studies of the muon beam possibilities at Fermilab, (6) studies of how to integrate RF into an HCC in preparation for a component development program, and (7) HTS conductor and magnet studies to prepare for an evaluation of the prospects for of an HTS high-field solenoid build for a muon cooling channel. 16. Collider Signal I :. Resonance Tait, Tim M. P. 2010-08-01 These TASI lectures were part of the summer school in 2008 and cover the collider signal associated with resonances in models of physics beyond the Standard Model. I begin with a review of the Z boson, one of the best-studied resonances in particle physics, and review how the Breit-Wigner form of the propagator emerges in perturbation theory and discuss the narrow width approximation. I review how the LEP and SLAC experiments could use the kinematics of Z events to learn about fermion couplings to the Z. I then make a brief survey of models of physics beyond the Standard Model which predict resonances, and discuss some of the LHC observables which we can use to discover and identify the nature of the BSM physics. I finish up with a discussion of the linear moose that one can use for an effective theory description of a massive color octet vector particle. 17. Physics goals of the next linear collider SciTech Connect Kuhlman, S.; Marciano, W.J.; Gunion, J. F.; NLC ZDR Design Group; NLC Physics Working Group 1996-05-01 We present the prospects for the next generation of high-energy physics experiments with electron-positron colliding beams. This report summarizes the current status of the design and technological basis of a linear collider of center of mass energy 500 GeV-1.5 TeV, and the opportunities for high-energy physics experiments that this machine is expected to open. 132 refs., 54 figs., 14 tabs. 18. Design of 325 MHz single and triple spoke resonators at FNAL SciTech Connect Lanfranco, G.; Apollinari, G.; Gonin, I.; Khabiboulline, T.; McConologue, F.; Romanov, G.; Wagner, R.; /Fermilab 2006-08-01 The proposed 8-GeV driver at FNAL is based on approximately 400 independently phased SC resonators. In this paper the design of 325 MHz Spoke Resonators, two single spoke resonators ({beta}=0.22 and {beta}=0.4) and a triple spoke resonator ({beta}=0.62), for the High Intensity Neutrino Source (HINS) front end is presented. We describe the optimization of the spoke resonators geometry, the goal being to minimize the E{sub peak}/E{sub acc} and B{sub peak}/E{sub acc} ratios. We report on the coupled ANSYS-MWS analysis on the resonators mechanical properties and power coupler RF design. The current status of mechanical design, slow tuning mechanism and cryostat are also presented. 19. Electron-Cloud Build-up in the FNAL Main Injector SciTech Connect Furman, M.A. 2007-06-04 We present a summary on ongoing simulation results for the electron-cloud buildup in the context of the proposed FNAL Main Injector (MI) intensity upgrade [1] in a fieldfree region at the location of the RFA electron detector [2]. By combining our simulated results for the electron flux at the vacuum chamber wall with the corresponding measurements obtained with the RFA we infer that the peak secondary electron yield (SEY) {delta}{sub max} is {approx}> 1.4, and the average electron density is n{sub e} {approx}> 10{sup 10} m{sup -3} at transition energy for the specific fill pattern and beam intensities defined below. The sensitivity of our results to several variables remains to be explored in order to reach more definitive results. Effects from the electron cloud on the beam are being investigated separately [3]. 20. Proposal for Drell-Yan Measurements of Nucleon and Nuclear Structure with the FNAL Main Injector SciTech Connect Isenhower, L.D.; Sadler, M.E.; Arrinton, J.; Geesamn, D.F.; Holt, R.J.; Jackson, H.E.; Reimer, P.E.; Potterveld, D.H.; Brown, C.N.; Garvey, G.T.; Leitch, M.J.; /Los Alamos /Rutgers U. /Texas A-M /Valparaiso U. 2001-04-01 We propose measuring the fractional momentum (x) dependence of the ratio of the anti-down to anti-up quark distributions in the proton, {bar d}(x)/{bar u}(x), using proton induced Drell-Yan reactions at 120 GeV. Recent measurements by FNAL E866 unexpectedly show considerable x dependence in this ratio for x > 0.2. A lower energy primary proton beam from the Main Injector makes it possible to extend the E866 measurements to larger x with much higher precision. The apparatus will also be used with nuclear targets to measure parton energy loss and modifications to anti-quark distributions in nuclear targets at large x (x > 0.2). 1. Reduction of beam current noise in the FNAL magnetron ion source SciTech Connect Bollinger, D. S. Karns, P. R. Tan, C. Y. 2015-04-08 The new FNAL Injector Line with a circular dimple magnetron ion source has been operational since December of 2012. Since the new injector came on line there have been variations in the H- beam current flattop observed near the downstream end of the Linac. Several different cathode geometries including a hollow cathode suggested by Dudnikov [1] were tried. Previous studies also showed that different mixtures of hydrogen and nitrogen had an effect on beam current noise [2]. We expanded on those studies by trying mixtures ranging from (0.25% nitrogen, 99.75% hydrogen) to (3% nitrogen, 97% hydrogen). The results of these studies in our test stand will be presented in this paper. 2. State of hadron collider physics SciTech Connect Grannis, P.D. \| 1993-12-01 The 9th Topical Workshop on Proton-Antiproton Collider Physics in Tsukuba Japan demonstrated clearly the enormous breadth of physics accessible in hadron cowders. Although no significant chinks were reported in the armor of the Standard Model, new results presented in this meeting have expanded our knowledge of the electroweak and strong interactions and have extended the searches for non-standard phenomena significantly. Much of the new data reported came from the CDF and D0 experiments at the Fermilab cowder. Superb operation of the Tevatron during the 1992-1993 Run and significant advances on the detector fronts -- in particular, the emergence of the new D0 detector as a productive physics instrument in its first outing and the addition of the CDF silicon vertex detector -- enabled much of this advance. It is noteworthy however that physics from the CERN collider experiments UA1 and UA4 continued to make a large impact at this meeting. In addition, very interesting summary talks were given on new results from HERA, cosmic ray experiments, on super-hadron collider physics, and on e{sup +}e{sup {minus}} experiments at LEP and TRISTAN. These summaries are reported in elsewhere in this volume. 3. SLAC Linear Collider SciTech Connect Richter, B. 1985-12-01 A report is given on the goals and progress of the SLAC Linear Collider. The status of the machine and the detectors are discussed and an overview is given of the physics which can be done at this new facility. Some ideas on how (and why) large linear colliders of the future should be built are given. 4. SLAC linear collider SciTech Connect Richter, B.; Bell, R.A.; Brown, K.L. 1980-06-01 The SLAC LINEAR COLLIDER is designed to achieve an energy of 100 GeV in the electron-positron center-of-mass system by accelerating intense bunches of particles in the SLAC linac and transporting the electron and positron bunches in a special magnet system to a point where they are focused to a radius of about 2 microns and made to collide head on. The rationale for this new type of colliding beam system is discussed, the project is described, some of the novel accelerator physics issues involved are discussed, and some of the critical technical components are described. 5. Fast feedback for linear colliders SciTech Connect Hendrickson, L.; Adolphsen, C.; Allison, S.; Gromme, T.; Grossberg, P.; Himel, T.; Krauter, K.; MacKenzie, R.; Minty, M.; Sass, R. 1995-05-01 A fast feedback system provides beam stabilization for the SLC. As the SLC is in some sense a prototype for future linear colliders, this system may be a prototype for future feedbacks. The SLC provides a good base of experience for feedback requirements and capabilities as well as a testing ground for performance characteristics. The feedback system controls a wide variety of machine parameters throughout the SLC and associated experiments, including regulation of beam position, angle, energy, intensity and timing parameters. The design and applications of the system are described, in addition to results of recent performance studies. 6. Photon Collider Physics with Real Photon Beams SciTech Connect Gronberg, J; Asztalos, S 2005-11-03 Photon-photon interactions have been an important probe into fundamental particle physics. Until recently, the only way to produce photon-photon collisions was parasitically in the collision of charged particles. Recent advances in short-pulse laser technology have made it possible to consider producing high intensity, tightly focused beams of real photons through Compton scattering. A linear e{sup +}e{sup -} collider could thus be transformed into a photon-photon collider with the addition of high power lasers. In this paper they show that it is possible to make a competitive photon-photon collider experiment using the currently mothballed Stanford Linear Collider. This would produce photon-photon collisions in the GeV energy range which would allow the discovery and study of exotic heavy mesons with spin states of zero and two. 7. Linear collider: a preview SciTech Connect Wiedemann, H. 1981-11-01 Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center. 8. Relativistic Heavy Ion Collider SciTech Connect Willen, E.H. 1986-01-01 The Relativistic Heavy Ion Collider (RHIC) is a proposed research facility at Brookhaven National Laboratory to study the collision of beams of heavy ions, up to gold in mass and at beam energies up to 100 GeV/nucleon. The physics to be explored by this collider is an overlap between the traditional disciplines of nuclear physics and high energy physics and is a continuation of the planned program of light and heavy ion physics at BNL. The machine is to be constructed in the now-empty tunnel built for the former CBA project. Various other facilities to support the collider are either in place or under construction at BNL. The collider itself, including the magnets, is in an advanced state of design, and a construction start is anticipated in the next several years. 9. Photon collider at TESLA Telnov, Valery 2001-10-01 High energy photon colliders ( γγ, γe) based on backward Compton scattering of laser light is a very natural addition to e +e - linear colliders. In this report, we consider this option for the TESLA project. Recent study has shown that the horizontal emittance in the TESLA damping ring can be further decreased by a factor of four. In this case, the γγ luminosity in the high energy part of spectrum can reach about (1/3) Le +e -. Typical cross-sections of interesting processes in γγ collisions are higher than those in e +e - collisions by about one order of magnitude, so the number of events in γγ collisions will be more than that in e +e - collisions. Photon colliders can, certainly, give additional information and they are the best for the study of many phenomena. The main question is now the technical feasibility. The key new element in photon colliders is a very powerful laser system. An external optical cavity is a promising approach for the TESLA project. A free electron laser is another option. However, a more straightforward solution is "an optical storage ring (optical trap)" with a diode pumped solid state laser injector which is today technically feasible. This paper briefly reviews the status of a photon collider based on the linear collider TESLA, its possible parameters and existing problems. 10. Commissioning and Operation of the FNAL Front end Injection Line and Ion Sources. SciTech Connect Karns, Patrick R. 2015-09-01 This thesis documents the efforts made in commissioning and operating the RFQ Injection Line (RIL) as a replacement for the Cockcroft Walton front end. The Low Energy Beam Transport (LEBT) was assembled and tested with multiwire position and emittance monitor measurements. The Radio Frequency Quadrupole (RFQ) commissioning was completed with the same measurements as well as output beam energy measurements that showed it initially accelerated beam only to 700 keV, which was 50 keV lower than the design energy. Working with the manufacturer solutions were found and instituted to continue testing. The Medium Energy Beam Transport (MEBT) was then connected as the RIL was installed as the new front end of Linac. Testing gave way to operation when the new front end was used as the source of all High Energy Physics (HEP) beam for Fermi National Accelerator Laboratory (FNAL). The magnetron ion source that provides the H- beam for the front end required several changes and eventual upgrades to operate well; such as new source operating points for vacuum pressure and cesium admixture, and new materials for critical source components. Further research was conducted on the cathode geometry and nitrogen doping of the hydrogen gas as well as using solid state switches for the extractor system high voltage. 11. Commissioning and operation of the FNAL front end injection line and ion sources Karns, Patrick R. This thesis documents the efforts made in commissioning and operating the RFQ Injection Line (RIL) as a replacement for the Cockcroft Walton front end. The Low Energy Beam Transport (LEBT) was assembled and tested with multiwire position and emittance monitor measurements. The Radio Frequency Quadrupole (RFQ) commissioning was completed with the same measurements as well as output beam energy measurements that showed it initially accelerated beam only to 700 keV, which was 50 keV lower than the design energy. Working with the manufacturer solutions were found and instituted to continue testing. The Medium Energy Beam Transport (MEBT) was then connected as the RIL was installed as the new front end of Linac. Testing gave way to operation when the new front end was used as the source of all High Energy Physics (HEP) beam for Fermi National Accelerator Laboratory (FNAL). The magnetron ion source that provides the H- beam for the front end required several changes and eventual upgrades to operate well; such as new source operating points for vacuum pressure and cesium admixture, and new materials for critical source components. Further research was conducted on the cathode geometry and nitrogen doping of the hydrogen gas as well as using solid state switches for the extractor system high voltage. 12. Physics at the linear collider Moortgat-Pick, G.; Baer, H.; Battaglia, M.; Belanger, G.; Fujii, K.; Kalinowski, J.; Heinemeyer, S.; Kiyo, Y.; Olive, K.; Simon, F.; Uwer, P.; Wackeroth, D.; Zerwas, P. M.; Arbey, A.; Asano, M.; Bagger, J.; Bechtle, P.; Bharucha, A.; Brau, J.; Brümmer, F.; Choi, S. Y.; Denner, A.; Desch, K.; Dittmaier, S.; Ellwanger, U.; Englert, C.; Freitas, A.; Ginzburg, I.; Godfrey, S.; Greiner, N.; Grojean, C.; Grünewald, M.; Heisig, J.; Höcker, A.; Kanemura, S.; Kawagoe, K.; Kogler, R.; Krawczyk, M.; Kronfeld, A. S.; Kroseberg, J.; Liebler, S.; List, J.; Mahmoudi, F.; Mambrini, Y.; Matsumoto, S.; Mnich, J.; Mönig, K.; Mühlleitner, M. M.; Pöschl, R.; Porod, W.; Porto, S.; Rolbiecki, K.; Schmitt, M.; Serpico, P.; Stanitzki, M.; Stål, O.; Stefaniak, T.; Stöckinger, D.; Weiglein, G.; Wilson, G. W.; Zeune, L.; Moortgat, F.; Xella, S.; Bagger, J.; Brau, J.; Ellis, J.; Kawagoe, K.; Komamiya, S.; Kronfeld, A. S.; Mnich, J.; Peskin, M.; Schlatter, D.; Wagner, A.; Yamamoto, H. 2015-08-01 A comprehensive review of physics at an linear collider in the energy range of GeV-3 TeV is presented in view of recent and expected LHC results, experiments from low-energy as well as astroparticle physics. The report focusses in particular on Higgs-boson, top-quark and electroweak precision physics, but also discusses several models of beyond the standard model physics such as supersymmetry, little Higgs models and extra gauge bosons. The connection to cosmology has been analysed as well. 13. Tevatron collider operations and plans SciTech Connect Peter H. Garbincius 2004-06-17 Fermilab's Tevatron is a proton-antiproton collider with center of mass energy of 1.96 TeV. The antiprotons are produced by 125 GeV protons from the Main Injector striking a stainless steel target. The 8 GeV antiprotons are collected and cooled in the Debuncher and Accumulator rings of the Antiproton Source and, just recently, in the Recycler ring before acceleration by the Main Injector and the Tevatron. In addition to energy, a vital parameter for generating physics data is the Luminosity delivered to the experiments given by a formula that is listed in detail in the paper. 14. Dynamic collimation for linear colliders SciTech Connect Merminga, N.; Ruth, R.D. 1990-06-01 Experience with the SLC has indicated that backgrounds caused by the tails of the transverse beam distribution will be a serious problem for a next generation linear collider. Mechanical scrapers may not provide the best solution, because they may be damaged by the tiny, intense beams, and also because they may induce wakefield kicks large enough to cause emittance dilution. In this paper, we present a possible solution, which uses several nonlinear lenses to drive the tails of the beam to large amplitudes where they can by more easily scraped mechanically. Simulations of several different schemes are presented and evaluated with respect to effectiveness, tolerances and wakefield effects. 4 refs., 6 figs. 15. B Physics at Hadron Colliders: Present and Future SciTech Connect Calvi, Marta 2005-10-12 An extensive program of B physics and CP violation measurements can be performed at Hadron Colliders. Results from the experiments CDF and DO at the Tevatron and prospects for future measurements from experiments at the LHC are presented here. 16. Electron-Cloud Build-Up Simulations for the FNAL Main Injector SciTech Connect Furman, Miguel .A. 2008-08-25 We present a summary on ongoing simulation results for the electron-cloud (EC) buildup in the context of the proposed FNAL Main Injector (MI) intensity upgrade effort [1]. Most of the results presented here are for the field-free region at the location of the retarding field analyzer (RFA) electron detector [2-4]. The primary input variable we exercise is the peak secondary electron yield (SEY) {delta}{sub max}, which we let vary in the range 1.2 {le} {delta}{sub max} {le} 1.7. By combining our simulated results for the electron flux at the vacuum chamber wall with the corresponding RFA measurements we infer that 1.25 {approx}< {delta}{sub max} {approx}< 1.35 at this location. From this piece of information we estimate features of the EC distribution for various fill patterns, including the average electron number density n{sub e}. We then compare the behavior of the EC for a hypothetical RF frequency f{sub RF} = 212 MHz with the current 53 MHz for a given total beam population N{sub tot}. The density n{sub e} goes through a clear threshold as a function of N{sub tot} in a field-free region. As expected, the higher frequency leads to a weaker EC effect: the threshold in N{sub tot} is a factor {approx} 2 higher for f{sub RF} = 212 MHz than for 53 MHz, and ne is correspondingly lower by a factor {approx} 2 when N{sub tot} is above threshold. We briefly describe further work that needs to be carried out, sensitivities in the calculation, and puzzles in the results that remain to be addressed. 17. The Muon Collider SciTech Connect Zisman, Michael S. 2011-01-05 We describe the scientific motivation for a new type of accelerator, the muon collider. This accelerator would permit an energy-frontier scientific program and yet would fit on the site of an existing laboratory. Such a device is quite challenging, and requires a substantial R&D program. After describing the ingredients of the facility, the ongoing R&D activities of the Muon Accelerator Program are discussed. A possible U.S. scenario that could lead to a muon collider at Fermilab is briefly mentioned. 18. Muon collider design SciTech Connect Palmer, R. \|; Sessler, A.; Skrinsky, A. 1996-03-01 The possibility of muon colliders was introduced by Skrinsky et al., Neuffer, and others. More recently, several workshops and collaboration meetings have greatly increased the level of discussion. In this paper we present scenarios for 4 TeV and 0.5 TeV colliders based on an optimally designed proton source, and for a lower luminosity 0.5 TeV demonstration based on an upgraded version of the AGS. It is assumed that a demonstration version based on upgrades of the FERMILAB machines would also be possible. 53 refs., 25 figs., 8 tabs. SciTech Connect Pondrom, L. 1991-10-03 An introduction to the techniques of analysis of hadron collider events is presented in the context of the quark-parton model. Production and decay of W and Z intermediate vector bosons are used as examples. The structure of the Electroweak theory is outlined. Three simple FORTRAN programs are introduced, to illustrate Monte Carlo calculation techniques. 25 refs. 20. Study of new FNAL-NICADD extruded scintillator as active media of large EMCal of ALICE at LHC SciTech Connect Oleg A. Grachov et al. 2004-05-04 The current conceptual design of proposed Large EMCal of ALICE at LHC is based largely on the scintillating mega-tile/fiber technology implemented in CDF Endplug upgrade project and in both barrel and endcap electromagnetic calorimeters of the STAR. The cost of scintillating material leads us to the choice of extruded polystyrene based scintillator, which is available in new FNAL-NICADD facility. Result of optical measurements, such as light yield and light yield variation, show that it is possible to use this material as active media of Large EMCal of ALICE at LHC. 1. Status of the Future Circular Collider Study Benedikt, Michael 2016-03-01 Following the 2013 update of the European Strategy for Particle Physics, the international Future Circular Collider (FCC) Study has been launched by CERN as host institute, to design an energy frontier hadron collider (FCC-hh) in a new 80-100 km tunnel with a centre-of-mass energy of about 100 TeV, an order of magnitude beyond the LHC's, as a long-term goal. The FCC study also includes the design of a 90-350 GeV high-luminosity lepton collider (FCC-ee) installed in the same tunnel, serving as Higgs, top and Z factory, as a potential intermediate step, as well as an electron-proton collider option (FCC-he). The physics cases for such machines will be assessed and concepts for experiments will be developed in time for the next update of the European Strategy for Particle Physics by the end of 2018. The presentation will summarize the status of machine designs and parameters and discuss the essential technical components to be developed in the frame of the FCC study. Key elements are superconducting accelerator-dipole magnets with a field of 16 T for the hadron collider and high-power, high-efficiency RF systems for the lepton collider. In addition the unprecedented beam power presents special challenges for the hadron collider for all aspects of beam handling and machine protection. First conclusions of geological investigations and implementation studies will be presented. The status of the FCC collaboration and the further planning for the study will be outlined. 2. Introductory Lectures on Collider Physics Tait, Tim M. P.; Wang, Lian-Tao 2013-12-01 These are elementary lectures about collider physics. They are aimed at graduate students who have some background in computing Feynman diagrams and the Standard Model, but assume no particular sophistication with the physics of high energy colliders. 3. Search for new physics at colliders SciTech Connect Chiarelli, Giorgio; /INFN, Pisa 2005-09-01 In this paper I present the most recent results of the ongoing searches, mainly from Tevatron Collider experiments, for new physics beyond the Standard Model. While no signal has been seen so far, many analyses are reaching the point in which either a discovery will take place or strong limit on currently popular theories will be set. 4. Physics Case for the International Linear Collider SciTech Connect Fujii, Keisuke; Grojean, Christophe; Peskin, Michael E.; Barklow, Tim; Gao, Yuanning; Kanemura, Shinya; Kim, Hyungdo; List, Jenny; Nojiri, Mihoko; Perelstein, Maxim; Poeschl, Roman; Reuter, Juergen; Simon, Frank; Tanabe, Tomohiko; Yu, Jaehoon; Wells, James D.; Murayama, Hitoshi; Yamamoto, Hitoshi; /Tohoku U. 2015-06-23 We summarize the physics case for the International Linear Collider (ILC). We review the key motivations for the ILC presented in the literature, updating the projected measurement uncertainties for the ILC experiments in accord with the expected schedule of operation of the accelerator and the results of the most recent simulation studies. 5. Collider Tests of the Little Higgs Model SciTech Connect Burdman, Gustavo; Perelstein, Maxim; Pierce, Aaron 2002-12-16 The little Higgs model provides an alternative to traditional candidates for new physics at the TeV scale. The new heavy gauge bosons predicted by this model should be observable at the Large Hadron Collider (LHC). We discuss how the LHC experiments could test the little Higgs model by studying the production and decay of these particles. 6. The Photon Collider at Tesla Badelek, B.; Blöchinger, C.; Blümlein, J.; Boos, E.; Brinkmann, R.; Burkhardt, H.; Bussey, P.; Carimalo, C.; Chyla, J.; Çiftçi, A. K.; Decking, W.; de Roeck, A.; Fadin, V.; Ferrario, M.; Finch, A.; Fraas, H.; Franke, F.; Galynskii, M.; Gamp, A.; Ginzburg, I.; Godbole, R.; Gorbunov, D. S.; Gounaris, G.; Hagiwara, K.; Han, L.; Heuer, R.-D.; Heusch, C.; Illana, J.; Ilyin, V.; Jankowski, P.; Jiang, Y.; Jikia, G.; Jönsson, L.; Kalachnikow, M.; Kapusta, F.; Klanner, R.; Klassen, M.; Kobayashi, K.; Kon, T.; Kotkin, G.; Krämer, M.; Krawczyk, M.; Kuang, Y. P.; Kuraev, E.; Kwiecinski, J.; Leenen, M.; Levchuk, M.; Ma, W. F.; Martyn, H.; Mayer, T.; Melles, M.; Miller, D. J.; Mtingwa, S.; Mühlleitner, M.; Muryn, B.; Nickles, P. V.; Orava, R.; Pancheri, G.; Penin, A.; Potylitsyn, A.; Poulose, P.; Quast, T.; Raimondi, P.; Redlin, H.; Richard, F.; Rindani, S. D.; Rizzo, T.; Saldin, E.; Sandner, W.; Schönnagel, H.; Schneidmiller, E.; Schreiber, H. J.; Schreiber, S.; Schüler, K. P.; Serbo, V.; Seryi, A.; Shanidze, R.; da Silva, W.; Söldner-Rembold, S.; Spira, M.; Stasto, A. M.; Sultansoy, S.; Takahashi, T.; Telnov, V.; Tkabladze, A.; Trines, D.; Undrus, A.; Wagner, A.; Walker, N.; Watanabe, I.; Wengler, T.; Will, I.; Wipf, S.; Yavaş, Ö.; Yokoya, K.; Yurkov, M.; Zarnecki, A. F.; Zerwas, P.; Zomer, F. High energy photon colliders (γγ,γe) are based on e-e- linear colliders where high energy photons are produced using Compton scattering of laser light on high energy electrons just before the interaction point. This paper is a part of the Technical Design Report of the linear collider TESLA.1 Physics program, possible parameters and some technical aspects of the photon collider at TESLA are discussed. 7. [Calorimeter based detectors for high energy hadron colliders]. [Progress report SciTech Connect Not Available 1992-08-04 This document provides a progress report on research that has been conducted under DOE Grant DEFG0292ER40697 for the past year, and describes proposed work for the second year of this 8 year grant starting November 15, 1992. Personnel supported by the contract include 4 faculty, 1 research faculty, 4 postdocs, and 9 graduate students. The work under this grant has in the past been directed in two complementary directions -- DO at Fermilab, and the second SSC detector GEM. A major effort has been towards the construction and commissioning of the new Fermilab Collider detector DO, including design, construction, testing, the commissioning of the central tracking and the central calorimeters. The first DO run is now underway, with data taking and analysis of the first events. Trigger algorithms, data acquisition, calibration of tracking and calorimetry, data scanning and analysis, and planning for future upgrades of the DO detector with the advent of the FNAL Main Injector are all involved. The other effort supported by this grant has been towards the design of GEM, a large and general-purpose SSC detector with special emphasis on accurate muon measurement over a large solid angle. This effort will culminate this year in the presentation to the SSC laboratory of the GEM Technical Design Report. Contributions are being made to the detector design, coordination, and physics simulation studies with special emphasis on muon final states. Collaboration with the RD5 group at CERN to study muon punch through and to test cathode strip chamber prototypes was begun. 8. High luminosity muon collider design SciTech Connect Palmer, R.; Gallardo, J. 1996-10-01 Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should be regarded as complementary. Parameters are given of 4 TeV high luminosity {mu}{sup +}{mu}{sup {minus}} collider, and of a 0.5 TeV lower luminosity demonstration machine. We discuss the various systems in such muon colliders. 9. Lattice of the NICA Collider Rings SciTech Connect Sidorin, Anatoly; Kozlov, Oleg; Meshkov, Igor; Mikhaylov, Vladimir; Trubnikov, Grigoriy; Lebedev, Valeri Nagaitsev, Sergei; Senichev, Yurij; /Julich, Forschungszentrum 2010-05-01 The Nuclotron-based Ion Collider fAcility (NICA) is a new accelerator complex being constructed at JINR. It is designed for collider experiments with ions and protons and has to provide ion-ion (Au{sup 79+}) and ion-proton collisions in the energy range 1 {divided_by} 4.5 GeV/n and collisions of polarized proton-proton and deuteron-deuteron beams. Collider conceptions with constant {gamma}{sub tr} and with possibility of its variation are considered. The ring has the racetrack shape with two arcs and two long straight sections. Its circumference is about 450m. The straight sections are optimized to have {beta} {approx} 35cm in two IPs and a possibility of final betatron tune adjustment. 10. Antiproton - Ion Collider for FAIR Project SciTech Connect Beller, P.; Franzke, B.; Kienle, P.; Kruecken, R.; Koop, I.; Parkhomchuk, V.; Shatunov, Y.; Skrinsky, A.; Vostrikov, V.; Widmann, E. 2006-03-20 An antiproton-ion collider (AIC), with extensive using of electron cooling, is proposed to determine rms radii for protons and neutrons in unstable and short lived nuclei by means of antiproton absorption at medium energies. The experiment makes use of the electron-ion collider complex with appropriate modifications of the electron ring to store, cool and collide antiprotons of 30 MeV energy with 740 MeV/unit ions in the NESR. Antiprotons are collected, cooled, decelerated up to 30 MeV and transferred to the electron storage ring. The radioactive nuclei beams are transferred to the CR and cooled at 740A MeV and transported via the RESR to NESR, in which especially short lived nuclei are accumulated continuously to increase the luminosity. Luminosities of about 1023 cm-2s-1 may be reached with 106 ions accumulated in the NESR in coasting mode of operation, used for Schottky spectroscopy of the fragments. 11. A New Boson with a Mass of 125 GeV Observed with the CMS Experiment at the Large Hadron Collider 2012-12-01 The Higgs boson was postulated nearly five decades ago within the framework of the standard model of particle physics and has been the subject of numerous searches at accelerators around the world. Its discovery would verify the existence of a complex scalar field thought to give mass to three of the carriers of the electroweak force—the W+, W-, and Z0 bosons—as well as to the fundamental quarks and leptons. The CMS Collaboration has observed, with a statistical significance of five standard deviations, a new particle produced in proton-proton collisions at the Large Hadron Collider at CERN. The evidence is strongest in the diphoton and four-lepton (electrons and/or muons) final states, which provide the best mass resolution in the CMS detector. The probability of the observed signal being due to a random fluctuation of the background is about 1 in 3 × 106. The new particle is a boson with spin not equal to 1 and has a mass of about 1.25 giga-electron volts. Although its measured properties are, within the uncertainties of the present data, consistent with those expected of the Higgs boson, more data are needed to elucidate the precise nature of the new particle. 12. A new boson with a mass of 125 GeV observed with the CMS experiment at the Large Hadron Collider. PubMed 2012-12-21 The Higgs boson was postulated nearly five decades ago within the framework of the standard model of particle physics and has been the subject of numerous searches at accelerators around the world. Its discovery would verify the existence of a complex scalar field thought to give mass to three of the carriers of the electroweak force-the W(+), W(-), and Z(0) bosons-as well as to the fundamental quarks and leptons. The CMS Collaboration has observed, with a statistical significance of five standard deviations, a new particle produced in proton-proton collisions at the Large Hadron Collider at CERN. The evidence is strongest in the diphoton and four-lepton (electrons and/or muons) final states, which provide the best mass resolution in the CMS detector. The probability of the observed signal being due to a random fluctuation of the background is about 1 in 3 × 10(6). The new particle is a boson with spin not equal to 1 and has a mass of about 125 [corrected] giga-electron volts. Although its measured properties are, within the uncertainties of the present data, consistent with those expected of the Higgs boson, more data are needed to elucidate the precise nature of the new particle. PMID:23258887 13. Physics and Analysis at a Hadron Collider - An Introduction (1/3) ScienceCinema None 2011-10-06 This is the first lecture of three which together discuss the physics of hadron colliders with an emphasis on experimental techniques used for data analysis. This first lecture provides a brief introduction to hadron collider physics and collider detector experiments as well as offers some analysis guidelines. The lectures are aimed at graduate students. 14. The International Linear Collider List, Benno 2014-04-01 The International Linear Collider (ILC) is a proposed e+e- linear collider with a centre-of-mass energy of 200-500 GeV, based on superconducting RF cavities. The ILC would be an ideal machine for precision studies of a light Higgs boson and the top quark, and would have a discovery potential for new particles that is complementary to that of LHC. The clean experimental conditions would allow the operation of detectors with extremely good performance; two such detectors, ILD and SiD, are currently being designed. Both make use of novel concepts for tracking and calorimetry. The Japanese High Energy Physics community has recently recommended to build the ILC in Japan. 15. Bouncing and Colliding Branes SciTech Connect Lehners, Jean-Luc 2007-11-20 In a braneworld description of our universe, we must allow for the possibility of having dynamical branes around the time of the big bang. Some properties of such domain walls in motion are discussed here, for example the ability of negative-tension domain walls to bounce off spacetime singularities and the consequences for cosmological perturbations. In this context, we will also review a colliding branes solution of heterotic M-theory that has been proposed as a model for early universe cosmology. 16. Muon Collider Progress: Accelerators SciTech Connect Zisman, Michael S. 2011-09-10 A muon collider would be a powerful tool for exploring the energy-frontier with leptons, and would complement the studies now under way at the LHC. Such a device would offer several important benefits. Muons, like electrons, are point particles so the full center-of-mass energy is available for particle production. Moreover, on account of their higher mass, muons give rise to very little synchrotron radiation and produce very little beamstrahlung. The first feature permits the use of a circular collider that can make efficient use of the expensive rf system and whose footprint is compatible with an existing laboratory site. The second feature leads to a relatively narrow energy spread at the collision point. Designing an accelerator complex for a muon collider is a challenging task. Firstly, the muons are produced as a tertiary beam, so a high-power proton beam and a target that can withstand it are needed to provide the required luminosity of ~1 × 10{sup 34} cm{sup –2}s{sup –1}. Secondly, the beam is initially produced with a large 6D phase space, which necessitates a scheme for reducing the muon beam emittance (“cooling”). Finally, the muon has a short lifetime so all beam manipulations must be done very rapidly. The Muon Accelerator Program, led by Fermilab and including a number of U.S. national laboratories and universities, has undertaken design and R&D activities aimed toward the eventual construction of a muon collider. Design features of such a facility and the supporting R&D program are described. 17. COLLIDING CRYSTALLINE BEAMS. SciTech Connect WEI, J. 1998-06-26 The understanding of crystalline beams has advanced to the point where one can now, with reasonable confidence, undertake an analysis of the luminosity of colliding crystalline beams. Such a study is reported here. It is necessary to observe the criteria, previously stated, for the creation and stability of crystalline beams. This requires, firstly, the proper design of a lattice. Secondly, a crystal must be formed, and this can usually be done at various densities. Thirdly, the crystals in a colliding-beam machine are brought into collision. We study all of these processes using the molecular dynamics (MD) method. The work parallels what was done previously, but the new part is to study the crystal-crystal interaction in collision. We initially study the zero-temperature situation. If the beam-beam force (or equivalent tune shift) is too large then overlapping crystals can not be created (rather two spatially separated crystals are formed). However, if the beam-beam force is less than but comparable to that of the space-charge forces between the particles, we find that overlapping crystals can be formed and the beam-beam tune shift can be of the order of unity. Operating at low but non-zero temperature can increase the luminosity by several orders of magnitude over that of a usual collider. The construction of an appropriate lattice, and the development of adequately strong cooling, although theoretically achievable, is a challenge in practice. 18. Colliding Crystalline Beams SciTech Connect Wei, Jie; Sessler, A.M. 1998-06-01 The understanding of crystalline beams has advanced to the point where one can now, with reasonable confidence, undertake an analysis of the luminosity of colliding crystalline beams. Such a study is reported here. It is necessary to observe the criteria, previously stated, for the creation and stability of crystalline beams. This requires, firstly, the proper design of a lattice. Secondly, a crystal must be formed, and this can usually be done at various densities. Thirdly, the crystals in a colliding-beam machine are brought into collision. We study all of these processes using the molecular dynamics (MD) method. The work parallels what was done previously, but the new part is to study the crystal-crystal interaction in collision. We initially study the zero-temperature situation. If the beam-beam force (or equivalent tune shift) is too large then over-lapping crystals can not be created (rather two spatially separated crystals are formed). However, if the beam-beam force is less than but comparable to that of the space-charge forces between the particles, we find that overlapping crystals can be formed and the beam-beam tune shift can be of the order of unity. Operating at low but non-zero temperature can increase the luminosity by several orders of magnitude over that of a usual collider. The construction of an appropriate lattice, and the development of adequately strong coding, although theoretically achievable, is a challenge in practice. 19. Scintillating Fibre Tracking at High Luminosity Colliders Joram, C.; Haefeli, G.; Leverington, B. 2015-08-01 The combination of small diameter scintillating plastic fibres with arrays of SiPM photodetectors has led to a new class of SciFi trackers usable at high luminosity collider experiments. After a short review of the main principles and history of the scintillating fibre technology, we describe the challenges and developments of the large area Scintillating Fibre Tracker currently under development for the upgraded LHCb experiment. 20. The performance of the Tevatron collider at Fermilab SciTech Connect Gelfand, N.M. 1991-10-01 This paper will describe the actual operating performance of the Tevatron, operating as a collider, and will indicate the planned upgrades which will enhance, the physics results coming from the experiments being performed at Fermilab. 1. Optimization of a closed-loop gas system for the operation of Resistive Plate Chambers at the Large Hadron Collider experiments Capeans, M.; Glushkov, I.; Guida, R.; Hahn, F.; Haider, S. 2012-01-01 Resistive Plate Chambers (RPCs), thanks to their fast time resolution (˜1 ns), suitable space resolution (˜1 cm) and low production cost (˜50 €/m2), are widely employed for the muon trigger systems at the Large Hadron Collider (LHC). Their large detector volume (they cover a surface of about 4000 m2 equivalent to 16 m3 of gas volume both in ATLAS and CMS) and the use of a relatively expensive Freon-based gas mixture make a closed-loop gas circulation unavoidable. It has been observed that the return gas of RPCs operated in conditions similar to the difficult experimental background foreseen at LHC contains a large amount of impurities potentially dangerous for long-term operation. Several gas-cleaning agents are currently in use in order to avoid accumulation of impurities in the closed-loop circuits. We present the results of a systematic study characterizing each of these cleaning agents. During the test, several RPCs were operated at the CERN Gamma Irradiation Facility (GIF) in a high radiation environment in order to observe the production of typical impurities: mainly fluoride ions, molecules of the Freon group and hydrocarbons. The polluted return gas was sent to several cartridges, each containing a different cleaning agent. The effectiveness of each material was studied using gas chromatography and mass-spectrometry techniques. Results of this test have revealed an optimized configuration of filters that is now under long-term validation.Gas optimization studies are complemented with a finite element simulation of gas flow distribution in the RPCs, aiming at its eventual optimization in terms of distribution and flow rate. 2. XXth Hadron Collider Physics Symposium In 2009, the Hadron Collider Physics Symposium took place in Evian (France), on the shore of the Geneva Lake, from 16-20 November. It was jointly organised by CERN and the French HEP community (CNRS-IN2P3 and CEA-IRFU). This year's symposium come at an important time for both the Tevatron and LHC communities. It stimulated the completion of analyses for a significant Tevatron data sample, and it allowed an in-depth review of the readiness of the LHC and its detectors just before first collisions. The programme includes sessions on top-quark and electro-weak physics, QCD, B physics, new phenomena, electro-weak symmetry breaking, heavy ions, and the status and commissioning of the LHC machine and its experiments. Conference website : http://hcp2009.in2p3.fr/ 3. Collider searches for extra dimensions SciTech Connect Landsberg, Greg; /Brown U. 2004-12-01 Searches for extra spatial dimensions remain among the most popular new directions in our quest for physics beyond the Standard Model. High-energy collider experiments of the current decade should be able to find an ultimate answer to the question of their existence in a variety of models. Until the start of the LHC in a few years, the Tevatron will remain the key player in this quest. In this paper, we review the most recent results from the Tevatron on searches for large, TeV{sup -1}-size, and Randall-Sundrum extra spatial dimensions, which have reached a new level of sensitivity and currently probe the parameter space beyond the existing constraints. While no evidence for the existence of extra dimensions has been found so far, an exciting discovery might be just steps away. 4. Artist rendering of dust grains colliding at low speeds NASA Technical Reports Server (NTRS) 2003-01-01 Clues to the formation of planets and planetary rings -- like Saturn's dazzling ring system -- may be found by studying how dust grains interact as they collide at low speeds. To study the question of low-speed dust collisions, NASA sponsored the COLLisions Into Dust Experiment (COLLIDE) at the University of Colorado. It was designed to spring-launch marble-size projectiles into trays of powder similar to space or lunar dust. COLLIDE-1 (1998) discovered that collisions below a certain energy threshold eject no material. COLLIDE-2 was designed to identify where the threshold is. In COLLIDE-2, scientists nudged small projectiles into dust beds and recorded how the dust splashed outward (video frame at top; artist's rendering at bottom). The slowest impactor ejected no material and stuck in the target. The faster impactors produced ejecta; some rebounded while others stuck in the target. 5. PERFORMANCE LIMITATIONS IN HIGH-ENERGY ION COLLIDERS SciTech Connect FISCHER, W. 2005-05-16 High-energy ion colliders (hadron colliders operating with ions other than protons) are premier research tools for nuclear physics. The collision energy and high luminosity are important design and operations considerations. The experiments also expect flexibility with frequent changes in the collision energy, detector fields, and ion species, including asymmetric collisions. For the creation, acceleration, and storage of bright intense ion beams limits are set by space charge, charge exchange, and intrabeam scattering effects. The latter leads to luminosity lifetimes of only a few hours for intense heavy ions beams. Currently, the Relativistic Heavy Ion Collider (RHIC) at BNL is the only operating high-energy ion collider. Later this decade the Large Hadron Collider (LHC), under construction at CERN, will also run with heavy ions. 6. New DIS and collider results on PDFs SciTech Connect Rizvi, E. 2015-05-15 The HERA ep collider experiments have measured the proton structure functions over a wide kinematic range. New data from the H1 experiment now extend the range to higher 4-momentum transfer (√(Q{sup 2})) over which a precision of ∼ 2% is achieved in the neutral current channel. A factor of two reduction in the systematic uncertainties over previous measurement is attained. The charged current structure function measurements are also significantly improved in precision. These data, when used in QCD analyses of the parton density functions (PDFs) reduce the PDF uncertainties particularly at high momentum fractions x which is relevant to low energy neutrino scattering cross sections. New data from the LHC pp collider experiments may also offer significant high x PDF improvements as the experimental uncertainties improve. 7. Colliding nuclei to colliding galaxies: Illustrations using a simple colliding liquid-drop apparatus Becchetti, F. D.; Mack, S. L.; Robinson, W. R.; Ojaruega, M. 2015-10-01 A simple apparatus suitable for observing the collisions between drops of fluids of various properties is described. Typical results are shown for experiments performed by undergraduate students using various types of fluids. The collisions take place under free-fall (zero-g) conditions, with analysis employing digital video. Two specific types of collisions are examined in detail, head-on collisions and peripheral, grazing collisions. The collisions for certain fluids illustrate many types of nuclear collisions and provide useful insight into these processes, including both fusion and non-fusion outcomes, often with the formation of exotic shapes or emission of secondary fragments. Collisions of other liquids show a more chaotic behavior, often resembling galactic collisions. As expected, the Weber number associated with a specific collision impact parameter is found to be the important quantity in determining the initial outcome of these colliding systems. The features observed resemble those reported by others using more elaborate experimental techniques. SciTech Connect Month, M.; Weng, W.T. 1983-06-21 The objective is to investigate whether existing technology might be extrapolated to provide the conceptual framework for a major hadron-hadron collider facility for high energy physics experimentation for the remainder of this century. One contribution to this large effort is to formalize the methods and mathematical tools necessary. In this report, the main purpose is to introduce the student to basic design procedures. From these follow the fundamental characteristics of the facility: its performance capability, its size, and the nature and operating requirements on the accelerator components, and with this knowledge, we can determine the technology and resources needed to build the new facility. 9. The super collider revisited SciTech Connect Hussein, M.S.; Pato, M.P. ) 1992-05-20 In this paper, the authors suggest a revised version of the Superconducting Super Collider (SSC) that employs the planned SSC first stage machine as an injector of 0.5 TeV protons into a power laser accelerator. The recently developed Non-linear Amplification of Inverse Bremsstrahlung Acceleration (NAIBA) concept dictates the scenario of the next stage of acceleration. Post Star Wars lasers, available at several laboratories, can be used for the purpose. The 40 TeV CM energy, a target of the SSC, can be obtained with a new machine which can be 20 times smaller than the planned SSC. 10. Muon Colliders and Neutrino Factories SciTech Connect Geer, Steve; /Fermilab 2009-11-01 Over the past decade, there has been significant progress in developing the concepts and technologies needed to produce, capture, and accelerate {Omicron}(10{sup 21}) muons per year. These developments have paved the way for a new type of neutrino source (neutrino factory) and a new type of very high energy lepton-antilepton collider (muon collider). This article reviews the motivation, design, and research and development for future neutrino factories and muon colliders. 11. Muon colliders and neutrino factories SciTech Connect Geer, S.; /Fermilab 2010-09-01 Over the last decade there has been significant progress in developing the concepts and technologies needed to produce, capture and accelerate {Omicron}(10{sup 21}) muons/year. This development prepares the way for a new type of neutrino source (Neutrino Factory) and a new type of very high energy lepton-antilepton collider (Muon Collider). This article reviews the motivation, design and R&D for Neutrino Factories and Muon Colliders. 12. Muon Colliders and Neutrino Factories * Geer, Steve 2009-11-01 Over the past decade, there has been significant progress in developing the concepts and technologies needed to produce, capture, and accelerate O(1021) muons per year. These developments have paved the way for a new type of neutrino source (neutrino factory) and a new type of very high energy lepton-antilepton collider (muon collider). This article reviews the motivation, design, and research and development for future neutrino factories and muon colliders. 13. Linear collider development at SLAC SciTech Connect Irwin, J. 1993-08-01 Linear collider R&D at SLAC comprises work on the present Stanford Linear Collider (SLC) and work toward the next linear collider (NLC). Recent SLC developments are summarized. NLC studies are divided into hardware-based and theoretical. We report on the status of the NLC Test Accelerator (NLCTA) and the final focus test beam (FFTB), describe plans for ASSET, an installation to measure accelerator structure wakefields, and mention IR design developments. Finally we review recent NLC theoretical studies, ending with the authors view of next linear collider parameter sets. 14. Future Accelerators, Muon Colliders, and Neutrino Factories SciTech Connect Richard A Carrigan, Jr. 2001-12-19 Particle physics is driven by five great topics. Neutrino oscillations and masses are now at the fore. The standard model with extensions to supersymmetry and a Higgs to generate mass explains much of the field. The origins of CP violation are not understood. The possibility of extra dimensions has raised tantalizing new questions. A fifth topic lurking in the background is the possibility of something totally different. Many of the questions raised by these topics require powerful new accelerators. It is not an overstatement to say that for some of the issues, the accelerator is almost the experiment. Indeed some of the questions require machines beyond our present capability. As this volume attests, there are parts of the particle physics program that have been significantly advanced without the use of accelerators such as the subject of neutrino oscillations and many aspects of the particle-cosmology interface. At this stage in the development of physics, both approaches are needed and important. This chapter first reviews the status of the great accelerator facilities now in operation or coming on within the decade. Next, midrange possibilities are discussed including linear colliders with the adjunct possibility of gamma-gamma colliders, muon colliders, with precursor neutrino factories, and very large hadron colliders. Finally visionary possibilities are considered including plasma and laser accelerators. 15. Linear Collider Physics Resource Book Snowmass 2001 SciTech Connect Ronan , M.T. 2001-06-01 The American particle physics community can look forward to a well-conceived and vital program of experimentation for the next ten years, using both colliders and fixed target beams to study a wide variety of pressing questions. Beyond 2010, these programs will be reaching the end of their expected lives. The CERN LHC will provide an experimental program of the first importance. But beyond the LHC, the American community needs a coherent plan. The Snowmass 2001 Workshop and the deliberations of the HEPAP subpanel offer a rare opportunity to engage the full community in planning our future for the next decade or more. A major accelerator project requires a decade from the beginning of an engineering design to the receipt of the first data. So it is now time to decide whether to begin a new accelerator project that will operate in the years soon after 2010. We believe that the world high-energy physics community needs such a project. With the great promise of discovery in physics at the next energy scale, and with the opportunity for the uncovering of profound insights, we cannot allow our field to contract to a single experimental program at a single laboratory in the world. We believe that an e{sup +}e{sup -} linear collider is an excellent choice for the next major project in high-energy physics. Applying experimental techniques very different from those used at hadron colliders, an e{sup +}e{sup -} linear collider will allow us to build on the discoveries made at the Tevatron and the LHC, and to add a level of precision and clarity that will be necessary to understand the physics of the next energy scale. It is not necessary to anticipate specific results from the hadron collider programs to argue for constructing an e{sup +}e{sup -} linear collider; in any scenario that is now discussed, physics will benefit from the new information that e{sup +}e{sup -} experiments can provide. This last point merits further emphasis. If a new accelerator could be designed and SciTech Connect Pondrom, L.G. ) 1990-12-14 The present status of hadron collider physics is reviewed. The total cross section for {bar p} + p has been measured at 1.8 TeV: {sigma}{sub tot} = 72.1 {plus minus} 3.3 mb. New data confirm the UA2 observation of W/Z {yields} {bar q}q. Precision measurements of M{sub W} by UA2 and CDF give an average value M{sub W} = 80.13 {plus minus} 0.30 GeV/c{sup 2}. When combined with measurements of M{sub Z} from LEP and SLC this number gives sin{sup 2}{theta}{sub W} = 0.227 {plus minus} 0.006, or m{sub top} = 130{sub {minus}60}{sup +40} GeV/c{sup 2} from the EWK radiative correction term {Delta}r. Evidence for hadron colliders as practical sources of b quarks has been strengthened, while searches for t quarks have pushed the mass above M{sub W}: m{sub top} > 89 GeV/c{sup 2} 95% cl (CDF Preliminary). Searches beyond the standard model based on the missing E{sub T} signature have not yet produced any positive results. Future prospects for the discovery of the top quark in the range m{sub top} < 200 GeV/c{sup 2} look promising. 80 refs., 35 figs., 7 tabs. 17. Current experiments in elementary particle physics. Revision SciTech Connect Galic, H.; Armstrong, F.E.; von Przewoski, B. 1994-08-01 This report contains summaries of 568 current and recent experiments in elementary particle physics. Experiments that finished taking data before 1988 are excluded. Included are experiments at BEPC (Beijing), BNL, CEBAF, CERN, CESR, DESY, FNAL, INS (Tokyo), ITEP (Moscow), IUCF (Bloomington), KEK, LAMPF, Novosibirsk, PNPI (St. Petersburg), PSI, Saclay, Serpukhov, SLAC, and TRIUMF, and also several underground and underwater experiments. Instructions are given for remote searching of the computer database (maintained under the SLAC/SPIRES system) that contains the summaries. 18. Contribution of inverse gluon emission to QCD corrections to the Drell-Yan process for experiments at the large hadron collider (LHC) SciTech Connect Zykunov, V. A. 2011-01-15 The contributions of inverse gluon emission to the lowest order QCD corrections to the Drell-Yan process for future experiments at LHC are calculated. The use of fully differential cross sections makes it possible to apply readily the results of these calculations for experimental purposes (in correcting data from future experiments at LHC). It is shown analytically that the present results are independent of the quark mass. A numerical analysis of respective radiative effects is performed by means of the READY FORTRAN code with allowance for the experimental cuts used at the Compact Muon Solenoid (CMS) detector. 19. TOP AND HIGGS PHYSICS AT THE HADRON COLLIDERS SciTech Connect Jabeen, Shabnam 2013-10-20 This review summarizes the recent results for top quark and Higgs boson measurements from experiments at Tevatron, a proton–antiproton collider at a center-of-mass energy of √ s =1 . 96 TeV, and the Large Hadron Collider, a proton–proton collider at a center- of-mass energy of √ s = 7 TeV. These results include the discovery of a Higgs-like boson and measurement of its various properties, and measurements in the top quark sector, e.g. top quark mass, spin, charge asymmetry and production of single top quark. 20. Longitudinal damping in the Tevatron collider SciTech Connect Kerns, Q.A.; Jackson, G.; Kerns, C.R.; Miller, H.; Reid, J.; Siemann, R.; Wildman, D. 1989-03-01 This paper describes the damper design for 6 proton on 6 pbar bunches in the Tevatron collider. Signal pickup, transient phase detection, derivative networks, and phase correction via the high-level rf are covered. Each rf station is controlled by a slow feedback loop. In addition, global feedback loops control each set of four cavities, one set for protons and one set for antiprotons. Operational experience with these systems is discussed. 7 refs., 9 figs. 1. Top physics at the Tevatron Collider SciTech Connect Margaroli, Fabrizio; /Purdue U. 2007-10-01 The top quark has been discovered in 1995 at the CDF and DO experiments located in the Tevatron ring at the Fermilab laboratory. After more than a decade the Tevatron collider, with its center-of-mass energy collisions of 1.96 TeV, is still the only machine capable of producing such exceptionally heavy particle. Here I present a selection of the most recent CDF and DO measurements performed analyzing {approx} 1 fb{sup -1} of integrated luminosity. 2. Accelerator Test Facility for Muon Collider and Neutrino Factory R&d 2010-06-01 Over the last decade there has been significant progress in developing the concepts and technologies needed to produce, capture, accelerate and collide high intensity beams of muons. At present, a high-luminosity multi-TeV muon collider presents a viable option for the next generation lepton-lepton collider, which is believed to be needed to fully explore high energy physics in the era following LHC discoveries. This article briefly reviews the needs and possibilities for a Muon Collider beam test facility to carry out the R&D program on the collider front-end and 6D cooling demonstration experiment. 3. Composite leptoquarks in hadronic colliders SciTech Connect Eboli, O.J.P.; Olinto, A.V. 1988-12-01 We study the production of composite scalar leptoquarks in hadronic colliders (CERN p-barp, Fermilab Tevatron p-barp, and the Superconducting Super Collider pp). We examine its direct single production via qg..-->..l+leptoquark, and its effect on the production of lepton pairs (p/sup (-)/p..-->..l/sup +/l/sup -/). 4. ALPs at colliders Mimasu, Ken; Sanz, Verónica 2015-06-01 New pseudo-scalars, often called axion-like particles (ALPs), abound in model-building and are often associated with the breaking of a new symmetry. Traditional searches and indirect bounds are limited to light axions, typically in or below the KeV range for ALPs coupled to photons. We present collider bounds on ALPs from mono-γ, tri-γ and mono-jet searches in a model independent fashion, as well as the prospects for the LHC and future machines. We find that they are complementary to existing searches, as they are sensitive to heavier ALPs and have the capability to cover an otherwise inaccessible region of parameter space. We also show that, assuming certain model dependent correlations between the ALP coupling to photons and gluons as well as considering the validity of the effective description of ALP interactions, mono-jet searches are in fact more suitable and effective in indirectly constraining ALP scenarios. 5. Positrons for linear colliders SciTech Connect Ecklund, S. 1987-11-01 The requirements of a positron source for a linear collider are briefly reviewed, followed by methods of positron production and production of photons by electromagnetic cascade showers. Cross sections for the electromagnetic cascade shower processes of positron-electron pair production and Compton scattering are compared. A program used for Monte Carlo analysis of electromagnetic cascades is briefly discussed, and positron distributions obtained from several runs of the program are discussed. Photons from synchrotron radiation and from channeling are also mentioned briefly, as well as positron collection, transverse focusing techniques, and longitudinal capture. Computer ray tracing is then briefly discussed, followed by space-charge effects and thermal heating and stress due to showers. (LEW) 6. Colliding Beam Fusion Reactors Rostoker, Norman; Qerushi, Artan; Binderbauer, Michl 2003-06-01 The recirculating power for virtually all types of fusion reactors has previously been calculated [1] with the Fokker-Planck equation. The reactors involve non-Maxwellian plasmas. The calculations are generic in that they do not relate to specific confinement devices. In all cases except for a Tokamak with D-T fuel the recirculating power was found to exceed the fusion power by a large factor. In this paper we criticize the generality claimed for this calculation. The ratio of circulating power to fusion power is calculated for the Colliding Beam Reactor with fuels D-T, D-He3 and p-B11. The results are respectively, 0.070, 0.141 and 0.493. 7. When Worlds Collide SciTech Connect Chang, Spencer; Kleban, Matthew; Levi, Thomas S E-mail: mk161@nyu.edu 2008-04-15 We analyze the cosmological signatures visible to an observer in a Coleman-de Luccia bubble when another such bubble collides with it. We use a gluing procedure to generalize the results of Freivogel, Horowitz and Shenker to the case of a general cosmological constant in each bubble and study the resulting spacetimes. The collision breaks the isotropy and homogeneity of the bubble universe and provides a cosmological 'axis of evil' which can affect the cosmic microwave background in several unique and potentially detectable ways. Unlike more conventional perturbations to the inflationary initial state, these signatures can survive even relatively long periods of inflation. In addition, we find that for a given collision the observers in the bubble with smaller cosmological constant are safest from collisions with domain walls, possibly providing another anthropic selection principle for small positive vacuum energy. 8. A model for computing at the SSC (Superconducting Super Collider) SciTech Connect Baden, D. . Dept. of Physics); Grossman, R. . Lab. for Advanced Computing) 1990-06-01 High energy physics experiments at the Superconducting Super Collider (SSC) will show a substantial increase in complexity and cost over existing forefront experiments, and computing needs may no longer be met via simple extrapolations from the previous experiments. We propose a model for computing at the SSC based on technologies common in private industry involving both hardware and software. 11 refs., 1 fig. 9. Introduction to colliding beams at Fermilab SciTech Connect Thompson, J. 1994-10-01 The Fermi National Accelerator Laboratory is currently the site of the worlds highest center-of-mass energy proton-antiproton colliding beam accelerator, the Tevatron. The CDF and D{O} detectors each envelop one of two luminous regions in the collider, and are thus wholly dependent on the accelerator for their success. The Tevatrons high operating energy, reliability, and record setting integrated luminosity have allowed both experiments to make world-class measurements and defined the region of physics that each can explore. The following sections are an overview of the highlights of the accelerator operation and are compiled from many sources. The major sources for each section are listed at the beginning of that section. 10. Collider signature of T-quarks SciTech Connect Carena, Marcela; Hubisz, Jay; Perelstein, Maxim; Verdier, Patrice; /Lyon, IPN 2006-10-01 Little Higgs models with T Parity contain new vector-like fermions, the T-odd quarks or ''T-quarks'', which can be produced at hadron colliders with a QCD-strength cross section. Events with two acoplanar jets and large missing transverse energy provide a simple signature of T-quark production. We show that searches for this signature with the Tevatron Run II data can probe a significant part of the Little Higgs model parameter space not accessible to previous experiments, exploring T-quark masses up to about 400 GeV. This reach covers parts of the parameter space where the lightest T-odd particle can account for the observed dark matter relic abundance. We also comment on the prospects for this search at the Large Hadron Collider (LHC). 11. The CERN SPS proton-antiproton collider Schmidt, Rudiger One of CERN's most ambitious and successful projects was the search for the intermediate bosons, W and Z [1]. The accelerator part of the project relied on a number of innovations in accelerator physics and technology. The invention of the method of stochastic cooling and the extension by many orders of magnitude beyond the initial proof of principle demonstration allowed the construction of the Antiproton Accumulator. Major modifications to the 26 GeV PS complex and the conversion of the 300 GeV SPS, which had just started up as an accelerator, to a pbar p collider were required. The SPS collider had to master the beam-beam effect far beyond limits reached before and had to function in a tight symbiosis with the UA1 and UA2 experiments. 12. Quantum-beamsstrahlung laser collider SciTech Connect Tajima, T.; Chattopadyay, S.; Xie, M. 1997-11-01 An e{sup +}e{sup {minus}} linear collider at energies beyond a TeV runs into a problem of severe beamsstrahlung, characterized by {Upsilon} on the order of unity (and beyond). In the regime of extremely high {Upsilon} the beamsstrahlung may be largely suppressed due to the quantum effect. In the design of an e{sup +}e{sup {minus}} collider there are two ways to satisfy the collider physics constraints. One is to decrease the number of particles per bunch (and thus to increase the repetition rate) and the other is to decrease the longitudinal bunch length. The former approach can limit {Upsilon}, while the latter boosts it. (It may be useful to reevaluate the future collider parameters in view of this.) The laser wakefield driver for a collider in comparison with the microwave driver naturally offers a very short bunch length, which is appropriate for the latter collider option. The authors show that this choice of collider design with a short bunch length and high {Upsilon} has advantages and provide sample design parameters at 5 TeV. Such sample design parameters challenge them in a number of fronts, such as the preservation of high quality bunches, efficient high repetition rate lasers, etc. The collision point physics simulated by the CAIN code shows a surprisingly well preserved luminosity spectrum. 13. Object based data access at the D0 experiment SciTech Connect Fuess, S.; D0 Collaboration 1995-11-01 The D{O} Experiment at Fermilab is currently participating in the FNAL Computing Divisions Computing for Analysis Project (CAP) to investigate object based data storage and access. Following a short description of the CAP system architecture, the D{O} data model is explored. A brief discussion of the method of operation of the CAP system leads into a concluding section. 14. The standard model and colliders SciTech Connect Hinchliffe, I. 1987-03-01 Some topics in the standard model of strong and electroweak interactions are discussed, as well as how these topics are relevant for the high energy colliders which will become operational in the next few years. The radiative corrections in the Glashow-Weinberg-Salam model are discussed, stressing how these corrections may be measured at LEP and the SLC. CP violation is discussed briefly, followed by a discussion of the Higgs boson and the searches which are relevant to hadron colliders are then discussed. Some of the problems which the standard model does not solve are discussed, and the energy ranges accessible to the new colliders are indicated. (LEW) 15. Hadron collider physics at UCR SciTech Connect Kernan, A.; Shen, B.C. 1997-07-01 This paper describes the research work in high energy physics by the group at the University of California, Riverside. Work has been divided between hadron collider physics and e{sup +}-e{sup {minus}} collider physics, and theoretical work. The hadron effort has been heavily involved in the startup activities of the D-Zero detector, commissioning and ongoing redesign. The lepton collider work has included work on TPC/2{gamma} at PEP and the OPAL detector at LEP, as well as efforts on hadron machines. 16. Vanilla technicolor at linear colliders Frandsen, Mads T.; Järvinen, Matti; Sannino, Francesco 2011-08-01 We analyze the reach of linear colliders for models of dynamical electroweak symmetry breaking. We show that linear colliders can efficiently test the compositeness scale, identified with the mass of the new spin-one resonances, until the maximum energy in the center of mass of the colliding leptons. In particular we analyze the Drell-Yan processes involving spin-one intermediate heavy bosons decaying either leptonically or into two standard model gauge bosons. We also analyze the light Higgs production in association with a standard model gauge boson stemming also from an intermediate spin-one heavy vector. 17. Radiation damage in the diamond based beam condition monitors of the CMS experiment at the Large Hadron Collider (LHC) at CERN Guthoff, Moritz; Afanaciev, Konstantin; Dabrowski, Anne; de Boer, Wim; Lange, Wolfgang; Lohmann, Wolfgang; Stickland, David 2013-12-01 The Beam Condition Monitor (BCM) of the CMS detector at the LHC is a protection device similar to the LHC Beam Loss Monitor system. While the electronics used is the same, poly-crystalline Chemical Vapor Deposition (pCVD) diamonds are used instead of ionization chambers as the BCM sensor material. The main purpose of the system is the protection of the silicon Pixel and Strip tracking detectors by inducing a beam dump, if the beam losses are too high in the CMS detector. By comparing the detector current with the instantaneous luminosity, the BCM detector efficiency can be monitored. The number of radiation-induced defects in the diamond, reduces the charge collection distance, and hence lowers the signal. The number of these induced defects can be simulated using the FLUKA Monte Carlo simulation. The cross-section for creating defects increases with decreasing energies of the impinging particles. This explains, why diamond sensors mounted close to heavy calorimeters experience more radiation damage, because of the high number of low energy neutrons in these regions. The signal decrease was stronger than expected from the number of simulated defects. Here polarization from trapped charge carriers in the defects is a likely candidate for explaining the difference, as suggested by Transient Current Technique (TCT) measurements. A single-crystalline (sCVD) diamond sensor shows a faster relative signal decrease than a pCVD sensor mounted at the same location. This is expected, since the relative increase in the number of defects is larger in sCVD than in pCVD sensors. 18. Neutrino alternatives for missing energy events at colliders SciTech Connect Chang, Spencer; Gouvea, Andre de 2009-07-01 If the dark matter consists of a weakly interacting massive particle, it can be produced and studied at future collider experiments like those at the LHC. The production of collider-stable weakly interacting massive particles is characterized by hard scattering events with large missing transverse energy. Here we emphasize and discuss the fact that the discovery of events inconsistent with the standard model with large missing transverse energy need not point to the existence of new, collider-stable particles. We explore an alternative explanation where the only sources of missing transverse energy are standard model neutrinos. We present concrete examples of such scenarios, focusing on supersymmetric models with R-parity violation. We also discuss means of differentiating neutrino missing energy signals from the production of new collider-stable particles. These include both model-dependent signals, such as particle tags and flavor counts, as well as model-independent tests that attempt to measure the missing particle mass. 19. When Black Holes Collide NASA Technical Reports Server (NTRS) Baker, John 2010-01-01 Among the fascinating phenomena predicted by General Relativity, Einstein's theory of gravity, black holes and gravitational waves, are particularly important in astronomy. Though once viewed as a mathematical oddity, black holes are now recognized as the central engines of many of astronomy's most energetic cataclysms. Gravitational waves, though weakly interacting with ordinary matter, may be observed with new gravitational wave telescopes, opening a new window to the universe. These observations promise a direct view of the strong gravitational dynamics involving dense, often dark objects, such as black holes. The most powerful of these events may be merger of two colliding black holes. Though dark, these mergers may briefly release more energy that all the stars in the visible universe, in gravitational waves. General relativity makes precise predictions for the gravitational-wave signatures of these events, predictions which we can now calculate with the aid of supercomputer simulations. These results provide a foundation for interpreting expect observations in the emerging field of gravitational wave astronomy. 20. The Relativistic Heavy Ion Collider Fischer, Wolfram The Relativistic Heavy Ion Collider (RHIC), shown in Fig. 1, was build to study the interactions of quarks and gluons at high energies [Harrison, Ludlam and Ozaki (2003)]. The theory of Quantum Chromodynamics (QCD) describes these interactions. One of the main goals for the RHIC experiments was the creation and study of the Quark-Gluon Plasma (QGP), which was expected to be formed after the collision of heavy ions at a temperature of approximately 2 trillion kelvin (or equivalently an energy of 150 MeV). The QGP is the substance which existed only a few microseconds after the Big Bang. The QGP was anticipated to be weakly interacting like a gas but turned out to be strongly interacting and more like a liquid. Among its unusual properties is its extremely low viscosity [Auerbach and Schlomo (2009)], which makes the QGP the substance closest to a perfect liquid known to date. The QGP is opaque to moderate energy quarks and gluons leading to a phenomenon called jet quenching, where of a jet and its recoil jet only one is observable and the other suppressed after traversing and interacting with the QGP [Jacak and Müller (2012)]... 1. Proton-antiproton collider physics SciTech Connect Shochet, M.J. 1995-07-01 The 9th {anti p}p Workshop was held in Tsukuba, Japan in October, 1993. A number of important issues remained after that meeting: Does QCD adequately describe the large cross section observed by CDF for {gamma} production below 30 GeV? Do the CDF and D0 b-production cross sections agree? Will the Tevatron live up to its billing as a world-class b-physics facility? How small will the uncertainty in the W mass be? Is there anything beyond the Minimal Standard Model? And finally, where is the top quark? Presentations at this workshop addressed all of these issues. Most of them are now resolved, but new questions have arisen. This summary focuses on the experimental results presented at the meeting by CDF and D0 physicists. Reviews of LEP and HERA results, future plans for hadron colliders and their experiments, as well as important theoretical presentations are summarized elsewhere in this volume. Section 1 reviews physics beyond the Minimal Standard Model. Issues in b and c physics are addressed in section 3. Section 4 focuses on the top quark. Electroweak physics is reviewed in section 5, followed by QCD studies in section 6. Conclusions are drawn in section 7. 2. Beam Collimation at Hadron Colliders Mokhov, N. V. 2003-12-01 Operational and accidental beam losses in hadron colliders can have a serious impact on machine and detector performance, resulting in effects ranging from minor to catastrophic. Principles and realization are described for a reliable beam collimation system required to sustain favorable background conditions in the collider detectors, provide quench stability of superconducting magnets, minimize irradiation of accelerator equipment, maintain operational reliability over the life of the machine, and reduce the impact of radiation on personnel and the environment. Based on detailed Monte-Carlo simulations, such a system has been designed and incorporated in the Tevatron collider. Its performance, comparison to measurements and possible ways to further improve the collimation efficiency are described in detail. Specifics of the collimation systems designed for the SSC, LHC, VLHC, and HERA colliders are discussed. 3. Beam Rounders for Circular Colliders SciTech Connect A. Burov; S. Nagaitsev; Ya. Derbenev 2001-07-01 By means of linear optics, an arbitrary uncoupled beam can be locally transformed into a round (rotation-invariant) state and then back. This provides an efficient way to round beams in the interaction region of circular colliders. 4. [New technology for linear colliders SciTech Connect McIntyre, P.M. 1992-08-12 This report discusses the following topics on research of microwave amplifiers for linear colliders: Context in current microwave technology development; gated field emission for microwave cathodes; cathode fabrication and tests; microwave cathode design using field emitters; and microwave localization. 5. Physicists dream of supersized collider Hao, Cindy 2015-12-01 Particle physicists in China are hopeful that the Chinese government will allocate 1 billion yuan (about £104m) to design what would be the world's largest particle accelerator - the Circular Electron Positron Collider (CEPC). 6. Muon muon collider: Feasibility study SciTech Connect 1996-06-18 A feasibility study is presented of a 2 + 2 TeV muon collider with a luminosity of L = 10{sup 35} cm{sup {minus}2} s{sup {minus}1}. The resulting design is not optimized for performance, and certainly not for cost; however, it does suffice--the authors believe--to allow them to make a credible case, that a muon collider is a serious possibility for particle physics and, therefore, worthy of R and D support so that the reality of, and interest in, a muon collider can be better assayed. The goal of this support would be to completely assess the physics potential and to evaluate the cost and development of the necessary technology. The muon collider complex consists of components which first produce copious pions, then capture the pions and the resulting muons from their decay; this is followed by an ionization cooling channel to reduce the longitudinal and transverse emittance of the muon beam. The next stage is to accelerate the muons and, finally, inject them into a collider ring which has a small beta function at the colliding point. This is the first attempt at a point design and it will require further study and optimization. Experimental work will be needed to verify the validity of diverse crucial elements in the design. 7. Physics at Future Circular Colliders Kotwal, Ashutosh 2016-03-01 The Large Hadron Collider has been a grand success with the discovery of the Higgs boson, with bright prospects for additional discoveries since the recent increase in collider energy and the anticipated large datasets. Big open questions such as the nature of dark matter, the origin of the matter-antimatter asymmetry in the Universe, and the theoretical puzzle of the finely-tuned parameters in the Higgs sector, demand new physics principles that extend the established Standard Model paradigm. Future circular colliders in a substantially larger tunnel can house both a high luminosity electron-positron collider for precision measurements of Higgs and electroweak parameters, as well as a very high energy proton-proton collider which can directly manifest particles associated with these new physics principles. We discuss the physics goals of these future circular colliders, and the prospects for elucidating fundamental new laws of nature that will significantly extend our understanding of the Universe. Detailed studies of the discovery potential in specific benchmark models will be presented, with implications for detector design. 8. Neutrino physics at a muon collider SciTech Connect King, B.J. 1998-02-01 This paper gives an overview of the neutrino physics possibilities at a future muon storage ring, which can be either a muon collider ring or a ring dedicated to neutrino physics that uses muon collider technology to store large muon currents. After a general characterization of the neutrino beam and its interactions, some crude quantitative estimates are given for the physics performance of a muon ring neutrino experiment (MURINE) consisting of a high rate, high performance neutrino detector at a 250 GeV muon collider storage ring. The paper is organized as follows. The next section describes neutrino production from a muon storage rings and gives expressions for event rates in general purpose and long baseline detectors. This is followed by a section outlining a serious design constraint for muon storage rings: the need to limit the radiation levels produced by the neutrino beam. The following two sections describe a general purpose detector and the experimental reconstruction of interactions in the neutrino target then, finally, the physics capabilities of a MURINE are surveyed. 9. Studies of E-Cloud Build up for the FNAL Main Injector and for theLHC SciTech Connect Furman, M.A. 2006-06-14 We present a summary of recent simulation studies of the electron-cloud (EC) build-up for the FNAL MI and for the LHC. In the first case we pay particular attention to the dependence on bunch intensity N{sub b} at injection energy assuming the nominal bunch spacing t{sub b} = 19 ns, and we focus on the dipole magnets and field-free regions. The saturated value of the average EC density shows a clear threshold in N{sub b} beyond which the beam will be approximately neutralized on average. For the case of the LHC we limit our discussion to arc dipoles at collision energy, and bunch spacings t{sub b} = 25 ns or t{sub b} = 75 ns. The main variables exercised in this study are N{sub b} and the peak value of the secondary emission yield (SEY) {delta}{sub max}. For t{sub b} = 25 ns we conclude that the EC power deposition is comfortably below the available cooling capacity of the cryogenic system if {delta}{sub max} is below {approx} 1.2 at nominal N{sub b}. For t{sub b} = 75 ns, the EC power deposition is insignificant. As a byproduct of this exercise, we reach a detailed understanding of the significant role played by the backscattered secondary electrons. This article summarizes the results, an slightly extends the discussions, presented in Refs. 1 and 2. 10. The Structure of Jets at Hadron Colliders SciTech Connect Larkoski, Andrew James 2012-08-01 Particle physics seeks to understand the interactions and properties of the fundamental particles. To gain understanding, there is an interplay between theory and experiment. Models are proposed to explain how particles behave and interact. These models make precise predictions that can be tested. Experiments are built and executed to measure the properties of these particles, providing necessary tests for the theories that attempt to explain the realm of fundamental particles. However, there is also another level of interaction between theory and experiment; the development of new experiments demands the study of how particles will behave with respect to the measured observables toward the goal of understanding the details and idiosyncrasies of the measurements very well. Only once these are well-modeled and understood can one be con dent that the data that are measured is trustworthy. The modeling and interpretation of the physics of a proton collider, such as the LHC, is the main topic of this thesis. 11. Collider study on the loop-induced dark matter mediation Tsai, Yuhsin 2016-06-01 Collider experiments are one of the most promising ways to constrain Dark Matter (DM) interactions. For DM couplings involving light mediators, especially for the loop-mediated interactions, a meaningful interpretation of the results requires to go beyond effective field theory. In this note we discuss the study of the magnetic dipole interacting DM, focusing on a model with anarchic dark flavor structure. By including the momentum-dependent form factors that mediate the coupling - given by the Dark Penguin - in collider processes, we study bounds from monophoton, diphoton, and non-pointing photon searches at the LHC. We also compare our results to constraints from the direct detection experiments. 12. R&D Toward a Neutrino Factory and Muon Collider SciTech Connect Zisman, Michael S 2011-03-20 Significant progress has been made in recent years in R&D towards a neutrino factory and muon collider. The U.S. Muon Accelerator Program (MAP) has been formed recently to expedite the R&D efforts. This paper will review the U.S. MAP R&D programs for a neutrino factory and muon collider. Muon ionization cooling research is the key element of the program. The first muon ionization cooling demonstration experiment, MICE (Muon Ionization Cooling Experiment), is under construction now at RAL (Rutherford Appleton Laboratory) in the UK. The current status of MICE will be described. 13. Current experiments in elementary-particle physics - March 1983 SciTech Connect Wohl, C.G.; Armstrong, F.E.; Rittenberg, A. 1983-03-01 Microfiche are included which contain summaries of 479 experiments in elementary particle physics. Experiments are included at the following laboratories: Brookhaven (BNL); CERN; CESR; DESY; Fermilab (FNAL); Institute for Nuclear Studies (INS); KEK; LAMPF; Serpukhov (SERP); SIN; SLAC; and TRIUMF. Also, summaries of proton decay experiments are included. A list of experiments and titles is included; and a beam-target-momentum index and a spokesperson index are given. Properties of beams at the facilities are tabulated. (WHK) 14. High energy accelerator and colliding beam user group SciTech Connect Not Available 1990-09-01 This report discusses the following topics: OPAL experiment at LEP; D{phi} experiment at Fermilab; deep inelastic muon interactions at TEV II; CYGNUS experiment; final results from {nu}{sub e}{sup {minus}e} elastic scattering; physics with CLEO detector at CESR; results from JADE at PETRA; rare kaon-decay experiment at BNL; search for top quark; and super conducting super collider activities. 15. Relativistic klystron research for linear colliders SciTech Connect Allen, M.A.; Callin, R.S.; Deruyter, H.; Eppley, K.R.; Fant, K.S.; Fowkes, W.R.; Herrmannsfeldt, W.B.; Higo, T.; Hoag, H.A.; Koontz, R.F. 1988-09-01 Relativistic klystrons are being developed as a power source for high gradient accelerator applications which include large linear electron-positron colliders, compact accelerators, and FEL sources. We have attained 200 MW peak power at 11.4 GHz from a relativistic klystron, and 140 MV/m longitudinal gradient in a short 11.4 GHz accelerator section. We report here on the design of our relativistic klystrons, the results of our experiments so far, and some of our plans for the near future. 5 refs., 9 figs., 1 tab. 16. Muon collider interaction region design SciTech Connect Alexahin, Y.I.; Gianfelice-Wendt, E.; Kashikhin, V.V.; Mokhov, N.V.; Zlobin, A.V.; Alexakhin, V.Y.; /Dubna, JINR 2010-05-01 Design of a muon collider interaction region (IR) presents a number of challenges arising from low {beta}* < 1 cm, correspondingly large beta-function values and beam sizes at IR magnets, as well as the necessity to protect superconducting magnets and collider detectors from muon decay products. As a consequence, the designs of the IR optics, magnets and machine-detector interface are strongly interlaced and iterative. A consistent solution for the 1.5 TeV c.o.m. muon collider IR is presented. It can provide an average luminosity of 10{sup 34} cm{sup -2}s{sup -1} with an adequate protection of magnet and detector components. 17. Luminosity determination at proton colliders Grafström, P.; Kozanecki, W. 2015-03-01 Luminosity is a key parameter in any particle collider, and its precise determination has proven particularly challenging at hadron colliders. After introducing the concept of luminosity in its multiple incarnations and offering a brief survey of the pp and p p bar colliders built to date, this article outlines the various methods that have been developed for relative-luminosity monitoring, as well as the complementary approaches considered for establishing an absolute luminosity scale. This is followed by a survey, from both a historical and a technical perspective, of luminosity determination at the ISR, the S p p ¯ S, the Tevatron, RHIC and the LHC. For each of these, we first delineate the interplay between the experimental context, the specificities of the accelerator, and the precision targets suggested by the physics program. We then detail how the different methods were applied to specific experimental environments and how successfully they meet the precision goals. 18. Beam-Based Alignment of the NuMI Target Station Components at FNAL SciTech Connect Zwaska, R.; Bishai, M.; Childress, S.; Drake, G.; Escobar, C.; Gouffon, P.; Harris, D.A.; Hylen, J.; Indurthy, D.; Koizumi, G.; Kopp, S.; /Argonne /Brookhaven /Frascati /Sao Paulo U. /Campinas State U. /Texas U. 2006-09-01 The Neutrinos at the Main Injector (NuMI) facility is a conventional horn-focused neutrino beam which produces muon neutrinos from a beam of mesons directed into a long evacuated decay volume. The relative alignment of the primary proton beam, target, and focusing horns affects the neutrino energy spectrum delivered to experiments. This paper describes a check of the alignment of these components using the proton beam. 19. The NuMI Beam at FNAL and its Use for Neutrino Cross Section Measurements SciTech Connect Kopp, Sacha E. 2007-12-21 The Neutrinos at the Main Injector (NuMI) facility at Fermilab began operations in late 2004. NuMI will deliver an intense {nu}{sub {mu}} beam of variable energy (2-20 GeV). Several aspects of the design and results from runs of the MINOS experiment are reviewed. I also discuss technique to measure directly the neutrino flux using a muon flux system at the end of the NuMI line. 20. The dark penguin shines light at colliders Primulando, Reinard; Salvioni, Ennio; Tsai, Yuhsin 2015-07-01 Collider experiments are one of the most promising ways to constrain Dark Matter (DM) interactions. For several types of DM-Standard Model couplings, a meaningful interpretation of the results requires to go beyond effective field theory, considering simplified models with light mediators. This is especially important in the case of loop-mediated interactions. In this paper we perform the first simplified model study of the magnetic dipole interacting DM, by including the one-loop momentum-dependent form factors that mediate the coupling — given by the Dark Penguin — in collider processes. We compute bounds from the monojet, monophoton, and diphoton searches at the 8 and 14 TeV LHC, and compare the results to those of direct and indirect detection experiments. Future searches at the 100 TeV hadron collider and at the ILC are also addressed. We find that the optimal search strategy requires loose cuts on the missing transverse energy, to capture the enhancement of the form factors near the threshold for on-shell production of the mediators. We consider both minimal models and models where an additional state beyond the DM is accessible. In the latter case, under the assumption of anarchic flavor structure in the dark sector, the LHC monophoton and diphoton searches will be able to set much stronger bounds than in the minimal scenario. A determination of the mass of the heavier dark fermion might be feasible using the M T2 variable. In addition, if the Dark Penguin flavor structure is almost aligned with that of the DM mass, a displaced signal from the decay of the heavier dark fermion into the DM and photon can be observed. This allows us to set constraints on the mixings and couplings of the model from an existing search for non-pointing photons. 1. Study of requirements and performances of the electromagnetic calorimeter for the Mu2e experiment at Fermilab SciTech Connect Soleti, S. 2015-06-15 In this thesis we discuss the simulation and tests carried out for the optimization and design of the electromagnetic calorimeter for the Mu2e (Muon to electron conversion) experiment, which is a proposed experiment part of the Muon Campus hosted at Fermi National Accelerator Laboratory (FNAL) in Batavia, United States. 2. Measurement of the radiation field surrounding the Collider Detector at Fermilab SciTech Connect K. Kordas et al. 2004-01-28 We present here the first direct and detailed measurements of the spatial distribution of the ionizing radiation surrounding a hadron collider experiment. Using data from two different exposures we measure the effect of additional shielding on the radiation field around the Collider Detector at Fermilab (CDF). Employing a simple model we parameterize the ionizing radiation field surrounding the detector. 3. Muon Muon Collider: Feasibility Study SciTech Connect Gallardo, J.C.; Palmer, R.B.; Tollestrup, A.V.; Sessler, A.M.; Skrinsky, A.N.; Ankenbrandt, C.; Geer, S.; Griffin, J.; Johnstone, C.; Lebrun, P.; McInturff, A.; Mills, Frederick E.; Mokhov, N.; Moretti, A.; Neuffer, D.; Ng, K.Y.; Noble, R.; Novitski, I.; Popovic, M.; Qian, C.; Van Ginneken, A. /Fermilab /Brookhaven /Wisconsin U., Madison /Tel Aviv U. /Indiana U. /UCLA /LBL, Berkeley /SLAC /Argonne /Sobolev IM, Novosibirsk /UC, Davis /Munich, Tech. U. /Virginia U. /KEK, Tsukuba /DESY /Novosibirsk, IYF /Jefferson Lab /Mississippi U. /SUNY, Stony Brook /MIT /Columbia U. /Fairfield U. /UC, Berkeley 2012-04-05 A feasibility study is presented of a 2 + 2 TeV muon collider with a luminosity of L = 10{sup 35} cm{sup -2}s{sup -1}. The resulting design is not optimized for performance, and certainly not for cost; however, it does suffice - we believe - to allow us to make a credible case, that a muon collider is a serious possibility for particle physics and, therefore, worthy of R and D support so that the reality of, and interest in, a muon collider can be better assayed. The goal of this support would be to completely assess the physics potential and to evaluate the cost and development of the necessary technology. The muon collider complex consists of components which first produce copious pions, then capture the pions and the resulting muons from their decay; this is followed by an ionization cooling channel to reduce the longitudinal and transverse emittance of the muon beam. The next stage is to accelerate the muons and, finally, inject them into a collider ring wich has a small beta function at the colliding point. This is the first attempt at a point design and it will require further study and optimization. Experimental work will be needed to verify the validity of diverse crucial elements in the design. Muons because of their large mass compared to an electron, do not produce significant synchrotron radiation. As a result there is negligible beamstrahlung and high energy collisions are not limited by this phenomena. In addition, muons can be accelerated in circular devices which will be considerably smaller than two full-energy linacs as required in an e{sup +} - e{sup -} collider. A hadron collider would require a CM energy 5 to 10 times higher than 4 TeV to have an equivalent energy reach. Since the accelerator size is limited by the strength of bending magnets, the hadron collider for the same physics reach would have to be much larger than the muon collider. In addition, muon collisions should be cleaner than hadron collisions. There are many detailed particle 4. Overview and performance of the FNAL KTeV DAQ system SciTech Connect Nakaya, T.; ODell, V.; Hazumi, M.; Yamanaka, T. 1995-11-01 KTeV is a new fixed target experiment at Fermilab designed to study CP violation in the neutral kaon system. The KTeV Data Acquisition System (DAQ) is out of the highest performance DAQs in the field of high energy physics. The sustained data throughput of the KTeV DAQ reaches 160 Mbytes/sec, and the available online level 3 processing power is 3600 Mips. In order to handle such high data throughput, the KTeV DAQ is designed around a memory matrix core where the data flow is divided and parallelized. In this paper, we present the architecture and test results of the KTeV DAQ system. 5. Muon Colliders: The Next Frontier ScienceCinema Tourun, Yagmur [Illinois Institute of Technology, Chicago, Illinois, United States 2010-01-08 Muon Colliders provide a path to the energy frontier in particle physics but have been regarded to be "at least 20 years away" for 20 years. I will review recent progress in design studies and hardware R&D and show that a Muon Collider can be established as a real option for the post-LHC era if the current vigorous R&D effort revitalized by the Muon Collider Task Force at Fermilab can be supported to its conclusion. All critical technologies are being addressed and no show-stoppers have emerged. Detector backgrounds have been studied in detail and appear to be manageable and the physics can be done with existing detector technology. A muon facility can be built through a staged scenario starting from a low-energy muon source with unprecedented intensity for exquisite reach for rare processes, followed by a Neutrino Factory with ultrapure neutrino beams with unparalleled sensitivity for disentangling neutrino mixing, leading to an energy frontier Muon Collider with excellent energy resolution. 6. Muon Colliders: The Next Frontier SciTech Connect Tourun, Yagmur 2009-07-29 Muon Colliders provide a path to the energy frontier in particle physics but have been regarded to be 'at least 20 years away' for 20 years. I will review recent progress in design studies and hardware R&D and show that a Muon Collider can be established as a real option for the post-LHC era if the current vigorous R&D effort revitalized by the Muon Collider Task Force at Fermilab can be supported to its conclusion. All critical technologies are being addressed and no show-stoppers have emerged. Detector backgrounds have been studied in detail and appear to be manageable and the physics can be done with existing detector technology. A muon facility can be built through a staged scenario starting from a low-energy muon source with unprecedented intensity for exquisite reach for rare processes, followed by a Neutrino Factory with ultrapure neutrino beams with unparalleled sensitivity for disentangling neutrino mixing, leading to an energy frontier Muon Collider with excellent energy resolution. 7. Muon Colliders: The Next Frontier SciTech Connect Tourun, Yagmur 2009-07-29 Muon Colliders provide a path to the energy frontier in particle physics but have been regarded to be "at least 20 years away" for 20 years. I will review recent progress in design studies and hardware R&D and show that a Muon Collider can be established as a real option for the post-LHC era if the current vigorous R&D effort revitalized by the Muon Collider Task Force at Fermilab can be supported to its conclusion. All critical technologies are being addressed and no show-stoppers have emerged. Detector backgrounds have been studied in detail and appear to be manageable and the physics can be done with existing detector technology. A muon facility can be built through a staged scenario starting from a low-energy muon source with unprecedented intensity for exquisite reach for rare processes, followed by a Neutrino Factory with ultrapure neutrino beams with unparalleled sensitivity for disentangling neutrino mixing, leading to an energy frontier Muon Collider with excellent energy resolution. 8. The very large hadron collider SciTech Connect 1998-09-01 This paper reviews the purposes to be served by a very large hadron collider and the organization and coordination of efforts to bring it about. There is some discussion of magnet requirements and R&D and the suitability of the Fermilab site. 9. Japanese lab spells out collider needs Banks, Michael 2016-02-01 Japan's High Energy Accelerator Research Organization (KEK) last month issued a plan for the International Linear Collider (ILC) that calls on Japan to ramp up its expertise as it prepares to host the world's next-generation particle collider. 10. Physics at high energy photon photon colliders SciTech Connect Chanowitz, M.S. 1994-06-01 I review the physic prospects for high energy photon photon colliders, emphasizing results presented at the LBL Gamma Gamma Collider Workshop. Advantages and difficulties are reported for studies of QCD, the electroweak gauge sector, supersymmetry, and electroweak symmetry breaking. 11. Searches for new gauge bosons at future colliders SciTech Connect Rizzo, T.G. 1996-09-01 The search reaches for new gauge bosons at future hadron and lepton colliders are summarized for a variety of extended gauge models. Experiments at these energies will vastly improve over present limits and will easily discover a Z and/or W in the multi-TeV range. 12. Latest results of searches for new physics in the D0 experiment SciTech Connect Popov, A. V. 2013-09-15 Results on searches for particles and phenomena beyond the Standard Model (new-physics effects) in the D0 experiment at the Tevatron accelerator (FNAL, USA) are examined. These results were obtained on the basis of a statistical sample corresponding to an integrated luminosity of 5 to 7 fb{sup -1} and were published in 2010 and 2011. 13. Work at FNAL to achieve long electron drift lifetime in liquid argon SciTech Connect Finley, D.; Jaskierny, W.; Kendziora, C.; Krider, J.; Pordes, S.; Rapidis, P.A.; Tope, T.; /Fermilab 2006-10-01 This note records some of the work done between July 2005 and July 2006 to achieve long (many milliseconds) electron drift lifetimes in liquid argon at Fermilab. The work is part of a process to develop some experience at Fermilab with the technology required to construct a large liquid argon TPC. This technology has been largely developed by the ICARUS collaboration in Europe and this process can be seen as technology transfer. The capability to produce liquid argon in which electrons have drift lifetimes of several milliseconds is crucial to a successful device. Liquid argon calorimeters have been successfully operated at Fermilab; their electro-negative contaminants are at the level of 10{sup -7} while the TPC we are considering requires a contamination level at the level of 10{sup -11}, tens of parts per trillion (ppt). As well as demonstrating the ability to produce liquid argon at this level of purity, the work is part of a program to test the effect on the electron drift time of candidate materials for the construction of a TPC in liquid argon. 14. From Neutrino Factory to Muon Collider SciTech Connect Geer, S.; /Fermilab 2010-01-01 Both Muon Colliders and Neutrino Factories require a muon source capable of producing and capturing {Omicron}(10{sup 21}) muons/year. This paper reviews the similarities and differences between Neutrino Factory and Muon Collider accelerator complexes, the ongoing R&D needed for a Muon Collider that goes beyond Neutrino Factory R&D, and some thoughts about how a Neutrino Factory on the CERN site might eventually be upgraded to a Muon Collider. 15. MIGHTY MURINES: NEUTRINO PHYSICS AT VERY HIGH ENERGY MUON COLLIDERS SciTech Connect KING,B.J. 2000-05-05 An overview is given of the potential for neutrino physics studies through parasitic use of the intense high energy neutrino beams that would be produced at future many-TeV muon colliders. Neutrino experiments clearly cannot compete with the collider physics. Except at the very highest energy muon colliders, the main thrust of the neutrino physics program would be to improve on the measurements from preceding neutrino experiments at lower energy muon colliders, particularly in the fields of B physics, quark mixing and CP violation. Muon colliders at the 10 TeV energy scale might already produce of order 10{sup 8} B hadrons per year in a favorable and unique enough experimental environment to have some analytical capabilities beyond any of the currently operating or proposed B factories. The most important of the quark mixing measurements at these energies might well be the improved measurements of the important CKM matrix elements {vert_bar}V{sub ub}{vert_bar} and {vert_bar}V{sub cb}{vert_bar} and, possibly, the first measurements of {vert_bar}V{sub td}{vert_bar} in the process of flavor changing neutral current interactions involving a top quark loop. Muon colliders at the highest center-of-mass energies that have been conjectured, 100--1,000 TeV, would produce neutrino beams for neutrino-nucleon interaction experiments with maximum center-of-mass energies from 300--1,000 GeV. Such energies are close to, or beyond, the discovery reach of all colliders before the turn-on of the LHC. In particular, they are comparable to the 314 GeV center-of-mass energy for electron-proton scattering at the currently operating HERA collider and so HERA provides a convenient benchmark for the physics potential. It is shown that these ultimate terrestrial neutrino experiments, should they eventually come to pass, would have several orders of magnitude more luminosity than HERA. This would potentially open up the possibility for high statistics studies of any exotic particles, such as 16. Collider Detector at Fermilab (CDF): Data from B Hadrons Research DOE Data Explorer The Collider Detector at Fermilab (CDF) is a Tevatron experiment at Fermilab. The Tevatron, a powerful particle accelerator, accelerates protons and antiprotons close to the speed of light, and then makes them collide head-on inside the CDF detector. The CDF detector is used to study the products of such collisions. The CDF Physics Group is organized into six working groups, each with a specific focus. The Bottom group studies the production and decay of B hadrons. Their public web page makes data and numerous figures available from both CDF Runs I and II. 17. Experimental demonstration of colliding beam lifetime improvement by electron lenses SciTech Connect Shiltsev, Vladimir; Alexahin, Yuri; Kamerdzhiev, Vsevolod; Kuznetsov, Gennady; Zhang, Xiao-Long; Bishofberger, Kip; /Los Alamos 2007-10-01 We report successful application of space-charge forces of a low-energy electron beam for improvement of particle lifetime determined by beam-beam interaction in high-energy collider. In our experiments, an electron lens, a novel instrument developed for the beam-beam compensation, was set on a 980-GeV proton bunch in the Tevatron proton-antiproton collider. The proton bunch losses due to its interaction with antiproton beam were reduced by a factor of 2 when the electron lens was operating. We describe the principle of electron lens operation and present experimental results. 18. Searches for scalar and vector leptoquarks at future hadron colliders SciTech Connect Rizzo, T.G. 1996-09-01 The search reaches for both scalar(S) and vector(V) leptoquarks at future hadron colliders are summarized. In particular the authors evaluate the production cross sections of both leptoquark types at TeV33 and LHC as well as the proposed 60 and 200 TeV colliders through both quark-antiquark annihilation and gluon-gluon fusion: q{anti q},gg {r_arrow} SS,VV. Experiments at these machines should easily discover such particles if their masses are not in excess of the few TeV range. 19. When shock waves collide DOE PAGESBeta Martinez, D.; Hartigan, P.; Frank, A.; Hansen, E.; Yirak, K.; Liao, A. S.; Graham, P.; Foster, J.; Wilde, B.; Blue, B.; et al 2016-06-01 Supersonic outflows from objects as varied as stellar jets, massive stars, and novae often exhibit multiple shock waves that overlap one another. When the intersection angle between two shock waves exceeds a critical value, the system reconfigures its geometry to create a normal shock known as a Mach stem where the shocks meet. Mach stems are important for interpreting emission-line images of shocked gas because a normal shock produces higher postshock temperatures, and therefore a higher-excitation spectrum than does an oblique shock. In this paper, we summarize the results of a series of numerical simulations and laboratory experiments designed tomore » quantify how Mach stems behave in supersonic plasmas that are the norm in astrophysical flows. The experiments test analytical predictions for critical angles where Mach stems should form, and quantify how Mach stems grow and decay as intersection angles between the incident shock and a surface change. While small Mach stems are destroyed by surface irregularities and subcritical angles, larger ones persist in these situations and can regrow if the intersection angle changes to become more favorable. Furthermore, the experimental and numerical results show that although Mach stems occur only over a limited range of intersection angles and size scales, within these ranges they are relatively robust, and hence are a viable explanation for variable bright knots observed in Hubble Space Telescope images at the intersections of some bow shocks in stellar jets.« less 20. When Shock Waves Collide Hartigan, P.; Foster, J.; Frank, A.; Hansen, E.; Yirak, K.; Liao, A. S.; Graham, P.; Wilde, B.; Blue, B.; Martinez, D.; Rosen, P.; Farley, D.; Paguio, R. 2016-06-01 Supersonic outflows from objects as varied as stellar jets, massive stars, and novae often exhibit multiple shock waves that overlap one another. When the intersection angle between two shock waves exceeds a critical value, the system reconfigures its geometry to create a normal shock known as a Mach stem where the shocks meet. Mach stems are important for interpreting emission-line images of shocked gas because a normal shock produces higher postshock temperatures, and therefore a higher-excitation spectrum than does an oblique shock. In this paper, we summarize the results of a series of numerical simulations and laboratory experiments designed to quantify how Mach stems behave in supersonic plasmas that are the norm in astrophysical flows. The experiments test analytical predictions for critical angles where Mach stems should form, and quantify how Mach stems grow and decay as intersection angles between the incident shock and a surface change. While small Mach stems are destroyed by surface irregularities and subcritical angles, larger ones persist in these situations and can regrow if the intersection angle changes to become more favorable. The experimental and numerical results show that although Mach stems occur only over a limited range of intersection angles and size scales, within these ranges they are relatively robust, and hence are a viable explanation for variable bright knots observed in Hubble Space Telescope images at the intersections of some bow shocks in stellar jets. 1. (Calorimeter based detectors for high energy hadron colliders). [State Univ. of New York SciTech Connect Not Available 1992-08-04 This document provides a progress report on research that has been conducted under DOE Grant DEFG0292ER40697 for the past year, and describes proposed work for the second year of this 8 year grant starting November 15, 1992. Personnel supported by the contract include 4 faculty, 1 research faculty, 4 postdocs, and 9 graduate students. The work under this grant has in the past been directed in two complementary directions -- DO at Fermilab, and the second SSC detector GEM. A major effort has been towards the construction and commissioning of the new Fermilab Collider detector DO, including design, construction, testing, the commissioning of the central tracking and the central calorimeters. The first DO run is now underway, with data taking and analysis of the first events. Trigger algorithms, data acquisition, calibration of tracking and calorimetry, data scanning and analysis, and planning for future upgrades of the DO detector with the advent of the FNAL Main Injector are all involved. The other effort supported by this grant has been towards the design of GEM, a large and general-purpose SSC detector with special emphasis on accurate muon measurement over a large solid angle. This effort will culminate this year in the presentation to the SSC laboratory of the GEM Technical Design Report. Contributions are being made to the detector design, coordination, and physics simulation studies with special emphasis on muon final states. Collaboration with the RD5 group at CERN to study muon punch through and to test cathode strip chamber prototypes was begun. 2. Single event effects and their mitigation for the Collider Detector at Fermilab SciTech Connect Tesarek, Richard J.; D'Auria, Saverio; Dong, Peter; Hocker, Andy; Kordas, Kostas; McGimpsey, Susan; Nicolas, Ludovic; Wallny, Rainer; Schmitt, Wayne; Worm, Steven; /Fermilab /Toronto U. /Glasgow U. /Rutherford /UCLA 2005-11-01 We present an overview of radiation induced failures and operational experiences from the Collider Detector at Fermilab (CDF). In our summary, we examine single event effects (SEE) in electronics located in and around the detector. We present results of experiments to identify the sources and composition of the radiation and steps to reduce the rate of SEEs in our electronics. Our studies have led to a better, more complete understanding of the radiation environment in a modern hadron collider experiment. 3. Advances in beam physics and technology: Colliders of the future 1996-02-01 Beams may be viewed as directed and focussed flow of energy and information, carried by particles and electromagnetic radiation fields (i.e. photons). Often, they are brought into interaction with each other (e.g. in high energy colliders) or with other forms of matter (e.g. in fixed target physics, synchrotron radiation sciences, neutron scattering experiments, laser chemistry and physics, medical therapy, etc.). The whole art and science of beams revolve around the fundamental quest for, and ultimate implementation of, mechanisms of production, storage, control and observation of beams—always directed towards studies of the basic structures and processes of the natural world and various practical applications. Tremendous progress has been made in all aspects of beam physics and technology in the last decades—nonlinear dynamics, superconducting magnets and radio frequency cavities, beam instrumentation and control, novel concepts and collider paradigms, to name a few. We will illustrate this progress via a few examples and remark on the emergence of new collider scenarios where some of these progress might come to use—the Gamma-Gamma Collider, the Muon Collider, laser acceleration, etc. We will close with an outline of future opportunities and outlook. 4. Vacuum technology issues for the SSC (Superconducting Super Collider) SciTech Connect Joestlein, H. 1989-10-23 The Superconducting Super Collider, to be built in Texas, will provide an energy of 40 TeV from colliding proton beams. This energy is twenty times higher than currently available from the only other cryogenic collider, the Fermilab Tevatron, and will allow experiments that can lead to a better understanding of the fundamental properties of matter. The energy scale and the size of the new machine pose intriguing challenges and opportunities for the its vacuum systems. The discussion will include the effects of synchrotron radiation on cryogenic beam tubes, cold adsorption pumps for hydrogen, methods of leak checking large cryogenic systems, the development of cold beam valves, and radiation damage to components, especially electronics. 9 figs., 1 tab. 5. Colliding Decimeter Dust Deckers, J.; Teiser, J. 2013-06-01 Collisional evolution is a key process in planetesimal formation and decimeter bodies play a key role in the different models. However, the outcome of collisions between two dusty decimeter bodies has never been studied experimentally. Therefore, we carried out microgravity collision experiments in the Bremen drop tower. The agglomerates consist of quartz with irregularly shaped micrometer-sized grains and the mean volume filling factor is 0.437 ± 0.004. The aggregates are cylindrical with 12 cm in height and 12 cm in diameter, and typical masses are 1.5 kg. These are the largest and most massive dust aggregates studied in collisions to date. We observed rebound and fragmentation but no sticking in the velocity range between 0.8 and 25.7 cm s-1. The critical fragmentation velocity for split up of an aggregate is 16.2 ± 0.4 cm s-1. At lower velocities the aggregates bounce off each other. In this velocity range, the coefficient of restitution decreases with increasing collision velocity from 0.8 to 0.3. While the aggregates are very weak, the critical specific kinetic energy for fragmentation Q μ = 1 is a factor of six larger than expected. Collisions of large bodies in protoplanetary disks are supposed to be much faster and the generation of smaller fragments is likely. In planetary rings, collision velocities are of the order of a few cm s-1 and are thereby in the same range investigated in these experiments. The coefficient of restitution of dust agglomerates and regolith-covered ice particles, which are common in planetary rings, are similar. SciTech Connect Litvinenko, V. 2010-05-23 Outstanding research potential of electron-hadron colliders (EHC) was clearly demonstrated by first - and the only - electron-proton collider HERA (DESY, Germany). Physics data from HERA revealed new previously unknown facets of Quantum Chromo-Dynamics (QCD). EHC is an ultimate microscope probing QCD in its natural environment, i.e. inside the hadrons. In contrast with hadrons, electrons are elementary particles with known initial state. Hence, scattering electrons from hadrons provides a clearest pass to their secrets. It turns EHC into an ultimate machine for high precision QCD studies and opens access to rich physics with a great discovery potential: solving proton spin puzzle, observing gluon saturation or physics beyond standard model. Access to this physics requires high-energy high-luminosity EHCs and a wide reach in the center-of-mass (CM) energies. This paper gives a brief overview of four proposed electron-hadron colliders: ENC at GSI (Darmstadt, Germany), ELIC/MEIC at TJNAF (Newport News, VA, USA), eRHIC at BNL (Upton, NY, USA) and LHeC at CERN (Geneva, Switzerland). Future electron-hadron colliders promise to deliver very rich physics not only in the quantity but also in the precision. They are aiming at very high luminosity two-to-four orders of magnitude beyond the luminosity demonstrated by the very successful HERA. While ENC and LHeC are on opposite side of the energy spectrum, eRHIC and ELIC are competing for becoming an electron-ion collider (EIC) in the U.S. Administrations of BNL and Jlab, in concert with US DoE office of Nuclear Physics, work on the strategy for down-selecting between eRHIC and ELIC. The ENC, EIC and LHeC QCD physics programs to a large degree are complimentary to each other and to the LHC physics. In last decade, an Electron Ion Collider (EIC) collaboration held about 25 collaboration meetings to develop physics program for EIC with CM energy {approx}100 GeV. One of these meetings was held at GSI, where ENC topic was in the 7. Dark Matter: Collider vs. direct searches Jacques, T. 2016-07-01 Effective Field Theories (EFTs) are a useful tool across a wide range of DM searches, including LHC searches and direct detection. Given the current lack of indications about the nature of the DM particle and its interactions, a model independent interpretation of the collider bounds appears mandatory, especially in complementarity with the reinterpretation of the exclusion limits within a choice of simplified models, which cannot exhaust the set of possible completions of an effective Lagrangian. However EFTs must be used with caution at LHC energies, where the energy scale of the interaction is at a scale where the EFT approximation can no longer be assumed to be valid. Here we introduce some tools that allow the validity of the EFT approximation to be quantified, and provide case studies for two operators. We also show a technique that allows EFT constraints from collider searches to be made substantially more robust, even at large center-of-mass energies. This allows EFT constraints from different classes of experiment to be compared in a much more robust manner. 8. Advances in Beam Cooling for Muon Colliders SciTech Connect R.P. Johnson, Y.S. Derbenev 2006-09-01 A six-dimensional (6D) ionization cooling channel based on helical magnets surrounding RF cavities filled with dense hydrogen gas is the basis for the latest plans for muon colliders. This helical cooling channel (HCC) has solenoidal, helical dipole, and helical quadrupole magnetic fields, where emittance exchange is achieved by using a continuous homogeneous absorber. Momentum-dependent path length differences in the dense hydrogen energy absorber provide the required correlation between momentum and ionization loss to accomplish longitudinal cooling. Recent studies of an 800 MHz RF cavity pressurized with hydrogen, as would be used in this application, show that the maximum gradient is not limited by a large external magnetic field, unlike vacuum cavities. Two new cooling ideas, Parametric-resonance Ionization Cooling and Reverse Emittance Exchange, will be employed to further reduce transverse emittances to a few mm-mr, which allows high luminosity with fewer muons than previously imagined. We describe these new ideas as well as a new precooling idea based on a HCC with z dependent fields that is being developed for an exceptional 6D cooling demonstration experiment. The status of the designs, simulations, and tests of the cooling components for a high luminosity, low emittance muon collider will be reviewed. 9. Overview of linear collider designs SciTech Connect Siemann, R.H. 1993-04-01 Linear collider design and development have become focused on a center-of-mass energy E{sub CM} = 0.5 TeV and a luminosity L {approximately} 5 {times} 10{sup 33} cm{sup {minus}2}sec{sup {minus}1}. There are diverse approaches to meeting these general objectives. The diversity arises from different judgements about the ease of developing new and improving existing technology, costs, extension to higher energies, experimental backgrounds and center-of-mass energy spectrum, and tolerances and beam power. The parameters of possible colliders are given in this paper. This report will focus on some of the common themes of these designs and the different between them. 10. Crab Cavities for Linear Colliders SciTech Connect Burt, G.; Ambattu, P.; Carter, R.; Dexter, A.; Tahir, I.; Beard, C.; Dykes, M.; Goudket, P.; Kalinin, A.; Ma, L.; McIntosh, P.; Shulte, D.; Jones, Roger M.; Bellantoni, L.; Chase, B.; Church, M.; Khabouline, T.; Latina, A.; Adolphsen, C.; Li, Z.; Seryi, Andrei; /SLAC 2011-11-08 Crab cavities have been proposed for a wide number of accelerators and interest in crab cavities has recently increased after the successful operation of a pair of crab cavities in KEK-B. In particular crab cavities are required for both the ILC and CLIC linear colliders for bunch alignment. Consideration of bunch structure and size constraints favour a 3.9 GHz superconducting, multi-cell cavity as the solution for ILC, whilst bunch structure and beam-loading considerations suggest an X-band copper travelling wave structure for CLIC. These two cavity solutions are very different in design but share complex design issues. Phase stabilisation, beam loading, wakefields and mode damping are fundamental issues for these crab cavities. Requirements and potential design solutions will be discussed for both colliders. 11. Reviews Exhibitions: Collider: Step inside the World's Greatest Experiment Equipment: Hero Steam Turbine Classroom Video: Most of Our Universe is Missing Book: Serving the Reich Book: Breakthrough to CLIL for Physics Book: The Good Research Guide Apps: Popplet Web Watch Apps 2014-03-01 WE RECOMMEND Collider: step inside the world's greatest experiment A great exhibition at the Science Museum in London Hero Steam Turbine Superb engine model gets up to 2500 rpm Most of Our Universe is Missing BBC video explores the dark truth Serving the Reich Science and morality in Nazi Germany The Good Research Guide A non-specialist book for teachers starting out in education research WORTH A LOOK Breakthrough to CLIL for Physics A book based on a physics curriculum for non-English students WEB WATCH Electric cycles online: patterns of use APPS The virtual laboratory advances personal skills 12. Dark matter searches at the large hadron collider Hoh, S. Y.; Komaragiri, J. R.; Wan Abdullah, W. A. T. 2016-01-01 Dark Matter is a hypothetical particle proposed to explain the missing matter expected from the cosmological observation. The motivation of Dark Matter is overwhelming however as it is mainly deduced from its gravitational interaction, for it does little to pinpoint what Dark Matter really is. In WIMPs Miracle, weakly interactive massive particle being the Dark Matter candidate is correctly producing the current thermal relic density at weak scale, implying the possibility of producing and detecting it in Large Hadron Collider. Assuming WIMPs being the maverick particle within collider, it is expected to be pair produced in association with a Standard Model particle. The presence of the WIMPs pair is inferred from the Missing Transverse Energy (MET) which is the vector sum of the imbalance in the transverse momentum plane recoils a Standard Model Particle. The collider is able to produce light mass Dark Matter which the traditional detection fail to detect due to the small momentum transfer involved in the interaction; on the other hand, the traditional detection is robust in detecting a higher Dark matter masses but the collider is suffered from the parton distribution function suppression. Topologically the processes are similar to the scattering processes in the direct detection thus complementary to the traditional Dark Matter detection. The collider searches are strongly motivated as the results are usually translated to the annihilation and scattering rates at more traditional Dark Matter-oriented experiments, thus a concordance approach is adapted. An overview of Dark Matter searches at the Large Hadron Collider will be covered in this paper. 13. Collider searches for nonperturbative low-scale gravity states Gingrich, Douglas M. 2015-12-01 The possibility of producing nonperturbative low-scale gravity states in collider experiments was first discussed in about 1998. The ATLAS and CMS experiments have searched for nonperturbative low-scale gravity states using the Large Hadron Collider with a proton-proton center-of-mass energy of 8 TeV. These experiments have now seriously confronted the possibility of producing nonperturbative low-scale gravity states which were proposed over 17 years ago. I will summarize the results of the searches, give a personal view of what they mean, and make some predictions for 13 TeV center-of-mass energy. I will also discuss early ATLAS 13 TeV center-of-mass energy results. 14. LHC: The Large Hadron Collider SciTech Connect Lincoln, Don 2015-03-04 The Large Hadron Collider (or LHC) is the world’s most powerful particle accelerator. In 2012, scientists used data taken by it to discover the Higgs boson, before pausing operations for upgrades and improvements. In the spring of 2015, the LHC will return to operations with 163% the energy it had before and with three times as many collisions per second. It’s essentially a new and improved version of itself. In this video, Fermilab’s Dr. Don Lincoln explains both some of the absolutely amazing scientific and engineering properties of this modern scientific wonder. 15. Colliding-beam-accelerator lattice SciTech Connect Claus, J.; Cornacchia, M.; Courant, E.D.; Parzen, G. 1983-01-01 We describe the lattice of the Colliding Beam Accelerator, a 400 x 400 GeV pp facility proposed for construction at Brookhaven National Laboratory. The structure adopted is very versatile, in part in consequence of its desirable behavior as function of momentum deviation and as function of the betatron tunes. Each of the six insertions can be arranged to meet specific requirements at the crossing points as illustrated by a discussion of the tuneable low-beta insertions. The luminosity in these low-beta insertions (2 x 10/sup 33/ cm/sup -2/ sec/sup -1/) would be an order of magnitude larger than the standard insertions. 16. Tevatron instrumentation: boosting collider performance SciTech Connect Shiltsev, Vladimir; Jansson, Andreas; Moore, Ronald; /Fermilab 2006-05-01 The Tevatron in Collider Run II (2001-present) is operating with six times more bunches, many times higher beam intensities and luminosities than in Run I (1992-1995). Beam diagnostics were crucial for the machine start-up and the never-ending luminosity upgrade campaign. We present the overall picture of the Tevatron diagnostics development for Run II, outline machine needs for new instrumentation, present several notable examples that led to Tevatron performance improvements, and discuss the lessons for the next big machines--LHC and ILC. 17. Detector Background at Muon Colliders SciTech Connect Mokhov, N.V.; Striganov, S.I.; /Fermilab 2011-09-01 Physics goals of a Muon Collider (MC) can only be reached with appropriate design of the ring, interaction region (IR), high-field superconducting magnets, machine-detector interface (MDI) and detector. Results of the most recent realistic simulation studies are presented for a 1.5-TeV MC. It is shown that appropriately designed IR and MDI with sophisticated shielding in the detector have a potential to substantially suppress the background rates in the MC detector. The main characteristics of backgrounds are studied. 18. Colliding with a crunching bubble SciTech Connect Freivogel, Ben; Freivogel, Ben; Horowitz, Gary T.; Shenker, Stephen 2007-03-26 In the context of eternal inflation we discuss the fate of Lambda = 0 bubbles when they collide with Lambda< 0 crunching bubbles. When the Lambda = 0 bubble is supersymmetric, it is not completely destroyed by collisions. If the domain wall separating the bubbles has higher tension than the BPS bound, it is expelled from the Lambda = 0 bubble and does not alter its long time behavior. If the domain wall saturates the BPS bound, then it stays inside the Lambda = 0 bubble and removes a finite fraction of future infinity. In this case, the crunch singularity is hidden behind the horizon of a stable hyperbolic black hole. 19. Estimates of Fermilab Tevatron collider performance SciTech Connect Dugan, G. 1991-09-01 This paper describes a model which has been used to estimate the average luminosity performance of the Tevatron collider. In the model, the average luminosity is related quantitatively to various performance parameters of the Fermilab Tevatron collider complex. The model is useful in allowing estimates to be developed for the improvements in average collider luminosity to be expected from changes in the fundamental performance parameters as a result of upgrades to various parts of the accelerator complex. 20. International Workshop on Linear Colliders 2010 ScienceCinema None 2011-10-06 IWLC2010 International Workshop on Linear Colliders 2010ECFA-CLIC-ILC joint meeting: Monday 18 October - Friday 22 October 2010Venue: CERN and CICG (International Conference Centre Geneva, Switzerland) This year, the International Workshop on Linear Colliders organized by the European Committee for Future Accelerators (ECFA) will study the physics, detectors and accelerator complex of a linear collider covering both CLIC and ILC options.Contact Workshop Secretariat IWLC2010 is hosted by CERN 1. Development work for a superconducting linear collider NASA Technical Reports Server (NTRS) Matheisen, Axel 1995-01-01 For future linear e(+)e(-) colliders in the TeV range several alternatives are under discussion. The TESLA approach is based on the advantages of superconductivity. High Q values of the accelerator structures give high efficiency for converting RF power into beam power. A low resonance frequency for the RF structures can be chosen to obtain a large number of electrons (positrons) per bunch. For a given luminosity the beam dimensions can be chosen conservatively which leads to relaxed beam emittance and tolerances at the final focus. Each individual superconducting accelerator component (resonator cavity) of this linear collider has to deliver an energy gain of 25 MeV/m to the beam. Today s.c. resonators are in use at CEBAF/USA, at DESY/Germany, Darmstadt/Germany KEK/Japan and CERN/Geneva. They show acceleration gradients between 5 MV/m and 10 MV/m. Encouraging experiments at CEA Saclay and Cornell University showed acceleration gradients of 20 MV/m and 25 MV/m in single and multicell structures. In an activity centered at DESY in Hamburg/Germany the TESLA collaboration is constructing a 500 MeV superconducting accelerator test facility (TTF) to demonstrate that a linear collider based on this technique can be built in a cost effective manner and that the necessary acceleration gradients of more than 15 MeV/m can be reached reproducibly. The test facility built at DESY covers an area of 3.000 m2 and is divided into 3 major activity areas: (1) The testlinac, where the performance ofthe modular components with an electron beam passing the 40 m long acceleration section can be demonstrated. (2) The test area, where all individual resonators are tested before installation into a module. (3) The preparation and assembly area, where assembly of cavities and modules take place. We report here on the design work to reach a reduction of costs compared to actual existing superconducting accelerator structures and on the facility set up to reach high acceleration gradients in 2. FUTURE LEPTON COLLIDERS AND LASER ACCELERATION SciTech Connect PARSA,Z. 2000-05-30 Future high energy colliders along with their physics potential, and relationship to new laser technology are discussed. Experimental approaches and requirements for New Physics exploration are also described. 3. Next-Generation Linear Collider Final Focus System Stability Tolerances SciTech Connect Roy, G.; Irwin, J.; /SLAC 2007-04-25 The design of final focus systems for the next generation of linear colliders has evolved largely from the experience gained with the design and operation of the Stanford Linear Collider (SLC) and with the design of the Final Focus Test Beam (FFTB). We will compare the tolerances for two typical designs for a next-generation linear collider final focus system. The chromaticity generated by strong focusing systems, like the final quadrupole doublet before the interaction point of a linear collider, can be canceled by the introduction of sextupoles in a dispersive region. These sextupoles must be inserted in pairs separated by a -I transformation (Chromatic Correction Section) in order to cancel the strong geometric aberrations generated by sextupoles. Designs proposed for both the JLC or NLC final focus systems have two separate chromatic correction sections, one for each transverse plane separated by a ''{beta}-exchanger'' to manipulate the {beta}-function between the two CCS. The introduction of sextupoles and bending magnets gives rise to higher order aberrations (long sextupole and chrome-geometries) and radiation induced aberrations (chromaticity unbalance and ''Oide effect'') and one must optimize the lattice accordingly. 4. Charge resolved electrostatic diagnostic of colliding copper laser plasma plumes SciTech Connect Yeates, P.; Fallon, C.; Kennedy, E. T.; Costello, J. T. 2011-10-15 The collision of two laser generated plasma plumes can result, under appropriate conditions, in the formation of a ''stagnation layer.'' The processes underlying this phenomenon are complex and time dependent. The majority of experiments over the last few decades have focused upon spectroscopic diagnostic of colliding plasmas. We have performed electrostatic diagnosis of multiply charged copper ions (Cu{sup +} to Cu{sup 5+}) generated via Q-switched pulsed laser ({lambda} = 1.06 {mu}m, {tau} = 6 ns, and E{sub L} = 52-525 mJ) generation of copper plasma plumes from a planar target. Time dependent current traces, charge yields, and kinetic energy (K{sub e}) distributions are obtained for single plasma plumes (S{sub p}) and colliding plasma plumes (C{sub p}). The charge yield from a C{sub p} relative to twice that from a S{sub p} is characterized by a charge yield ratio (CYR) parameter. Superior ion yields for all charge states occur for a discrete range of fluences (F) from colliding plasma plumes leading to a CYR parameter exceeding unity. The kinetic energy distributions from colliding plasma plumes display well defined energy compression via narrowing of the distributions for all fluences and charge states. The extent of this energy compression is charge dependent. Space charge forces within the stagnation layer and the resulting charge dependent acceleration of ions are proposed to account for the transfer of ion kinetic energy in favour of collisional ionization mechanisms. 5. New technology for linear colliders SciTech Connect McIntyre, P.M. 1991-08-01 The purpose of this contract is to develop and evaluate new technology for future e{sup +}e{sup {minus}} linac colliders. TeV linac colliders will require major improvements in the performance of microwave power tubes: >100 mW/m peak power, {approximately}20 GHz frequency, and high frequency. For the past three years we have been developing gigatron, a new design concept for microwave power tubes. It incorporates three key innovations: a gated field-emitter cathode which produces a fully modulated electron beam directly into the vacuum; a ribbon beam geometry which eliminates space charge and phase dispersion, and a traveling wave coupler which provides optimum output coupling even over a wide ribbon beam. During the past year we have built prototypes of two cathode designs: a stripline edge-emitter array and a porous silicon dioxide cathode. A highlight of our results is the development and testing of the porous SiO{sub 2} cathode. It delivers exceptional performance as a modulated electron source in general and for gigatron in particular. Its high emitter density and low work function accommodate higher tube gain, simpler cathode coupling, and higher peak power than any other technology. The protection of the active emitting surface by {approximately}2 {mu}m of porous SiO{sub 2} should provide for rugged operation in a tube environment. SciTech Connect Chao, A.W.; Palmer, R.B.; Evans, L.; Gareyte, J.; Siemann, R.H. 1992-12-31 The nominal SSC and LHC designs should operate conservatively at luminosities up to 10{sup 33} cm{sup {minus}2} s{sup {minus}1}. This luminosity is dictated by the event rates that can be handled by the detectors. However, this limit is event dependent (e.g. it does not take much of a detector to detect the event pp {yields} elephant; all one needs is extremely high luminosity). As such, it is useful to explore the possibility of going beyond the 10{sup 33} cm{sup {minus}2} s{sup {minus}1} level. Such exploration will also improve the accelerator physics understanding of pp collider designs. If the detector limitations are removed, the first accelerator limits occur when the luminosity is at the level of 10{sup 34} cm{sup {minus}2}s{sup {minus}1}. These accelerator limits will first be reviewed. The authors will then continue on to explore even higher luminosity as the ultimate limit of pp colliders. Accelerator technologies needed to achieve this ultimate luminosity as well as the R and D needed to reach it are discussed. 7. Very large hadron collider (VLHC) SciTech Connect 1998-09-01 A VLHC informal study group started to come together at Fermilab in the fall of 1995 and at the 1996 Snowmass Study the parameters of this machine took form. The VLHC as now conceived would be a 100 TeV hadron collider. It would use the Fermilab Main Injector (now nearing completion) to inject protons at 150 GeV into a new 3 TeV Booster and then into a superconducting pp collider ring producing 100 TeV c.m. interactions. A luminosity of {approximately}10{sup 34} cm{sup -2}s{sup -1} is planned. Our plans were presented to the Subpanel on the Planning for the Future of US High- Energy Physics (the successor to the Drell committee) and in February 1998 their report stated The Subpanel recommends an expanded program of R&D on cost reduction strategies, enabling technologies, and accelerator physics issues for a VLHC. These efforts should be coordinated across laboratory and university groups with the aim of identifying design concepts for an economically and technically viable facility The coordination has been started with the inclusion of physicists from Brookhaven National Laboratory (BNL), Lawrence Berkeley National Laboratory (LBNL), and Cornell University. Clearly, this collaboration must expanded internationally as well as nationally. The phrase economically and technically viable facility presents the real challenge. 8. The muon collider (Sandro's snake) SciTech Connect Ruggiero, A.G. 1992-01-01 This paper describes a feasibility study for the design of a muon collider. Recognized the fact that the particle lifetime increases linearly with the energy, we have adopted a scheme where steps of cooling and acceleration are entwined. We have indeed found convenient to accelerate the beam as fast as possible to increase its chances of survival, and necessary to dilute the action of cooling throughout the entire accelerating process to make it more effective and affordable. All acceleration and cooling steps are executed in a single pass essentially along a curvilinear and open path. We do not believe it is possible to handle the beam otherwise in circular and closed rings, as it has been proposed in the past. The example shown in this paper describes a muon collider at the energy of 250 GeV per beam and a luminosity of 4 [times] 10[sup 28] cm[sup [minus]2]s[sup [minus]1]. We have adopted an extrapolation of the stochastic cooling method for the reduction of the beam emittance. 9. Physics and technology of the next linear collider SciTech Connect 1996-06-01 The authors present the prospects for the next generation of high-energy physics experiments with electron-positron colliding beams. This report summarizes the current status of the design and technological basis of a linear collider of center-of-mass energy 0.5--1.5 TeV, and the opportunities for high-energy physics experiments that this machine is expected to open. The physics goals discussed here are: Standard Model processes and simulation; top quark physics; Higgs boson searches and properties; supersymmetry; anomalous gauge boson couplings; strong WW scattering; new gauge bosons and exotic particles; e{sup {minus}}e{sup {minus}}, e{sup {minus}}{gamma}, and {gamma}{gamma} interactions; and precision tests of QCD. 10. Non-collider searches for stable massive particles Burdin, S.; Fairbairn, M.; Mermod, P.; Milstead, D.; Pinfold, J.; Sloan, T.; Taylor, W. 2015-06-01 The theoretical motivation for exotic stable massive particles (SMPs) and the results of SMP searches at non-collider facilities are reviewed. SMPs are defined such that they would be sufficiently long-lived so as to still exist in the cosmos either as Big Bang relics or secondary collision products, and sufficiently massive such that they are typically beyond the reach of any conceivable accelerator-based experiment. The discovery of SMPs would address a number of important questions in modern physics, such as the origin and composition of dark matter and the unification of the fundamental forces. This review outlines the scenarios predicting SMPs and the techniques used at non-collider experiments to look for SMPs in cosmic rays and bound in matter. The limits so far obtained on the fluxes and matter densities of SMPs which possess various detection-relevant properties such as electric and magnetic charge are given. 11. Design and performance of the Stanford Linear Collider Control System SciTech Connect Melen, R.E. 1984-10-01 The success of the Stanford Linear Collider (SLC) will be dependent upon the implementation of a very large advanced computer-based instrumentation and control system. This paper describes the architectural design of this system as well as a critique of its performance. This critique is based on experience obtained from its use in the control and monitoring of 1/3 of the SLAC linac and in support of an expensive experimental machine physics experimental program. 11 references, 3 figures. 12. COMPILATION OF CURRENT HIGH ENERGY PHYSICS EXPERIMENTS SciTech Connect Wohl, C.G.; Kelly, R.L.; Armstrong, F.E.; Horne, C.P.; Hutchinson, M.S.; Rittenberg, A.; Trippe, T.G.; Yost, G.P.; Addis, L.; Ward, C.E.W.; Baggett, N.; Goldschmidt-Clermong, Y.; Joos, P.; Gelfand, N.; Oyanagi, Y.; Grudtsin, S.N.; Ryabov, Yu.G. 1981-05-01 This is the fourth edition of our compilation of current high energy physics experiments. It is a collaborative effort of the Berkeley Particle Data Group, the SLAC library, and nine participating laboratories: Argonne (ANL), Brookhaven (BNL), CERN, DESY, Fermilab (FNAL), the Institute for Nuclear Study, Tokyo (INS), KEK, Serpukhov (SERP), and SLAC. The compilation includes summaries of all high energy physics experiments at the above laboratories that (1) were approved (and not subsequently withdrawn) before about April 1981, and (2) had not completed taking of data by 1 January 1977. We emphasize that only approved experiments are included. 13. Research and Development of Future Muon Collider SciTech Connect Yonehara, K.; /Fermilab 2012-05-01 Muon collider is a considerable candidate of the next generation high-energy lepton collider machine. A novel accelerator technology must be developed to overcome several intrinsic issues of muon acceleration. Recent research and development of critical beam elements for a muon accelerator, especially muon beam phase space ionization cooling channel, are reviewed in this paper. 14. Search for top quark at Fermilab Collider SciTech Connect Sliwa, K.; The CDF Collaboration 1991-10-01 The status of a search for the top quark with Collider Detector at Fermilab (CDF), based on a data sample recorded during the 1988--1989 run is presented. The plans for the next Fermilab Collider run in 1992--1993 and the prospects of discovering the top quark are discussed. 19 refs., 4 figs., 2 tabs. 15. ACCELERATION FOR A HIGH ENERGY MUON COLLIDER SciTech Connect BERG,J.S 2000-04-07 The authors describe a method for designing the acceleration systems for a muon collider, with particular application and examples for a high energy muon collider. This paper primarily concentrates on design considerations coming from longitudinal motion, but some transverse issues are briefly discussed. 16. Polarization Effects at a Muon Collider SciTech Connect Parsa, Z. 1998-11-01 For Muon Colliders, Polarization will be a useful tool if high polarization is achievable with little luminosity loss. Formulation and effects of beam polarization and luminosity including polarization effects in Higgs resonance studies are discussed for improving precision measurements and Higgs resonance ''discovery'' capability e.g. at the First Muon Collider (FMC). 17. Mutual colliding impact fast ignition Winterberg, Friedwardt 2014-09-01 It is proposed to apply the well established colliding beam technology of high energy physics to the fast hot spot ignition of a highly compressed DT (deuterium-tritium) target igniting a larger D (deuterium) burn, by accelerating a small amount of solid deuterium, and likewise a small amount of tritium, making a head-on collision in the center of the target, projecting them through conical ducts situated at the opposite side of the target and converging in its center. In their head-on collision, the relative collision velocity is 5/3 times larger compared to the collision velocity of a stationary target. The two pieces have for this reason to be accelerated to a smaller velocity than would otherwise be needed to reach upon impact the same temperature. Since the velocity distribution of the two head-on colliding projectiles is with its two velocity peaks non-Maxwellian, the maximum cross section velocity product turns out to be substantially larger than the maximum if averaged over a Maxwellian. The D and T projectiles would have to be accelerated with two sabots driven by powerful particle or laser beams, permitting a rather large acceleration length. With the substantially larger cross section-velocity product by virtue of the non-Maxwellian velocity distribution, a further advantage is that the head-on collision produces a large magnetic field by the thermomagnetic Nernst effect, enhancing propagating burn. With this concept, the ignition of the neutron-less hydrogen-boron (HB11) reaction might even be possible in a heterogeneous assembly of the hydrogen and the boron to reduce the bremsstrahlung-losses, resembling the heterogeneous assembly in a graphite-natural uranium reactor, there to reduce the neutron losses. 18. Mutual colliding impact fast ignition SciTech Connect Winterberg, Friedwardt 2014-09-15 It is proposed to apply the well established colliding beam technology of high energy physics to the fast hot spot ignition of a highly compressed DT (deuterium-tritium) target igniting a larger D (deuterium) burn, by accelerating a small amount of solid deuterium, and likewise a small amount of tritium, making a head-on collision in the center of the target, projecting them through conical ducts situated at the opposite side of the target and converging in its center. In their head-on collision, the relative collision velocity is 5/3 times larger compared to the collision velocity of a stationary target. The two pieces have for this reason to be accelerated to a smaller velocity than would otherwise be needed to reach upon impact the same temperature. Since the velocity distribution of the two head-on colliding projectiles is with its two velocity peaks non-Maxwellian, the maximum cross section velocity product turns out to be substantially larger than the maximum if averaged over a Maxwellian. The D and T projectiles would have to be accelerated with two sabots driven by powerful particle or laser beams, permitting a rather large acceleration length. With the substantially larger cross section-velocity product by virtue of the non-Maxwellian velocity distribution, a further advantage is that the head-on collision produces a large magnetic field by the thermomagnetic Nernst effect, enhancing propagating burn. With this concept, the ignition of the neutron-less hydrogen-boron (HB{sup 11}) reaction might even be possible in a heterogeneous assembly of the hydrogen and the boron to reduce the bremsstrahlung-losses, resembling the heterogeneous assembly in a graphite-natural uranium reactor, there to reduce the neutron losses. 19. Critical transitions in colliding cascades PubMed Gabrielov; Keilis-Borok; Zaliapin; Newman 2000-07-01 We consider here the interaction of direct and inverse cascades in a hierarchical nonlinear system that is continuously loaded by external forces. The load is applied to the largest element and is transferred down the hierarchy to consecutively smaller elements, thereby forming a direct cascade. The elements of the system fail (i. e., break down) under the load. The smallest elements fail first. The failures gradually expand up the hierarchy to the larger elements, thus forming an inverse cascade. Eventually the failures heal, ensuring that the system will function indefinitely. The direct and inverse cascades collide and interact. Loading triggers the failures, while failures release and redistribute the load. Notwithstanding its relative simplicity, this model reproduces the major dynamical features observed in seismicity, including the seismic cycle, intermittence of seismic regime, power-law energy distribution, clustering in space and time, long-range correlations, and a set of seismicity patterns premonitory to a strong earthquake. In this context, the hierarchical structure of the model crudely imitates a system of tectonic blocks spread by a network of faults (note that the behavior of such a network is different from that of a single fault). Loading mimics the impact of tectonic forces, and failures simulate earthquakes. The model exhibits three basic types of premonitory pattern reflecting seismic activity, clustering of earthquakes in space and time, and the range of correlation between the earthquakes. The colliding-cascade model seemingly exhibits regularities that are common in a wide class of complex hierarchical systems, not necessarily Earth specific. PMID:11088457 20. R&D Toward a Neutrino Factory and Muon Collider SciTech Connect Zisman, Michael S 2009-04-29 There is considerable interest in the use of muon beams to create either an intense source of decay neutrinos aimed at a detector located 3000-7500 km away (a Neutrino Factory), or a Muon Collider that produces high-luminosity collisions at the energy frontier. R&D aimed at producing these facilities has been under way for more than 10 years. This paper will review experimental results from MuCool, MERIT, and MICE and indicate the extent to which they will provide proof-of-principle demonstrations of the key technologies required for a Neutrino Factory or Muon Collider. Progress in constructing components for the MICE experiment will also be described. 1. The technical challenges of the Large Hadron Collider. PubMed Collier, Paul 2015-01-13 The Large Hadron Collider (LHC) is a 27km circumference hadron collider, built at CERN to explore the energy frontier of particle physics. Approved in 1994, it was commissioned and began operation for data taking in 2009. The design and construction of the LHC presented many design, engineering and logistical challenges which involved pushing a number of technologies well beyond their level at the time. Since the start-up of the machine, there has been a very successful 3-year run with an impressive amount of data delivered to the LHC experiments. With an increasingly large stored energy in the beam, the operation of the machine itself presented many challenges and some of these will be discussed. Finally, the planning for the next 20 years has been outlined with progressive upgrades of the machine, first to nominal energy, then to progressively higher collision rates. At each stage the technical challenges are illustrated with a few examples. PMID:26949802 2. Colliding Laser Pulses for Laser-Plasma Accelerator Injection Control SciTech Connect Plateau, G. R.; Geddes, C. G. R.; Matlis, N. H.; Mittelberger, D. E.; Nakamura, K.; Schroeder, C. B.; Esarey, E.; Leemans, W. P.; Cormier-Michel, E. 2010-11-04 Decoupling injection from acceleration is a key challenge to achieve compact, reliable, tunable laser-plasma accelerators (LPA). In colliding pulse injection the beat between multiple laser pulses can be used to control energy, energy spread, and emittance of the electron beam by injecting electrons in momentum and phase into the accelerating phase of the wake trailing the driver laser pulse. At LBNL, using automated control of spatiotemporal overlap of laser pulses, two-pulse experiments showed stable operation and reproducibility over hours of operation. Arrival time of the colliding beam was scanned, and the measured timing window and density of optimal operation agree with simulations. The accelerator length was mapped by scanning the collision point. 3. Colliding Laser Pulses for Laser-Plasma Accelerator Injection Control Plateau, G. R.; Geddes, C. G. R.; Matlis, N. H.; Cormier-Michel, E.; Mittelberger, D. E.; Nakamura, K.; Schroeder, C. B.; Esarey, E.; Leemans, W. P. 2010-11-01 Decoupling injection from acceleration is a key challenge to achieve compact, reliable, tunable laser-plasma accelerators (LPA) [1, 2]. In colliding pulse injection the beat between multiple laser pulses can be used to control energy, energy spread, and emittance of the electron beam by injecting electrons in momentum and phase into the accelerating phase of the wake trailing the driver laser pulse [3, 4, 5, 6, 7]. At LBNL, using automated control of spatiotemporal overlap of laser pulses, two-pulse experiments showed stable operation and reproducibility over hours of operation. Arrival time of the colliding beam was scanned, and the measured timing window and density of optimal operation agree with simulations [8]. The accelerator length was mapped by scanning the collision point. 4. Higgs Boson Searches at Hadron Colliders (1/4) ScienceCinema None 2011-10-06 In these Academic Training lectures, the phenomenology of Higgs bosons and search strategies at hadron colliders are discussed. After a brief introduction on Higgs bosons in the Standard Model and a discussion of present direct and indirect constraints on its mass the status of the theoretical cross section calculations for Higgs boson production at hadron colliders is reviewed. In the following lectures important experimental issues relevant for Higgs boson searches (trigger, measurements of leptons, jets and missing transverse energy) are presented. This is followed by a detailed discussion of the discovery potential for the Standard Model Higgs boson for both the Tevatron and the LHC experiments. In addition, various scenarios beyond the Standard Model, primarily the MSSM, are considered. Finally, the potential and strategies to measured Higgs boson parameters and the investigation of alternative symmetry breaking scenarios are addressed. 5. Optimizing integrated luminosity of future hadron colliders Benedikt, Michael; Schulte, Daniel; Zimmermann, Frank 2015-10-01 The integrated luminosity, a key figure of merit for any particle-physics collider, is closely linked to the peak luminosity and to the beam lifetime. The instantaneous peak luminosity of a collider is constrained by a number of boundary conditions, such as the available beam current, the maximum beam-beam tune shift with acceptable beam stability and reasonable luminosity lifetime (i.e., the empirical "beam-beam limit"), or the event pileup in the physics detectors. The beam lifetime at high-luminosity hadron colliders is largely determined by particle burn off in the collisions. In future highest-energy circular colliders synchrotron radiation provides a natural damping mechanism, which can be exploited for maximizing the integrated luminosity. In this article, we derive analytical expressions describing the optimized integrated luminosity, the corresponding optimum store length, and the time evolution of relevant beam parameters, without or with radiation damping, while respecting a fixed maximum value for the total beam-beam tune shift or for the event pileup in the detector. Our results are illustrated by examples for the proton-proton luminosity of the existing Large Hadron Collider (LHC) at its design parameters, of the High-Luminosity Large Hadron Collider (HL-LHC), and of the Future Circular Collider (FCC-hh). 6. Compensatable muon collider calorimeter with manageable backgrounds SciTech Connect Raja, Rajendran 2015-02-17 A method and system for reducing background noise in a particle collider, comprises identifying an interaction point among a plurality of particles within a particle collider associated with a detector element, defining a trigger start time for each of the pixels as the time taken for light to travel from the interaction point to the pixel and a trigger stop time as a selected time after the trigger start time, and collecting only detections that occur between the start trigger time and the stop trigger time in order to thereafter compensate the result from the particle collider to reduce unwanted background detection. 7. Beamstrahlung spectra in next generation linear colliders SciTech Connect Barklow, T.; Chen, P. ); Kozanecki, W. ) 1992-04-01 For the next generation of linear colliders, the energy loss due to beamstrahlung during the collision of the e{sup +}e{sup {minus}} beams is expected to substantially influence the effective center-of-mass energy distribution of the colliding particles. In this paper, we first derive analytical formulae for the electron and photon energy spectra under multiple beamstrahlung processes, and for the e{sup +}e{sup {minus}} and {gamma}{gamma} differential luminosities. We then apply our formulation to various classes of 500 GeV e{sup +}e{sup {minus}} linear collider designs currently under study. 8. SLAC linear collider conceptual design report SciTech Connect Not Available 1980-06-01 The linear collider system is described in detail, including the transport system, the collider lattice, final focusing system, positron production, beam damping and compression, high current electron source, instrumentation and control, and the beam luminosity. The experimental facilities and the experimental uses are discussed along with the construction schedule and estimated costs. Appendices include a discussion of space charge effects in the linear accelerator, emittance growth in the collider, the final focus system, beam-beam instabilities and pinch effects, and detector backgrounds. (GHT) 9. The principles and construction of linear colliders SciTech Connect Rees, J. 1986-09-01 The problems posed to the designers and builders of high-energy linear colliders are discussed. Scaling laws of linear colliders are considered. The problem of attainment of small interaction areas is addressed. The physics of damping rings, which are designed to condense beam bunches in phase space, is discussed. The effect of wake fields on a particle bunch in a linac, particularly the conventional disk-loaded microwave linac structures, are discussed, as well as ways of dealing with those effects. Finally, the SLAC Linear Collider is described. 18 refs., 17 figs. (LEW) 10. Electron-ion collider eRHIC In this article, we describe our planned future electron-ion collider (EIC), based on the existing Relativistic Heavy Ion Collider (RHIC) hadron facility, with two intersecting superconducting rings, each 3.8 km in circumference [1]. We plan to add a polarized electron beam with energy tunable within the 5-30-GeV range to collide with variety of species in the existing RHIC accelerator complex, from polarized protons with a maximum energy of 250 GeV, to heavy, fully striped ions with energies up to 100 GeV/u. 11. Proposal for Research and Development: Vertexing, Tracking, and Data Acquisition for the Bottom Collider Detector SciTech Connect Castro, H.; Gomez, B.; Rivera, F.; Sanabria, J.-C.; Yager, P.; Barsotti, E.; Bowden, M.; Childress, S.; Lebrun, P.; Morfin, J.; Roberts, L.A.; /Fermilab /Florida U. /Houston U. /IIT /Iowa U. /Northeastern U. /Northern Illinois U. /Ohio State U. /Oklahoma U. /Pennsylvania U. 1989-01-01 The authors propose a program of research and development into the detector systems needed for a B-physics experiment at the Fermilab p-{bar p} Collider. The initial emphasis is on the critical issues of vertexting, tracking, and data acquisition in the high-multiplicity, high-rate collider environment. R and D for the particle-identification systems (RICH counters, TRD's, and EM calorimeter) will be covered in a subsequent proposal. To help focus their efforts in a timely manner, they propose the first phase of the R and D should culminate in a system test at the C0 collider intersect during the 1990-1991 run: a small fraction of the eventual vertex detector would be used to demonstrate that secondary-decay vertices can be found at a hadron collider. The proposed budget for the r and D program is $800k in 1989,$1.5M in 1990, and 1.6M in 1991. 12. Nonglobal correlations in collider physics DOE PAGESBeta Moult, Ian; Larkoski, Andrew J. 2016-01-13 Despite their importance for precision QCD calculations, correlations between in- and out-of-jet regions of phase space have never directly been observed. These so-called non-global effects are present generically whenever a collider physics measurement is not explicitly dependent on radiation throughout the entire phase space. In this paper, we introduce a novel procedure based on mutual information, which allows us to isolate these non-global correlations between measurements made in different regions of phase space. We study this procedure both analytically and in Monte Carlo simulations in the context of observables measured on hadronic final states produced in e+e- collisions, though itmore » is more widely applicable.The procedure exploits the sensitivity of soft radiation at large angles to non-global correlations, and we calculate these correlations through next-to-leading logarithmic accuracy. The bulk of these non-global correlations are found to be described in Monte Carlo simulation. They increase by the inclusion of non-perturbative effects, which we show can be incorporated in our calculation through the use of a model shape function. As a result, this procedure illuminates the source of non-global correlations and has connections more broadly to fundamental quantities in quantum field theory.« less 13. Nonglobal correlations in collider physics NASA Astrophysics Data System (ADS) Larkoski, Andrew J.; Moult, Ian 2016-01-01 Despite their importance for precision QCD calculations, correlations between in- and out-of-jet regions of phase space have never directly been observed. These so-called nonglobal effects are present generically whenever a collider physics measurement is not explicitly dependent on radiation throughout the entire phase space. In this paper, we introduce a novel procedure based on mutual information, which allows us to isolate these nonglobal correlations between measurements made in different regions of phase space. We study this procedure both analytically and in Monte Carlo simulations in the context of observables measured on hadronic final states produced in e+e- collisions, though it is more widely applicable. The procedure exploits the sensitivity of soft radiation at large angles to nonglobal correlations, and we calculate these correlations through next-to-leading logarithmic accuracy. The bulk of these nonglobal correlations are found to be described in Monte Carlo simulation. They increase by the inclusion of nonperturbative effects, which we show can be incorporated in our calculation through the use of a model shape function. This procedure illuminates the source of nonglobal correlations and has connections more broadly to fundamental quantities in quantum field theory. 14. Vertex detectors and the linear collider NASA Astrophysics Data System (ADS) Damerell, C. J. S. 2006-11-01 We review the physics requirements for the ILC vertex detectors, which lead to the specification of silicon pixel sensors arranged as nested barrels, possibly augmented by endcap detectors for enhanced coverage of small polar angles. We describe how the detector requirements are a natural outgrowth of 25 years development of CCD-based vertex detectors in fixed-target and colliding beam experiments, culminating in the 307 Mpixel SLD vertex detector. We discuss how the technology has recently branched out into about a dozen architectures which might be made to work at the ILC, where the main challenge is to increase the effective readout rate by about a factor 1000 compared to conventional CCDs, while preserving the small pixels (˜20 μm) and low-power dissipation. Preserving gaseous cooling as at SLD opens the door to layer thicknesses as low as 0.1% X0. Finally, we consider how best to manage electromagnetic interference associated with the beam wakefields and other RF sources during the bunch train. In conclusion, we suggest a strategy for moving on from the present rich R&D programmes to optimal detectors for the startup of the ILC physics programme. 15. Electron Lenses for the Large Hadron Collider SciTech Connect Stancari, Giulio; Valishev, Alexander; Bruce, Roderik; Redaelli, Stefano; Rossi, Adriana; Salvachua, Belen 2014-07-01 Electron lenses are pulsed, magnetically confined electron beams whose current-density profile is shaped to obtain the desired effect on the circulating beam. Electron lenses were used in the Fermilab Tevatron collider for bunch-by-bunch compensation of long-range beam-beam tune shifts, for removal of uncaptured particles in the abort gap, for preliminary experiments on head-on beam-beam compensation, and for the demonstration of halo scraping with hollow electron beams. Electron lenses for beam-beam compensation are being commissioned in RHIC at BNL. Within the US LHC Accelerator Research Program and the European HiLumi LHC Design Study, hollow electron beam collimation was studied as an option to complement the collimation system for the LHC upgrades. This project is moving towards a technical design in 2014, with the goal to build the devices in 2015-2017, after resuming LHC operations and re-assessing needs and requirements at 6.5 TeV. Because of their electric charge and the absence of materials close to the proton beam, electron lenses may also provide an alternative to wires for long-range beam-beam compensation in LHC luminosity upgrade scenarios with small crossing angles. 16. Governance of the International Linear Collider Project SciTech Connect Foster, B.; Barish, B.; Delahaye, J.P.; Dosselli, U.; Elsen, E.; Harrison, M.; Mnich, J.; Paterson, J.M.; Richard, F.; Stapnes, S.; Suzuki, A.; Wormser, G.; Yamada, S.; /KEK, Tsukuba 2012-05-31 Governance models for the International Linear Collider Project are examined in the light of experience from similar international projects around the world. Recommendations for one path which could be followed to realize the ILC successfully are outlined. The International Linear Collider (ILC) is a unique endeavour in particle physics; fully international from the outset, it has no 'host laboratory' to provide infrastructure and support. The realization of this project therefore presents unique challenges, in scientific, technical and political arenas. This document outlines the main questions that need to be answered if the ILC is to become a reality. It describes the methodology used to harness the wisdom displayed and lessons learned from current and previous large international projects. From this basis, it suggests both general principles and outlines a specific model to realize the ILC. It recognizes that there is no unique model for such a laboratory and that there are often several solutions to a particular problem. Nevertheless it proposes concrete solutions that the authors believe are currently the best choices in order to stimulate discussion and catalyze proposals as to how to bring the ILC project to fruition. The ILC Laboratory would be set up by international treaty and be governed by a strong Council to whom a Director General and an associated Directorate would report. Council would empower the Director General to give strong management to the project. It would take its decisions in a timely manner, giving appropriate weight to the financial contributions of the member states. The ILC Laboratory would be set up for a fixed term, capable of extension by agreement of all the partners. The construction of the machine would be based on a Work Breakdown Structure and value engineering and would have a common cash fund sufficiently large to allow the management flexibility to optimize the project's construction. Appropriate contingency, clearly 17. LINEAR COLLIDER PHYSICS RESOURCE BOOK FOR SNOWMASS 2001. SciTech Connect ABE,T.; DAWSON,S.; HEINEMEYER,S.; MARCIANO,W.; PAIGE,F.; TURCOT,A.S.; ET AL 2001-05-03 The American particle physics community can look forward to a well-conceived and vital program of experimentation for the next ten years, using both colliders and fixed target beams to study a wide variety of pressing questions. Beyond 2010, these programs will be reaching the end of their expected lives. The CERN LHC will provide an experimental program of the first importance. But beyond the LHC, the American community needs a coherent plan. The Snowmass 2001 Workshop and the deliberations of the HEPAP subpanel offer a rare opportunity to engage the full community in planning our future for the next decade or more. A major accelerator project requires a decade from the beginning of an engineering design to the receipt of the first data. So it is now time to decide whether to begin a new accelerator project that will operate in the years soon after 2010. We believe that the world high-energy physics community needs such a project. With the great promise of discovery in physics at the next energy scale, and with the opportunity for the uncovering of profound insights, we cannot allow our field to contract to a single experimental program at a single laboratory in the world. We believe that an e{sup +}e{sup {minus}} linear collider is an excellent choice for the next major project in high-energy physics. Applying experimental techniques very different from those used at hadron colliders, an e{sup +}e{sup {minus}} linear collider will allow us to build on the discoveries made at the Tevatron and the LHC, and to add a level of precision and clarity that will be necessary to understand the physics of the next energy scale. It is not necessary to anticipate specific results from the hadron collider programs to argue for constructing an e{sup +}e{sup {minus}} linear collider; in any scenario that is now discussed, physics will benefit from the new information that e{sup +}e{sup {minus}} experiments can provide. 18. Linear accelerators for TeV colliders SciTech Connect Wilson, P.B. 1985-05-01 This paper summarizes four tutorial lectures on linear electron accelerators: Electron Linacs for TeV Colliders, Emittance and Damping Rings, Wake Fields: Basic Concepts, and Wake Field Effects in Linacs. 19. The Status of the International Linear Collider NASA Astrophysics Data System (ADS) Harrison, Michael 2016-03-01 The International Linear Collider is under consideration in Japan as the next major global high energy physics facility. In this talk we shall describe the site and accelerator footprint together with the latest technical information on the superconducting RF technology. 20. Topcolor and the First Muon Collider SciTech Connect Hill, C.T. 1998-04-01 We describe a class of models of electroweak symmetry breaking that involve strong dynamics and top quark condensation. A new scheme based upon a seesaw mechanism appears particularly promising. Various implications for the first-stage muon collider are discussed. 1. Heavy flavor physics at hadron colliders SciTech Connect Barbaro-Galtieri, A. 1991-12-01 The search for the top quark has dominated heavy flavor physics at hadron colliders. For Standard model decay of top the present mass limit in m{sub t} > 89 GeV (95% C.L.). Bottom production cross sections are quite large at hadron colliders, thus providing enough statistics for extensive studies. Results on cross sections, B{sup 0} {minus} {bar B}{sup 0} mixing, exclusive channels and rare B decays will be summarized. 2. RF pulse compression for future linear colliders SciTech Connect Wilson, P.B. 1995-05-01 Future (nonsuperconducting) linear colliders will require very high values of peak rf power per meter of accelerating structure. The role of rf pulse compression in producing this power is examined within the context of overall rf system design for three future colliders at energies of 1.0--1.5 TeV, 5 TeV and 25 TeV. In order keep the average AC input power and the length of the accelerator within reasonable limits, a collider in the 1.0--1.5 TeV energy range will probably be built at an x-band rf frequency, and will require a peak power on the order of 150--200 MW per meter of accelerating structure. A 5 TeV collider at 34 GHz with a reasonable length (35 km) and AC input power (225 MW) would require about 550 MW per meter of structure. Two-beam accelerators can achieve peak powers of this order by applying dc pulse compression techniques (induction linac modules) to produce the drive beam. Klystron-driven colliders achieve high peak power by a combination of dc pulse compression (modulators) and rf pulse compression, with about the same overall rf system efficiency (30--40%) as a two-beam collider. A high gain (6.8) three-stage binary pulse compression system with high efficiency (80%) is described, which (compared to a SLED-11 system) can be used to reduce the klystron peak power by about a factor of two, or alternately, to cut the number of klystrons in half for a 1.0--1.5 TeV x-band collider. For a 5 TeV klystron-driven collider, a high gain, high efficiency rf pulse compression system is essential. 3. Accelerator considerations of large circular colliders NASA Astrophysics Data System (ADS) Chao, Alex 2016-07-01 As we consider the tremendous physics reaches of the big future circular electron-positron and proton-proton colliders, it might be advisable to keep a close track of what accelerator challenges they face. Good progresses are being made, and yet it is reported here that substantial investments in funding, manpower, as well as a long sustained time to the R&D efforts will be required in preparation to realize these dream colliders. 4. Photon Linear Collider Gamma-Gamma Summary SciTech Connect Gronberg, J 2012-02-27 High energy photon - photon collisions can be achieved by adding high average power short-pulse lasers to the Linear Collider, enabling an expanded physics program for the facility. The technology required to realize a photon linear collider continues to mature. Compton back-scattering technology is being developed around the world for low energy light source applications and high average power lasers are being developed for Inertial Confinement Fusion. 5. World lays groundwork for future linear collider SciTech Connect Feder, Toni 2010-07-15 With the Large Hadron Collider at CERN finally working, the particle-physics community can now afford to divide its attention between achieving LHC results and preparing for the next machine on its wish list, an electron-positron linear collider. The preparations involve developing and deciding on the technology for such a machine, the mode of its governance, and how to balance regional and global particle- and accelerator-physics programs. 6. Signal of doubly charged Higgs at e+e- colliders NASA Astrophysics Data System (ADS) Hue, L. T.; Huong, D. T.; Long, H. N.; Hung, H. T.; Thao, N. H. 2015-11-01 The masses and signals of the production of doubly charged Higgses (DCH) in the framework of the supersymmetric reduced minimal 3-3-1 model are investigated. In the DCH sector, we prove that there always exists a region of the parameter space where the mass of the lightest DCH is of the order of O(100) GeV even when all other new particles are very heavy. The lightest DCH mainly decays to two same-sign leptons while the dominant decay channels of the heavy DCHs are those decaying to heavy particles. We analyze each production cross section for e^+e^- ⇒ H^{++} H^{-} as a function of a few kinematic variables, which are useful to discuss the creation of DCHs in e^+e^- colliders as an indicator of new physics beyond the Standard Model. A numerical study shows that the cross sections for creating the lightest DCH can reach values of a few pb. The other two DCHs are too heavy, beyond the observable range of experiments. The lightest DCH may be detected by the International Linear Collider or the Compact Linear Collider by searching for its decay to a same-sign charged lepton pair. 7. Low-cost hadron colliders at Fermilab: A discussion paper SciTech Connect Foster, G.W.; Malamud, E. 1996-06-21 New more economic approaches are required to continue the dramatic exponential rise in collider energies as represented by the well known Livingston plot. The old idea of low cost, low field iron dominated magnets in a small diameter pipe may become feasible in the next decade with dramatic recent advances in technology: (1) advanced tunneling technologies for small diameter, non human accessible tunnels, (2) accurate remote guidance systems for tunnel survey and boring machine steering, (3) high T{sub c} superconductors operating at liquid N{sub 2} or liquid H{sub 2} temperatures, (4) industrial applications of remote manipulation and robotics, (5) digitally multiplexed electronics to minimize cables, (6) achievement of high luminosities in p-p and p-{anti P} colliders. The goal of this paper is to stimulate continuing discussions on approaches to this new collider and to identify critical areas needing calculations, construction of models, proof of principle experiments, and full scale prototypes in order to determine feasibility and arrive at cost estimates. 8. Future proton and electron colliders: Dreams for the 1990's SciTech Connect Richter, B. 1988-10-01 In this paper I have reviewed the possibilities for new colliders that might be available in the 1990's. One or more new proton should be available in the late-90s based on plans of Europe, the US and the USSR. The two very high energy machines, LHC and SSC, are quite expensive, and their construction will be more decided by the politicians' view on the availability of resources than by the physicists' view of the need for new machines. Certainly something will be built, but the question is when. New electron colliders beyond LEP II could be available in the late 1990's as well. Most of the people who have looked at this problem believe that at a minimum three years of RandD are required before a proposal can be made, two years will be required to convince the authorities to go ahead, and five years will be required to build such a machine. Thus the earliest time a new electron collider at high energy could be available is around 1988. A strong international RandD program will be required to meet that schedule. In the field of B factories, PSI's proposal is the first serious step beyond the capabilities of CESR. There are other promising techniques but these need more RandD. The least RandD would be required for the asymmetric storage ring systems, while the most would be required for high luminosity linear colliders. For the next decade, high energy physics will be doing its work at the high energy frontier with Tevatron I and II, UNK, SLC, LEP I and II, and HERA. The opportunities for science presented by experiments at these facilities are very great, and it is to be hoped that the pressure for funding to construct the next generation facilities will not badly affect the operating budgets of the ones we now have or which will soon be turning on. 9 refs., 12 figs., 6 tabs. 9. Current experiments in particle physics - particle data group SciTech Connect Galic, H.; Lehar, F.; Kettle, P.R. 1996-09-01 This report contains summaries of current and recent experiments in Particle Physics. Included are experiments at BEPC (Beijing), BNL, CEBAF, CERN, CESR, DESY, FNAL, Frascati, ITEP (Moscow), JINR (Dubna), KEK, LAMPF, Novosibirsk, PNPI (St. Petersburg), PSI, Saclay, Serpukhov, SLAC, and TRIUMF, and also several proton decay and solar neutrino experiments. Excluded are experiments that finished taking data before 1991. Instructions are given for the World Wide Web (WWW) searching of the computer database (maintained under the SLAC-SPIRES system) that contains the summaries. 10. Taking Energy to the Physics Classroom from the Large Hadron Collider at CERN ERIC Educational Resources Information Center Cid, Xabier; Cid, Ramon 2009-01-01 In 2008, the greatest experiment in history began. When in full operation, the Large Hadron Collider (LHC) at CERN will generate the greatest amount of information that has ever been produced in an experiment before. It will also reveal some of the most fundamental secrets of nature. Despite the enormous amount of information available on this… 11. T864 (MiniMax): A search for disoriented chiral condensate at the Fermilab Collider SciTech Connect Bjorken, J.D. 1996-10-01 A small test/experiment has been performed at the Fermilab Collider to measure charged particle and photon multiplicities in the forward direction, {eta} {approximately} 4.1. The primary goal is to search for disoriented chiral condensate (DCC). The experiment and analysis methods are described, and preliminary results of the DCC search are presented. 12. Ecloud Build-Up Simulations for the FNAL MI for a Mixed Fill Pattern: Dependence on Peak SEY and Pulse Intensity During the Ramp SciTech Connect Furman, M. A. 2010-12-11 We present simulation results of the build-up of the electron-cloud density n{sub e} in three regions of the FNAL Main Injector (MI) for a beam fill pattern made up of 5 double booster batches followed by a 6th single batch. We vary the pulse intensity in the range N{sub t} = (2-5) x 10{sup 13}, and the beam kinetic energy in the range E{sub k} = 8-120 GeV. We assume a secondary electron emission model qualitatively corresponding to TiN, except that we let the peak value of the secondary electron yield (SEY) {delta}{sub max} vary as a free parameter in a fairly broad range. Our main conclusions are: (1) At fixed N{sub t} there is a clear threshold behavior of n{sub e} as a function of {delta}{sub max} in the range {approx} 1.1-1.3. (2) At fixed {delta}{sub max}, there is a threshold behavior of n{sub e} as a function of N{sub t} provided {delta}{sub max} is sufficiently high; the threshold value of N{sub t} is a function of the characteristics of the region being simulated. (3) The dependence on E{sub k} is weak except possibly at transition energy. Most of these results were informally presented to the relevant MI personnel in April 2010. 13. Beyond standard model physics at current and future colliders NASA Astrophysics Data System (ADS) Liu, Zhen The Large Hadron Collider (LHC), a multinational experiment which began running in 2009, is highly expected to discover new physics that will help us understand the nature of the universe and begin to find solutions to many of the unsolved puzzles of particle physics. For over 40 years the Standard Model has been the accepted theory of elementary particle physics, except for one unconfirmed component, the Higgs boson. The experiments at the LHC have recently discovered this Standard-Model-like Higgs boson. This discovery is one of the most exciting achievements in elementary particle physics. Yet, a profound question remains: Is this rather light, weakly-coupled boson nothing but a Standard Model Higgs or a first manifestation of a deeper theory? Also, the recent discoveries of neutrino mass and mixing, experimental evidences of dark matter and dark energy, matter-antimatter asymmetry, indicate that our understanding of fundamental physics is currently incomplete. For the next decade and more, the LHC and future colliders will be at the cutting-edge of particle physics discoveries and will shed light on many of these unanswered questions. There are many promising beyond-Standard-Model theories that may help solve the central puzzles of particle physics. To fill the gaps in our knowledge, we need to know how these theories will manifest themselves in controlled experiments, such as high energy colliders. I discuss how we can probe fundamental physics at current and future colliders directly through searches for new phenomena such as resonances, rare Higgs decays, exotic displaced signatures, and indirectly through precision measurements on Higgs in this work. I explore beyond standard model physics effects from different perspectives, including explicit models such as supersymmetry, generic models in terms of resonances, as well as effective field theory approach in terms of higher dimensional operators. This work provides a generic and broad overview of the physics 14. String resonances at hadron colliders NASA Astrophysics Data System (ADS) Anchordoqui, Luis A.; Antoniadis, Ignatios; Dai, De-Chang; Feng, Wan-Zhe; Goldberg, Haim; Huang, Xing; Lüst, Dieter; Stojkovic, Dejan; Taylor, Tomasz R. 2014-09-01 We consider extensions of the standard model based on open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. Assuming that the fundamental string mass scale Ms is in the TeV range and that the theory is weakly coupled, we discuss possible signals of string physics at the upcoming HL-LHC run (integrated luminosity =3000 fb-1) with a center-of-mass energy of √s =14 TeV and at potential future pp colliders, HE-LHC and VLHC, operating at √s =33 and 100 TeV, respectively (with the same integrated luminosity). In such D-brane constructions, the dominant contributions to full-fledged string amplitudes for all the common QCD parton subprocesses leading to dijets and γ +jet are completely independent of the details of compactification and can be evaluated in a parameter-free manner. We make use of these amplitudes evaluated near the first (n=1) and second (n=2) resonant poles to determine the discovery potential for Regge excitations of the quark, the gluon, and the color singlet living on the QCD stack. We show that for string scales as large as 7.1 TeV (6.1 TeV) lowest massive Regge excitations are open to discovery at the ≥5σ in dijet (γ +jet) HL-LHC data. We also show that for n=1 the dijet discovery potential at HE-LHC and VLHC exceedingly improves: up to 15 TeV and 41 TeV, respectively. To compute the signal-to-noise ratio for n=2 resonances, we first carry out a complete calculation of all relevant decay widths of the second massive level string states (including decays into massless particles and a massive n=1 and a massless particle), where we rely on factorization and conformal field theory techniques. Helicity wave functions of arbitrary higher spin massive bosons are also constructed. We demonstrate that for string scales Ms≲10.5 TeV (Ms≲28 TeV) detection of n =2 Regge recurrences at HE-LHC (VLHC) would become the smoking gun for D 15. PROSPECTS FOR COLLIDERS AND COLLIDER PHYSICS TO THE 1 PEV ENERGY SCALE SciTech Connect KING,B.J. 2000-05-05 A review is given of the prospects for future colliders and collider physics at the energy frontier. A proof-of-plausibility scenario is presented for maximizing the authors progress in elementary particle physics by extending the energy reach of hadron and lepton colliders as quickly and economically as might be technically and financially feasible. The scenario comprises 5 colliders beyond the LHC--one each of e{sup +}e{sup {minus}} and hadron colliders and three {mu}{sup +}{mu}{sup {minus}} colliders--and is able to hold to the historical rate of progress in the log-energy reach of hadron and lepton colliders, reaching the 1 PeV constituent mass scale by the early 2040's. The technical and fiscal requirements for the feasibility of the scenario are assessed and relevant long-term R and D projects are identified. Considerations of both cost and logistics seem to strongly favor housing most or all of the colliders in the scenario in a new world high energy physics laboratory. 16. Physics at the e⁺e⁻ linear collider DOE PAGESBeta Moortgat-Picka, G.; Kronfeld, A. S. 2015-08-14 A comprehensive review of physics at an e⁺e⁻ linear collider in the energy range of √s = 92 GeV–3 TeV is presented in view of recent and expected LHC results, experiments from low-energy as well as astroparticle physics. The report focuses in particular on Higgs-boson, top-quark and electroweak precision physics, but also discusses several models of beyond the standard model physics such as supersymmetry, little Higgs models and extra gauge bosons. The connection to cosmology has been analysed as well. 17. CLIC Project Overview (In Conjunction with the Muon Collider Workshop) ScienceCinema Latina, Andrea 2010-01-08 The CLIC study is exploring the scheme for an electron-positron collider with a centre-of-mass energy of 3 TeV in order to make the multi-TeV range accessible for physics. The current goal of the project is to demonstrate the feasibility of the technology by the year 2010. Recently, important progress has been made concerning the high-gradient accelerating structure tests and the experiments with beam in the CLIC test facility, CTF3. On the organizational side, the CLIC international collaborations have significantly gained momentum, boosting the CLIC study. 18. Superconducting final focus for the SLAC Linear Collider SciTech Connect Ash, W.W.; Barrera, F.; Burgess, W.; Cook, K.; Cutler, H.; Ferrie, J.; Petersen, H.; Sawyer, D.; Rinta, R. 1992-05-01 Triplets composed of superconducting quadrupoles have been built and installed as the final focusing element for the high-energy positron and electron beams of the SLAC Linear Collider. Special features include independent alignment to 100-micron tolerance inside a common cryostat; non-magnetic materials to allow operation inside the detectors solenoid field; a continuous-flow helium-only system using 50-meter-long flexible transfer lines; and complete operation of the system before installation. The mechanical design and cryogenic operation experience are presented. 19. Superconducting final focus for the SLAC Linear Collider SciTech Connect Ash, W.W.; Barrera, F.; Burgess, W.; Cook, K.; Cutler, H.; Ferrie, J.; Petersen, H.; Sawyer, D.; Rinta, R. 1992-05-01 Triplets composed of superconducting quadrupoles have been built and installed as the final focusing element for the high-energy positron and electron beams of the SLAC Linear Collider. Special features include independent alignment to 100-micron tolerance inside a common cryostat; non-magnetic materials to allow operation inside the detector's solenoid field; a continuous-flow helium-only system using 50-meter-long flexible transfer lines; and complete operation of the system before installation. The mechanical design and cryogenic operation experience are presented. 20. SSC (Superconducting Super Collider) dipole coil production tooling SciTech Connect Carson, J.A.; Barczak, E.J.; Bossert, R.C.; Brandt, J.S.; Smith, G.A. 1989-03-01 Superconducting Super Collider dipole coils must be produced to high precision to ensure uniform prestress and even conductor distribution within the collared coil assembly. Tooling is being prepared at Fermilab for the production of high precision 1M and 16.6M SSC dipole coils suitable for mass production. The design and construction methods builds on the Tevatron tooling and production experience. Details of the design and construction methods and measured coil uniformity of 1M coils will be presented. 4 refs., 10 figs. 1. Stagnation and interpenetration of laser-created colliding plasmas SciTech Connect Pollaine, S.M.; Albritton, J.R.; Kauffman, R.; Keane, C.J. ); Berger, R.L.; Bosch, R.; Delameter, N.D.; Failor, B.H. ) 1990-11-05 A KMS laser experiment collides Aluminum (A1) and Magnesium (Mg) plasmas. The measurements include electron density, time and space resolved Ly-alpha and He-alpha lines of Al and Mg, and x-ray images. These measurements were analyzed with a hydrodynamic code, LASNEX, and a special two-fluid code OFIS. The results strongly suggest that at early times, the Al interpenetrates the counterstreaming Mg and deposits in the dense Mg region. At late times, the Al plasma stagnates against the Mg plasma. 2. Minimax: Multiparticle physics at the TeVatron collider SciTech Connect Bjorken, J.D. 1994-01-01 The author and two dozen others are engaged in a small test/experiment in the Fermilab Tevatron collider. It is called Minimax, and its purpose is to explore large-cross-section physics in the forward direction. The primary goal of Minimax is search for events containing the residue of disoriented chiral condensate (dcc) produced in the primary collision. The theoretical ideas are very speculative. But if they are right, they could provide an interpretation of the Centauro/anti-Centauro anomalies claimed to have been seen in cosmic-ray events. In this paper, the history and status of Minimax is described. 3. Status of the SLAC Linear Collider Project SciTech Connect Stiening, R. 1983-01-01 The SLAC Linear Collider Project has two principal goals. The first is to serve as a prototype for a future very high energy linear electron-positron collider. The second is to quickly, at low cost, achieve sufficient luminosity at 100 GeV center-of-mass energy to explore the physics of the Z/sup 0/. The first goal is important to the future of electron-positron physics because the rapid increase of synchrotron radiation with energy causes the cost of circular storage ring colliders to whereas the cost of linear colliders increases only in proportion to the center-of-mass energy. The second is important because the existance at SLAC of a linear accelerator which can be converted at low cost to collider operation makes possible a unique opportunity to quickly achieve 100 GeV center-of-mass collisions. At the design luminosity of 6.0 x 10/sup 30/ many thousands of Z/sup 0/ decays should be observed in each day of operation. 4. Top Quark Mass from the Tevatron and LHC Colliders NASA Astrophysics Data System (ADS) Brigliadori, Luca 2015-03-01 The discovery of the top quark in 1995 has been one of the great successes of the CDF and D0 experiments at the Fermilab Tevatron collider. Since then, many measurements of the top quark properties have been performed in different channels and using many methods. The importance of measuring its mass lies in the possibility of verifying the predictions and the consistency of the Standard Model as well as in setting constraints on possible, still unobserved, physics. In 2010, the new CERN experiments, ATLAS and CMS, started to measure the top quark properties exploiting the large amount of data collected at the Large Hadron Collider. In March 2014, the very first combination of measurements from all the four experiments has been performed yielding Mtop = 173.34 ± 0.76 GeV, with a precision below 0.5%. In these proceedings a selected review of the most recent or relevant results obtained by the Tevatron and LHC Collaborations is presented. 5. Compilation of current high-energy physics experiments SciTech Connect Wohl, C.G.; Kelly, R.L.; Armstrong, F.E. 1981-05-01 This is the fourth edition of the compilation of current high energy physics experiments. It is a collaborative effort of the Berkeley Particle Data Group, the SLAC library, and nine participating laboratories: Argonne (ANL), Brookhaven (BNL), CERN, DESY, Fermilab (FNAL), the Institute for Nuclear Study, Tokyo (INS), KEK, Serpukhov (SERP), and SLAC. The compilation includes summaries of all high energy physics experiments at the above laboratories that (1) were approved (and not subsequently withdrawn) before about April 1981, and (2) had not completed taking of data by 1 January 1977. Only approved experiments are included. 6. The Large Hadron Collider: Redefining High Energy SciTech Connect Demers, Sarah 2007-06-19 Particle physicists have a description of the forces of nature known as the Standard Model that has successfully withstood decades of testing at laboratories around the world. Though the Standard Model is powerful, it is not complete. Important details like the masses of particles are not explained well, and realities as fundamental as gravity, dark matter, and dark energy are left out altogether. I will discuss gaps in the model and why there is hope that some puzzles will be solved by probing high energies with the Large Hadron Collider. Beginning next year, this machine will accelerate protons to record energies, hurling them around a 27 kilometer ring before colliding them 40 million times per second. Detectors the size of five-story buildings will record the debris of these collisions. The new energy frontier made accessible by the Large Hadron Collider will allow thousands of physicists to explore nature's fundamental forces and particles from a fantastic vantage point. 7. The Relativistic Heavy Ion Collider at Brookhaven SciTech Connect Hahn, H. 1989-01-01 The conceptual design of a collider capable of accelerating and colliding heavy ions and to be constructed in the existing 3.8 km tunnel at Brookhaven has been developed. The collider has been designed to provide collisions of gold ions at six intersection points with a luminosity of about 2 /times/ 10/sup 26/ cm/sup /minus/2/sec/sup /minus/1/ at an energy per nucleon of 100 GeV in each beam. Collisions with different ion species, including protons, will be possible. The salient design features and the reasons for major design choices of the proposed machine are discussed in this paper. 28 refs., 2 figs., 1 tab. 8. Seismic studies for Fermilab future collider projects SciTech Connect Lauh, J.; Shiltsev, V. 1997-11-01 Ground motion can cause significant beam emittance growth and orbit oscillations in large hadron colliders due to a vibration of numerous focusing magnets. Larger accelerator ring circumference leads to smaller revolution frequency and, e.g. for the Fermilab Very Large Hadron Collider(VLHC) 50-150 Hz vibrations are of particular interest as they are resonant with the beam betatron frequency. Seismic measurements at an existing large accelerator under operation can help to estimate the vibrations generated by the technical systems in future machines. Comparison of noisy and quiet microseismic conditions might be useful for proper choice of technical solutions for future colliders. This article presents results of wide-band seismic measurements at the Fermilab site, namely, in the tunnel of the Tevatron and on the surface nearby, and in two deep tunnels in the Illinois dolomite which is though to be a possible geological environment of the future accelerators. 9. Dynamics of laser ablated colliding plumes SciTech Connect Gupta, Shyam L.; Pandey, Pramod K.; Thareja, Raj K. 2013-01-15 We report the dynamics of single and two collinearly colliding laser ablated plumes of ZnO studied using fast imaging and the spectroscopic measurements. Two dimensional imaging of expanding plume and temporal evolution of various species in interacting zones of plumes are used to calculate plume front velocity, electron temperature, and density of plasma. The two expanding plumes interact with each other at early stage of expansion ({approx}20 ns) resulting in an interaction zone that propagates further leading to the formation of stagnation layer at later times (>150 ns) at the lateral collision front of two plumes. Colliding plumes have larger concentration of higher ionic species, higher temperature, and increased electron density in the stagnation region. A one-to-one correlation between the imaging and optical emission spectroscopic observations in interaction zone of the colliding plumes is reported. 10. Collider and detector protection at beam accidents SciTech Connect I. L. Rakhno; N. V. Mokhov; A. I. Drozhdin 2003-12-10 Dealing with beam loss due to abort kicker prefire is considered for hadron colliders. The prefires occurred at Tevatron (Fermilab) during Run I and Run II are analyzed and a protection system implemented is described. The effect of accidental beam loss in the Large Hadron Collider (LHC) at CERN on machine and detector components is studied via realistic Monte Carlo calculations. The simulations show that beam loss at an unsynchronized beam abort would result in severe heating of conventional and superconducting magnets and possible damage to the collider detector elements. A proposed set of collimators would reduce energy deposition effects to acceptable levels. Special attention is paid to reducing peak temperature rise within the septum magnet and minimizing quench region length downstream of the LHC beam abort straight section. 11. Quirky collider signals of folded supersymmetry NASA Astrophysics Data System (ADS) Burdman, Gustavo; Chacko, Z.; Goh, Hock-Seng; Harnik, Roni; Krenke, Christopher A. 2008-10-01 We investigate the collider signals associated with scalar quirks (squirks) in folded supersymmetric models. As opposed to regular superpartners in supersymmetric models these particles are uncolored, but are instead charged under a new confining group, leading to radically different collider signals. Because of the new strong dynamics, squirks that are pair produced do not hadronize separately, but rather form a highly excited bound state. The excited squirkonium loses energy to radiation before annihilating back into standard model particles. We calculate the branching fractions into various channels for this process, which is prompt on collider time scales. The most promising annihilation channel for discovery is W+photon which dominates for squirkonium near its ground state. We demonstrate the feasibility of the LHC search, showing that the mass peak is visible above the SM continuum background and estimate the discovery reach. 12. 2009 Linear Collider Workshop of the Americas SciTech Connect Seidel, Sally 2009-09-29 The 2009 Linear Collider Workshop of the Americas was held on the campus of the University of New Mexico from 29 September to 3 October, 2009. This was a joint meeting of the American Linear Collider Physics Group and the ILC Global Design Effort. Two hundred fifty people attended. The number of scientific contributions was 333. The complete agenda, with links to all of the presentations, is available at physics.unm.edu/LCWA09/. The meeting brought together international experts as well as junior scientists, to discuss the physics potential of the linear collider and advances in detector technology. The validation of detector designs was announced, and the detector design groups planned the next phase of the effort. Detector R&D teams reported on progress on many topics including calorimetry and tracking. Recent accelerator design considerations were discussed in a special session for experimentalists and theorists. 13. The Tevatron Hadron Collider: A short history SciTech Connect Tollestrup, A.V. 1994-11-01 The subject of this presentation was intended to cover the history of hadron colliders. However this broad topic is probably better left to historians. I will cover a much smaller portion of this subject and specialize my subject to the history of the Tevatron. As we will see, the Tevatron project is tightly entwined with the progress in collider technology. It occupies a unique place among accelerators in that it was the first to make use of superconducting magnets and indeed the basic design now forms a template for all machines using this technology. It was spawned in an incredibly productive era when new ideas were being generated almost monthly and it has matured into our highest energy collider complete with two large detectors that provide the major facility in the US for probing high Pt physics for the coming decade. 14. Calorimetry At Very High Energy Colliders SciTech Connect Chiu, Mickey 2011-06-01 The capability of hadron colliders has increased to where it will soon be possible to collide protons at center of mass energies of 14 TeV with the advent of the LHC. With increasing collision energy, calorimeters become ever more essential components of a detector, and collaborations often choose very different technologies to meet their goals. From the perspective of a high energy particle and nuclear physicist, a survey is presented of the differences in design considerations and actual performance of the wide variety of calorimeters used in modern hadron colliders such as the Tevatron, RHIC, and LHC. The lessons learned and some ideas for future development of calorimetry will also be discussed. 15. International linear collider reference design report SciTech Connect Aarons, G. 2007-06-22 The International Linear Collider will give physicists a new cosmic doorway to explore energy regimes beyond the reach of today's accelerators. A proposed electron-positron collider, the ILC will complement the Large Hadron Collider, a proton-proton collider at the European Center for Nuclear Research (CERN) in Geneva, Switzerland, together unlocking some of the deepest mysteries in the universe. With LHC discoveries pointing the way, the ILC -- a true precision machine -- will provide the missing pieces of the puzzle. Consisting of two linear accelerators that face each other, the ILC will hurl some 10 billion electrons and their anti-particles, positrons, toward each other at nearly the speed of light. Superconducting accelerator cavities operating at temperatures near absolute zero give the particles more and more energy until they smash in a blazing crossfire at the centre of the machine. Stretching approximately 35 kilometres in length, the beams collide 14,000 times every second at extremely high energies -- 500 billion-electron-volts (GeV). Each spectacular collision creates an array of new particles that could answer some of the most fundamental questions of all time. The current baseline design allows for an upgrade to a 50-kilometre, 1 trillion-electron-volt (TeV) machine during the second stage of the project. This reference design provides the first detailed technical snapshot of the proposed future electron-positron collider, defining in detail the technical parameters and components that make up each section of the 31-kilometer long accelerator. The report will guide the development of the worldwide R&D program, motivate international industrial studies and serve as the basis for the final engineering design needed to make an official project proposal later this decade. 16. Collider physics for the late 1980's SciTech Connect Hinchliffe, I. 1987-02-27 Topics in the Standard Model of strong and electroweak interactions and how these topics are relevant for the high energy colliders are discussed. Radiative corrections in the Glashow-Weinberg-Salam model are discussed, stressing how these corrections may be measured at LEP and the SLC. CP violation is discussed, followed by a discussion of the Higgs boson and the searches which can be carried out for it. Some features of quantum chromodynamics are discussed which are relevant to hadron colliders. Some of the problems which the Standard Model does not solve are discussed. 115 refs., 53 figs. (LEW) 17. Top quark studies at hadron colliders SciTech Connect Sinervo, P.K.; CDF Collaboration 1996-08-01 The techniques used to study top quarks at hadron colliders are presented. The analyses that discovered the top quark are described, with emphasis on the techniques used to tag {ital b} quark jets in candidate events. The most recent measurements of top quark properties by the CDF and D{null} collaborations are reviewed, including the top quark cross section, mass, branching fractions and production properties. Future top quark studies at hadron colliders are discussed, and predictions for event yields and uncertainties in the measurements of top quark properties are presented. 18. Top quark studies at hadron colliders SciTech Connect Sinervo, P.K. 1997-01-01 The techniques used to study top quarks at hadron colliders are presented. The analyses that discovered the top quark are described, with emphasis on the techniques used to tag b quark jets in candidate events. The most recent measurements of top quark properties by the CDF and DO Collaborations are reviewed, including the top quark cross section, mass, branching fractions, and production properties. Future top quark studies at hadron colliders are discussed, and predictions for event yields and uncertainties in the measurements of top quark properties are presented. 19. Beam instrumentation for the Tevatron Collider SciTech Connect Moore, Ronald S.; Jansson, Andreas; Shiltsev, Vladimir; /Fermilab 2009-10-01 The Tevatron in Collider Run II (2001-present) is operating with six times more bunches and many times higher beam intensities and luminosities than in Run I (1992-1995). Beam diagnostics were crucial for the machine start-up and the never-ending luminosity upgrade campaign. We present the overall picture of the Tevatron diagnostics development for Run II, outline machine needs for new instrumentation, present several notable examples that led to Tevatron performance improvements, and discuss the lessons for future colliders. 20. Suppressing Electron Cloud in Future Linear Colliders SciTech Connect Pivi, M; Kirby, R.E.; Raubenheimer, T.O.; Le Pimpec, F.; /PSI, Villigen 2005-05-27 Any accelerator circulating positively charged beams can suffer from a build-up of an electron cloud (EC) in the beam pipe. The cloud develops through ionization of residual gases, synchrotron radiation and secondary electron emission and, when severe, can cause instability, emittance blow-up or loss of the circulating beam. The electron cloud is potentially a luminosity limiting effect for both the Large Hadron Collider (LHC) and the International Linear Collider (ILC). For the ILC positron damping ring, the development of the electron cloud must be suppressed. This paper discusses the state-of-the-art of the ongoing SLAC and international R&D program to study potential remedies. 1. Physics Beyond the Standard Model at Colliders NASA Astrophysics Data System (ADS) Matchev, Konstantin These lectures introduce the modern machinery used in searches and studies of new physics Beyond the Standard Model (BSM) at colliders. The first lecture provides an overview of the main simulation tools used in high energy physics, including automated parton-level calculators, general purpose event generators, detector simulators, etc. The second lecture is a brief introduction to low energy supersymmetry (SUSY) as a representative BSM paradigm. The third lecture discusses the main collider signatures of SUSY and methods for measuring the masses of new particles in events with missing energy. 2. FFAG Designs for Muon Collider Acceleration SciTech Connect Berg, J. Scott 2014-01-13 I estimate FFAG parameters for a muon collider with a 70mm longitudinal emittance. I do not discuss the lower emittance beam for a Higgs factory. I produce some example designs, giving only parameters relevant to estimating cost and performance. The designs would not track well, but the parameters of a good design will be close to those described. I compare these cost estimates to those for a fast-ramping synchrotron and a recirculating linear accelerator. I conclude that FFAGs do not appear to be cost-effective for the large longitudinal emittance in a high-energy muon collider. 3. Luminosity measurements at hadron colliders SciTech Connect Papadimitriou, Vaia; /Fermilab 2008-04-01 In this paper we discuss luminosity measurements at Tevatron and HERA as well as plans for luminosity measurements at LHC. We discuss luminosity measurements using the luminosity detectors of the experiments as well as measurements by the machine. We address uncertainties of the measurements, challenges and lessons learned. 4. Report of Snowmass 2001 working group E2: Electron - positron colliders from the phi to the Z SciTech Connect Zhen-guo Zhao et al. 2002-12-23 We report on the status and plans of experiments now running or proposed for electron-positron colliders at energies between the {phi} and the Z. The e{sup +}e{sup -}B and charm factories we considered were PEP-II/BABAR, KEKB/Belle, superKEK, SuperBABAR, and CESR-c/CLEO-c. We reviewed the programs at the {phi} factory at Frascati and the proposed PEP-N facility at Stanford Linear Accelerator Center. We studied the prospects for B physics with a dedicated linear collider Z factory, associated with the TESLA high energy linear collider. In all cases, we compared the physics reach of these facilities with that of alternative experiments at hadron colliders or fixed target facilities. 5. Present optics options for TeV colliders SciTech Connect Spencer, J.E. 1986-05-01 A practical approach for implementing TeV collider optics with high luminosities pounds approx. = 10/sup 33/ (cm/sup 2/ s)/sup -1/ but without large pinch effects is given using current alternatives. Characteristics are considered that constrain the optics and the types and orders of magnets required. A modified linac FoDo cell based on permanent magnet hybrid quadrupoles is discussed. Similarly, a demagnifying, permanent magnet telescopic system that allows variation of beta, eta and energy is suggested for the final focus. The basic cell for low emittance damping rings can also be constructed solely from permanent magnets. Small diameter, low permeability, high field permanent magnets have proven useful for injection and extraction lines and are also compatible with the large particle near the interaction regions as well as with exotic experiments for production and use of secondary beams or for multi-bunch coalescing schemes for control of longitudinal bunch distribution. An 8-10 GeV prototype cell and final focus experiment is proposed to verify and study such systems as well as do some interesting physics tests. One example, which could be used with the PEP storage ring, would convert an external electron beam into a photon beam to avoid beamstrahlung effects - a major problem for high energy e+- colliders. 6. Beam dynamics issues for linear colliders SciTech Connect Ruth, R.D. 1987-09-01 In this paper we discuss various beam dynamics issues for linear colliders. The emphasis is to explore beam dynamics effects which lead to an effective dilution of the emittance of the beam and thus to a loss of luminosity. These considerations lead to various tolerances which are evaluated for a particular parameter set. 7. Proton-proton colliding beam facility ISABELLE SciTech Connect Hahn, H 1980-01-01 This paper attempts to present the status of the ISABELLE construction project, which has the objective of building a 400 + 400 GeV proton colliding beam facility. The major technical features of the superconducting accelerators with their projected performance are described. Progress made so far, difficulties encountered, and the program until completion in 1986 is briefly reviewed. 8. Difficult Decisions: The Superconducting Super Collider. ERIC Educational Resources Information Center Newton, David E.; Slesnick, Irwin L. 1990-01-01 The fundamental principles of the superconducting super collider are presented. Arguments for the construction of this apparatus and policy issues surrounding its construction are discussed. Charts of the fundamental atomic particles and forces and the history of particle accelerators are provided. An activity for discussing this controversial… 9. Cost optimization of a hadron collider SciTech Connect Vadim V. Kashikhin and Peter J. Limon 2001-11-30 This paper discusses cost scaling laws and optimization of hadron colliders based on high field magnets. Using a few simplifying assumptions that should give a reasonable approximation, cost of the magnet is divided among several major components. Scaling law for every component is determined along with the weight factors that allow cost comparison between different magnet designs. Cost of hadron collider as a function of field, aperture size and critical current density in superconductor is described analytically that allows cost optimization by changing magnet parameters. The optimum magnetic field is determined for machines based on NbTi superconductor, operating at 4.2 K or 1.9 K and NB{sub 3}Sn superconductor operating at 4.2 K. Analyzed influence of main magnet design parameters on a machine cost provided information on ways leading to the magnet cost reduction. Economical justification of a NB{sub 3}Sn collider is performed, which lets to determine the maximum price ratio between NB{sub 3}Sn and NbTi superconductors that makes NB{sub 3}Sn collider economically effective. 10. From the LHC to Future Colliders SciTech Connect De Roeck, A.; Ellis, J.; Grojean, C.; Heinemeyer, S.; Jakobs, K.; Weiglein, G.; Azuelos, G.; Dawson, S.; Gripaios, B.; Han, T.; Hewett, J.; Lancaster, M.; Mariotti, C.; Moortgat, F.; Moortgat-Pick, G.; Polesello, G.; Riemann, S.; Assamagan, K.; Bechtle, P.; Carena, M.; Chachamis, G.; /more authors.. 2010-06-11 Discoveries at the LHC will soon set the physics agenda for future colliders. This report of a CERN Theory Institute includes the summaries of Working Groups that reviewed the physics goals and prospects of LHC running with 10 to 300 fb{sup -1} of integrated luminosity, of the proposed sLHC luminosity upgrade, of the ILC, of CLIC, of the LHeC and of a muon collider. The four Working Groups considered possible scenarios for the first 10 fb{sup -1} of data at the LHC in which (i) a state with properties that are compatible with a Higgs boson is discovered, (ii) no such state is discovered either because the Higgs properties are such that it is difficult to detect or because no Higgs boson exists, (iii) a missing-energy signal beyond the Standard Model is discovered as in some supersymmetric models, and (iv) some other exotic signature of new physics is discovered. In the contexts of these scenarios, theWorking Groups reviewed the capabilities of the future colliders to study in more detail whatever new physics may be discovered by the LHC. Their reports provide the particle physics community with some tools for reviewing the scientific priorities for future colliders after the LHC produces its first harvest of new physics from multi-TeV collisions. 11. Beam-beam issues in asymmetric colliders SciTech Connect Furman, M.A. 1992-07-01 We discuss generic beam-beam issues for proposed asymmetric e{sup +}- e{sup -} colliders. We illustrate the issues by choosing, as examples, the proposals by Cornell University (CESR-B), KEK, and SLAC/LBL/LLNL (PEP-II). 12. Black Holes and the Large Hadron Collider ERIC Educational Resources Information Center Roy, Arunava 2011-01-01 The European Center for Nuclear Research or CERN's Large Hadron Collider (LHC) has caught our attention partly due to the film "Angels and Demons." In the movie, an antimatter bomb attack on the Vatican is foiled by the protagonist. Perhaps just as controversial is the formation of mini black holes (BHs). Recently, the American Physical Society… 13. Towards a Future Linear Collider and The Linear Collider Studies at CERN ScienceCinema None 2011-10-06 During the week 18-22 October, more than 400 physicists will meet at CERN and in the CICG (International Conference Centre Geneva) to review the global progress towards a future linear collider. The 2010 International Workshop on Linear Colliders will study the physics, detectors and accelerator complex of a linear collider covering both the CLIC and ILC options. Among the topics presented and discussed will be the progress towards the CLIC Conceptual Design Report in 2011, the ILC Technical Design Report in 2012, physics and detector studies linked to these reports, and an increasing numbers of common working group activities. The seminar will give an overview of these topics and also CERN?s linear collider studies, focusing on current activities and initial plans for the period 2011-16. n.b: The Council Chamber is also reserved for this colloquium with a live transmission from the Main Auditorium. 14. The Collider Principle in Causal Reasoning: Why the Monty Hall Dilemma Is So Hard ERIC Educational Resources Information Center Burns, Bruce D.; Wieth, Mareike 2004-01-01 The authors tested the thesis that people find the Monty Hall dilemma (MHD) hard because they fail to understand the implications of its causal structure, a collider structure in which 2 independent causal factors influence a single outcome. In 4 experiments, participants performed better in versions of the MHD involving competition, which… 15. High Energy Accelerator and Colliding Beam User Group: Progress report, March 1, 1988--February 28, 1989 SciTech Connect Not Available 1988-09-01 This report discusses work carried out by the High Energy Accelerator and Colliding Beam User Group at the University of Maryland. Particular topics discussed are: OPAL experiment at LEP; deep inelastic muon interactions; B physics with the CLEO detector at CESR; further results from JADE; and search for ''small'' violation of the Pauli principle. (LSP) 16. High-brightness injectors for hadron colliders SciTech Connect Wangler, T.P. 1990-01-01 The counterrotating beams in collider rings consist of trains of beam bunches with N{sub B} particles per bunch, spaced a distance S{sub B} apart. When the bunches collide, the interaction rate is determined by the luminosity, which is defined as the interaction rate per unit cross section. For head-on collisions between cylindrical Gaussian beams moving at speed {beta}c, the luminosity is given by L = N{sub B}{sup 2}{beta}c/4{pi}{sigma}{sup 2}S{sub B}, where {sigma} is the rms beam size projected onto a transverse plane (the two transverse planes are assumed identical) at the interaction point. This beam size depends on the rms emittance of the beam and the focusing strength, which is a measure of the 2-D phase-space area in each transverse plane, and is defined in terms of the second moments of the beam distribution. Our convention is to use the rms normalized emittance, without factors of 4 or 6 that are sometimes used. The quantity {tilde {beta}} is the Courant-Synder betatron amplitude function at the interaction point, a characteristic of the focusing lattice and {gamma} is the relativistic Lorentz factor. Achieving high luminosity at a given energy, and at practical values of {tilde {beta}} and S{sub B}, requires a large value for the ratio N{sub B}{sup 2}/{var epsilon}{sub n}, which implies high intensity and small emittance. Thus, specification of the luminosity sets the requirements for beam intensity and emittance, and establishes the requirements on the performance of the injector to the collider ring. In general, for fixed N{sub B}, the luminosity can be increased if {var epsilon}{sub n} can be reduced. The minimum emittance of the collider is limited by the performance of the injector; consequently the design of the injector is of great importance for the ultimate performance of the collider. 17. Current Experiments in Particle Physics (September 1996) SciTech Connect Galic, H.; Lehar, F.; Klyukhin, V.I.; Ryabov, Yu.G.; Bilak, S.V.; Illarionova, N.S.; Khachaturov, B.A.; Strokovsky, E.A.; Hoffman, C.M.; Kettle, P.-R.; Olin, A.; Armstrong, F.E. 1996-09-01 This report contains summaries of current and recent experiments in Particle Physics. Included are experiments at BEPC (Beijing), BNL, CEBAF, CERN, CESR, DESY, FNAL, Frascati, ITEP (Moscow), JINR (Dubna), KEK, LAMPF, Novosibirsk, PNPI (St. Petersburg), PSI, Saclay, Serpukhov, SLAC, and TRIUMF, and also several proton decay and solar neutrino experiments. Excluded are experiments that finished taking data before 1991. Instructions are given for the World Wide Web (WWW) searching of the computer database (maintained under the SLAC-SPIRES system) that contains the summaries. This report contains full summaries of 180 approved current and recent experiments in elementary particle physics. The focus of the report is on selected experiments which directly contribute to our better understanding of elementary particles and their properties such as masses, widths or lifetimes, and branching fractions. 18. Department of Energy assessment of the Large Hadron Collider SciTech Connect 1996-06-01 This report summarizes the conclusions of the committee that assessed the cost estimate for the Large Hadron Collider (LHC). This proton-proton collider will be built at CERN, the European Laboratory for Particle Physics near Geneva, Switzerland. The committee found the accelerator-project cost estimate of 2.3 billion in 1995 Swiss francs, or about2 billion US, to be adequate and reasonable. The planned project completion date of 2005 also appears achievable, assuming the resources are available when needed. The cost estimate was made using established European accounting procedures. In particular, the cost estimate does not include R and D, prototyping and testing, spare parts, and most of the engineering labor. Also excluded are costs for decommissioning the Large Electron-Positron collider (LEP) that now occupies the tunnel, modifications to the injector system, the experimental areas, preoperations costs, and CERN manpower. All these items are assumed by CERN to be included in the normal annual operations budget rather than the construction budget. Finally, contingency is built into the base estimate, in contrast to Department of Energy (DOE) estimates that explicitly identify contingency. The committees charge, given by Dr. James F. Decker, Deputy Directory of the DOE Office of Energy Research, was to understand the basis for the LHC cost estimate, identify uncertainties, and judge the overall validity of the estimate, proposed schedule, and related issues. The committee met at CERN April 22--26, 1996. The assessment was based on the October 1995 LHC Conceptual Design Report or Yellow Book, cost estimates and formal presentations made by the CERN staff, site inspection, detailed discussions with LHC technical experts, and the committee members considerable experience. 19. Compilation of current high-energy-physics experiments SciTech Connect Wohl, C.G.; Kelly, R.L.; Armstrong, F.E. 1980-04-01 This is the third edition of a compilation of current high energy physics experiments. It is a collaborative effort of the Berkeley Particle Data Group, the SLAC library, and ten participating laboratories: Argonne (ANL), Brookhaven (BNL), CERN, DESY, Fermilab (FNAL), the Institute for Nuclear Study, Tokyo (INS), KEK, Rutherford (RHEL), Serpukhov (SERP), and SLAC. The compilation includes summaries of all high energy physics experiments at the above laboratories that (1) were approved (and not subsequently withdrawn) before about January 1980, and (2) had not completed taking of data by 1 January 1976. 20. Collider Detector at Fermilab (CDF): Data from the Top Group's Top Quark Research DOE Data Explorer The Collider Detector at Fermilab (CDF) is a Tevatron experiment at Fermilab. The Tevatron, a powerful particle accelerator, accelerates protons and antiprotons close to the speed of light, and then makes them collide head-on inside the CDF detector. The CDF detector is used to study the products of such collisions. The CDF Physics Group at Fermilab is organized into six working groups, each with a specific focus. The Top group studies the properties of the top quark, the heaviest known fundamental particle. Their public web page makes data and numerous figures available from both CDF Runs I and II. 1. Collider Detector at Fermilab (CDF): Data from Supersymmetry, New Phenomena Research of the CDF Exotics Group DOE Data Explorer The Collider Detector at Fermilab (CDF) is a Tevatron experiment at Fermilab. The Tevatron, a powerful particle accelerator, accelerates protons and antiprotons close to the speed of light, and then makes them collide head-on inside the CDF detector. The CDF detector is used to study the products of such collisions. The CDF Physics Group at Fermilab is organized into six working groups, each with a specific focus. The Exotics group searches for Supersymmetry and other New Phenomena. Their public web page makes data and numerous figures available from both CDF Runs I and II. 2. Higgs bosons, electroweak symmetry breaking, and the physics of the Large Hadron Collider SciTech Connect Quigg, Chris; /Fermilab /CERN 2007-02-01 The Large Hadron Collider, a 7 {circle_plus} 7 TeV proton-proton collider under construction at CERN (the European Laboratory for Particle Physics in Geneva), will take experiments squarely into a new energy domain where mysteries of the electroweak interaction will be unveiled. What marks the 1-TeV scale as an important target? Why is understanding how the electroweak symmetry is hidden important to our conception of the world around us? What expectations do we have for the agent that hides the electroweak symmetry? Why do particle physicists anticipate a great harvest of discoveries within reach of the LHC? 3. An Afterburner at the ILC: The Collider Viewpoint SciTech Connect Raubenheimer, Tor O. 2004-12-07 The concept of a high-gradient plasma wakefield accelerator is considered as an upgrade path for the International Linear Collider, a future linear collider. Basic parameters are presented based on those developed for the SLC 'Afterburner'. Basic layout considerations are described and the primary concerns related to the collider operation are discussed. 4. An Afterburner at the ILC: The Collider Viewpoint SciTech Connect Raubenheimer, T 2004-09-01 The concept of a high-gradient plasma wakefield accelerator is considered as an upgrade path for the International Linear Collider, a future linear collider. Basic parameters are presented based on those developed for the SLC ''Afterburner.'' Basic layout considerations are described and the primary concerns related to the collider operation are discussed. 5. Higgs boson and Z physics at the first muon collider SciTech Connect Demarteau, M.; Han, T. 1998-01-01 The potential for the Higgs boson and Z-pole physics at the first muon collider is summarized, based on the discussions at the Workshop on the Physics at the First Muon Collider and at the Front End of a Muon Collider. 6. LASER-PLASMA-ACCELERATOR-BASED GAMMA GAMMA COLLIDERS SciTech Connect Schroeder, C. B.; Esarey, E.; Toth, Cs.; Geddes, C. G. R.; Leemans, W. P. 2009-05-04 Design considerations for a next-generation linear collider based on laser-plasma-accelerators are discussed, and a laser-plasma-accelerator-based gamma-gamma collider is considered. An example of the parameters for a 0.5 TeV laser-plasma-accelerator gamma gamma collider is presented. 7. Laser triggered injection of electrons in a laser wakefield accelerator with the colliding pulse method SciTech Connect Nakamura, K.; Fubiani, G.; Geddes, C.G.R.; Michel, P.; van Tilborg, J.; Toth, C.; Esarey, E.; Schroeder, C.B.; Leemans, W.P. 2004-10-22 An injection scheme for a laser wakefield accelerator that employs a counter propagating laser (colliding with the drive laser pulse, used to generate a plasma wake) is discussed. The threshold laser intensity for electron injection into the wakefield was analyzed using a heuristic model based on phase-space island overlap. Analysis shows that the injection can be performed using modest counter propagating laser intensity a{sub 1} < 0.5 for a drive laser intensity of a{sub 0} = 1.0. Preliminary experiments were preformed using a drive beam and colliding beam. Charge enhancement by the colliding pulse was observed. Increasing the signal-to-noise ratio by means of a preformed plasma channel is discussed. 8. J. J. Sakurai Prize for Theoretical Particle Physics Talk: Collider Physics: Yesterday, Today and Tomorrow Eichten, Estia 2011-04-01 More than a quarter century ago, theoretical issues with the Standard Model scalar boson sector inspired theorists to develop alternative models of electroweak symmetry breaking. The goal of the EHLQ study of hadron collider physics was to help determine the basic parameters of a supercollider that could distinguish these alternatives. Now we await data from the CMS and ATLAS experiments at CERN's Large Hadron Collider to solve this mystery. Does the Standard Model survive or, as theorists generally expect, does new physics appear (Strong Dynamics, SUSY, Extra Dimensions,...)? Even well into the LHC era it is likely that questions about the origin of fermion mass and mixings will remain and new physics will bring new puzzles. This time, the associated new scales are unknown. The opportunity to address new physics at a future multi-TeV lepton collider is briefly addressed. 9. A photon-photon collider in a vacuum hohlraum Pike, O. J.; Mackenroth, F.; Hill, E. G.; Rose, S. J. 2014-06-01 The ability to create matter from light is amongst the most striking predictions of quantum electrodynamics. Experimental signatures of this have been reported in the scattering of ultra-relativistic electron beams with laser beams, intense laser-plasma interactions and laser-driven solid target scattering. However, all such routes involve massive particles. The simplest mechanism by which pure light can be transformed into matter, Breit-Wheeler pair production (γγ' --> e+e-), has never been observed in the laboratory. Here, we present the design of a new class of photon-photon collider in which a gamma-ray beam is fired into the high-temperature radiation field of a laser-heated hohlraum. Matching experimental parameters to current-generation facilities, Monte Carlo simulations suggest that this scheme is capable of producing of the order of 105 Breit-Wheeler pairs in a single shot. This would provide the first realization of a pure photon-photon collider, representing the advent of a new type of high-energy physics experiment. 10. The Electroweak Phase Transition: Corralling the Higgs with Colliders & Cosmology Long, Andrew J. Through this thesis, I investigate the way in which the electroweak phase transition, and therefore the Higgs boson, bridges high energy particle physics and early universe cosmology; moreover, I argue that it is particularly interesting to explore this bridge today as experiments such as the Large Hadron Collider begin to uncover the nature of physics at the electroweak scale. I will discuss how measurements of the properties of the Higgs boson at the Large Hadron Collider allow one to determine the nature of the phase transition that was responsible for electroweak symmetry breaking in the early universe. That information in turn will allow one to assess whether the asymmetry between the abundances of matter and anti-matter in the universe may have been generated during the electroweak phase transition. Additionally, I will discuss the impact of the electroweak phase transition on another cosmological relic: namely, the dark matter. Precise measurements of the mass and abundance of dark matter today yield further information about the nature of the electroweak phase transition, in some scenarios. This information may be used to test the hypothesis that the cosmological constant, assumed to be a good model of dark energy, is finely tuned. In this way, I hope to demonstrate the importance of the electroweak phase transition as a bridge between terrestrial tests of high energy physics and cosmological tests of the physics of the early universe. 11. TARGETRY FOR A MU+MU- COLLIDER. SciTech Connect KIRK,H.G. 1999-03-29 The requirement for high luminosity in a {mu}{sup +}{mu}{sup -} collider leads one to conclude that a prodigious source of pions is needed followed by an efficient capture/decay channel. Significant targetry issues are raised by these demands. Among these are (1) the best target configuration to tolerate a high-rep rate, high-power proton beam ({approx} 10{sup 14} ppp at 15 Hz), (2) the pion spectra of the produced pions and (3) the best configuration for maximizing the quantity of captured pions. In this paper, the current thinking of the {mu}{sup +}{mu}{sup -} collider collaboration for solutions to these issues is discussed. In addition, we give a description of the R&D program designed to provide a proof-of-principle for a muon capture system capable of meeting the demands of a future high-luminosity machine. 12. Global QCD Analysis and Hadron Collider Physics SciTech Connect Tung, W.-K. 2005-03-22 The role of global QCD analysis of parton distribution functions (PDFs) in collider physics at the Tevatron and LHC is surveyed. Current status of PDF analyses are reviewed, emphasizing the uncertainties and the open issues. The stability of NLO QCD global analysis and its prediction on 'standard candle' W/Z cross sections at hadron colliders are discussed. The importance of the precise measurement of various W/Z cross sections at the Tevatron in advancing our knowledge of PDFs, hence in enhancing the capabilities of making significant progress in W mass and top quark parameter measurements, as well as the discovery potentials of Higgs and New Physics at the Tevatron and LHC, is emphasized. 13. Future high energy colliders symposium. Summary report SciTech Connect Parsa, Z. \| 1996-12-31 A Future High Energy Colliders Symposium was held October 21-25, 1996 at the Institute for Theoretical Physics (ITP) in Santa Barbara. This was one of the 3 symposia hosted by the ITP and supported by its sponsor, the National Science Foundation, as part of a 5 month program on New Ideas for Particle Accelerators. The long term program and symposia were organized and coordinated by Dr. Zohreh Parsa of Brookhaven National Laboratory/ITP. The purpose of the symposium was to discuss the future direction of high energy physics by bringing together leaders from the theoretical, experimental and accelerator physics communities. Their talks provided personal perspectives on the physics objectives and the technology demands of future high energy colliders. Collectively, they formed a vision for where the field should be heading and how it might best reach its objectives. 14. Initial operation of the Tevatron collider SciTech Connect Johnson, R. 1987-03-01 The Tevatron is now the highest energy proton synchrotron and the only accelerator made with superconducting magnets. Operating since 1983 as a fixed-target machine at energies up to 800 GeV, it has now been modified to operate as a 900 GeV antiproton-proton collider. This paper describes the initial operation of the machine in this mode. The new features of the Fermilab complex, including the antiproton source and the Main Ring injector with its two overpasses and new rf requirements, are discussed. Beam characteristics in the Tevatron (including lifetimes, emittances, luminosity, beam-beam tune shifts, backgrounds, and low beta complications), the coordination of the steps in the accelerator chain, and the commissioning history are also discussed. Finally, some plans for the improvement of the collider are presented. 15. Reverse Emittance Exchange for Muon Colliders SciTech Connect V. Ivanov, A. Afanasev, C.M. Ankenbrandt, R.P. Johnson, G.M. Wang, S.A. Bogacz, Y.S. Derbenev 2009-05-01 Muon collider luminosity depends on the number of muons in the storage ring and on the transverse size of the beams in collision. Ionization cooling as it is currently envisioned will not cool the beam sizes sufficiently well to provide adequate luminosity without large muon intensities. Six-dimensional cooling schemes will reduce the longitudinal emittance of a muon beam so that smaller high frequency RF cavities can be used for later stages of cooling and for acceleration. However, the bunch length at collision energy is then shorter than needed to match the interaction region beta function. New ideas to shrink transverse beam dimensions by lengthening each bunch will help achieve high luminosity in muon colliders. Analytic expressions for the reverse emittance exchange mechanism were derived, including a new resonant method of beam focusing. 16. Collider Detector (CDF) at FERMILAB: an overview SciTech Connect Theriot, D. 1984-07-01 CDF, the Collider Detector at Fermilab, is a collaboration of almost 150 physicists from ten US universities (University of Chicago, Brandeis University, Harvard University, University of Illinois, University of Pennsylvania, Purdue University, Rockefeller University, Rutgers University, Texas A and M University, and University of Wisconsin), three US DOE supported national laboratories (Fermilab, Argonne National Laboratory, and Lawrence Berkeley Laboratory), Italy (Frascati Laboratory and University of Pisa), and Japan (KEK National Laboratory and Unversity of Tsukuba). The primary physics goal for CDF is to study the general features of proton-antiproton collisions at 2 TeV center-of-mass energy. On general grounds, we expect that parton subenergies in the range 50 to 500 GeV will provide the most interesting physics at this energy. Work at the present CERN Collider has already demonstrated the richness of the 100 GeV scale in parton subenergies. 17. 1987 DOE review: First collider run operation SciTech Connect Childress, S.; Crawford, J.; Dugan, G.; Edwards, H.; Finley, D.A.; Fowler, W.B.; Harrison, M.; Holmes, S.; Makara, J.N.; Malamud, E. 1987-05-01 This review covers the operations of the first run of the 1.8 TeV superconducting super collider. The papers enclosed cover: PBAR source status, fixed target operation, Tevatron cryogenic reliability and capacity upgrade, Tevatron Energy upgrade progress and plans, status of the D0 low beta insertion, 1.8 K and 4.7 K refrigeration for low-..beta.. quadrupoles, progress and plans for the LINAC and booster, near term and long term and long term performance improvements. 18. Polarized muon beams for muon collider Skrinsky, A. N. 1996-11-01 An option for the production of intense and highly polarized muon beams, suitable for a high-luminosity muon collider, is described briefly. It is based on a multi-channel pion-collection system, narrow-band pion-to-muon decay channels, proper muon spin gymnastics, and ionization cooling to combine all of the muon beams into a single bunch of ultimately low emittance. 19. ψψ production at collider energies Humpert, B.; Méry, P. 1983-03-01 We estimate ψψ production at collider energies in the framework of perturbative QCD. The O(α{/s 2})-(α{/s 4}) parton cross-sections, with the non-relativistic approximation for the heavy quark bound states, are used. This first insight into the characteristics of the kinematical distributions allows predictions on the predominance of the quark, gluon or B meson production mechanisms in particular kinematical regions. 20. Progress report on the SLAC Linear Collider SciTech Connect Rees, J. 1986-06-01 The SLAC Linear Collider project (SLC) is reported as being near completion. The performance specifications are tabulated both for the initial form and for eventual goals. Various parts of the SLC are described and the status of their construction is reported, including the front end electron gun and booster, the linac, damping ring, positron source, SLC arcs, and conventional facilities. 5 refs., 12 figs. (LEW) 1. 2009: A Colliding-Wind Odyssey Fahed, R.; Moffat, A. F. J.; Zorec, J.; Eversberg, T.; Chené, A. N.; Alves, F.; Arnold, W.; Bergmann, T.; Corcoran, M. F.; Correia Viegas, N. G.; Dougherty, S. M.; Fernando, A.; Frémat, Y.; Gouveia Carreira, L. F.; Hunger, T.; Knapen, J. H.; Leadbeater, R.; Marques Dias, F.; Martayan, C.; Morel, T.; Pittard, J. M.; Pollock, A. M. T.; Rauw, G.; Reinecke, N.; Ribeiro, J.; Romeo, N.; Sánchez-Gallego, J. R.; dos Santos, E. M.; Schanne, L.; Stahl, O.; Stober, Ba.; Stober, Be.; Vollmann, K.; Williams, P. M. 2012-12-01 We present the results from two optical spectroscopic campaigns on colliding-wind binaries (CWB) which both occurred in 2009. The first one was on WR 140 (WC7pd + O5.5fc), the archetype of CWB, which experienced periastron passage of its highly elliptical 8-year orbit in January. The WR 140 campaign consisted of a unique and constructive collaboration between amateur and professional astronomers and took place at half a dozen locations, including Teide Observatory, Observatoire de Haute Provence, Dominion Astrophysical Observatory, Observatoire du Mont-Mégantic and at several small private observatories. The second campaign was on a selection of 5 short-period WR + O binaries not yet studied for colliding-wind effects: WR 12 (WN8h), WR 21 (WN5o + O7 V), WR 30 (WC6 + O7.5 V), WR 31 (WN4o + O8), and WR 47 (WN6o + O5). The campaign took place at Leoncito Observatory, Argentina, during 1 month. We provide updated values of most of these systems for the orbital parameters, new estimates for the WR and O star masses and new constraints on the mass-loss rates and colliding wind geometry. 2. Muon Collider Machine-Detector Interface SciTech Connect Mokhov, Nikolai V.; /Fermilab 2011-08-01 In order to realize the high physics potential of a Muon Collider (MC) a high luminosity of {mu}{sup +}{mu}{sup -}-collisions at the Interaction Point (IP) in the TeV range must be achieved ({approx}10{sup 34} cm{sup -2}s{sup -1}). To reach this goal, a number of demanding requirements on the collider optics and the IR hardware - arising from the short muon lifetime and from relatively large values of the transverse emittance and momentum spread in muon beams that can realistically be obtained with ionization cooling should be satisfied. These requirements are aggravated by limitations on the quadrupole gradients as well as by the necessity to protect superconducting magnets and collider detectors from muon decay products. The overall detector performance in this domain is strongly dependent on the background particle rates in various sub-detectors. The deleterious effects of the background and radiation environment produced by the beam in the ring are very important issues in the Interaction Region (IR), detector and Machine-Detector Interface (MDI) designs. This report is based on studies presented very recently. 3. Structure and Dynamics of Colliding Plasma Jets DOE PAGESBeta Li, C.; Ryutov, D.; Hu, S.; Rosenberg, M.; Zylstra, A.; Seguin, F.; Frenje, J.; Casey, D.; Gatu Johnson, M.; Manuel, M.; et al 2013-12-01 Monoenergetic-proton radiographs of laser-generated, high-Mach-number plasma jets colliding at various angles shed light on the structures and dynamics of these collisions. The observations compare favorably with results from 2D hydrodynamic simulations of multistream plasma jets, and also with results from an analytic treatment of electron flow and magnetic field advection. In collisions of two noncollinear jets, the observed flow structure is similar to the analytic model’s prediction of a characteristic feature with a narrow structure pointing in one direction and a much thicker one pointing in the opposite direction. Spontaneous magnetic fields, largely azimuthal around the colliding jets and generatedmore » by the well-known ∇Te ×∇ne Biermann battery effect near the periphery of the laser spots, are demonstrated to be “frozen in” the plasma (due to high magnetic Reynolds number RM ~5×10⁴) and advected along the jet streamlines of the electron flow. These studies provide novel insight into the interactions and dynamics of colliding plasma jets.« less 4. The Relativistic Heavy Ion Collider at Brookhaven SciTech Connect Hahn, H. 1988-01-01 The conceptual design of a Relativistic Heavy Ion Collider (RACK) to be constructed in the existing 3.8 km tunnel at Brookhaven has been developed. The collider has been designed to provide collisions of gold ions at six intersection points with a luminosity of about 5 /times/ 10/sup 26/cm/sup /minus/2/sec/sup /minus/1/ at an energy of 100 GeV/u in each beam. Collisions with different ion species, including protons, will be possible. The collider consists of two interlaced, but otherwise separate, superconducting magnet rings. The 9.7 m long dipoles will operate at 3.5 T. Their 8 cm aperture was determined by the dimensions of gold ion beams taking into account diffusion due to intrabeam scattering. Heavy ion beams will be available from the Tandem Van de Graaff/Booster/AGS complex. The salient design features and the reasons for major design choices of the proposed machine are discussed in this paper. 24 refs., 7 figs., 2 tabs. 5. Linear collider IR and final focus introduction SciTech Connect Irwin, J.; Burke, D. 1991-09-01 The Linear Collider subgroup of the Accelerator Physics working group concerned itself with all aspects of the Next Linear Collider (NLC) design from the end of the accelerating structure to and through the interaction region. Within this region are: (1) a collimation section, (2) muon protection (of the detector from the collimator), (3) final focus system, (4) interaction point physics, and (5) detector masking from synchrotron radiation and beam-beam pair production. These areas of study are indicated schematically in Fig. 1. The parameters for the Next Linear Collider are still in motion, but attention has settled on a handful of parameter sets. Energies under consideration vary from 0.5 to 1.5 TeV in the center of mass, and luminosities vary from 10{sup 33} to 10{sup 34} cm{sup {minus}2}s{sup {minus}1}. To be concrete we chose as a guide for our studies the parameter sets labeled F and G, Table 1 from Palmer. These cover large and small crossing angle cases and 0.4 m to 1.8 m of free length at the interaction point. 6. Structure and Dynamics of Colliding Plasma Jets SciTech Connect Li, C.; Ryutov, D.; Hu, S.; Rosenberg, M.; Zylstra, A.; Seguin, F.; Frenje, J.; Casey, D.; Gatu Johnson, M.; Manuel, M.; Rinderknecht, H.; Petrasso, R.; Amendt, P.; Park, H.; Remington, B.; Wilks, S.; Betti, R.; Froula, D.; Knauer, J.; Meyerhofer, D.; Drake, R.; Kuranz, C.; Young, R.; Koenig, M. 2013-12-01 Monoenergetic-proton radiographs of laser-generated, high-Mach-number plasma jets colliding at various angles shed light on the structures and dynamics of these collisions. The observations compare favorably with results from 2D hydrodynamic simulations of multistream plasma jets, and also with results from an analytic treatment of electron flow and magnetic field advection. In collisions of two noncollinear jets, the observed flow structure is similar to the analytic model’s prediction of a characteristic feature with a narrow structure pointing in one direction and a much thicker one pointing in the opposite direction. Spontaneous magnetic fields, largely azimuthal around the colliding jets and generated by the well-known ∇Te ×∇ne Biermann battery effect near the periphery of the laser spots, are demonstrated to be “frozen in” the plasma (due to high magnetic Reynolds number RM ~5×10⁴) and advected along the jet streamlines of the electron flow. These studies provide novel insight into the interactions and dynamics of colliding plasma jets. 7. Neutrino Factory and Muon Collider Fellow SciTech Connect Hanson, Gail G.; Snopak, Pavel; Bao, Yu 2015-03-20 Muons are fundamental particles like electrons but much more massive. Muon accelerators can provide physics opportunities similar to those of electron accelerators, but because of the larger mass muons lose less energy to radiation, allowing more compact facilities with lower operating costs. The way muon beams are produced makes them too large to fit into the vacuum chamber of a cost-effective accelerator, and the short muon lifetime means that the beams must be reduced in size rather quickly, without losing too many of the muons. This reduction in size is called "cooling." Ionization cooling is a new technique that can accomplish such cooling. Intense muon beams can then be accelerated and injected into a storage ring, where they can be used to produce neutrino beams through their decays or collided with muons of the opposite charge to produce a muon collider, similar to an electron-positron collider. We report on the research carried out at the University of California, Riverside, towards producing such muon accelerators, as part of the Muon Accelerator Program based at Fermilab. Since this research was carried out in a university environment, we were able to involve both undergraduate and graduate students. 8. Interpenetration and stagnation in colliding laser plasmas SciTech Connect Al-Shboul, K. F.; Harilal, S. S. Hassan, S. M.; Hassanein, A.; Costello, J. T.; Yabuuchi, T.; Tanaka, K. A.; Hirooka, Y. 2014-01-15 We have investigated plasma stagnation and interaction effects in colliding laser-produced plasmas. For generating colliding plasmas, two split laser beams were line-focused onto a hemi-circular target and the seed plasmas so produced were allowed to expand in mutually orthogonal directions. This experimental setup forced the expanding seed plasmas to come to a focus at the center of the chamber. The interpenetration and stagnation of plasmas of candidate fusion wall materials, viz., carbon and tungsten, and other materials, viz., aluminum, and molybdenum were investigated in this study. Fast-gated imaging, Faraday cup ion analysis, and optical emission spectroscopy were used for diagnosing seed and colliding plasma plumes. Our results show that high-Z target (W, Mo) plasma ions interpenetrate each other, while low-Z (C, Al) plasmas stagnate at the collision plane. For carbon seed plasmas, an intense stagnation was observed resulting in longer plasma lifetime; in addition, the stagnation layer was found to be rich with C{sub 2} dimers. 9. Measurement of Boer-Mulders Function via Drell-Yan Process by SeaQuest Experiment at Fermilab Nakano, Kenichi 2016-02-01 The SeaQuest experiment is being carried out at Fermi National Accelerator Lab (FNAL) to investigate the nucleon structure with the Drell-Yan process. It utilizes the 120-GeV proton beam extracted from the FNAL Main Injector and targets of liquid hydrogen, liquid deuterium, carbon, iron and tungsten. The solid targets are used to measure the nuclear effects. This paper describes the flavor asymmetry of light anti-quark distributions in the proton (d¯/ū) and the angular distribution of Drell-Yan process. The Boer-Mulders function (h1⊥(x,k T)) can be derived from the size (ν) of cos 2ϕ modulation. SeaQuest finished the second data-taking period in August 2014. Preliminary results of d¯/ū and ν are reported. 10. Probing neutrino oscillations in supersymmetric models at the Large Hadron Collider SciTech Connect Campos, F. de; Eboli, O. J. P.; Hirsch, M.; Valle, J. W. F.; Porod, W. 2010-10-01 The lightest supersymmetric particle may decay with branching ratios that correlate with neutrino oscillation parameters. In this case the CERN Large Hadron Collider (LHC) has the potential to probe the atmospheric neutrino mixing angle with sensitivity competitive to its low-energy determination by underground experiments. Under realistic detection assumptions, we identify the necessary conditions for the experiments at CERN's LHC to probe the simplest scenario for neutrino masses induced by minimal supergravity with bilinear R parity violation. 11. Indiana University High Energy Physics, Task A. Technical progress report, 1992--1993 SciTech Connect Brabson, B.; Crittenden, R.; Dzierba, A. 1993-10-01 This report discusses research at Indians University on the following high energy physics experiments: A search for mesons with unusual quantum numbers; hadronic states produced in association with high-mass dimuons; FNAL E740 (D0); superconducting super collider; and OPAL experiment at CERN. 12. Jet Reconstruction and Spectroscopy at Hadron Colliders Bellettini, Giorgio 2011-11-01 Dear colleagues and friends, Major new particle discoveries were made in the past by exploring the mass spectrum of lepton pairs. These searches still have great potential. However, new particle searches are now being extended to masses larger than the W, Z mass. More and more decay channels open up and the branching ratios into lepton pairs are reduced. Also, physics may dictate that states with heavy bosons and quarks become dominant. Examples are the decay of top quarks, and the expected final states of the standard model Higgs boson. Supersymmetry in any of its wide spectrum of models predicts intrigued final states where jets are major observables. To reconstruct masses and to study the dynamics of these states one must exploit the energy-momentum four-vectors of jets. Past experiments at the CERN SPS collider, at HERA, at LEP and now at the Tevatron collider and at LHC, have studied how best to reconstruct hadron jets. However, originally the role of jets in searching for new physics was primarily to sense new parton contact interactions by means of increased large pt tails in inclusive jet spectra, or studying jet events with large missing Et, or measuring branching ratios into jets of different flavour. These studies did not require as accurate a measure of jet four-momenta as needed in new particle searches in multi-jets final states. Figure 1 Figure 1. W, Z associated production in CDF events with large Et, miss and 2 jets. Consider for example (figure 1) the mass spectrum of dijets in events with large missing Et recently measured by CDF [1]. Trigger and analysis cuts were chosen so as to favour production of heavy boson pairs, with decay of one Z boson into neutrinos tagging the event and another W or Z boson decaying into jets. Associated production of boson pairs is observed, but the dijet mass resolution does not allow the separation of W from Z. A broad agreement of the overall observed rate with expectation is found, but a comparative study of the 13. Search for New Fermions (''Quirks'') at the Fermilab Tevatron Collider SciTech Connect Abazov, V. M.; Alexeev, G. D.; Golovanov, G.; Kharzheev, Y. N.; Malyshev, V. L.; Tokmenin, V. V.; Vertogradov, L. S.; Yatsunenko, Y. A.; Abbott, B.; Gutierrez, P.; Hossain, S.; Severini, H.; Skubic, P.; Strauss, M.; Abolins, M.; Benitez, J. A.; Brock, R.; Edmunds, D.; Fisher, W.; Kraus, J. 2010-11-19 We report results of a search for particles with anomalously high ionization in events with a high transverse energy jet and large missing transverse energy in 2.4 fb{sup -1} of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron pp collider. Production of such particles (quirks) is expected in scenarios with extra QCD-like SU(N) sectors, and this study is the first dedicated search for such signatures. We find no evidence of a signal and set a lower mass limit of 107, 119, and 133 GeV for the mass of a charged quirk with strong dynamics scale {Lambda} in the range from 10 keV to 1 MeV and N=2, 3, and 5, respectively. 14. Dark Matter and Collider Physics in Split-UED SciTech Connect Chan Park, Seong; Shu Jing 2010-02-10 Kaluza-Klein dark matter is an attractive weakly interacting massive particle in universal extra dimension model. In the recent extension 'split-UED', annihilation of Kaluza-Klein dark matter with a mass range 600-1000 GeV provides excellent fits to the recently observed excesses in cosmic electron and positron fluxes of Pamela, ATIC and Fermi-LAT experiments. The cosmic gamma-ray flux in the same process can be significant around 300 GeV, thus can be observed or constrained by the forthcoming Fermi-LAT diffuse gamma-ray data. The collider signal at the LHC is the resonance in the dijets channels and the large missing energy in the missing energy plus jets. 15. Search for New Fermions (Quirks'') at the Fermilab Tevatron Collider Abazov, V. M.; Abbott, B.; Abolins, M.; Acharya, B. S.; Adams, M.; Adams, T.; Alexeev, G. D.; Alkhazov, G.; Alton, A.; Alverson, G.; Alves, G. A.; Ancu, L. S.; Aoki, M.; Arnoud, Y.; Arov, M.; Askew, A.; Åsman, B.; Atramentov, O.; Avila, C.; Backusmayes, J.; Badaud, F.; Bagby, L.; Baldin, B.; Bandurin, D. V.; Banerjee, S.; Barberis, E.; Baringer, P.; Barreto, J.; Bartlett, J. F.; Bassler, U.; Beale, S.; Bean, A.; Begalli, M.; Begel, M.; Belanger-Champagne, C.; Bellantoni, L.; Benitez, J. A.; Beri, S. B.; Bernardi, G.; Bernhard, R.; Bertram, I.; Besançon, M.; Beuselinck, R.; Bezzubov, V. A.; Bhat, P. C.; Bhatnagar, V.; Blazey, G.; Blessing, S.; Bloom, K.; Boehnlein, A.; Boline, D.; Bolton, T. A.; Boos, E. E.; Borissov, G.; Bose, T.; Brandt, A.; Brandt, O.; Brock, R.; Brooijmans, G.; Bross, A.; Brown, D.; Brown, J.; Bu, X. B.; Buchholz, D.; Buehler, M.; Buescher, V.; Bunichev, V.; Burdin, S.; Burnett, T. H.; Buszello, C. P.; Calpas, B.; Calvet, S.; Camacho-Pérez, E.; Carrasco-Lizarraga, M. A.; Carrera, E.; Casey, B. C. K.; Castilla-Valdez, H.; Chakrabarti, S.; Chakraborty, D.; Chan, K. M.; Chandra, A.; Chen, G.; Chevalier-Théry, S.; Cho, D. K.; Cho, S. W.; Choi, S.; Choudhary, B.; Christoudias, T.; Cihangir, S.; Claes, D.; Clutter, J.; Cooke, M.; Cooper, W. E.; Corcoran, M.; Couderc, F.; Cousinou, M.-C.; Croc, A.; Cutts, D.; Ćwiok, M.; Das, A.; Davies, G.; de, K.; de Jong, S. J.; de La Cruz-Burelo, E.; Déliot, F.; Demarteau, M.; Demina, R.; Denisov, D.; Denisov, S. P.; Desai, S.; Devaughan, K.; Diehl, H. T.; Diesburg, M.; Dominguez, A.; Dorland, T.; Dubey, A.; Dudko, L. V.; Duggan, D.; Duperrin, A.; Dutt, S.; Dyshkant, A.; Eads, M.; Edmunds, D.; Ellison, J.; Elvira, V. D.; Enari, Y.; Eno, S.; Evans, H.; Evans, J. A.; Evdokimov, A.; Evdokimov, V. N.; Facini, G.; Ferapontov, A. V.; Ferbel, T.; Fiedler, F.; Filthaut, F.; Fisher, W.; Fisk, H. E.; Fortner, M.; Fox, H.; Fuess, S.; Gadfort, T.; Garcia-Bellido, A.; Gavrilov, V.; Gay, P.; Geist, W.; Geng, W.; Gerbaudo, D.; Gerber, C. E.; Gershtein, Y.; Ginther, G.; Golovanov, G.; Goussiou, A.; Grannis, P. D.; Greder, S.; Greenlee, H.; Greenwood, Z. D.; Gregores, E. M.; Grenier, G.; Gris, Ph.; Grivaz, J.-F.; Grohsjean, A.; Grünendahl, S.; Grünewald, M. W.; Guo, F.; Guo, J.; Gutierrez, G.; Gutierrez, P.; Haas, A.; Hagopian, S.; Haley, J.; Han, L.; Harder, K.; Harel, A.; Hauptman, J. M.; Hays, J.; Hebbeker, T.; Hedin, D.; Hegab, H.; Heinson, A. P.; Heintz, U.; Hensel, C.; Heredia-de La Cruz, I.; Herner, K.; Hesketh, G.; Hildreth, M. D.; Hirosky, R.; Hoang, T.; Hobbs, J. D.; Hoeneisen, B.; Hohlfeld, M.; Hossain, S.; Hubacek, Z.; Huske, N.; Hynek, V.; Iashvili, I.; Illingworth, R.; Ito, A. S.; Jabeen, S.; Jaffré, M.; Jain, S.; Jamin, D.; Jesik, R.; Johns, K.; Johnson, M.; Johnston, D.; Jonckheere, A.; Jonsson, P.; Joshi, J.; Juste, A.; Kaadze, K.; Kajfasz, E.; Karmanov, D.; Kasper, P. A.; Katsanos, I.; Kehoe, R.; Kermiche, S.; Khalatyan, N.; Khanov, A.; Kharchilava, A.; Kharzheev, Y. N.; Khatidze, D.; Kirby, M. H.; Kohli, J. M.; Kozelov, A. V.; Kraus, J.; Kumar, A.; Kupco, A.; Kurča, T.; Kuzmin, V. A.; Kvita, J.; Lammers, S.; Landsberg, G.; Lebrun, P.; Lee, H. S.; Lee, S. W.; Lee, W. M.; Lellouch, J.; Li, L.; Li, Q. Z.; Lietti, S. M.; Lim, J. K.; Lincoln, D.; Linnemann, J.; Lipaev, V. V.; Lipton, R.; Liu, Y.; Liu, Z.; Lobodenko, A.; Lokajicek, M.; Love, P.; Lubatti, H. J.; Luna-Garcia, R.; Luty, M. A.; Lyon, A. L.; Maciel, A. K. A.; Mackin, D.; Madar, R.; Magaña-Villalba, R.; Malik, S.; Malyshev, V. L.; Maravin, Y.; Martínez-Ortega, J.; McCarthy, R.; McGivern, C. L.; Meijer, M. M.; Melnitchouk, A.; Menezes, D.; Mercadante, P. G.; Merkin, M.; Meyer, A.; Meyer, J.; Mondal, N. K.; Muanza, G. S.; Mulhearn, M.; Nagy, E.; Naimuddin, M.; Narain, M.; Nayyar, R.; Neal, H. A.; Negret, J. P.; Neustroev, P.; Nilsen, H.; Novaes, S. F.; Nunnemann, T.; Obrant, G.; Onoprienko, D.; Orduna, J.; Osman, N.; Osta, J.; Otero Y Garzón, G. J.; Owen, M.; Padilla, M.; Pangilinan, M.; Parashar, N.; Parihar, V.; Park, S. K.; Parsons, J.; Partridge, R.; Parua, N.; Patwa, A.; Penning, B.; Perfilov, M.; Peters, K.; Peters, Y.; Petrillo, G.; Pétroff, P.; Piegaia, R.; Piper, J.; Pleier, M.-A.; Podesta-Lerma, P. L. M.; Podstavkov, V. M.; Pol, M.-E.; Polozov, P.; Popov, A. V.; Prewitt, M.; Price, D.; Protopopescu, S.; Qian, J.; Quadt, A.; Quinn, B.; Rangel, M. S.; Ranjan, K.; Ratoff, P. N.; Razumov, I.; Renkel, P.; Rich, P.; Rijssenbeek, M.; Ripp-Baudot, I.; Rizatdinova, F.; Rominsky, M.; Royon, C.; Rubinov, P.; Ruchti, R.; Safronov, G.; Sajot, G.; Sánchez-Hernández, A.; Sanders, M. P.; Sanghi, B.; Santos, A. S.; Savage, G.; Sawyer, L.; Scanlon, T.; Schamberger, R. D.; Scheglov, Y.; Schellman, H.; Schliephake, T.; Schlobohm, S.; Schwanenberger, C.; Schwienhorst, R.; Sekaric, J.; Severini, H.; Shabalina, E.; Shary, V.; Shchukin, A. A.; Shivpuri, R. K.; Simak, V.; Sirotenko, V.; Skubic, P.; Slattery, P.; Smirnov, D.; Smith, K. J.; Snow, G. R.; Snow, J.; Snyder, S.; Söldner-Rembold, S.; Sonnenschein, L.; Sopczak, A.; Sosebee, M.; Soustruznik, K.; Spurlock, B.; Stark, J.; Stolin, V.; Stoyanova, D. A.; Strauss, E.; Strauss, M.; Strom, D.; Stutte, L.; Svoisky, P.; Takahashi, M.; Tanasijczuk, A.; Taylor, W.; Titov, M.; Tokmenin, V. V.; Tsybychev, D.; Tuchming, B.; Tully, C.; Tuts, P. M.; Uvarov, L.; Uvarov, S.; Uzunyan, S.; van Kooten, R.; van Leeuwen, W. M.; Varelas, N.; Varnes, E. W.; Vasilyev, I. A.; Verdier, P.; Vertogradov, L. S.; Verzocchi, M.; Vesterinen, M.; Vilanova, D.; Vint, P.; Vokac, P.; Wahl, H. D.; Wang, M. H. L. S.; Warchol, J.; Watts, G.; Wayne, M.; Weber, M.; Wetstein, M.; White, A.; Wicke, D.; Williams, M. R. J.; Wilson, G. W.; Wimpenny, S. J.; Wobisch, M.; Wood, D. R.; Wyatt, T. R.; Xie, Y.; Xu, C.; Yacoob, S.; Yamada, R.; Yang, W.-C.; Yasuda, T.; Yatsunenko, Y. A.; Ye, Z.; Yin, H.; Yip, K.; Yoo, H. D.; Youn, S. W.; Yu, J.; Zelitch, S.; Zhao, T.; Zhou, B.; Zhu, J.; Zielinski, M.; Zieminska, D.; Zivkovic, L. 2010-11-01 We report results of a search for particles with anomalously high ionization in events with a high transverse energy jet and large missing transverse energy in 2.4fb-1 of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron pp¯ collider. Production of such particles (quirks) is expected in scenarios with extra QCD-like SU(N) sectors, and this study is the first dedicated search for such signatures. We find no evidence of a signal and set a lower mass limit of 107, 119, and 133 GeV for the mass of a charged quirk with strong dynamics scale Λ in the range from 10 keV to 1 MeV and N=2, 3, and 5, respectively. 16. 120 MW, 800 MHz Magnicon for a Future Muon Collider SciTech Connect Jay L. Hirshfield 2005-12-15 Development of a pulsed magnicon at 800 MHz was carried out for the muon collider application, based on experience with similar amplifiers in the frequency range between 915 MHz and 34.3 GHz. Numerical simulations using proven computer codes were employed for the conceptual design, while established design technologies were incorporated into the engineering design. A cohesive design for the 800 MHz magnicon amplifier was carried out, including design of a 200 MW diode electron gun, design of the magnet system, optimization of beam dynamics including space charge effects in the transient and steady-state regimes, design of the drive, gain, and output cavities including an rf choke in the beam exit aperture, analysis of parasitic oscillations and design means to eliminate them, and design of the beam collector capable of 20 kW average power operation. 17. Search for quirks at the Fermilab Tevatron Collider SciTech Connect Abazov, V.M.; Abbott, B.; Abolins, M.; Acharya, B.S.; Adams, M.; Adams, T.; Alexeev, G.D.; Alkhazov, G.; Alton, A.; Alverson, G.; Alves, G.A.; /Rio de Janeiro, CBPF /NIKHEF, Amsterdam 2010-08-01 We report results of a search for particles with anomalously high ionization in events with a high transverse energy jet and large missing transverse energy in 2.4 fb{sup -1} of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron p{bar p} collider. Production of such particles (quirks) is expected in scenarios with extra QCD-like SU(N) sectors, and this study is the first dedicated search for such signatures. We find no evidence of a signal and set a lower mass limit of 107 GeV for the mass of a charged quirk with strong dynamics scale {Lambda} in the range from 10 keV to 1 MeV. 18. Extrapolation technique pitfalls in asymmetry measurements at colliders Colletti, Katrina; Hong, Ziqing; Toback, David; Wilson, Jonathan S. 2016-09-01 Asymmetry measurements are common in collider experiments and can sensitively probe particle properties. Typically, data can only be measured in a finite region covered by the detector, so an extrapolation from the visible asymmetry to the inclusive asymmetry is necessary. Often a constant multiplicative factor is advantageous for the extrapolation and this factor can be readily determined using simulation methods. However, there is a potential, avoidable pitfall involved in the determination of this factor when the asymmetry in the simulated data sample is small. We find that to obtain a reliable estimate of the extrapolation factor, the number of simulated events required rises as the inverse square of the simulated asymmetry; this can mean that an unexpectedly large sample size is required when determining the extrapolation factor. 19. Collider signatures of Higgs-portal scalar dark matter Han, Huayong; Yang, Jin Min; Zhang, Yang; Zheng, Sibo 2016-05-01 In the simplest Higgs-portal scalar dark matter model, the dark matter mass has been restricted to be either near the resonant mass (mh / 2) or in a large-mass region by the direct detection at LHC Run 1 and LUX. While the large-mass region below roughly 3 TeV can be probed by the future Xenon1T experiment, most of the resonant mass region is beyond the scope of Xenon1T. In this paper, we study the direct detection of such scalar dark matter in the narrow resonant mass region at the 14 TeV LHC and the future 100 TeV hadron collider. We show the luminosities required for the 2σ exclusion and 5σ discovery. 20. Self-sustaining charging of identical colliding particles. PubMed Siu, Theo; Cotton, Jake; Mattson, Gregory; Shinbrot, Troy 2014-05-01 Recent experiments have demonstrated that identical material samples can charge one another after being brought into symmetric contact. The mechanism for this charging is not known. In this article, we use a simplified one-dimensional lattice model to analyze charging in the context of agitated particles. We find that the electric field from a single weakly polarized grain can feed back on itself by polarizing its neighbors, leading to an exponential growth in polarization. We show that, by incorporating partial neutralization between neighboring polarized particles, either uniform alignment of dipoles or complex charge and polarization waves can be produced. We reproduce a polarized state experimentally using identical colliding particles and raise several issues for future study. PMID:25353788 1. An Energy Recovery Electron Linac On Ring Collider SciTech Connect Nikolitsa Merminga; Geoffrey Krafft; Valeri Lebedev; Ilan Ben-Zvi 2001-09-01 Electron-proton/ion colliders with center of mass energies between 14 GeV and 100 GeV (protons) or 63 GeV/A (ions) and luminosities at the 10{sup 33} (per nucleon) level have been proposed recently as a means for studying hadronic structure. Electron beam polarization appears to be crucial for many of the experiments. Two accelerator design scenarios have been examined in detail: colliding rings and recirculating linac-on-ring. Although the linac-on-ring scenario is not as well developed as the ring-ring scenario, comparable luminosities appear feasible. The linac-on-ring option presents significant advantages with respect to: (1) spin manipulations; (2) reduction of the synchrotron radiation load in the detectors; (3) a wide range of continuous energy variability. Rf power and beam dump considerations require that the electron linac recover the beam energy. This technology has been demonstrated at Jefferson Lab's IR FEL with cw current up to 5 mA and beam energy up to 50 MeV. Based on extrapolations from actual measurements and calculations, energy recovery is expected to be feasible at higher currents (a few hundred mA) and higher energies (a few GeV) as well. The report begins with a brief overview of Jefferson Lab's experience with energy recovery and summarize its benefits. Luminosity projections for the linac-ring scenario based on fundamental limitations are presented next. The feasibility of an energy recovery electron linac-on-proton ring collider is investigated and four conceptual point designs are shown corresponding to electron to proton energies of: 3 GeV on 15 GeV, 5 GeV on 50 GeV and 10 GeV on 250 GeV, and for gold ions with 100 GeV/A. The last two designs assume that the protons or ions are stored in the existing RHIC accelerator. Accelerator physics issues relevant to proton rings and energy recovery linacs are discussed next and a list of required R and D for the realization of such a design is presented. 2. Test of Relativistic Gravity for Propulsion at the Large Hadron Collider Felber, Franklin 2010-01-01 A design is presented of a laboratory experiment that could test the suitability of relativistic gravity for propulsion of spacecraft to relativistic speeds. An exact time-dependent solution of Einstein's gravitational field equation confirms that even the weak field of a mass moving at relativistic speeds could serve as a driver to accelerate a much lighter payload from rest to a good fraction of the speed of light. The time-dependent field of ultrarelativistic particles in a collider ring is calculated. An experiment is proposed as the first test of the predictions of general relativity in the ultrarelativistic limit by measuring the repulsive gravitational field of bunches of protons in the Large Hadron Collider (LHC). The estimated antigravity beam' signal strength at a resonant detector of each proton bunch is 3 nm/s2 for 2 ns during each revolution of the LHC. This experiment can be performed off-line, without interfering with the normal operations of the LHC. 3. Solid State Technology Meets Collider Challenge SciTech Connect Hazi, A 2005-09-20 Probing the frontiers of particle physics and delving into the mysteries of the universe and its beginnings require machines that can accelerate beams of fundamental particles to very high energies and then collide those beams together, producing a multitude of exotic subatomic particles. The proposed Next Linear Collider (NLC), being developed by Stanford Linear Accelerator Center (SLAC), Lawrence Livermore and Lawrence Berkeley national laboratories, and Fermi National Accelerator Laboratory (Fermilab), is such a machine. The NLC is expected to produce a variety of subatomic particles by smashing together electrons and their antimatter counterparts (positrons) at nearly the speed of light with energies in the teraelectronvolt (TeV) range. Plans are that the NLC will initially operate at 0.5 TeV and ultimately be scaled up to 1.5 TeV. (See S&TR, April 2000, pp. 12-16.) Work at the facility will complement the research to be conducted at another high-energy particle accelerator, the 14-TeV Large Hadron Collider at the European Laboratory for Particle Physics (commonly known by the acronym CERN from its former name) in Geneva, which is scheduled for completion in 2007. Achieving beam energy levels in the TeV range requires modulator systems that can convert ac line power--the same type of power one gets from the wall plug--into dc pulses. Ultimately, these pulses are transformed into radiofrequency (rf) pulses that ''kick'' the particles up to the required energy levels. Livermore scientists and engineers have designed a solid-state modulator to replace oldstyle modulators based on vacuum-tube technology. These new modulators promise to be far more efficient, reliable, and serviceable than the previous components. Livermore's Laboratory Directed Research and Development Program supported the basic research and development on the solid-state modulator technology, and SLAC supported the systems integration. 4. Chromaticity correction for a muon collider optics SciTech Connect Alexahin, Y.; Gianfelice-Wendt, E.; Kapin, V.; /Fermilab 2011-03-01 Muon Collider (MC) is a promising candidate for the next energy frontier machine. However, in order to obtain peak luminosity in the 10{sup 34} cm{sup 2}s{sup -1} range the collider lattice designmust satisfy a number of stringent requirements. In particular the expected large momentum spread of the muon beam and the very small {beta}* call for a careful correction of the chromatic effects. Here we present a particular solution for the interaction region (IR) optics whose distinctive feature is a three-sextupole local chromatic correction scheme. The scheme may be applied to other future machines where chromatic effects are expected to be large. The expected large muon energy spread requires the optics to be stable over a wide range of momenta whereas the required luminosity calls for {beta}* in the mm range. To avoid luminosity degradation due to hour-glass effect, the bunch length must be comparatively small. To keep the needed RF voltage within feasible limits the momentum compaction factor must be small over the wide range of momenta. A low {beta}* means high sensitivity to alignment and field errors of the Interaction Region (IR) quadrupoles and large chromatic effects which limit the momentum range of optics stability and require strong correction sextupoles, which eventually limit the Dynamic Aperture (DA). Finally, the ring circumference should be as small as possible, luminosity being inversely proportional to the collider length. A promising solution for a 1.5 TeV center of mass energy MC with {beta}* = 1 m in both planes has been proposed. This {beta}* value has been chosen as a compromise between luminosity and feasibility based on the magnet design and energy deposition considerations. The proposed solution for the IR optics together with a new flexible momentum compaction arc cell design allows to satisfy all requirements and is relatively insensitive to the beam-beam effect. 5. Electron Cloud Effect in the Linear Colliders SciTech Connect Pivi, M 2004-09-13 Beam induced multipacting, driven by the electric field of successive positively charged bunches, may arise from a resonant motion of electrons, generated by secondary emission, bouncing back and forth between opposite walls of the vacuum chamber. The electron-cloud effect (ECE) has been observed or is expected at many storage rings [1]. In the beam pipe of the Damping Ring (DR) of a linear collider, an electron cloud is produced initially by ionization of the residual gas and photoelectrons from the synchrotron radiation. The cloud is then sustained by secondary electron emission. This electron cloud can reach equilibrium after the passage of only a few bunches. The electron-cloud effect may be responsible for collective effects as fast coupled-bunch and single-bunch instability, emittance blow-up or incoherent tune shift when the bunch current exceeds a certain threshold, accompanied by a large number of electrons in the vacuum chamber. The ECE was identified as one of the most important R&D topics in the International Linear Collider Report [2]. Systematic studies on the possible electron-cloud effect have been initiated at SLAC for the GLC/NLC and TESLA linear colliders, with particular attention to the effect in the positron main damping ring (MDR) and the positron Low Emittance Transport which includes the bunch compressor system (BCS), the main linac, and the beam delivery system (BDS). We present recent computer simulation results for the main features of the electron cloud generation in both machine designs. Thus, single and coupled-bunch instability thresholds are estimated for the GLC/NLC design. 6. Accelerator R&D toward Muon Collider and Neutrino Factory SciTech Connect 2009-10-01 Over the last decade there has been significant progress in developing the concepts and technologies needed to produce, capture, accelerate and collide high intensity beams of muons. At present, a high-luminosity multi-TeV muon collider presents a viable option for the next generation lepton-lepton collider, which is believed to be needed to fully explore high energy physics in the era following LHC discoveries. Such a collider can offer superb energy resolution, smaller size, and potentially cost and power consumption compared to multi-TeV e{sup +}e{sup -} linear colliders. This article briefly reviews the motivation, design and status of accelerator R&D for Muon Collider and Neutrino Factory. 7. Accelerator R&D toward Muon Collider and Neutrino Factory Shiltsev, V. 2010-12-01 Over the last decade there has been significant progress in developing the concepts and technologies needed to produce, capture, accelerate and collide high intensity beams of muons. At present, a high-luminosity multi-TeV muon collider presents a viable option for the next generation lepton-lepton collider, which is believed to be needed to fully explore high energy physics in the era following LHC discoveries. Such a collider can offer superb energy resolution, smaller size, and potentially cost and power consumption compared to multi-TeV e + e - linear colliders. This article briefly reviews the motivation, design and status of accelerator R&D for Muon Collider and Neutrino Factory. 8. Black Holes and the Large Hadron Collider Roy, Arunava 2011-12-01 The European Center for Nuclear Research or CERN's Large Hadron Collider (LHC) has caught our attention partly due to the film Angels and Demons.'' In the movie, an antimatter bomb attack on the Vatican is foiled by the protagonist. Perhaps just as controversial is the formation of mini black holes (BHs). Recently, the American Physical Society1 website featured an article on BH formation at the LHC.2 This article examines some aspects of mini BHs and explores the possibility of their detection at the LHC. 9. Current Correlations from a Mesoscopic Anyon Collider. PubMed Rosenow, Bernd; Levkivskyi, Ivan P; Halperin, Bertrand I 2016-04-15 Fermions and bosons are fundamental realizations of exchange statistics, which governs the probability for two particles being close to each other spatially. Anyons in the fractional quantum Hall effect are an example for exchange statistics intermediate between bosons and fermions. We analyze a mesoscopic setup in which two dilute beams of anyons collide with each other, and relate the correlations of current fluctuations to the probability of particles excluding each other spatially. While current correlations for fermions vanish, negative correlations for anyons are a clear signature of a reduced spatial exclusion as compared to fermions. PMID:27127979 10. Magnetic merging in colliding flux tubes NASA Technical Reports Server (NTRS) Zweibel, Ellen G.; Rhoads, James E. 1995-01-01 We develop an analytical theory of reconnection between colliding, twisted magnetic flux tubes. Our analysis is restricted to direct collisions between parallel tubes and is based on the collision dynamics worked out by Bogdan (1984). We show that there is a range of collision velocities for which neutral point reconnection of the Parker-Sweet type can occur, and a smaller range for which reconnection leads to coalescence. Mean velocities within the solar convection zone are probably significantly greater than the upper limit for coalescence. This suggests that the majority of flux tube collisions do not result in merging, unless the frictional coupling of the tubes to the background flow is extremely strong. 11. Next linear collider test accelerator injector upgrade SciTech Connect Yeremian, A.D.; Miller, R.H. 1995-12-31 The Next Linear Collider Test Accelerator (NLCTA) is being constructed at SLAC to demonstrate multibunch beam loading compensation, suppression of higher order deflecting modes and measure transverse components of the accelerating fields in X-band accelerating structures. Currently a simple injector which provides the average current necessary for the beam loading compensations studies is under construction. An injector upgrade is planned to produce bunch trains similar to that of the NLC with microbunch intensity, separation and energy spread, identical to that of NLC. We discuss the design of the NLCTA injector upgrade. 12. The next linear collider damping ring lattices SciTech Connect Wolski, Andrzej; Corlett, John N. 2001-06-20 We report on the lattice design of the Next Linear Collider (NLC) damping rings. The damping rings are required to provide low emittance electron and positron bunch trains to the NLC linacs, at a rate of 120 Hz. We present an optical design, based on a theoretical minimum emittance (TME) lattice, to produce the required normalized extracted beam emittances gex = 3 mm-mrad and gey = 0.02 mm mrad. An assessment of dynamic aperture and non-linear effects is given. The positron pre-damping ring, required to reduce the emittance of the positron beam such that it may be accepted by a main damping ring, is also described. 13. Simulations of high disruption colliding beams SciTech Connect Boyce, J.R.; Heifets, S.; Krafft, G.A. 1990-09-01 Recent B-factory proposals that use a linac beam colliding with the beam from a storage ring to achieve high luminosities (L > 10{sup 34} cm{sup {minus}2}sec{sup {minus}1}) result in very high disruption of the linac beam. The effects of such high disruption have been studied using the relativistic, 3-D code SWARM. We discuss the assumptions, parameters, and results of a series of runs that model such collisions. Regimes of high beam loss and methods to avoid them are also discussed. 5 refs., 4 figs. 14. Stochastic cooling requirements for a muon collider SciTech Connect Ruggiero, A.G. 1993-12-31 The most severe limitation to the muon production for a large-energy muon collider is the short time allowed for cooling the beam to dimensions small enough to provide reasonably high luminosity. The limitation is caused by the short lifetime of the particles. It appears to be desirable to accelerate the beam quickly in very short bunches. This paper describes the requirements of single-pass, fast stochastic cooling for very short bunches. Bandwidth, amplifier gain and Schottky power do not seem to be of major concern. Problems do arise with the ultimate low emittance that can be achieved, the value of which is seriously affected by the front-end noise. 15. Broader Impacts of the International Linear Collider SciTech Connect Bardeen, M.; Ruchti, R. 2005-08-01 Large-scale scientific endeavors such as the International Linear Collider Project can have a lasting impact on education and outreach to our society. The ILC will provide a discovery platform for frontier physical science and it will also provide a discovery platform for broader impacts and social science. The importance of Broader Impacts of Science in general and the ILC in particular are described. Additionally, a synopsis of education and outreach activities carried out as an integral part of the Snowmass ILC Workshop is provided. 16. Black holes at the Large Hadron Collider. PubMed Dimopoulos, S; Landsberg, G 2001-10-15 If the scale of quantum gravity is near TeV, the CERN Large Hadron Collider will be producing one black hole (BH) about every second. The decays of the BHs into the final states with prompt, hard photons, electrons, or muons provide a clean signature with low background. The correlation between the BH mass and its temperature, deduced from the energy spectrum of the decay products, can test Hawking's evaporation law and determine the number of large new dimensions and the scale of quantum gravity. PMID:11690198 17. Precision Event Simulation for Hadron Colliders Hoeche, Stefan 2016-03-01 Hadron colliders are workhorses of particle physics, enabling scientific breakthroughs such as the discovery of the Higgs boson. Hadron beams reach the highest energies, but they also produce very complex collisions. Studying the underlying dynamics requires involved multi-particle calculations. Over the past decades Monte-Carlo simulation programs were developed to tackle this task. They have by now evolved into precision tools for theorists and experimenters alike. This talk will give an introduction to event generators and discuss the current status of development. 18. Drell-Yan production at collider energies SciTech Connect Neerven, W.L. Van 1995-07-01 We present some results of the Drell-Yan cross sections d{sigma}/dm and {sigma}{sub tot} which includes the O ({alpha}{sub s}{sup 2}) contribution to the coefficient function. In particular we study the total cross section {sigma}{sub tot} for vector boson production and d{sigma}/dm for low invariant masses m of the lepton pairs at large hadron collider energies. This study includes a detailed discussion of the dependence of the cross sections on the chosen scheme ({bar M}S versus DIS) and the factorization scale. 19. Quantum production of black holes at colliders Arsene, Nicusor; Casadio, Roberto; Micu, Octavian 2016-07-01 We investigate black hole production in p p collisions at the Large Hadron Collider by employing the horizon quantum mechanics for models of gravity with extra spatial dimensions. This approach can be applied to processes around the fundamental gravitational scale and naturally yields a suppression below the fundamental gravitational scale and for increasing number of extra dimensions. The results of numerical simulations performed with the black hole event generator BLACKMAX are here reported in order to illustrate the main differences in the numbers of expected black hole events and mass distributions. 20. Rf power sources for linear colliders SciTech Connect Allen, M.A.; Callin, R.S.; Caryotakis, G.; Deruyter, H.; Eppley, K.R.; Fant, K.S.; Farkas, Z.D.; Fowkes, W.R.; Hoag, H.A.; Feinstein, J.; Ko, K.; Koontz, R.F.; Kroll, N.M.; Lavine, T.L.; Lee, T.G.; Loew, G.A.; Miller, R.H.; Nelson, E.M.; Ruth, R.D.; Vlieks, A.E.; Wang, J.W.; Wilson, P.B. ); Boyd, J.K.; Houk, T.; Ryne, R.D.; Westenskow, G.A.; Yu, S.S. (Lawrence Live 1990-06-01 The next generation of linear colliders requires peak power sources of over 200 MW per meter at frequencies above 10 GHz at pulse widths of less than 100 nsec. Several power sources are under active development, including a conventional klystron with rf pulse compression, a relativistic klystron (RK) and a crossed-field amplifier. Power from one of these has energized a 0.5 meter two- section High Gradient Accelerator (HGA) and accelerated a beam at over 80 MeV meter. Results of tests with these experimental devices are presented here. 1. A COMPLETE SCHEME FOR A MUON COLLIDER. SciTech Connect PALMER,R.B.; BERG, J.S.; FERNOW, R.C.; GALLARDO, J.C.; KIRK, H.G.; ALEXAHIN, Y.; NEUFFER, D.; KAHN, S.A.; SUMMERS, D. 2007-09-01 A complete scheme for production, cooling, acceleration, and ring for a 1.5 TeV center of mass muon collider is presented, together with parameters for two higher energy machines. The schemes starts with the front end of a proposed neutrino factory that yields bunch trains of both muon signs. Six dimensional cooling in long-period helical lattices reduces the longitudinal emittance until it becomes possible to merge the trains into single bunches, one of each sign. Further cooling in all dimensions is applied to the single bunches in further helical lattices. Final transverse cooling to the required parameters is achieved in 50 T solenoids. 2. Two gauge boson physics at future colliders SciTech Connect Cahn, R.N. 1988-05-13 Electroweak unification suggests that there should be WW and ZZ physics analogous to {gamma}{gamma} physics. Indeed, WW and ZZ collisions will provide an opportunity to search for the Higgs boson at future high energy colliders. Cross sections in the picobarn range are predicted for Higgs boson production at the proposed 40-TeV SSC. While other states may be produced by WW and ZZ collisions, it is the Higgs boson that looms as the most attractive objective. 31 refs., 5 figs. 3. String resonances at the Large Hadron Collider SciTech Connect Roy, Arunava; Cavaglia, Marco 2009-07-01 The Large Hadron Collider promises to discover new physics beyond the standard model. An exciting possibility is the formation of string resonances at the TeV scale. In this article, we show how string resonances may be detected at the LHC in the pp{yields}{gamma}+jet channel. Our study is based on event-shape variables, missing energy and momentum, maximum transverse momentum of photons and dijet invariant mass. These observables provide interesting signatures which enable us to discriminate string events from the standard model background. 4. High energy accelerator and colliding beam user group. Progress report, March 1, 1983-February 29, 1984 SciTech Connect Not Available 1983-01-01 Topics covered in this research summary include: status of the OPAL collaboration at LEP, CERN; two-photon physics at PLUTO; search for new particles at JADE; neutrinoless double beta decay at DESY; Fermilab jet experiment; neutrino deuterium experiment in the 15 foot bubble chamber at Fermilab; deep inelastic muon experiment at Fermilab; new experiments at the proton-antiproton collider; neutrino-electron scattering at Los Alamos; parity violation in proton-proton scattering; an upgrade of laboratory and computer facilities; and a study of bismuth germanate as a durable scintillation crystal. (GHT) 5. From the SLAC linear collider to the next linear collider: A status report and road map SciTech Connect Richter, B. 1992-02-01 In this presentation, I will review what we have learned about linear colliders, the problems that have been uncovered, and the technology-development program aimed at realizing the next high energy machine. I will then close with a few comments on how to get on with the job of building it. 6. Higgs boson production with heavy quarks at hadron colliders Jackson, Christopher B. 2005-11-01 One of the remaining puzzles in particle physics is the origin of electroweak symmetry breaking. In the Standard Model (SM), a single doublet of complex scalar fields is responsible for breaking the SU(2) L x U(1)Y gauge symmetry thus giving mass to the electroweak gauge bosons via the Higgs mechanism and to the fermions via Yukawa couplings. The remnant of the process is a vet to he discovered scalar particle, the Higgs boson (h). However, current and future experiments at hadron colliders hold great promise. Of particular interest at hadron colliders is the production of a Higgs boson in association with a pair of heavy quarks, pp¯(pp) → QQ¯h, where Q can be either a top or a bottom quark. Indeed, the production of a Higgs boson with a pair of top quarks provides a very distinctive signal in hadronic collisions where background processes are formidable, and it will be instrumental in the discovery of a Higgs boson below about 130 GeV at the LHC. On the other hand, the production of a Higgs boson with bottom quarks can be strongly enhanced in models of new physics beyond the SM, e.g. supersymmetric models. If this is the case, bb¯h production will play a crucial role at the Tevatron where it could provide the first signal of new physics. Given the prominent role that Higgs production with heavy quarks can play at hadron colliders, it becomes imperative to have precise theoretical predictions for total and differential cross sections. In this dissertation, we outline and present detailed results for the next-to-leading order (NLO) calculation of the Quantum Chromodynamic (QCD) corrections to QQ¯h production at both the Tevatron and the LHC. This calculation involves several difficult issues due to the three massive particles in the final state, a situation which is at the frontier of radiative correction calculations in quantum field theory. We detail the novel techniques developed to deal with these challenges. The calculation of pp¯(pp) → bb¯h at NLO in 7. Numerical calculation of ion polarization in the NICA collider Kovalenko, A. D.; Butenko, A. V.; Kekelidze, V. D.; Mikhaylov, V. A.; Kondratenko, M. A.; Kondratenko, A. M.; Filatov, Yu N. 2016-02-01 The NICA Collider with two solenoid Siberian snakes is “transparent” to the spin. The collider transparent to the spin provides a unique capability to control any polarization direction of protons and deuterons using additional weak solenoids without affecting orbital parameters of the beam. The spin tune induced by the control solenoids must significantly exceed the strength of the zero-integer spin resonance, which contains a coherent part associated with errors in the collider's magnetic structure and an incoherent part associated with the beam emittances. We present calculations of the coherent part of the resonance strength in the NICA collider for proton and deuteron beams. 8. Far Future Colliders and Required R&D Program SciTech Connect Shiltsev, V.; /Fermilab 2012-06-01 Particle colliders for high energy physics have been in the forefront of scientific discoveries for more than half a century. The accelerator technology of the collider has progressed immensely, while the beam energy, luminosity, facility size and the cost have grown by several orders of magnitude. The method of colliding beams has not fully exhausted its potential but its pace of progress has greatly slowed down. In this paper we very briefly review the R&D toward near future colliders and make an attempt to look beyond the current horizon and outline the changes in the paradigm required for the next breakthroughs. 9. Tau anomalous magnetic moment in γγ colliders Peressutti, Javier; Sampayo, Oscar A. 2012-08-01 We investigate the possibility of setting model independent limits for a nonstandard anomalous magnetic moment aτNP of the tau lepton, in future γγ colliders based on Compton backscattering. For a hypothetical collider we find that, at various levels of confidence, the limits for aτNP could be improved, compared to previous studies based on LEP1, LEP2 and SLD data. We show the results for a realistic range of the center of mass energy of the e+e- collider. As a more direct application, we also present the results of the simulation for the photon collider at the TESLA project. 10. Fast cooling, muon acceleration and the prospect of muon colliders Palmer, Mark Facilities based on stored muons offer unique potential for future high-energy physics capabilities. Three key characteristics of the muon make this possible: * The muon is a lepton; * The muon is roughly 200 times as massive as the electron; * The muon decays to an electron and two neutrinos. As the next heavier members of the lepton family with respect to the electron and positron, μ+ and μ-. beams can be collided to provide a precision lepton probe of the electroweak couplings. This makes a muon collider a suitable option for a lepton collider companion to a hadron collider discovery machine... 11. The Very Large Hadron Collider: The farthest energy frontier SciTech Connect Barletta, William A. 2001-06-21 The Very Large Hadron Collider (or Eloisatron) represents what may well be the final step on the energy frontier of accelerator-based high energy physics. While an extremely high luminosity proton collider at 100-200 TeV center of mass energy can probably be built in one step with LHC technology, that machine would cost more than what is presently politically acceptable. This talk summarizes the strategies of collider design including staged deployment, comparison with electron-positron colliders, opportunities for major innovation, and the technical challenges of reducing costs to manageable proportions. It also presents the priorities for relevant R and D for the next few years. 12. Klystron switching power supplies for the Internation Linear Collider SciTech Connect Fraioli, Andrea; /Cassino U. /INFN, Pisa 2009-12-01 The International Linear Collider is a majestic High Energy Physics particle accelerator that will give physicists a new cosmic doorway to explore energy regimes beyond the reach of today's accelerators. ILC will complement the Large Hadron Collider (LHC), a proton-proton collider at the European Center for Nuclear Research (CERN) in Geneva, Switzerland, by producing electron-positron collisions at center of mass energy of about 500 GeV. In particular, the subject of this dissertation is the R&D for a solid state Marx Modulator and relative switching power supply for the International Linear Collider Main LINAC Radio Frequency stations. 13. ICOOL: A TOOL FOR MUON COLLIDER SIMULATIONS. SciTech Connect FERNOW,R.C. 2001-09-28 Current ideas for designing neutrino factories [ 1,2] and muon colliders [3] require unique configurations of fields and materials to prepare the muon beam for acceleration. This so-called front end system must accomplish the goals of phase rotation, bunching and cooling. We have continued the development of a 3-D tracking code, ICOOL [4], for examining possible muon collider front end configurations. A system is described in terms of a series of longitudinal regions with associated material and field properties. The tracking takes place in a coordinate system that follows a reference orbit through the system. The code takes into account decays and interactions of {approx}50-500 MeV/c muons in matter. Material geometry regions include cylinders and wedges. A number of analytic models are provided for describing the field configurations. Simple diagnostics are built into the code, including calculation of emittances and correlations, longitudinal traces, histograms and scatter plots. A number of auxiliary codes can be used for pre-processing, post-processing and optimization. 14. The Large Hadron Collider, a personal recollection Evans, Lyndon 2014-03-01 The construction of the Large Hadron Collider (LHC) has been a massive endeavor spanning almost 30 years from conception to commissioning. Building the machine with the highest possible energy (7 TeV) in the existing LEP tunnel of 27 km circumference and with a tunnel diameter of only 3.8 m has required considerable innovation. The first was the development of an idea first proposed by Bob Palmer at Brookhaven National Laboratory in 1978, where the two rings are integrated into a single magnetic structure. This compact 2-in-1 structure was essential for the LHC due to both the limited space available in the existing Large Electron-Positron collider tunnel and the cost. The second innovation was the bold move to use superfluid helium cooling on a massive scale, which was imposed by the need to achieve a high (8.3 T) magnetic field using an affordable Nb-Ti superconductor. In this article, no attempt is made to give a comprehensive review of the machine design. This can be found in the LHC Design Report [1], which gives a detailed description of the machine as it was built and comprehensive references. A more popular description of the LHC and its detectors can be found in [2]. Instead, this is a more personal account of the project from approval to commissioning, describing some of the main technologies and some of the trials and tribulations encountered in bringing this truly remarkable machine alive. 15. The muon collider (Sandros snake) SciTech Connect Ruggiero, A.G. 1992-12-31 This paper describes a feasibility study for the design of a muon collider. Recognized the fact that the particle lifetime increases linearly with the energy, we have adopted a scheme where steps of cooling and acceleration are entwined. We have indeed found convenient to accelerate the beam as fast as possible to increase its chances of survival, and necessary to dilute the action of cooling throughout the entire accelerating process to make it more effective and affordable. All acceleration and cooling steps are executed in a single pass essentially along a curvilinear and open path. We do not believe it is possible to handle the beam otherwise in circular and closed rings, as it has been proposed in the past. The example shown in this paper describes a muon collider at the energy of 250 GeV per beam and a luminosity of 4 {times} 10{sup 28} cm{sup {minus}2}s{sup {minus}1}. We have adopted an extrapolation of the stochastic cooling method for the reduction of the beam emittance. 16. Protection of the CERN Large Hadron Collider Schmidt, R.; Assmann, R.; Carlier, E.; Dehning, B.; Denz, R.; Goddard, B.; Holzer, E. B.; Kain, V.; Puccio, B.; Todd, B.; Uythoven, J.; Wenninger, J.; Zerlauth, M. 2006-11-01 The Large Hadron Collider (LHC) at CERN will collide two counter-rotating proton beams, each with an energy of 7 TeV. The energy stored in the superconducting magnet system will exceed 10 GJ, and each beam has a stored energy of 362 MJ which could cause major damage to accelerator equipment in the case of uncontrolled beam loss. Safe operation of the LHC will therefore rely on a complex system for equipment protection. The systems for protection of the superconducting magnets in case of quench must be fully operational before powering the magnets. For safe injection of the 450 GeV beam into the LHC, beam absorbers must be in their correct positions and specific procedures must be applied. Requirements for safe operation throughout the cycle necessitate early detection of failures within the equipment, and active monitoring of the beam with fast and reliable beam instrumentation, mainly beam loss monitors (BLM). When operating with circulating beams, the time constant for beam loss after a failure extends from apms to a few minutes—failures must be detected sufficiently early and transmitted to the beam interlock system that triggers a beam dump. It is essential that the beams are properly extracted on to the dump blocks at the end of a fill and in case of emergency, since the beam dump blocks are the only elements of the LHC that can withstand the impact of the full beam. 17. Mass reach scaling for future hadron colliders Rizzo, Thomas G. 2015-04-01 The primary goal of any future hadron collider is to discover new physics (NP) associated with a high mass scale, , beyond the range of the LHC. In order to maintain the same relative mass reach for rate-limited NP, , as increases, Richter recently reminded us that the required integrated luminosity obtainable at future hadron colliders (FHC) must grow rapidly, , in the limit of naive scaling. This would imply, e.g., a 50-fold increase in the required integrated luminosity when going from the 14 TeV LHC to a FHC with TeV, an increase that would prove quite challenging on many different fronts. In this paper we point out, due to the scaling violations associated with the evolution of the parton density functions (PDFs) and the running of the strong coupling, , that the actual luminosity necessary in order to maintain any fixed value of the relative mass reach is somewhat greater than this scaling result indicates. However, the actual values of the required luminosity scaling are found to be dependent upon the detailed nature of the NP being considered. Here we elucidate this point explicitly by employing several specific benchmark examples of possible NP scenarios and briefly discuss the (relatively weak) search impact in each case if these luminosity goals are not met. 18. Letter of Intent for a Tevatron Collider Beauty Factory SciTech Connect Volk, J.T.; Yager, P.M.; Edelstein, R.; Christian, D.; Lundberg, B.; Reay, N.W.; Reibel, K.; Sidwell, R.A.; Stanton, N.; Kalbfleisch, G.R.; Skubic, P.; /Oklahoma U. 1987-01-01 A hadron collider beauty production experiment which will increase our knowledge of mixing, rare decay modes and even of CP violation could be performed using a new type of detector at the upgraded Fermilab Tevatron. In order to progress from the hundreds of thousands of B{bar B} events which can be tagged per year at a luminosity of several times 10{sup 29}/cm{sup 2}-sec to an ultimate yield of tens of millions at a luminosity of several times 10{sup 31}/cm{sup 2}-sec, they also must embark on a learning curve which will take many years and will require development both of hardware and software before achieving a final system. A new high-luminosity intersection region would have to be included as part of the presently-planned Tevatron Collider upgrade. Designing and constructing an initial system will take four years. Thus, in the light of the positive decision on the SSC, a start must be made soon if Fermilab is ever to play a strong role in this exciting area of physics. Designing even the initial system will require several man-years of effort by a dedicated group of people, together with concurrent work in prototyping and testing. They therefore ask that the Physics Advisory Committee give us their opinion of the priority such a project should be given at Fermilab, within the context that eventually it will require a devoted interaction region which accesses the full achieved luminosity of the machine. Initially, they discuss physics accessible as the B{bar B} yield increases. Subsequently, they outline a detector which can be staged, increasing its power (and cost) as we progress along our learning curve. Finally, costs and time schedules are estimated for the initial version of this detector and possible locations are discussed. 19. Strong Electroweak Symmetry Breaking in the Large Hadron Collider Era Evans, Jared Andrew 2011-12-01 With the Large Hadron Collider collecting data, both the pursuit of novel detection techniques and the exploration of new ideas are more important than ever. Novel detection techniques are essential in order for the community to garner the most worth from the machine. New ideas are needed both to expand the boundaries of what could be observed and to foster the creative mindset of the community that moves particle physics into fascinating, and often unexpected, directions. Discovering whether electroweak symmetry is broken strongly or weakly is one of the most pressing questions to be answered. Exploring the possibility of strong electroweak symmetry breaking is the topic of this work. The first of two major sectors in this work concerns the theory of conformal technicolor. We present the low energy minimal model for conformal technicolor and verify that it can satisfy current constraints from experiment. We will also provide a UV completion for this model, which realistically extends the sector with high-energy supersymmetry. Two complete models of flavor are presented. This is the first example of a complete, consistent model of strong electroweak symmetry breaking. The second of the two sectors discusses experimental signatures arising in a large class of general technicolor models at the Large Hadron Collider. The possible existence of narrow scalar states that can be produced via gluon-gluon fusion is first discussed. These states can decay into exotic final states of multiple electroweak gauge bosons, third generation particles and even light composite Higgs particles. A two Higgs doublet model is proposed as an effective way to model these exciting states. Lastly, we discuss the array of possible final states and their possible discovery. 20. B factory at RHIC (Relativistic Heavy Ion Collider) SciTech Connect Lockyer, N.S.; Van Berg, R.; Newcomer, F.M.; Foley, K.; Morse, W.; Paige, F.; Polychronakos, V.; Protopopescu, S.; Rehak, P.; Sidwell, R. 1988-01-01 A dedicated B physics experiment located in the proposed Relativistic Heavy Ion Collider at Brookhaven (RHIC) is considered. The machine may operate in a p-p mode with a luminosity in excess of 10/sup 32/ cm/sup /minus/2/ sec/sup /minus/1/ at 250 /times/ 250 GeV. The estimated B/bar B/ cross section at these energies is about 10 ..mu..barns and a run of 10/sup 7/ sec would produce roughly 10/sup 10/ B/bar B/ pairs. A comparison to similar ideas proposed for the Fermilab Tevatron Upgrade and the SSC are discussed. The most ambitious physics objective of such an experiment would be the study of CP nonconservation. Particular emphasis at this workshop was given to the self tagging mode B ..-->.. K/sup +/..pi../sup /minus//. Experimental techniques developed during this experiment would be extremely useful for more ambitious projects anticipated at the SSC. 36 refs., 10 figs. 1. Turbulent amplification of magnetic fields in colliding laboratory jets Tzeferacos, P.; Meinecke, J.; Bell, A. R.; Doyle, H.; Bingham, R.; Churazov, E. M.; Crowston, R.; Murphy, C. D.; Woolsey, N. C.; Drake, R. P.; Kuranz, C. C.; MacDonald, M. J.; Wan, W. C.; Koenig, M.; Pelka, A.; Ravasio, A.; Yurchak, R.; Kuramitsu, Y.; Sakawa, Y.; Park, H.-S.; Reville, B.; Miniati, F.; Schekochihin, A. A.; Lamb, D. Q.; Gregori, G. 2015-11-01 Turbulence and magnetic fields are ubiquitous in the universe. In galaxy clusters, turbulence is believed to amplify seed magnetic fields to values of a few μG, as observed through diffuse radio-synchrotron emission and Faraday rotation measurements. In this study we present experiments that emulate such a process in a controlled laboratory environment. Two laser-driven plasma flows collide to mimic the dynamics of a cluster merger. From the measured density fluctuations we infer the development of Kolmogorov-like turbulence. Measurements of the magnetic field show it is amplified by turbulent motions, reaching a non-linear regime that is a precursor to turbulent dynamo. We also present numerical simulations with the FLASH code that model these experiments. The simulations reproduce the measured plasma properties and enable us to disentangle and characterize the complex physical processes that occur in the experiment. This study provides a promising experimental platform to probe magnetic field amplification by turbulence in plasmas, a process thought to occur in many astrophysical phenomena. 2. Neutralino dark matter in minimal supergravity: Direct detection versus collider searches SciTech Connect Baer, H.; Brhlik, M. 1998-01-01 We calculate expected event rates for direct detection of relic neutralinos as a function of parameter space of the minimal supergravity model. Numerical results are presented for the specific case of a {sup 73}Ge detector. We find significant detection rates (R{gt}0.01events/kg/day) in regions of parameter space most favored by constraints from B{r_arrow}X{sub s}{gamma} and the cosmological relic density of neutralinos. The detection rates are especially large in regions of large tan{beta}, where many conventional signals for supersymmetry at collider experiments are difficult to detect. If the parameter tan{beta} is large, then there is a significant probability that the first direct evidence for supersymmetry could come from direct detection experiments, rather than from collider searches for sparticles. {copyright} {ital 1997} {ital The American Physical Society} 3. Search of strangelets and “forward” physics on the collider Kurepin, A. B. 2016-01-01 A new stage of the collider experiments at the maximum energy of protons and nuclei at the LHC may lead to the discovery of new phenomena, as well as to confirm the effects previously observed only at very high energies in cosmic rays. A specific program of the experiments is so-called “forward” physics, i.e. the study of low-angle processes. Of the most interesting phenomena can be noted the detection in cosmic rays events called Centauro, which could be explained as the strangelets production. Centauro represent events with small multiplicity and with a strong suppression of electromagnetic component. Since the energy of the beams at the collider and kinematic parameters of the forward detectors CASTOR (CMS), TOTEM, LHCf and the ADA and ADC (ALICE) are close to the parameters and energies of abnormal events in cosmic rays, it is possible to reproduce and investigate in details these events in the laboratory. 4. Muon colliders: New prospects for precision physics and the high energy frontier SciTech Connect King, B.J. 1998-06-01 An overview is given of muon collider technology and of the current status of the muon collider research program. The exciting potential of muon colliders for both neutrino physics and collider physics studies is then described and illustrated using self-consistent collider parameter sets at 0.1 TeV to 100 TeV center-of-mass energies. 5. Model SSC (Superconducting Super Collider) dipole magnet cryostat assembly at Fermilab SciTech Connect Niemann, R.C. 1989-03-01 The Superconducting Super Collider (SSC) magnet development program includes the design, fabrication and testing of full length model dipole magnets. A result of the program has been the development of a magnet cryostat design. The cryostat subsystems consist of cold mass connection-slide, suspension, thermal shields, insulation, vacuum vessel and interconnections. Design details are presented along with model magnet production experience. 6 refs., 13 figs. 6. Probing neutral gauge boson self-interactions in ZZ production at hadron colliders Baur, U.; Rainwater, D. 2000-12-01 A detailed analysis of ZZ production at the upgraded Fermilab Tevatron and the CERN Large Hadron Collider is presented for general ZZZ and ZZγ couplings. Deviations from the standard model gauge theory structure for each of these can be parametrized in terms of two form factors which are severely restricted by unitarity at high energy. Achievable limits on these couplings are shown to be a dramatic improvement over the limits currently obtained by e+e- experiments. 7. SDA-based diagnostic and analysis tools for Collider Run II SciTech Connect Bolshakov, T.B.; Lebrun, P.; Panacek, S.; Papadimitriou, V.; Slaughter, J.; Xiao, A.; /Fermilab 2005-05-01 Operating and improving the understanding of the Fermilab Accelerator Complex for the colliding beam experiments requires advanced software methods and tools. The Shot Data Analysis (SDA) has been developed to fulfill this need. Data from the Fermilab Accelerator Complex is stored in a relational database, and is served to programs and users via Web-based tools. Summary tables are systematically generated during and after a store. These tables (the Supertable, the Recomputed Emittances, the Recomputed Intensities and other tables) are discussed here. 8. e-A PHYSICS AT A COLLIDER. SciTech Connect G. T. GARVEY 2001-01-09 An electron-nucleus (e-A) collider with center-of-mass energy in excess of 50 GeV per electron-nucleon collision will allow the physics community to obtain unprecedented new knowledge of the partonic structure of nuclei. If reliable information is to be extracted on these partonic densities, it is essential to realize that with our current level of understanding of QCD, momentum transfers to the struck partons greater than 1 GeV/c are necessary. This requirement puts a priority on high center-of-mass energy if partonic densities are to be measured over a wide range. Comparing the partonic structure of the free nucleon to that of bound nucleons and measuring the systematic changes in that structure as a function of nucleon number (A) will provide deeper insight into the origins and dynamics of nuclear binding. In addition, e-A collisions will allow the exploration of partonic densities appreciably higher than is accessible in e-p collisions. An e-A collider will allow one to measure the gluonic structure functions of nuclei down to x {approx} 10{sup -3}, information valuable in its own right and essential to a quantitative understanding of highly relativistic A-A collisions. The time-space evolution of partons can only be investigated by studying the modifications of hard collisions that take place when nuclear targets are employed. In a hard collision the partonic fragments interact, hadronize, and reinteract on their way to the distant detectors without revealing their evolution into the hadrons finally detected. Nuclear targets of differing A place varying amounts of nuclear matter in proximity to the hard collision producing unique information about the quantum fluctuations of incident projectile prior to the collision and on the early evolution of the produced partons. Using charged leptons (e, {mu}) to investigate this physics has been the richest source of information to date and extending the reach of these investigations by the constructing an e -A collider 9. Multianode Photomultiplier Tube Alignment for the MINERvA Experiment at Fermilab Bruno, Jorge 2006-10-01 The MINERvA experiment (Main INjector ExpeRiment vA) at FNAL will study the neutrino-nucleon and neutrino-nucleus interaction. The light collection from the detector will be done via optic fibers using Hamamatsu H8804 64-channel photomultiplier tubes (PMT). Each PMT channel needs to be precisely aligned with the corresponding optic fiber. The MINERvA PMT optical boxes contain precision machined optic cookies'' which capture the 8x8 array of optic fibers. Each PMT-cookie pair needs to be aligned as precisely as possible. This contribution will describe the alignment setup and procedure implemented at James Madison University. 10. Colliding superposed waves in the Einstein-Maxwell theory SciTech Connect Halilsoy, M. 1989-04-15 We reformulate the initial data on the characteristic surface for colliding waves in the Einstein-Maxwell theory. This approach takes into account the superposition principle for gravitational and electromagnetic waves. Finding exact solutions for colliding superposed waves happens to be a rather challenging problem. 11. Design considerations for a laser-plasma linear collider SciTech Connect Schroeder, C. B.; Esarey, E.; Geddes, C. G. R.; Toth, Cs.; Leemans, W. P. 2009-01-22 Design considerations for a next-generation electron-positron linear collider based on laser-plasma-accelerators are discussed. Several of the advantages and challenges of laser-plasma-based accelerator technology are addressed. An example of the parameters for a 1 TeV laser-plasma-based collider is presented. 12. Event simulation for colliders — A basic overview Reuschle, Christian 2015-05-01 In this article we will discuss the basic calculational concepts to simulate particle physics events at high energy colliders. We will mainly focus on the physics in hadron colliders and particularly on the simulation of the perturbative parts, where we will in turn focus on the next-to-leading order QCD corrections. 13. The Threshold of Embedded M Collider Bias and Confounding Bias ERIC Educational Resources Information Center Kelcey, Benjamin; Carlisle, Joanne 2011-01-01 Of particular import to this study, is collider bias originating from stratification on retreatment variables forming an embedded M or bowtie structural design. That is, rather than assume an M structural design which suggests that "X" is a collider but not a confounder, the authors adopt what they consider to be a more reasonable position and… 14. Implementation of Stochastic Cooling Hardware at Fermilab's Tevatron Collider SciTech Connect Pasquinelli, Ralph J.; /Fermilab 2011-08-01 The invention of Stochastic cooling by Simon van der Meer made possible the increase in phase space density of charged particle beams. In particular, this feedback technique allowed the development of proton antiproton colliders at both CERN and Fermilab. This paper describes the development of hardware systems necessary to cool antiprotons at the Fermilab Tevatron Collider complex. 15. Implementation of stochastic cooling hardware at Fermilab's Tevatron collider Pasquinelli, Ralph J. 2011-08-01 The invention of Stochastic cooling by Simon van der Meer made possible the increase in phase space density of charged particle beams. In particular, this feedback technique allowed the development of proton antiproton colliders at both CERN and Fermilab. This paper describes the development of hardware systems necessary to cool antiprotons at the Fermilab Tevatron Collider complex. 16. Design considerations for a laser-plasma linear collider SciTech Connect Schroeder, C. B.; Esarey, E.; Geddes, C. G. R.; Toth, Cs.; Leemans, W. P. 2008-08-01 Design considerations for a next-generation electron-positron linear collider based on laser-plasma-accelerators are discussed. Several of the advantages and challenges of laser-plasma based accelerator technology are addressed. An example of the parameters for a 1 TeV laser-plasma based collider is presented. 17. RF power generation for future linear colliders SciTech Connect Fowkes, W.R.; Allen, M.A.; Callin, R.S.; Caryotakis, G.; Eppley, K.R.; Fant, K.S.; Farkas, Z.D.; Feinstein, J.; Ko, K.; Koontz, R.F.; Kroll, N.; Lavine, T.L.; Lee, T.G.; Miller, R.H.; Pearson, C.; Spalek, G.; Vlieks, A.E.; Wilson, P.B. 1990-06-01 The next linear collider will require 200 MW of rf power per meter of linac structure at relatively high frequency to produce an accelerating gradient of about 100 MV/m. The higher frequencies result in a higher breakdown threshold in the accelerating structure hence permit higher accelerating gradients per meter of linac. The lower frequencies have the advantage that high peak power rf sources can be realized. 11.42 GHz appears to be a good compromise and the effort at the Stanford Linear Accelerator Center (SLAC) is being concentrated on rf sources operating at this frequency. The filling time of the accelerating structure for each rf feed is expected to be about 80 ns. Under serious consideration at SLAC is a conventional klystron followed by a multistage rf pulse compression system, and the Crossed-Field Amplifier. These are discussed in this paper. 18. Beam dynamics issues in linear colliders SciTech Connect Seeman, J.T. 1989-06-01 The primary goal of present and future linear colliders is to maximize the integrated luminosity for the experimental program. Beam dynamics plays a central role in the maximization of integrated luminosity. It is the major issue in the production of small beam sizes and low experimental backgrounds and is also an important factor in the production of particle numbers, in the acceleration process, and in the number of bunches. The beam dynamics effects on bunches which are extracted from the damping rings, accelerated in the linac, collimated, momentum analyzed, and finally delivered to the final focus are reviewed. The effects of bunch compression, transverse and longitudinal wakefields, BNS damping, energy definition, dispersion, emittance, bunch aspect ratio, feedback, and stability are all important. 11 refs., 1 tab. 19. Small air showers and collider physics NASA Technical Reports Server (NTRS) Capdevielle, J. N.; Gawin, J.; Grochalska, B. 1985-01-01 At energies lower than 2.5 X 10 to the 5 GeV (in Lab. system), more accurate information on nucleon-nucleon collision (p-p collider and on primary composition now exist. The behavior of those both basic elements in cosmic ray phenomenology from ISR energy suggests some tendencies for reasonable extrapolation in the next decade 2.0x10 to the 5 to 2.0x10 to the 6 GeV. Small showers in altitude, recorded in the decade 2 X 10 to the 4 to 2 X 10 to the 5 GeV offers a good tool to testify the validity of all the Monte-Carlo simulation analysis and appreciate how nucleon-air collision are different from nucleon-nucleon collisions. 20. Galaxies Collide to Create Hot, Huge Galaxy NASA Technical Reports Server (NTRS) 2009-01-01 This image of a pair of colliding galaxies called NGC 6240 shows them in a rare, short-lived phase of their evolution just before they merge into a single, larger galaxy. The prolonged, violent collision has drastically altered the appearance of both galaxies and created huge amounts of heat turning NGC 6240 into an 'infrared luminous' active galaxy. A rich variety of active galaxies, with different shapes, luminosities and radiation profiles exist. These galaxies may be related astronomers have suspected that they may represent an evolutionary sequence. By catching different galaxies in different stages of merging, a story emerges as one type of active galaxy changes into another. NGC 6240 provides an important 'missing link' in this process. This image was created from combined data from the infrared array camera of NASA's Spitzer Space Telescope at 3.6 and 8.0 microns (red) and visible light from NASA's Hubble Space Telescope (green and blue). 1. QCD and jets at hadron colliders Sapeta, Sebastian 2016-07-01 We review various aspects of jet physics in the context of hadron colliders. We start by discussing the definitions and properties of jets and recent development in this area. We then consider the question of factorization for processes with jets, in particular for cases in which jets are produced in special configurations, like for example in the region of forward rapidities. We review numerous perturbative methods for calculating predictions for jet processes, including the fixed-order calculations as well as various matching and merging techniques. We also discuss the questions related to non-perturbative effects and the role they play in precision jet studies. We describe the status of calculations for processes with jet vetoes and we also elaborate on production of jets in forward direction. Throughout the article, we present selected comparisons between state-of-the-art theoretical predictions and the data from the LHC. 2. Illuminating new electroweak states at hadron colliders Ismail, Ahmed; Izaguirre, Eder; Shuve, Brian 2016-07-01 In this paper, we propose a novel powerful strategy to perform searches for new electroweak states. Uncolored electroweak states appear in generic extensions of the Standard Model (SM) and yet are challenging to discover at hadron colliders. This problem is particularly acute when the lightest state in the electroweak multiplet is neutral and all multiplet components are approximately degenerate. In this scenario, production of the charged fields of the multiplet is followed by decay into nearly invisible states; if this decay occurs promptly, the only way to infer the presence of the reaction is through its missing energy signature. Our proposal relies on emission of photon radiation from the new charged states as a means of discriminating the signal from SM backgrounds. We demonstrate its broad applicability by studying two examples: a pure Higgsino doublet and an electroweak quintuplet field. 3. Big Science and the Large Hadron Collider Giudice, Gian Francesco 2012-03-01 The Large Hadron Collider (LHC), the particle accelerator operating at CERN, is probably the most complex and ambitious scientific project ever accomplished by humanity. The sheer size of the enterprise, in terms of financial and human resources, naturally raises the question whether society should support such costly basic-research programs. I address this question by first reviewing the process that led to the emergence of Big Science and the role of large projects in the development of science and technology. I then compare the methodologies of Small and Big Science, emphasizing their mutual linkage. Finally, after examining the cost of Big Science projects, I highlight several general aspects of their beneficial implications for society. 4. A proof of the conformal collider bounds Hofman, Diego M.; Li, Daliang; Meltzer, David; Poland, David; Rejon-Barrera, Fernando 2016-06-01 In this paper, we prove that the "conformal collider bounds" originally proposed in [1] hold for any unitary parity-preserving conformal field theory (CFT) with a unique stress tensor in dimensions d ≥ 3. In particular this implies that the ratio of central charges for a unitary 4d CFT lies in the interval 31/18ge a/cge 1/3 . For superconformal theories this is further reduced to 3/2ge a/cge 1/2 . The proof relies only on CFT first principles — in particular, bootstrap methods — and thus constitutes the first complete field theory proof of these bounds. We further elaborate on similar bounds for non-conserved currents and relate them to results obtained recently from deep inelastic scattering. 5. Ground motion data for International Collider models SciTech Connect Volk, J.T.; LeBrun, P.; Shiltsev, V.; Singatulin, S.; /Fermilab 2007-11-01 The proposed location for the International Linear Collider (ILC) in the Americas region is Fermilab in Batavia Illinois. If built at this location the tunnels would be located in the Galena Platteville shale at a depth of 100 or more meters below the surface. Studies using hydro static water levels and seismometers have been conducted in the MINOS hall and the LaFrange Mine in North Aurora Illinois to determine the level of ground motion. Both these locations are in the Galena Platteville shale and indicate the typical ground motion to be expected for the ILC. The data contains both natural and cultural noise. Coefficients for the ALT law are determined. Seismic measurements at the surface and 100 meters below the surface are presented. 6. Beam Dynamics Considerations in Electron Ion Colliders Krafft, Geoffrey 2015-04-01 The nuclear physics community is converging on the idea that the next large project after FRIB should be an electron-ion collider. Both Brookhaven National Lab and Thomas Jefferson National Accelerator Facility have developed accelerator designs, both of which need novel solutions to accelerator physics problems. In this talk we discuss some of the problems that must be solved and their solutions. Examples in novel beam optics systems, beam cooling, and beam polarization control will be presented. Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. The U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce this manuscript for U.S. Government purposes. 7. Colliding Beam Fusion Reactor Space Propulsion System Cheung, A.; Binderbauer, M.; Liu, F.; Qerushi, A.; Rostoker, N.; Wessel, F. J. 2004-02-01 The Colliding Beam Fusion Reactor Space Propulsion System, CBFR-SPS, is an aneutronic, magnetic-field-reversed configuration, fueled by an energetic-ion mixture of hydrogen and boron11 (H-B11). Particle confinement and transport in the CBFR-SPS are classical, hence the system is scaleable. Fusion products are helium ions, α-particles, expelled axially out of the system. α-particles flowing in one direction are decelerated and their energy recovered to power'' the system; particles expelled in the opposite direction provide thrust. Since the fusion products are charged particles, the system does not require the use of a massive-radiation shield. This paper describes a 100 MW CBFR-SPS design, including estimates for the propulsion-system parameters and masses. Specific emphasis is placed on the design of a closed-cycle, Brayton-heat engine, consisting of heat-exchangers, turbo-alternator, compressor, and finned radiators. 8. Time resolved diagnostics of ions in colliding carbon plasmas SciTech Connect Singh, Ravi Pratap; Gupta, Shyam L.; Thareja, Raj K. 2014-11-14 We report a comparative study of the dynamic behaviour of ions at different pressures in laser ablated colliding and single plasma plumes using 2D imaging, optical emission spectroscopy (OES) and a retarding field analyser (RFA). 2D imaging shows the splitting of plasma plumes due to different velocities of various plasma species. OES shows enhancement in abundance of ionic species with their presence for a longer time in colliding plume. C{sub 2} molecular formation is seen at later time in colliding plume compared to single plume and is attributed to dominating collisional processes in the colliding region of the plumes. The time of flight distribution of ions traced by the RFA shows the variation with change in fluence as well as ambient pressure for both colliding and single plume. Time of flight analysis of ions also shows the appearance of a fast peak in ion signal due to acceleration of ions at larger fluence. 9. The Relativistic Heavy Ion Collider control system SciTech Connect Clifford, T.S.; Barton, D.S.; Oerter, B.R. 1997-12-01 The Relativistic Heavy Ion Collider control system has been used in the commissioning of the AGS to RHIC transfer line and in the first RHIC sextant test. Much of the controls infrastructure for networks and links has been installed throughout the collider. All of the controls hardware modules needed to be built for early RHIC operations have been designed and tested. Many of these VME modules are already being used in normal AGS operations. Over 150 VME based front end computers and device controllers will be installed by the Summer of 1998 in order to be ready for Fall of 1998. A few features are being added to the front end computer core software. The bulk of the Accelerator Device Objects (ADOs) which are instantiated in the FECs, have been written and tested in the early commissioning. A configuration database has been designed. Generic control and display of ADO parameters via a spreadsheet like program on the console level computers was provided early on in the control system development. User interface tools that were developed for the AGS control system have been used in RHIC applications. Some of the basic operations programs, like alarm display and save/restore, that are used in the AGS operations have been or will be expanded to support RHIC operations. A model for application programs which involves a console level manager servicing ADOs have been verified with a few RHIC applications. More applications need to be written for the Fall of 1998 commissioning effort. A sequencer for automatic control of the fill is being written with the expectation that it will be useful in early commissioning. 10. Linear Collider Flavour Identification status report: Sensors for the International Linear Collider Stefanov, K. D. 2007-12-01 The Linear Collider Flavour Identification (LCFI) collaboration is continuing the work to develop column-parallel CCDs (CPCCD) and CMOS readout chips to be used in the vertex detector at the international linear collider (ILC). The CPCCD achieves several orders of magnitude faster readout than conventional CCDs because every column is equipped with amplifier and ADC, enabling efficient data taking with low occupancy. Already two generations of CPCCDs and readout chips have been manufactured and the first chips have been fully tested. The second generation devices are now being evaluated. A new CCD-based device, the in-situ storage image sensor (ISIS) has also been developed. The ISIS offers numerous advantages in terms of relaxed readout, increased radiation hardness and great immunity to EMI. In this paper we present the results from the tests of the CPCCDs, readout chips and ISIS, as well as the plans for future developments. 11. Detectors for Linear Colliders: Calorimetry at a Future Electron-Positron Collider (3/4) SciTech Connect 2010-02-17 Calorimetry will play a central role in determining the physics reach at a future e+e- collider. The requirements for calorimetry place the emphasis on achieving an excellent jet energy resolution. The currently favoured option for calorimetry at a future e+e- collider is the concept of high granularity particle flow calorimetry. Here granularity and a high pattern recognition capability is more important than the single particle calorimetric response. In this lecture I will describe the recent progress in understanding the reach of high granularity particle flow calorimetry and the related R&D; efforts which concentrate on test beam demonstrations of the technological options for highly granular calorimeters. I will also discuss alternatives to particle flow, for example the technique of dual readout calorimetry. 12. Detectors for Linear Colliders: Calorimetry at a Future Electron-Positron Collider (3/4) ScienceCinema None 2011-10-06 Calorimetry will play a central role in determining the physics reach at a future e+e- collider. The requirements for calorimetry place the emphasis on achieving an excellent jet energy resolution. The currently favoured option for calorimetry at a future e+e- collider is the concept of high granularity particle flow calorimetry. Here granularity and a high pattern recognition capability is more important than the single particle calorimetric response. In this lecture I will describe the recent progress in understanding the reach of high granularity particle flow calorimetry and the related R&D; efforts which concentrate on test beam demonstrations of the technological options for highly granular calorimeters. I will also discuss alternatives to particle flow, for example the technique of dual readout calorimetry. 13. Status and future directions for advanced accelerator research - conventional and non-conventional collider concepts SciTech Connect Siemann, R.H. 1997-01-01 The relationship between advanced accelerator research and future directions for particle physics is discussed. Comments are made about accelerator research trends in hadron colliders, muon colliders, and e{sup +}3{sup {minus}} linear colliders. 14. Beam tube vacuum in future superconducting proton colliders SciTech Connect Turner, W. 1994-10-01 The beam tube vacuum requirements in future superconducting proton colliders that have been proposed or discussed in the literature -- SSC, LHC, and ELN -- are reviewed. The main beam tube vacuum problem encountered in these machines is how to deal with the magnitude of gas desorption and power deposition by synchrotron radiation while satisfying resistivity, impedance, and space constraints in the cryogenic environment of superconducting magnets. A beam tube vacuum model is developed that treats photodesorption of tightly bound H, C, and 0, photodesorption of physisorbed molecules, and the isotherm vapor pressure of H{sub 2}. Experimental data on cold tube photodesorption experiments are reviewed and applied to model calculations of beam tube vacuum performance for simple cold beam tube and liner configurations. Particular emphasis is placed on the modeling and interpretation of beam tube photodesorpiion experiments at electron synchrotron light sources. The paper also includes discussion of the constraints imposed by beam image current heating, the growth rate of the resistive wall instability, and single-bunch instability impedance limits. 15. A tevatron collider beauty factory. [Final report, 1980--1992 SciTech Connect Not Available 1992-12-31 This document which is labeled a final report consists of several different items. The first is a proposal for a detector to be developed for beauty physics. The detector is proposed for the Fermilab Tevatron, and would be designed to measure mixing reactions, rare decay modes, and even CP violation in hadron collider beauty production. The general outline of the work proposed is given, and an estimate of the time to actually design the detector is presented, along with proposed changes to the Tevatron to accommodate the system. A preliminary report on an experiment to verify a reported observation of a 17 keV neutrino in tritium decay is presented. The present results in the decay spectra actually show a depression below expected levels, which is not consistent with a massive neutrino. Additional interest has been shown in finishing an electrostatic beta spectrometer which was started several years previously. The instrument uses hemispherical electrostatic electric fields to retard electrons emitted in tritium decay, allowing measurement of integral spectra. The design goal has a 5 eV energy resolution, which may be achievable. A new PhD student is pursuing this experiment. Also the report contains a proposal for additional work in the field of non-perturbative quantum field theory by the theoretical group at OU. The work which is proposed will be applied to electroweak and strong interactions, as well as to quantum gravitational phenomena. 16. Beam tube vacuum in future superconducting proton colliders Turner, William C. 1995-02-01 The beam tube vacuum requirements in future superconducting proton colliders that have been proposed or discussed in the literature—SSC, LHC, and ELN—are reviewed. The main beam tube vacuum problem encountered in these machines is how to deal with the magnitude of gas desorption and power deposition by synchrotron radiation while satisfying resistivity, impedance, and space constraints in the cryogenic environment of superconducting magnets. A beam tube vacuum model is developed that treats photodesorption of tightly bound H, C, and O, photodesorption of physisorbed molecules, and the isotherm vapor pressure of H2. Experimental data on cold tube photodesorption experiments are reviewed and applied to model calculations of beam tube vacuum performance for simple cold beam tube and liner configurations. Particular emphasis is placed on the modeling and interpretation of beam tube photodesorption experiments at electron synchrotron light sources. The paper also includes discussion of the constraints imposed by beam image current heating, the growth rate of the resistive wall instability, and single-bunch instability impedance limits. 17. Collider Detector at Fermilab (CDF): Data from Standard Model and Supersymmetric Higgs Bosons Research of the Higgs Group DOE Data Explorer The Collider Detector at Fermilab (CDF) is a Tevatron experiment at Fermilab. The Tevatron, a powerful particle accelerator, accelerates protons and antiprotons close to the speed of light, and then makes them collide head-on inside the CDF detector. The CDF detector is used to study the products of such collisions. The CDF Physics Group at Fermilab is organized into six working groups, each with a specific focus. The Higgs group searches for Standard Model and Supersymmetric Higgs bosons. Their public web page makes data and numerous figures available from both CDF Runs I and II. 18. Collider Detector at Fermilab (CDF): Data from the QCD Group's Research into Properties of the Strong Interaction DOE Data Explorer , The Collider Detector at Fermilab (CDF) is a Tevatron experiment at Fermilab. The Tevatron, a powerful particle accelerator, accelerates protons and antiprotons close to the speed of light, and then makes them collide head-on inside the CDF detector. The CDF detector is used to study the products of such collisions. The CDF Physics Group at Fermilab is organized into six working groups, each with a specific focus. The QCD group studies the properties of the strong interaction. Their public web page makes data and numerous figures available from both CDF Runs I and II. 19. Studies of Magnetic Reconnection in Colliding Laser-Produced Plasmas Rosenberg, Michael 2013-10-01 Novel images of magnetic fields and measurements of electron and ion temperatures have been obtained in the magnetic reconnection region of high- β, laser-produced plasmas. Experiments using laser-irradiated foils produce expanding, hemispherical plasma plumes carrying MG Biermann-battery magnetic fields, which can be driven to interact and reconnect. Thomson-scattering measurements of electron and ion temperatures in the interaction region of two colliding, magnetized plasmas show no thermal enhancement due to reconnection, as expected for β ~ 8 plasmas. Two different proton radiography techniques used to image the magnetic field structures show deformation, pileup, and annihilation of magnetic flux. High-resolution images reveal unambiguously reconnection-induced jets emerging from the interaction region and show instabilities in the expanding plasma plumes and supersonic, hydrodynamic jets due to the plasma collision. Quantitative magnetic flux data show that reconnection in experiments with asymmetry in the scale size, density, temperature, and plasma flow across the reconnection region occurs less efficiently than in similar, symmetric experiments. This result is attributed to disruption of the Hall mechanism mediating collisionless reconnection. The collision of plasmas carrying parallel magnetic fields has also been probed, illustrating the deformation of magnetic field structures in high-energy-density plasmas in the absence of reconnection. These experiments are particularly relevant to high- β reconnection environments, such as the magnetopause. This work was performed in collaboration with C. Li, F. Séguin, A. Zylstra, H. Rinderknecht, H. Sio, J. Frenje, and R. Petrasso (MIT), I. Igumenshchev, V. Glebov, C. Stoeckl, and D. Froula (LLE), J. Ross and R. Town (LLNL), W. Fox (UNH), and A. Nikroo (GA), and was supported in part by the NLUF, FSC/UR, U.S. DOE, LLNL, and LLE. 20. Alighment and Vibration Issues in TeV Linear Collider Design SciTech Connect Fischer, G.E.; /SLAC 2005-08-12 The next generation of linear colliders will require alignment accuracies and stabilities of component placement at least one, perhaps two, orders of magnitude better than can be achieved by the conventional methods and procedures in practice today. The magnitudes of these component-placement tolerances for current designs of various linear collider subsystems are tabulated. In the micron range, long-term ground motion is sufficiently rapid that on-line reference and mechanical correction systems are called for. Some recent experiences with the upgraded SLAC laser alignment systems and examples of some conceivable solutions for the future are described. The so called ''girder'' problem is discussed in the light of ambient and vibratory disturbances. The importance of the quality of the underlying geology is stressed. The necessity and limitations of particle-beam-derived placement information are mentioned. 1. Alignment and vibration issues in TeV linear collider design SciTech Connect Fischer, G.E. 1989-07-01 The next generation of linear colliders will require alignment accuracies and stabilities of component placement at least one, perhaps two, orders of magnitude better than can be achieved by the conventional methods and procedures in practice today. The magnitudes of these component-placement tolerances for current designs of various linear collider subsystems are tabulated. In the micron range, long-term ground motion is sufficiently rapid that on-line reference and mechanical correction systems are called for. Some recent experiences with the upgraded SLAC laser alignment systems and examples of some conceivable solutions for the future are described. The so called ''girder'' problem is discussed in the light of ambient and vibratory disturbances. The importance of the quality of the underlying geology is stressed. The necessity and limitations of public-beam-derived placement information are mentioned. 40 refs., 4 figs., 1 tab. 2. Probing charged Higgs boson couplings at a future circular hadron collider Ćakır, I. T.; Kuday, S.; Saygın, H.; Şenol, A.; ćakır, O. 2016-07-01 Many of the new physics models predict a light Higgs boson similar to the Higgs boson of the Standard Model (SM) and also extra scalar bosons. Beyond the search channels for a SM Higgs boson, the future collider experiments will explore additional channels that are specific to extended Higgs sectors. We study the charged Higgs boson production within the framework of two Higgs doublet models (THDM) in the proton-proton collisions at a future circular hadron collider (FCC-hh). With an integrated luminosity of Lint=500 fb-1 at very high energy frontier (√{s }=100 TeV ), we obtain a significant coverage of the parameter space and distinguish the charged Higgs-top-bottom interaction within the THDM or other new physics models with charged Higgs boson mass up to 1.5 TeV. 3. DEPFET Active Pixel Detectors for a Future Linear e(+}e({-)) Collider Alonso, O.; Casanova, R.; Dieguez, A.; Dingfelder, J.; Hemperek, T.; Kishishita, T.; Kleinohl, T.; Koch, M.; Kruger, H.; Lemarenko, M.; Lutticke, F.; Marinas, C.; Schnell, M.; Wermes, N.; Campbell, A.; Ferber, T.; Kleinwort, C.; Niebuhr, C.; Soloviev, Y.; Steder, M.; Volkenborn, R.; Yaschenko, S.; Fischer, P.; Kreidl, C.; Peric, I.; Knopf, J.; Ritzert, M.; Curras, E.; Lopez-Virto, A.; Moya, D.; Vila, I.; Boronat, M.; Esperante, D.; Fuster, J.; Garcia, I. Garcia; Lacasta, C.; Oyanguren, A.; Ruiz, P.; Timon, G.; Vos, M.; Gessler, T.; Kuhn, W.; Lange, S.; Munchow, D.; Spruck, B.; Frey, A.; Geisler, C.; Schwenker, B.; Wilk, F.; Barvich, T.; Heck, M.; Heindl, S.; Lutz, O.; Muller, Th.; Pulvermacher, C.; Simonis, H. J.; Weiler, T.; Krausser, T.; Lipsky, O.; Rummel, S.; Schieck, J.; Schluter, T.; Ackermann, K.; Andricek, L.; Chekelian, V.; Chobanova, V.; Dalseno, J.; Kiesling, C.; Koffmane, C.; Gioi, L. Li; Moll, A.; Moser, H. G.; Muller, F.; Nedelkovska, E.; Ninkovic, J.; Petrovics, S.; Prothmann, K.; Richter, R.; Ritter, A.; Ritter, M.; Simon, F.; Vanhoefer, P.; Wassatsch, A.; Dolezal, Z.; Drasal, Z.; Kodys, P.; Kvasnicka, P.; Scheirich, J. 2013-04-01 The DEPFET collaboration develops highly granular, ultra-transparent active pixel detectors for high-performance vertex reconstruction at future collider experiments. The characterization of detector prototypes has proven that the key principle, the integration of a first amplification stage in a detector-grade sensor material, can provide a comfortable signal to noise ratio of over 40 for a sensor thickness of 50-75 $\\mathrm{\\mathbf{\\mu m}}$. ASICs have been designed and produced to operate a DEPFET pixel detector with the required read-out speed. A complete detector concept is being developed, including solutions for mechanical support, cooling and services. In this paper the status of DEPFET R & D project is reviewed in the light of the requirements of the vertex detector at a future linear $\\mathbf{e^+ e^-}$ collider. 4. Tevatron Collider Run II status and novel technologies for luminosity upgrades SciTech Connect 2004-07-20 Over the past 2 years the Tevatron peak luminosity steadily progressed and reached the level of 92e30 cm-2s-1 which exceeds the original Run IIa goal. Over 0.57fb-1 have being delivered to each CDF and D0 experiments since the beginning of the Run II. In parallel to the Collider operation, we have started a project of the luminosity upgrade which should lead to peak luminosities of about 270e30 and total integrated luminosity of 4.4-8.5 fb-1 through FY2009. In this paper we describe the status of the Tevatron Collider complex, essence of the upgrades and novel accelerator technologies to be employed. 5. Linear collider signals of an invisible Higgs boson in theories of large extra dimensions SciTech Connect Datta, Anindya; Huitu, Katri; Laamanen, Jari; Mukhopadhyaya, Biswarup 2004-10-01 We discuss the possibility of detecting a Higgs boson in electron-positron collider experiments if large extra dimensions are realized in nature. In such a case, the Higgs boson can decay invisibly by oscillating into a graviscalar Kaluza-Klein tower. We show that the search for such a Higgs boson at an e{sup +}e{sup -} linear collider entails more complications than are usually thought of in relation to an invisibly decaying Higgs boson. The main sources of such complications are due to the simultaneous presence of a continuum graviton production and the broadening of the Higgs peak. We discuss possible ways of overcoming such difficulties and conclude that the detection of such a Higgs boson might still be a problem beyond the mass range of 250-300 GeV. 6. Beam induced backgrounds: CDF experience SciTech Connect Tesarek, R.J.; /Fermilab 2008-05-01 We summarize the experiences of the Collider Detector at Fermilab (CDF) experiment in the presence of backgrounds originating from the counter circulating beams in the Fermilab Tevatron. These backgrounds are measured and their sources identified. Finally, we outline the strategies employed to reduce the effects of these backgrounds on the experiment. 7. Run scenarios for the linear collider SciTech Connect M. Battaglia et al. 2002-12-23 We have examined how a Linear Collider program of 1000 fb{sup -1} could be constructed in the case that a very rich program of new physics is accessible at {radical}s {le} 500 GeV. We have examined possible run plans that would allow the measurement of the parameters of a 120 GeV Higgs boson, the top quark, and could give information on the sparticle masses in SUSY scenarios in which many states are accessible. We find that the construction of the run plan (the specific energies for collider operation, the mix of initial state electron polarization states, and the use of special e{sup -}e{sup -} runs) will depend quite sensitively on the specifics of the supersymmetry model, as the decay channels open to particular sparticles vary drastically and discontinuously as the underlying SUSY model parameters are varied. We have explored this dependence somewhat by considering two rather closely related SUSY model points. We have called for operation at a high energy to study kinematic end points, followed by runs in the vicinity of several two body production thresholds once their location is determined by the end point studies. For our benchmarks, the end point runs are capable of disentangling most sparticle states through the use of specific final states and beam polarizations. The estimated sparticle mass precisions, combined from end point and scan data, are given in Table VIII and the corresponding estimates for the mSUGRA parameters are in Table IX. The precision for the Higgs boson mass, width, cross-sections, branching ratios and couplings are given in Table X. The errors on the top quark mass and width are expected to be dominated by the systematic limits imposed by QCD non-perturbative effects. The run plan devotes at least two thirds of the accumulated luminosity near the maximum LC energy, so that the program would be sensitive to unexpected new phenomena at high mass scales. We conclude that with a 1 ab{sup -1} program, expected to take the first 6-7 years 8. Multi-waveband observations of colliding galaxies NASA Technical Reports Server (NTRS) Appleton, P. N.; Robson, E. I.; Schombert, James M. 1990-01-01 Colliding galaxies represent a major challenge to both theorists and observers because of the large variety of phenomena which are expected to come into play during the interaction. Strong gravitational fluctuations may drive non-linear waves and instabilities throughout the stars and gas leading to enhanced star formation, nuclear activity and ultimately a mixing of the morphological components of the original galaxies. One relatively uncomplicated class of colliding galaxy where stellar waves play an important role in star formation are ring galaxies. Ring galaxies are probably formed when a companion galaxy passes through the center of a disk system driving circular waves through the disk (Lynds and Toomre 1976, Toomre 1978, Struck-Marcell 1990). Off-center collisions can generate non-circular waves and can be loosely described as banana-shaped although they may exhibit more complex forms as the waves expand into the disk. The propagation of such stellar and gaseous waves through the disk leads to enhanced star formation (e.g., Appleton and Struck-Marcell 1987a; Jeske 1986) and provides a unique probe of the response of the interstellar medium (ISM) to a propagating wave (see Appleton and Struck-Marcell 1987b). Here, the authors report results for 3 systems; the irregular ring Arp 143 (=VV 117); Wakamatsu's Seyfert ring (A0959-755; see Wakamatsu and Nishida 1987) and the brighter member of the pair of ring galaxies comprising of AM 1358-221. The most complete multi-wavelength data is for Arp 143. Optical charge coupled device (CCD) observations made with the 60 inch Palomar telescope at BV and r band, near-IR images at J (1.25 microns), H (1.65 microns) and k (2.2 microns) bands from the infrared camera (IRCAM) InSb array camera on the 3.8m United Kingdon Infrared Telescope (UKIRT) telescope and very large array (VLA) observations at 20cm in both the neutral hydrogen line and radio continuum are described. The observations of Wakamatsu's ring and AM 1358 were 9. Overview of the Tevatron Collider Complex: Goals, Operations and Performance SciTech Connect Holmes, Stephen; Moore, Ronald S.; Shiltsev, Vladimir 2011-06-01 For more than two decades the Tevatron proton-antiproton collider was the centerpiece of the world's high energy physics program. The collider was arguably one of the most complex research instruments ever to reach the operation stage and is widely recognized for numerous physics discoveries and for many technological breakthroughs. In this article we outline the historical background that led to the construction of the Tevatron Collider, the strategy applied to evolution of performance goals over the Tevatron's operational history, and briefly describe operations of each accelerator in the chain and achieved performance. 10. Beamstrahlung spectra in next generation linear colliders. Revision SciTech Connect Barklow, T.; Chen, P.; Kozanecki, W. 1992-04-01 For the next generation of linear colliders, the energy loss due to beamstrahlung during the collision of the e{sup +}e{sup {minus}} beams is expected to substantially influence the effective center-of-mass energy distribution of the colliding particles. In this paper, we first derive analytical formulae for the electron and photon energy spectra under multiple beamstrahlung processes, and for the e{sup +}e{sup {minus}} and {gamma}{gamma} differential luminosities. We then apply our formulation to various classes of 500 GeV e{sup +}e{sup {minus}} linear collider designs currently under study. 11. LCFIPlus: A framework for jet analysis in linear collider studies Suehara, Taikan; Tanabe, Tomohiko 2016-02-01 We report on the progress in flavor identification tools developed for a future e+e- linear collider such as the International Linear Collider (ILC) and Compact Linear Collider (CLIC). Building on the work carried out by the LCFIVertex collaboration, we employ new strategies in vertex finding and jet finding, and introduce new discriminating variables for jet flavor identification. We present the performance of the new algorithms in the conditions simulated using a detector concept designed for the ILC. The algorithms have been successfully used in ILC physics simulation studies, such as those presented in the ILC Technical Design Report. 12. Heavy flavor production and top quark search at hadron colliders SciTech Connect Baer, H.A. 1991-01-01 We review heavy flavor production at hadron colliders, with an eye towards the physics of the top quark. Motivation for existence of top, and current status of top search are reviewed. The physics of event simulation at hadron colliders is reviewed. We discuss characteristics of top quark events at p{bar p} colliders that may aid in distinguishing the top quark signal from Standard Model backgrounds, and illustrate various cuts which may be useful for top discovery. Top physics at hadron supercolliders is commented upon, as well as top quark mass measurement techniques. 22 refs., 5 figs. 13. Laser cooling of electron beams for linear colliders SciTech Connect Telnov, V. 1996-10-01 A novel method of electron beam cooling is considered which can be used for linear colliders. The electron beam is cooled during collision with focused powerful laser pulse. With reasonable laser parameters (laser flash energy about 10 J) one can decrease transverse beam emittances by a factor about 10 per one stage. The ultimate transverse emittances are much below that given by other methods. Depolarization of a beam during the cooling is about 5--15% for one stage. This method is especially useful for photon colliders and open new possibilities for e{sup +}e{sup {minus}} colliders and x-ray FEL based on high energy linacs. 14. Cryostat design for the Superconducting Super Collider SciTech Connect Nicol, T.H. 1990-09-01 The cryostat of an SSC dipole magnet consists of all magnet components except the cold mass assembly. It serves to support the cold mass accurately and reliably within the vacuum vessel, provide all required cryogenic piping, and to insulate the cold mass from heat radiated and conducted from the environment. It must function reliably during storage, shipping and handling, normal magnet operation, quenches, and seismic excitations and must be manufacturable at low cost. The major components of the cryostat are the vacuum vessel, thermal shields, multilayer insulation (MLI) system, cryogenic piping, interconnections, and suspension system. The overall design of a cryostat for superconducting accelerator magnets requires consideration of fluid flow, proper selection of materials for their thermal and structural performance at both ambient and operating temperature, and knowledge of the environment to which the magnets will be subjected over the course their 25 year expected life. This paper describes the design of the current SSC collider dipole magnet cryostat and includes discussions on the thermal, structural, and dynamic considerations involved in the development of each of the major systems. 7 refs., 4 figs. 15. Multimegawatt rf power sources for linear colliders SciTech Connect Caryotakis, G. 1991-04-01 Conceptual designs for a future linear collider operating at 11.4 GHz call for peak rf power as high as 240 MW per meter, with an accelerator length of 14 km. This is an extremely high total power, which results in requirements for microwave sources that cannot be met with existing microwave tubes. While some new tube concepts are being considered, work is proceeding at several laboratories in the US and abroad on conventional 100 MW klystrons for this application. The electron beam necessary for this power to be generated, unless carefully controlled, can easily cause intrapulse melting at the klystron output circuit. This, coupled to the need for good efficiency, high production yield, and long life, poses some difficult problems to the klystron designer. Experimental klystrons at SLAC and other laboratories are approaching the goal of 100 MW in 800 nsec pulses, but much work remains to be done before a design is available which is suitable for manufacturing thousands of these tubes. 4 figs., 1 tab. 16. A large hadron electron collider at CERN DOE PAGESBeta Abelleira Fernandez, J. L. 2015-04-06 This document provides a brief overview of the recently published report on the design of the Large Hadron Electron Collider (LHeC), which comprises its physics programme, accelerator physics, technology and main detector concepts. The LHeC exploits and develops challenging, though principally existing, accelerator and detector technologies. This summary is complemented by brief illustrations of some of the highlights of the physics programme, which relies on a vastly extended kinematic range, luminosity and unprecedented precision in deep inelastic scattering. Illustrations are provided regarding high precision QCD, new physics (Higgs, SUSY) and eletron-ion physics. The LHeC is designed to run synchronously withmore » the LHC in the twenties and to achieve an integrated luminosity of O(100)fb–1. It will become the cleanest high resolution microscope of mankind and will substantially extend as well as complement the investigation of the physics of the TeV energy scale, which has been enabled by the LHC.« less 17. Conformal collider physics from the lightcone bootstrap Li, Daliang; Meltzer, David; Poland, David 2016-02-01 We analytically study the lightcone limit of the conformal bootstrap equations for 4-point functions containing global symmetry currents and the stress tensor in 3d CFTs. We show that the contribution of the stress tensor to the anomalous dimensions of large spin double-twist states is negative if and only if the conformal collider physics bounds are satisfied. In the context of AdS/CFT these results indicate a relation between the attractiveness of AdS gravity and positivity of the CFT energy flux. We also study the contribution of non-Abelian conserved currents to the anomalous dimensions of double- twist operators, corresponding to the gauge binding energy of 2-particle states in AdS. We show that the representation of the double-twist state determines the sign of the gauge binding energy if and only if the coefficients appearing in the current 3-point function satisfies a similar bound, which is equivalent to an upper bound on the charge flux asymmetry of the CFT. 18. Colliding beam fusion reactor space propulsion system Wessel, Frank J.; Binderbauer, Michl W.; Rostoker, Norman; Rahman, Hafiz Ur; O'Toole, Joseph 2000-01-01 We describe a space propulsion system based on the Colliding Beam Fusion Reactor (CBFR). The CBFR is a high-beta, field-reversed, magnetic configuration with ion energies in the range of hundreds of keV. Repetitively-pulsed ion beams sustain the plasma distribution and provide current drive. The confinement physics is based on the Vlasov-Maxwell equation, including a Fokker Planck collision operator and all sources and sinks for energy and particle flow. The mean azimuthal velocities and temperatures of the fuel ion species are equal and the plasma current is unneutralized by the electrons. The resulting distribution functions are thermal in a moving frame of reference. The ion gyro-orbit radius is comparable to the dimensions of the confinement system, hence classical transport of the particles and energy is expected and the device is scaleable. We have analyzed the design over a range of 106-109 Watts of output power (0.15-150 Newtons thrust) with a specific impulse of, Isp~106 sec. A 50 MW propulsion system might involve the following parameters: 4-meters diameter×10-meters length, magnetic field ~7 Tesla, ion beam current ~10 A, and fuels of either D-He3,P-B11,P-Li6,D-Li6, etc. . 19. Macroscopic strings and quirks'' at colliders Kang, Junhai; Luty, Markus A. 2009-11-01 We consider extensions of the standard model containing additional heavy particles (quirks'') charged under a new unbroken non-abelian gauge group as well as the standard model. We assume that the quirk mass m is in the phenomenologically interesting range 100 GeV-TeV, and that the new gauge group gets strong at a scale Λ < m. In this case breaking of strings is exponentially suppressed, and quirk production results in strings that are long compared to Λ-1. The existence of these long stable strings leads to highly exotic events at colliders. For 100 eV lsimΛ <~ keV the strings are macroscopic, giving rise to events with two separated quirk tracks with measurable curvature toward each other due to the string interaction. For keV <~ Λ <~ MeV the typical strings are mesoscopic: too small to resolve in the detector, but large compared to atomic scales. In this case, the bound state appears as a single particle, but its mass is the invariant mass of a quirk pair, which has an event-by-event distribution. For MeV <~ Λ <~ m, the strings are microscopic, and the quirks annihilate promptly within the detector. For colored quirks, this can lead to hadronic fireball events with ~ 103 hadrons with energy of order GeV emitted in conjunction with hard decay products from the final annihilation. 20. 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https://www.science.gov/topicpages/f/finding+approximate+expression.html	#### Sample records for finding approximate expression 1. A polynomial time biclustering algorithm for finding approximate expression patterns in gene expression time series PubMed Central Madeira, Sara C; Oliveira, Arlindo L 2009-01-01 Background The ability to monitor the change in expression patterns over time, and to observe the emergence of coherent temporal responses using gene expression time series, obtained from microarray experiments, is critical to advance our understanding of complex biological processes. In this context, biclustering algorithms have been recognized as an important tool for the discovery of local expression patterns, which are crucial to unravel potential regulatory mechanisms. Although most formulations of the biclustering problem are NP-hard, when working with time series expression data the interesting biclusters can be restricted to those with contiguous columns. This restriction leads to a tractable problem and enables the design of efficient biclustering algorithms able to identify all maximal contiguous column coherent biclusters. Methods In this work, we propose e-CCC-Biclustering, a biclustering algorithm that finds and reports all maximal contiguous column coherent biclusters with approximate expression patterns in time polynomial in the size of the time series gene expression matrix. This polynomial time complexity is achieved by manipulating a discretized version of the original matrix using efficient string processing techniques. We also propose extensions to deal with missing values, discover anticorrelated and scaled expression patterns, and different ways to compute the errors allowed in the expression patterns. We propose a scoring criterion combining the statistical significance of expression patterns with a similarity measure between overlapping biclusters. Results We present results in real data showing the effectiveness of e-CCC-Biclustering and its relevance in the discovery of regulatory modules describing the transcriptomic expression patterns occurring in Saccharomyces cerevisiae in response to heat stress. In particular, the results show the advantage of considering approximate patterns when compared to state of the art methods that require 2. Finding approximate gene clusters with Gecko 3 PubMed Central Winter, Sascha; Jahn, Katharina; Wehner, Stefanie; Kuchenbecker, Leon; Marz, Manja; Stoye, Jens; Böcker, Sebastian 2016-01-01 Gene-order-based comparison of multiple genomes provides signals for functional analysis of genes and the evolutionary process of genome organization. Gene clusters are regions of co-localized genes on genomes of different species. The rapid increase in sequenced genomes necessitates bioinformatics tools for finding gene clusters in hundreds of genomes. Existing tools are often restricted to few (in many cases, only two) genomes, and often make restrictive assumptions such as short perfect conservation, conserved gene order or monophyletic gene clusters. We present Gecko 3, an open-source software for finding gene clusters in hundreds of bacterial genomes, that comes with an easy-to-use graphical user interface. The underlying gene cluster model is intuitive, can cope with low degrees of conservation as well as misannotations and is complemented by a sound statistical evaluation. To evaluate the biological benefit of Gecko 3 and to exemplify our method, we search for gene clusters in a dataset of 678 bacterial genomes using Synechocystis sp. PCC 6803 as a reference. We confirm detected gene clusters reviewing the literature and comparing them to a database of operons; we detect two novel clusters, which were confirmed by publicly available experimental RNA-Seq data. The computational analysis is carried out on a laptop computer in <40 min. PMID:27679480 3. Finding the Best Quadratic Approximation of a Function ERIC Educational Resources Information Center Yang, Yajun; Gordon, Sheldon P. 2011-01-01 This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact… 4. Finding the Best Quadratic Approximation of a Function ERIC Educational Resources Information Center Yang, Yajun; Gordon, Sheldon P. 2011-01-01 This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact… 5. Two Efficient Techniques to Find Approximate Overlaps between Sequences PubMed Central 2017-01-01 The next-generation sequencing (NGS) technology outputs a huge number of sequences (reads) that require further processing. After applying prefiltering techniques in order to eliminate redundancy and to correct erroneous reads, an overlap-based assembler typically finds the longest exact suffix-prefix match between each ordered pair of the input reads. However, another trend has been evolving for the purpose of solving an approximate version of the overlap problem. The main benefit of this direction is the ability to skip time-consuming error-detecting techniques which are applied in the prefiltering stage. In this work, we present and compare two techniques to solve the approximate overlap problem. The first adapts a compact prefix tree to efficiently solve the approximate all-pairs suffix-prefix problem, while the other utilizes a well-known principle, namely, the pigeonhole principle, to identify a potential overlap match in order to ultimately solve the same problem. Our results show that our solution using the pigeonhole principle has better space and time consumption over an FM-based solution, while our solution based on prefix tree has the best space consumption between all three solutions. The number of mismatches (hamming distance) is used to define the approximate matching between strings in our work. PMID:28293632 6. Two Efficient Techniques to Find Approximate Overlaps between Sequences. PubMed Haj Rachid, Maan 2017-01-01 The next-generation sequencing (NGS) technology outputs a huge number of sequences (reads) that require further processing. After applying prefiltering techniques in order to eliminate redundancy and to correct erroneous reads, an overlap-based assembler typically finds the longest exact suffix-prefix match between each ordered pair of the input reads. However, another trend has been evolving for the purpose of solving an approximate version of the overlap problem. The main benefit of this direction is the ability to skip time-consuming error-detecting techniques which are applied in the prefiltering stage. In this work, we present and compare two techniques to solve the approximate overlap problem. The first adapts a compact prefix tree to efficiently solve the approximate all-pairs suffix-prefix problem, while the other utilizes a well-known principle, namely, the pigeonhole principle, to identify a potential overlap match in order to ultimately solve the same problem. Our results show that our solution using the pigeonhole principle has better space and time consumption over an FM-based solution, while our solution based on prefix tree has the best space consumption between all three solutions. The number of mismatches (hamming distance) is used to define the approximate matching between strings in our work. 7. An Improved Direction Finding Algorithm Based on Toeplitz Approximation PubMed Central Wang, Qing; Chen, Hua; Zhao, Guohuang; Chen, Bin; Wang, Pichao 2013-01-01 In this paper, a novel direction of arrival (DOA) estimation algorithm called the Toeplitz fourth order cumulants multiple signal classification method (TFOC-MUSIC) algorithm is proposed through combining a fast MUSIC-like algorithm termed the modified fourth order cumulants MUSIC (MFOC-MUSIC) algorithm and Toeplitz approximation. In the proposed algorithm, the redundant information in the cumulants is removed. Besides, the computational complexity is reduced due to the decreased dimension of the fourth-order cumulants matrix, which is equal to the number of the virtual array elements. That is, the effective array aperture of a physical array remains unchanged. However, due to finite sampling snapshots, there exists an estimation error of the reduced-rank FOC matrix and thus the capacity of DOA estimation degrades. In order to improve the estimation performance, Toeplitz approximation is introduced to recover the Toeplitz structure of the reduced-dimension FOC matrix just like the ideal one which has the Toeplitz structure possessing optimal estimated results. The theoretical formulas of the proposed algorithm are derived, and the simulations results are presented. From the simulations, in comparison with the MFOC-MUSIC algorithm, it is concluded that the TFOC-MUSIC algorithm yields an excellent performance in both spatially-white noise and in spatially-color noise environments. PMID:23296331 8. An improved direction finding algorithm based on Toeplitz approximation. PubMed Wang, Qing; Chen, Hua; Zhao, Guohuang; Chen, Bin; Wang, Pichao 2013-01-07 In this paper, a novel direction of arrival (DOA) estimation algorithm called the Toeplitz fourth order cumulants multiple signal classification method (TFOC-MUSIC) algorithm is proposed through combining a fast MUSIC-like algorithm termed the modified fourth order cumulants MUSIC (MFOC-MUSIC) algorithm and Toeplitz approximation. In the proposed algorithm, the redundant information in the cumulants is removed. Besides, the computational complexity is reduced due to the decreased dimension of the fourth-order cumulants matrix, which is equal to the number of the virtual array elements. That is, the effective array aperture of a physical array remains unchanged. However, due to finite sampling snapshots, there exists an estimation error of the reduced-rank FOC matrix and thus the capacity of DOA estimation degrades. In order to improve the estimation performance, Toeplitz approximation is introduced to recover the Toeplitz structure of the reduced-dimension FOC matrix just like the ideal one which has the Toeplitz structure possessing optimal estimated results. The theoretical formulas of the proposed algorithm are derived, and the simulations results are presented. From the simulations, in comparison with the MFOC-MUSIC algorithm, it is concluded that the TFOC-MUSIC algorithm yields an excellent performance in both spatially-white noise and in spatially-color noise environments. 9. Approximate reanalysis based on the exact analytic expressions 1992-06-01 Fuchs has recently given the exact analytic expressions of the inverse of the stiffness matrix, the nodal displacements, and the stress resultants in linear elastic structures composed of prismatic elements. For structures of constant geometry, the expressions are explicit in terms of the unimodal stiffnesses of the components of the structures. However, the expressions are intractable in their exact form due to their inordinate length. It all has to do with the number of statically determinate substructures embedded in common engineering structures. This paper describes some preliminary results obtained from approximate analysis models for the internal forces using truncated expressions that are similar in form to the exact analytic ones. The approach is illustrated with numerical examples. 10. Mars Express recent findings and future plans Titov, Dmitrij; Bibring, Jean-Pierre; Cardesin, Alejandro; Duxbury, Thomas; Forget, Francois; Giuranna, Marco; González-Galindo, Francisco; Holmström, Mats; Jaumann, Ralf; Määttänen, Anni; Martin, Patrick; Montmessin, Franck; Orosei, Roberto; Pätzold, Martin; Plaut, Jeffrey; MEx SGS Team 2017-04-01 Mars Express remains one of ESA's most scientifically productive missions whose publication record now exceeds 1000 papers. Characterization of geological processes on a local-to-regional scale by HRSC, OMEGA and partner experiments on NASA spacecraft has allowed constraining land-forming processes in space and time. Recent results suggest episodic geological activity as well as the presence of large bodies of liquid water in several provinces (e.g. Eridania Planum, Terra Chimeria) in the early and middle Amazonian epoch and formation of vast sedimentary plains north of the Hellas basin. Mars Express observations and experimental teams provided an essential contribution to the selection of the Mars-2020 landing sites. More than a decade-long record of atmospheric parameters such as temperature, dust loading, water vapor and ozone abundance, water ice and CO2 clouds distribution, collected by SPICAM, PFS and OMEGA spectrometers as well as subsequent modeling have provided key contributions to our understanding of the martian climate. The ASPERA-3 observations of ion escape covering a complete solar cycle have revealed important dependencies of the atmospheric erosion rate on parameters of the solar wind and EUV flux. Structure of the ionosphere sounded by the MARSIS radar and the MaRS radio science experiment was found to be significantly affected by the solar activity, the crustal magnetic field, as well as by the influx of meteorite and cometary dust. MARSIS and ASPERA-3 observations suggest that the sunlit ionosphere over the regions with strong crustal fields is denser and extends to higher altitudes as compared to the regions with no crustal anomalies. The ionospheric plasma expands to higher altitudes where it contacts with the solar wind plasma. Reconnection of solar magnetic field lines carried by the solar wind with field lines of crustal origin opens channels through which the ionospheric plasma escapes to space, producing strong and narrow cavities in the 11. Approximate expression to estimate signal-to-noise ratio improvement in cylindrical near-field measurements Romeu, Jordi; Jofre, Lluis; Cardama, Angel 1994-07-01 A very simple approximate expression for the process gain (PG) for the cylindrical case is derived. The different approximations and assumptions required to obtain this expression are shown. This expression might be useful for most practical cylindrical near-field measurements, providing a very simple mean to assess the near-field dynamic range requirements to obtain a desired far-field signal-to-noise ratio (SNR). 12. Pomelo II: finding differentially expressed genes. PubMed Morrissey, Edward R; Diaz-Uriarte, Ramón 2009-07-01 Pomelo II (http://pomelo2.bioinfo.cnio.es) is an open-source, web-based, freely available tool for the analysis of gene (and protein) expression and tissue array data. Pomelo II implements: permutation-based tests for class comparisons (t-test, ANOVA) and regression; survival analysis using Cox model; contingency table analysis with Fisher's exact test; linear models (of which t-test and ANOVA are especial cases) that allow additional covariates for complex experimental designs and use empirical Bayes moderated statistics. Permutation-based and Cox model analysis use parallel computing, which permits taking advantage of multicore CPUs and computing clusters. Access to, and further analysis of, additional biological information and annotations (PubMed references, Gene Ontology terms, KEGG and Reactome pathways) are available either for individual genes (from clickable links in tables and figures) or sets of genes. The source code is available, allowing for extending and reusing the software. A comprehensive test suite is also available, and covers both the user interface and the numerical results. The possibility of including additional covariates, parallelization of computation, open-source availability of the code and comprehensive testing suite make Pomelo II a unique tool. 13. Pomelo II: finding differentially expressed genes PubMed Central Morrissey, Edward R.; Diaz-Uriarte, Ramón 2009-01-01 Pomelo II (http://pomelo2.bioinfo.cnio.es) is an open-source, web-based, freely available tool for the analysis of gene (and protein) expression and tissue array data. Pomelo II implements: permutation-based tests for class comparisons (t-test, ANOVA) and regression; survival analysis using Cox model; contingency table analysis with Fisher's exact test; linear models (of which t-test and ANOVA are especial cases) that allow additional covariates for complex experimental designs and use empirical Bayes moderated statistics. Permutation-based and Cox model analysis use parallel computing, which permits taking advantage of multicore CPUs and computing clusters. Access to, and further analysis of, additional biological information and annotations (PubMed references, Gene Ontology terms, KEGG and Reactome pathways) are available either for individual genes (from clickable links in tables and figures) or sets of genes. The source code is available, allowing for extending and reusing the software. A comprehensive test suite is also available, and covers both the user interface and the numerical results. The possibility of including additional covariates, parallelization of computation, open-source availability of the code and comprehensive testing suite make Pomelo II a unique tool. PMID:19435879 14. Mars EXpress: status and recent findings Titov, Dmitri; Bibring, Jean-Pierre; Cardesin, Alejandro; Duxbury, Tom; Forget, Francois; Giuranna, Marco; Holmstroem, Mats; Jaumann, Ralf; Martin, Patrick; Montmessin, Franck; Orosei, Roberto; Paetzold, Martin; Plaut, Jeff; MEX SGS Team 2016-04-01 Mars Express has entered its second decade in orbit in excellent health. The mission extension in 2015-2016 aims at augmenting of the surface coverage by imaging and spectral imaging instruments, continuing monitoring of the climate parameters and their variability, study of the upper atmosphere and its interaction with the solar wind in collaboration with NASA's MAVEN mission. Characterization of geological processes and landforms on Mars on a local-to-regional scale by HRSC camera constrained the martian geological activity in space and time and suggested its episodicity. Six years of spectro-imaging observations by OMEGA allowed correction of the surface albedo for presence of the atmospheric dust and revealed changes associated with the dust storm seasons. Imaging and spectral imaging of the surface shed light on past and present aqueous activity and contributed to the selection of the Mars-2018 landing sites. More than a decade long record of climatological parameters such as temperature, dust loading, water vapor, and ozone abundance was established by SPICAM and PFS spectrometers. Observed variations of HDO/H2O ratio above the subliming North polar cap suggested seasonal fractionation. The distribution of aurora was found to be related to the crustal magnetic field. ASPERA observations of ion escape covering a complete solar cycle revealed important dependences of the atmospheric erosion rate on parameters of the solar wind and EUV flux. Structure of the ionosphere sounded by MARSIS radar and MaRS radio science experiment was found to be significantly affected by the solar activity, crustal magnetic field as well as by influx of meteorite and cometary dust. The new atlas of Phobos based on the HRSC imaging was issued. The talk will give the mission status and review recent science highlights. 15. Sequential Experimentation: Comparing Stochastic Approximation Methods Which Find the "Right" Value of the Independent Variable. ERIC Educational Resources Information Center Hummel, Thomas J.; Johnston, Charles B. This research investigates stochastic approximation procedures of the Robbins-Monro type. Following a brief introduction to sequential experimentation, attention is focused on formal methods for selecting successive values of a single independent variable. Empirical results obtained through computer simulation are used to compare several formal… 16. Children's discomfort may vary among different treatments for initial approximal caries lesions: preliminary findings of a randomized controlled clinical trial. PubMed Mattos-Silveira, Juliana; Floriano, Isabela; Ferreira, Fernanda R; Viganó, Maria Eduarda F; Mendes, Fausto M; Braga, Mariana M 2015-07-01 Longer and more complex dental procedures could negatively affect patient's acceptability of minimal invasive techniques. Therefore, this short communication aims to show the preliminary findings regarding children's discomfort reported after some minimal invasive treatments in treating initial caries lesions on approximal surfaces: flossing instruction, silver diamine fluoride (SDF) application and caries resin infiltration. Children allocated in the infiltration group showed higher levels of discomfort than those in the SDF and control groups. These findings suggest that the simplest interventions for approximal initial caries lesions cause less discomfort for children and should be applied where possible. © 2014 BSPD, IAPD and John Wiley & Sons A/S. Published by John Wiley & Sons Ltd. 17. An efficient approximation algorithm for finding a maximum clique using Hopfield network learning. PubMed Wang, Rong Long; Tang, Zheng; Cao, Qi Ping 2003-07-01 In this article, we present a solution to the maximum clique problem using a gradient-ascent learning algorithm of the Hopfield neural network. This method provides a near-optimum parallel algorithm for finding a maximum clique. To do this, we use the Hopfield neural network to generate a near-maximum clique and then modify weights in a gradient-ascent direction to allow the network to escape from the state of near-maximum clique to maximum clique or better. The proposed parallel algorithm is tested on two types of random graphs and some benchmark graphs from the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS). The simulation results show that the proposed learning algorithm can find good solutions in reasonable computation time. 18. Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion ERIC Educational Resources Information Center Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi 2011-01-01 An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the… 19. Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion ERIC Educational Resources Information Center Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi 2011-01-01 An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the… 20. Analytical approximations for spatial stochastic gene expression in single cells and tissues PubMed Central Smith, Stephen; Cianci, Claudia; Grima, Ramon 2016-01-01 Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686 1. Analytical approximations for spatial stochastic gene expression in single cells and tissues. PubMed Smith, Stephen; Cianci, Claudia; Grima, Ramon 2016-05-01 Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction-diffusion master equation (RDME) describing stochastic reaction-diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction-diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. 2. Drug effects on responses to emotional facial expressions: recent findings PubMed Central Miller, Melissa A.; Bershad, Anya K.; de Wit, Harriet 2016-01-01 Many psychoactive drugs increase social behavior and enhance social interactions, which may, in turn, increase their attractiveness to users. Although the psychological mechanisms by which drugs affect social behavior are not fully understood, there is some evidence that drugs alter the perception of emotions in others. Drugs can affect the ability to detect, attend to, and respond to emotional facial expressions, which in turn may influence their use in social settings. Either increased reactivity to positive expressions or decreased response to negative expressions may facilitate social interaction. This article reviews evidence that psychoactive drugs alter the processing of emotional facial expressions using subjective, behavioral, and physiological measures. The findings lay the groundwork for better understanding how drugs alter social processing and social behavior more generally. PMID:26226144 3. Drug effects on responses to emotional facial expressions: recent findings. PubMed Miller, Melissa A; Bershad, Anya K; de Wit, Harriet 2015-09-01 Many psychoactive drugs increase social behavior and enhance social interactions, which may, in turn, increase their attractiveness to users. Although the psychological mechanisms by which drugs affect social behavior are not fully understood, there is some evidence that drugs alter the perception of emotions in others. Drugs can affect the ability to detect, attend to, and respond to emotional facial expressions, which in turn may influence their use in social settings. Either increased reactivity to positive expressions or decreased response to negative expressions may facilitate social interaction. This article reviews evidence that psychoactive drugs alter the processing of emotional facial expressions using subjective, behavioral, and physiological measures. The findings lay the groundwork for better understanding how drugs alter social processing and social behavior more generally. 4. Efficiently finding regulatory elements using correlation with gene expression. PubMed Bannai, Hideo; Inenaga, Shunsuke; Shinohara, Ayumi; Takeda, Masayuki; Miyano, Satoru 2004-06-01 We present an efficient algorithm for detecting putative regulatory elements in the upstream DNA sequences of genes, using gene expression information obtained from microarray experiments. Based on a generalized suffix tree, our algorithm looks for motif patterns whose appearance in the upstream region is most correlated with the expression levels of the genes. We are able to find the optimal pattern, in time linear in the total length of the upstream sequences. We implement and apply our algorithm to publicly available microarray gene expression data, and show that our method is able to discover biologically significant motifs, including various motifs which have been reported previously using the same data set. We further discuss applications for which the efficiency of the method is essential, as well as possible extensions to our algorithm. 5. Approximate expressions of mean eddy current torque acted on space debris Lin, Hou-yuan; Zhao, Chang-yin 2017-02-01 Rotational state of space debris will be influenced by eddy current torque which is produced by the conducting body rotating within the geomagnetic field. Former expressions of instantaneous torque established in body-fixed coordinate system will change in space during rotation due to the variation of the coordinate system. In order to further investigate the evolution of the rotation of space debris subjected to the eddy current torque, approximate expressions of mean eddy current torque in inertial coordinate system are obtained from the average of the Euler dynamics equations under the assumption that two of the principal moments of inertia of the space debris are similar. Then the expressions are verified through numerical simulation, in which the orientation of the averaged variation of angular momentum is in agreement with the torque from the expressions, which is on an identical plane with magnetic field and the angular momentum. The torque and the averaged variation of the angular momentum have the same evolution trend during rotation in spite of minor deviations of their values. 6. Fast and accurate approximate inference of transcript expression from RNA-seq data PubMed Central Hensman, James; Papastamoulis, Panagiotis; Glaus, Peter; Honkela, Antti; Rattray, Magnus 2015-01-01 Motivation: Assigning RNA-seq reads to their transcript of origin is a fundamental task in transcript expression estimation. Where ambiguities in assignments exist due to transcripts sharing sequence, e.g. alternative isoforms or alleles, the problem can be solved through probabilistic inference. Bayesian methods have been shown to provide accurate transcript abundance estimates compared with competing methods. However, exact Bayesian inference is intractable and approximate methods such as Markov chain Monte Carlo and Variational Bayes (VB) are typically used. While providing a high degree of accuracy and modelling flexibility, standard implementations can be prohibitively slow for large datasets and complex transcriptome annotations. Results: We propose a novel approximate inference scheme based on VB and apply it to an existing model of transcript expression inference from RNA-seq data. Recent advances in VB algorithmics are used to improve the convergence of the algorithm beyond the standard Variational Bayes Expectation Maximization algorithm. We apply our algorithm to simulated and biological datasets, demonstrating a significant increase in speed with only very small loss in accuracy of expression level estimation. We carry out a comparative study against seven popular alternative methods and demonstrate that our new algorithm provides excellent accuracy and inter-replicate consistency while remaining competitive in computation time. Availability and implementation: The methods were implemented in R and C++, and are available as part of the BitSeq project at github.com/BitSeq. The method is also available through the BitSeq Bioconductor package. The source code to reproduce all simulation results can be accessed via github.com/BitSeq/BitSeqVB_benchmarking. Contact: james.hensman@sheffield.ac.uk or panagiotis.papastamoulis@manchester.ac.uk or Magnus.Rattray@manchester.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online 7. Soft mean spherical approximation for dusty plasma liquids: Level of accuracy and analytic expressions SciTech Connect Tolias, P.; Ratynskaia, S.; Angelis, U. de 2015-08-15 The soft mean spherical approximation is employed for the study of the thermodynamics of dusty plasma liquids, the latter treated as Yukawa one-component plasmas. Within this integral theory method, the only input necessary for the calculation of the reduced excess energy stems from the solution of a single non-linear algebraic equation. Consequently, thermodynamic quantities can be routinely computed without the need to determine the pair correlation function or the structure factor. The level of accuracy of the approach is quantified after an extensive comparison with numerical simulation results. The approach is solved over a million times with input spanning the whole parameter space and reliable analytic expressions are obtained for the basic thermodynamic quantities. 8. An Approximate Expression of Slip Velocity Time Function for Simulation of Near-field Strong Ground Motion Miyatake, T. 2002-12-01 Nakamura and Miyatake (2000) proposed an approximate expression of slip velocity time function for simulation of near-field strong ground motion on the basis of the numerical solution of 2D and 3D crack simulations including a slip-weakening friction law. The approximate slip rate time functions are applied to near-source seismic waves from various fault models, (a) rectangular crack in which rupture propagate unilaterally, (b) asperity model (c) square shaped crack in which rupture start around bottom corner and propagate circularly, and then compared with those from dynamic rupture model. The approximate slip rate time functions are implemented as a double couple force systems in 3D finite difference calculation (Graves, 1998). Dynamic rupture calculation is also carried out in same staggered grid 3D FD model with stress or frictional condition imposed on the fault-ruptured area. The waveform from approximate expressed slip rate function fits well to that from dynamic crack models but there exists discrepancy between them near the starting point or first asperity. In the present paper, we also discuss an approximate expression of non-uniform slip rate time function for a propagating crack. The near-fault ground motion with slip weakening friction above mentioned (a), (b), and (c). The revised expression improves the fitting. 9. Partition resampling and extrapolation averaging: approximation methods for quantifying gene expression in large numbers of short oligonucleotide arrays. PubMed Goldstein, Darlene R 2006-10-01 Studies of gene expression using high-density short oligonucleotide arrays have become a standard in a variety of biological contexts. Of the expression measures that have been proposed to quantify expression in these arrays, multi-chip-based measures have been shown to perform well. As gene expression studies increase in size, however, utilizing multi-chip expression measures is more challenging in terms of computing memory requirements and time. A strategic alternative to exact multi-chip quantification on a full large chip set is to approximate expression values based on subsets of chips. This paper introduces an extrapolation method, Extrapolation Averaging (EA), and a resampling method, Partition Resampling (PR), to approximate expression in large studies. An examination of properties indicates that subset-based methods can perform well compared with exact expression quantification. The focus is on short oligonucleotide chips, but the same ideas apply equally well to any array type for which expression is quantified using an entire set of arrays, rather than for only a single array at a time. Software implementing Partition Resampling and Extrapolation Averaging is under development as an R package for the BioConductor project. 10. Finding Balance: T cell Regulatory Receptor Expression during Aging. PubMed Cavanagh, Mary M; Qi, Qian; Weyand, Cornelia M; Goronzy, Jörg J 2011-10-01 Aging is associated with a variety of changes to immune responsiveness. Reduced protection against infection, reduced responses to vaccination and increased risk of autoimmunity are all hallmarks of advanced age. Here we consider how changes in the expression of regulatory receptors on the T cell surface contribute to altered immunity during aging. 11. Finding regulatory modules from gene expression data II Tang, Chao; Kloster, Morten; Wingreen, Ned 2004-03-01 We tested the Progressive Iterative Signature Algorithm (PISA) on synthetic data and on a large gene-expression data set for the yeast Saccharomyces cerevisiae. For synthetic data, the false-positive rate for identifying transcriptional modules was extremely low. For the yeast data set of 1012 experimental conditions for 6206 genes, PISA identified a large number of modules, most of which could be readily assigned to specific biological functions. These included many small modules (with as few as five genes) that could not be easily found by ISA. We compared the set of modules we found to the Gene Ontology annotation database and found many significant overlaps. The modules identified by PISA also compare favorably to experimentally and theoretically determined sets of genes regulated by individual transcription factors. 12. Mars Express scientists find a different Mars underneath the surface 2006-12-01 Observations by MARSIS, the first subsurface sounding radar used to explore a planet, strongly suggest that ancient impact craters lie buried beneath the smooth, low plains of Mars' northern hemisphere. The technique uses echoes of radio waves that have penetrated below the surface. MARSIS found evidence that these buried impact craters - ranging from about 130 to 470 kilometres in diameter - are present under much of the northern lowlands. The findings appear in the 14 December 2006 issue of the journal Nature. With MARSIS "it's almost like having X-ray vision," said Thomas R. Watters of the National Air and Space Museum's Center for Earth and Planetary Studies, Washington, and lead author of the results. "Besides finding previously unknown impact basins, we've also confirmed that some subtle, roughly circular, topographic depressions in the lowlands are related to impact features." Studies of how Mars evolved help in understanding early Earth. Some signs of the forces at work a few thousand million years ago are harder to detect on Earth because many of them have been obliterated by tectonic activity and erosion. The new findings bring planetary scientists closer to understanding one of the most enduring mysteries about the geological evolution and history of Mars. In contrast to Earth, Mars shows a striking difference between its northern and southern hemispheres. Almost the entire southern hemisphere has rough, heavily cratered highlands, while most of the northern hemisphere is smoother and lower in elevation. Since the impacts that cause craters can happen anywhere on a planet, the areas with fewer craters are generally interpreted as younger surfaces where geological processes have erased the impact scars. The surface of Mars' northern plains is young and smooth, covered by vast amounts of volcanic lava and sediment. However, the new MARSIS data indicate that the underlying crust is extremely old. “The number of buried impact craters larger than 200 13. Findings MedlinePlus ... Issue All Issues Explore Findings by Topic Cell Biology Cellular Structures, Functions, Processes, Imaging, Stress Response Chemistry ... Glycobiology, Synthesis, Natural Products, Chemical Reactions Computers in Biology Bioinformatics, Modeling, Systems Biology, Data Visualization Diseases Cancer, ... 14. An Approximate Analytic Expression for the Flux Density of Scintillation Light at the Photocathode SciTech Connect Braverman, Joshua B; Harrison, Mark J; Ziock, Klaus-Peter 2012-01-01 The flux density of light exiting scintillator crystals is an important factor affecting the performance of radiation detectors, and is of particular importance for position sensitive instruments. Recent work by T. Woldemichael developed an analytic expression for the shape of the light spot at the bottom of a single crystal [1]. However, the results are of limited utility because there is generally a light pipe and photomultiplier entrance window between the bottom of the crystal and the photocathode. In this study, we expand Woldemichael s theory to include materials each with different indices of refraction and compare the adjusted light spot shape theory to GEANT 4 simulations [2]. Additionally, light reflection losses from index of refraction changes were also taken into account. We found that the simulations closely agree with the adjusted theory. 15. An approximate analytical expression for the nuclear quadrupole transverse relaxation rate of half-integer spins in liquids. PubMed Wu, Gang 2016-08-01 The nuclear quadrupole transverse relaxation process of half-integer spins in liquid samples is known to exhibit multi-exponential behaviors. Within the framework of Redfield's relaxation theory, exact analytical expressions for describing such a process exist only for spin-3/2 nuclei. As a result, analyses of nuclear quadrupole transverse relaxation data for half-integer quadrupolar nuclei with spin >3/2 must rely on numerical diagonalization of the Redfield relaxation matrix over the entire motional range. In this work we propose an approximate analytical expression that can be used to analyze nuclear quadrupole transverse relaxation data of any half-integer spin in liquids over the entire motional range. The proposed equation yields results that are in excellent agreement with the exact numerical calculations. 16. FINDING REGULATORY ELEMENTS USING JOINT LIKELIHOODS FOR SEQUENCE AND EXPRESSION PROFILE DATA. SciTech Connect IAN HOLMES, UC BERKELEY, CA, WILLIAM J. BRUNO, LANL 2000-08-20 A recent, popular method of finding promoter sequences is to look for conserved motifs up-stream of genes clustered on the basis of expression data. This method presupposes that the clustering is correct. Theoretically, one should be better able to find promoter sequences and create more relevant gene clusters by taking a unified approach to these two problems. We present a likelihood function for a sequence-expression model giving a joint likelihood for a promoter sequence and its corresponding expression levels. An algorithm to estimate sequence-expression model parameters using Gibbs sampling and Expectation/Maximization is described. A program, called kimono, that implements this algorithm has been developed and the source code is freely available over the internet. 17. Approximation algorithms PubMed Central Schulz, Andreas S.; Shmoys, David B.; Williamson, David P. 1997-01-01 Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science. PMID:9370525 18. The recognition of facial expressions of emotion in Alzheimer's disease: a review of findings. PubMed McLellan, Tracey; Johnston, Lucy; Dalrymple-Alford, John; Porter, Richard 2008-10-01 To provide a selective review of the literature on the recognition of facial expressions of emotion in Alzheimer's disease (AD), to evaluate whether these patients show variation in their ability to recognise different emotions and whether any such impairments are instead because of a general decline in cognition. A narrative review based on relevant articles identified from PubMed and PsycInfo searches from 1987 to 2007 using keywords 'Alzheimer's', 'facial expression recognition', 'dementia' and 'emotion processing'. Although the literature is as yet limited, with several methodological inconsistencies, AD patients show poorer recognition of facial expressions, with particular difficulty with sad expressions. It is unclear whether poorer performance reflects the general cognitive decline and/or verbal or spatial deficits associated with AD or whether the deficits reflect specific neuropathology. This under-represented field of study may help to extend our understanding of social functioning in AD. Future work requires more detailed analyses of ancillary cognitive measures, more ecologically valid facial displays of emotion and a reference situation that more closely approximates an actual social interaction. 19. Gene × smoking interactions on human brain gene expression: Finding common mechanisms in adolescents and adults PubMed Central Wolock, Samuel; Yates, Andrew; Petrill, Stephen A.; Bohland, Jason W.; Blair, Clancy; Li, Ning; Machiraju, Raghu; Huang, Kun; Bartlett, Christopher W. 2013-01-01 Background Numerous studies have examined gene × environment interactions (G×E) in cognitive and behavioral domains. However, these studies have been limited in that they have not been able to directly assess differential patterns of gene expression in the human brain. Here we assessed G×E interactions using two publically-available datasets to assess if DNA variation is associated with post-mortem brain gene expression changes based on smoking behavior, a biobehavioral construct that is part of a complex system of genetic and environmental influences. Methods We conducted an expression quantitative trait locus (eQTL) study on two independent human brain gene expression datasets assessing G×E for selected psychiatric genes and smoking status. We employed linear regression to model the significance of the Gene×Smoking interaction term, followed by meta-analysis across datasets. Results Overall, we observed that the effect of DNA variation on gene expression is moderated by smoking status. Expression of 16 genes were significantly associated with single nucleotide polymorphisms that demonstrated G×E effects. The strongest finding (p = 1.9×10−11) was neurexin 3-alpha (NRXN3), a synaptic cell-cell adhesion molecule involved in maintenance of neural connections (such as the maintenance of smoking behavior). Other significant G×E associations include four glutamate genes. Conclusions This is one of the first studies to demonstrate G×E effects within the human brain. In particular, this study implicated NRXN3 in the maintenance of smoking. The effect of smoking on NRXN3 expression and downstream behavior is different based upon SNP genotype, indicating that DNA profiles based on SNPs could be useful in understanding the effects of smoking behaviors. These results suggest that better measurement of psychiatric conditions, and the environment in post-mortem brain studies may yield an important avenue for understanding the biological mechanisms of G 20. Approximate expressions that describe the profiles of sessile and pendent drops for the cases of small Bond numbers and strong wetting Galaktionov, E. V.; Galaktionova, N. E.; Tropp, E. A. 2016-12-01 Variational formulations of the problems of sessile and pendent drops are given taking into account the force of gravity in the axially symmetric case. Approximate expressions that describe the surface profiles of these drops by the asymptotic method for small Bond numbers have been obtained by the linearization method in the case of strong wetting. 1. Glomerular expression and elevated serum Bcl-2 and Fas proteins in lupus nephritis: preliminary findings. PubMed Fathi, N A; Hussein, M R; Hassan, H I; Mosad, E; Galal, H; Afifi, N A 2006-11-01 Programmed cell death (apoptosis) is involved in glomerular injuries leading to glomerulonephritis. Bcl-2 and Fas are proteins that promote cell survival and death, respectively. This study tests the hypothesis that lupus nephritis is associated with alterations of Bcl-2 and Fas protein expression. Thirty-six patients with lupus nephritis and 10 controls (normal individuals) were included in this study. Bcl-2 and Fas positive cells were examined in kidney biopsies by immunohistochemistry. Bcl-2 and Fas serum levels were evaluated by enzyme-linked immunosorbent assay (ELISA). In the glomeruli of normal kidneys, Bcl-2 and Fas proteins were completely absent. In lupus nephritis patients, glomerular expression of Bcl-2 and Fas was seen in mesangial cells (1.3 +/- 0.1 and 2.0 +/- 0.1 for Bcl-2 and Fas, respectively). Similarly, a statistically significantly higher Bcl-2 (217.1 +/- 85.9) and Fas (767.9 +/- 271) serum levels were found in lupus patients compared to controls (148.6 +/- 87, 550.3 +/- 91 for Bcl-2 and Fas, P < 0.05). A direct correlation between serum Bcl-2 and Fas and chronicity index was also found. Compared to normal controls, lupus nephritis is associated with glomerular expression and elevated serum levels of Bcl-2 and Fas proteins. These findings suggest possible roles for Bcl-2 and Fas in glomerular injury during evolution of lupus nephritis. The diagnostic, prognostic and therapeutic ramifications of our findings are open to further investigation. 2. Oestrogen receptor-alpha and -beta expression in breast implant capsules: experimental findings and clinical correlates. PubMed Persichetti, Paolo; Segreto, Francesco; Carotti, Simone; Marangi, Giovanni Francesco; Tosi, Daniele; Morini, Sergio 2014-03-01 Myofibroblasts provide a force to decrease the surface area of breast implant capsules as the collagen matrix matures. 17-β-Oestradiol promotes myofibroblast differentiation and contraction. The aim of the study was to investigate the expression of oestrogen receptors α and β in capsular tissue. The study enrolled 70 women (80 capsules) who underwent expander or implant removal, following breast reconstruction. Specimens were stained with haematoxylin/eosin, Masson trichrome and immunohistochemistry and immunofluorescence stainings for alpha-smooth muscle actin (α-SMA), oestrogen receptor-alpha (ER-α) and oestrogen receptor-beta (ER-β). The relationship between anti-oestrogenic therapy and capsular severity was evaluated. A retrospective analysis of 233 cases of breast reconstruction was conducted. Myofibroblasts expressed ER-α, ER-β or both. In the whole sample, α-SMA score positively correlated with ER-α (p = 0.022) and ER-β expression (p < 0.004). ER-β expression negatively correlated with capsular thickness (p < 0.019). In capsules surrounding expanders α-SMA and ER-α, expressions negatively correlated with time from implantation (p = 0.002 and p = 0.016, respectively). The incidence of grade III-IV contracture was higher in patients who did not have anti-oestrogenic therapy (p < 0.036); retrospective analysis of 233 cases confirmed this finding (p < 0.0001). This study demonstrates the expression of oestrogen receptors in myofibroblasts of capsular tissue. A lower contracture severity was found in patients who underwent anti-oestrogenic therapy. 3. Exact expressions and improved approximations for interaction rates of neutrinos with free nucleons in a high-temperature, high-density gas NASA Technical Reports Server (NTRS) Schinder, Paul J. 1990-01-01 The exact expressions needed in the neutrino transport equations for scattering of all three flavors of neutrinos and antineutrinos off free protons and neutrons, and for electron neutrino absorption on neutrons and electron antineutrino absorption on protons, are derived under the assumption that nucleons are noninteracting particles. The standard approximations even with corrections for degeneracy, are found to be poor fits to the exact results. Improved approximations are constructed which are adequate for nondegenerate nucleons for neutrino energies from 1 to 160 MeV and temperatures from 1 to 50 MeV. 4. Exact expressions and improved approximations for interaction rates of neutrinos with free nucleons in a high-temperature, high-density gas NASA Technical Reports Server (NTRS) Schinder, Paul J. 1990-01-01 The exact expressions needed in the neutrino transport equations for scattering of all three flavors of neutrinos and antineutrinos off free protons and neutrons, and for electron neutrino absorption on neutrons and electron antineutrino absorption on protons, are derived under the assumption that nucleons are noninteracting particles. The standard approximations even with corrections for degeneracy, are found to be poor fits to the exact results. Improved approximations are constructed which are adequate for nondegenerate nucleons for neutrino energies from 1 to 160 MeV and temperatures from 1 to 50 MeV. 5. Approximate expression for the potential energy of the double-layer interaction between two parallel ion-penetrable membranes at small separations in an electrolyte solution. PubMed Ohshima, Hiroyuki 2010-10-01 An approximate expression for the potential energy of the double-layer interaction between two parallel similar ion-penetrable membranes in a symmetrical electrolyte solution is derived via a linearization method, in which the nonlinear Poisson-Boltzmann equations in the regions inside and outside the membranes are linearized with respect to the deviation of the electric potential from the Donnan potential. This approximation works quite well for small membrane separations h for all values of the density of fixed charges in the membranes (or the Donnan potential) and gives a correct limiting form of the interaction energy (or the interaction force) as h-->0. 6. Glomerular expression and elevated serum Bcl-2 and Fas proteins in lupus nephritis: preliminary findings PubMed Central Fathi, N A; Hussein, M R; Hassan, H I; Mosad, E; Galal, H; Afifi, N A 2006-01-01 Programmed cell death (apoptosis) is involved in glomerular injuries leading to glomerulonephritis. Bcl-2 and Fas are proteins that promote cell survival and death, respectively. This study tests the hypothesis that lupus nephritis is associated with alterations of Bcl-2 and Fas protein expression. Thirty-six patients with lupus nephritis and 10 controls (normal individuals) were included in this study. Bcl-2 and Fas positive cells were examined in kidney biopsies by immunohistochemistry. Bcl-2 and Fas serum levels were evaluated by enzyme-linked immunosorbent assay (ELISA). In the glomeruli of normal kidneys, Bcl-2 and Fas proteins were completely absent. In lupus nephritis patients, glomerular expression of Bcl-2 and Fas was seen in mesangial cells (1·3 ± 0·1 and 2·0 ± 0·1 for Bcl-2 and Fas, respectively). Similarly, a statistically significantly higher Bcl-2 (217·1 ± 85·9) and Fas (767·9 ± 271) serum levels were found in lupus patients compared to controls (148·6 ± 87, 550·3 ± 91 for Bcl-2 and Fas, P < 0·05). A direct correlation between serum Bcl-2 and Fas and chronicity index was also found. Compared to normal controls, lupus nephritis is associated with glomerular expression and elevated serum levels of Bcl-2 and Fas proteins. These findings suggest possible roles for Bcl-2 and Fas in glomerular injury during evolution of lupus nephritis. The diagnostic, prognostic and therapeutic ramifications of our findings are open to further investigation. PMID:17034587 7. Approximate spatial reasoning NASA Technical Reports Server (NTRS) Dutta, Soumitra 1988-01-01 A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning. 8. Approximate spatial reasoning NASA Technical Reports Server (NTRS) Dutta, Soumitra 1988-01-01 A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning. 9. Finding Meaning in Written Emotional Expression by Family Caregivers of Persons With Dementia. PubMed Butcher, Howard K; Gordon, Jean K; Ko, Ji Woon; Perkhounkova, Yelena; Cho, Jun Young; Rinner, Andrew; Lutgendorf, Susan 2016-12-01 This study tested the effect of written emotional expression on the ability to find meaning in caregiving and the effects of finding meaning on emotional state and psychological burden in 91 dementia family caregivers. In a pretest-posttest design, participants were randomly assigned to either an experimental or a comparison group. Experimental caregivers (n = 57) wrote about their deepest thoughts and feelings about caring for a family member with dementia, whereas those in the comparison group (n = 34) wrote about nonemotional topics. Results showed enhanced meaning-making abilities in experimental participants relative to comparison participants, particularly for those who used more positive emotion words. Improved meaning-making ability was in turn associated with psychological benefits at posttest, but experimental participants did not show significantly more benefit than comparison participants. We explore the mediating roles of the meaning-making process as well as some of the background characteristics of the individual caregivers and their caregiving environments. © The Author(s) 2016. 10. Approximate forms of the pair-density-functional kinetic energy on the basis of a rigorous expression with coupling-constant integration Higuchi, Katsuhiko; Higuchi, Masahiko 2014-12-01 We propose approximate kinetic energy (KE) functionals of the pair-density (PD)-functional theory on the basis of the rigorous expression with the coupling-constant integration (RECCI) that has been recently derived [Phys. Rev. A 85, 062508 (2012), 10.1103/PhysRevA.85.062508]. These approximate functionals consist of the noninteracting KE and correlation energy terms. It is found that the Thomas-Fermi-Weizsäcker functional is shown to be better as the noninteracting KE term than the Thomas-Fermi and Gaussian model functionals. It is also shown that the correlation energy term is also indispensable for the reduction of the KE error, i.e., reductions of both inappropriateness of the approximate functional and error of the resultant PD. Concerning the correlation energy term, we further propose an approximate functional in addition to using the existing familiar functionals. This functional satisfies the scaling property of the KE functional, and yields a reasonable PD in a sense that the KE, electron-electron interaction, and potentials energies tend to be improved with satisfying the virial theorem. The present results not only suggest the usefulness of the RECCI but also provide the guideline for the further improvement of the RECCI-based KE functional. 11. Low-momentum-transfer nonrelativistic limit of the relativistic impulse approximation expression for Compton-scattering doubly differential cross sections and characterization of their relativistic contributions SciTech Connect LaJohn, L. A. 2010-04-15 The nonrelativistic (nr) impulse approximation (NRIA) expression for Compton-scattering doubly differential cross sections (DDCS) for inelastic photon scattering is recovered from the corresponding relativistic expression (RIA) of Ribberfors [Phys. Rev. B 12, 2067 (1975)] in the limit of low momentum transfer (q{yields}0), valid even at relativistic incident photon energies {omega}{sub 1}>m provided that the average initial momentum of the ejected electron is not too high, that is, m using nr expressions when {theta} is small. For example, a 1% accuracy can be obtained when {omega}{sub 1}=1 MeV if {theta}<20 deg. However as {omega}{sub 1} increases into the MeV range, the maximum {theta} at which an accurate Compton peak can be obtained from nr expressions approaches closer to zero, because the {theta} at which the relativistic shift of CP to higher energy is greatest, which starts at 180 deg. when {omega}{sub 1}<300 keV, begins to decrease, approaching zero even though the {theta} at which the relativistic increase in the CP magnitude remains greatest around {theta}=180 deg. The relativistic contribution to the prediction of Compton doubly differential cross sections (DDCS) is characterized in simple terms using Ribberfors further approximation to his full RIA expression. This factorable form is given by DDCS=KJ, where K is the kinematic factor and J the Compton profile. This form makes it possible to account for the relativistic shift of CP to higher energy and the increase in the CP magnitude as being due to the dependence of J(p{sub min},{rho}{sub rel}) (where p{sub min} is the relativistic version of the z 12. Green Ampt approximations Barry, D. A.; Parlange, J.-Y.; Li, L.; Jeng, D.-S.; Crapper, M. 2005-10-01 The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10 -5%. This error is orders of magnitude lower than any existing analytical approximations. 13. Gene × Smoking Interactions on Human Brain Gene Expression: Finding Common Mechanisms in Adolescents and Adults ERIC Educational Resources Information Center Wolock, Samuel L.; Yates, Andrew; Petrill, Stephen A.; Bohland, Jason W.; Blair, Clancy; Li, Ning; Machiraju, Raghu; Huang, Kun; Bartlett, Christopher W. 2013-01-01 Background: Numerous studies have examined gene × environment interactions (G × E) in cognitive and behavioral domains. However, these studies have been limited in that they have not been able to directly assess differential patterns of gene expression in the human brain. Here, we assessed G × E interactions using two publically available datasets… 14. Gene × Smoking Interactions on Human Brain Gene Expression: Finding Common Mechanisms in Adolescents and Adults ERIC Educational Resources Information Center Wolock, Samuel L.; Yates, Andrew; Petrill, Stephen A.; Bohland, Jason W.; Blair, Clancy; Li, Ning; Machiraju, Raghu; Huang, Kun; Bartlett, Christopher W. 2013-01-01 Background: Numerous studies have examined gene × environment interactions (G × E) in cognitive and behavioral domains. However, these studies have been limited in that they have not been able to directly assess differential patterns of gene expression in the human brain. Here, we assessed G × E interactions using two publically available datasets… 15. Finding the Muse: Teaching Musical Expression to Adolescents in the One-to-One Studio Environment ERIC Educational Resources Information Center McPhee, Eleanor A. 2011-01-01 One-to-one music lessons are a common and effective way of learning a musical instrument. This investigation into one-to-one music teaching at the secondary school level explores the teaching of musical expression by two instrumental music teachers of brass and strings. The lessons of the two teachers with two students each were video recorded… 16. p16 Expression in Prostate Cancer and Nonmalignant Lesions: Novel Findings and Review of the Literature. PubMed Remo, Andrea; Pancione, Massimo; Zanella, Caterina; Manfrin, Erminia 2016-03-01 Prostatic specimens occasionally may contain proliferative foci of the small atypical acini that display some but not all features of prostate carcinoma. p504s is the only prostatic cancer (PC)-specific marker that, in combination with basal cell markers, help in the diagnosis of malignant lesions. Very little is known about the diagnostic importance of p16 in primary prostate carcinoma and nonmalignant elements. We recruited 137 of routinely diagnostic prostatic specimens (between 2009 and 2013), which consisted of 21 prostatectomy, 15 transurethral prostatic resection, and 101 needle biopsy. We evaluated p16, in comparison with p504s, in prostatic carcinoma and benign glands. In this study, both nuclear and cytoplasmatic p16 expression were considered positive. We observed p16 expression in 86% of PC specimens and 16% of benign elements (P=0.001). Interestingly, p16 alone retained a high diagnostic potential in prostatectomy (95%) and in needle biopsy (84%), exhibiting a close association with PC. p504s had a high sensitivity (97%) and predictive negative value (98%) but a low specificity (71%) and predictive positive value (63%). In contrast, p16-positive expression showed a higher specificity (84%) and predictive positive value (74%) than p504s. Two prostatic carcinoma negative for p504s were positive for p16, whereas 7 cases negative for p16 were positive for p504s, and notably none was negative for both markers. In prostatectomy, p16 showed a higher diagnostic accuracy but not on transurethral prostatic resection. In needle biopsies, both markers were complementary, indicating that their combined detection may help in performing an accurate diagnosis.In conclusion, our data suggest that p16 expression is significantly enhanced in prostate carcinoma as compared with nonmalignant elements. Our results provide evidence that p16 and p504s together could improve the diagnosis of PC in prostatectomy and needle biopsies. 17. Efficiency Analysis of Competing Tests for Finding Differentially Expressed Genes in Lung Adenocarcinoma PubMed Central Jordan, Rick; Patel, Satish; Hu, Hai; Lyons-Weiler, James 2008-01-01 In this study, we introduce and use Efficiency Analysis to compare differences in the apparent internal and external consistency of competing normalization methods and tests for identifying differentially expressed genes. Using publicly available data, two lung adenocarcinoma datasets were analyzed using caGEDA (http://bioinformatics2.pitt.edu/GE2/GEDA.html) to measure the degree of differential expression of genes existing between two populations. The datasets were randomly split into at least two subsets, each analyzed for differentially expressed genes between the two sample groups, and the gene lists compared for overlapping genes. Efficiency Analysis is an intuitive method that compares the differences in the percentage of overlap of genes from two or more data subsets, found by the same test over a range of testing methods. Tests that yield consistent gene lists across independently analyzed splits are preferred to those that yield less consistent inferences. For example, a method that exhibits 50% overlap in the 100 top genes from two studies should be preferred to a method that exhibits 5% overlap in the top 100 genes. The same procedure was performed using all available normalization and transformation methods that are available through caGEDA. The ‘best’ test was then further evaluated using internal cross-validation to estimate generalizable sample classification errors using a Naïve Bayes classification algorithm. A novel test, termed D1 (a derivative of the J5 test) was found to be the most consistent, and to exhibit the lowest overall classification error, and highest sensitivity and specificity. The D1 test relaxes the assumption that few genes are differentially expressed. Efficiency Analysis can be misleading if the tests exhibit a bias in any particular dimension (e.g. expression intensity); we therefore explored intensity-scaled and segmented J5 tests using data in which all genes are scaled to share the same intensity distribution range 18. Efficiency analysis of competing tests for finding differentially expressed genes in lung adenocarcinoma. PubMed Jordan, Rick; Patel, Satish; Hu, Hai; Lyons-Weiler, James 2008-01-01 In this study, we introduce and use Efficiency Analysis to compare differences in the apparent internal and external consistency of competing normalization methods and tests for identifying differentially expressed genes. Using publicly available data, two lung adenocarcinoma datasets were analyzed using caGEDA (http://bioinformatics2.pitt.edu/GE2/GEDA.html) to measure the degree of differential expression of genes existing between two populations. The datasets were randomly split into at least two subsets, each analyzed for differentially expressed genes between the two sample groups, and the gene lists compared for overlapping genes. Efficiency Analysis is an intuitive method that compares the differences in the percentage of overlap of genes from two or more data subsets, found by the same test over a range of testing methods. Tests that yield consistent gene lists across independently analyzed splits are preferred to those that yield less consistent inferences. For example, a method that exhibits 50% overlap in the 100 top genes from two studies should be preferred to a method that exhibits 5% overlap in the top 100 genes. The same procedure was performed using all available normalization and transformation methods that are available through caGEDA. The 'best' test was then further evaluated using internal cross-validation to estimate generalizable sample classification errors using a Naïve Bayes classification algorithm. A novel test, termed D1 (a derivative of the J5 test) was found to be the most consistent, and to exhibit the lowest overall classification error, and highest sensitivity and specificity. The D1 test relaxes the assumption that few genes are differentially expressed. Efficiency Analysis can be misleading if the tests exhibit a bias in any particular dimension (e.g. expression intensity); we therefore explored intensity-scaled and segmented J5 tests using data in which all genes are scaled to share the same intensity distribution range 19. Pathologic finding of increased expression of interleukin-17 in the synovial tissue of rheumatoid arthritis patients PubMed Central Li, Ning; Wang, Jun C; Liang, Toong H; Zhu, Ming H; Wang, Jia Y; Fu, Xue L; Zhou, Jie R; Zheng, Song G; Chan, Paul; Han, Jie 2013-01-01 Rheumatoid arthritis (RA) is a common autoimmune disease of chronic systemic inflammatory disorder that will affect multiple tissues and organs such as skin, heart or lungs; but it principally attacks the joints, producing a nonsuppurative inflammatory and proliferative synovitis that often progresses to major damaging of articular cartilage and joint ankylosis. Although the definite etiology is still unknown, recent studies suggest that T-helper cells (Th17) may play a pivotal role in the pathogenesis of RA. And interleukin-17 (IL-17), which is a cytokine of Th17 cells, may be a key factor in the occurrence of RA. The binding of IL-17 to specific receptor results in the expression of fibroblasts, endothelial and epithelial cells and also synthesis of several major factors such as tumor necrosis factor alpha (TNF-α), IL-1β that result in the structural damage of RA joints. Though some previous studies have shown that IL-17 exists in the synovium of RA, few has definite proof quantitatively by pathology about its existence in synovial membrane. This study comprised of 30 RA patients and 10 healthy control, pathologic study of the synovial membrane showed increased expression of IL-17 in the synovial tissue of RA patients, the intensity is compatible with clinical severity of disease as validated by DAS28 score and disease duration. Northern blot study also confirmed the increased expression of IL-17 in the synovial tissues. This study sheds further light that IL-17 may be a key factor in the pathogenesis of RA and a determinant of disease severity. PMID:23826419 20. Exact expressions and accurate approximations for the dependences of radius and index of refraction of solutions of inorganic solutes on relative humidity SciTech Connect Lewis, E.R.; Schwartz, S. 2010-03-15 Light scattering by aerosols plays an important role in Earth’s radiative balance, and quantification of this phenomenon is important in understanding and accounting for anthropogenic influences on Earth’s climate. Light scattering by an aerosol particle is determined by its radius and index of refraction, and for aerosol particles that are hygroscopic, both of these quantities vary with relative humidity RH. Here exact expressions are derived for the dependences of the radius ratio (relative to the volume-equivalent dry radius) and index of refraction on RH for aqueous solutions of single solutes. Both of these quantities depend on the apparent molal volume of the solute in solution and on the practical osmotic coefficient of the solution, which in turn depend on concentration and thus implicitly on RH. Simple but accurate approximations are also presented for the RH dependences of both radius ratio and index of refraction for several atmospherically important inorganic solutes over the entire range of RH values for which these substances can exist as solution drops. For all substances considered, the radius ratio is accurate to within a few percent, and the index of refraction to within ~0.02, over this range of RH. Such parameterizations will be useful in radiation transfer models and climate models. 1. The lived experience of women with cancer: phenomenological findings expressed through poetry. PubMed Duffy, Lynne; Aquino-Russell, Catherine 2007-01-01 Cancer rates for Canadian women between the ages of 22 and 44 are increasing. Improved survival times and more treatment choices, however create new challenges. Little research has been done to uncover the lived experience of long-term survival. This pilot study describes the meaning of living with cancer for three Canadian women who were diagnosed more than four years ago. The process of inquiry was Giorgi's descriptive phenomenological method for analysis-synthesis of a general structural description (the meaning of the experience). The findings have been interpreted creatively through poetry in an effort to enhance understanding of the experience of living with cancer Each section of the poem is discussed in relation to the literature to encourage nurses and other health professionals to consider the importance of understanding patients' lived experiences and the meanings they ascribe, in order to provide quality, holistic, and individualized care. 2. Anoctamin 5 muscular dystrophy in Denmark: prevalence, genotypes, phenotypes, cardiac findings, and muscle protein expression. PubMed Witting, Nanna; Duno, Morten; Petri, Helle; Krag, Thomas; Bundgaard, Henning; Kober, Lars; Vissing, John 2013-08-01 Since the initial description in 2010 of anoctamin 5 deficiency as a cause of muscular dystrophy, a handful of papers have described this disease in cases of mixed populations. We report the first large regional study and present data on new aspects of prevalence, muscular and cardiac phenotypic characteristics, and muscle protein expression. All patients in our neuromuscular unit with genetically unclassified, recessive limb girdle muscular dystrophy (LGMD2), Miyoshi-type distal myopathy (MMD) or persistent asymptomatic hyperCK-emia (PACK) were assessed for mutations in the ANO5 gene. Genetically confirmed patients were evaluated with muscular and cardiopulmonary examination. Among 40 unclassified patients (28 LGMD2, 5 MMD, 7 PACK), 20 were homozygous or compound heterozygous for ANO5 mutations, (13 LGMD2, 5 MMD, 2 PACK). Prevalence of ANO5 deficiency in Denmark was estimated at 1:100.000 and ANO5 mutations caused 11 % of our total cohort of LGMD2 cases making it the second most common LGMD2 etiology in Denmark. Eight patients complained of dysphagia and 3 dated symptoms of onset in childhood. Cardiac examinations revealed increased frequency of premature ventricular contractions. Four novel putative pathogenic mutations were discovered. Total prevalence and distribution of phenotypes of ANO5 disease in a representative regional cohort are described for the first time. A high prevalence of ANO5 deficiency was found among patients with unclassified LGMD2 (46 %) and MMD (100 %). The high incidence of reported dysphagia is a new phenotypic feature not previously reported, and cardiac investigations revealed that ANO5-patients may have an increased risk of ventricular arrhythmia. 3. Somatostatin and dopamine receptor expression in neuroendocrine neoplasms: correlation of immunohistochemical findings with somatostatin receptor scintigraphy visual scores. PubMed Diakatou, Evanthia; Alexandraki, Krystallenia I; Tsolakis, Apostolos V; Kontogeorgos, George; Chatzellis, Eleftherios; Leonti, Anastasia; Kaltsas, Gregory A 2015-09-01 The expression of somatostatin (sstr1-5) and dopamine (DR) receptors in neuroendocrine neoplasms (NENs) facilitates diagnosis by tumour visualization with somatostatin receptor scintigraphy (SRS) and directs towards specific treatment with peptide receptor radionuclide therapy (PRRT) with radiolabelled somatostatin analogues. To investigate the co-expression of sstrs, D2R in relation to pre-operative SRSs in NENs. Prospective two-centre study. We analysed pre-operative SRS of 60 patients [44 with gastrointestinal (GI) NENs and 16 with lung NENs] and compared SRS results with immunohistochemical (IHC) reactivity for sstr2, sstr3, sstr5 in sample tissues from primary (n = 54) and metastatic (n = 27) lesions and IHC reactivity for D2R in 23 samples from primary GI-NENs lesions. Sstr2 was the commonest sstr expressed (65·4%) and was co-expressed with sstr3 and sstr5 in 32·1% and 24·7% of the specimens, respectively. In 67 of 81 specimens (82·7%), there was concordance of sstr2 immunohistochemistry with SRS findings (P < 0·001). D2R was expressed in only 8 of 23 (34·8%) GI-NENs while was co-expressed with sstr2 in all cases. SRS grade, as per Krenning scale, was higher in metastatic foci, large-size (>2 cm) tumours and GI-NENs, whereas sstr2 intensity was greater in GI compared to lung NENs. SRS grade showed higher correlation with sstr2 (r = 0·6, P < 0·001) and D2R (r = 0·5, P < 0·001) IHC intensity scores than tumour size (r = 0·4, P < 0·001) and sstr3 (r = 0·4, P < 0·001) intensity score. Sstr2 IHC expression and SRS are useful tools for the diagnosis and management of NENs because they display a high concordance. IHC expression of DR2 seems to be of potential clinical significance in GI-NENs tumours. © 2015 John Wiley & Sons Ltd. 4. Multicriteria approximation through decomposition SciTech Connect Burch, C.; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E. 1998-06-01 The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of their technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. Their method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) the authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing; (2) they also show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems. 5. Multicriteria approximation through decomposition SciTech Connect Burch, C. \|; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E. \| 1997-12-01 The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems. 6. Bioinformatic methods for finding differentially expressed genes in cDNA libraries, applied to the identification of tumour vascular targets. PubMed Herbert, John M J; Stekel, Dov J; Mura, Manuela; Sychev, Michail; Bicknell, Roy 2011-01-01 The aim of this method is to guide a bench scientist to maximise cDNA library analyses to predict biologically relevant genes to pursue in the laboratory. Many groups have successfully utilised cDNA libraries to discover novel and/or differentially expressed genes in pathologies of interest. This is despite the high cost of cDNA library production using the Sanger method of sequencing, which produces modest numbers of expressed sequences compared to the total transcriptome. Both public and propriety cDNA libraries can be utilised in this way, and combining biologically relevant data can reveal biologically interesting genes. Pivotal to the quality of target identification are the selection of biologically relevant libraries, the accuracy of Expressed Sequence Tag to gene assignment, and the statistics used. The key steps, methods, and tools used to this end will be described using vascular targeting as an example. With the advent of next-generation sequencing, these or similar methods can be applied to find novel genes with this new source of data. 7. A phase I clinical trial of interferon-beta gene therapy for high-grade glioma: novel findings from gene expression profiling and autopsy. PubMed Wakabayashi, Toshihiko; Natsume, Atsushi; Hashizume, Yoshio; Fujii, Masazumi; Mizuno, Masaaki; Yoshida, Jun 2008-04-01 High-grade gliomas are highly lethal neoplasms representing approximately 20% of all intracranial tumors. Cationic liposome-mediated interferon-beta (IFN-beta) gene transfer has been found to induce regression of experimental glioma. We have previously performed a pilot clinical trial to evaluate the safety and effectiveness of this IFN-beta gene therapy in five patients with high-grade glioma. Two patients showed more than 50% reduction while others had stable disease 10 weeks after treatment initiation. To identify alterations in gene expression in brain tumors 2 weeks after the gene therapy trial, we used a microarray technology and Gene Ontology analysis. The results were validated by patients' clinical course and findings of histology and autopsy. Using hierarchical clustering and principal component analysis, five series of gene therapy trials were classified according to the response to IFN-beta gene therapy. Significant changes in gene expression related to immunoresponse and apoptosis were observed. Moreover, novel patterns of altered gene expression, such as inhibition of neovascularization, were identified, suggesting the involvement of pathways reported previously as not involved. Autopsy and histological examinations revealed dramatic changes in the tumor tissues after therapy in all patients. Many tumor cells showed necrotic changes, and immunohistochemistry identified numerous CD8-positive lymphocytes and macrophages infiltrating the tumor and surrounding tissues; these were probably the effects of therapy. Simultaneously, CD34-immunoreactive vessels were notably decreased in the vector-injected brain. This study facilitates the understanding of the antitumor mechanism and helps identify candidate target molecules for new approaches. However, additional clinical trials are warranted. (c) 2008 John Wiley & Sons, Ltd. 8. Optimizing the Zeldovich approximation NASA Technical Reports Server (NTRS) Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F. 1994-01-01 We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment 9. [A case of intractable epilepsy: diagnosis of tuberous sclerosis based on histopathological findings and immunohistochemical expression of hamartin and tuberin]. PubMed Takaishi, Yasuko; Hashimoto, Kiyoshi; Fujino, Osamu; Arai, Nobutaka; Mizuguchi, Masashi; Maehara, Taketoshi; Shimizu, Hiroyuki 2002-01-01 We report here a 14-year-old boy suffering from intractable epilepsy since the age of 2. Neuroimaging showed a lesion in the left temporal lobe. He underwent resection of the left temporal lobe and multiple subpial transection of the left frontal lobe at the age of 8. Histopathological findings of surgical specimens were similar to those of tubers of tuberous sclerosis (TSC), although he had no other TSC stigmata. To discriminate from cortical dysplasia grade III, we examined the immunohistochemical expression of hamartin and tuberin, the TSC1 and TSC2 gene products. Based on results, we diagnosed this case as having TSC. He has been seizure free since the operation. Although lower than preoperatively, his intelligence quotient has not been declining progressively. 10. Toxicological Study No. 75-51-YJ81-93, 4-Amino-2-Nitrotoluene (4A2NT) Oral Approximate Lethal Dose 14-day Range Finding 90-Day Subchronic Feeding Studies in Rats, August 1991-November 1993 DTIC Science & Technology 1994-07-01 NOVEMBER 1993 1. PURPOSE. The oral approximate lethal dose study was conducted todetennine an approximate dosage range at which to begin the 14-day...5000 mg/Kg. The 14-day range fmding study suggested a probable compound related effect in the薘~m (high dose ) exposure groups of both sexes and a...possible compound related effect mIlle 1000 ppm (middle dose ) exposure groups of both sexes. An NOAEL was not established for the 90-day subchronic 11. Interpolation and Approximation Theory. ERIC Educational Resources Information Center Kaijser, Sten 1991-01-01 Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH) 12. Rapid light-induced shifts in opsin expression: finding new opsins, discerning mechanisms of change, and implications for visual sensitivity. PubMed Fuller, Rebecca C; Claricoates, Kristin M 2011-08-01 13. Approximate flavor symmetries SciTech Connect Rasin, A. 1994-04-01 We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed. 14. Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. 1. Approximate expression for the free energy of hydrophobic association based on a Gaussian-overlap model. PubMed Makowski, Mariusz; Liwo, Adam; Scheraga, Harold A 2007-03-22 A physics-based model is proposed to derive approximate analytical expressions for the cavity component of the free energy of hydrophobic association of spherical and spheroidal solutes in water. The model is based on the difference between the number and context of the water molecules in the hydration sphere of a hydrophobic dimer and of two isolated hydrophobic solutes. It is assumed that the water molecules touching the convex part of the molecular surface of the dimer and those in the hydration spheres of the monomers contribute equally to the free energy of solvation, and those touching the saddle part of the molecular surface of the dimer result in a more pronounced increase in free energy because of their more restricted mobility (entropy loss) and fewer favorable electrostatic interactions with other water molecules. The density of water in the hydration sphere around a single solute particle is approximated by the derivative of a Gaussian centered on the solute molecule with respect to its standard deviation. On the basis of this approximation, the number of water molecules in different parts of the hydration sphere of the dimer is expressed in terms of the first and the second mixed derivatives of the two Gaussians centered on the first and second solute molecules, respectively, with respect to the standard deviations of these Gaussians, and plausible analytical expressions for the cavity component of the hydrophobic-association energy of spherical and spheroidal solutes are introduced. As opposed to earlier hydration-shell models, our expressions reproduce the desolvation maxima in the potentials of mean force of pairs of nonpolar solutes in water, and their advantage over the models based on molecular-surface area is that they have continuous gradients in the coordinates of solute centers. 15. Approximation of Laws Niiniluoto, Ilkka 2014-03-01 Approximation of laws is an important theme in the philosophy of science. If we can make sense of the idea that two scientific laws are "close" to each other, then we can also analyze such methodological notions as approximate explanation of laws, approximate reduction of theories, approximate empirical success of theories, and approximate truth of laws. Proposals for measuring the distance between quantitative scientific laws were given in Niiniluoto (1982, 1987). In this paper, these definitions are reconsidered as a response to the interesting critical remarks by Liu (1999). 16. IMP-3 EXPRESSION IN BENIGN MELANOCYTIC NEVI, DYSPLASTIC NEVI AND MALIGNANT MELANOMA: PRELIMINARY FINDINGS IN BULGARIAN PATIENTS. PubMed Chokoeva, A A; Ananiev, J; Wollina, U; Tana, C; Lotti, T; Cardoso, J C; Tchernev, G 2015-01-01 IMP-3 is generally considered as an oncofetal protein, which plays a critical role in regulation of cell proliferation via an IGF-II-dependent pathway in K562 leukemia cells. IMP-3 expression has been detected in malignancies with various origins, while its appearance in adult tissue is generally considered abnormal, with some exceptions. IMP3 is also considered a prognostic biomarker in patients with renal cell carcinoma and clear-cell type ovarian carcinoma, hepatocellular carcinoma, pancreatic ductal adenocarcinoma and in patients with poorly differentiated thyroid carcinoma and uterine cervical carcinomas, testicular cancer and malignant melanoma. To our knowledge, no more than 4 PubMed-indexed studies have investigated the expression of IMP-3 in melanocytic lesions, namely its role in the differentiation between benign and malignant neoplasms. We investigated the expression of IMP-3 in a small series of benign melanocytic lesions, dysplastic nevi and melanomas, aiming to establish its significance as a marker for their distinction, comparing the results with those from the literature. IMP- 3 immunostaining was performed in 30 melanocytic lesions: 10 malignant melanomas, 10 dysplastic nevi and 10 benign melanocytic nevi. Our results revealed expression in 20% of dysplastic lesions and 40% of melanoma cases, while none of the benign nevi showed positive expression. These data contradict some of the results from other studies and raise some questions regarding the correlation between IMP- 3 and the degree of dysplasia of melanocytic nevi, as well as its potential relationship with prognostic parameters in melanoma, including tumor thickness and mitotic rate. Our results suggest that IMP-3 expression could be only an auxiliary marker for differentiation between dysplastic nevi and benign nevi, since although it is not expressed in all dysplastic lesions, staining correlates with the degree of dysplasia/atypia. It seems that IMP-3 expression is not a useful 17. Approximate symmetries of Hamiltonians Chubb, Christopher T.; Flammia, Steven T. 2017-08-01 We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest. 18. Approximation method for the kinetic Boltzmann equation NASA Technical Reports Server (NTRS) Shakhov, Y. M. 1972-01-01 The further development of a method for approximating the Boltzmann equation is considered and a case of pseudo-Maxwellian molecules is treated in detail. A method of approximating the collision frequency is discussed along with a method for approximating the moments of the Boltzmann collision integral. Since the return collisions integral and the collision frequency are expressed through the distribution function moments, use of the proposed methods make it possible to reduce the Boltzmann equation to a series of approximating equations. 19. Finding immune gene expression differences induced by marine bacterial pathogens in the deep-sea hydrothermal vent mussel Bathymodiolus azoricus Martins, E.; Queiroz, A.; Serrão Santos, R.; Bettencourt, R. 2013-02-01 The deep-sea hydrothermal vent mussel Bathymodiolus azoricus lives in a natural environment characterized by extreme conditions of hydrostatic pressure, temperature, pH, high concentrations of heavy metals, methane and hydrogen sulphide. The deep-sea vent biological systems represent thus the opportunity to study and provide new insights into the basic physiological principles that govern the defense mechanisms in vent animals and to understand how they cope with microbial infections. Hence, the importance of understanding this animal's innate defense mechanisms, by examining its differential immune gene expressions toward different pathogenic agents. In the present study, B. azoricus mussels were infected with single suspensions of marine bacterial pathogens, consisting of Vibrio splendidus, Vibrio alginolyticus, or Vibrio anguillarum, and a pool of these Vibrio strains. Flavobacterium suspensions were also used as an irrelevant bacterium. Gene expression analyses were carried out using gill samples from animals dissected at 12 h and 24 h post-infection times by means of quantitative-Polymerase Chain Reaction aimed at targeting several immune genes. We also performed SDS-PAGE protein analyses from the same gill tissues. We concluded that there are different levels of immune gene expression between the 12 h and 24 h exposure times to various bacterial suspensions. Our results from qPCR demonstrated a general pattern of gene expression, decreasing from 12 h over 24 h post-infection. Among the bacteria tested, Flavobacterium is the microorganism species inducing the highest gene expression level in 12 h post-infections animals. The 24 h infected animals revealed, however, greater gene expression levels, using V. splendidus as the infectious agent. The SDS-PAGE analysis also pointed at protein profile differences between 12 h and 24 h, particularly around a protein area, of 18 KDa molecular mass, where most dissimilarities were found. Multivariate analyses 20. Finding immune gene expression differences induced by marine bacterial pathogens in the Deep-sea hydrothermal vent mussel Bathymodiolus azoricus Martins, E.; Queiroz, A.; Serrão Santos, R.; Bettencourt, R. 2013-11-01 The deep-sea hydrothermal vent mussel Bathymodiolus azoricus lives in a natural environment characterised by extreme conditions of hydrostatic pressure, temperature, pH, high concentrations of heavy metals, methane and hydrogen sulphide. The deep-sea vent biological systems represent thus the opportunity to study and provide new insights into the basic physiological principles that govern the defense mechanisms in vent animals and to understand how they cope with microbial infections. Hence, the importance of understanding this animal's innate defense mechanisms, by examining its differential immune gene expressions toward different pathogenic agents. In the present study, B. azoricus mussels were infected with single suspensions of marine bacterial pathogens, consisting of Vibrio splendidus, Vibrio alginolyticus, or Vibrio anguillarum, and a pool of these Vibrio bacteria. Flavobacterium suspensions were also used as a non-pathogenic bacterium. Gene expression analyses were carried out using gill samples from infected animals by means of quantitative-Polymerase Chain Reaction aimed at targeting several immune genes. We also performed SDS-PAGE protein analyses from the same gill tissues. We concluded that there are different levels of immune gene expression between the 12 h to 24 h exposure times to various bacterial suspensions. Our results from qPCR demonstrated a general pattern of gene expression, decreasing from 12 h over 24 h post-infection. Among the bacteria tested, Flavobacterium is the bacterium inducing the highest gene expression level in 12 h post-infections animals. The 24 h infected animals revealed, however, greater gene expression levels, using V. splendidus as the infectious agent. The SDS-PAGE analysis also pointed at protein profile differences between 12 h and 24 h, particularly evident for proteins of 18-20 KDa molecular mass, where most dissimilarity was found. Multivariate analyses demonstrated that immune genes, as well as experimental 1. New strategies in diffuse large B-cell lymphoma: translating findings from gene expression analyses into clinical practice. PubMed Friedberg, Jonathan W 2011-10-01 Gene expression profiling has had a major impact on our understanding of the biology and heterogeneity of diffuse large B-cell lymphoma (DLBCL). Using this technology, investigators can identify biologic subgroups of DLBCL that provide unique targets for rational therapeutic intervention. This review summarizes these potential targets and updates the progress of clinical development of exciting novel agents for the treatment of DLBCL. Results of ongoing studies suggest that in the near future, we will be able to use gene expression profiling, or an accurate surrogate, to define the best therapeutic approach for individual patients with DLBCL. ©2011 AACR 2. Compressive Imaging via Approximate Message Passing DTIC Science & Technology 2015-09-04 We propose novel compressive imaging algorithms that employ approximate message passing (AMP), which is an iterative signal estimation algorithm that...Approved for Public Release; Distribution Unlimited Final Report: Compressive Imaging via Approximate Message Passing The views, opinions and/or findings...Research Triangle Park, NC 27709-2211 approximate message passing , compressive imaging, compressive sensing, hyperspectral imaging, signal reconstruction 3. Approximating random quantum optimization problems Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L. 2013-06-01 We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem k-body quantum satisfiability (k-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random k-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random k-QSAT in a two-dimensional energy-density-clause-density space. 4. Adaptive approximation models in optimization SciTech Connect Voronin, A.N. 1995-05-01 The paper proposes a method for optimization of functions of several variables that substantially reduces the number of objective function evaluations compared to traditional methods. The method is based on the property of iterative refinement of approximation models of the optimand function in approximation domains that contract to the extremum point. It does not require subjective specification of the starting point, step length, or other parameters of the search procedure. The method is designed for efficient optimization of unimodal functions of several (not more than 10-15) variables and can be applied to find the global extremum of polymodal functions and also for optimization of scalarized forms of vector objective functions. 5. Anger expression and sleep quality in patients with coronary heart disease: findings from the Heart and Soul Study. PubMed Caska, Catherine M; Hendrickson, Bethany E; Wong, Michelle H; Ali, Sadia; Neylan, Thomas; Whooley, Mary A 2009-04-01 To evaluate if anger expression affects sleep quality in patients with coronary heart disease (CHD). Research has indicated that poor sleep quality independently predicts adverse outcomes in patients with CHD. Risk factors for poor sleep quality include older age, socioeconomic factors, medical comorbidities, lack of exercise, and depression. We sought to examine the association of anger expression with sleep quality in 1020 outpatients with CHD from the Heart and Soul Study. We assessed anger-in, anger-out, and anger temperament, using the Spielberger State-Trait Anger Expression Inventory 2, and measured sleep quality, using items from the Cardiovascular Health Study and Pittsburgh Sleep Quality Index. We used multivariate analysis of variance to examine the association between anger expression and sleep quality, adjusting for potential confounding variables. Each standard deviation (SD) increase in anger-in was associated with an 80% greater odds of poor sleep quality (odds ratio (OR) = 1.8, 95% Confidence Interval (CI) = 1.6-2.1; p < .0001). This association remained strong after adjusting for demographics, comorbidities, lifestyle factors, medications, cardiac function, depressive symptoms, anger-out, and anger temperament (adjusted OR = 1.4, 95% CI = 1.5-1.7; p = .001). In the same model, each SD increase in anger-out was associated with a 21% decreased odds of poor sleep quality (OR = 0.79, 95% CI = 0.64-0.98; p = .03). Anger temperament was not independently associated with sleep quality. Anger suppression is associated with poor sleep quality in patients with CHD. Whether modifying anger expression can improve sleep quality or reduce cardiovascular morbidity and mortality deserves further study. 6. Anger Expression and Sleep Quality in Patients With Coronary Heart Disease: Findings From the Heart and Soul Study PubMed Central Caska, Catherine M.; Hendrickson, Bethany E.; Wong, Michelle H.; Ali, Sadia; Neylan, Thomas; Whooley, Mary A. 2009-01-01 Objective To evaluate if anger expression affects sleep quality in patients with coronary heart disease (CHD). Research has indicated that poor sleep quality independently predicts adverse outcomes in patients with CHD. Risk factors for poor sleep quality include older age, socioeconomic factors, medical comorbidities, lack of exercise, and depression. Methods We sought to examine the association of anger expression with sleep quality in 1020 outpatients with CHD from the Heart and Soul Study. We assessed anger-in, anger-out, and anger temperament, using the Spielberger State-Trait Anger Expression Inventory 2, and measured sleep quality, using items from the Cardiovascular Health Study and Pittsburgh Sleep Quality Index. We used multivariate analysis of variance to examine the association between anger expression and sleep quality, adjusting for potential confounding variables. Results Each standard deviation (SD) increase in anger-in was associated with an 80% greater odds of poor sleep quality (odds ratio (OR) = 1.8, 95% Confidence Interval (CI) = 1.6–2.1; p < .0001). This association remained strong after adjusting for demographics, comorbidities, lifestyle factors, medications, cardiac function, depressive symptoms, anger-out, and anger temperament (adjusted OR = 1.4, 95% CI = 1.5–1.7; p = .001). In the same model, each SD increase in anger-out was associated with a 21% decreased odds of poor sleep quality (OR = 0.79, 95% CI = 0.64–0.98; p = .03). Anger temperament was not independently associated with sleep quality. Conclusions Anger suppression is associated with poor sleep quality in patients with CHD. Whether modifying anger expression can improve sleep quality or reduce cardiovascular morbidity and mortality deserves further study. PMID:19251866 7. Cosmic shear covariance: the log-normal approximation Hilbert, S.; Hartlap, J.; Schneider, P. 2011-12-01 Context. Accurate estimates of the errors on the cosmological parameters inferred from cosmic shear surveys require accurate estimates of the covariance of the cosmic shear correlation functions. Aims: We seek approximations to the cosmic shear covariance that are as easy to use as the common approximations based on normal (Gaussian) statistics, but yield more accurate covariance matrices and parameter errors. Methods: We derive expressions for the cosmic shear covariance under the assumption that the underlying convergence field follows log-normal statistics. We also derive a simplified version of this log-normal approximation by only retaining the most important terms beyond normal statistics. We use numerical simulations of weak lensing to study how well the normal, log-normal, and simplified log-normal approximations as well as empirical corrections to the normal approximation proposed in the literature reproduce shear covariances for cosmic shear surveys. We also investigate the resulting confidence regions for cosmological parameters inferred from such surveys. Results: We find that the normal approximation substantially underestimates the cosmic shear covariances and the inferred parameter confidence regions, in particular for surveys with small fields of view and large galaxy densities, but also for very wide surveys. In contrast, the log-normal approximation yields more realistic covariances and confidence regions, but also requires evaluating slightly more complicated expressions. However, the simplified log-normal approximation, although as simple as the normal approximation, yields confidence regions that are almost as accurate as those obtained from the log-normal approximation. The empirical corrections to the normal approximation do not yield more accurate covariances and confidence regions than the (simplified) log-normal approximation. Moreover, they fail to produce positive-semidefinite data covariance matrices in certain cases, rendering them 8. Expression of CD30 antigen in superficial mycotic infections of the skin: a possible non-specific finding without clinical relevance. PubMed Müller, C S L; Schmaltz, R; Vogt, T; Pföhler, C 2011-09-01 Expression of CD30 is a distinct marker of lymphocytic activation, originally described in Reed-Sternberg cells of Hodgkin's disease. Recently, the first two cases in which CD30 was expressed in tissue samples derived from superficial cutaneous fungal infections have been reported. The objective of this study was to investigate the expression of CD30 in tinea corporis and to discuss the clinical relevance of CD30. Twenty-three skin biopsies from 23 patients with mycotic infections of the skin were analysed retrospectively. The immunophenotypic expression of CD30 was investigated. In the series investigated, some large CD30-positive cells located in the upper dermal infiltrate were noted in two of 23 biopsy specimens (8.7%). The existence of CD30-positive cells was independent of the density and composition of the accompanying inflammatory infiltrate. We showed that the expression of CD30 in dermatophytoses is not a consistent finding. Instead, as a sign of lymphocytic activation, CD30 expression is observed coincidentally in cutaneous fungal infections. Our data confirm the observation that CD30 antigen is expressed in a variety of benign and malignant skin disorders, including cutaneous fungal infections, probably as an epiphenomenon without clinical relevance. 9. Gadgets, approximation, and linear programming SciTech Connect Trevisan, L.; Sudan, M.; Sorkin, G.B.; Williamson, D.P. 1996-12-31 We present a linear-programming based method for finding {open_quotes}gadgets{close_quotes}, i.e., combinatorial structures reducing constraints of one optimization problems to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by on how to prove the optimality of gadgets-we show how LP duality gives such proofs. The new gadgets improve hardness results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 60/61 and 44/45 respectively is N P-hard. We also use the gadgets to obtain an improved approximation algorithm for MAX 3SAT which guarantees an approximation ratio of .801. This improves upon the previous best bound of .7704. 10. Intrinsic Nilpotent Approximation. DTIC Science & Technology 1985-06-01 RD-A1II58 265 INTRINSIC NILPOTENT APPROXIMATION(U) MASSACHUSETTS INST 1/2 OF TECH CAMBRIDGE LAB FOR INFORMATION AND, DECISION UMCLRSSI SYSTEMS C...TYPE OF REPORT & PERIOD COVERED Intrinsic Nilpotent Approximation Technical Report 6. PERFORMING ORG. REPORT NUMBER LIDS-R-1482 7. AUTHOR(.) S...certain infinite-dimensional filtered Lie algebras L by (finite-dimensional) graded nilpotent Lie algebras or g . where x E M, (x,,Z) E TM/O. It 11. Anomalous diffraction approximation limits Videen, Gorden; Chýlek, Petr It has been reported in a recent article [Liu, C., Jonas, P.R., Saunders, C.P.R., 1996. Accuracy of the anomalous diffraction approximation to light scattering by column-like ice crystals. Atmos. Res., 41, pp. 63-69] that the anomalous diffraction approximation (ADA) accuracy does not depend on particle refractive index, but instead is dependent on the particle size parameter. Since this is at odds with previous research, we thought these results warranted further discussion. 12. Approximate spatial reasoning NASA Technical Reports Server (NTRS) Dutta, Soumitra 1988-01-01 Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains. 13. Approximate kernel competitive learning. PubMed Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang 2015-03-01 Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. 14. Primary Mucinous Cystadenocarcinoma of the Breast: Cytologic Finding and Expression of MUC5 Are Different from Mucinous Carcinoma. PubMed Kim, Sung Eun; Park, Ji Hye; Hong, Soonwon; Koo, Ja Seung; Jeong, Joon; Jung, Woo-Hee 2012-12-01 Mucinous cystadenocarcinoma (MCA) in the breast is a rare neoplasm. There have been 13 cases of primary breast MCA reported. The MCA presents as a large, partially cystic mass in postmenopausal woman with a good prognosis. The microscopic findings resemble those of ovarian, pancreatic, or appendiceal MCA. The aspiration findings showed mucin-containing cell clusters in the background of mucin and necrotic material. The cell clusters had intracytoplasmic mucin displacing atypical nuclei to the periphery. Histologically, the tumor revealed an abundant mucin pool with small floating clusters of mucin-containing tumor cells. There were also small cysts lined by a single layer of tall columnar mucinous cells, resembling those of the uterine endocervix. The cancer cells were positive for mucin (MUC) 5 and negative for MUC2 and MUC6. This mucin profile is different from ordinary mucinous carcinoma and may be a unique characteristic of breast MCA. 15. Finding the Best-Fit Polynomial Approximation in Evaluating Drill Data: the Application of a Generalized Inverse Matrix / Poszukiwanie Najlepszej ZGODNOŚCI W PRZYBLIŻENIU Wielomianowym Wykorzystanej do Oceny Danych Z ODWIERTÓW - Zastosowanie UOGÓLNIONEJ Macierzy Odwrotnej Karakus, Dogan 2013-12-01 In mining, various estimation models are used to accurately assess the size and the grade distribution of an ore body. The estimation of the positional properties of unknown regions using random samples with known positional properties was first performed using polynomial approximations. Although the emergence of computer technologies and statistical evaluation of random variables after the 1950s rendered the polynomial approximations less important, theoretically the best surface passing through the random variables can be expressed as a polynomial approximation. In geoscience studies, in which the number of random variables is high, reliable solutions can be obtained only with high-order polynomials. Finding the coefficients of these types of high-order polynomials can be computationally intensive. In this study, the solution coefficients of high-order polynomials were calculated using a generalized inverse matrix method. A computer algorithm was developed to calculate the polynomial degree giving the best regression between the values obtained for solutions of different polynomial degrees and random observational data with known values, and this solution was tested with data derived from a practical application. In this application, the calorie values for data from 83 drilling points in a coal site located in southwestern Turkey were used, and the results are discussed in the context of this study. W górnictwie wykorzystuje się rozmaite modele estymacji do dokładnego określenia wielkości i rozkładu zawartości pierwiastka użytecznego w rudzie. Estymację położenia i właściwości skał w nieznanych obszarach z wykorzystaniem próbek losowych o znanym położeniu przeprowadzano na początku z wykorzystaniem przybliżenia wielomianowego. Pomimo tego, że rozwój technik komputerowych i statystycznych metod ewaluacji próbek losowych sprawiły, że po roku 1950 metody przybliżenia wielomianowego straciły na znaczeniu, nadal teoretyczna powierzchnia 16. Covariant approximation averaging Shintani, Eigo; Arthur, Rudy; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph 2015-06-01 We present a new class of statistical error reduction techniques for Monte Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in Nf=2 +1 lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte Carlo calculations over conventional methods for the same cost. 17. An efficient approach to finding Siraitia grosvenorii triterpene biosynthetic genes by RNA-seq and digital gene expression analysis. PubMed Tang, Qi; Ma, Xiaojun; Mo, Changming; Wilson, Iain W; Song, Cai; Zhao, Huan; Yang, Yanfang; Fu, Wei; Qiu, Deyou 2011-07-05 Siraitia grosvenorii (Luohanguo) is an herbaceous perennial plant native to southern China and most prevalent in Guilin city. Its fruit contains a sweet, fleshy, edible pulp that is widely used in traditional Chinese medicine. The major bioactive constituents in the fruit extract are the cucurbitane-type triterpene saponins known as mogrosides. Among them, mogroside V is nearly 300 times sweeter than sucrose. However, little is known about mogrosides biosynthesis in S. grosvenorii, especially the late steps of the pathway. In this study, a cDNA library generated from of equal amount of RNA taken from S. grosvenorii fruit at 50 days after flowering (DAF) and 70 DAF were sequenced using Illumina/Solexa platform. More than 48,755,516 high-quality reads from a cDNA library were generated that was assembled into 43,891 unigenes. De novo assembly and gap-filling generated 43,891 unigenes with an average sequence length of 668 base pairs. A total of 26,308 (59.9%) unique sequences were annotated and 11,476 of the unique sequences were assigned to specific metabolic pathways by the Kyoto Encyclopedia of Genes and Genomes. cDNA sequences for all of the known enzymes involved in mogrosides backbone synthesis were identified from our library. Additionally, a total of eighty-five cytochrome P450 (CYP450) and ninety UDP-glucosyltransferase (UDPG) unigenes were identified, some of which appear to encode enzymes responsible for the conversion of the mogroside backbone into the various mogrosides. Digital gene expression profile (DGE) analysis using Solexa sequencing was performed on three important stages of fruit development, and based on their expression pattern, seven CYP450s and five UDPGs were selected as the candidates most likely to be involved in mogrosides biosynthesis. A combination of RNA-seq and DGE analysis based on the next generation sequencing technology was shown to be a powerful method for identifying candidate genes encoding enzymes responsible for the 18. An efficient approach to finding Siraitia grosvenorii triterpene biosynthetic genes by RNA-seq and digital gene expression analysis PubMed Central 2011-01-01 Background Siraitia grosvenorii (Luohanguo) is an herbaceous perennial plant native to southern China and most prevalent in Guilin city. Its fruit contains a sweet, fleshy, edible pulp that is widely used in traditional Chinese medicine. The major bioactive constituents in the fruit extract are the cucurbitane-type triterpene saponins known as mogrosides. Among them, mogroside V is nearly 300 times sweeter than sucrose. However, little is known about mogrosides biosynthesis in S. grosvenorii, especially the late steps of the pathway. Results In this study, a cDNA library generated from of equal amount of RNA taken from S. grosvenorii fruit at 50 days after flowering (DAF) and 70 DAF were sequenced using Illumina/Solexa platform. More than 48,755,516 high-quality reads from a cDNA library were generated that was assembled into 43,891 unigenes. De novo assembly and gap-filling generated 43,891 unigenes with an average sequence length of 668 base pairs. A total of 26,308 (59.9%) unique sequences were annotated and 11,476 of the unique sequences were assigned to specific metabolic pathways by the Kyoto Encyclopedia of Genes and Genomes. cDNA sequences for all of the known enzymes involved in mogrosides backbone synthesis were identified from our library. Additionally, a total of eighty-five cytochrome P450 (CYP450) and ninety UDP-glucosyltransferase (UDPG) unigenes were identified, some of which appear to encode enzymes responsible for the conversion of the mogroside backbone into the various mogrosides. Digital gene expression profile (DGE) analysis using Solexa sequencing was performed on three important stages of fruit development, and based on their expression pattern, seven CYP450s and five UDPGs were selected as the candidates most likely to be involved in mogrosides biosynthesis. Conclusion A combination of RNA-seq and DGE analysis based on the next generation sequencing technology was shown to be a powerful method for identifying candidate genes encoding 19. Quirks of Stirling's Approximation ERIC Educational Resources Information Center Macrae, Roderick M.; Allgeier, Benjamin M. 2013-01-01 Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy… 20. Quirks of Stirling's Approximation ERIC Educational Resources Information Center Macrae, Roderick M.; Allgeier, Benjamin M. 2013-01-01 Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy… 1. Approximate Bayesian Computation Cisewski, Jessi 2015-08-01 Explicitly specifying a likelihood function is becoming increasingly difficult for many problems in astronomy. Astronomers often specify a simpler approximate likelihood - leaving out important aspects of a more realistic model. Approximate Bayesian computation (ABC) provides a framework for performing inference in cases where the likelihood is not available or intractable. I will introduce ABC and explain how it can be a useful tool for astronomers. In particular, I will focus on the eccentricity distribution for a sample of exoplanets with multiple sub-populations. 2. Two-peak approximation in kinetic capillary electrophoresis. PubMed Cherney, Leonid T; Krylov, Sergey N 2012-04-07 Kinetic capillary electrophoresis (KCE) constitutes a toolset of homogeneous kinetic affinity methods for measuring rate constants of formation (k(+)) and dissociation (k(-)) of non-covalent biomolecular complexes, C, formed from two binding partners, A and B. A parameter-based approach of extracting k(+) and k(-) from KCE electropherograms relies on a small number of experimental parameters found from the electropherograms and used in explicit expressions for k(+) and k(-) derived from approximate solutions to mass transfer equations. Deriving the explicit expressions for k(+) and k(-) is challenging but it is justified as the parameter-based approach is the simplest way of finding k(+) and k(-) from KCE electropherograms. Here, we introduce a unique approximate analytical solution of mass transfer equations in KCE termed a "two-peak approximation" and a corresponding parameter-based method for finding k(+) and k(-). The two-peak approximation is applicable to any KCE method in which: (i) A binds B to form C* (the asterisk denotes a detectable label on A), (ii) two peaks can be identified in a KCE electropherogram and (iii) the concentration of B remains constant. The last condition holds if B is present in access to A* and C* throughout the capillary. In the two-peak approximation, the labeling of A serves only for detection of A and C and, therefore, is not required if A (and thus C) can be observed with a label-free detection technique. We studied the proposed two-peak approximation, in particular, its accuracy, by using the simulated propagation patterns built with the earlier-developed exact solution of the mass-transfer equations for A* and C. Our results prove that the obtained approximate solution of mass transfer equations is correct. They also show that the two-peak approximation facilitates finding k(+) and k(-) with a relative error of less than 10% if two peaks can be identified on a KCE electropherogram. Importantly, the condition of constant 3. Rough Set Approximations in Formal Concept Analysis Yamaguchi, Daisuke; Murata, Atsuo; Li, Guo-Dong; Nagai, Masatake Conventional set approximations are based on a set of attributes; however, these approximations cannot relate an object to the corresponding attribute. In this study, a new model for set approximation based on individual attributes is proposed for interval-valued data. Defining an indiscernibility relation is omitted since each attribute value itself has a set of values. Two types of approximations, single- and multiattribute approximations, are presented. A multi-attribute approximation has two solutions: a maximum and a minimum solution. A maximum solution is a set of objects that satisfy the condition of approximation for at least one attribute. A minimum solution is a set of objects that satisfy the condition for all attributes. The proposed set approximation is helpful in finding the features of objects relating to condition attributes when interval-valued data are given. The proposed model contributes to feature extraction in interval-valued information systems. 4. Matrix product approximations to conformal field theories König, Robert; Scholz, Volkher B. 2017-07-01 We establish rigorous error bounds for approximating correlation functions of conformal field theories (CFTs) by certain finite-dimensional tensor networks. For chiral CFTs, the approximation takes the form of a matrix product state. For full CFTs consisting of a chiral and an anti-chiral part, the approximation is given by a finitely correlated state. We show that the bond dimension scales polynomially in the inverse of the approximation error and sub-exponentially in inverse of the minimal distance between insertion points. We illustrate our findings using Wess-Zumino-Witten models, and show that there is a one-to-one correspondence between group-covariant MPS and our approximation. 5. TGR5 expression in benign, preneoplastic and neoplastic lesions of Barrett’s esophagus: Case series and findings PubMed Central Marketkar, Shivali; Li, Dan; Yang, Dongfang; Cao, Weibiao 2017-01-01 AIM To examined the bile acid receptor TGR5 expression in squamous mucosa, Barrett’s mucosa, dysplasia and esophageal adenocarcinoma (EA). METHODS Slides were stained with TGR5 antibody. The staining intensity was scored as 1+, 2+ and 3+. The extent of staining (percentage of cells staining) was scored as follows: 1+, 1%-10%, 2+, 11%-50%, 3+, 51%-100%. A combined score of intensity and extent was calculated and categorized as negative, weak, moderate and strong staining. TGR5 mRNA was measured by real time PCR. RESULTS We found that levels of TGR5 mRNA were significantly increased in Barrett’s dysplastic cell line CP-D and EA cell line SK-GT-4, when compared with Barrett’s cell line CP-A. Moderate to strong TGR5 staining was significantly higher in high-grade dysplasia and EA cases than in Barrett’s esophagus (BE) or in low-grade dysplasia. Moderate to strong staining was slightly higher in low-grade dysplasia than in BE mucosa, but there is no statistical significance. TGR5 staining had no significant difference between high-grade dysplasia and EA. In addition, TGR5 staining intensity was not associated with the clinical stage, the pathological stage and the status of lymph node metastasis. CONCLUSION We conclude that TGR5 immunostaining was much stronger in high-grade dysplasia and EA than in BE mucosa or low-grade dysplasia and that its staining intensity was not associated with the clinical stage, the pathological stage and the status of lymph node metastasis. TGR5 might be a potential marker for the progression from BE to high-grade dysplasia and EA. PMID:28293080 6. On Stochastic Approximation. ERIC Educational Resources Information Center Wolff, Hans This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic… 7. Approximating Integrals Using Probability ERIC Educational Resources Information Center Maruszewski, Richard F., Jr.; Caudle, Kyle A. 2005-01-01 As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of… 8. Approximating Integrals Using Probability ERIC Educational Resources Information Center Maruszewski, Richard F., Jr.; Caudle, Kyle A. 2005-01-01 As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of… 9. Applied Routh approximation NASA Technical Reports Server (NTRS) Merrill, W. C. 1978-01-01 The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization. 10. Maternal Prenatal Mental Health and Placental 11β-HSD2 Gene Expression: Initial Findings from the Mercy Pregnancy and Emotional Wellbeing Study. PubMed Seth, Sunaina; Lewis, Andrew James; Saffery, Richard; Lappas, Martha; Galbally, Megan 2015-11-17 High intrauterine cortisol exposure can inhibit fetal growth and have programming effects for the child's subsequent stress reactivity. Placental 11beta-hydroxysteroid dehydrogenase (11β-HSD2) limits the amount of maternal cortisol transferred to the fetus. However, the relationship between maternal psychopathology and 11β-HSD2 remains poorly defined. This study examined the effect of maternal depressive disorder, antidepressant use and symptoms of depression and anxiety in pregnancy on placental 11β-HSD2 gene (HSD11B2) expression. Drawing on data from the Mercy Pregnancy and Emotional Wellbeing Study, placental HSD11B2 expression was compared among 33 pregnant women, who were selected based on membership of three groups; depressed (untreated), taking antidepressants and controls. Furthermore, associations between placental HSD11B2 and scores on the State-Trait Anxiety Inventory (STAI) and Edinburgh Postnatal Depression Scale (EPDS) during 12-18 and 28-34 weeks gestation were examined. Findings revealed negative correlations between HSD11B2 and both the EPDS and STAI (r = -0.11 to -0.28), with associations being particularly prominent during late gestation. Depressed and antidepressant exposed groups also displayed markedly lower placental HSD11B2 expression levels than controls. These findings suggest that maternal depression and anxiety may impact on fetal programming by down-regulating HSD11B2, and antidepressant treatment alone is unlikely to protect against this effect. 11. Maternal Prenatal Mental Health and Placental 11β-HSD2 Gene Expression: Initial Findings from the Mercy Pregnancy and Emotional Wellbeing Study PubMed Central Seth, Sunaina; Lewis, Andrew James; Saffery, Richard; Lappas, Martha; Galbally, Megan 2015-01-01 High intrauterine cortisol exposure can inhibit fetal growth and have programming effects for the child’s subsequent stress reactivity. Placental 11beta-hydroxysteroid dehydrogenase (11β-HSD2) limits the amount of maternal cortisol transferred to the fetus. However, the relationship between maternal psychopathology and 11β-HSD2 remains poorly defined. This study examined the effect of maternal depressive disorder, antidepressant use and symptoms of depression and anxiety in pregnancy on placental 11β-HSD2 gene (HSD11B2) expression. Drawing on data from the Mercy Pregnancy and Emotional Wellbeing Study, placental HSD11B2 expression was compared among 33 pregnant women, who were selected based on membership of three groups; depressed (untreated), taking antidepressants and controls. Furthermore, associations between placental HSD11B2 and scores on the State-Trait Anxiety Inventory (STAI) and Edinburgh Postnatal Depression Scale (EPDS) during 12–18 and 28–34 weeks gestation were examined. Findings revealed negative correlations between HSD11B2 and both the EPDS and STAI (r = −0.11 to −0.28), with associations being particularly prominent during late gestation. Depressed and antidepressant exposed groups also displayed markedly lower placental HSD11B2 expression levels than controls. These findings suggest that maternal depression and anxiety may impact on fetal programming by down-regulating HSD11B2, and antidepressant treatment alone is unlikely to protect against this effect. PMID:26593902 12. Topics in Metric Approximation Leeb, William Edward This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis. 13. Approximate reasoning using terminological models NASA Technical Reports Server (NTRS) Yen, John; Vaidya, Nitin 1992-01-01 Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved. 14. Spline approximations for nonlinear hereditary control systems NASA Technical Reports Server (NTRS) Daniel, P. L. 1982-01-01 A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized. 15. Cosmological applications of Padé approximant SciTech Connect Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan E-mail: 764644314@qq.com 2014-01-01 As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation. 16. Approximate option pricing SciTech Connect Chalasani, P.; Saias, I.; Jha, S. 1996-04-08 As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest. 17. Beyond the Kirchhoff approximation NASA Technical Reports Server (NTRS) Rodriguez, Ernesto 1989-01-01 The three most successful models for describing scattering from random rough surfaces are the Kirchhoff approximation (KA), the small-perturbation method (SPM), and the two-scale-roughness (or composite roughness) surface-scattering (TSR) models. In this paper it is shown how these three models can be derived rigorously from one perturbation expansion based on the extinction theorem for scalar waves scattering from perfectly rigid surface. It is also shown how corrections to the KA proportional to the surface curvature and higher-order derivatives may be obtained. Using these results, the scattering cross section is derived for various surface models. 18. Hierarchical Approximate Bayesian Computation PubMed Central Turner, Brandon M.; Van Zandt, Trisha 2013-01-01 Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function. PMID:24297436 19. Approximate strip exchanging. PubMed Roy, Swapnoneel; Thakur, Ashok Kumar 2008-01-01 Genome rearrangements have been modelled by a variety of primitives such as reversals, transpositions, block moves and block interchanges. We consider such a genome rearrangement primitive Strip Exchanges. Given a permutation, the challenge is to sort it by using minimum number of strip exchanges. A strip exchanging move interchanges the positions of two chosen strips so that they merge with other strips. The strip exchange problem is to sort a permutation using minimum number of strip exchanges. We present here the first non-trivial 2-approximation algorithm to this problem. We also observe that sorting by strip-exchanges is fixed-parameter-tractable. Lastly we discuss the application of strip exchanges in a different area Optical Character Recognition (OCR) with an example. 20. Peripheral Blood Leukocyte Gene Expression Patterns and Metabolic Parameters in Habitually Snoring and Non-Snoring Children with Normal Polysomnographic Findings PubMed Central Khalyfa, Abdelnaby; Gharib, Sina A.; Kim, Jinkwan; Capdevila, Oscar Sans; Kheirandish-Gozal, Leila; Bhattacharjee, Rakesh; Hegazi, Mohamed; Gozal, David 2011-01-01 Background: Children who snore but do not have gas exchange abnormalities or alterations of sleep architecture have primary snoring (PS). Since increasing evidence suggest that PS may be associated with morbidity, we hypothesized that assessing genome-wide gene expression in peripheral blood leukocytes (PBL) will identify a distinct signature in PS children. Methods: Children (aged 4–9 years) with and without habitual snoring and a normal PSG were designated as either PS or controls. Whole genome expression profiles of PBL and metabolic parameters in 30 children with PS and 30 age-, gender-, ethnicity-, and BMI-matched controls were compared. Pathway-focused gene network analysis of the PBL transcriptome was performed. Metabolic parameters were measured in an independent follow-up cohort of 98 children (64 PS and 34 controls) to evaluate the computationally derived findings. Results: PS was not associated with a distinct transcriptional signature in PBL. Exploratory functional network analysis of enriched gene sets identified a number of putative pathways—including those mapping to insulin signaling, adipocyte differentiation, and obesity—with significant alterations in glucose metabolism and insulin sensitivity emerging in the follow-up cohort of children with PS, but no differences in lipid profiles. Conclusions: PS children do not exhibit global perturbations in their PBL transcriptional response, suggesting that current normative PSG criteria are overall valid. However, subtle differences in functionally coherent pathways involved in glycemic homeostasis were detected and confirmed in a larger independent pediatric cohort indicating that PS may carry increased risk for end-organ morbidity in susceptible children. Citation: Khalyfa A; Gharib SA; Kim J; Capdevila OS; Kheirandish-Gozal L; Bhattacharjee R; Hegazi M; Gozal D. Peripheral blood leukocyte gene expression patterns and metabolic parameters in habitually snoring and non-snoring children with normal 1. Histopathological findings, phenotyping of inflammatory cells, and expression of markers of nitritative injury in joint tissue samples from calves after vaccination and intraarticular challenge with Mycoplasma bovis strain 1067 PubMed Central 2014-01-01 Background The pathogenesis of caseonecrotic lesions developing in lungs and joints of calves infected with Mycoplasma bovis is not clear and attempts to prevent M. bovis-induced disease by vaccines have been largely unsuccessful. In this investigation, joint samples from 4 calves, i.e. 2 vaccinated and 2 non-vaccinated, of a vaccination experiment with intraarticular challenge were examined. The aim was to characterize the histopathological findings, the phenotypes of inflammatory cells, the expression of class II major histocompatibility complex (MHC class II) molecules, and the expression of markers for nitritative stress, i.e. inducible nitric oxide synthase (iNOS) and nitrotyrosine (NT), in synovial membrane samples from these calves. Furthermore, the samples were examined for M. bovis antigens including variable surface protein (Vsp) antigens and M. bovis organisms by cultivation techniques. Results The inoculated joints of all 4 calves had caseonecrotic and inflammatory lesions. Necrotic foci were demarcated by phagocytic cells, i.e. macrophages and neutrophilic granulocytes, and by T and B lymphocytes. The presence of M. bovis antigens in necrotic tissue lesions was associated with expression of iNOS and NT by macrophages. Only single macrophages demarcating the necrotic foci were positive for MHC class II. Microbiological results revealed that M. bovis had spread to approximately 27% of the non-inoculated joints. Differences in extent or severity between the lesions in samples from vaccinated and non-vaccinated animals were not seen. Conclusions The results suggest that nitritative injury, as in pneumonic lung tissue of M. bovis-infected calves, is involved in the development of caseonecrotic joint lesions. Only single macrophages were positive for MHC class II indicating down-regulation of antigen-presenting mechanisms possibly caused by local production of iNOS and NO by infiltrating macrophages. PMID:25162202 2. Approximate probability distributions of the master equation. PubMed Thomas, Philipp; Grima, Ramon 2015-07-01 Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems. 3. Approximate probability distributions of the master equation Thomas, Philipp; Grima, Ramon 2015-07-01 Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems. 4. Approximate approaches to the one-dimensional finite potential well Singh, Shilpi; Pathak, Praveen; Singh, Vijay A. 2011-11-01 The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (mi) is taken to be distinct from mass outside (mo). A relevant parameter is the mass discontinuity ratio β = mi/mo. To correctly account for the mass discontinuity, we apply the BenDaniel-Duke boundary condition. We obtain approximate solutions for two cases: when the well is shallow and when the well is deep. We compare the approximate results with the exact results and find that higher-order approximations are quite robust. For the shallow case, the approximate solution can be expressed in terms of a dimensionless parameter σl = 2moV0L2/planck2 (or σ = β2σl for the deep case). We show that the lowest-order results are related by a duality transform. We also discuss how the energy upscales with L (E~1/Lγ) and obtain the exponent γ. Exponent γ → 2 when the well is sufficiently deep and β → 1. The ratio of the masses dictates the physics. Our presentation is pedagogical and should be useful to students on a first course on elementary quantum mechanics or low-dimensional semiconductors. 5. Hybrid Approximate Message Passing Rangan, Sundeep; Fletcher, Alyson K.; Goyal, Vivek K.; Byrne, Evan; Schniter, Philip 2017-09-01 The standard linear regression (SLR) problem is to recover a vector $\\mathbf{x}^0$ from noisy linear observations $\\mathbf{y}=\\mathbf{Ax}^0+\\mathbf{w}$. The approximate message passing (AMP) algorithm recently proposed by Donoho, Maleki, and Montanari is a computationally efficient iterative approach to SLR that has a remarkable property: for large i.i.d.\\ sub-Gaussian matrices $\\mathbf{A}$, its per-iteration behavior is rigorously characterized by a scalar state-evolution whose fixed points, when unique, are Bayes optimal. AMP, however, is fragile in that even small deviations from the i.i.d.\\ sub-Gaussian model can cause the algorithm to diverge. This paper considers a "vector AMP" (VAMP) algorithm and shows that VAMP has a rigorous scalar state-evolution that holds under a much broader class of large random matrices $\\mathbf{A}$: those that are right-rotationally invariant. After performing an initial singular value decomposition (SVD) of $\\mathbf{A}$, the per-iteration complexity of VAMP can be made similar to that of AMP. In addition, the fixed points of VAMP's state evolution are consistent with the replica prediction of the minimum mean-squared error recently derived by Tulino, Caire, Verd\\'u, and Shamai. The effectiveness and state evolution predictions of VAMP are confirmed in numerical experiments. 6. Countably QC-Approximating Posets PubMed Central Mao, Xuxin; Xu, Luoshan 2014-01-01 As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σc(L)op of all σ-Scott-closed subsets of L is weakly generalized countably approximating. PMID:25165730 7. Approximate knowledge compilation: The first order case SciTech Connect Val, A. del 1996-12-31 Knowledge compilation procedures make a knowledge base more explicit so as make inference with respect to the compiled knowledge base tractable or at least more efficient. Most work to date in this area has been restricted to the propositional case, despite the importance of first order theories for expressing knowledge concisely. Focusing on (LUB) approximate compilation, our contribution is twofold: (1) We present a new ground algorithm for approximate compilation which can produce exponential savings with respect to the previously known algorithm. (2) We show that both ground algorithms can be lifted to the first order case preserving their correctness for approximate compilation. 8. Laguerre approximation of random foams Liebscher, André 2015-09-01 Stochastic models for the microstructure of foams are valuable tools to study the relations between microstructure characteristics and macroscopic properties. Owing to the physical laws behind the formation of foams, Laguerre tessellations have turned out to be suitable models for foams. Laguerre tessellations are weighted generalizations of Voronoi tessellations, where polyhedral cells are formed through the interaction of weighted generator points. While both share the same topology, the cell curvature of foams allows only an approximation by Laguerre tessellations. This makes the model fitting a challenging task, especially when the preservation of the local topology is required. In this work, we propose an inversion-based approach to fit a Laguerre tessellation model to a foam. The idea is to find a set of generator points whose tessellation best fits the foam's cell system. For this purpose, we transform the model fitting into a minimization problem that can be solved by gradient descent-based optimization. The proposed algorithm restores the generators of a tessellation if it is known to be Laguerre. If, as in the case of foams, no exact solution is possible, an approximative solution is obtained that maintains the local topology. 9. Interplay of approximate planning strategies. PubMed Huys, Quentin J M; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J; Dayan, Peter; Roiser, Jonathan P 2015-03-10 Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or "options." 10. Hybrid sequencing and map finding (HySeMaFi): optional strategies for extensively deciphering gene splicing and expression in organisms without reference genome PubMed Central Ning, Guogui; Cheng, Xu; Luo, Ping; Liang, Fan; Wang, Zhen; Yu, Guoliang; Li, Xin; Wang, Depeng; Bao, Manzhu 2017-01-01 Using second-generation sequencing (SGS) RNA-Seq strategies, extensive alterative splicing prediction is impractical and high variability of isoforms expression quantification is inevitable in organisms without true reference dataset. we report the development of a novel analysis method, termed hybrid sequencing and map finding (HySeMaFi) which combines the specific strengths of third-generation sequencing (TGS) (PacBio SMRT sequencing) and SGS (Illumina Hi-Seq/MiSeq sequencing) to effectively decipher gene splicing and to reliably estimate the isoforms abundance. Error-corrected long reads from TGS are capable of capturing full length transcripts or as large partial transcript fragments. Both true and false isoforms, from a particular gene, as well as that containing all possible exons, could be generated by employing different assembly methods in SGS. We first develop an effective method which can establish the mapping relationship between the error-corrected long reads and the longest assembled contig in every corresponding gene. According to the mapping data, the true splicing pattern of the genes was reliably detected, and quantification of the isoforms was also effectively determined. HySeMaFi is also the optimal strategy by which to decipher the full exon expression of a specific gene when the longest mapped contigs were chosen as the reference set. PMID:28272530 11. Fast approximate stochastic tractography. PubMed Iglesias, Juan Eugenio; Thompson, Paul M; Liu, Cheng-Yi; Tu, Zhuowen 2012-01-01 Many different probabilistic tractography methods have been proposed in the literature to overcome the limitations of classical deterministic tractography: (i) lack of quantitative connectivity information; and (ii) robustness to noise, partial volume effects and selection of seed region. However, these methods rely on Monte Carlo sampling techniques that are computationally very demanding. This study presents an approximate stochastic tractography algorithm (FAST) that can be used interactively, as opposed to having to wait several minutes to obtain the output after marking a seed region. In FAST, tractography is formulated as a Markov chain that relies on a transition tensor. The tensor is designed to mimic the features of a well-known probabilistic tractography method based on a random walk model and Monte-Carlo sampling, but can also accommodate other propagation rules. Compared to the baseline algorithm, our method circumvents the sampling process and provides a deterministic solution at the expense of partially sacrificing sub-voxel accuracy. Therefore, the method is strictly speaking not stochastic, but provides a probabilistic output in the spirit of stochastic tractography methods. FAST was compared with the random walk model using real data from 10 patients in two different ways: 1. the probability maps produced by the two methods on five well-known fiber tracts were directly compared using metrics from the image registration literature; and 2. the connectivity measurements between different regions of the brain given by the two methods were compared using the correlation coefficient ρ. The results show that the connectivity measures provided by the two algorithms are well-correlated (ρ = 0.83), and so are the probability maps (normalized cross correlation 0.818 ± 0.081). The maps are also qualitatively (i.e., visually) very similar. The proposed method achieves a 60x speed-up (7 s vs. 7 min) over the Monte Carlo sampling scheme, therefore 12. Approximating maximum clique with a Hopfield network. PubMed Jagota, A 1995-01-01 In a graph, a clique is a set of vertices such that every pair is connected by an edge. MAX-CLIQUE is the optimization problem of finding the largest clique in a given graph and is NP-hard, even to approximate well. Several real-world and theory problems can be modeled as MAX-CLIQUE. In this paper, we efficiently approximate MAX-CLIQUE in a special case of the Hopfield network whose stable states are maximal cliques. We present several energy-descent optimizing dynamics; both discrete (deterministic and stochastic) and continuous. One of these emulates, as special cases, two well-known greedy algorithms for approximating MAX-CLIQUE. We report on detailed empirical comparisons on random graphs and on harder ones. Mean-field annealing, an efficient approximation to simulated annealing, and a stochastic dynamics are the narrow but clear winners. All dynamics approximate much better than one which emulates a "naive" greedy heuristic. 13. Power spectra beyond the slow roll approximation in theories with non-canonical kinetic terms SciTech Connect De Bruck, Carsten van; Robinson, Mathew E-mail: app11mrr@sheffield.ac.uk 2014-08-01 We derive analytical expressions for the power spectra at the end of inflation in theories with two inflaton fields and non-canonical kinetic terms. We find that going beyond the slow-roll approximation is necessary and that the nature of the non-canonical terms have an important impact on the final power spectra at the end of inflation. We study five models numerically and find excellent agreement with our analytical results. Our results emphasise the fact that going beyond the slow-roll approximation is important in times of high-precision data coming from cosmological observations. 14. Approximate von Neumann entropy for directed graphs. PubMed Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R 2014-05-01 In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks. 15. Approximate analytic solutions to the NPDD: Short exposure approximations Close, Ciara E.; Sheridan, John T. 2014-04-01 There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed. 16. Ideal amino acid exchange forms for approximating substitution matrices. PubMed Pokarowski, Piotr; Kloczkowski, Andrzej; Nowakowski, Szymon; Pokarowska, Maria; Jernigan, Robert L; Kolinski, Andrzej 2007-11-01 We have analyzed 29 published substitution matrices (SMs) and five statistical protein contact potentials (CPs) for comparison. We find that popular, 'classical' SMs obtained mainly from sequence alignments of globular proteins are mostly correlated by at least a value of 0.9. The BLOSUM62 is the central element of this group. A second group includes SMs derived from alignments of remote homologs or transmembrane proteins. These matrices correlate better with classical SMs (0.8) than among themselves (0.7). A third group consists of intermediate links between SMs and CPs - matrices and potentials that exhibit mutual correlations of at least 0.8. Next, we show that SMs can be approximated with a correlation of 0.9 by expressions c(0) + x(i)x(j) + y(i)y(j) + z(i)z(j), 1approximation were used to derive ideal amino acid interaction forms from CPs. Both approximations allow us to understand general trends in amino acid similarity and can help improve multiple sequence alignments using the fast Fourier transform (MAFFT), fast threading or another methods based on alignments of physicochemical profiles of protein sequences. The use of this approximation in sequence alignments instead of a classical SM yields results that differ by less than 5%. Intermediate links between SMs and CPs, new formulas for approximating these matrices, and the highly significant dependence of classical SMs on coil preferences are new findings. 17. DALI: Derivative Approximation for LIkelihoods Sellentin, Elena 2015-07-01 DALI (Derivative Approximation for LIkelihoods) is a fast approximation of non-Gaussian likelihoods. It extends the Fisher Matrix in a straightforward way and allows for a wider range of posterior shapes. The code is written in C/C++. 18. Taylor Approximations and Definite Integrals ERIC Educational Resources Information Center Gordon, Sheldon P. 2007-01-01 We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.) 19. Taylor Approximations and Definite Integrals ERIC Educational Resources Information Center Gordon, Sheldon P. 2007-01-01 We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.) 20. Approximate equilibria for Bayesian games Mallozzi, Lina; Pusillo, Lucia; Tijs, Stef 2008-07-01 In this paper the problem of the existence of approximate equilibria in mixed strategies is central. Sufficient conditions are given under which approximate equilibria exist for non-finite Bayesian games. Further one possible approach is suggested to the problem of the existence of approximate equilibria for the class of multicriteria Bayesian games. 1. Recent advances in discrete dipole approximation Flatau, P. J. 2012-12-01 I will describe recent advances and results related to Discrete Dipole Approximation. I will concentrate on Discrete Dipole Scattering (DDSCAT) code which has been jointly developed by myself and Bruce T. Draine. Discussion will concentrate on calculation of scattering and absorption by isolated particles (e.g., dust grains, ice crystals), calculations of scattering by periodic structures with applications to studies of scattering and absorption by periodic arrangement of finite cylinders, cubes, etc), very fast near field calculation, ways to display scattering targets and their composition using three dimensional graphical codes. I will discuss possible extensions. References Flatau, P. J. and Draine, B. T., 2012, Fast near field calculations in the discrete dipole approximation for regular rectilinear grids, Optics Express, 20, 1247-1252. Draine B. T. and Flatau P. J., 2008, Discrete-dipole approximation for periodic targets: theory and tests , J. Opt. Soc. Am. A., 25, 2693-2703. Draine BT and Flatau PJ, 2012, User Guide for the Discrete Dipole Approximation Code DDSCAT 7.2, arXiv:1202.3424v3.ear field calculations (Fast near field calculations in the discrete dipole approximation for regular rectilinear grids P. J. Flatau and B. T. Draine, Optics Express, Vol. 20, Issue 2, pp. 1247-1252 (2012)) 2. A Survey of Techniques for Approximate Computing SciTech Connect Mittal, Sparsh 2016-03-18 Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is to provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems. 3. A Survey of Techniques for Approximate Computing DOE PAGES Mittal, Sparsh 2016-03-18 Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is tomore » provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.« less 4. Frankenstein's glue: transition functions for approximate solutions Yunes, Nicolás 2007-09-01 Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate analytic solutions together. In particular, we propose certain sufficient conditions on these functions and prove that these conditions guarantee that the joined solution still satisfies the Einstein equations analytically to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, then the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter shell, whose stress energy tensor depends on derivatives of these functions. 5. Characterizing inflationary perturbations: The uniform approximation SciTech Connect Habib, Salman; Heinen, Andreas; Heitmann, Katrin; Jungman, Gerard; Molina-Paris, Carmen 2004-10-15 The spectrum of primordial fluctuations from inflation can be obtained using a mathematically controlled, and systematically extendable, uniform approximation. Closed-form expressions for power spectra and spectral indices may be found without making explicit slow-roll assumptions. Here we provide details of our previous calculations, extend the results beyond leading-order in the approximation, and derive general error bounds for power spectra and spectral indices. Already at next-to-leading-order, the errors in calculating the power spectrum are less than a percent. This meets the accuracy requirement for interpreting next-generation cosmic microwave background observations. 6. Randomized approximate nearest neighbors algorithm PubMed Central Jones, Peter Wilcox; Osipov, Andrei; Rokhlin, Vladimir 2011-01-01 We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {xj} in , the algorithm attempts to find k nearest neighbors for each of xj, where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T·N·(d·(log d) + k·(d + log k)·(log N)) + N·k2·(d + log k), with T the number of iterations performed. The memory requirements of the procedure are of the order N·(d + k). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among {xj} for an arbitrary point . The cost of each such query is proportional to T·(d·(log d) + log(N/k)·k·(d + log k)), and the memory requirements for the requisite data structure are of the order N·(d + k) + T·(d + N). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme’s behavior for certain types of distributions of {xj} and illustrate its performance via several numerical examples. PMID:21885738 7. Interplay of approximate planning strategies PubMed Central Huys, Quentin J. M.; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J.; Dayan, Peter; Roiser, Jonathan P. 2015-01-01 Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or “options.” PMID:25675480 8. Femtolensing: Beyond the semiclassical approximation NASA Technical Reports Server (NTRS) Ulmer, Andrew; Goodman, Jeremy 1995-01-01 Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths. 9. Express Integrated Risk Information System (IRIS) Express ; CASRN 101200 - 48 - 0 Human health assessment information on a chemical substance is included in the IRIS database only after a comprehensive review of toxicity data , as outlined in the IRIS assessment development process . Sections I ( Health Hazard Assessments for Noncarcinogenic Effect 10. Combining global and local approximations NASA Technical Reports Server (NTRS) Haftka, Raphael T. 1991-01-01 A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model. 11. Combining global and local approximations SciTech Connect Haftka, R.T. ) 1991-09-01 A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model. 6 refs. 12. Phenomenological applications of rational approximants Gonzàlez-Solís, Sergi; Masjuan, Pere 2016-08-01 We illustrate the powerfulness of Padé approximants (PAs) as a summation method and explore one of their extensions, the so-called quadratic approximant (QAs), to access both space- and (low-energy) time-like (TL) regions. As an introductory and pedagogical exercise, the function 1 zln(1 + z) is approximated by both kind of approximants. Then, PAs are applied to predict pseudoscalar meson Dalitz decays and to extract Vub from the semileptonic B → πℓνℓ decays. Finally, the π vector form factor in the TL region is explored using QAs. 13. Estimation of distribution algorithms with Kikuchi approximations. PubMed Santana, Roberto 2005-01-01 The question of finding feasible ways for estimating probability distributions is one of the main challenges for Estimation of Distribution Algorithms (EDAs). To estimate the distribution of the selected solutions, EDAs use factorizations constructed according to graphical models. The class of factorizations that can be obtained from these probability models is highly constrained. Expanding the class of factorizations that could be employed for probability approximation is a necessary step for the conception of more robust EDAs. In this paper we introduce a method for learning a more general class of probability factorizations. The method combines a reformulation of a probability approximation procedure known in statistical physics as the Kikuchi approximation of energy, with a novel approach for finding graph decompositions. We present the Markov Network Estimation of Distribution Algorithm (MN-EDA), an EDA that uses Kikuchi approximations to estimate the distribution, and Gibbs Sampling (GS) to generate new points. A systematic empirical evaluation of MN-EDA is done in comparison with different Bayesian network based EDAs. From our experiments we conclude that the algorithm can outperform other EDAs that use traditional methods of probability approximation in the optimization of functions with strong interactions among their variables. 14. Approximate solutions of the hyperbolic Kepler equation Avendano, Martín; Martín-Molina, Verónica; Ortigas-Galindo, Jorge 2015-12-01 We provide an approximate zero widetilde{S}(g,L) for the hyperbolic Kepler's equation S-g {{arcsinh}}(S)-L=0 for gin (0,1) and Lin [0,∞ ). We prove, by using Smale's α -theory, that Newton's method starting at our approximate zero produces a sequence that converges to the actual solution S( g, L) at quadratic speed, i.e. if S_n is the value obtained after n iterations, then \|S_n-S\|≤ 0.5^{2^n-1}\|widetilde{S}-S\|. The approximate zero widetilde{S}(g,L) is a piecewise-defined function involving several linear expressions and one with cubic and square roots. In bounded regions of (0,1) × [0,∞ ) that exclude a small neighborhood of g=1, L=0, we also provide a method to construct simpler starters involving only constants. 15. On L convergence of Neumann series approximation in missing data problems. PubMed Chen, Hua Yun 2010-05-15 The inverse of the nonparametric information operator is key to finding doubly robust estimators and the semiparametric efficient estimator in missing data problems. It is known that no closed-form expression for the inverse of the nonparametric information operator exists when missing data form nonmonotone patterns. Neumann series is usually applied to approximate the inverse. However, Neumann series approximation is only known to converge in L(2) norm, which is not sufficient for establishing statistical properties of the estimators yielded from the approximation. In this article, we show that L(∞) convergence of the Neumann series approximations to the inverse of the non-parametric information operator and to the efficient scores in missing data problems can be obtained under very simple conditions. This paves the way to the study of the asymptotic properties of the doubly robust estimators and the locally semiparametric efficient estimator in those difficult situations. 16. Approximating Functions with Exponential Functions ERIC Educational Resources Information Center Gordon, Sheldon P. 2005-01-01 The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"… 17. Local density approximations from finite systems Entwistle, M. T.; Hodgson, M. J. P.; Wetherell, J.; Longstaff, B.; Ramsden, J. D.; Godby, R. W. 2016-11-01 The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We introduce an alternative set of LDAs constructed from slablike systems of one, two, and three electrons that resemble the HEG within a finite region, and illustrate the concept in one dimension. Comparing with the exact densities and Kohn-Sham potentials for various test systems, we find that the LDAs give a good account of the self-interaction correction, but are less reliable when correlation is stronger or currents flow. 18. Rock Finding ERIC Educational Resources Information Center Rommel-Esham, Katie; Constable, Susan D. 2006-01-01 In this article, the authors discuss a literature-based activity that helps students discover the importance of making detailed observations. In an inspiring children's classic book, "Everybody Needs a Rock" by Byrd Baylor (1974), the author invites readers to go "rock finding," laying out 10 rules for finding a "perfect" rock. In this way, the… 19. Rock Finding ERIC Educational Resources Information Center Rommel-Esham, Katie; Constable, Susan D. 2006-01-01 In this article, the authors discuss a literature-based activity that helps students discover the importance of making detailed observations. In an inspiring children's classic book, "Everybody Needs a Rock" by Byrd Baylor (1974), the author invites readers to go "rock finding," laying out 10 rules for finding a "perfect" rock. In this way, the… 20. Structural optimization with approximate sensitivities NASA Technical Reports Server (NTRS) Patnaik, S. N.; Hopkins, D. A.; Coroneos, R. 1994-01-01 Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization. 1. Approximate circuits for increased reliability DOEpatents Hamlet, Jason R.; Mayo, Jackson R. 2015-12-22 Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit. 2. Approximate circuits for increased reliability SciTech Connect Hamlet, Jason R.; Mayo, Jackson R. 2015-08-18 Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit. 3. Analytical approximations for the collapse of an empty spherical bubble. PubMed Obreschkow, D; Bruderer, M; Farhat, M 2012-06-01 The Rayleigh equation 3/2R+RR+pρ(-1)=0 with initial conditions R(0)=R(0), R(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density ρ. The solution for r≡R/R(0) as a function of time t≡T/T(c), where R(T(c))≡0, is independent of R(0), p, and ρ. While no closed-form expression for r(t) is known, we find that r(0)(t)=(1-t(2))(2/5) approximates r(t) with an error below 1%. A systematic development in orders of t(2) further yields the 0.001% approximation r()(t)=r(0)(t)[1-a(1)Li(2.21)(t(2))], where a(1)≈-0.01832099 is a constant and Li is the polylogarithm. The usefulness of these approximations is demonstrated by comparison to high-precision cavitation data obtained in microgravity. 4. Approximate number and approximate time discrimination each correlate with school math abilities in young children. PubMed Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin 2016-01-01 What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright 5. Approximating subtree distances between phylogenies. PubMed Bonet, Maria Luisa; St John, Katherine; Mahindru, Ruchi; Amenta, Nina 2006-10-01 We give a 5-approximation algorithm to the rooted Subtree-Prune-and-Regraft (rSPR) distance between two phylogenies, which was recently shown to be NP-complete. This paper presents the first approximation result for this important tree distance. The algorithm follows a standard format for tree distances. The novel ideas are in the analysis. In the analysis, the cost of the algorithm uses a "cascading" scheme that accounts for possible wrong moves. This accounting is missing from previous analysis of tree distance approximation algorithms. Further, we show how all algorithms of this type can be implemented in linear time and give experimental results. 6. Counting independent sets using the Bethe approximation SciTech Connect Chertkov, Michael; Chandrasekaran, V; Gamarmik, D; Shah, D; Sin, J 2009-01-01 The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques. 7. Rytov approximation in electron scattering Krehl, Jonas; Lubk, Axel 2017-06-01 In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the phase grating approximation, have reached their limits in current and foreseeable applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy, we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy. 8. Dual approximations in optimal control NASA Technical Reports Server (NTRS) Hager, W. W.; Ianculescu, G. D. 1984-01-01 A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented. 9. Fostering Formal Commutativity Knowledge with Approximate Arithmetic. PubMed Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A; Gaschler, Robert 2015-01-01 How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. 10. Fostering Formal Commutativity Knowledge with Approximate Arithmetic PubMed Central Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A.; Gaschler, Robert 2015-01-01 How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. PMID:26560311 11. Exponential approximations in optimal design NASA Technical Reports Server (NTRS) Belegundu, A. D.; Rajan, S. D.; Rajgopal, J. 1990-01-01 One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis. 12. Mathematical algorithms for approximate reasoning NASA Technical Reports Server (NTRS) Murphy, John H.; Chay, Seung C.; Downs, Mary M. 1988-01-01 Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away 13. Approximation techniques for neuromimetic calculus. PubMed Vigneron, V; Barret, C 1999-06-01 Approximation Theory plays a central part in modern statistical methods, in particular in Neural Network modeling. These models are able to approximate a large amount of metric data structures in their entire range of definition or at least piecewise. We survey most of the known results for networks of neurone-like units. The connections to classical statistical ideas such as ordinary least squares (LS) are emphasized. 14. Independent association of PD-L1 expression with noninactivated VHL clear cell renal cell carcinoma-A finding with therapeutic potential. PubMed Kammerer-Jacquet, Solène-Florence; Crouzet, Laurence; Brunot, Angélique; Dagher, Julien; Pladys, Adélaïde; Edeline, Julien; Laguerre, Brigitte; Peyronnet, Benoit; Mathieu, Romain; Verhoest, Grégory; Patard, Jean-Jacques; Lespagnol, Alexandra; Mosser, Jean; Denis, Marc; Messai, Yosra; Gad-Lapiteau, Sophie; Chouaib, Salem; Belaud-Rotureau, Marc-Antoine; Bensalah, Karim; Rioux-Leclercq, Nathalie 2017-01-01 Clear cell renal cell carcinoma (ccRCC) is an aggressive tumor that is characterized in most cases by inactivation of the tumor suppressor gene VHL. The VHL/HIF/VEGF pathway thus plays a major role in angiogenesis and is currently targeted by anti-angiogenic therapy. The emergence of resistance is leading to the use of targeted immunotherapy against immune checkpoint PD1/PDL1 that restores antitumor immune response. The correlation between VHL status and PD-L1 expression has been little investigated. In this study, we retrospectively reviewed 98 consecutive cases of ccRCC and correlated PD-L1 expression by immunohistochemistry (IHC) with clinical data (up to 10-year follow-up), pathological criteria, VEGF, PAR-3, CAIX and PD-1 expressions by IHC and complete VHL status (deletion, mutation and promoter hypermethylation). PD-L1 expression was observed in 69 ccRCC (70.4%) and the corresponding patients had a worse prognosis, with a median specific survival of 52 months (p = 0.03). PD-L1 expression was significantly associated with poor prognostic factors such as a higher ISUP nucleolar grade (p = 0.01), metastases at diagnosis (p = 0.01), a sarcomatoid component (p = 0.04), overexpression of VEGF (p = 0.006), and cytoplasmic PAR-3 expression (p = 0.01). PD-L1 expression was also associated with dense PD-1 expression (p = 0.007) and with ccRCC with 0 or 1 alteration(s) (non-inactivated VHL tumors; p = 0.007) that remained significant after multivariate analysis (p = 0.004 and p = 0.024, respectively). Interestingly, all wild-type VHL tumors (no VHL gene alteration, 11.2%) expressed PD-L1. In this study, we found PD-L1 expression to be associated with noninactivated VHL tumors and in particular wild-type VHL ccRCC, which may benefit from therapies inhibiting PD-L1/PD-1. 15. Wavelet Sparse Approximate Inverse Preconditioners NASA Technical Reports Server (NTRS) Chan, Tony F.; Tang, W.-P.; Wan, W. L. 1996-01-01 There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm. 16. Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics ERIC Educational Resources Information Center Schlitt, D. W. 1977-01-01 Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH) 17. Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics ERIC Educational Resources Information Center Schlitt, D. W. 1977-01-01 Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH) 18. Is Approximate Number Precision a Stable Predictor of Math Ability? PubMed Central Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin 2013-01-01 Previous research shows that children’s ability to estimate numbers of items using their Approximate Number System (ANS) predicts later math ability. To more closely examine the predictive role of early ANS acuity on later abilities, we assessed the ANS acuity, math ability, and expressive vocabulary of preschoolers twice, six months apart. We also administered attention and memory span tasks to ask whether the previously reported association between ANS acuity and math ability is ANS-specific or attributable to domain-general cognitive skills. We found that early ANS acuity predicted math ability six months later, even when controlling for individual differences in age, expressive vocabulary, and math ability at the initial testing. In addition, ANS acuity was a unique concurrent predictor of math ability above and beyond expressive vocabulary, attention, and memory span. These findings of a predictive relationship between early ANS acuity and later math ability add to the growing evidence for the importance of early numerical estimation skills. PMID:23814453 19. Rational approximations for tomographic reconstructions Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas 2013-06-01 We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp-Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. 20. Approximate solutions to fractional subdiffusion equations Hristov, J. 2011-03-01 The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile. The solution was performed with Riemann-Liouville time-fractional derivative since the integral approach avoids the definition of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems): 1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed through the M-Wright function. The solutions demonstrate some basic issues of the suggested integral approach, among them: a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical results allowing comparisons to the known solutions expressed to the M-Wright function and error estimations. 1. Approximated solutions to Born-Infeld dynamics Ferraro, Rafael; Nigro, Mauro 2016-02-01 The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field. 2. Flow past a porous approximate spherical shell Srinivasacharya, D. 2007-07-01 In this paper, the creeping flow of an incompressible viscous liquid past a porous approximate spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier Stokes equation. The flow within the porous annulus region of the shell is governed by Darcy’s Law. The boundary conditions used at the interface are continuity of the normal velocity, continuity of the pressure and Beavers and Joseph slip condition. An exact solution for the problem is obtained. An expression for the drag on the porous approximate spherical shell is obtained. The drag experienced by the shell is evaluated numerically for several values of the parameters governing the flow. 3. Heat pipe transient response approximation. SciTech Connect Reid, R. S. 2001-01-01 A simple and concise routine that approximates the response of an alkali metal heat pipe to changes in evaporator heat transfer rate is described. This analytically based routine is compared with data from a cylindrical heat pipe with a crescent-annular wick that undergoes gradual (quasi-steady) transitions through the viscous and condenser boundary heat transfer limits. The sonic heat transfer limit can also be incorporated into this routine for heat pipes with more closely coupled condensers. The advantages and obvious limitations of this approach are discussed. For reference, a source code listing for the approximation appears at the end of this paper. 4. Approximating spatially exclusive invasion processes. PubMed Ross, Joshua V; Binder, Benjamin J 2014-05-01 A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates. 5. Galerkin approximations for dissipative magnetohydrodynamics NASA Technical Reports Server (NTRS) Chen, Hudong; Shan, Xiaowen; Montgomery, David 1990-01-01 A Galerkin approximation scheme is proposed for voltage-driven, dissipative magnetohydrodynamics. The trial functions are exact eigenfunctions of the linearized continuum equations and represent helical deformations of the axisymmetric, zero-flow, driven steady state. The lowest nontrivial truncation is explored: one axisymmetric trial function and one helical trial function each for the magnetic and velocity fields. The system resembles the Lorenz approximation to Benard convection, but in the region of believed applicability, its dynamical behavior is rather different, including relaxation to a helically deformed state similar to those that have emerged in the much higher resolution computations of Dahlburg et al. 6. Second Approximation to Conical Flows DTIC Science & Technology 1950-12-01 Public Release WRIGHT AIR DEVELOPMENT CENTER AF-WP-(B)-O-29 JUL 53 100 NOTICES ’When Government drawings, specifications, or other data are used V...so that the X, the approximation always depends on the ( "/)th, etc. Here the second approximation, i.e., the terms in C and 62, are computed and...the scheme shown in Fig. 1, the isentropic equations of motion are (cV-X2) +~X~C 6 +- 4= -x- 1 It is assumed that + Ux !E . O’/ + (8) Introducing Eqs 7. Exponential Approximations Using Fourier Series Partial Sums NASA Technical Reports Server (NTRS) Banerjee, Nana S.; Geer, James F. 1997-01-01 The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples. 8. Pythagorean Approximations and Continued Fractions ERIC Educational Resources Information Center Peralta, Javier 2008-01-01 In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers… 9. Pythagorean Approximations and Continued Fractions ERIC Educational Resources Information Center Peralta, Javier 2008-01-01 In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers… 10. Singularly Perturbed Lie Bracket Approximation SciTech Connect Durr, Hans-Bernd; Krstic, Miroslav; Scheinker, Alexander; Ebenbauer, Christian 2015-03-27 Here, we consider the interconnection of two dynamical systems where one has an input-affine vector field. We show that by employing a singular perturbation analysis and the Lie bracket approximation technique, the stability of the overall system can be analyzed by regarding the stability properties of two reduced, uncoupled systems. 11. Correlations between p21 expression and clinicopathological findings, p53 gene and protein alterations, and survival in patients with endometrial carcinoma. PubMed Ito, K; Sasano, H; Matsunaga, G; Sato, S; Yajima, A; Nasim, S; Garret, C T 1997-11-01 The p21 protein inhibits cyclin-dependent kinases and mediates cell-cycle arrest and cell differentiation. It is induced by wild-type p53, but not by mutant p53. This study of 75 patients with endometrial carcinoma investigates the relationship between p21 expression and the functional status of p53, and the usefulness of p21 as a prognostic marker. Correlations were determined between p21 immunoreactivity, p53 overexpression as examined by immunohistochemistry, p53 DNA mutations as examined by polymerase chain reaction-single-stranded conformation polymorphism (PCR-SSCP) analysis, and clinicopathological features, including the clinical outcome. Immunoreactivity for p21 and p53 mutations were detected in 47 (62.7 per cent), 37 (49 per cent), and 23 (31 per cent) patients, respectively. There were no significant correlations between the presence or absence of p21 immunoreactivity and p53 overexpression and DNA mutations. Survival curves revealed that patients with p53 overexpression tended to have a poorer prognosis than those without p53 overexpression (P = 0.104), that patients with p53 mutations had a significantly worse prognosis than those without mutations (P = 0.035), and that patients with p21 expression tended to have a better prognosis than those without p21 expression (P = 0.074). Immunohistochemical analysis of p21 was not useful for evaluating the functional status of p53 in patients with endometrial carcinoma. Both p21 expression and p53 abnormalities were considered as prognostic indicators in patients with endometrioid endometrial carcinoma. 12. Localization and stationary phase approximation on supermanifolds NASA Astrophysics Data System (ADS) Zakharevich, Valentin 2017-08-01 Given an odd vector field Q on a supermanifold M and a Q-invariant density μ on M, under certain compactness conditions on Q, the value of the integral ∫Mμ is determined by the value of μ on any neighborhood of the vanishing locus N of Q. We present a formula for the integral in the case where N is a subsupermanifold which is appropriately non-degenerate with respect to Q. In the process, we discuss the linear algebra necessary to express our result in a coordinate independent way. We also extend the stationary phase approximation and the Morse-Bott lemma to supermanifolds. 13. Curved Finite Elements and Curve Approximation NASA Technical Reports Server (NTRS) Baart, M. L. 1985-01-01 The approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves. 14. Finding food PubMed Central Forsyth, Ann; Lytle, Leslie; Riper, David Van 2011-01-01 A significant amount of travel is undertaken to find food. This paper examines challenges in measuring access to food using Geographic Information Systems (GIS), important in studies of both travel and eating behavior. It compares different sources of data available including fieldwork, land use and parcel data, licensing information, commercial listings, taxation data, and online street-level photographs. It proposes methods to classify different kinds of food sales places in a way that says something about their potential for delivering healthy food options. In assessing the relationship between food access and travel behavior, analysts must clearly conceptualize key variables, document measurement processes, and be clear about the strengths and weaknesses of data. PMID:21837264 15. A Mathematica program for the approximate analytical solution to a nonlinear undamped Duffing equation by a new approximate approach NASA Astrophysics Data System (ADS) Wu, Dongmei; Wang, Zhongcheng 2006-03-01 According to Mickens [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563], the general HB (harmonic balance) method is an approximation to the convergent Fourier series representation of the periodic solution of a nonlinear oscillator and not an approximation to an expansion in terms of a small parameter. Consequently, for a nonlinear undamped Duffing equation with a driving force Bcos(ωx), to find a periodic solution when the fundamental frequency is identical to ω, the corresponding Fourier series can be written as y˜(x)=∑n=1m acos[(2n-1)ωx]. How to calculate the coefficients of the Fourier series efficiently with a computer program is still an open problem. For HB method, by substituting approximation y˜(x) into force equation, expanding the resulting expression into a trigonometric series, then letting the coefficients of the resulting lowest-order harmonic be zero, one can obtain approximate coefficients of approximation y˜(x) [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563]. But for nonlinear differential equations such as Duffing equation, it is very difficult to construct higher-order analytical approximations, because the HB method requires solving a set of algebraic equations for a large number of unknowns with very complex nonlinearities. To overcome the difficulty, forty years ago, Urabe derived a computational method for Duffing equation based on Galerkin procedure [M. Urabe, A. Reiter, Numerical computation of nonlinear forced oscillations by Galerkin's procedure, J. Math. Anal. Appl. 14 (1966) 107-140]. Dooren obtained an approximate solution of the Duffing oscillator with a special set of parameters by using Urabe's method [R. van Dooren, Stabilization of Cowell's classic finite difference method for numerical integration, J. Comput. Phys. 16 (1974) 186-192]. In this paper, in the frame of the general HB method 16. An accurate two-phase approximate solution to the acute viral infection model SciTech Connect Perelson, Alan S 2009-01-01 During an acute viral infection, virus levels rise, reach a peak and then decline. Data and numerical solutions suggest the growth and decay phases are linear on a log scale. While viral dynamic models are typically nonlinear with analytical solutions difficult to obtain, the exponential nature of the solutions suggests approximations can be found. We derive a two-phase approximate solution to the target cell limited influenza model and illustrate the accuracy using data and previously established parameter values of six patients infected with influenza A. For one patient, the subsequent fall in virus concentration was not consistent with our predictions during the decay phase and an alternate approximation is derived. We find expressions for the rate and length of initial viral growth in terms of the parameters, the extent each parameter is involved in viral peaks, and the single parameter responsible for virus decay. We discuss applications of this analysis in antiviral treatments and investigating host and virus heterogeneities. 17. Gene expression profiles for the human pancreas and purified islets in Type 1 diabetes: new findings at clinical onset and in long-standing diabetes PubMed Central Planas, R; Carrillo, J; Sanchez, A; Ruiz de Villa, M C; Nuñez, F; Verdaguer, J; James, R F L; Pujol-Borrell, R; Vives-Pi, M 2010-01-01 Type 1 diabetes (T1D) is caused by the selective destruction of the insulin-producing β cells of the pancreas by an autoimmune response. Due to ethical and practical difficulties, the features of the destructive process are known from a small number of observations, and transcriptomic data are remarkably missing. Here we report whole genome transcript analysis validated by quantitative reverse transcription–polymerase chain reaction (qRT–PCR) and correlated with immunohistological observations for four T1D pancreases (collected 5 days, 9 months, 8 and 10 years after diagnosis) and for purified islets from two of them. Collectively, the expression profile of immune response and inflammatory genes confirmed the current views on the immunopathogenesis of diabetes and showed similarities with other autoimmune diseases; for example, an interferon signature was detected. The data also supported the concept that the autoimmune process is maintained and balanced partially by regeneration and regulatory pathway activation, e.g. non-classical class I human leucocyte antigen and leucocyte immunoglobulin-like receptor, subfamily B1 (LILRB1). Changes in gene expression in islets were confined mainly to endocrine and neural genes, some of which are T1D autoantigens. By contrast, these islets showed only a few overexpressed immune system genes, among which bioinformatic analysis pointed to chemokine (C-C motif) receptor 5 (CCR5) and chemokine (CXC motif) receptor 4) (CXCR4) chemokine pathway activation. Remarkably, the expression of genes of innate immunity, complement, chemokines, immunoglobulin and regeneration genes was maintained or even increased in the long-standing cases. Transcriptomic data favour the view that T1D is caused by a chronic inflammatory process with a strong participation of innate immunity that progresses in spite of the regulatory and regenerative mechanisms. PMID:19912253 18. Approximate gauge symmetry of composite vector bosons NASA Astrophysics Data System (ADS) Suzuki, Mahiko 2010-08-01 It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries. 19. Ab initio dynamical vertex approximation NASA Astrophysics Data System (ADS) Galler, Anna; Thunström, Patrik; Gunacker, Patrik; Tomczak, Jan M.; Held, Karsten 2017-03-01 Diagrammatic extensions of dynamical mean-field theory (DMFT) such as the dynamical vertex approximation (DΓ A) allow us to include nonlocal correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an Ab initio DΓ A approach (AbinitioDΓ A ) for electronic structure calculations of materials. The starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare nonlocal Coulomb interaction and all local vertex corrections. From this, we calculate the full nonlocal vertex and the nonlocal self-energy through the Bethe-Salpeter equation. The AbinitioDΓ A approach naturally generates all local DMFT correlations and all nonlocal G W contributions, but also further nonlocal correlations beyond: mixed terms of the former two and nonlocal spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO3. 20. Random-Phase Approximation Methods NASA Astrophysics Data System (ADS) Chen, Guo P.; Voora, Vamsee K.; Agee, Matthew M.; Balasubramani, Sree Ganesh; Furche, Filipp 2017-05-01 Random-phase approximation (RPA) methods are rapidly emerging as cost-effective validation tools for semilocal density functional computations. We present the theoretical background of RPA in an intuitive rather than formal fashion, focusing on the physical picture of screening and simple diagrammatic analysis. A new decomposition of the RPA correlation energy into plasmonic modes leads to an appealing visualization of electron correlation in terms of charge density fluctuations. Recent developments in the areas of beyond-RPA methods, RPA correlation potentials, and efficient algorithms for RPA energy and property calculations are reviewed. The ability of RPA to approximately capture static correlation in molecules is quantified by an analysis of RPA natural occupation numbers. We illustrate the use of RPA methods in applications to small-gap systems such as open-shell d- and f-element compounds, radicals, and weakly bound complexes, where semilocal density functional results exhibit strong functional dependence. 1. Testing the frozen flow approximation NASA Technical Reports Server (NTRS) Lucchin, Francesco; Matarrese, Sabino; Melott, Adrian L.; Moscardini, Lauro 1993-01-01 We investigate the accuracy of the frozen-flow approximation (FFA), recently proposed by Matarrese, et al. (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a number of statistics between results of the FFA and n-body simulations, including those used by Melott, Pellman & Shandarin (1993) to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense, e.g. in reproducing the counts-in-cell distribution, at small scales, but it does poorly in the crosscorrelation with n-body which means it is generally not moving mass to the right place, especially in models with high small-scale power. 2. Potential of the approximation method SciTech Connect Amano, K.; Maruoka, A. 1996-12-31 Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices: For 5 {le} s {le} m/4, a monotone circuit computing CLIQUE(m, s) contains at least (1/2)1.8{sup min}({radical}s-1/2,m/(4s)) gates: If a non-monotone circuit computes CLIQUE using a {open_quotes}small{close_quotes} amount of negation, then the circuit contains an exponential number of gates. The former is proved very simply using so called bottleneck counting argument within the framework of approximation, whereas the latter is verified introducing a notion of restricting negation and generalizing the sunflower contraction. 3. Nonlinear Filtering and Approximation Techniques DTIC Science & Technology 1991-09-01 Shwartz), Academic Press (1991). [191 M.Cl. ROUTBAUD, Fiting lindairc par morceaux avec petit bruit d’obserration, These. Universit6 de Provence ( 1990...Kernel System (GKS), Academic Press (1983). 181 H.J. KUSHNER, Probability methods for approximations in stochastic control and for elliptic equations... Academic Press (1977). [9] F. LE GLAND, Time discretization of nonlinear filtering equations, in: 28th. IEEE CDC, Tampa, pp. 2601-2606. IEEE Press (1989 4. Analytical solution approximation for bearing NASA Astrophysics Data System (ADS) Hanafi, Lukman; Mufid, M. Syifaul 2017-08-01 The purpose of lubrication is to separate two surfaces sliding past each other with a film of some material which can be sheared without causing any damage to the surfaces. Reynolds equation is a basic equation for fluid lubrication which is applied in the bearing problem. This equation can be derived from Navier-Stokes equation and continuity equation. In this paper Reynolds equation is solved using analytical approximation by making simplification to obtain pressure distribution. 5. Ultrafast approximation for phylogenetic bootstrap. PubMed Minh, Bui Quang; Nguyen, Minh Anh Thi; von Haeseler, Arndt 2013-05-01 Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and the Shimodaira-Hasegawa-like approximate likelihood ratio test have been introduced to speed up the bootstrap. Here, we suggest an ultrafast bootstrap approximation approach (UFBoot) to compute the support of phylogenetic groups in maximum likelihood (ML) based trees. To achieve this, we combine the resampling estimated log-likelihood method with a simple but effective collection scheme of candidate trees. We also propose a stopping rule that assesses the convergence of branch support values to automatically determine when to stop collecting candidate trees. UFBoot achieves a median speed up of 3.1 (range: 0.66-33.3) to 10.2 (range: 1.32-41.4) compared with RAxML RBS for real DNA and amino acid alignments, respectively. Moreover, our extensive simulations show that UFBoot is robust against moderate model violations and the support values obtained appear to be relatively unbiased compared with the conservative standard bootstrap. This provides a more direct interpretation of the bootstrap support. We offer an efficient and easy-to-use software (available at http://www.cibiv.at/software/iqtree) to perform the UFBoot analysis with ML tree inference. 6. Approximate Counting of Graphical Realizations. PubMed Erdős, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos 2015-01-01 In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. 7. Approximate Counting of Graphical Realizations PubMed Central 2015-01-01 In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994 8. Computer Experiments for Function Approximations SciTech Connect Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C 2007-10-15 This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative. 9. CMB-lensing beyond the Born approximation NASA Astrophysics Data System (ADS) Marozzi, Giovanni; Fanizza, Giuseppe; Di Dio, Enea; Durrer, Ruth 2016-09-01 We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles l lesssim 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments. 10. Analytic approximate radiation effects due to Bremsstrahlung SciTech Connect Ben-Zvi I. 2012-02-01 The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R&D Energy Recovery Linac. 11. Variational extensions of the mean spherical approximation NASA Astrophysics Data System (ADS) Blum, L.; Ubriaco, M. 2000-04-01 In a previous work we have proposed a method to study complex systems with objects of arbitrary size. For certain specific forms of the atomic and molecular interactions, surprisingly simple and accurate theories (The Variational Mean Spherical Scaling Approximation, VMSSA) [(Velazquez, Blum J. Chem. Phys. 110 (1990) 10 931; Blum, Velazquez, J. Quantum Chem. (Theochem), in press)] can be obtained. The basic idea is that if the interactions can be expressed in a rapidly converging sum of (complex) exponentials, then the Ornstein-Zernike equation (OZ) has an analytical solution. This analytical solution is used to construct a robust interpolation scheme, the variation mean spherical scaling approximation (VMSSA). The Helmholtz excess free energy Δ A=Δ E- TΔ S is then written as a function of a scaling matrix Γ. Both the excess energy Δ E( Γ) and the excess entropy Δ S( Γ) will be functionals of Γ. In previous work of this series the form of this functional was found for the two- (Blum, Herrera, Mol. Phys. 96 (1999) 821) and three-exponential closures of the OZ equation (Blum, J. Stat. Phys., submitted for publication). In this paper we extend this to M Yukawas, a complete basis set: We obtain a solution for the one-component case and give a closed-form expression for the MSA excess entropy, which is also the VMSSA entropy. 12. Recent SFR calibrations and the constant SFR approximation NASA Astrophysics Data System (ADS) Cerviño, M.; Bongiovanni, A.; Hidalgo, S. 2016-05-01 Aims: Star formation rate (SFR) inferences are based on the so-called constant SFR approximation, where synthesis models are required to provide a calibration. We study the key points of such an approximation with the aim to produce accurate SFR inferences. Methods: We use the intrinsic algebra of synthesis models and explore how the SFR can be inferred from the integrated light without any assumption about the underlying star formation history (SFH). Results: We show that the constant SFR approximation is a simplified expression of deeper characteristics of synthesis models: It characterizes the evolution of single stellar populations (SSPs), from which the SSPs as a sensitivity curve over different measures of the SFH can be obtained. As results, we find that (1) the best age to calibrate SFR indices is the age of the observed system (i.e., about 13 Gyr for z = 0 systems); (2) constant SFR and steady-state luminosities are not required to calibrate the SFR; (3) it is not possible to define a single SFR timescale over which the recent SFH is averaged, and we suggest to use typical SFR indices (ionizing flux, UV fluxes) together with untypical ones (optical or IR fluxes) to correct the SFR for the contribution of the old component of the SFH. We show how to use galaxy colors to quote age ranges where the recent component of the SFH is stronger or softer than the older component. Conclusions: Despite of SFR calibrations are unaffected by this work, the meaning of results obtained by SFR inferences does. In our framework, results such as the correlation of SFR timescales with galaxy colors, or the sensitivity of different SFR indices to variations in the SFH, fit naturally. This framework provides a theoretical guide-line to optimize the available information from data and numerical experiments to improve the accuracy of SFR inferences. 13. Convergence to approximate solutions and perturbation resilience of iterative algorithms NASA Astrophysics Data System (ADS) Reich, Simeon; Zaslavski, Alexander J. 2017-04-01 We first consider nonexpansive self-mappings of a metric space and study the asymptotic behavior of their inexact orbits. We then apply our results to the analysis of iterative methods for finding approximate fixed points of nonexpansive mappings and approximate zeros of monotone operators. 14. Optimal Markov approximations and generalized embeddings NASA Astrophysics Data System (ADS) Holstein, Detlef; Kantz, Holger 2009-05-01 Based on information theory, we present a method to determine an optimal Markov approximation for modeling and prediction from time series data. The method finds a balance between minimal modeling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples, and the consequences for prediction are evaluated by means of the root-mean-squared prediction error for point prediction. 15. The monoenergetic approximation in stellarator neoclassical calculations NASA Astrophysics Data System (ADS) Landreman, Matt 2011-08-01 In 'monoenergetic' stellarator neoclassical calculations, to expedite computation, ad hoc changes are made to the kinetic equation so speed enters only as a parameter. Here we examine the validity of this approach by considering the effective particle trajectories in a model magnetic field. We find monoenergetic codes systematically under-predict the true trapped particle fraction. The error in the trapped ion fraction can be of order unity for large but experimentally realizable values of the radial electric field, suggesting some results of these codes may be unreliable in this regime. This inaccuracy is independent of any errors introduced by approximation of the collision operator. 16. Neighbourhood approximation using randomized forests. PubMed Konukoglu, Ender; Glocker, Ben; Zikic, Darko; Criminisi, Antonio 2013-10-01 Leveraging available annotated data is an essential component of many modern methods for medical image analysis. In particular, approaches making use of the "neighbourhood" structure between images for this purpose have shown significant potential. Such techniques achieve high accuracy in analysing an image by propagating information from its immediate "neighbours" within an annotated database. Despite their success in certain applications, wide use of these methods is limited due to the challenging task of determining the neighbours for an out-of-sample image. This task is either computationally expensive due to large database sizes and costly distance evaluations, or infeasible due to distance definitions over semantic information, such as ground truth annotations, which is not available for out-of-sample images. This article introduces Neighbourhood Approximation Forests (NAFs), a supervised learning algorithm providing a general and efficient approach for the task of approximate nearest neighbour retrieval for arbitrary distances. Starting from an image training database and a user-defined distance between images, the algorithm learns to use appearance-based features to cluster images approximating the neighbourhood structured induced by the distance. NAF is able to efficiently infer nearest neighbours of an out-of-sample image, even when the original distance is based on semantic information. We perform experimental evaluation in two different scenarios: (i) age prediction from brain MRI and (ii) patch-based segmentation of unregistered, arbitrary field of view CT images. The results demonstrate the performance, computational benefits, and potential of NAF for different image analysis applications. Copyright © 2013 Elsevier B.V. All rights reserved. 17. Topics in Multivariate Approximation Theory. DTIC Science & Technology 1982-05-01 of the Bramble -Hilbert lemma (see Bramble & H𔃻hert (13ŕ). Kergin’s scheme raises some questions. In .ontrast £.t its univar- iate antecedent, it...J. R. Rice (19791# An adaptive algorithm for multivariate approximation giving optimal convergence rates, J.Approx. Theory 25, 337-359. J. H. Bramble ...J.Numer.Anal. 7, 112-124. J. H. Bramble & S. R. Hilbert (19711, BoUnds for a class of linear functionals with applications to Hermite interpolation 18. Approximate transferability in conjugated polyalkenes NASA Astrophysics Data System (ADS) Eskandari, Keiamars; Mandado, Marcos; Mosquera, Ricardo A. 2007-03-01 QTAIM computed atomic and bond properties, as well as delocalization indices (obtained from electron densities computed at HF, MP2 and B3LYP levels) of several linear and branched conjugated polyalkenes and O- and N-containing conjugated polyenes have been employed to assess approximate transferable CH groups. The values of these properties indicate the effects of the functional group extend to four CH groups, whereas those of the terminal carbon affect up to three carbons. Ternary carbons also modify significantly the properties of atoms in α, β and γ. 19. Improved non-approximability results SciTech Connect Bellare, M.; Sudan, M. 1994-12-31 We indicate strong non-approximability factors for central problems: N{sup 1/4} for Max Clique; N{sup 1/10} for Chromatic Number; and 66/65 for Max 3SAT. Underlying the Max Clique result is a proof system in which the verifier examines only three {open_quotes}free bits{close_quotes} to attain an error of 1/2. Underlying the Chromatic Number result is a reduction from Max Clique which is more efficient than previous ones. 20. Approximation for Bayesian Ability Estimation. DTIC Science & Technology 1987-02-18 posterior pdfs of ande are given by p(-[Y) p(F) F P((y lei’ j)P )d. SiiJ i (4) a r~d p(e Iy) - p(t0) 1 J i P(Yij ei, (5) As shown in Tsutakawa and Lin...inverse A Hessian of the log of (27) with respect to , evaulatedat a Then, under regularity conditions, the marginal posterior pdf of O is...two-way contingency tables. Journal of Educational Statistics, 11, 33-56. Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos Estadistica , 31 1. Fermion tunneling beyond semiclassical approximation SciTech Connect Majhi, Bibhas Ranjan 2009-02-15 Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in R. Banerjee and B. R. Majhi, J. High Energy Phys. 06 (2008) 095 for the scalar particle, Hawking radiation as tunneling of the Dirac particle through an event horizon is analyzed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly. 2. Generalized Gradient Approximation Made Simple SciTech Connect Perdew, J.P.; Burke, K.; Ernzerhof, M. 1996-10-01 Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.} 3. Risk analysis using a hybrid Bayesian-approximate reasoning methodology. SciTech Connect Bott, T. F.; Eisenhawer, S. W. 2001-01-01 Analysts are sometimes asked to make frequency estimates for specific accidents in which the accident frequency is determined primarily by safety controls. Under these conditions, frequency estimates use considerable expert belief in determining how the controls affect the accident frequency. To evaluate and document beliefs about control effectiveness, we have modified a traditional Bayesian approach by using approximate reasoning (AR) to develop prior distributions. Our method produces accident frequency estimates that separately express the probabilistic results produced in Bayesian analysis and possibilistic results that reflect uncertainty about the prior estimates. Based on our experience using traditional methods, we feel that the AR approach better documents beliefs about the effectiveness of controls than if the beliefs are buried in Bayesian prior distributions. We have performed numerous expert elicitations in which probabilistic information was sought from subject matter experts not trained In probability. We find it rnuch easier to elicit the linguistic variables and fuzzy set membership values used in AR than to obtain the probability distributions used in prior distributions directly from these experts because it better captures their beliefs and better expresses their uncertainties. 4. Using OPLS-DA to find new hypotheses in vast amounts of gene expression data - studying the progression of cardiac hypertrophy in the heart of aorta ligated rat. PubMed Gennebäck, Nina; Malm, Linus; Hellman, Urban; Waldenström, Anders; Mörner, Stellan 2013-06-10 One of the great problems facing science today lies in data mining of the vast amount of data. In this study we explore a new way of using orthogonal partial least squares-discrimination analysis (OPLS-DA) to analyze multidimensional data. Myocardial tissues from aorta ligated and control rats (sacrificed at the acute, the adaptive and the stable phases of hypertrophy) were analyzed with whole genome microarray and OPLS-DA. Five functional gene transcript groups were found to show interesting clusters associated with the aorta ligated or the control animals. Clustering of "ECM and adhesion molecules" confirmed previous results found with traditional statistics. The clustering of "Fatty acid metabolism", "Glucose metabolism", "Mitochondria" and "Atherosclerosis" which are new results is hard to interpret, thereby being possible subject to new hypothesis formation. We propose that OPLS-DA is very useful in finding new results not found with traditional statistics, thereby presenting an easy way of creating new hypotheses. 5. Strong washout approximation to resonant leptogenesis NASA Astrophysics Data System (ADS) Garbrecht, Björn; Gautier, Florian; Klaric, Juraj 2014-09-01 We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ɛ=Xsin(2varphi)/(X2+sin2varphi), where X=8πΔ/(\|Y1\|2+\|Y2\|2), Δ=4(M1-M2)/(M1+M2), varphi=arg(Y2/Y1), and M1,2, Y1,2 are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where \|Y1,2\|2gg Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space. 6. Wavelet Approximation in Data Assimilation NASA Technical Reports Server (NTRS) Tangborn, Andrew; Atlas, Robert (Technical Monitor) 2002-01-01 Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation. 7. Rational approximations to fluid properties SciTech Connect Kincaid, J.M. 1990-05-01 The purpose of this report is to summarize some results that were presented at the Spring AIChE meeting in Orlando, Florida (20 March 1990). We report on recent attempts to develop a systematic method, based on the technique of rational approximation, for creating mathematical models of real-fluid equations of state and related properties. Equation-of-state models for real fluids are usually created by selecting a function {tilde p} (T,{rho}) that contains a set of parameters {l brace}{gamma}{sub i}{r brace}; the {l brace}{gamma}{sub i}{r brace} is chosen such that {tilde p}(T,{rho}) provides a good fit to the experimental data. (Here p is the pressure, T the temperature and {rho} is the density). In most cases a nonlinear least-squares numerical method is used to determine {l brace}{gamma}{sub i}{r brace}. There are several drawbacks to this method: one has essentially to guess what {tilde p}(T,{rho}) should be; the critical region is seldom fit very well and nonlinear numerical methods are time consuming and sometimes not very stable. The rational approximation approach we describe may eliminate all of these drawbacks. In particular it lets the data choose the function {tilde p}(T,{rho}) and its numerical implementation involves only linear algorithms. 27 refs., 5 figs. 8. Methodology for approximating and implementing fixed-point approximations of cosines for order-16 DCT NASA Astrophysics Data System (ADS) Hinds, Arianne T. 2011-09-01 Spatial transformations whose kernels employ sinusoidal functions for the decorrelation of signals remain as fundamental components of image and video coding systems. Practical implementations are designed in fixed precision for which the most challenging task is to approximate these constants with values that are both efficient in terms of complexity and accurate with respect to their mathematical definitions. Scaled architectures, for example, as used in the implementations of the order-8 Discrete Cosine Transform and its corresponding inverse both specified in ISO/IEC 23002-2 (MPEG C Pt. 2), can be utilized to mitigate the complexity of these approximations. That is, the implementation of the transform can be designed such that it is completed in two stages: 1) the main transform matrix in which the sinusoidal constants are roughly approximated, and 2) a separate scaling stage to further refine the approximations. This paper describes a methodology termed the Common Factor Method, for finding fixed-point approximations of such irrational values suitable for use in scaled architectures. The order-16 Discrete Cosine Transform provides a framework in which to demonstrate the methodology, but the methodology itself can be employed to design fixed-point implementations of other linear transformations. 9. Solving Math Problems Approximately: A Developmental Perspective PubMed Central Ganor-Stern, Dana 2016-01-01 Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. PMID:27171224 10. Solving Math Problems Approximately: A Developmental Perspective. PubMed Ganor-Stern, Dana 2016-01-01 Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. 11. Capacitor-Chain Successive-Approximation ADC NASA Technical Reports Server (NTRS) Cunningham, Thomas 2003-01-01 A proposed successive-approximation analog-to-digital converter (ADC) would contain a capacitively terminated chain of identical capacitor cells. Like a conventional successive-approximation ADC containing a bank of binary-scaled capacitors, the proposed ADC would store an input voltage on a sample-and-hold capacitor and would digitize the stored input voltage by finding the closest match between this voltage and a capacitively generated sum of binary fractions of a reference voltage (Vref). However, the proposed capacitor-chain ADC would offer two major advantages over a conventional binary-scaled-capacitor ADC: (1) In a conventional ADC that digitizes to n bits, the largest capacitor (representing the most significant bit) must have 2(exp n-1) times as much capacitance, and hence, approximately 2(exp n-1) times as much area as does the smallest capacitor (representing the least significant bit), so that the total capacitor area must be 2(exp n) times that of the smallest capacitor. In the proposed capacitor-chain ADC, there would be three capacitors per cell, each approximately equal to the smallest capacitor in the conventional ADC, and there would be one cell per bit. Therefore, the total capacitor area would be only about 3(exp n) times that of the smallest capacitor. The net result would be that the proposed ADC could be considerably smaller than the conventional ADC. (2) Because of edge effects, parasitic capacitances, and manufacturing tolerances, it is difficult to make capacitor banks in which the values of capacitance are scaled by powers of 2 to the required precision. In contrast, because all the capacitors in the proposed ADC would be identical, the problem of precise binary scaling would not arise. 12. Prevalence of self-reported myocardial infarction in a Greek sample: findings from a population-based study in an urban area (medical express 2002). PubMed Gikas, A; Sotiropoulos, A; Panagiotakos, D; Pappas, S 2004-12-01 During the 1970s and 1980s, Greece was known as a country with low prevalence and incidence of coronary heart disease, compared to Western populations. However, during the past decades, the Greek population has experienced marked but uneven socio-economic development, as well as change in lifestyle habits. We assessed the prevalence of self-reported myocardial infarction (MI) in a sample of the general population, aged 20-94 years. The overall prevalence of self-reported MI was 4.1% (6.3% in men and 1.9% in women). The age-adjusted prevalence was found to be 3.6%, showing a threefold increase compared to 1980s. Age, gender (male), low educational level, obesity/overweight, hypercholesterolemia, diabetes, hypertension, smoking and origin were strongly associated with prevalence of MI. Our findings indicate that the prevalence of MI increased dramatically during the past years, reflecting the change in lifestyle habits that have gradually given way to "Western"-type diets and a more sedentary lifestyle. Therefore, the need for urgent intervention is considered essential in order to prevent a further increase of disease burden. 13. Analytical approximations for spiral waves SciTech Connect Löber, Jakob Engel, Harald 2013-12-15 We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium. 14. Indexing the approximate number system. PubMed Inglis, Matthew; Gilmore, Camilla 2014-01-01 Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects. 15. Approximating metal-insulator transitions NASA Astrophysics Data System (ADS) Danieli, Carlo; Rayanov, Kristian; Pavlov, Boris; Martin, Gaven; Flach, Sergej 2015-12-01 We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step, the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate Metal-Insulator Transitions (MIT) at the finite iteration steps. We also report evidence on mobility edges, which are at variance to the celebrated Aubry-André model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity in the metallic phase, similar to the divergence of the localization length in the insulating phase. 16. Analytical approximations for spiral waves. PubMed Löber, Jakob; Engel, Harald 2013-12-01 We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R(0). For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R(+)) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R(+) with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium. 17. Closed-Form Approximations of First-Passage Distributions for a Stochastic Decision-Making Model. PubMed Broderick, Tamara; Wong-Lin, Kong Fatt; Holmes, Philip 2009-06-01 In free response choice tasks, decision making is often modeled as a first-passage problem for a stochastic differential equation. In particular, drift-diffusion processes with constant or time-varying drift rates and noise can reproduce behavioral data (accuracy and response-time distributions) and neuronal firing rates. However, no exact solutions are known for the first-passage problem with time-varying data. Recognizing the importance of simple closed-form expressions for modeling and inference, we show that an interrogation or cued-response protocol, appropriately interpreted, can yield approximate first-passage (response time) distributions for a specific class of time-varying processes used to model evidence accumulation. We test these against exact expressions for the constant drift case and compare them with data from a class of sigmoidal functions. We find that both the direct interrogation approximation and an error-minimizing interrogation approximation can capture a variety of distribution shapes and mode numbers but that the direct approximation, in particular, is systematically biased away from the correct free response distribution. 18. IONIS: Approximate atomic photoionization intensities NASA Astrophysics Data System (ADS) Heinäsmäki, Sami 2012-02-01 A program to compute relative atomic photoionization cross sections is presented. The code applies the output of the multiconfiguration Dirac-Fock method for atoms in the single active electron scheme, by computing the overlap of the bound electron states in the initial and final states. The contribution from the single-particle ionization matrix elements is assumed to be the same for each final state. This method gives rather accurate relative ionization probabilities provided the single-electron ionization matrix elements do not depend strongly on energy in the region considered. The method is especially suited for open shell atoms where electronic correlation in the ionic states is large. Program summaryProgram title: IONIS Catalogue identifier: AEKK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1149 No. of bytes in distributed program, including test data, etc.: 12 877 Distribution format: tar.gz Programming language: Fortran 95 Computer: Workstations Operating system: GNU/Linux, Unix Classification: 2.2, 2.5 Nature of problem: Photoionization intensities for atoms. Solution method: The code applies the output of the multiconfiguration Dirac-Fock codes Grasp92 [1] or Grasp2K [2], to compute approximate photoionization intensities. The intensity is computed within the one-electron transition approximation and by assuming that the sum of the single-particle ionization probabilities is the same for all final ionic states. Restrictions: The program gives nonzero intensities for those transitions where only one electron is removed from the initial configuration(s). Shake-type many-electron transitions are not computed. The ionized shell must be closed in the initial state. Running time: Few seconds for a 19. Thermodynamics of an interacting Fermi system in the static fluctuation approximation SciTech Connect Nigmatullin, R. R.; Khamzin, A. A. Popov, I. I. 2012-02-15 We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable approximation allows obtaining the so-called far-distance equations. These equations connecting the quantum states of a Fermi particle with variables of the local field operator contain all necessary information related to the calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system. The basic expressions for the mean energy and heat capacity for the electron gas at low temperatures in the high-density limit were obtained. All expressions are given in the units of r{sub s}, where r{sub s} determines the ratio of a mean distance between electrons to the Bohr radius a{sub 0}. In these expressions, we calculate terms of the respective order r{sub s} and r{sub s}{sup 2}. It is also shown that the static fluctuation approximation allows finding the terms related to higher orders of the decomposition with respect to the parameter r{sub s}. 20. An approximate compact analytical expression for the Blasius velocity profile NASA Astrophysics Data System (ADS) Savaş, Ö. 2012-10-01 A single-term, two-parameter, hyperbolic tangent function is presented to describe the flow profiles in the Blasius boundary layer, which reproduces the streamwise velocity profile within 0.003 (0.3% of free stream velocity) of its numerical exact solution throughout the flow. The function can be inverted for an implicit description of the velocity profile. 1. Network Games and Approximation Algorithms DTIC Science & Technology 2008-01-03 I also spend time during the last three years writing a textbook on Algorithm Design (with Jon Kleinberg) that had now been adopted by a number of...Minimum-Size Bounded-Capacity Cut (MSBCC) problem, in which we are given a graph with an identified source and seek to find a cut minimizing the number ...Distributed Computing (Special Issue PODC 05) Volume 19, Number 4, 2007, 255-266. http://www.springerlink.com/content/x 148746507861 np7/ ?p 2. Optimal Approximation of Quadratic Interval Functions NASA Technical Reports Server (NTRS) Koshelev, Misha; Taillibert, Patrick 1997-01-01 Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones. 3. Nested Taylor decomposition of univariate functions under fluctuationlessness approximation NASA Astrophysics Data System (ADS) Gürvit, Ercan; Baykara, N. A. 2014-10-01 Taylor decomposition of an analytic function and the use of the remainder part of this decomposition expressed in integral form on which Fluctuationlessness theorem is applied was already known in the litterature, but application of Fluctuationlessness approximation twice on the remainder part adds up an amelioration to the approximation. Organisation of the decomposition in such a way that this is made possible is explained in detail in this work. 4. Multidimensional stochastic approximation Monte Carlo NASA Astrophysics Data System (ADS) Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang 2016-06-01 Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) . 5. Approximate Solutions of the Nonlinear Schrödinger Equation for Ground and Excited States of Bose-Einstein Condensates. PubMed Dodd, R J 1996-01-01 I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths, a, and find an analytical expression for the large-N0 limit of the vortex critical frequency for a > 0, by approximate solution of the time-independent nonlinear Schrödinger equation. 6. Approximate Solutions of the Nonlinear Schrödinger Equation for Ground and Excited States of Bose-Einstein Condensates PubMed Central Dodd, R. J. 1996-01-01 I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths, a, and find an analytical expression for the large-N0 limit of the vortex critical frequency for a > 0, by approximate solution of the time-independent nonlinear Schrödinger equation. PMID:27805107 7. Strong washout approximation to resonant leptogenesis SciTech Connect Garbrecht, Björn; Gautier, Florian; Klaric, Juraj E-mail: florian.gautier@tum.de 2014-09-01 We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ε=Xsin(2φ)/(X{sup 2}+sin{sup 2}φ), where X=8πΔ/(\|Y{sub 1}\|{sup 2}+\|Y{sub 2}\|{sup 2}), Δ=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), φ=arg(Y{sub 2}/Y{sub 1}), and M{sub 1,2}, Y{sub 1,2} are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where \|Y{sub 1,2}\|{sup 2}>> Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space. 8. Diffraction by a Hard Half-Plane Useful Approximations to AN Exact Formulation NASA Astrophysics Data System (ADS) OUIS, D. 2002-04-01 In this paper, the problem of diffraction of a spherical wave by a hard half-plane is considered. The starting point is the Biot-Tolstoy theory of diffraction of a spherical wave by a fluid wedge with hard boundaries. In this theory, the field at a point in the fluid is composed eventually of a geometrical part: i.e., a direct component, one or two components due to the reflections on the sides of the hard wedge, and a diffracted component due exclusively to the presence of the edge of the wedge. The mathematical expression of this latter component has originally been given in an explicit closed form for the case of a unit momentum wave incidence, but Medwin has further developed its expression for the more useful case of a Dirac delta point excitation. The expression of this form is given in the time domain, but it is quite difficult to find exactly its Fourier transform for studying the frequency behaviour of the diffracted field. It is thus the aim of this paper to present various useful approximations of the exact expression. Among the approximations treated, three are most accurate for engineering purposes, and one of them is proposed, for its simplicity, as appropriate for most occurring practical situations. 9. Uncertainty relations and approximate quantum error correction NASA Astrophysics Data System (ADS) Renes, Joseph M. 2016-09-01 The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the outcome. Two variants are possible: either Alice tells Bob which observable she measured, or he has to furnish guesses for both cases. Here I derive uncertainty relations for both, formulated directly in terms of Bob's guessing probabilities. For the former these relate to the entanglement that can be recovered by action on Bob's system alone. This gives an explicit quantum circuit for approximate quantum error correction using the guessing measurements for "amplitude" and "phase" information, implicitly used in the recent construction of efficient quantum polar codes. I also find a relation on the guessing probabilities for the latter game, which has application to wave-particle duality relations. 10. Squashed entanglement and approximate private states NASA Astrophysics Data System (ADS) Wilde, Mark M. 2016-11-01 The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it log 2K) in an ɛ -approximate private state is bounded from above by the squashed entanglement of that state plus a term that depends only ɛ and log 2K. Importantly, the extra term does not depend on the dimension of the shield systems of the private state. The result holds for the bipartite squashed entanglement, and an extension of this result is established for two different flavors of the multipartite squashed entanglement. 11. Approximate flavor symmetries in the lepton sector SciTech Connect Rasin, A. ); Silva, J.P. ) 1994-01-01 Approximate flavor symmetries in the quark sector have been used as a handle on physics beyond the standard model. Because of the great interest in neutrino masses and mixings and the wealth of existing and proposed neutrino experiments it is important to extend this analysis to the leptonic sector. We show that in the seesaw mechanism the neutrino masses and mixing angles do not depend on the details of the right-handed neutrino flavor symmetry breaking, and are related by a simple formula. We propose several [ital Ansa][ital uml]---[ital tze] which relate different flavor symmetry-breaking parameters and find that the MSW solution to the solar neutrino problem is always easily fit. Further, the [nu][sub [mu]-][nu][sub [tau 12. Fast Approximate Quadratic Programming for Graph Matching PubMed Central Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E. 2015-01-01 Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624 13. Fast approximate quadratic programming for graph matching. PubMed Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E 2015-01-01 Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. 14. Adiabatic approximation and fluctuations in exciton-polariton condensates Bobrovska, Nataliya; Matuszewski, Michał 2015-07-01 We study the relation between the models commonly used to describe the dynamics of nonresonantly pumped exciton-polariton condensates, namely the ones described by the complex Ginzburg-Landau equation, and by the open-dissipative Gross-Pitaevskii equation including a separate equation for the reservoir density. In particular, we focus on the validity of the adiabatic approximation and small density fluctuations approximation that allow one to reduce the coupled condensate-reservoir dynamics to a single partial differential equation. We find that the adiabatic approximation consists of three independent analytical conditions that have to be fulfilled simultaneously. By investigating stochastic versions of the two corresponding models, we verify that the breakdown of these approximations can lead to discrepancies in correlation lengths and distributions of fluctuations. Additionally, we consider the phase diffusion and number fluctuations of a condensate in a box, and show that self-consistent description requires treatment beyond the typical Bogoliubov approximation. 15. Approximation algorithms for maximum two-dimensional pattern matching SciTech Connect Arikati, S.R.; Dessmark, A.; Lingas, A.; Marathe, M. 1996-07-01 We introduce the following optimization version of the classical pattern matching problem (referred to as the maximum pattern matching problem). Given a two-dimensional rectangular text and a 2- dimensional rectangular pattern find the maximum number of non- overlapping occurrences of the pattern in the text. Unlike the classical 2-dimensional pattern matching problem, the maximum pattern matching problem is NP - complete. We devise polynomial time approximation algorithms and approximation schemes for this problem. We also briefly discuss how the approximation algorithms can be extended to include a number of other variants of the problem. 16. Producing approximate answers to database queries NASA Technical Reports Server (NTRS) Vrbsky, Susan V.; Liu, Jane W. S. 1993-01-01 We have designed and implemented a query processor, called APPROXIMATE, that makes approximate answers available if part of the database is unavailable or if there is not enough time to produce an exact answer. The accuracy of the approximate answers produced improves monotonically with the amount of data retrieved to produce the result. The exact answer is produced if all of the needed data are available and query processing is allowed to continue until completion. The monotone query processing algorithm of APPROXIMATE works within the standard relational algebra framework and can be implemented on a relational database system with little change to the relational architecture. We describe here the approximation semantics of APPROXIMATE that serves as the basis for meaningful approximations of both set-valued and single-valued queries. We show how APPROXIMATE is implemented to make effective use of semantic information, provided by an object-oriented view of the database, and describe the additional overhead required by APPROXIMATE. 17. Grover's quantum search algorithm and Diophantine approximation SciTech Connect Dolev, Shahar; Pitowsky, Itamar; Tamir, Boaz 2006-02-15 In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O({radical}(N)) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using iterations of Grover's basic step only, and no other algorithm. Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m<2{radical}(N)/({radical}(K)-{radical}(M)) obtains. This bound reproduces previous results based on more elaborate algorithms, and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics. 18. Approximated analytical solution to an Ebola optimal control problem Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M. 2016-11-01 An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods. 19. Subdural empyema: CT findings SciTech Connect Zimmerman, R.D.; Leeds, N.E.; Danziger, A. 1984-02-01 CT scans in 49 patients with surgically proven subdural empyema were evaluated. The empyemas were crescentic or lentiform extra-axial hypodense collections (density approximating that of cerebrospinal fluid) with prominent, sharply etched medial rim enhancement. Enhancement of the adjacent cerebral cortex was identified in many cases. Mass effect was always present and in 10 cases so extensive that it overshadowed a small extra-axial collection. CT allowed for precise localization of the lesion, including contiguous or isolated involvement of the interhemispheric subdural space. Mortality was 12% (6/49 cases), a marked improvement when compared with mortality figures obtained prior to the advent of CT (40%). CT findings indicative of involvement of the adjacent parenchyma via retrograde thrombophlebitis with resultant infarction and/or abscess formation were associated with poor prognosis. Improvement in prognosis since the advent of CT is the direct result of early accurate diagnosis and timely intervention. 20. The Guarding Problem - Complexity and Approximation Reddy, T. V. Thirumala; Krishna, D. Sai; Rangan, C. Pandu Let G = (V, E) be the given graph and G R = (V R ,E R ) and G C = (V C ,E C ) be the sub graphs of G such that V R ∩ V C = ∅ and V R ∪ V C = V. G C is referred to as the cops region and G R is called as the robber region. Initially a robber is placed at some vertex of V R and the cops are placed at some vertices of V C . The robber and cops may move from their current vertices to one of their neighbours. While a cop can move only within the cops region, the robber may move to any neighbour. The robber and cops move alternatively. A vertex v ∈ V C is said to be attacked if the current turn is the robber's turn, the robber is at vertex u where u ∈ V R , (u,v) ∈ E and no cop is present at v. The guarding problem is to find the minimum number of cops required to guard the graph G C from the robber's attack. We first prove that the decision version of this problem when G R is an arbitrary undirected graph is PSPACE-hard. We also prove that the complexity of the decision version of the guarding problem when G R is a wheel graph is NP-hard. We then present approximation algorithms if G R is a star graph, a clique and a wheel graph with approximation ratios H(n 1), 2 H(n 1) and left( H(n1) + 3/2 right) respectively, where H(n1) = 1 + 1/2 + ... + 1/n1 and n 1 = ∣ V R ∣. 1. Signal Approximation with a Wavelet Neural Network DTIC Science & Technology 1992-12-01 specialized electronic devices like the Intel Electronically Trainable Analog Neural Network (ETANN) chip. The WNN representation allows the...accurately approximated with a WNN trained with irregularly sampled data. Signal approximation, Wavelet neural network . 2. New Tests of the Fixed Hotspot Approximation Gordon, R. G.; Andrews, D. L.; Horner-Johnson, B. C.; Kumar, R. R. 2005-05-01 We present new methods for estimating uncertainties in plate reconstructions relative to the hotspots and new tests of the fixed hotspot approximation. We find no significant motion between Pacific hotspots, on the one hand, and Indo-Atlantic hotspots, on the other, for the past ~ 50 Myr, but large and significant apparent motion before 50 Ma. Whether this motion is truly due to motion between hotspots or alternatively due to flaws in the global plate motion circuit can be tested with paleomagnetic data. These tests give results consistent with the fixed hotspot approximation and indicate significant misfits when a relative plate motion circuit through Antarctica is employed for times before 50 Ma. If all of the misfit to the global plate motion circuit is due to motion between East and West Antarctica, then that motion is 800 ± 500 km near the Ross Sea Embayment and progressively less along the Trans-Antarctic Mountains toward the Weddell Sea. Further paleomagnetic tests of the fixed hotspot approximation can be made. Cenozoic and Cretaceous paleomagnetic data from the Pacific plate, along with reconstructions of the Pacific plate relative to the hotspots, can be used to estimate an apparent polar wander (APW) path of Pacific hotspots. An APW path of Indo-Atlantic hotspots can be similarly estimated (e.g. Besse & Courtillot 2002). If both paths diverge in similar ways from the north pole of the hotspot reference frame, it would indicate that the hotspots have moved in unison relative to the spin axis, which may be attributed to true polar wander. If the two paths diverge from one another, motion between Pacific hotspots and Indo-Atlantic hotspots would be indicated. The general agreement of the two paths shows that the former is more important than the latter. The data require little or no motion between groups of hotspots, but up to ~10 mm/yr of motion is allowed within uncertainties. The results disagree, in particular, with the recent extreme interpretation of 3. An approximation technique for jet impingement flow SciTech Connect Najafi, Mahmoud; Fincher, Donald; Rahni, Taeibi; Javadi, KH.; Massah, H. 2015-03-10 The analytical approximate solution of a non-linear jet impingement flow model will be demonstrated. We will show that this is an improvement over the series approximation obtained via the Adomian decomposition method, which is itself, a powerful method for analysing non-linear differential equations. The results of these approximations will be compared to the Runge-Kutta approximation in order to demonstrate their validity. 4. Energy conservation - A test for scattering approximations NASA Technical Reports Server (NTRS) Acquista, C.; Holland, A. C. 1980-01-01 The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method. 5. Energy conservation - A test for scattering approximations NASA Technical Reports Server (NTRS) Acquista, C.; Holland, A. C. 1980-01-01 The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method. 6. Approximate Model for Turbulent Stagnation Point Flow. SciTech Connect Dechant, Lawrence 2016-01-01 Here we derive an approximate turbulent self-similar model for a class of favorable pressure gradient wedge-like flows, focusing on the stagnation point limit. While the self-similar model provides a useful gross flow field estimate this approach must be combined with a near wall model is to determine skin friction and by Reynolds analogy the heat transfer coefficient. The combined approach is developed in detail for the stagnation point flow problem where turbulent skin friction and Nusselt number results are obtained. Comparison to the classical Van Driest (1958) result suggests overall reasonable agreement. Though the model is only valid near the stagnation region of cylinders and spheres it nonetheless provides a reasonable model for overall cylinder and sphere heat transfer. The enhancement effect of free stream turbulence upon the laminar flow is used to derive a similar expression which is valid for turbulent flow. Examination of free stream enhanced laminar flow suggests that the rather than enhancement of a laminar flow behavior free stream disturbance results in early transition to turbulent stagnation point behavior. Excellent agreement is shown between enhanced laminar flow and turbulent flow behavior for high levels, e.g. 5% of free stream turbulence. Finally the blunt body turbulent stagnation results are shown to provide realistic heat transfer results for turbulent jet impingement problems. 7. A simple, approximate model of parachute inflation SciTech Connect Macha, J.M. 1992-01-01 A simple, approximate model of parachute inflation is described. The model is based on the traditional, practical treatment of the fluid resistance of rigid bodies in nonsteady flow, with appropriate extensions to accommodate the change in canopy inflated shape. Correlations for the steady drag and steady radial force as functions of the inflated radius are required as input to the dynamic model. In a novel approach, the radial force is expressed in terms of easily obtainable drag and reefing fine tension measurements. A series of wind tunnel experiments provides the needed correlations. Coefficients associated with the added mass of fluid are evaluated by calibrating the model against an extensive and reliable set of flight data. A parameter is introduced which appears to universally govern the strong dependence of the axial added mass coefficient on motion history. Through comparisons with flight data, the model is shown to realistically predict inflation forces for ribbon and ringslot canopies over a wide range of sizes and deployment conditions. 8. A simple, approximate model of parachute inflation SciTech Connect Macha, J.M. 1992-11-01 A simple, approximate model of parachute inflation is described. The model is based on the traditional, practical treatment of the fluid resistance of rigid bodies in nonsteady flow, with appropriate extensions to accommodate the change in canopy inflated shape. Correlations for the steady drag and steady radial force as functions of the inflated radius are required as input to the dynamic model. In a novel approach, the radial force is expressed in terms of easily obtainable drag and reefing fine tension measurements. A series of wind tunnel experiments provides the needed correlations. Coefficients associated with the added mass of fluid are evaluated by calibrating the model against an extensive and reliable set of flight data. A parameter is introduced which appears to universally govern the strong dependence of the axial added mass coefficient on motion history. Through comparisons with flight data, the model is shown to realistically predict inflation forces for ribbon and ringslot canopies over a wide range of sizes and deployment conditions. 9. Fractal Trigonometric Polynomials for Restricted Range Approximation Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K. 2016-05-01 One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions. 10. On Approximation of Distribution and Density Functions. ERIC Educational Resources Information Center Wolff, Hans Stochastic approximation algorithms for least square error approximation to density and distribution functions are considered. The main results are necessary and sufficient parameter conditions for the convergence of the approximation processes and a generalization to some time-dependent density and distribution functions. (Author) 11. Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation. PubMed Traytak, Sergey D 2014-06-14 The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results. 12. Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation SciTech Connect Traytak, Sergey D. 2014-06-14 The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results. 13. Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation Traytak, Sergey D. 2014-06-01 The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results. 14. An approximate form of the Rayleigh reflection loss and its phase: application to reverberation calculation. PubMed Harrison, Chris H 2010-07-01 A useful approximation to the Rayleigh reflection coefficient for two half-spaces composed of water over sediment is derived. This exhibits dependence on angle that may deviate considerably from linear in the interval between grazing and critical. It shows that the non-linearity can be expressed as a separate function that multiplies the linear loss coefficient. This non-linearity term depends only on sediment density and does not depend on sediment sound speed or volume absorption. The non-linearity term tends to unity, i.e., the reflection loss becomes effectively linear, when the density ratio is about 1.27. The reflection phase in the same approximation leads to the well-known "effective depth" and "lateral shift." A class of closed-form reverberation (and signal-to-reverberation) expressions has already been developed [C. H. Harrison, J. Acoust. Soc. Am. 114, 2744-2756 (2003); C. H. Harrison, J. Comput. Acoust. 13, 317-340 (2005); C. H. Harrison, IEEE J. Ocean. Eng. 30, 660-675 (2005)]. The findings of this paper enable one to convert these reverberation expressions from simple linear loss to more general reflecting environments. Correction curves are calculated in terms of sediment density. These curves are applied to a test case taken from a recent ONR-funded Reverberation Workshop. 15. Double power series method for approximating cosmological perturbations Wren, Andrew J.; Malik, Karim A. 2017-04-01 We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online. 16. An Approximate Approach to Automatic Kernel Selection. PubMed Ding, Lizhong; Liao, Shizhong 2016-02-02 Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection. 17. A unified approach to the Darwin approximation SciTech Connect Krause, Todd B.; Apte, A.; Morrison, P. J. 2007-10-15 There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting. 18. Interpolation function for approximating knee joint behavior in human gait Toth-Taşcǎu, Mirela; Pater, Flavius; Stoia, Dan Ioan 2013-10-01 Starting from the importance of analyzing the kinematic data of the lower limb in gait movement, especially the angular variation of the knee joint, the paper propose an approximation function that can be used for processing the correlation among a multitude of knee cycles. The approximation of the raw knee data was done by Lagrange polynomial interpolation on a signal acquired using Zebris Gait Analysis System. The signal used in approximation belongs to a typical subject extracted from a lot of ten investigated subjects, but the function domain of definition belongs to the entire group. The study of the knee joint kinematics plays an important role in understanding the kinematics of the gait, this articulation having the largest range of motion in whole joints, in gait. The study does not propose to find an approximation function for the adduction-abduction movement of the knee, this being considered a residual movement comparing to the flexion-extension. 19. A coefficient average approximation towards Gutzwiller wavefunction formalism. PubMed Liu, Jun; Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming 2015-06-24 Gutzwiller wavefunction is a physically well-motivated trial wavefunction for describing correlated electron systems. In this work, a new approximation is introduced to facilitate the evaluation of the expectation value of any operator within the Gutzwiller wavefunction formalism. The basic idea is to make use of a specially designed average over Gutzwiller wavefunction coefficients expanded in the many-body Fock space to approximate the ratio of expectation values between a Gutzwiller wavefunction and its underlying noninteracting wavefunction. To check with the standard Gutzwiller approximation (GA), we test its performance on single band systems and find quite interesting properties. On finite systems, we noticed that it gives superior performance over GA, while on infinite systems it asymptotically approaches GA. Analytic analysis together with numerical tests are provided to support this claimed asymptotical behavior. Finally, possible improvements on the approximation and its generalization towards multiband systems are illustrated and discussed. 20. A test of the adhesion approximation for gravitational clustering NASA Technical Reports Server (NTRS) Melott, Adrian L.; Shandarin, Sergei F.; Weinberg, David H. 1994-01-01 We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place. 1. A test of the adhesion approximation for gravitational clustering NASA Technical Reports Server (NTRS) Melott, Adrian L.; Shandarin, Sergei F.; Weinberg, David H. 1994-01-01 We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place. 2. A test of the adhesion approximation for gravitational clustering NASA Technical Reports Server (NTRS) Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H. 1993-01-01 We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place. 3. Univariate approximate integration via nested Taylor multivariate function decomposition Gürvit, Ercan; Baykara, N. A. 2014-12-01 This work is based on the idea of nesting one or more Taylor decompositions in the remainder term of a Taylor decomposition of a function. This provides us with a better approximation quality to the original function. In addition to this basic idea each side of the Taylor decomposition is integrated and the limits of integrations are arranged in such a way to obtain a universal [0;1] interval without losing from the generality. Thus a univariate approximate integration technique is formed at the cost of getting multivariance in the remainder term. Moreover the remainder term expressed as an integral permits us to apply Fluctuationlessness theorem to it and obtain better results. 4. Stopping power beyond the adiabatic approximation DOE PAGES Caro, M.; Correa, A. A.; Artacho, E.; ... 2017-06-01 Energetic ions traveling in solids deposit energy in a variety of ways, being nuclear and electronic stopping the two avenues in which dissipation is usually treated. This separation between electrons and ions relies on the adiabatic approximation in which ions interact via forces derived from the instantaneous electronic ground state. In a more detailed view, in which non-adiabatic effects are explicitly considered, electronic excitations alter the atomic bonding, which translates into changes in the interatomic forces. In this work, we use time dependent density functional theory and forces derived from the equations of Ehrenfest dynamics that depend instantaneously on themore » time-dependent electronic density. With them we analyze how the inter-ionic forces are affected by electronic excitations in a model of a Ni projectile interacting with a Ni target, a metallic system with strong electronic stopping and shallow core level states. We find that the electronic excitations induce substantial modifications to the inter-ionic forces, which translate into nuclear stopping power well above the adiabatic prediction. Particularly, we observe that most of the alteration of the adiabatic potential in early times comes from the ionization of the core levels of the target ions, not readily screened by the valence electrons.« less 5. Approximate Methods for State-Space Models. PubMed Koyama, Shinsuke; Pérez-Bolde, Lucia Castellanos; Shalizi, Cosma Rohilla; Kass, Robert E 2010-03-01 State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This Laplace-Gaussian filter (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time. 6. Phase shift approximation for the post-critical seismic wave Zhang, Xinyan; Zhang, Zhongjie; Xu, Tao; Bai, Zhiming; Harris, Jerry M. 2012-10-01 Post-critical seismic waves are widely used in crustal exploration of the seismic velocity structure, and are gaining interest in the oil/gas seismic community to image the deeper structure beneath the high velocity basalt layer. They are featured with their phase shifts and strength changes, which should be taken into account in seismic data processing, such as velocity analysis and true amplitude migration, etc. In order to simplify the exact but complicated formula of reflection and transmission coefficients, numerous approximate expressions for reflection and transmission coefficients for pre-critical incidence are obtained. In the post-critical case, there is Downton's approximation with acceptable accuracy approximation when the velocity changes smoothly. However if the velocity model changes rapidly, the error will be relatively very large, limiting the use of the approach. In order to improve the post-critical approximation, we utilize Taylor expansion of ray parameters with angle increment (compared to critical angle) in wide-angle seismic reflection and transmission coefficients. The explicit expressions for amplitude and phase shift (time shift) for the post-critical incident angle are obtained. Our results confirm that the wide-angle seismic reflection/transmission phase shifts are strongly frequency dependent; phase shifts of low frequency wide-angle seismic waves are more predominant and their correction should be considered in seismic processing and imaging. Numerical examples demonstrate that (1) the accuracies of these approximations are high compared to the classic Aki's formula and Downton's approximation, and (2) the wide-angle effect can be effectively reduced with phase-shift correction by utilizing our time-shift approximation to the seismic traveltimes. 7. Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao 2014-12-01 In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N4). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as < hat{S}2rangle are also developed and tested. 8. Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations. PubMed Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao 2014-12-07 In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N(4)). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as ⟨Ŝ(2)⟩ are also developed and tested. 9. Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations SciTech Connect Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao 2014-12-07 In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N{sup 4}). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S{sup ^2}〉 are also developed and tested. 10. Low rank approximation in G0W0 calculations DOE PAGES Shao, MeiYue; Lin, Lin; Yang, Chao; ... 2016-06-04 The single particle energies obtained in a Kohn-Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in tr ansport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green’s function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The G0W0 approximation is a widely used technique in whichmore » the self energy is expressed as the convolution of a noninteracting Green’s function (G0) and a screened Coulomb interaction (W0) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating W 0 at multiple frequencies. In this paper, we discuss how the cost of G0W0 calculation can be reduced by constructing a low rank approximation to the frequency dependent part of W 0 . In particular, we examine the effect of such a low rank approximation on the accuracy of the G0W0 approximation. We also discuss how the numerical convolution of G0 and W0 can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.« less 11. Surface expression of the Chicxulub crater PubMed Pope, K O; Ocampo, A C; Kinsland, G L; Smith, R 1996-06-01 Analyses of geomorphic, soil, and topographic data from the northern Yucatan Peninsula, Mexico, confirm that the buried Chicxulub impact crater has a distinct surface expression and that carbonate sedimentation throughout the Cenozoic has been influenced by the crater. Late Tertiary sedimentation was mostly restricted to the region within the buried crater, and a semicircular moat existed until at least Pliocene time. The topographic expression of the crater is a series of features concentric with the crater. The most prominent is an approximately 83-km-radius trough or moat containing sinkholes (the Cenote ring). Early Tertiary surfaces rise abruptly outside the moat and form a stepped topography with an outer trough and ridge crest at radii of approximately 103 and approximately 129 km, respectively. Two discontinuous troughs lie within the moat at radii of approximately 41 and approximately 62 km. The low ridge between the inner troughs corresponds to the buried peak ring. The moat corresponds to the outer edge of the crater floor demarcated by a major ring fault. The outer trough and the approximately 62-km-radius inner trough also mark buried ring faults. The ridge crest corresponds to the topographic rim of the crater as modified by postimpact processes. These interpretations support previous findings that the principal impact basin has a diameter of approximately 180 km, but concentric, low-relief slumping extends well beyond this diameter and the eroded crater rim may extend to a diameter of approximately 260 km. 12. Generalized stationary phase approximations for mountain waves Knight, H.; Broutman, D.; Eckermann, S. D. 2016-04-01 Large altitude asymptotic approximations are derived for vertical displacements due to mountain waves generated by hydrostatic wind flow over arbitrary topography. This leads to new asymptotic analytic expressions for wave-induced vertical displacement for mountains with an elliptical Gaussian shape and with the major axis oriented at any angle relative to the background wind. The motivation is to understand local maxima in vertical displacement amplitude at a given height for elliptical mountains aligned at oblique angles to the wind direction, as identified in Eckermann et al. ["Effects of horizontal geometrical spreading on the parameterization of orographic gravity-wave drag. Part 1: Numerical transform solutions," J. Atmos. Sci. 72, 2330-2347 (2015)]. The standard stationary phase method reproduces one type of local amplitude maximum that migrates downwind with increasing altitude. Another type of local amplitude maximum stays close to the vertical axis over the center of the mountain, and a new generalized stationary phase method is developed to describe this other type of local amplitude maximum and the horizontal variation of wave-induced vertical displacement near the vertical axis of the mountain in the large altitude limit. The new generalized stationary phase method describes the asymptotic behavior of integrals where the asymptotic parameter is raised to two different powers (1/2 and 1) rather than just one power as in the standard stationary phase method. The vertical displacement formulas are initially derived assuming a uniform background wind but are extended to accommodate both vertical shear with a fixed wind direction and vertical variations in the buoyancy frequency. 13. Approximate dynamic model of a turbojet engine NASA Technical Reports Server (NTRS) Artemov, O. A. 1978-01-01 An approximate dynamic nonlinear model of a turbojet engine is elaborated on as a tool in studying the aircraft control loop, with the turbojet engine treated as an actuating component. Approximate relationships linking the basic engine parameters and shaft speed are derived to simplify the problem, and to aid in constructing an approximate nonlinear dynamic model of turbojet engine performance useful for predicting aircraft motion. 14. The JWKB approximation in loop quantum cosmology Craig, David; Singh, Parampreet 2017-01-01 We explore the JWKB approximation in loop quantum cosmology in a flat universe with a scalar matter source. Exact solutions of the quantum constraint are studied at small volume in the JWKB approximation in order to assess the probability of tunneling to small or zero volume. Novel features of the approximation are discussed which appear due to the fact that the model is effectively a two-dimensional dynamical system. Based on collaborative work with Parampreet Singh. 15. Approximation by Ridge Functions and Neural Networks DTIC Science & Technology 1997-01-01 univariate spaces Xn Other authors most notably Micchelli and Mhaskar MM MM and Mhaskar M have also considered approximation problems of the...type treated here The work of Micchelli and Mhaskar does not give the best order of approximation Mhaskar M has given best possible results but...function from its projections Duke Math J pp M H Mhaskar Neural networks for optimal approximation of smooth and ana lytic 16. Piecewise linear approximation for hereditary control problems NASA Technical Reports Server (NTRS) Propst, Georg 1990-01-01 This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. 17. Bent approximations to synchrotron radiation optics SciTech Connect Heald, S. 1981-01-01 Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors. 18. Massive neutrinos in cosmology: Analytic solutions and fluid approximation SciTech Connect Shoji, Masatoshi; Komatsu, Eiichiro 2010-06-15 We study the evolution of linear density fluctuations of free-streaming massive neutrinos at redshift of z<1000, with an explicit justification on the use of a fluid approximation. We solve the collisionless Boltzmann equation in an Einstein de-Sitter (EdS) universe, truncating the Boltzmann hierarchy at l{sub max}=1 and 2, and compare the resulting density contrast of neutrinos {delta}{sub {nu}}{sup fluid} with that of the exact solutions of the Boltzmann equation that we derive in this paper. Roughly speaking, the fluid approximation is accurate if neutrinos were already nonrelativistic when the neutrino density fluctuation of a given wave number entered the horizon. We find that the fluid approximation is accurate at subpercent levels for massive neutrinos with m{sub {nu}>}0.05 eV at the scale of k < or approx. 1.0h Mpc{sup -1} and redshift of z<100. This result validates the use of the fluid approximation, at least for the most massive species of neutrinos suggested by the neutrino oscillation experiments. We also find that the density contrast calculated from fluid equations (i.e., continuity and Euler equations) becomes a better approximation at a lower redshift, and the accuracy can be further improved by including an anisotropic stress term in the Euler equation. The anisotropic stress term effectively increases the pressure term by a factor of 9/5. 19. Algebraic approximations for transcendental equations with applications in nanophysics Barsan, Victor 2015-09-01 Using algebraic approximations of trigonometric or hyperbolic functions, a class of transcendental equations can be transformed in tractable, algebraic equations. Studying transcendental equations this way gives the eigenvalues of Sturm-Liouville problems associated to wave equation, mainly to Schroedinger equation; these algebraic approximations provide approximate analytical expressions for the energy of electrons and phonons in quantum wells, quantum dots (QDs) and quantum wires, in the frame of one-particle models of such systems. The advantage of this approach, compared to the numerical calculations, is that the final result preserves the functional dependence on the physical parameters of the problem. The errors of this method, situated between some few percentages and ?, are carefully analysed. Several applications, for quantum wells, QDs and quantum wires, are presented. 20. Correlation Energies from the Two-Component Random Phase Approximation. PubMed Kühn, Michael 2014-02-11 The correlation energy within the two-component random phase approximation accounting for spin-orbit effects is derived. The resulting plasmon equation is rewritten-analogously to the scalar relativistic case-in terms of the trace of two Hermitian matrices for (Kramers-restricted) closed-shell systems and then represented as an integral over imaginary frequency using the resolution of the identity approximation. The final expression is implemented in the TURBOMOLE program suite. The code is applied to the computation of equilibrium distances and vibrational frequencies of heavy diatomic molecules. The efficiency is demonstrated by calculation of the relative energies of the Oh-, D4h-, and C5v-symmetric isomers of Pb6. Results within the random phase approximation are obtained based on two-component Kohn-Sham reference-state calculations, using effective-core potentials. These values are finally compared to other two-component and scalar relativistic methods, as well as experimental data. 1. Cluster and propensity based approximation of a network PubMed Central 2013-01-01 Background The models in this article generalize current models for both correlation networks and multigraph networks. Correlation networks are widely applied in genomics research. In contrast to general networks, it is straightforward to test the statistical significance of an edge in a correlation network. It is also easy to decompose the underlying correlation matrix and generate informative network statistics such as the module eigenvector. However, correlation networks only capture the connections between numeric variables. An open question is whether one can find suitable decompositions of the similarity measures employed in constructing general networks. Multigraph networks are attractive because they support likelihood based inference. Unfortunately, it is unclear how to adjust current statistical methods to detect the clusters inherent in many data sets. Results Here we present an intuitive and parsimonious parametrization of a general similarity measure such as a network adjacency matrix. The cluster and propensity based approximation (CPBA) of a network not only generalizes correlation network methods but also multigraph methods. In particular, it gives rise to a novel and more realistic multigraph model that accounts for clustering and provides likelihood based tests for assessing the significance of an edge after controlling for clustering. We present a novel Majorization-Minimization (MM) algorithm for estimating the parameters of the CPBA. To illustrate the practical utility of the CPBA of a network, we apply it to gene expression data and to a bi-partite network model for diseases and disease genes from the Online Mendelian Inheritance in Man (OMIM). Conclusions The CPBA of a network is theoretically appealing since a) it generalizes correlation and multigraph network methods, b) it improves likelihood based significance tests for edge counts, c) it directly models higher-order relationships between clusters, and d) it suggests novel clustering 2. Approximate entropy and support vector machines for electroencephalogram signal classification PubMed Central Zhang, Zhen; Zhou, Yi; Chen, Ziyi; Tian, Xianghua; Du, Shouhong; Huang, Ruimei 2013-01-01 The automatic detection and identification of electroencephalogram waves play an important role in the prediction, diagnosis and treatment of epileptic seizures. In this study, a nonlinear dynamics index–approximate entropy and a support vector machine that has strong generalization ability were applied to classify electroencephalogram signals at epileptic interictal and ictal periods. Our aim was to verify whether approximate entropy waves can be effectively applied to the automatic real-time detection of epilepsy in the electroencephalogram, and to explore its generalization ability as a classifier trained using a nonlinear dynamics index. Four patients presenting with partial epileptic seizures were included in this study. They were all diagnosed with neocortex localized epilepsy and epileptic foci were clearly observed by electroencephalogram. The electroencephalogram data form the four involved patients were segmented and the characteristic values of each segment, that is, the approximate entropy, were extracted. The support vector machine classifier was constructed with the approximate entropy extracted from one epileptic case, and then electroencephalogram waves of the other three cases were classified, reaching a 93.33% accuracy rate. Our findings suggest that the use of approximate entropy allows the automatic real-time detection of electroencephalogram data in epileptic cases. The combination of approximate entropy and support vector machines shows good generalization ability for the classification of electroencephalogram signals for epilepsy. PMID:25206493 3. Analytical approximations to the spectra of quark antiquark potentials Amore, Paolo; DePace, Arturo; Lopez, Jorge 2006-07-01 A method recently devised to obtain analytical approximations to certain classes of integrals is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of our results is verified by comparing them both with the literature on the subject and with the numerical results obtained with a Fortran code. As an application of the method that we propose, we consider meson spectroscopy with various phenomenological potentials. 4. Inversion and approximation of Laplace transforms NASA Technical Reports Server (NTRS) Lear, W. M. 1980-01-01 A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator. 5. Approximate methods for equations of incompressible fluid Galkin, V. A.; Dubovik, A. O.; Epifanov, A. A. 2017-02-01 Approximate methods on the basis of sequential approximations in the theory of functional solutions to systems of conservation laws is considered, including the model of dynamics of incompressible fluid. Test calculations are performed, and a comparison with exact solutions is carried out. 6. Computing Functions by Approximating the Input ERIC Educational Resources Information Center Goldberg, Mayer 2012-01-01 In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their… 7. An approximation for inverse Laplace transforms NASA Technical Reports Server (NTRS) Lear, W. M. 1981-01-01 Programmable calculator runs simple finite-series approximation for Laplace transform inversions. Utilizing family of orthonormal functions, approximation is used for wide range of transforms, including those encountered in feedback control problems. Method works well as long as F(t) decays to zero as it approaches infinity and so is appliable to most physical systems. 8. Piecewise linear approximation for hereditary control problems NASA Technical Reports Server (NTRS) Propst, Georg 1987-01-01 Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations. 9. Approximate error conjugation gradient minimization methods DOEpatents Kallman, Jeffrey S 2013-05-21 In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems. 10. Origin of Quantum Criticality in Yb-Al-Au Approximant Crystal and Quasicrystal Watanabe, Shinji; Miyake, Kazumasa 2016-06-01 To get insight into the mechanism of emergence of unconventional quantum criticality observed in quasicrystal Yb15Al34Au51, the approximant crystal Yb14Al35Au51 is analyzed theoretically. By constructing a minimal model for the approximant crystal, the heavy quasiparticle band is shown to emerge near the Fermi level because of strong correlation of 4f electrons at Yb. We find that charge-transfer mode between 4f electron at Yb on the 3rd shell and 3p electron at Al on the 4th shell in Tsai-type cluster is considerably enhanced with almost flat momentum dependence. The mode-coupling theory shows that magnetic as well as valence susceptibility exhibits χ ˜ T-0.5 for zero-field limit and is expressed as a single scaling function of the ratio of temperature to magnetic field T/B over four decades even in the approximant crystal when some condition is satisfied by varying parameters, e.g., by applying pressure. The key origin is clarified to be due to strong locality of the critical Yb-valence fluctuation and small Brillouin zone reflecting the large unit cell, giving rise to the extremely-small characteristic energy scale. This also gives a natural explanation for the quantum criticality in the quasicrystal corresponding to the infinite limit of the unit-cell size. 11. On the validity of the adiabatic approximation in compact binary inspirals Maselli, Andrea; Gualtieri, Leonardo; Pannarale, Francesco; Ferrari, Valeria 2012-08-01 Using a semianalytical approach recently developed to model the tidal deformations of neutron stars in inspiralling compact binaries, we study the dynamical evolution of the tidal tensor, which we explicitly derive at second post-Newtonian order, and of the quadrupole tensor. Since we do not assume a priori that the quadrupole tensor is proportional to the tidal tensor, i.e., the so-called “adiabatic approximation,” our approach enables us to establish to which extent such approximation is reliable. We find that the ratio between the quadrupole and tidal tensors (i.e., the Love number) increases as the inspiral progresses, but this phenomenon only marginally affects the emitted gravitational waveform. We estimate the frequency range in which the tidal component of the gravitational signal is well described using the Stationary phase approximation at next-to-leading post-Newtonian order, comparing different contributions to the tidal phase. We also derive a semianalytical expression for the Love number, which reproduces within a few percentage points the results obtained so far by numerical integrations of the relativistic equations of stellar perturbations. 12. The Zeeman effect in the Sobolev approximation: applications to spherical stellar winds Ignace, R.; Gayley, K. G. 2003-05-01 Modern spectropolarimeters are capable of detecting subkilogauss field strengths using the Zeeman effect in line profiles from the static photosphere, but supersonic Doppler broadening makes it more difficult to detect the Zeeman effect in the wind lines of hot stars. Nevertheless, the recent advances in observational capability motivate an assessment of the potential for detecting the magnetic fields threading such winds. We incorporate the weak-field longitudinal Zeeman effect in the Sobolev approximation to yield integral expressions for the flux of circularly polarized emission. To illustrate the results, two specific wind flows are considered: (i) spherical constant expansion with v(r) =v∞ and (ii) homologous expansion with v(r) ~r. Axial and split monopole magnetic fields are used to schematically illustrate the polarized profiles. For constant expansion, optically thin lines yield the well-known flat-topped' total intensity emission profiles and an antisymmetric circularly polarized profile. For homologous expansion, we include occultation and wind absorption to provide a more realistic observational comparison. Occultation severely reduces the circularly polarized flux in the redshifted component, and in the blueshifted component, the polarization is reduced by partially offsetting emission and absorption contributions. We find that for a surface field of approximately 100 G, the largest polarizations result for thin but strong recombination emission lines. Peak polarizations are approximately 0.05 per cent, which presents a substantial although not inconceivable sensitivity challenge for modern instrumentation. 13. Particle-number projection in the finite-temperature mean-field approximation Fanto, P.; Alhassid, Y.; Bertsch, G. F. 2017-07-01 Finite-temperature mean-field theories, such as the Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) theories, are formulated in the grand-canonical ensemble, and their applications to the calculation of statistical properties of nuclei such as level densities require a reduction to the canonical ensemble. In a previous publication [Y. Alhassid et al., Phys. Rev. C 93, 044320 (2016), 10.1103/PhysRevC.93.044320], it was found that ensemble-reduction methods based on the saddle-point approximation are not reliable in cases in which rotational symmetry or particle-number conservation is broken. In particular, the calculated HFB canonical entropy can be unphysical as a result of the inherent violation of particle-number conservation. In this work, we derive a general formula for exact particle-number projection after variation in the HFB approximation, assuming that the HFB Hamiltonian preserves time-reversal symmetry. This formula reduces to simpler known expressions in the HF and Bardeen-Cooper-Schrieffer (BCS) limits of the HFB. We apply this formula to calculate the thermodynamic quantities needed for level densities in the heavy nuclei 162Dy, 148Sm, and 150Sm. We find that the exact particle-number projection gives better physical results and is significantly more computationally efficient than the saddle-point methods. However, the fundamental limitations caused by broken symmetries in the mean-field approximation are still present. 14. How to Use SNP_TATA_Comparator to Find a Significant Change in Gene Expression Caused by the Regulatory SNP of This Gene's Promoter via a Change in Affinity of the TATA-Binding Protein for This Promoter. PubMed Ponomarenko, Mikhail; Rasskazov, Dmitry; Arkova, Olga; Ponomarenko, Petr; Suslov, Valentin; Savinkova, Ludmila; Kolchanov, Nikolay 2015-01-01 The use of biomedical SNP markers of diseases can improve effectiveness of treatment. Genotyping of patients with subsequent searching for SNPs more frequent than in norm is the only commonly accepted method for identification of SNP markers within the framework of translational research. The bioinformatics applications aimed at millions of unannotated SNPs of the "1000 Genomes" can make this search for SNP markers more focused and less expensive. We used our Web service involving Fisher's Z-score for candidate SNP markers to find a significant change in a gene's expression. Here we analyzed the change caused by SNPs in the gene's promoter via a change in affinity of the TATA-binding protein for this promoter. We provide examples and discuss how to use this bioinformatics application in the course of practical analysis of unannotated SNPs from the "1000 Genomes" project. Using known biomedical SNP markers, we identified 17 novel candidate SNP markers nearby: rs549858786 (rheumatoid arthritis); rs72661131 (cardiovascular events in rheumatoid arthritis); rs562962093 (stroke); rs563558831 (cyclophosphamide bioactivation); rs55878706 (malaria resistance, leukopenia), rs572527200 (asthma, systemic sclerosis, and psoriasis), rs371045754 (hemophilia B), rs587745372 (cardiovascular events); rs372329931, rs200209906, rs367732974, and rs549591993 (all four: cancer); rs17231520 and rs569033466 (both: atherosclerosis); rs63750953, rs281864525, and rs34166473 (all three: malaria resistance, thalassemia). 15. How to Use SNP_TATA_Comparator to Find a Significant Change in Gene Expression Caused by the Regulatory SNP of This Gene's Promoter via a Change in Affinity of the TATA-Binding Protein for This Promoter PubMed Central Rasskazov, Dmitry; Arkova, Olga; Ponomarenko, Petr; Suslov, Valentin; Savinkova, Ludmila; Kolchanov, Nikolay 2015-01-01 The use of biomedical SNP markers of diseases can improve effectiveness of treatment. Genotyping of patients with subsequent searching for SNPs more frequent than in norm is the only commonly accepted method for identification of SNP markers within the framework of translational research. The bioinformatics applications aimed at millions of unannotated SNPs of the “1000 Genomes” can make this search for SNP markers more focused and less expensive. We used our Web service involving Fisher's Z-score for candidate SNP markers to find a significant change in a gene's expression. Here we analyzed the change caused by SNPs in the gene's promoter via a change in affinity of the TATA-binding protein for this promoter. We provide examples and discuss how to use this bioinformatics application in the course of practical analysis of unannotated SNPs from the “1000 Genomes” project. Using known biomedical SNP markers, we identified 17 novel candidate SNP markers nearby: rs549858786 (rheumatoid arthritis); rs72661131 (cardiovascular events in rheumatoid arthritis); rs562962093 (stroke); rs563558831 (cyclophosphamide bioactivation); rs55878706 (malaria resistance, leukopenia), rs572527200 (asthma, systemic sclerosis, and psoriasis), rs371045754 (hemophilia B), rs587745372 (cardiovascular events); rs372329931, rs200209906, rs367732974, and rs549591993 (all four: cancer); rs17231520 and rs569033466 (both: atherosclerosis); rs63750953, rs281864525, and rs34166473 (all three: malaria resistance, thalassemia). PMID:26516624 16. Semiclassical approximation for strong-laser-field processes Milošević, D. B. 2017-08-01 The exact time-evolution operator of an atom in the presence of a strong laser field is expressed using the phase-space path integral. Presenting this result in the form of a perturbative expansion in the effective interaction of the electron with the rest of the atom enables straightforward derivation of the well-known strong-field approximation and its higher-order corrections. Alternatively, one can use this exact result to obtain a semiclassical approximation by expansion in powers of small fluctuations around the classical trajectories. We present a derivation of such a semiclassical approximation. The obtained result for the momentum-space matrix element of the total time-evolution operator can be useful for studying various processes in strong-field physics. Using the example of above-threshold ionization, it is shown how this approximation can be applied to laser-induced processes. More attention is devoted to the laser-assisted scattering. Using the example of few-cycle laser-pulse-assisted electron-atom potential scattering, we show similarities and differences between the semiclassical and the strong-field approximations. For low energies, the semiclassical scattering cross section is modified and there are trajectories along which the electron is temporarily captured by the atomic potential. Applying stationary-phase method to the integral over the scattering time, we clearly identified relevant semiclassical electron trajectories. 17. Rational trigonometric approximations using Fourier series partial sums NASA Technical Reports Server (NTRS) Geer, James F. 1993-01-01 A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented. 18. Dynamical exchange-correlation potentials beyond the local density approximation Tao, Jianmin; Vignale, Giovanni 2006-03-01 Approximations for the static exchange-correlation (xc) potential of density functional theory (DFT) have reached a high level of sophistication. By contrast, time-dependent xc potentials are still being treated in a local (although velocity-dependent) approximation [G. Vignale, C. A. Ullrich and S. Conti, PRL 79, 4879 (1997)]. Unfortunately, one of the assumptions upon which the dynamical local approximation is based appears to break down in the important case of d.c. transport. Here we propose a new approximation scheme, which should allow a more accurate treatment of molecular transport problems. As a first step, we separate the exact adiabatic xc potential, which has the same form as in the static theory and can be treated by a generalized gradient approximation (GGA) or a meta-GGA. In the second step, we express the high-frequency limit of the xc stress tensor (whose divergence gives the xc force density) in terms of the exact static xc energy functional. Finally, we develop a perturbative scheme for the calculation of the frequency dependence of the xc stress tensor in terms of the ground-state Kohn-Sham orbitals and eigenvalues. 19. Approximate formulation of redistribution in the Ly-alpha, Ly-beta, H-alpha system NASA Technical Reports Server (NTRS) Cooper, J.; Ballagh, R. J.; Hubeny, I. 1989-01-01 Simple approximate formulas are given for the coupled redistribution of Ly-alpha, Ly-beta, and H-alpha, by using well-defined approximations to an essentially exact formulation. These formulas incorporate all the essential physics including Raman scattering, lower state radiative decay, and correlated terms representing emission during a collision which must be retained in order that the emission coefficients are properly behaved in the line wings. Approximate expressions for the appropriate line broadening parameters are collected. Finally, practical expressions for the source functions are given. These are formulated through newly introduced nonimpact redistribution functions, which are shown to be reasonably approximated by existing (ordinary and generalized) redistribution functions. 20. Stochastic population dynamics: The Poisson approximation Solari, Hernán G.; Natiello, Mario A. 2003-03-01 We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention. The deterministic approximation for the population fractions and the Langevin-type approximation for the fluctuations around the mean value are recovered within the framework of the Poisson approximation as particular limit cases. However, the proposed framework allows to treat other limit cases and general situations with small populations that lie outside the scope of the standard approaches. The Poisson approximation can be viewed as a general (numerical) integration scheme for this family of problems in population dynamics. 1. Quasiadiabatic Grover search via the Wentzel-Kramers-Brillouin approximation Muthukrishnan, Siddharth; Lidar, Daniel A. 2017-07-01 In various applications one is interested in quantum dynamics at intermediate evolution times, for which the adiabatic approximation is inadequate. Here we develop a quasiadiabatic approximation based on the WKB method, designed to work for such intermediate evolution times. We apply it to the problem of a single qubit in a time-varying magnetic field, and to the Hamiltonian Grover search problem, and show that already at first order the quasiadiabatic WKB captures subtle features of the dynamics that are missed by the adiabatic approximation. However, we also find that the method is sensitive to the type of interpolation schedule used in the Grover problem and can give rise to nonsensical results for the wrong schedule. Conversely, it reproduces the quadratic Grover speedup when the well-known optimal schedule is used. 2. Fast approximation of self-similar network traffic SciTech Connect Paxson, V. 1995-01-01 Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with self-similar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate self-similar sample paths and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate a closer approximation to true self-similar sample paths than the other known fast method (Random Midpoint Displacement). We then discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittles estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time series. 3. Error bounded conic spline approximation for NC code Shen, Liyong 2012-01-01 Curve fitting is an important preliminary work for data compression and path interpolator in numerical control (NC). The paper gives a simple conic spline approximation algorithm for G01 code. The algorithm is mainly formed by three steps: divide the G01 code to subsets by discrete curvature detection, find the polygon line segment approximation for each subset within a given error and finally, fit each polygon line segment approximation with a conic Bezier spline. Naturally, B-spline curve can be obtained by proper knots selection. The algorithm is designed straightforward and efficient without solving any global equation system or optimal problem. It is complete with the selection of curve's weight. To design the curve more suitable for NC, we present an interval for the weight selection and the error is then computed. 4. Error bounded conic spline approximation for NC code Shen, Liyong 2011-12-01 Curve fitting is an important preliminary work for data compression and path interpolator in numerical control (NC). The paper gives a simple conic spline approximation algorithm for G01 code. The algorithm is mainly formed by three steps: divide the G01 code to subsets by discrete curvature detection, find the polygon line segment approximation for each subset within a given error and finally, fit each polygon line segment approximation with a conic Bezier spline. Naturally, B-spline curve can be obtained by proper knots selection. The algorithm is designed straightforward and efficient without solving any global equation system or optimal problem. It is complete with the selection of curve's weight. To design the curve more suitable for NC, we present an interval for the weight selection and the error is then computed. 5. On current sheet approximations in models of eruptive flares NASA Technical Reports Server (NTRS) Bungey, T. N.; Forbes, T. G. 1994-01-01 We consider an approximation sometimes used for current sheets in flux-rope models of eruptive flares. This approximation is based on a linear expansion of the background field in the vicinity of the current sheet, and it is valid when the length of the current sheet is small compared to the scale length of the coronal magnetic field. However, we find that flux-rope models which use this approximation predict the occurrence of an eruption due to a loss of ideal-MHD equilibrium even when the corresponding exact solution shows that no such eruption occurs. Determination of whether a loss of equilibrium exists can only be obtained by including higher order terms in the expansion of the field or by using the exact solution. 6. Approximating Light Rays in the Schwarzschild Field Semerák, O. 2015-02-01 A short formula is suggested that approximates photon trajectories in the Schwarzschild field better than other simple prescriptions from the literature. We compare it with various "low-order competitors," namely, with those following from exact formulas for small M, with one of the results based on pseudo-Newtonian potentials, with a suitably adjusted hyperbola, and with the effective and often employed approximation by Beloborodov. Our main concern is the shape of the photon trajectories at finite radii, yet asymptotic behavior is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usable—and very accurate—for practically solving the ray-deflection exercise. 7. Approximate Bruechner orbitals in electron propagator calculations SciTech Connect Ortiz, J.V. 1999-12-01 Orbitals and ground-state correlation amplitudes from the so-called Brueckner doubles approximation of coupled-cluster theory provide a useful reference state for electron propagator calculations. An operator manifold with hold, particle, two-hole-one-particle and two-particle-one-hole components is chosen. The resulting approximation, third-order algebraic diagrammatic construction [2ph-TDA, ADC (3)] and 3+ methods. The enhanced versatility of this approximation is demonstrated through calculations on valence ionization energies, core ionization energies, electron detachment energies of anions, and on a molecule with partial biradical character, ozone. 8. Alternative approximation concepts for space frame synthesis NASA Technical Reports Server (NTRS) Lust, R. V.; Schmit, L. A. 1985-01-01 A method for space frame synthesis based on the application of a full gamut of approximation concepts is presented. It is found that with the thoughtful selection of design space, objective function approximation, constraint approximation and mathematical programming problem formulation options it is possible to obtain near minimum mass designs for a significant class of space frame structural systems while requiring fewer than 10 structural analyses. Example problems are presented which demonstrate the effectiveness of the method for frame structures subjected to multiple static loading conditions with limits on structural stiffness and strength. 9. APPROXIMATING LIGHT RAYS IN THE SCHWARZSCHILD FIELD SciTech Connect Semerák, O. 2015-02-10 A short formula is suggested that approximates photon trajectories in the Schwarzschild field better than other simple prescriptions from the literature. We compare it with various ''low-order competitors'', namely, with those following from exact formulas for small M, with one of the results based on pseudo-Newtonian potentials, with a suitably adjusted hyperbola, and with the effective and often employed approximation by Beloborodov. Our main concern is the shape of the photon trajectories at finite radii, yet asymptotic behavior is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usable—and very accurate—for practically solving the ray-deflection exercise. 10. Information geometry of mean-field approximation. PubMed Tanaka, T 2000-08-01 I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics. 11. ReliefSeq: a gene-wise adaptive-K nearest-neighbor feature selection tool for finding gene-gene interactions and main effects in mRNA-Seq gene expression data. PubMed McKinney, Brett A; White, Bill C; Grill, Diane E; Li, Peter W; Kennedy, Richard B; Poland, Gregory A; Oberg, Ann L 2013-01-01 Relief-F is a nonparametric, nearest-neighbor machine learning method that has been successfully used to identify relevant variables that may interact in complex multivariate models to explain phenotypic variation. While several tools have been developed for assessing differential expression in sequence-based transcriptomics, the detection of statistical interactions between transcripts has received less attention in the area of RNA-seq analysis. We describe a new extension and assessment of Relief-F for feature selection in RNA-seq data. The ReliefSeq implementation adapts the number of nearest neighbors (k) for each gene to optimize the Relief-F test statistics (importance scores) for finding both main effects and interactions. We compare this gene-wise adaptive-k (gwak) Relief-F method with standard RNA-seq feature selection tools, such as DESeq and edgeR, and with the popular machine learning method Random Forests. We demonstrate performance on a panel of simulated data that have a range of distributional properties reflected in real mRNA-seq data including multiple transcripts with varying sizes of main effects and interaction effects. For simulated main effects, gwak-Relief-F feature selection performs comparably to standard tools DESeq and edgeR for ranking relevant transcripts. For gene-gene interactions, gwak-Relief-F outperforms all comparison methods at ranking relevant genes in all but the highest fold change/highest signal situations where it performs similarly. The gwak-Relief-F algorithm outperforms Random Forests for detecting relevant genes in all simulation experiments. In addition, Relief-F is comparable to the other methods based on computational time. We also apply ReliefSeq to an RNA-Seq study of smallpox vaccine to identify gene expression changes between vaccinia virus-stimulated and unstimulated samples. ReliefSeq is an attractive tool for inclusion in the suite of tools used for analysis of mRNA-Seq data; it has power to detect both main 12. ReliefSeq: A Gene-Wise Adaptive-K Nearest-Neighbor Feature Selection Tool for Finding Gene-Gene Interactions and Main Effects in mRNA-Seq Gene Expression Data PubMed Central McKinney, Brett A.; White, Bill C.; Grill, Diane E.; Li, Peter W.; Kennedy, Richard B.; Poland, Gregory A.; Oberg, Ann L. 2013-01-01 Relief-F is a nonparametric, nearest-neighbor machine learning method that has been successfully used to identify relevant variables that may interact in complex multivariate models to explain phenotypic variation. While several tools have been developed for assessing differential expression in sequence-based transcriptomics, the detection of statistical interactions between transcripts has received less attention in the area of RNA-seq analysis. We describe a new extension and assessment of Relief-F for feature selection in RNA-seq data. The ReliefSeq implementation adapts the number of nearest neighbors (k) for each gene to optimize the Relief-F test statistics (importance scores) for finding both main effects and interactions. We compare this gene-wise adaptive-k (gwak) Relief-F method with standard RNA-seq feature selection tools, such as DESeq and edgeR, and with the popular machine learning method Random Forests. We demonstrate performance on a panel of simulated data that have a range of distributional properties reflected in real mRNA-seq data including multiple transcripts with varying sizes of main effects and interaction effects. For simulated main effects, gwak-Relief-F feature selection performs comparably to standard tools DESeq and edgeR for ranking relevant transcripts. For gene-gene interactions, gwak-Relief-F outperforms all comparison methods at ranking relevant genes in all but the highest fold change/highest signal situations where it performs similarly. The gwak-Relief-F algorithm outperforms Random Forests for detecting relevant genes in all simulation experiments. In addition, Relief-F is comparable to the other methods based on computational time. We also apply ReliefSeq to an RNA-Seq study of smallpox vaccine to identify gene expression changes between vaccinia virus-stimulated and unstimulated samples. ReliefSeq is an attractive tool for inclusion in the suite of tools used for analysis of mRNA-Seq data; it has power to detect both main 13. Linear Approximation SAR Azimuth Processing Study NASA Technical Reports Server (NTRS) Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G. 1979-01-01 A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution. 14. AN APPROXIMATE EQUATION OF STATE OF SOLIDS. DTIC Science & Technology research. By generalizing experimental data and obtaining unified relations describing the thermodynamic properties of solids, and approximate equation of state is derived which can be applied to a wide class of materials. (Author) 15. Approximate Controllability Results for Linear Viscoelastic Flows Chowdhury, Shirshendu; Mitra, Debanjana; Ramaswamy, Mythily; Renardy, Michael 2017-09-01 We consider linear viscoelastic flow of a multimode Maxwell or Jeffreys fluid in a bounded domain with smooth boundary, with a distributed control in the momentum equation. We establish results on approximate and exact controllability. 16. Approximation concepts for efficient structural synthesis NASA Technical Reports Server (NTRS) Schmit, L. A., Jr.; Miura, H. 1976-01-01 It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role. 17. Computational aspects of pseudospectral Laguerre approximations NASA Technical Reports Server (NTRS) Funaro, Daniele 1989-01-01 Pseudospectral approximations in unbounded domains by Laguerre polynomials lead to ill-conditioned algorithms. Introduced are a scaling function and appropriate numerical procedures in order to limit these unpleasant phenomena. 18. Polynomial approximation of functions in Sobolev spaces SciTech Connect Dupont, T.; Scott, R. 1980-04-01 Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces. 19. Computing functions by approximating the input Goldberg, Mayer 2012-12-01 In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their output. Our approach assumes only the most rudimentary knowledge of algebra and trigonometry, and makes no use of calculus. 20. Approximate String Matching with Reduced Alphabet Salmela, Leena; Tarhio, Jorma We present a method to speed up approximate string matching by mapping the factual alphabet to a smaller alphabet. We apply the alphabet reduction scheme to a tuned version of the approximate Boyer-Moore algorithm utilizing the Four-Russians technique. Our experiments show that the alphabet reduction makes the algorithm faster. Especially in the k-mismatch case, the new variation is faster than earlier algorithms for English data with small values of k. 1. Some Recent Progress for Approximation Algorithms Kawarabayashi, Ken-ichi We survey some recent progress on approximation algorithms. Our main focus is the following two problems that have some recent breakthroughs; the edge-disjoint paths problem and the graph coloring problem. These breakthroughs involve the following three ingredients that are quite central in approximation algorithms: (1) Combinatorial (graph theoretical) approach, (2) LP based approach and (3) Semi-definite programming approach. We also sketch how they are used to obtain recent development. 2. Polynomial approximation of functions in Sobolev spaces NASA Technical Reports Server (NTRS) Dupont, T.; Scott, R. 1980-01-01 Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces. 3. Polynomial approximation of functions in Sobolev spaces NASA Technical Reports Server (NTRS) Dupont, T.; Scott, R. 1980-01-01 Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces. 4. Nonlinear Stochastic PDEs: Analysis and Approximations DTIC Science & Technology 2016-05-23 3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations We compare Wiener chaos and stochastic collocation methods for linear advection-reaction...ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 nonlinear stochastic PDEs (SPDEs), nonlocal SPDEs, Navier...3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations Report Title We compare Wiener chaos and stochastic collocation methods for linear 5. Approximations and Solution Estimates in Optimization DTIC Science & Technology 2016-04-06 Approximations and Solution Estimates in Optimization Johannes O. Royset Operations Research Department Naval Postgraduate School joroyset@nps.edu...Abstract. Approximation is central to many optimization problems and the supporting theory pro- vides insight as well as foundation for algorithms. In...functions quantifies epi-convergence, we are able to obtain estimates of optimal solutions and optimal values through estimates of that distance. In 6. The closure approximation in the hierarchy equations. NASA Technical Reports Server (NTRS) 1971-01-01 The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the ?self-consistent field' approximation in nonequilibrium statistical mechanics are clarified. The error at any level of the hierarchy can be given and can be avoided by the use of the iterative method. 7. An improved proximity force approximation for electrostatics SciTech Connect Fosco, Cesar D.; Lombardo, Fernando C.; Mazzitelli, Francisco D. 2012-08-15 A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called 'proximity force approximation' the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction in atomic force microscopes. - Highlights: Black-Right-Pointing-Pointer The proximity force approximation (PFA) has been widely used in different areas. Black-Right-Pointing-Pointer The PFA can be improved using a derivative expansion in the shape of the surfaces. Black-Right-Pointing-Pointer We use the improved PFA to compute electrostatic forces between conductors. Black-Right-Pointing-Pointer The results can be used as an analytic benchmark for numerical calculations in AFM. Black-Right-Pointing-Pointer Insight is provided for people who use the PFA to compute nuclear and Casimir forces. 8. Approximating centrality in evolving graphs: toward sublinearity Priest, Benjamin W.; Cybenko, George 2017-05-01 The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm. 9. Approximate scaling properties of RNA free energy landscapes NASA Technical Reports Server (NTRS) 1996-01-01 RNA free energy landscapes are analysed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "time series". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and self-affine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately self-affine on timescales up to approximately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(1) model and the exponents characterizing self-affinity. 10. Inverse eigenproblem for R-symmetric matrices and their approximation Yuan, Yongxin 2009-11-01 Let be a nontrivial involution, i.e., R=R-1[not equal to]±In. We say that is R-symmetric if RGR=G. The set of all -symmetric matrices is denoted by . In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors in and a set of complex numbers , find a matrix such that and are, respectively, the eigenvalues and eigenvectors of A. We then consider the following approximation problem: Given an n×n matrix , find such that , where is the solution set of IEP and \|\|[dot operator]\|\| is the Frobenius norm. We provide an explicit formula for the best approximation solution by means of the canonical correlation decomposition. 11. A Multithreaded Algorithm for Network Alignment Via Approximate Matching SciTech Connect Khan, Arif; Gleich, David F.; Pothen, Alex; Halappanavar, Mahantesh 2012-11-16 Network alignment is an optimization problem to find the best one-to-one map between the vertices of a pair of graphs that overlaps in as many edges as possible. It is a relaxation of the graph isomorphism problem and is closely related to the subgraph isomorphism problem. The best current approaches are entirely heuristic, and are iterative in nature. They generate real-valued heuristic approximations that must be rounded to find integer solutions. This rounding requires solving a bipartite maximum weight matching problem at each step in order to avoid missing high quality solutions. We investigate substituting a parallel, half-approximation for maximum weight matching instead of an exact computation. Our experiments show that the resulting difference in solution quality is negligible. We demonstrate almost a 20-fold speedup using 40 threads on an 8 processor Intel Xeon E7-8870 system (from 10 minutes to 36 seconds). 12. Dissociation between exact and approximate addition in developmental dyslexia. PubMed Yang, Xiujie; Meng, Xiangzhi 2016-09-01 13. Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability NASA Technical Reports Server (NTRS) Ito, K. 1984-01-01 The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm. 14. Legendre-tau approximation for functional differential equations. III - Eigenvalue approximations and uniform stability NASA Technical Reports Server (NTRS) Ito, K. 1985-01-01 The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm. 15. Approximate formula and bounds for the time-varying susceptible-infected-susceptible prevalence in networks Van Mieghem, P. 2016-05-01 Based on a recent exact differential equation, the time dependence of the SIS prevalence, the average fraction of infected nodes, in any graph is first studied and then upper and lower bounded by an explicit analytic function of time. That new approximate "tanh formula" obeys a Riccati differential equation and bears resemblance to the classical expression in epidemiology of Kermack and McKendrick [Proc. R. Soc. London A 115, 700 (1927), 10.1098/rspa.1927.0118] but enhanced with graph specific properties, such as the algebraic connectivity, the second smallest eigenvalue of the Laplacian of the graph. We further revisit the challenge of finding tight upper bounds for the SIS (and SIR) epidemic threshold for all graphs. We propose two new upper bounds and show the importance of the variance of the number of infected nodes. Finally, a formula for the epidemic threshold in the cycle (or ring graph) is presented. 16. Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions. PubMed Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning 2016-11-21 We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones. 17. Beyond the small-angle approximation for MBR anisotropy from seeds SciTech Connect Stebbins, A. ); Veeraraghavan, S. ) 1995-02-15 In this paper we give a general expression for the energy shift of massless particles traveling through the gravitational field of an arbitrary matter distribution as calculated in the weak field limit in an asymptotically flat space-time. It is [ital not] assumed that matter is nonrelativistic. We demonstrate the surprising result that if the matter is illuminated by a uniform brightness background that the brightness pattern observed at a given point in space-time (modulo a term dependent on the observer's velocity) depends only on the matter distribution on the observer's past light cone. These results apply directly to the cosmological MBR anisotropy pattern generated in the immediate vicinity of an object such as a cosmic string or global texture. We apply these results to cosmic strings, finding a correction to previously published results in the small-angle approximation. We also derive the full-sky anisotropy pattern of a collapsing texture knot. 18. Thermodynamic properties and static structure factor for a Yukawa fluid in the mean spherical approximation. PubMed Montes-Perez, J; Cruz-Vera, A; Herrera, J N 2011-12-01 This work presents the full analytic expressions for the thermodynamic properties and the static structure factor for a hard sphere plus 1-Yukawa fluid within the mean spherical approximation. To obtain these properties of the fluid type Yukawa analytically it was necessary to solve an equation of fourth order for the scaling parameter on a large scale. The physical root of this equation was determined by imposing physical conditions. The results of this work are obtained from seminal papers of Blum and Høye. We show that is not necessary the use the series expansion to solve the equation for the scaling parameter. We applied our theoretical result to find the thermodynamic and the static structure factor for krypton. Our results are in good agreement with those obtained in an experimental form or by simulation using the Monte Carlo method. 19. Gravitational scattering of two black holes at the fourth post-Newtonian approximation Bini, Donato; Damour, Thibault 2017-09-01 We compute the (center-of-mass frame) scattering angle χ of hyperboliclike encounters of two spinning black holes, at the fourth post-Newtonian approximation level for orbital effects, and at the next-to-next-to-leading order for spin-dependent effects. We find it convenient to compute the gauge-invariant scattering angle (expressed as a function of energy, orbital angular momentum and spins) by using the effective-one-body formalism. The contribution to scattering associated with nonlocal, tail effects is computed by generalizing to the case of unbound motions the method of time localization of the action introduced in the case of (small-eccentricity) bound motions by Damour et al. [Phys. Rev. D 91, 084024 (2015), 10.1103/PhysRevD.91.084024]. 20. The tendon approximator device in traumatic injuries. PubMed Forootan, Kamal S; Karimi, Hamid; Forootan, Nazilla-Sadat S 2015-01-01 Precise and tension-free approximation of two tendon endings is the key predictor of outcomes following tendon lacerations and repairs. We evaluate the efficacy of a new tendon approximator device in tendon laceration repairs. In a comparative study, we used our new tendon approximator device in 99 consecutive patients with laceration of 266 tendons who attend a university hospital and evaluated the operative time to repair the tendons, surgeons' satisfaction as well as patient's outcomes in a long-term follow-up. Data were compared with the data of control patients undergoing tendon repair by conventional method. Totally 266 tendons were repaired by approximator device and 199 tendons by conventional technique. 78.7% of patients in first group were male and 21.2% were female. In approximator group 38% of patients had secondary repair of cut tendons and 62% had primary repair. Patients were followed for a mean period of 3years (14-60 months). Time required for repair of each tendon was significantly reduced with the approximator device (2 min vs. 5.5 min, p<0.0001). After 3-4 weeks of immobilization, passive and active physiotherapy was started. Functional Results of tendon repair were identical in the two groups and were not significantly different. 1% of tendons in group A and 1.2% in group B had rupture that was not significantly different. The new nerve approximator device is cheap, feasible to use and reduces the time of tendon repair with sustained outcomes comparable to the conventional methods. 1. Revised Thomas-Fermi approximation for singular potentials Dufty, James W.; Trickey, S. B. 2016-08-01 Approximations for the many-fermion free-energy density functional that include the Thomas-Fermi (TF) form for the noninteracting part lead to singular densities for singular external potentials (e.g., attractive Coulomb). This limitation of the TF approximation is addressed here by a formal map of the exact Euler equation for the density onto an equivalent TF form characterized by a modified Kohn-Sham potential. It is shown to be a "regularized" version of the Kohn-Sham potential, tempered by convolution with a finite-temperature response function. The resulting density is nonsingular, with the equilibrium properties obtained from the total free-energy functional evaluated at this density. This new representation is formally exact. Approximate expressions for the regularized potential are given to leading order in a nonlocality parameter, and the limiting behavior at high and low temperatures is described. The noninteracting part of the free energy in this approximation is the usual Thomas-Fermi functional. These results generalize and extend to finite temperatures the ground-state regularization by R. G. Parr and S. Ghosh [Proc. Natl. Acad. Sci. U.S.A. 83, 3577 (1986), 10.1073/pnas.83.11.3577] and by L. R. Pratt, G. G. Hoffman, and R. A. Harris [J. Chem. Phys. 88, 1818 (1988), 10.1063/1.454105] and formally systematize the finite-temperature regularization given by the latter authors. 2. On uniform approximation of elliptic functions by Padé approximants Khristoforov, Denis V. 2009-06-01 Diagonal Padé approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is constructed from two neighbouring Padé approximants and approximates an elliptic function locally uniformly in the Stahl domain. The proof of the convergence of this sequence is based on deriving strong asymptotic formulae for the remainder function and Padé polynomials and on the analysis of the behaviour of a spurious pole. Bibliography: 23 titles. 3. Approximation of Bivariate Functions via Smooth Extensions PubMed Central Zhang, Zhihua 2014-01-01 For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained. PMID:24683316 4. Why criteria for impulse approximation in Compton scattering fail in relativistic regimes Lajohn, L. A.; Pratt, R. H. 2014-05-01 The assumption behind impulse approximation (IA) for Compton scattering is that the momentum transfer q is much greater than the average < p > of the initial bound state momentum distribution p. Comparing with S-matrix results, we find that at relativistic incident photon energies (ωi) and for high Z elements, one requires information beyond < p > / q to predict the accuracy of relativistic IA (RIA) diferential cross sections. The IA expression is proportional to the product of a kinematic factor Xnr and the symmetrical Compton profile J, where Xnr = 1 + cos2 θ (θ is the photon scattering angle). In the RIA case, Xnr, independent of p, is replaced by Xrel (ω , θ , p) in the integrand which determines J. At nr energies there is virtually no RIA error in the position of the Compton peak maximum (ωfpk) in the scattered photon energy (ωf), while RIA error in the peak magnitude can be characterized by < p > / q . This is because at low ωi, the kinematic effects described by S-matrix (also RIA) expressions behave like Xnr, while in relativistic regimes (high ωi and Z), kinematic factors treated accurately by S-matrix but not RIA expressions become significant and do not factor out. 5. Structural Reliability Analysis and Optimization: Use of Approximations NASA Technical Reports Server (NTRS) Grandhi, Ramana V.; Wang, Liping 1999-01-01 This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different 6. Partially Coherent Scattering in Stellar Chromospheres. Part 4; Analytic Wing Approximations NASA Technical Reports Server (NTRS) Gayley, K. G. 1993-01-01 Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas. The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series. 7. Fourier Analysis of the Approximation Power of Principal Shift-Invariant Spaces DTIC Science & Technology 1991-07-01 finite, and hence arbitrary linear combinations are allowed in this sum. Approximation properties are primarily studied via approximation orders: for the...approximation order (and hopes of course to match them). The standard approach to lower bounds is via the quasi-interpolation argument: first, a space H C...crux of all the analysis here is the linkage between the Fourier transform and Fourier series via the periodization argument, and which is best expressed 8. Expectation values of single-particle operators in the random phase approximation ground state. PubMed Kosov, D S 2017-02-07 We developed a method for computing matrix elements of single-particle operators in the correlated random phase approximation ground state. Working with the explicit random phase approximation ground state wavefunction, we derived a practically useful and simple expression for a molecular property in terms of random phase approximation amplitudes. The theory is illustrated by the calculation of molecular dipole moments for a set of representative molecules. 9. Mathematical analysis of recent analytical approximations to the collapse of an empty spherical bubble. PubMed Amore, Paolo; Fernández, Francisco M 2013-02-28 We analyze the Rayleigh equation for the collapse of an empty bubble and provide an explanation for some recent analytical approximations to the model. We derive the form of the singularity at the second boundary point and discuss the convergence of the approximants. We also give a rigorous proof of the asymptotic behavior of the coefficients of the power series that are the basis for the approximate expressions. 10. Expectation values of single-particle operators in the random phase approximation ground state Kosov, D. S. 2017-02-01 We developed a method for computing matrix elements of single-particle operators in the correlated random phase approximation ground state. Working with the explicit random phase approximation ground state wavefunction, we derived a practically useful and simple expression for a molecular property in terms of random phase approximation amplitudes. The theory is illustrated by the calculation of molecular dipole moments for a set of representative molecules. 11. The Cell Cycle Switch Computes Approximate Majority Cardelli, Luca; Csikász-Nagy, Attila 2012-09-01 Both computational and biological systems have to make decisions about switching from one state to another. The Approximate Majority' computational algorithm provides the asymptotically fastest way to reach a common decision by all members of a population between two possible outcomes, where the decision approximately matches the initial relative majority. The network that regulates the mitotic entry of the cell-cycle in eukaryotes also makes a decision before it induces early mitotic processes. Here we show that the switch from inactive to active forms of the mitosis promoting Cyclin Dependent Kinases is driven by a system that is related to both the structure and the dynamics of the Approximate Majority computation. We investigate the behavior of these two switches by deterministic, stochastic and probabilistic methods and show that the steady states and temporal dynamics of the two systems are similar and they are exchangeable as components of oscillatory networks. 12. Ancilla-approximable quantum state transformations SciTech Connect Blass, Andreas; Gurevich, Yuri 2015-04-15 We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation. 13. Separable approximations of two-body interactions Haidenbauer, J.; Plessas, W. 1983-01-01 We perform a critical discussion of the efficiency of the Ernst-Shakin-Thaler method for a separable approximation of arbitrary two-body interactions by a careful examination of separable 3S1-3D1 N-N potentials that were constructed via this method by Pieper. Not only the on-shell properties of these potentials are considered, but also a comparison is made of their off-shell characteristics relative to the Reid soft-core potential. We point out a peculiarity in Pieper's application of the Ernst-Shakin-Thaler method, which leads to a resonant-like behavior of his potential 3SD1D. It is indicated where care has to be taken in order to circumvent drawbacks inherent in the Ernst-Shakin-Thaler separable approximation scheme. NUCLEAR REACTIONS Critical discussion of the Ernst-Shakin-Thaler separable approximation method. Pieper's separable N-N potentials examined on shell and off shell. 14. Fast wavelet based sparse approximate inverse preconditioner SciTech Connect Wan, W.L. 1996-12-31 Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices. 15. Approximation methods in gravitational-radiation theory NASA Technical Reports Server (NTRS) Will, C. M. 1986-01-01 The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes. 16. Approximation methods in gravitational-radiation theory NASA Technical Reports Server (NTRS) Will, C. M. 1986-01-01 The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes. 17. Dynamical eikonal approximation in breakup reactions of {sup 11}Be SciTech Connect Goldstein, G.; Baye, D. 2006-02-15 The dynamical eikonal approximation is a quantal method unifying the semiclassical time-dependent and eikonal methods by taking into account interference effects. The principle of the calculation is described and expressions for different types of cross sections are established for two variants of the method, differing by a phase choice. The 'coherent' variant respects rotational symmetry around the beam axis and is therefore prefered. A good agreement is obtained with experimental differential and integrated cross sections for the elastic breakup of the {sup 11}Be halo nucleus on {sup 12}C and {sup 208}Pb near 70 MeV/nucleon, without any parameter adjustment. The dynamical approximation is compared with the traditional eikonal method. Differences are analyzed and the respective merits of both methods are discussed. 18. Functional approximation and optimal specification of the mechanical risk index. PubMed Kaiser, Mark J; Pulsipher, Allan G 2005-10-01 The mechanical risk index (MRI) is a numerical measure that quantifies the complexity of drilling a well. The purpose of this article is to examine the role of the component factors of the MRI and its structural and parametric assumptions. A meta-modeling methodology is applied to derive functional expressions of the MRI, and it is shown that the MRI can be approximated in terms of a linear functional. The variation between the MRI measure and its functional specification is determined empirically, and for a reasonable design space, the functional specification is shown to a good approximating representation. A drilling risk index is introduced to quantify the uncertainty in the time and cost associated with drilling a well. A general methodology is outlined to create an optimal MRI specification. 19. Post-Newtonian approximation in Maxwell-like form SciTech Connect Kaplan, Jeffrey D.; Nichols, David A.; Thorne, Kip S. 2009-12-15 The equations of the linearized first post-Newtonian approximation to general relativity are often written in 'gravitoelectromagnetic' Maxwell-like form, since that facilitates physical intuition. Damour, Soffel, and Xu (DSX) (as a side issue in their complex but elegant papers on relativistic celestial mechanics) have expressed the first post-Newtonian approximation, including all nonlinearities, in Maxwell-like form. This paper summarizes that DSX Maxwell-like formalism (which is not easily extracted from their celestial mechanics papers), and then extends it to include the post-Newtonian (Landau-Lifshitz-based) gravitational momentum density, momentum flux (i.e. gravitational stress tensor), and law of momentum conservation in Maxwell-like form. The authors and their colleagues have found these Maxwell-like momentum tools useful for developing physical intuition into numerical-relativity simulations of compact binaries with spin. 20. An approximate solution for the free vibrations of rotating uniform cantilever beams NASA Technical Reports Server (NTRS) Peters, D. A. 1973-01-01 Approximate solutions are obtained for the uncoupled frequencies and modes of rotating uniform cantilever beams. The frequency approximations for flab bending, lead-lag bending, and torsion are simple expressions having errors of less than a few percent over the entire frequency range. These expressions provide a simple way of determining the relations between mass and stiffness parameters and the resultant frequencies and mode shapes of rotating uniform beams. 1. Comments on "a study of the collisional fragmentation problem using the gamma distribution approximation". PubMed 2007-04-15 M. Kostoglou and A.J. Karabelas [J. Colloid Interface Sci. 303 (2006) 419-429] proposed using a gamma distribution approximation to study a collisional fragmentation problem. This approximation involved two types of integrals and the use of continued fraction expansions for their computation. In this Comment, explicit expressions are derived for computing the integrals. 2. Marrow cell kinetics model: Equivalent prompt dose approximations for two special cases SciTech Connect Morris, M.D.; Jones, T.D. 1992-11-01 Two simple algebraic expressions are described for approximating the equivalent prompt dose as defined in the model of Jones et al. (1991). These approximations apply to two specific radiation exposure patterns: (1) a pulsed dose immediately followed by a protracted exposure at relatively low, constant dose rate and (2) an exponentially decreasing exposure field. 3. Marrow cell kinetics model: Equivalent prompt dose approximations for two special cases SciTech Connect Morris, M.D.; Jones, T.D. 1992-11-01 Two simple algebraic expressions are described for approximating the equivalent prompt dose'' as defined in the model of Jones et al. (1991). These approximations apply to two specific radiation exposure patterns: (1) a pulsed dose immediately followed by a protracted exposure at relatively low, constant dose rate and (2) an exponentially decreasing exposure field. 4. Impulse formalism for atom-molecule collisions: Inadequacy of the peaking approximation SciTech Connect Sharma, R. D.; Bakshi, P. M.; Sindoni, J. M. 1989-08-01 Expressions for differential and total cross sections for atom-diatomscattering are derived using the impulse formalism without any approximations.Results for the rotational-vibrational scattering are obtained without usingthe peaking approximation (PA). For the specific case of a hard-core potential,it is shown that, except for elastic scattering, PA results are substantiallydifferent from the true impulse results. 5. Approximating W projection as a separable kernel Merry, Bruce 2016-02-01 W projection is a commonly used approach to allow interferometric imaging to be accelerated by fast Fourier transforms, but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show that they can be closely approximated by separable kernels. The error scales with the fourth power of the field of view, and so is small enough to be ignored at mid- to high frequencies. We also show that hybrid imaging algorithms combining W projection with either faceting, snapshotting, or W stacking allow the error to be made arbitrarily small, making the approximation suitable even for high-resolution wide-field instruments. 6. Approximate convective heating equations for hypersonic flows NASA Technical Reports Server (NTRS) Zoby, E. V.; Moss, J. N.; Sutton, K. 1979-01-01 Laminar and turbulent heating-rate equations appropriate for engineering predictions of the convective heating rates about blunt reentry spacecraft at hypersonic conditions are developed. The approximate methods are applicable to both nonreacting and reacting gas mixtures for either constant or variable-entropy edge conditions. A procedure which accounts for variable-entropy effects and is not based on mass balancing is presented. Results of the approximate heating methods are in good agreement with existing experimental results as well as boundary-layer and viscous-shock-layer solutions. 7. Bronchopulmonary segments approximation using anatomical atlas Busayarat, Sata; Zrimec, Tatjana 2007-03-01 Bronchopulmonary segments are valuable as they give more accurate localization than lung lobes. Traditionally, determining the segments requires segmentation and identification of segmental bronchi, which, in turn, require volumetric imaging data. In this paper, we present a method for approximating the bronchopulmonary segments for sparse data by effectively using an anatomical atlas. The atlas is constructed from a volumetric data and contains accurate information about bronchopulmonary segments. A new ray-tracing based image registration is used for transferring the information from the atlas to a query image. Results show that the method is able to approximate the segments on sparse HRCT data with slice gap up to 25 millimeters. 8. Congruence Approximations for Entrophy Endowed Hyperbolic Systems NASA Technical Reports Server (NTRS) Barth, Timothy J.; Saini, Subhash (Technical Monitor) 1998-01-01 Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation. 9. Very fast approximate reconstruction of MR images. PubMed Angelidis, P A 1998-11-01 The ultra fast Fourier transform (UFFT) provides the means for a very fast computation of a magnetic resonance (MR) image, because it is implemented using only additions and no multiplications at all. It achieves this by approximating the complex exponential functions involved in the Fourier transform (FT) sum with computationally simpler periodic functions. This approximation introduces erroneous spectrum peaks of small magnitude. We examine the performance of this transform in some typical MRI signals. The results show that this transform can very quickly provide an MR image. It is proposed to be used as a replacement of the classically used FFT whenever a fast general overview of an image is required. 10. An Approximation Scheme for Delay Equations. DTIC Science & Technology 1980-06-16 AD-Am" 155 BtO~i UNkIV PROVIDENCE RI LEFSCI4ETZ CENTER FOR DYNAMI-flO F/f 12/ 1 AN APPROXIMATION SCIEME FOR DELAY EQUATIONS (U) JUN 80 F KAPPEL DAA629...for publ.ic release IAM 19.. and 1s aftnaotaton in unhi tea.0 ( f) 1 DDC UtB Distwifeaton A_._il .rd/or 1 . Introduction. In recent years one can see...Banach spaces. Fundamental for our approach is the following approximation theorem for semigroups of type W: Theorem 1 ([10]). Let AN, N - 1,2,..., and A 11. Approximate learning algorithm in Boltzmann machines. PubMed Yasuda, Muneki; Tanaka, Kazuyuki 2009-11-01 Boltzmann machines can be regarded as Markov random fields. For binary cases, they are equivalent to the Ising spin model in statistical mechanics. Learning systems in Boltzmann machines are one of the NP-hard problems. Thus, in general we have to use approximate methods to construct practical learning algorithms in this context. In this letter, we propose new and practical learning algorithms for Boltzmann machines by using the belief propagation algorithm and the linear response approximation, which are often referred as advanced mean field methods. Finally, we show the validity of our algorithm using numerical experiments. 12. Gaussian streaming with the truncated Zel'dovich approximation Kopp, Michael; Uhlemann, Cora; Achitouv, Ixandra 2016-12-01 We calculate the halo correlation function in redshift space using the Gaussian streaming model (GSM). To determine the scale-dependent functions entering the GSM, we use local Lagrangian bias together with convolution Lagrangian perturbation theory (CLPT), which constitutes an approximation to the Post-Zel'dovich approximation. On the basis of N -body simulations, we demonstrate that a smoothing of the initial conditions with the Lagrangian radius improves the Zel'dovich approximation and its ability to predict the displacement field of protohalos. Based on this observation, we implement a "truncated" CLPT by smoothing the initial power spectrum and investigate the dependence of the streaming model ingredients on the smoothing scale. We find that the real space correlation functions of halos and their mean pairwise velocity are optimized if the coarse graining scale is chosen to be 1 Mpc /h at z =0 , while the pairwise velocity dispersion is optimized if the smoothing scale is chosen to be the Lagrangian size of the halo. We compare theoretical results for the halo correlation function in redshift space to measurements within the Horizon run 2 N -body simulation halo catalog. We find that this simple two-filter smoothing procedure in the spirit of the truncated Zel'dovich approximation significantly improves the GSM +CLPT prediction of the redshift space halo correlation function over the whole mass range from large galaxy to galaxy cluster-sized halos. We expect that the necessity for two filter scales is an artifact of our local bias model, and that once a more physical bias model is implemented in CLPT, the only physically relevant smoothing scale will be related to the Lagrangian radius, in accord with our findings based on N -body simulations. 13. Homotopic approximate solutions for the perturbed CKdV equation with variable coefficients. PubMed Lu, Dianchen; Chen, Tingting; Hong, Baojian 2014-01-01 This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order approximate solutions and the second order approximate solutions of the variable coefficients CKdV equation in perturbation εu (n) are also induced. 14. Homotopic Approximate Solutions for the Perturbed CKdV Equation with Variable Coefficients PubMed Central Lu, Dianchen; Chen, Tingting 2014-01-01 This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order approximate solutions and the second order approximate solutions of the variable coefficients CKdV equation in perturbation εu n are also induced. PMID:24737983 15. Finding Dental Care MedlinePlus ... Finding Dental Care Where can I find low-cost dental care? Dental schools often have clinics that allow dental ... can I find more information? See Finding Low Cost Dental Care . WWNRightboxRadEditor2 Contact Us 1-866-232-4528 nidcrinfo@ ... 16. An approximate classical unimolecular reaction rate theory Zhao, Meishan; Rice, Stuart A. 1992-05-01 We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data. 17. Alternative approximation concepts for space frame synthesis NASA Technical Reports Server (NTRS) Lust, R. V.; Schmit, L. A. 1985-01-01 A structural synthesis methodology for the minimum mass design of 3-dimensionall frame-truss structures under multiple static loading conditions and subject to limits on displacements, rotations, stresses, local buckling, and element cross-sectional dimensions is presented. A variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses. Available options include: (A) formulation of the nonlinear mathematcal programming problem in either reciprocal section property (RSP) or cross-sectional dimension (CSD) space; (B) two alternative approximate problem structures in each design space; and (C) three distinct assumptions about element end-force variations. Fixed element, design element linking, and temporary constraint deletion features are also included. The solution of each approximate problem, in either its primal or dual form, is obtained using CONMIN, a feasible directions program. The frame-truss synthesis methodology is implemented in the COMPASS computer program and is used to solve a variety of problems. These problems were chosen so that, in addition to exercising the various approximation concepts options, the results could be compared with previously published work. 18. Approximations For Controls Of Hereditary Systems NASA Technical Reports Server (NTRS) Milman, Mark H. 1988-01-01 Convergence properties of controls, trajectories, and feedback kernels analyzed. Report discusses use of factorization techniques to approximate optimal feedback gains in finite-time, linear-regulator/quadratic-cost-function problem of system governed by retarded-functional-difference equations RFDE's with control delays. Presents approach to factorization based on discretization of state penalty leading to simple structure for feedback control law. 19. Progressive Image Coding by Hierarchical Linear Approximation. ERIC Educational Resources Information Center Wu, Xiaolin; Fang, Yonggang 1994-01-01 Proposes a scheme of hierarchical piecewise linear approximation as an adaptive image pyramid. A progressive image coder comes naturally from the proposed image pyramid. The new pyramid is semantically more powerful than regular tessellation but syntactically simpler than free segmentation. This compromise between adaptability and complexity… 20. Quickly Approximating the Distance Between Two Objects NASA Technical Reports Server (NTRS) Hammen, David 2009-01-01 A method of quickly approximating the distance between two objects (one smaller, regarded as a point; the other larger and complexly shaped) has been devised for use in computationally simulating motions of the objects for the purpose of planning the motions to prevent collisions. 1. Approximate Solution to the Generalized Boussinesq Equation Telyakovskiy, A. S.; Mortensen, J. 2010-12-01 The traditional Boussinesq equation describes motion of water in groundwater flows. It models unconfined groundwater flow under the Dupuit assumption that the equipotential lines are vertical, making the flowlines horizontal. The Boussinesq equation is a nonlinear diffusion equation with diffusivity depending linearly on water head. Here we analyze a generalization of the Boussinesq equation, when the diffusivity is a power law function of water head. For example polytropic gases moving through porous media obey this equation. Solving this equation usually requires numerical approximations, but for certain classes of initial and boundary conditions an approximate analytical solution can be constructed. This work focuses on the latter approach, using the scaling properties of the equation. We consider one-dimensional semi-infinite initially empty aquifer with boundary conditions at the inlet in case of cylindrical symmetry. Such situation represents the case of an injection well. Solutions would propagate with the finite speed. We construct an approximate scaling function, and we compare the approximate solution with the direct numerical solutions obtained by using the scaling properties of the equations. 2. Semiclassical Approximations and Predictability in Ocean Acoustics DTIC Science & Technology 1999-09-30 the ONR-funded work being performed by P. Worcester (SIO), J. Colosi (WHOI), M. Wolfson (WSU), J. Spiesberger (UPenn), S. 2 Tomsovic (WSU), G...Acoust. Soc. Am. 103, 2232-2235. Tappert, F. D., Spiesberger , J. L., and L. Boden (1995) New full-wave approximation for ocean acoustic travel time 3. Approximated integrability of the Dicke model Relaño, A.; Bastarrachea-Magnani, M. A.; Lerma-Hernández, S. 2016-12-01 A very approximate second integral of motion of the Dicke model is identified within a broad energy region above the ground state, and for a wide range of values of the external parameters. This second integral, obtained from a Born-Oppenheimer approximation, classifies the whole regular part of the spectrum in bands, coming from different semi-classical energy surfaces, and labelled by its corresponding eigenvalues. Results obtained from this approximation are compared with exact numerical diagonalization for finite systems in the superradiant phase, obtaining a remarkable accord. The region of validity of our approach in the parameter space, which includes the resonant case, is unveiled. The energy range of validity goes from the ground state up to a certain upper energy where chaos sets in, and extends far beyond the range of applicability of a simple harmonic approximation around the minimal energy configuration. The upper energy validity limit increases for larger values of the coupling constant and the ratio between the level splitting and the frequency of the field. These results show that the Dicke model behaves like a two-degree-of-freedom integrable model for a wide range of energies and values of the external parameters. 4. Can Distributional Approximations Give Exact Answers? ERIC Educational Resources Information Center Griffiths, Martin 2013-01-01 Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and… 5. Local discontinuous Galerkin approximations to Richards’ equation Li, H.; Farthing, M. W.; Dawson, C. N.; Miller, C. T. 2007-03-01 We consider the numerical approximation to Richards' equation because of its hydrological significance and intrinsic merit as a nonlinear parabolic model that admits sharp fronts in space and time that pose a special challenge to conventional numerical methods. We combine a robust and established variable order, variable step-size backward difference method for time integration with an evolving spatial discretization approach based upon the local discontinuous Galerkin (LDG) method. We formulate the approximation using a method of lines approach to uncouple the time integration from the spatial discretization. The spatial discretization is formulated as a set of four differential algebraic equations, which includes a mass conservation constraint. We demonstrate how this system of equations can be reduced to the solution of a single coupled unknown in space and time and a series of local constraint equations. We examine a variety of approximations at discontinuous element boundaries, permeability approximations, and numerical quadrature schemes. We demonstrate an optimal rate of convergence for smooth problems, and compare accuracy and efficiency for a wide variety of approaches applied to a set of common test problems. We obtain robust and efficient results that improve upon existing methods, and we recommend a future path that should yield significant additional improvements. 6. Approximating a nonlinear MTFDE from physiology Teodoro, M. Filomena 2016-12-01 This paper describes a numerical scheme which approximates the solution of a nonlinear mixed type functional differential equation from nerve conduction theory. The solution of such equation is defined in all the entire real axis and tends to known values at ±∞. A numerical method extended from linear case is developed and applied to solve a nonlinear equation. 7. Large Hierarchies from Approximate R Symmetries SciTech Connect Kappl, Rolf; Ratz, Michael; Schmidt-Hoberg, Kai; Nilles, Hans Peter; Ramos-Sanchez, Saul; Vaudrevange, Patrick K. S. 2009-03-27 We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales. 8. Block Addressing Indices for Approximate Text Retrieval. ERIC Educational Resources Information Center Baeza-Yates, Ricardo; Navarro, Gonzalo 2000-01-01 Discusses indexing in large text databases, approximate text searching, and space-time tradeoffs for indexed text searching. Studies the space overhead and retrieval times as functions of the text block size, concludes that an index can be sublinear in space overhead and query time, and applies the analysis to the Web. (Author/LRW) ERIC Educational Resources Information Center Lambert, Zarrel V.; And Others 1991-01-01 A method is presented that eliminates some interpretational limitations arising from assumptions implicit in the use of arbitrary rules of thumb to interpret exploratory factor analytic results. The bootstrap method is presented as a way of approximating sampling distributions of estimated factor loadings. Simulated datasets illustrate the… 10. Inhomogeneous random phase approximation: A solvable model SciTech Connect Lemm, J.C. 1995-11-15 A recently developed method to include particle-hole correlations into the time-independent mean field theory for scattering (TIMF) by an inhomogeneous random phase approximation (IRPA) is applied to a numerically solvable model. Having adapted the procedure according to numerical requirements, IRPA calculations turn out to be tractable. The obtained results improve TIMF results. 8 refs., 28 figs., 3 tabs. 11. Block Addressing Indices for Approximate Text Retrieval. ERIC Educational Resources Information Center Baeza-Yates, Ricardo; Navarro, Gonzalo 2000-01-01 Discusses indexing in large text databases, approximate text searching, and space-time tradeoffs for indexed text searching. Studies the space overhead and retrieval times as functions of the text block size, concludes that an index can be sublinear in space overhead and query time, and applies the analysis to the Web. (Author/LRW) 12. Sensing Position With Approximately Constant Contact Force NASA Technical Reports Server (NTRS) Sturdevant, Jay 1996-01-01 Computer-controlled electromechanical system uses number of linear variable-differential transformers (LVDTs) to measure axial positions of selected points on surface of lens, mirror, or other precise optical component with high finish. Pressures applied to pneumatically driven LVDTs adjusted to maintain small, approximately constant contact forces as positions of LVDT tips vary. 13. Padé approximations and diophantine geometry PubMed Central Chudnovsky, D. V.; Chudnovsky, G. V. 1985-01-01 Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves. PMID:16593552 14. Can Distributional Approximations Give Exact Answers? ERIC Educational Resources Information Center Griffiths, Martin 2013-01-01 Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and… 15. Approximate model for laser ablation of carbon Shusser, Michael 2010-08-01 The paper presents an approximate kinetic theory model of ablation of carbon by a nanosecond laser pulse. The model approximates the process as sublimation and combines conduction heat transfer in the target with the gas dynamics of the ablated plume which are coupled through the boundary conditions at the interface. The ablated mass flux and the temperature of the ablating material are obtained from the assumption that the ablation rate is restricted by the kinetic theory limitation on the maximum mass flux that can be attained in a phase-change process. To account for non-uniform distribution of the laser intensity while keeping the calculation simple the quasi-one-dimensional approximation is used in both gas and solid phases. The results are compared with the predictions of the exact axisymmetric model that uses the conservation relations at the interface derived from the momentum solution of the Boltzmann equation for arbitrary strong evaporation. It is seen that the simpler approximate model provides good accuracy. 16. Kravchuk functions for the finite oscillator approximation NASA Technical Reports Server (NTRS) Atakishiyev, Natig M.; Wolf, Kurt Bernardo 1995-01-01 Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion. 17. Variance approximations for assessments of classification accuracy Treesearch R. L. Czaplewski 1994-01-01 Variance approximations are derived for the weighted and unweighted kappa statistics, the conditional kappa statistic, and conditional probabilities. These statistics are useful to assess classification accuracy, such as accuracy of remotely sensed classifications in thematic maps when compared to a sample of reference classifications made in the field. Published... 18. Multidimensional stochastic approximation using locally contractive functions NASA Technical Reports Server (NTRS) Lawton, W. M. 1975-01-01 A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions. 19. Approximation algorithms for planning and control NASA Technical Reports Server (NTRS) Boddy, Mark; Dean, Thomas 1989-01-01 A control system operating in a complex environment will encounter a variety of different situations, with varying amounts of time available to respond to critical events. Ideally, such a control system will do the best possible with the time available. In other words, its responses should approximate those that would result from having unlimited time for computation, where the degree of the approximation depends on the amount of time it actually has. There exist approximation algorithms for a wide variety of problems. Unfortunately, the solution to any reasonably complex control problem will require solving several computationally intensive problems. Algorithms for successive approximation are a subclass of the class of anytime algorithms, algorithms that return answers for any amount of computation time, where the answers improve as more time is allotted. An architecture is described for allocating computation time to a set of anytime algorithms, based on expectations regarding the value of the answers they return. The architecture described is quite general, producing optimal schedules for a set of algorithms under widely varying conditions. 20. Approximating the efficiency characteristics of blade pumps Shekun, G. D. 2007-11-01 Results from a statistical investigation into the experimental efficiency characteristics of commercial type SD centrifugal pumps and type SDS swirl flow pumps are presented. An exponential function for approximating the efficiency characteristics of blade pumps is given. The versatile nature of this characteristic is confirmed by the fact that the use of different systems of relative units gives identical results. 1. Theory of Casimir Forces without the Proximity-Force Approximation. PubMed Lapas, Luciano C; Pérez-Madrid, Agustín; Rubí, J Miguel 2016-03-18 We analyze both the attractive and repulsive Casimir-Lifshitz forces recently reported in experimental investigations. By using a kinetic approach, we obtain the Casimir forces from the power absorbed by the materials. We consider collective material excitations through a set of relaxation times distributed in frequency according to a log-normal function. A generalized expression for these forces for arbitrary values of temperature is obtained. We compare our results with experimental measurements and conclude that the model goes beyond the proximity-force approximation. 2. Probabilistic conflict detection algorithm based on saddlepoint approximation Liu, Jianliang; Yang, Yihuang; Xu, Yang 2017-04-01 With the development of the air transport industry, air traffic flow increased significantly, conflict detection becomes an important part of the Next Generation Air Transportation System (NextGen). This paper is proposed a probabilistic conflict detection algorithm based on the 4D trajectory prediction. The relative distance of two aircraft can be represented by a Gaussian random variable and the problem of conflict probability calculation is express as tail probability of the quadratic form of Gaussian random variables, and solved by saddlepoint approximation. The efficiency and accuracy of the proposed method is demonstrated through a pairwise aircraft encounter scenario. 3. Corrections to the thin wall approximation in general relativity NASA Technical Reports Server (NTRS) Garfinkle, David; Gregory, Ruth 1989-01-01 The question is considered whether the thin wall formalism of Israel applies to the gravitating domain walls of a lambda phi(exp 4) theory. The coupled Einstein-scalar equations that describe the thick gravitating wall are expanded in powers of the thickness of the wall. The solutions of the zeroth order equations reproduce the results of the usual Israel thin wall approximation for domain walls. The solutions of the first order equations provide corrections to the expressions for the stress-energy of the wall and to the Israel thin wall equations. The modified thin wall equations are then used to treat the motion of spherical and planar domain walls. 4. Cosmic-ray streaming in the Born approximation NASA Technical Reports Server (NTRS) Bieber, J. W.; Burger, R. A. 1990-01-01 The present work invokes the Born approximation to derive a more accurate expression for the streaming of cosmic rays parallel to the mean magnetic field. While all prior results pertaining to the helicity dependence of the diffusion coefficient and convection speed can be recovered as special cases from this streaming equation, it is concluded that a new set of transport parameters presented here is more appropriate for the solar modulation of galactic cosmic rays. In addition, a new parameter related to time variability, which may be a dominant cause of charge sign-dependent transport of solar particles, is introduced. 5. Relaxation approximation in the theory of shear turbulence NASA Technical Reports Server (NTRS) Rubinstein, Robert 1995-01-01 Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory. 6. Cosmic-ray streaming in the Born approximation NASA Technical Reports Server (NTRS) Bieber, J. W.; Burger, R. A. 1990-01-01 The present work invokes the Born approximation to derive a more accurate expression for the streaming of cosmic rays parallel to the mean magnetic field. While all prior results pertaining to the helicity dependence of the diffusion coefficient and convection speed can be recovered as special cases from this streaming equation, it is concluded that a new set of transport parameters presented here is more appropriate for the solar modulation of galactic cosmic rays. In addition, a new parameter related to time variability, which may be a dominant cause of charge sign-dependent transport of solar particles, is introduced. 7. Systematic Approximations to Susceptible-Infectious-Susceptible Dynamics on Networks PubMed Central Cooper, Alison J. 2016-01-01 Network-based infectious disease models have been highly effective in elucidating the role of contact structure in the spread of infection. As such, pair- and neighbourhood-based approximation models have played a key role in linking findings from network simulations to standard (random-mixing) results. Recently, for SIR-type infections (that produce one epidemic in a closed population) on locally tree-like networks, these approximations have been shown to be exact. However, network models are ideally suited for Sexually Transmitted Infections (STIs) due to the greater level of detail available for sexual contact networks, and these diseases often possess SIS-type dynamics. Here, we consider the accuracy of three systematic approximations that can be applied to arbitrary disease dynamics, including SIS behaviour. We focus in particular on low degree networks, in which the small number of neighbours causes build-up of local correlations between the state of adjacent nodes that are challenging to capture. By examining how and when these approximation models converge to simulation results, we generate insights into the role of network structure in the infection dynamics of SIS-type infections. PMID:27997542 8. How Good Are Statistical Models at Approximating Complex Fitness Landscapes? PubMed Central du Plessis, Louis; Leventhal, Gabriel E.; Bonhoeffer, Sebastian 2016-01-01 Fitness landscapes determine the course of adaptation by constraining and shaping evolutionary trajectories. Knowledge of the structure of a fitness landscape can thus predict evolutionary outcomes. Empirical fitness landscapes, however, have so far only offered limited insight into real-world questions, as the high dimensionality of sequence spaces makes it impossible to exhaustively measure the fitness of all variants of biologically meaningful sequences. We must therefore revert to statistical descriptions of fitness landscapes that are based on a sparse sample of fitness measurements. It remains unclear, however, how much data are required for such statistical descriptions to be useful. Here, we assess the ability of regression models accounting for single and pairwise mutations to correctly approximate a complex quasi-empirical fitness landscape. We compare approximations based on various sampling regimes of an RNA landscape and find that the sampling regime strongly influences the quality of the regression. On the one hand it is generally impossible to generate sufficient samples to achieve a good approximation of the complete fitness landscape, and on the other hand systematic sampling schemes can only provide a good description of the immediate neighborhood of a sequence of interest. Nevertheless, we obtain a remarkably good and unbiased fit to the local landscape when using sequences from a population that has evolved under strong selection. Thus, current statistical methods can provide a good approximation to the landscape of naturally evolving populations. PMID:27189564 9. How Good Are Statistical Models at Approximating Complex Fitness Landscapes? PubMed du Plessis, Louis; Leventhal, Gabriel E; Bonhoeffer, Sebastian 2016-09-01 Fitness landscapes determine the course of adaptation by constraining and shaping evolutionary trajectories. Knowledge of the structure of a fitness landscape can thus predict evolutionary outcomes. Empirical fitness landscapes, however, have so far only offered limited insight into real-world questions, as the high dimensionality of sequence spaces makes it impossible to exhaustively measure the fitness of all variants of biologically meaningful sequences. We must therefore revert to statistical descriptions of fitness landscapes that are based on a sparse sample of fitness measurements. It remains unclear, however, how much data are required for such statistical descriptions to be useful. Here, we assess the ability of regression models accounting for single and pairwise mutations to correctly approximate a complex quasi-empirical fitness landscape. We compare approximations based on various sampling regimes of an RNA landscape and find that the sampling regime strongly influences the quality of the regression. On the one hand it is generally impossible to generate sufficient samples to achieve a good approximation of the complete fitness landscape, and on the other hand systematic sampling schemes can only provide a good description of the immediate neighborhood of a sequence of interest. Nevertheless, we obtain a remarkably good and unbiased fit to the local landscape when using sequences from a population that has evolved under strong selection. Thus, current statistical methods can provide a good approximation to the landscape of naturally evolving populations. © The Author 2016. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. 10. The coupled states approximation for scattering of two diatoms NASA Technical Reports Server (NTRS) Heil, T. G.; Kouri, D. J.; Green, S. 1978-01-01 The paper presents a detailed development of the coupled-states approximation for the general case of two colliding diatomic molecules. The high-energy limit of the exact Lippman-Schwinger equation is applied, and the analysis follows the Shimoni and Kouri (1977) treatment of atom-diatom collisions where the coupled rotor angular momentum and projection replace the single diatom angular momentum and projection. Parallels to the expression for the differential scattering amplitude, the opacity function, and the nondiagonality of the T matrix are reported. Symmetrized expressions and symmetrized coupled equations are derived. The present correctly labeled coupled-states theory is tested by comparing its calculated results with other computed results for three cases: H2-H2 collisions, ortho-para H2-H2 scattering, and H2-HCl. 11. The coupled states approximation for scattering of two diatoms NASA Technical Reports Server (NTRS) Heil, T. G.; Kouri, D. J.; Green, S. 1978-01-01 The paper presents a detailed development of the coupled-states approximation for the general case of two colliding diatomic molecules. The high-energy limit of the exact Lippman-Schwinger equation is applied, and the analysis follows the Shimoni and Kouri (1977) treatment of atom-diatom collisions where the coupled rotor angular momentum and projection replace the single diatom angular momentum and projection. Parallels to the expression for the differential scattering amplitude, the opacity function, and the nondiagonality of the T matrix are reported. Symmetrized expressions and symmetrized coupled equations are derived. The present correctly labeled coupled-states theory is tested by comparing its calculated results with other computed results for three cases: H2-H2 collisions, ortho-para H2-H2 scattering, and H2-HCl. 12. Finite difference methods for approximating Heaviside functions Towers, John D. 2009-05-01 We present a finite difference method for discretizing a Heaviside function H(u(x→)), where u is a level set function u:Rn ↦ R that is positive on a bounded region Ω⊂Rn. There are two variants of our algorithm, both of which are adapted from finite difference methods that we proposed for discretizing delta functions in [J.D. Towers, Two methods for discretizing a delta function supported on a level set, J. Comput. Phys. 220 (2007) 915-931; J.D. Towers, Discretizing delta functions via finite differences and gradient normalization, Preprint at http://www.miracosta.edu/home/jtowers/; J.D. Towers, A convergence rate theorem for finite difference approximations to delta functions, J. Comput. Phys. 227 (2008) 6591-6597]. We consider our approximate Heaviside functions as they are used to approximate integrals over Ω. We prove that our first approximate Heaviside function leads to second order accurate quadrature algorithms. Numerical experiments verify this second order accuracy. For our second algorithm, numerical experiments indicate at least third order accuracy if the integrand f and ∂Ω are sufficiently smooth. Numerical experiments also indicate that our approximations are effective when used to discretize certain singular source terms in partial differential equations. We mostly focus on smooth f and u. By this we mean that f is smooth in a neighborhood of Ω, u is smooth in a neighborhood of ∂Ω, and the level set u(x)=0 is a manifold of codimension one. However, our algorithms still give reasonable results if either f or u has jumps in its derivatives. Numerical experiments indicate approximately second order accuracy for both algorithms if the regularity of the data is reduced in this way, assuming that the level set u(x)=0 is a manifold. Numerical experiments indicate that dependence on the placement of Ω with respect to the grid is quite small for our algorithms. Specifically, a grid shift results in an O(hp) change in the computed solution 13. Typical performance of approximation algorithms for NP-hard problems Takabe, Satoshi; Hukushima, Koji 2016-11-01 Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linear-programming relaxation, loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using a statistical-mechanical technique, whereas the average-case analysis of the last one is conducted using the generating function method. These algorithms have a threshold in the typical performance with increasing average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases, determined by the order of the typical performance thresholds. In addition, we provide some conditions for classification of the graph ensembles and demonstrate explicitly some examples for the difference in thresholds. 14. Training the Approximate Number System Improves Math Proficiency PubMed Central Park, Joonkoo; Brannon, Elizabeth M. 2013-01-01 Humans share with nonhuman animals an approximate number system (ANS) that permits estimation and rough calculation of number without symbols. Recent studies show a correlation between the acuity of the ANS and symbolic math performance throughout development and into adulthood, suggesting that the ANS may serve as a cognitive foundation for the uniquely human capacity for symbolic mathematics. Such a proposition leads to the untested prediction that training aimed at improving ANS performance will transfer to improvement in symbolic mathematics. Here, in two experiments, we show that ANS training on approximate addition and subtraction of arrays of dots, selectively improves symbolic addition and subtraction. This finding strongly supports the hypothesis that complex math skills are fundamentally linked to rudimentary preverbal quantitative abilities, provides the first direct evidence that ANS and symbolic math may be causally related, and raises the possibility that interventions aimed at the ANS could benefit children and adults who struggle with math. PMID:23921769 15. Adiabatic approximation for the Rabi model with broken inversion symmetry Shen, Li-Tuo; Yang, Zhen-Biao; Wu, Huai-Zhi 2017-01-01 We study the properties and behavior of the Rabi model with broken inversion symmetry. Using an adiabatic approximation approach, we explore the high-frequency qubit and oscillator regimes, and obtain analytical solutions for the qubit-oscillator system. We demonstrate that, due to broken inversion symmetry, the positions of two potentials and zero-point energies in the oscillators become asymmetric and have a quadratic dependence on the mean dipole moments within the high-frequency oscillator regime. Furthermore, we find that there is a critical point above which the qubit-oscillator system becomes unstable, and the position of this critical point has a quadratic dependence on the mean dipole moments within the high-frequency qubit regime. Finally, we verify this critical point based on the method of semiclassical approximation. 16. Weak impedance difference approximations of thin-bed PP-wave reflection responses Yang, Chun; Wang, Yun; Lu, Jun 2017-08-01 Under the assumptions of weak impedance differences and small incident angles, the PP-wave reflections approximation of a single thin bed is studied. Three analytical equations, defined as weak impedance difference approximation, the fourth-order power series approximation and the second-order power series approximation, are given as functions of incident angle, bed thickness, frequency and elastic parameters (density, P-wave and S-wave velocities) differences of the thin bed; in particular, the latter two approximations are expressed in the power series form of the incident angle’s sine value. Two kinds of thin-bed models and a well log are used to test the approximation equations’ precision and acceptability. Numerical simulations show that these three approximations are not suitable in the case of thin-bed models with strong impedance differences. For thin-bed models with unequal-magnitude reflectivity, weak impedance difference approximation has high approximation accuracy (errors <12%) in pre-critical angle, the fourth-order and the second-order power series approximations are acceptable as the maximum incident angles are about 10 degrees less than the critical angles (if available). For thin-bed models with opposite-polarity and equal-magnitude reflectivity, the three approximations are more suitable for a thin bed with polarities (-, +) than with (+, -). The second-order power series approximation has similar approximation accuracy (errors <10%) with the other two approximation equations with small incident angles. PP-wave synthetic seismograms comparisons of exact and approximate reflections in the case of the well log show that the approximation equations are applicable in the actual sand-shale inter-bedding reservoirs. 17. Approximation techniques of a selective ARQ protocol Kim, B. G. Approximations to the performance of selective automatic repeat request (ARQ) protocol with lengthy acknowledgement delays are presented. The discussion is limited to packet-switched communication systems in a single-hop environment such as found with satellite systems. It is noted that retransmission of errors after ARQ is a common situation. ARQ techniques, e.g., stop-and-wait and continuous, are outlined. A simplified queueing analysis of the selective ARQ protocol shows that exact solutions with long delays are not feasible. Two approximation models are formulated, based on known exact behavior of a system with short delays. The buffer size requirements at both ends of a communication channel are cited as significant factor for accurate analysis, and further examinations of buffer overflow and buffer lock-out probability and avoidance are recommended. 18. Approximate inverse preconditioners for general sparse matrices SciTech Connect 1994-12-31 Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection. 19. Multiwavelet neural network and its approximation properties. PubMed Jiao, L; Pan, J; Fang, Y 2001-01-01 A model of multiwavelet-based neural networks is proposed. Its universal and L(2) approximation properties, together with its consistency are proved, and the convergence rates associated with these properties are estimated. The structure of this network is similar to that of the wavelet network, except that the orthonormal scaling functions are replaced by orthonormal multiscaling functions. The theoretical analyses show that the multiwavelet network converges more rapidly than the wavelet network, especially for smooth functions. To make a comparison between both networks, experiments are carried out with the Lemarie-Meyer wavelet network, the Daubechies2 wavelet network and the GHM multiwavelet network, and the results support the theoretical analysis well. In addition, the results also illustrate that at the jump discontinuities, the approximation performance of the two networks are about the same. 20. A Varifold Approach to Surface Approximation Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon 2017-06-01 We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we introduce the notion of approximate mean curvature and show various convergence results that hold, in particular, for sequences of discrete varifolds associated with point clouds or pixel/voxel-type discretizations of d-surfaces in the Euclidean n-space, without restrictions on dimension and codimension. The variational nature of the approach also allows us to consider surfaces with singularities, and in that case the approximate mean curvature is consistent with the generalized mean curvature of the limit surface. A series of numerical tests are provided in order to illustrate the effectiveness and generality of the method. 1. Planetary ephemerides approximation for radar astronomy NASA Technical Reports Server (NTRS) 1991-01-01 The planetary ephemerides approximation for radar astronomy is discussed, and, in particular, the effect of this approximation on the performance of the programmable local oscillator (PLO) used in Goldstone Solar System Radar is presented. Four different approaches are considered and it is shown that the Gram polynomials outperform the commonly used technique based on Chebyshev polynomials. These methods are used to analyze the mean square, the phase error, and the frequency tracking error in the presence of the worst case Doppler shift that one may encounter within the solar system. It is shown that in the worst case the phase error is under one degree and the frequency tracking error less than one hertz when the frequency to the PLO is updated every millisecond. 2. Smooth polynomial approximation of spiral arcs Cripps, R. J.; Hussain, M. Z.; Zhu, S. 2010-03-01 Constructing fair curve segments using parametric polynomials is difficult due to the oscillatory nature of polynomials. Even NURBS curves can exhibit unsatisfactory curvature profiles. Curve segments with monotonic curvature profiles, for example spiral arcs, exist but are intrinsically non-polynomial in nature and thus difficult to integrate into existing CAD systems. A method of constructing an approximation to a generalised Cornu spiral (GCS) arc using non-rational quintic Bézier curves matching end points, end slopes and end curvatures is presented. By defining an objective function based on the relative error between the curvature profiles of the GCS and its Bézier approximation, a curve segment is constructed that has a monotonic curvature profile within a specified tolerance. 3. Flexible least squares for approximately linear systems Kalaba, Robert; Tesfatsion, Leigh 1990-10-01 A probability-free multicriteria approach is presented to the problem of filtering and smoothing when prior beliefs concerning dynamics and measurements take an approximately linear form. Consideration is given to applications in the social and biological sciences, where obtaining agreement among researchers regarding probability relations for discrepancy terms is difficult. The essence of the proposed flexible-least-squares (FLS) procedure is the cost-efficient frontier, a curve in a two-dimensional cost plane which provides an explicit and systematic way to determine the efficient trade-offs between the separate costs incurred for dynamic and measurement specification errors. The FLS estimates show how the state vector could have evolved over time in a manner minimally incompatible with the prior dynamic and measurement specifications. A FORTRAN program for implementing the FLS filtering and smoothing procedure for approximately linear systems is provided. 4. Quantum fluctuations beyond the Gutzwiller approximation Fabrizio, Michele 2017-02-01 We present a simple scheme to evaluate linear response functions including quantum fluctuation corrections on top of the Gutzwiller approximation. The method is derived for a generic multiband lattice Hamiltonian without any assumption about the dynamics of the variational correlation parameters that define the Gutzwiller wave function, and which thus behave as genuine dynamical degrees of freedom that add on those of the variational uncorrelated Slater determinant. We apply the method to the standard half-filled single-band Hubbard model. We are able to recover known results, but, as a by-product, we also obtain a few other results. In particular, we show that quantum fluctuations can reproduce, almost quantitatively, the behavior of the uniform magnetic susceptibility uncovered by dynamical mean-field theory, which, though enhanced by correlations, is found to be smooth across the paramagnetic Mott transition. By contrast, the simple Gutzwiller approximation predicts that susceptibility to diverge at the transition. 5. Approximate maximum likelihood estimation of scanning observer templates Abbey, Craig K.; Samuelson, Frank W.; Wunderlich, Adam; Popescu, Lucretiu M.; Eckstein, Miguel P.; Boone, John M. 2015-03-01 In localization tasks, an observer is asked to give the location of some target or feature of interest in an image. Scanning linear observer models incorporate the search implicit in this task through convolution of an observer template with the image being evaluated. Such models are becoming increasingly popular as predictors of human performance for validating medical imaging methodology. In addition to convolution, scanning models may utilize internal noise components to model inconsistencies in human observer responses. In this work, we build a probabilistic mathematical model of this process and show how it can, in principle, be used to obtain estimates of the observer template using maximum likelihood methods. The main difficulty of this approach is that a closed form probability distribution for a maximal location response is not generally available in the presence of internal noise. However, for a given image we can generate an empirical distribution of maximal locations using Monte-Carlo sampling. We show that this probability is well approximated by applying an exponential function to the scanning template output. We also evaluate log-likelihood functions on the basis of this approximate distribution. Using 1,000 trials of simulated data as a validation test set, we find that a plot of the approximate log-likelihood function along a single parameter related to the template profile achieves its maximum value near the true value used in the simulation. This finding holds regardless of whether the trials are correctly localized or not. In a second validation study evaluating a parameter related to the relative magnitude of internal noise, only the incorrect localization images produces a maximum in the approximate log-likelihood function that is near the true value of the parameter. 6. JIMWLK evolution in the Gaussian approximation Iancu, E.; Triantafyllopoulos, D. N. 2012-04-01 We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors N c . This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it re-produces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite N c . Any higher n-point function with n ≥ 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes. 7. Barycentric approximation in financial decision making SciTech Connect Frauendorfer, K. 1994-12-31 We consider dynamic portfolio selection problems which are exposed to interest rate risk and credit risk caused by stochastic cash-flows and interest rates. For maximizing the expected net present value, we apply the barycentric approximation scheme of stochastic programming and discuss its features to be utilized in financial decision making. In particular, we focus on the martingale property, the term structure of interest rates, cash-flow dynamics, and correlations of the later two. 8. Beyond the Kirchhoff approximation. II - Electromagnetic scattering NASA Technical Reports Server (NTRS) Rodriguez, Ernesto 1991-01-01 In a paper by Rodriguez (1981), the momentum transfer expansion was introduced for scalar wave scattering. It was shown that this expansion can be used to obtain wavelength-dependent curvature corrections to the Kirchhoff approximation. This paper extends the momentum transfer perturbation expansion to electromagnetic waves. Curvature corrections to the surface current are obtained. Using these results, the specular field and the backscatter cross section are calculated. 9. Stochastic approximation boosting for incomplete data problems. PubMed Sexton, Joseph; Laake, Petter 2009-12-01 Boosting is a powerful approach to fitting regression models. This article describes a boosting algorithm for likelihood-based estimation with incomplete data. The algorithm combines boosting with a variant of stochastic approximation that uses Markov chain Monte Carlo to deal with the missing data. Applications to fitting generalized linear and additive models with missing covariates are given. The method is applied to the Pima Indians Diabetes Data where over half of the cases contain missing values. 10. Nonlinear amplitude approximation for bilinear systems Jung, Chulwoo; D'Souza, Kiran; Epureanu, Bogdan I. 2014-06-01 An efficient method to predict vibration amplitudes at the resonant frequencies of dynamical systems with piecewise-linear nonlinearity is developed. This technique is referred to as bilinear amplitude approximation (BAA). BAA constructs a single vibration cycle at each resonant frequency to approximate the periodic steady-state response of the system. It is postulated that the steady-state response is piece-wise linear and can be approximated by analyzing the response over two time intervals during which the system behaves linearly. Overall the dynamics is nonlinear, but the system is in a distinct linear state during each of the two time intervals. Thus, the approximated vibration cycle is constructed using linear analyses. The equation of motion for analyzing the vibration of each state is projected along the overlapping space spanned by the linear mode shapes active in each of the states. This overlapping space is where the vibratory energy is transferred from one state to the other when the system switches from one state to the other. The overlapping space can be obtained using singular value decomposition. The space where the energy is transferred is used together with transition conditions of displacement and velocity compatibility to construct a single vibration cycle and to compute the amplitude of the dynamics. Since the BAA method does not require numerical integration of nonlinear models, computational costs are very low. In this paper, the BAA method is first applied to a single-degree-of-freedom system. Then, a three-degree-of-freedom system is introduced to demonstrate a more general application of BAA. Finally, the BAA method is applied to a full bladed disk with a crack. Results comparing numerical solutions from full-order nonlinear analysis and results obtained using BAA are presented for all systems. 11. Development of New Density Functional Approximations Su, Neil Qiang; Xu, Xin 2017-05-01 Kohn-Sham density functional theory has become the leading electronic structure method for atoms, molecules, and extended systems. It is in principle exact, but any practical application must rely on density functional approximations (DFAs) for the exchange-correlation energy. Here we emphasize four aspects of the subject: (a) philosophies and strategies for developing DFAs; (b) classification of DFAs; (c) major sources of error in existing DFAs; and (d) some recent developments and future directions. 12. Oscillation of boson star in Newtonian approximation Jarwal, Bharti; Singh, S. Somorendro 2017-03-01 Boson star (BS) rotation is studied under Newtonian approximation. A Coulombian potential term is added as perturbation to the radial potential of the system without disturbing the angular momentum. The results of the stationary states of these ground state, first and second excited state are analyzed with the correction of Coulombian potential. It is found that the results with correction increased in the amplitude of oscillation of BS in comparison to potential without perturbation correction. 13. Approximation methods for stochastic petri nets NASA Technical Reports Server (NTRS) Jungnitz, Hauke Joerg 1992-01-01 Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay 14. Empirical progress and nomic truth approximation revisited. PubMed Kuipers, Theo A F 2014-06-01 In my From Instrumentalism to Constructive Realism (2000) I have shown how an instrumentalist account of empirical progress can be related to nomic truth approximation. However, it was assumed that a strong notion of nomic theories was needed for that analysis. In this paper it is shown, in terms of truth and falsity content, that the analysis already applies when, in line with scientific common sense, nomic theories are merely assumed to exclude certain conceptual possibilities as nomic possibilities. 15. Numerical quadratures for approximate computation of ERBS Zanaty, Peter 2013-12-01 In the ground-laying paper [3] on expo-rational B-splines (ERBS), the default numerical method for approximate computation of the integral with C∞-smooth integrand in the definition of ERBS is Romberg integration. In the present work, a variety of alternative numerical quadrature methods for computation of ERBS and other integrals with smooth integrands are studied, and their performance is compared on several benchmark examples. 16. Numerical Approximation to the Thermodynamic Integrals Johns, S. M.; Ellis, P. J.; Lattimer, J. M. 1996-12-01 We approximate boson thermodynamic integrals as polynomials in two variables chosen to give the correct limiting expansion and to smoothly interpolate into other regimes. With 10 free parameters, an accuracy of better than 0.009% is achieved for the pressure, internal energy density, and number density. We also revisit the fermion case, originally addressed by Eggleton, Faulkner, & Flannery (1973), and substantially improve the accuracy of their fits. 17. Coherent population transfer beyond rotating wave approximation Rhee, Yongjoo; Kwon, Duck-Hee; Han, Jaemin; Park, Hyunmin; Kim, Sunkook 2002-05-01 The mechanism of coherent population transfer in a three-level system of lamda type interacting with strong and ultra-short laser pulses is investigated beyond the rotating wave approximation (RWA). The characteristics of population transfer arising from the consideration without RWA are numerically shown and interpreted in the point of view of dressed states both for the typical Stimulated Raman Adiabatic Passage(STIRAP) and for Optimal Detuning Method(ODM) which uses large wavelength-detuned lasers without time delay. 18. Three Definitions of Best Linear Approximation DTIC Science & Technology 1976-04-01 Three definitions of best (in the least squares sense) linear approximation to given data points are presented. The relationships between these three area discussed along with their relationship to basic statistics such as mean values, the covariance matrix, and the (linear) correlation coefficient . For each of the three definitions, and best line is solved in closed form in terms of the data centroid and the covariance matrix. 19. Approximate active fault detection and control Škach, Jan; Punčochář, Ivo; Šimandl, Miroslav 2014-12-01 This paper deals with approximate active fault detection and control for nonlinear discrete-time stochastic systems over an infinite time horizon. Multiple model framework is used to represent fault-free and finitely many faulty models. An imperfect state information problem is reformulated using a hyper-state and dynamic programming is applied to solve the problem numerically. The proposed active fault detector and controller is illustrated in a numerical example of an air handling unit. 20. Microscopic justification of the equal filling approximation SciTech Connect Perez-Martin, Sara; Robledo, L. M. 2008-07-15 The equal filling approximation, a procedure widely used in mean-field calculations to treat the dynamics of odd nuclei in a time-reversal invariant way, is justified as the consequence of a variational principle over an average energy functional. The ideas of statistical quantum mechanics are employed in the justification. As an illustration of the method, the ground and lowest-lying states of some octupole deformed radium isotopes are computed. 1. Variational Bayesian Approximation methods for inverse problems 2012-09-01 Variational Bayesian Approximation (VBA) methods are recent tools for effective Bayesian computations. In this paper, these tools are used for inverse problems where the prior models include hidden variables and where where the estimation of the hyper parameters has also to be addressed. In particular two specific prior models (Student-t and mixture of Gaussian models) are considered and details of the algorithms are given. 2. Parameter Biases Introduced by Approximate Gravitational Waveforms Farr, Benjamin; Coughlin, Scott; Le, John; Skeehan, Connor; Kalogera, Vicky 2013-04-01 The production of the most accurate gravitational waveforms from compact binary mergers require Einstein's equations to be solved numerically, a process far too expensive to produce the ˜10^7 waveforms necessary to estimate the parameters of a measured gravitational wave signal. Instead, parameter estimation depends on approximate or phenomenological waveforms to characterize measured signals. As part of the Ninja collaboration, we study the biases introduced by these methods when estimating the parameters of numerically produced waveforms. 3. Analytical inversions in remote sensing of particle size distributions. I - Multispectral extinctions in the anomalous diffraction approximation. II Angular and spectral scattering in diffraction approximations NASA Technical Reports Server (NTRS) Fymat, A. L. 1978-01-01 Consideration is given to analytical inversions in the remote sensing of particle size distributions, noting multispectral extinctions in anomalous diffraction approximation and angular and spectral scattering in diffraction approximation. A closed-form analytical inverse solution is derived in order to reconstruct the size distribution of atmospheric aerosols. The anomalous diffraction approximation to Mie's solution is used to describe the particles. Experimental data yield the geometrical area of aerosol polydispersion. Size distribution is thus found from a set of multispectral extinction measurements. In terms of the angular and spectral scattering of light in a narrow forward cone, it is shown that an analytical inverse solution may also be found for the Fraunhofer approximation to the Kirchhoff diffraction, and for an improved expression of this approximation due to Penndorf (1962) and Shifrin-Punina (1968). 4. Green-Ampt approximations: A comprehensive analysis Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K. 2016-04-01 Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems. 5. A coastal ocean model with subgrid approximation Walters, Roy A. 2016-06-01 A wide variety of coastal ocean models exist, each having attributes that reflect specific application areas. The model presented here is based on finite element methods with unstructured grids containing triangular and quadrilateral elements. The model optimizes robustness, accuracy, and efficiency by using semi-implicit methods in time in order to remove the most restrictive stability constraints, by using a semi-Lagrangian advection approximation to remove Courant number constraints, and by solving a wave equation at the discrete level for enhanced efficiency. An added feature is the approximation of the effects of subgrid objects. Here, the Reynolds-averaged Navier-Stokes equations and the incompressibility constraint are volume averaged over one or more computational cells. This procedure gives rise to new terms which must be approximated as a closure problem. A study of tidal power generation is presented as an example of this method. A problem that arises is specifying appropriate thrust and power coefficients for the volume averaged velocity when they are usually referenced to free stream velocity. A new contribution here is the evaluation of three approaches to this problem: an iteration procedure and two mapping formulations. All three sets of results for thrust (form drag) and power are in reasonable agreement. 6. Approximation abilities of neuro-fuzzy networks Mrówczyńska, Maria 2010-01-01 The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artificial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules "if-then", generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of "classic" neural networks. In its final part the article presents selected areas of application of neuro-fuzzy systems in the field of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration. 7. An Origami Approximation to the Cosmic Web Neyrinck, Mark C. 2016-10-01 The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in polygonal' or `polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time. 8. Approximate Graph Edit Distance in Quadratic Time. PubMed Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst 2015-09-14 Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification. 9. Ranking Support Vector Machine with Kernel Approximation PubMed Central Dou, Yong 2017-01-01 Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. PMID:28293256 10. Ranking Support Vector Machine with Kernel Approximation. PubMed Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi 2017-01-01 Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. 11. Using Approximations to Accelerate Engineering Design Optimization NASA Technical Reports Server (NTRS) Torczon, Virginia; Trosset, Michael W. 1998-01-01 Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor. 12. Jacobian transformed and detailed balance approximations for photon induced scattering Wienke, B. R.; Budge, K. G.; Chang, J. H.; Dahl, J. A.; Hungerford, A. L. 2012-01-01 Photon emission and scattering are enhanced by the number of photons in the final state, and the photon transport equation reflects this in scattering-emission kernels and source terms. This is often a complication in both theoretical and numerical analyzes, requiring approximations and assumptions about background and material temperatures, incident and exiting photon energies, local thermodynamic equilibrium, plus other related aspects of photon scattering and emission. We review earlier schemes parameterizing photon scattering-emission processes, and suggest two alternative schemes. One links the product of photon and electron distributions in the final state to the product in the initial state by Jacobian transformation of kinematical variables (energy and angle), and the other links integrands of scattering kernels in a detailed balance requirement for overall (integrated) induced effects. Compton and inverse Compton differential scattering cross sections are detailed in appropriate limits, numerical integrations are performed over the induced scattering kernel, and for tabulation induced scattering terms are incorporated into effective cross sections for comparisons and numerical estimates. Relativistic electron distributions are assumed for calculations. Both Wien and Planckian distributions are contrasted for impact on induced scattering as LTE limit points. We find that both transformed and balanced approximations suggest larger induced scattering effects at high photon energies and low electron temperatures, and smaller effects in the opposite limits, compared to previous analyzes, with 10-20% increases in effective cross sections. We also note that both approximations can be simply implemented within existing transport modules or opacity processors as an additional term in the effective scattering cross section. Applications and comparisons include effective cross sections, kernel approximations, and impacts on radiative transport solutions in 1D 13. Analyzing the errors of DFT approximations for compressed water systems. PubMed Alfè, D; Bartók, A P; Csányi, G; Gillan, M J 2014-07-07 We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm(3) where the experimental pressure is 15 kilobars; second, thermal samples of compressed water clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mE(h) ≃ 15 meV/monomer for the liquid and the 14. Find a Surgeon MedlinePlus ... find out more. Head, Neck and Oral Pathology Head, Neck and Oral Pathology Close to 49,750 Americans ... find out more. Head, Neck and Oral Pathology Head, Neck and Oral Pathology Close to 49,750 Americans ... 15. Find a Massage Therapist MedlinePlus ... Newsletter Student Experience Newsletter AMTA News Find a Massage Therapist Find a qualified massage therapist near you ... massage therapy school Proprietary Information and Legal Notice Massage is Good Medicine 25 Reasons to Get a ... 16. Approximations for column effect in airplane wing spars NASA Technical Reports Server (NTRS) Warner, Edward P; Short, Mac 1927-01-01 The significance attaching to "column effect" in airplane wing spars has been increasingly realized with the passage of time, but exact computations of the corrections to bending moment curves resulting from the existence of end loads are frequently omitted because of the additional labor involved in an analysis by rigorously correct methods. The present report represents an attempt to provide for approximate column effect corrections that can be graphically or otherwise expressed so as to be applied with a minimum of labor. Curves are plotted giving approximate values of the correction factors for single and two bay trusses of varying proportions and with various relationships between axial and lateral loads. It is further shown from an analysis of those curves that rough but useful approximations can be obtained from Perry's formula for corrected bending moment, with the assumed distance between points of inflection arbitrarily modified in accordance with rules given in the report. The discussion of general rules of variation of bending stress with axial load is accompanied by a study of the best distribution of the points of support along a spar for various conditions of loading. 17. A Surface Approximation Method for Image and Video Correspondences. PubMed Huang, Jingwei; Wang, Bin; Wang, Wenping; Sen, Pradeep 2015-12-01 Although finding correspondences between similar images is an important problem in image processing, the existing algorithms cannot find accurate and dense correspondences in images with significant changes in lighting/transformation or with the non-rigid objects. This paper proposes a novel method for finding accurate and dense correspondences between images even in these difficult situations. Starting with the non-rigid dense correspondence algorithm [1] to generate an initial correspondence map, we propose a new geometric filter that uses cubic B-Spline surfaces to approximate the correspondence mapping functions for shared objects in both images, thereby eliminating outliers and noise. We then propose an iterative algorithm which enlarges the region containing valid correspondences. Compared with the existing methods, our method is more robust to significant changes in lighting, color, or viewpoint. Furthermore, we demonstrate how to extend our surface approximation method to video editing by first generating a reliable correspondence map between a given source frame and each frame of a video. The user can then edit the source frame, and the changes are automatically propagated through the entire video using the correspondence map. To evaluate our approach, we examine applications of unsupervised image recognition and video texture editing, and show that our algorithm produces better results than those from state-of-the-art approaches. 18. Significant Inter-Test Reliability across Approximate Number System Assessments PubMed Central DeWind, Nicholas K.; Brannon, Elizabeth M. 2016-01-01 The approximate number system (ANS) is the hypothesized cognitive mechanism that allows adults, infants, and animals to enumerate large sets of items approximately. Researchers usually assess the ANS by having subjects compare two sets and indicate which is larger. Accuracy or Weber fraction is taken as an index of the acuity of the system. However, as Clayton et al. (2015) have highlighted, the stimulus parameters used when assessing the ANS vary widely. In particular, the numerical ratio between the pairs, and the way in which non-numerical features are varied often differ radically between studies. Recently, Clayton et al. (2015) found that accuracy measures derived from two commonly used stimulus sets are not significantly correlated. They argue that a lack of inter-test reliability threatens the validity of the ANS construct. Here we apply a recently developed modeling technique to the same data set. The model, by explicitly accounting for the effect of numerical ratio and non-numerical features, produces dependent measures that are less perturbed by stimulus protocol. Contrary to their conclusion we find a significant correlation in Weber fraction across the two stimulus sets. Nevertheless, in agreement with Clayton et al. (2015) we find that different protocols do indeed induce differences in numerical acuity and the degree of influence of non-numerical stimulus features. These findings highlight the need for a systematic investigation of how protocol idiosyncrasies affect ANS assessments. PMID:27014126 19. Direct application of Padé approximant for solving nonlinear differential equations. PubMed Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario 2014-01-01 This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30. 20. Local Approximations to the Gravitational Collapse of Cold Matter Hui, Lam; Bertschinger, Edmund 1996-11-01 We investigate three different local approximations for nonlinear gravitational instability in the framework of cosmological Lagrangian fluid dynamics of cold dust By local we mean that the evolution is described by a set of ordinary differential equations in time for each mass element, with no coupling to other mass elements aside from those implied by the initial conditions. We first show that the Zel'dovich approximation (ZA) can be cast in this form. Next, we consider extensions involving the evolution of the Newtonian tidal tensor. We show that two approximations can be found that are exact for plane-parallel and spherical perturbations. The first one ("nonmagnetic" approximation, or NMA) neglects the Newtonian counterpart of the magnetic part of the Weyl tensor in the fluid frame and was investigated previously by Bertschinger & Jain. A new approximation ("local tidal," or LTA) involves neglecting still more terms in the tidal evolution equation. It is motivated by the analytic demonstration that it is exact for any perturbations whose gravitational and velocity equipotentials have the same constant shape with time. Thus, the LTA is exact for spherical, cylindrical, and plane-parallel perturbations. It corresponds physically to neglecting the curl of the magnetic part of the Weyl tensor in the comoving threading as well as an advection term in the tidal evolution equation. All three approximations can be applied up to the point of orbit crossing. We tested them in the case of the collapse of a homogeneous triaxial ellipsoid, for which an exact solution exists for an ellipsoid embedded in empty space and an excellent approximation is known in the cosmological context. We find that the LTA is significantly more accurate in general than the ZA and the NMA. Like the ZA, but unlike the NMA, the LTA generically leads to pancake collapse. For a randomly chosen mass element in an Sitter universe, assuming a Gaussian random field of initial density fluctuations, the 1. Approximating nonlinear forces with phase-space decoupling Folsom, B.; Laface, E. 2017-07-01 Beam tracking software for accelerators typically falls into two categories: fast envelope simulations limited to linear beam optics, and slower multiparticle simulations that can model nonlinear effects. To find a middle ground between these approaches, we introduce virtual coordinates in position and momentum which have a cross-dependency (i.e. p* = f (x 0) where x 0 is an initial position and p* is a virtual projection of momentum onto the position axis). This technique approximates multiparticle simulations with a significant reduction in calculation cost. 2. Validity of the local approximation in iron pnictides and chalcogenides Sémon, Patrick; Haule, Kristjan; Kotliar, Gabriel 2017-05-01 We introduce a methodology to treat different degrees of freedom at different levels of approximation. We use cluster DMFT (dynamical mean field theory) for the t2 g electrons and single site DMFT for the eg electrons to study the normal state of the iron pnictides and chalcogenides. In the regime of moderate mass renormalizations, the self-energy is very local, justifying the success of single site DMFT for these materials and for other Hunds metals. We solve the corresponding impurity model with CTQMC (continuous time quantum Monte Carlo) and find that the minus sign problem is not severe in regimes of moderate mass renormalization. 3. The Zeldovich & Adhesion approximations and applications to the local universe Hidding, Johan; van de Weygaert, Rien; Shandarin, Sergei 2016-10-01 The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A 3 lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe. 4. Isotropic polarizability of ozone from double-hybrid approximations Alipour, Mojtaba 2016-01-01 Literature survey on the electric response properties of ozone reveals that the accurate prediction of its dipole polarizability and resolving the discrepancies in this context is a challenging case to current structure theories. In this Letter, we report the results of approximations from the highest rung of Jacob's ladder, double-hybrid (DH) functionals, for dipole polarizability of ozone. Benchmarking the two families of DHs, parameterized and parameter-free models, we find that the functionals B2Ͽ-PLYP and PBE0-DH as empirical and nonempirical DHs, respectively, provide the results in line with those obtained from the high correlated ab initio approaches. 5. Convergence of finite element approximations of large eddy motion. SciTech Connect Iliescu, T.; John, V.; Layton, W. J.; Mathematics and Computer Science; Otto-von-Guericke Univ.; Univ. of Pittsburgh 2002-11-01 This report considers 'numerical errors' in LES. Specifically, for one family of space filtered flow models, we show convergence of the finite element approximation of the model and give an estimate of the error. Keywords: Navier Stokes equations, large eddy simulation, finite element method I. INTRODUCTION Consider the (turbulent) flow of an incompressible fluid. One promising and common approach to the simulation of the motion of the large fluid structures is Large Eddy Simulation (LES). Various models are used in LES; a common one is to find (w, q), where w : {Omega} 6. Polynomial approximations of a class of stochastic multiscale elasticity problems Hoang, Viet Ha; Nguyen, Thanh Chung; Xia, Bingxing 2016-06-01 We consider a class of elasticity equations in {mathbb{R}^d} whose elastic moduli depend on n separated microscopic scales. The moduli are random and expressed as a linear expansion of a countable sequence of random variables which are independently and identically uniformly distributed in a compact interval. The multiscale Hellinger-Reissner mixed problem that allows for computing the stress directly and the multiscale mixed problem with a penalty term for nearly incompressible isotropic materials are considered. The stochastic problems are studied via deterministic problems that depend on a countable number of real parameters which represent the probabilistic law of the stochastic equations. We study the multiscale homogenized problems that contain all the macroscopic and microscopic information. The solutions of these multiscale homogenized problems are written as generalized polynomial chaos (gpc) expansions. We approximate these solutions by semidiscrete Galerkin approximating problems that project into the spaces of functions with only a finite number of N gpc modes. Assuming summability properties for the coefficients of the elastic moduli's expansion, we deduce bounds and summability properties for the solutions' gpc expansion coefficients. These bounds imply explicit rates of convergence in terms of N when the gpc modes used for the Galerkin approximation are chosen to correspond to the best N terms in the gpc expansion. For the mixed problem with a penalty term for nearly incompressible materials, we show that the rate of convergence for the best N term approximation is independent of the Lamé constants' ratio when it goes to {infty}. Correctors for the homogenization problem are deduced. From these we establish correctors for the solutions of the parametric multiscale problems in terms of the semidiscrete Galerkin approximations. For two-scale problems, an explicit homogenization error which is uniform with respect to the parameters is deduced. Together 7. Photoelectron spectroscopy and the dipole approximation SciTech Connect Hemmers, O.; Hansen, D.L.; Wang, H. 1997-04-01 Photoelectron spectroscopy is a powerful technique because it directly probes, via the measurement of photoelectron kinetic energies, orbital and band structure in valence and core levels in a wide variety of samples. The technique becomes even more powerful when it is performed in an angle-resolved mode, where photoelectrons are distinguished not only by their kinetic energy, but by their direction of emission as well. Determining the probability of electron ejection as a function of angle probes the different quantum-mechanical channels available to a photoemission process, because it is sensitive to phase differences among the channels. As a result, angle-resolved photoemission has been used successfully for many years to provide stringent tests of the understanding of basic physical processes underlying gas-phase and solid-state interactions with radiation. One mainstay in the application of angle-resolved photoelectron spectroscopy is the well-known electric-dipole approximation for photon interactions. In this simplification, all higher-order terms, such as those due to electric-quadrupole and magnetic-dipole interactions, are neglected. As the photon energy increases, however, effects beyond the dipole approximation become important. To best determine the range of validity of the dipole approximation, photoemission measurements on a simple atomic system, neon, where extra-atomic effects cannot play a role, were performed at BL 8.0. The measurements show that deviations from {open_quotes}dipole{close_quotes} expectations in angle-resolved valence photoemission are observable for photon energies down to at least 0.25 keV, and are quite significant at energies around 1 keV. From these results, it is clear that non-dipole angular-distribution effects may need to be considered in any application of angle-resolved photoelectron spectroscopy that uses x-ray photons of energies as low as a few hundred eV. 8. Product-State Approximations to Quantum States Brandão, Fernando G. S. L.; Harrow, Aram W. 2016-02-01 We show that for any many-body quantum state there exists an unentangled quantum state such that most of the two-body reduced density matrices are close to those of the original state. This is a statement about the monogamy of entanglement, which cannot be shared without limit in the same way as classical correlation. Our main application is to Hamiltonians that are sums of two-body terms. For such Hamiltonians we show that there exist product states with energy that is close to the ground-state energy whenever the interaction graph of the Hamiltonian has high degree. This proves the validity of mean-field theory and gives an explicitly bounded approximation error. If we allow states that are entangled within small clusters of systems but product across clusters then good approximations exist when the Hamiltonian satisfies one or more of the following properties: (1) high degree, (2) small expansion, or (3) a ground state where the blocks in the partition have sublinear entanglement. Previously this was known only in the case of small expansion or in the regime where the entanglement was close to zero. Our approximations allow an extensive error in energy, which is the scale considered by the quantum PCP (probabilistically checkable proof) and NLTS (no low-energy trivial-state) conjectures. Thus our results put restrictions on the possible Hamiltonians that could be used for a possible proof of the qPCP or NLTS conjectures. By contrast the classical PCP constructions are often based on constraint graphs with high degree. Likewise we show that the parallel repetition that is possible with classical constraint satisfaction problems cannot also be possible for quantum Hamiltonians, unless qPCP is false. The main technical tool behind our results is a collection of new classical and quantum de Finetti theorems which do not make any symmetry assumptions on the underlying states. 9. An approximate projection method for incompressible flow Stevens, David E.; Chan, Stevens T.; Gresho, Phil 2002-12-01 This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139-1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40-65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency.A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake. 10. Approximate protein structural alignment in polynomial time PubMed Central Kolodny, Rachel; Linial, Nathan 2004-01-01 Alignment of protein structures is a fundamental task in computational molecular biology. Good structural alignments can help detect distant evolutionary relationships that are hard or impossible to discern from protein sequences alone. Here, we study the structural alignment problem as a family of optimization problems and develop an approximate polynomial-time algorithm to solve them. For a commonly used scoring function, the algorithm runs in O(n10/ε6) time, for globular protein of length n, and it detects alignments that score within an additive error of ε from all optima. Thus, we prove that this task is computationally feasible, although the method that we introduce is too slow to be a useful everyday tool. We argue that such approximate solutions are, in fact, of greater interest than exact ones because of the noisy nature of experimentally determined protein coordinates. The measurement of similarity between a pair of protein structures used by our algorithm involves the Euclidean distance between the structures (appropriately rigidly transformed). We show that an alternative approach, which relies on internal distance matrices, must incorporate sophisticated geometric ingredients if it is to guarantee optimality and run in polynomial time. We use these observations to visualize the scoring function for several real instances of the problem. Our investigations yield insights on the computational complexity of protein alignment under various scoring functions. These insights can be used in the design of scoring functions for which the optimum can be approximated efficiently and perhaps in the development of efficient algorithms for the multiple structural alignment problem. PMID:15304646 11. Relativistic Random Phase Approximation At Finite Temperature SciTech Connect Niu, Y. F.; Paar, N.; Vretenar, D.; Meng, J. 2009-08-26 The fully self-consistent finite temperature relativistic random phase approximation (FTRRPA) has been established in the single-nucleon basis of the temperature dependent Dirac-Hartree model (FTDH) based on effective Lagrangian with density dependent meson-nucleon couplings. Illustrative calculations in the FTRRPA framework show the evolution of multipole responses of {sup 132}Sn with temperature. With increased temperature, in both monopole and dipole strength distributions additional transitions appear in the low energy region due to the new opened particle-particle and hole-hole transition channels. 12. Analytic Approximation to Randomly Oriented Spheroid Extinction DTIC Science & Technology 1993-12-01 104 times faster than by the T - matrix code . Since the T-matrix scales as at least the cube of the optical size whereas the analytic approximation is...coefficient estimate, and with the Rayleigh formula. Since it is difficult estimate the accuracy near the limit of stability of the T - matrix code some...additional error due to the T - matrix code could be present. UNCLASSIFIED 30 Max Ret Error, Analytic vs T-Mat, r= 1/5 0.0 20 25 10 ~ 0.5 100 . 7.5 S-1.0 13. Relativistic mean field approximation to baryons SciTech Connect Dmitri Diakonov 2005-02-01 We stress the importance of the spontaneous chiral symmetry breaking for understanding the low-energy structure of baryons. The Mean Field Approximation to baryons is formulated, which solves several outstanding paradoxes of the naive quark models, and which allows to compute parton distributions at low virtuality in a consistent way. We explain why this approach to baryons leads to the prediction of relatively light exotic pentaquark baryons, in contrast to the constituent models which do not take seriously the importance of chiral symmetry breaking. We briefly discuss why, to our mind, it is easier to produce exotic pentaquarks at low than at high energies. 14. Approximation of Dynamical System's Separatrix Curves Cavoretto, Roberto; Chaudhuri, Sanjay; De Rossi, Alessandra; Menduni, Eleonora; Moretti, Francesca; Rodi, Maria Caterina; Venturino, Ezio 2011-09-01 In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This problem is rather common especially in population dynamics models, like prey-predator or competition systems. In this paper we construct programs for the detection of points lying on the separatrix curve, i.e. the curve which partitions the domain. Finally, an efficient algorithm, which is based on the Partition of Unity method with local approximants given by Wendland's functions, is used for reconstructing the separatrix curve. 15. Approximation concepts for numerical airfoil optimization NASA Technical Reports Server (NTRS) Vanderplaats, G. N. 1979-01-01 An efficient algorithm for airfoil optimization is presented. The algorithm utilizes approximation concepts to reduce the number of aerodynamic analyses required to reach the optimum design. Examples are presented and compared with previous results. Optimization efficiency improvements of more than a factor of 2 are demonstrated. Improvements in efficiency are demonstrated when analysis data obtained in previous designs are utilized. The method is a general optimization procedure and is not limited to this application. The method is intended for application to a wide range of engineering design problems. 16. Semiclassical approximations to quantum time correlation functions Egorov, S. A.; Skinner, J. L. 1998-09-01 Over the last 40 years several ad hoc semiclassical approaches have been developed in order to obtain approximate quantum time correlation functions, using as input only the corresponding classical time correlation functions. The accuracy of these approaches has been tested for several exactly solvable gas-phase models. In this paper we test the accuracy of these approaches by comparing to an exactly solvable many-body condensed-phase model. We show that in the frequency domain the Egelstaff approach is the most accurate, especially at high frequencies, while in the time domain one of the other approaches is more accurate. de Berg, Mark; Gerrits, Dirk H. P. Inspired by air traffic control and other applications where moving objects have to be labeled, we consider the following (static) point labeling problem: given a set P of n points in the plane and labels that are unit squares, place a label with each point in P in such a way that the number of free labels (labels not intersecting any other label) is maximized. We develop efficient constant-factor approximation algorithms for this problem, as well as PTASs, for various label-placement models. 18. Shear viscosity in the postquasistatic approximation SciTech Connect Peralta, C.; Rosales, L.; Rodriguez-Mueller, B.; Barreto, W. 2010-05-15 We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic nonadiabatic radiating and dissipative distributions in general relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in noncomoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases, the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity. 19. Approximations of nonlinear systems having outputs NASA Technical Reports Server (NTRS) Hunt, L. R.; Su, R. 1985-01-01 For a nonlinear system with output derivative x = f(x) and y = h(x), two types of linearizations about a point x(0) in state space are considered. One is the usual Taylor series approximation, and the other is defined by linearizing the appropriate Lie derivatives of the output with respect to f about x(0). The latter is called the obvservation model and appears to be quite natural for observation. It is noted that there is a coordinate system in which these two kinds of linearizations agree. In this coordinate system, a technique to construct an observer is introduced. 20. Approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8587723970413208, "perplexity": 1828.9927290571907}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806455.2/warc/CC-MAIN-20171122031440-20171122051440-00503.warc.gz"}
https://www.physicsforums.com/threads/hausdorff-dimension-of-this-set.690950/	# Hausdorff Dimension of this set 1. May 10, 2013 ### Bachelier Define: $$\mathbb{Y} = C \times C^{c} \subset \mathbb{R}^{2}$$ where $C$ is the Cantor set and $C^{c}$ is its complement in $[0,1]$ First I think $\mathbb{Y}$ is neither open nor closed. Second, the Hausdorff dimension of $C$ is $\Large \frac{log2}{log3}$. How do we compute the $HD$ of the Cartesian product of sets? For instance $HD(ℝ^{k})= k$ hence can we compute $HD(\mathbb{Y})?$ 2. May 10, 2013 ### micromass 3. May 13, 2013 ### Bachelier So that gives the $Hausdorff \ dim$ of $C^c$ to be 1. makes sense.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9664925336837769, "perplexity": 430.3406309067146}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864798.12/warc/CC-MAIN-20180522151159-20180522171159-00111.warc.gz"}
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http://www.sparknotes.com/physics/gravitation/kepler/terms.html	# Kepler and Gravitation ## Contents #### Terms Period - The period of an orbit, usually denoted $T$, is the total time taken for an object to complete one full revolution on its orbit. Kepler's First Law - The planets orbit the sun in ellipses, with the sun at one focus. Kepler's Second Law - The radius of a planet sweeps out a constant area per unit time. Kepler's Third Law - $$T^2 = \frac{4\pi^2a^3}{GM}$$ where $T$ is the period, $G$ is the gravitational constant, and $M$ is the mass of the sun. Eccentricity - The eccentricity is a measure of the elongation of an ellipse. It is defined as: $$\epsilon = \sqrt{1 - \frac{b^2}{a^2}}$$ where $a$ and $b$ are the semimajor and semiminor axis lengths respectively. Aphelion - The point of a planet's furthest distance from the sun on its orbit. Perihelion - Is the point of a planet's closest approach to the sun. Apogee - For an earth orbit, the furthest distance from the earth. Perigee - For an earth orbit, the closest distance to the earth.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9457106590270996, "perplexity": 558.107250959389}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170875.20/warc/CC-MAIN-20170219104610-00009-ip-10-171-10-108.ec2.internal.warc.gz"}
https://www.semanticscholar.org/paper/Modularity-of-generating-series-of-divisors-on-Bruinier-Howard/2c81edc179ce8f2170b34627b6d045c9deb60cd0	# Modularity of generating series of divisors on unitary Shimura varieties @article{Bruinier2020ModularityOG, title={Modularity of generating series of divisors on unitary Shimura varieties}, author={Jan H. Bruinier and Benjamin J. Howard and Stephen S. Kudla and Michael Rapoport and Tonghai Yang}, journal={Ast{\'e}risque}, year={2020} } We form generating series of special divisors, valued in the Chow group and in the arithmetic Chow group, on the compactified integral model of a Shimura variety associated to a unitary group of signature (n-1,1), and prove their modularity. The main ingredient of the proof is the calculation of the vertical components appearing in the divisor of a Borcherds product on the integral model. 10 Citations Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications • Mathematics Astérisque • 2020 We form generating series of special divisors, valued in the Chow group and in the arithmetic Chow group, on the compactified integral model of a Shimura variety associated to a unitary group of Special cycles on unitary Shimura curves at ramified primes In this paper, we study special cycles on the Kramer model of $\mathrm{GU}(1,1)(F)$ Rapoport-Zink spaces where $F$ is a ramified extension of $\mathbb{Q}_p$ with the assumption that the underlying Deformations of Theta Integrals and A Conjecture of Gross-Zagier • Mathematics • 2022 In this paper, we complete the proof of Gross-Zagier’s conjecture concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an Kudla program for unitary Shimura varieties • Mathematics SCIENTIA SINICA Mathematica • 2021 In this paper, we first review and summarize some recent progress in Kudla program on unitary Shimura varieties. We show how the local arithmetic Siegel-Weil formula implies the global arithmetic On the Arithmetic Fundamental Lemma conjecture over a general $p$-adic field • Mathematics • 2021 We prove the arithmetic fundamental lemma conjecture over a general p-adic field with odd residue cardinality q ≥ dimV . Our strategy is similar to the one used by the second author during his proof Picard rank jumps for K3 surfaces with bad reduction Let X be a K3 surface over a number field. We prove that X has infinitely many specializations where its Picard rank jumps, hence extending our previous work with Shankar–Shankar–Tang to the case Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields • Mathematics • 2019 Given a K3 surface $X$ over a number field $K$, we prove that the set of primes of $K$ where the geometric Picard rank jumps is infinite, assuming that $X$ has everywhere potentially good reduction. Theta series and generalized special cycles on Hermitian locally symmetric manifolds We study generalized special cycles on Hermitian locally symmetric spaces $\Gamma \backslash D$ associated to the groups $G=\mathrm{U}(p,q)$, $\mathrm{Sp}(2n,\mathbb{R})$ and $\mathrm{O}^*(2n)$. Picard ranks of K3 surfaces over function fields and the Hecke orbit conjecture • Mathematics Inventiones mathematicae • 2022 Let $\mathscr{X} \rightarrow C$ be a non-isotrivial and generically ordinary family of K3 surfaces over a proper curve $C$ in characteristic $p \geq 5$. We prove that the geometric Picard rank jumps Special cycles on toroidal compactifications of orthogonal Shimura varieties • Mathematics Mathematische Annalen • 2021 We determine the behavior of automorphic Green functions along the boundary components of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define boundary	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9110465049743652, "perplexity": 688.7493187952739}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571147.84/warc/CC-MAIN-20220810040253-20220810070253-00016.warc.gz"}
https://cs.stackexchange.com/questions/146347/shortest-possible-path-between-closest-pair-of-specific-nodes-in-a-maze	# Shortest possible path between closest pair of specific nodes in a maze Need to find the shortest distance between the closest pair of 'r' and 'b' nodes. You can traverse along '.' elements, but not 'o' elements. How can we do this in $$O(MN)$$ time? (M rows, N cols). $$O(RMN)$$ time would also be sufficient (R is numbers of 'r' nodes). Below is an adopted version the Lee algorithm from here that uses BFS to find the shortest distance between a given a single source node and a single destination node in $$O(MN)$$ time. Can I extend this framework for the problem at hand? Any ideas are much appreciated. import sys from collections import deque # Below lists detail all four possible movements from a cell row = [-1, 0, 0, 1] col = [0, -1, 1, 0] # Function to check if it is possible to go to position (row, col) # from the current position. The function returns false if row, col # is not a valid position or has a value 0 or already visited. def isValid(mat, visited, row, col): return (row >= 0) and (row < len(mat)) and (col >= 0) and (col < len(mat[0])) \ and mat[row][col] == '.' or mat[row][col] == 'r' or mat[row][col] == 'b' and not visited[row][col] # Find the shortest possible route in a matrix mat from source src to # destination dest def findShortestPathLength(mat): src = (1, 1) (M, N) = (len(mat), len(mat[0])) dest = (M-2, N-2) # get source cell (i, j) i, j = src # get destination cell (x, y) x, y = dest # base case: invalid input if not mat or len(mat) == 0 or mat[i][j] == 'o' or mat[x][y] == 'o': return -1 # construct a matrix to keep track of visited cells visited = [[False for x in range(N)] for y in range(M)] # create an empty queue q = deque() # mark the source cell as visited and enqueue the source node visited[i][j] = True # (i, j, dist) represents matrix cell coordinates, and their # minimum distance from the source q.append((i, j, 0)) # stores length of the longest path from source to destination min_dist = sys.maxsize # loop till queue is empty while q: # dequeue front node and process it (i, j, dist) = q.popleft() # (i, j) represents a current cell, and dist stores its # minimum distance from the source # if the destination is found, update min_dist and stop if i == x and j == y: min_dist = dist break # check for all four possible movements from the current cell # and enqueue each valid movement for k in range(4): # check if it is possible to go to position # (i + row[k], j + col[k]) from current position if isValid(mat, visited, i + row[k], j + col[k]): # mark next cell as visited and enqueue it visited[i + row[k]][j + col[k]] = True q.append((i + row[k], j + col[k], dist + 1)) if min_dist != sys.maxsize: return min_dist else: return sys.maxsize mat = [ ['o','o','o','o','o','o'], ['o','r','.','.','b','o'], ['o','r','.','.','b','o'], ['o','r','.','.','b','o'], ['o','o','o','o','o','o'], ] print(findShortestPathLength(mat)) mat = [ ['o','o','o','o','o'], ['o','r','o','o','o'], ['o','o','o','o','o'], ['o','o','o','b','o'], ['o','o','o','o','o'], ] print(findShortestPathLength(mat)) mat = [ ['o','o','o','o','o','o','o','o'], ['o','.','.','r','.','.','.','o'], ['o','o','o','o','o','o','.','o'], ['o','.','.','.','.','.','.','o'], ['o','.','o','o','o','o','o','o'], ['o','.','.','b','.','.','.','o'], ['o','o','o','o','o','o','o','o'], ] print(findShortestPathLength(mat)) $$$$ • Hmm, I have been using this "Lee algorithm" for tens of times, if not hundreds of times. This is the first time I have heard of that name. Dec 3, 2021 at 8:38 • @JohnL. Same here. This "Lee algorithm" is a flood fill with a very thin disguise. Dec 4, 2021 at 11:09 You can append all 'r' nodes to the initial empty queue. Instead of checking whether the front node is the single destination node, check whether the front node is in the set of all destination nodes. With the two extensions above, the Lee algorithm will be able to find the shortest distance between the closest pair of 'r' and 'b' nodes in $$O(MN)$$ time. Here is an implementation in Python. Instead of checking the front node, i.e., when the node is popped out of the queue, this implementation check each node when it was pushed into the queue. This minor change improves the performance slightly. from collections import deque def find_shortest_path_length(mat): """Return the length of the shortest route from an 'r' node to a 'b' node mat is a 2-dimensional list of nodes. There are four kinds of node. An 'r' node is a source node. A 'b' node is a destination node. A '.' node can be passed while a 'o' node is an obstructed node that cannot be passed. """ m, n = len(mat), len(mat[0]) visited = [[False] * n for row in range(m)] q = deque() destinations = set() def should_visit(row, col): """Return true if (row,col) is a valid position not processed yet""" return 0 <= row < m and 0 <= col < n and \ mat[row][col] != 'o' and not visited[row][col] for r in range(m): for c in range(n): if mat[r][c] == 'r': q.append((r, c)) visited[r][c] = True elif mat[r][c] == 'b': dist = 1 # the level in breadth-first-search. while q: for _ in range(len(q)): (r, c) = q.popleft() for (new_r, new_c) in ((r - 1, c), (r + 1, c), (r, c - 1), (r, c + 1)): if should_visit(new_r, new_c): if (new_r, new_c) in destinations: return dist q.append((new_r, new_c)) visited[new_r][new_c] = True dist += 1 # The destinations can not be reached. return -1 • Can you elaborate what you mean by front node? Also, in order to append all 'r' nodes to the initial empty queue, I would need to know their position in the maze. How would I obtain their positions? Thanks Dec 3, 2021 at 8:57 • "front node" as in this line of comment of your code, "dequeue front node and process it". Dec 3, 2021 at 9:16 • Loop through all nodes, adding each node to the initial queue whenever the node is an 'r' node. Also add each node to the set of all destination nodes whenever the node is a 'b'` node. Dec 3, 2021 at 9:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.16411127150058746, "perplexity": 4553.557999600545}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104141372.60/warc/CC-MAIN-20220702131941-20220702161941-00540.warc.gz"}
https://math.stackexchange.com/questions/3013670/is-the-sum-of-all-rational-numbers-between-two-integers-infinity	# Is the sum of all rational numbers between two integers infinity If there are infinite numbers between two rational numbers then would that entail that the sum of all numbers, say between 1 and 2, be infinity? I believe that this cannot be true and has to do something with area under a curve? • No, you cannot conclude from the fact that there are infinitely many rationals that the sum must be infinite. This is the error behind Zeno's paradox of the Achilles (e.g., $\sum \frac{1}{2^n}$ is finite, even though you are adding infinitely many positive rational numbers). – Arturo Magidin Nov 26 '18 at 1:21 • However, the sum is potentially infinite anyway; certainly it is infinite for all rationals between $1$ and $2$, since this includes countably many rationals that are greater than or equal to $1$, so the sum is strictly larger than any positive integer. – Arturo Magidin Nov 26 '18 at 1:23 • I was just about to type that last comment, @ArturoMagidin. Summing infinitely many numbers greater than $1$ must, almost by definition, be infinite. – The Count Nov 26 '18 at 1:24 • And the rationals between $0$ and $1$ include all rationals of the form $\frac{1}{n}$, and since the harmonic series diverges... so, the answer is that the sum of all rationals between two integers is always infinite, but not for the reason you provide; and the sum of all rationals between any two rationals should also be infinite, verifiable by using a linear transformation to take, say, $[1,2]$ to $[q_1,q_2]$ in a way that maps rationals to rationals, and use it to put lower bounds on the sum. – Arturo Magidin Nov 26 '18 at 1:27 • You want to get into thorny matters? Ask whether the sum of all rational numbers between $-1$ and $1$ is infinite. – Brian Tung Nov 26 '18 at 1:48 Before you can answer this question you need a definition for what it means to "add up infinitely many numbers". For the moment, assume those numbers are listed in some order: $$a_1, a_2, \ldots .$$ Then mathematicians define the infinite sum to be the limit (if it exists) of the numbers $$a_1, \quad a_1 + a_2, \quad a_1 + a_2 + a_3, \ldots .$$ Then, for example, you could show that the "infinite sum" $$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$$ is $$2$$. So sometimes the sum of infinitely many numbers is finite. With that definition, you clearly can't sum all the rational numbers between $$1$$ and $$2$$ since all of them are greater than $$1$$, so those partial sums will grow without bound. You can't sum all the rational numbers between $$0$$ and $$0.0001$$ since infinitely many of them are greater than $$0.00001$$. So you are more or less correct - mathematicians prefer to say you can't sum them, not that the sum is infinity. When you learn calculus (that "something with area under a curve") you will see how to add up more and more and more pieces without growing to infinity because at each stage the pieces are smaller and smaller and smaller. • "You can't sum all the numbers between [...]" See that OP asks for all the rational numbers. It doesn't seems obvious to me that your proof holds... – rafa11111 Nov 26 '18 at 1:35 • @rafa11111 There are infinitely many rational numbers in the interval that are larger than the midpoint. I edited the answer. – Ethan Bolker Nov 26 '18 at 1:42 • Typo: $1+\frac12+\frac14+\frac18+\cdots = 2$, not $1$. – Brian Tung Nov 26 '18 at 1:47 • @BrianTung I fixed it thanks. You could have. – Ethan Bolker Nov 26 '18 at 1:48 • @EthanBolker: I know. I like to allow the answerer to fix it first in the way they think best. If you hadn't come back to fix it, I'd have done it eventually. – Brian Tung Nov 26 '18 at 1:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9187998175621033, "perplexity": 225.74124639211314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027318894.83/warc/CC-MAIN-20190823150804-20190823172804-00449.warc.gz"}
https://arxiv.org/abs/0802.0587	astro-ph (what is this?) # Title: Exoplanet HD 209458b : Evaporation strengthened Abstract: Following re-analysis of Hubble Space Telescope observations of primary transits of the extrasolar planet HD209458b at Lyman-alpha, Ben-Jaffel (2007, BJ007) claims that no sign of evaporation is observed. Here we show that, in fact, this new analysis is consistent with the one of Vidal-Madjar et al. (2003, VM003) and supports the detection of evaporation. The apparent disagreement is mainly due to the disparate wavelength ranges that are used to derive the transit absorption depth. VM003 derives a (15+/-4)% absorption depth during transit over the core of the stellar Lyman-alpha line (from -130 km/s to +100 km/s), and this result agrees with the (8.9+/-2.1)% absorption depth reported by BJ007 from a slightly expanded dataset but over a larger wavelength range (+/-200 km/s). These measurements agree also with the (5+/-2)% absorption reported by Vidal-Madjar et al. (2004) over the whole Lyman-alpha line from independent, lower-resolution data. We show that stellar Lyman-alpha variability is unlikely to significantly affect those detections. The HI atoms must necessarily have velocities above the escape velocities and/or be outside the Roche lobe, given the lobe shape and orientation. Absorption by HI in HD209458b's atmosphere has thus been detected with different datasets, and now with independent analyses. All these results strengthen the concept of evaporating hot-Jupiters, as well as the modelization of this phenomenon. Comments: To be published in ApJL Subjects: Astrophysics (astro-ph) DOI: 10.1086/587036 Cite as: arXiv:0802.0587 [astro-ph] (or arXiv:0802.0587v1 [astro-ph] for this version) ## Submission history From: Alain Lecavelier des Etangs [view email] [v1] Tue, 5 Feb 2008 11:15:11 GMT (144kb)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8046037554740906, "perplexity": 6839.705567820316}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824819.92/warc/CC-MAIN-20171021133807-20171021153807-00746.warc.gz"}
http://nag.com/numeric/FL/nagdoc_fl24/html/M01/m01cbf.html	M01 Chapter Contents M01 Chapter Introduction NAG Library Manual NAG Library Routine DocumentM01CBF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose M01CBF rearranges a vector of integer numbers into ascending or descending order. 2 Specification SUBROUTINE M01CBF ( IV, M1, M2, ORDER, IFAIL) INTEGER IV(M2), M1, M2, IFAIL CHARACTER(1) ORDER 3 Description M01CBF is based on Singleton's implementation of the ‘median-of-three’ Quicksort algorithm (see Singleton (1969)), but with two additional modifications. First, small subfiles are sorted by an insertion sort on a separate final pass (see Sedgewick (1978)) Second, if a subfile is partitioned into two very unbalanced subfiles, the larger of them is flagged for special treatment: before it is partitioned, its end points are swapped with two random points within it; this makes the worst case behaviour extremely unlikely. 4 References Sedgewick R (1978) Implementing Quicksort programs Comm. ACM 21 847–857 Singleton R C (1969) An efficient algorithm for sorting with minimal storage: Algorithm 347 Comm. ACM 12 185–187 5 Parameters 1: IV(M2) – INTEGER arrayInput/Output On entry: elements M1 to M2 of IV must contain integer values to be sorted. On exit: these values are rearranged into sorted order. 2: M1 – INTEGERInput On entry: the index of the first element of IV to be sorted. Constraint: ${\mathbf{M1}}>0$. 3: M2 – INTEGERInput On entry: the index of the last element of IV to be sorted. Constraint: ${\mathbf{M2}}\ge {\mathbf{M1}}$. 4: ORDER – CHARACTER(1)Input On entry: if ${\mathbf{ORDER}}=\text{'A'}$, the values will be sorted into ascending (i.e., nondecreasing) order. If ${\mathbf{ORDER}}=\text{'D'}$, into descending order. Constraint: ${\mathbf{ORDER}}=\text{'A'}$ or $\text{'D'}$. 5: IFAIL – INTEGERInput/Output On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details. For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit. On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6). 6 Error Indicators and Warnings If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF). Errors or warnings detected by the routine: ${\mathbf{IFAIL}}=1$ On entry, ${\mathbf{M2}}<1$, or ${\mathbf{M1}}<1$, or ${\mathbf{M1}}>{\mathbf{M2}}$. ${\mathbf{IFAIL}}=2$ On entry, ORDER is not 'A' or 'D'. 7 Accuracy Not applicable. The average time taken by the routine is approximately proportional to $n×\mathrm{log}n$, where $n={\mathbf{M2}}-{\mathbf{M1}}+1$. The worst case time is proportional to ${n}^{2}$ but this is extremely unlikely to occur. 9 Example This example reads a list of integers and sorts them into descending order. 9.1 Program Text Program Text (m01cbfe.f90) 9.2 Program Data Program Data (m01cbfe.d) 9.3 Program Results Program Results (m01cbfe.r)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 23, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9754037857055664, "perplexity": 3082.35660803298}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400379190.66/warc/CC-MAIN-20141119123259-00009-ip-10-235-23-156.ec2.internal.warc.gz"}
https://mitpress.mit.edu/books/introduction-computation-and-programming-using-python-1	Paperback \| $45.00 X \| £37.95 \| 472 pp. \| 7 x 9 in \| 258 figures \| August 2016 \| ISBN: 9780262529624 eBook \|$45.00 X \| August 2016 \| ISBN: 9780262337380 Mouseover for Online Attention Data ## Introduction to Computation and Programming Using Python, Second Edition With Application to Understanding Data ## Overview This book introduces students with little or no prior programming experience to the art of computational problem solving using Python and various Python libraries, including PyLab. It provides students with skills that will enable them to make productive use of computational techniques, including some of the tools and techniques of data science for using computation to model and interpret data. The book is based on an MIT course (which became the most popular course offered through MIT’s OpenCourseWare) and was developed for use not only in a conventional classroom but in in a massive open online course (MOOC). This new edition has been updated for Python 3, reorganized to make it easier to use for courses that cover only a subset of the material, and offers additional material including five new chapters. Students are introduced to Python and the basics of programming in the context of such computational concepts and techniques as exhaustive enumeration, bisection search, and efficient approximation algorithms. Although it covers such traditional topics as computational complexity and simple algorithms, the book focuses on a wide range of topics not found in most introductory texts, including information visualization, simulations to model randomness, computational techniques to understand data, and statistical techniques that inform (and misinform) as well as two related but relatively advanced topics: optimization problems and dynamic programming. This edition offers expanded material on statistics and machine learning and new chapters on Frequentist and Bayesian statistics.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1538221836090088, "perplexity": 1027.87483519702}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886120573.0/warc/CC-MAIN-20170823132736-20170823152736-00421.warc.gz"}
https://physics.stackexchange.com/questions/178044/boat-hull-drag-in-shallow-water/202424	# Boat Hull Drag in Shallow Water I paddle several different types of small craft in the ocean and bays near my home. One phenomenon I've observed is beyond my understanding of drag on a narrow displacement hull. When paddling in water less than maybe 6 feet in depth, there is a very noticeable increase in drag, which increases as the depth decreases. This is true for all the types of boats I paddle, from a large 6-person Hawaiian outrigger canoe (L=40', width=2', draft=0.67') to a one-person racing kayak (L=20', width=1.5', draft=0.33'). I should add that hull speeds are generally in the 6-8 mph range. I've read that rowing shells also encounter this same drag and they are longer, narrower, but with drafts in more or less the same range. I've read one explanation that the boundary layer on the hull makes contact with the bottom and the bottom increases the drag on the outer part of the boundary layer which in turn is transmitted to the hull. This seems highly unlikely to me, especially when the water is more than a maybe a foot deep. I don't believe the boundary layer from a 20 foot kayak extends that deep. As I said, this is noticable at water depths up to 6 feet or more. I've also heard that pressure waves from the hull bounce off the bottom and reflect back up to the hull and cause drag but as an engineer that doesn't really sound very rigorous to me. It seems to me there might be some interaction between the bow wave of a boat and the bottom, since I know that the dynamics of surface waves do extend approximately as deep as their wavelenth, and at these speeds the wavelength of a bow wave is certainly on par with the water depth. Can anyone give me a properly defensible answer to this? • Here are a couple of data points: Aircraft start to feel a "ground effect" as they approach the ground. This results in increased lift and decreased drag, starting at an altitude of roughly ten chord lengths above the ground. Also, it is possible to detect and track (moving) submarines at hundreds of feet depth by looking for the wake-bulge on the surface. So the pressure wave of a body moving through water goes out a long way. – David Rose Apr 24 '15 at 2:15 Your experience with more resistance in water of depth of ~ 6ft is probably due to increased resistance of the boat against the bow wave which itself is beginning to "feel bottom". There is an excellent post on the Earth Science Stack that explains what it means to "feel bottom" here. If you can estimate the size of the bow wave (wavelength) then possibly you can use the mathematical relationships posted there to determine if the bow wave is considered a deep water wave, shallow water wave or otherwise in the region of transition. If the calculated regime is either shallow water or transition, that could explain your observation. • I read the post you suggested and I agree that's probably the mechanism I've experienced. The theoretical hull speeds of the boats I paddle would put the bow wave wavelength at around 20 feet and therefore the critical shallow water depth at around 10 feet. Pretty close to my guess, especially since the effect would become more noticeable at shallower depths. – PJNoes Apr 24 '15 at 17:15 As I am not allowed to comment on the above answer I need to add a new one: You do not need to estimate the wavelength of your vessel, you can calculate it: $\lambda = 2 \cdot \pi \cdot Fn^2 \cdot L_{pp}$ where Fn is the Froude number and Lpp is the length of your canoe. $Fn = \frac{v}{\sqrt{g \cdot L_{pp}}}$ where v is the forward speed and g is the Earth's gravitational acceleration. • You might want to rethink this. Expand Fn^2 and you get a term of Lpp in the denominator which cancels the product term. This gives a result which is independent of length, and depends only on the square of velocity and 1/g. You sure about that? – WhatRoughBeast Aug 25 '15 at 12:33 • The (secondary) wave system depends on velocity squared. But the above formulation is more frequently used in naval arcitecture as velocities are often expressed in terms of Froude numbers. – some_weired_user Aug 25 '15 at 15:50 When waves roll in from deeper seas to a shallow shelving shore, they become steeper, pile up and eventually break as the amplitude of the wave increases. This may be caused by a shallow bottom interfering with the circular motion of water molecules as they are displaced by the passing wave energy. If the bow wave of your boat builds higher than it would in deeper water, that creates a greater volume of displaced water that must be handled by the stern of your boat. This means more drag and less velocity. One way for you to reduce this effect is to design a shallow water rowing boat with a long overhanging stern which the displaced bow wave can roll under. Incidentally, if you row so fast in shallow water that the bow wave becomes significantly more than the stern of your boat can handle, the boat may nose down into the bow wave and try to become a submarine. Obviously, this would have a detrimental effect on velocity over the surface of the water, as you would be rowing partially in the direction of a downward sloping vector. When rowing a coracle style boat in shallow water along the shore a significant displacement of water is most noted on the shore side. My guess is horizontal water displacement is more restrictive to movement. The boat's shore side rises further out of the water, perhaps negating the drag as I couldn't note directional change.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7483832240104675, "perplexity": 754.2295226407401}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371886991.92/warc/CC-MAIN-20200410043735-20200410074235-00124.warc.gz"}
https://rd.springer.com/article/10.1007%2Fs11425-017-9314-x	# A bound on judicious bipartitions of directed graphs • Jianfeng Hou • Huawen Ma • Xingxing Yu • Xia Zhang Articles ## Abstract Judicious partitioning problems on graphs ask for partitions that bound several quantities simultaneously, which have received much attention lately. Scott (2005) asked the following natural question: What is the maximum constant cd such that every directed graph D with m arcs and minimum outdegree d admits a bipartition V(D) = V1V2 satisfying min{e(V1, V2), e(V2, V1)} ⩾ cdm? Here, for i = 1, 2, e(Vi, V3-i) denotes the number of arcs in D from Vi to V3-i. Lee et al. (2016) conjectured that every directed graph D with m arcs and minimum outdegree at least d ⩾ 2 admits a bipartition V(D) = V1V2 such that $$\min \left\{ {e\left( {V_1 ,V_2 } \right),e\left( {V_2 ,V_1 } \right)} \right\} \geqslant \left( {\frac{{d - 1}}{{2\left( {2d - 1} \right)}} + o\left( 1 \right)} \right)m$$ . In this paper, we show that this conjecture holds under the additional natural condition that the minimum indegree is also at least d. ## Keywords directed graph partition outdegree indegree tight component 05C20 05C35 ## Notes ### Acknowledgements The first author was supported by National Natural Science Foundation of China (Grant No. 11671087). The third author was supported by National Science Foundation of USA (Grant No. DMS-1600738) and the Hundred Talents Program of Fujian Province. The fourth author was supported by the Shandong Provincial Natural Science Foundation of China (Grant No. ZR2014JL001) and the Excellent Young Scholars Research Fund of Shandong Normal University of China. The authors thank the anonymous referees for their helpful comments and suggestions. ## References 1. 1. Alon N. Bipartite subgraphs. Combinatorica, 1996, 16: 301–311 2. 2. Alon N, Bollobás B, Gyárfás A, et al. Maximum directed cuts in acyclic digraphs. J Graph Theory, 2007, 55: 1–13 3. 3. Azuma K. Weighted sums of certain dependent random variables. Tokuku Math J, 1967, 19: 357–367 4. 4. Bollobás B, Scott A. Judicious partitions of hypergraphs. J Combin Theory Ser A, 1997, 78: 15–31 5. 5. Bollobás B, Scott A. Problems and results on judicious partitions. Random Struct Algbra, 2002, 21: 414–430 6. 6. Chen G, Gu M, Li N. On maximum edge cuts of connected digraphs. J Graph Theory, 2014, 76: 1–19 7. 7. Edwards C S. Some extremal properties of bipartite graphs. Canad J Math 1973, 3: 475–485 8. 8. Edwards C S. An improved lower bound for the number of edges in a largest bipartite subgraph. In: Recent Advances in Graph Theory. Proceedings of the 2nd Czechoslovak Symposium on Graph Theory. Prague: Czechoslovak Academy of Sciences, 1975, 167–181Google Scholar 9. 9. Fan G, Hou J. Bounds for pairs in judicious partitioning of graphs. Random Struct Algebra, 2017, 50: 59–70 10. 10. Fan G, Hou J, Yu X. Bisections of graphs without short cycles. Combin Probab Comput, 2018, 27: 44–59 11. 11. Hoeffding W. Probability inequalities for sums of bounded random variables. J Amer Statist Assoc, 1963, 58: 13–30 12. 12. Hou J, Wu S. Bipartitions of oriented graphs. J Combin Theory Ser B, 2018, 132: 107–133 13. 13. Hou J, Wu S, Yan G. On bisections of directed graphs. European J Combin, 2017, 63: 44–58 14. 14. Hou J, Wu S, Yan G. On judicious partitions of uniform hypergraphs. J Combin Theory Ser A, 2016, 141: 16–32 15. 15. Hou J, Wu S, Zeng Q, et al. The Bollobás-Scott conjecture for 4-uniform hypergraphs. SIAM J Discrete Math, 2018 32: 505–521 16. 16. Janson S, Luczak T, Ruciński A. Random Graphs. New York: Wiley, 2000 17. 17. Lee C, Loh P, Sudakov B. Bisections of graphs. J Comb Theory Ser B, 2013, 103: 599–629 18. 18. Lee C, Loh P, Sudakov B. Judicious partitions of directed graphs. Random Struct Algebra, 2016, 48: 147–170 19. 19. Liu M, Xu B. Bipartition of graph under degree constraints. Sci China Math, 2015, 58: 869–874 20. 20. Lu C, Wang K, Yu X. On tight components and anti-tight components. Graphs Combin, 2015, 31: 2293–2297 21. 21. Ma J, Yen P, Yu X. On several partitioning problems of Bollobás and Scott. J Combin Theory Ser B, 2010, 100: 631–649 22. 22. Scott A. Judicious partitions and related problems. Surv Combin, 2005, 327: 95–117 23. 23. Xu B, Yu X. Triangle-free subcubic graphs with minimum bipartite density. J Combin Theory Ser B, 2008, 98: 516–537 24. 24. Xu B, Yu X, Zhang X, et al. An SDP randomized approximation algorithm for max hypergraph cut with limited unbalance. Sci China Math, 2014, 57: 2437–2462 25. 25. Yannakakis M. Node- and edge-deletion NP-complete problems. STOC, 1978, 253–264Google Scholar 26. 26. Zhu X. Bipartite density of triangle-free subcubic graphs. Discrete Appl Math, 2009, 157: 710–714 © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019 ## Authors and Affiliations • Jianfeng Hou • 1 • Huawen Ma • 1 • Xingxing Yu • 2 Email author • Xia Zhang • 3 1. 1.Center for Discrete MathematicsFuzhou UniversityFuzhouChina 2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA 3. 3.School of Mathematics and StatisticsShandong Normal UniversityJinanChina	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8962864875793457, "perplexity": 9843.716867559007}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249508792.98/warc/CC-MAIN-20190223162938-20190223184938-00501.warc.gz"}
https://proceedings.mlr.press/v180/xiong22a.html	# Deterministic policy gradient: Convergence analysis Huaqing. Xiong, Tengyu Xu, Lin Zhao, Yingbin Liang, Wei Zhang Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:2159-2169, 2022. #### Abstract The deterministic policy gradient (DPG) method proposed in Silver et al. [2014] has been demonstrated to exhibit superior performance particularly for applications with multi-dimensional and continuous action spaces. However, it remains unclear whether DPG converges, and if so, how fast it converges and whether it converges as efficiently as other PG methods. In this paper, we provide a theoretical analysis of DPG to answer those questions. We study the single timescale DPG (often the case in practice) in both on-policy and off-policy settings, and show that both algorithms attain an $\epsilon$-accurate stationary policy with a sample complexity of $\mathcal{O}(\epsilon^{-2})$. Moreover, we establish the convergence rate for DPG under Gaussian noise exploration, which is widely adopted in practice to improve the performance of DPG. To our best knowledge, this is the first non-asymptotic convergence characterization for DPG methods.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9120621085166931, "perplexity": 682.6583307278252}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945292.83/warc/CC-MAIN-20230325002113-20230325032113-00505.warc.gz"}
https://link.springer.com/article/10.1007/s11207-016-1041-8?error=cookies_not_supported&code=d5e700d4-12ed-4cb2-8840-9bc66f4f88bf	# Coronal Holes and Open Magnetic Flux over Cycles 23 and 24 ## Abstract As the observational signature of the footprints of solar magnetic field lines open into the heliosphere, coronal holes provide a critical measure of the structure and evolution of these lines. Using a combination of Solar and Heliospheric Observatory/Extreme ultraviolet Imaging Telescope (SOHO/EIT), Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA), and Solar Terrestrial Relations Observatory/Extreme Ultraviolet Imager (STEREO/EUVI A/B) extreme ultraviolet (EUV) observations spanning 1996 – 2015 (nearly two solar cycles), coronal holes are automatically detected and characterized. Coronal hole area distributions show distinct behavior in latitude, defining the domain of polar and low-latitude coronal holes. The northern and southern polar regions show a clear asymmetry, with a lag between hemispheres in the appearance and disappearance of polar coronal holes. ## Introduction Coronal holes are the observational signatures of regions of open solar magnetic field. Early observations were conducted in extreme ultraviolet (EUV) wavelengths (Tousey, Sandlin, and Purcell, 1968). Magnetic field lines within the solar corona can either connect back down to the solar surface or extend outward into the heliosphere, denoting closed and open field, respectively. In regions of open magnetic field, coronal plasma is free to follow these field lines outward, creating the solar wind and a plasma density depletion at the field footpoints. Appearing as dark regions in X-ray and EUV images, coronal holes correspond with reduced emission from solar plasma localized to open magnetic field footpoints (Wang, 2009). Cranmer (2009) discusses a complete review of coronal holes in exhaustive detail. The Sun’s open magnetic field and coronal hole structure varies alongside the overall solar activity cycle, running through a magnetic polarity swap every 11 years. The connection between coronal hole activity and open magnetic flux throughout the solar cycle has been considered by several studies (Harvey and Recely, 2002; Wang, 2009). Harvey and Recely (2002) assessed the properties of polar coronal holes throughout Solar Cycles 22 and 23. With the help of a series of He i 10,830 Å spectroheliograms, polar coronal holes were identified over the period 1989 September to 2002 March, and their area and the enclosed magnetic flux was measured. The authors found that polar coronal holes throughout this period initially develop at lower latitudes of about 50 – 60 degrees, and extend to the poles within three subsequent rotations. These polar coronal holes then have an observed lifetime of between 8.3 and 8.7 years. An asymmetry was observed in the timing of the initial appearance and evolution of coronal holes at each pole, with a difference of several months between poles. This mirrors earlier observations by Webb, Davis, and McIntosh (1984), who found a lag of 9 and 6 months between polar coronal hole appearances between Cycles 19 – 20 and 20 – 21, respectively. The relative areal extent of each polar coronal hole can also show an asymmetry from one solar cycle to the next (Broussard et al., 1978; Sheeley, 1980). Wang and Sheeley (2002) explored in detail the relationship between active region evolution and consequent coronal hole distribution through observation and modeling. In particular, they noted the evolution of polar coronal holes as a consequence of remaining flux that is transported from lower latitudes. More recent work by McIntosh et al. (2013) explored the hemispheric asymmetry of photospheric magnetism throughout Cycle 23 and the early stages of Cycle 24. While He i 10,830 Å observations of coronal holes can provide accurate results in polar regions, there is discrepancy at lower latitudes (Kahler, Davis, and Harvey, 1983; Schrijver and De Rosa, 2003; Malanushenko and Jones, 2005). Despite the relatively long history of observations of the solar activity cycle, continuous and full-disk magnetic field and solar corona observations extend back only to cover the previous two cycles. The Solar and Heliospheric Observatory (SOHO) began this observational campaign from 1995 through 2011, with results from the Solar Dynamics Observatory (SDO) picking up since May 2010. McIntosh et al. (2014) recently conducted a comprehensive analysis of observations by these spacecraft, showing that distributions of EUV bright points and structures of surface magnetic elements, characterized by the magnetic range of influence (MRoI), both migrate from high latitudes ($${\pm}\,55~\mbox{degrees}$$) toward the equator in a time period of 19 years. In addition, the evolution of low-latitude coronal holes and records of coronal green line emissions also overlaps with this trend. Robbrecht et al. (2010) explored this apparent extended cycle as observed from coronal emission in simulations of green line emission and Extreme ultraviolet Imaging Telescope (EIT) EUV observations. They suggested that these overlapping band structures, rather than indicating an extended cycle, are merely remnants of reconnection between low latitude and polar flux from the current cycle. Observing the progress of the activity bands formed by these very different features helps decipher the underlying solar magnetism in a cycle structure, and can help to shed additional light on these processes. Among these features, coronal holes map the footprints of open magnetic field at locations that vary with the solar cycle. McIntosh et al. (2014) showed that low-latitude coronal holes migrate toward the equator as the cycle progresses, whereas during solar minimum, holes exist primarily in polar regions, where EUV bright points and coronal green line emission is sparse. These areas are of crucial importance in the solar magnetic activity cycle. The polar region is usually dominated by a magnetic field of one polarity, and each cycle begins with the reversal of this polarity at the end of the solar minimum, when the meridional convective flow has recycled the field to the poles and flux cancellation takes place (Upton and Hathaway, 2014). Existing models of the global solar magnetic field often make the point to focus on a comparison of computed open field models with the observed coronal holes at the poles, or with the total heliospheric open magnetic flux (Mackay, Priest, and Lockwood, 2002a,b; Yeates et al., 2010). On the other hand, much effort is also needed to examine coronal holes evolving across the latitudes. Tracking open magnetic flux on the Sun following coronal hole evolution from the poles to the low latitudes adds a valuable piece to the puzzle of the solar magnetic activity cycle. The continuous full-disk coronal and magnetic field observations in the past two decades provide the opportunity to study the evolution of coronal holes and open magnetic flux in Solar Cycles 23 and 24. Lowder et al. (2014) developed an automated technique to detect persistent coronal holes and characterize their properties using a database of full-disk EUV images obtained by several spacecraft instruments over a time span from 1996 May to 2013 January. In this present study, we use the same technique and the same database, which is further extended to August 2014, however. The extended database covers a significant portion of the current Solar Cycle 24, and hence provides an opportunity to compare coronal hole properties between the past Cycle 23 and this special new cycle, which, after an unexpectedly deep minimum, slowly started around 2010, and rose to a low maximum in early 2014 (McIntosh et al., 2015). Lowder et al. (2014) have also measured coronal hole areas, and the unsigned and signed total flux measured in these holes, distinguishing polar regions from low latitudes with an arbitrary division at $${\pm}\,65~\mbox{degrees}$$. This article presents a more careful and detailed examination of the latitude dependence of coronal hole properties, where a contrast between the consecutive two cycles is apparent. A brief review of the database and technique is presented in Section 2. Section 3 presents the latitude dependence of coronal hole properties and their variations from the last cycle to the current cycle, followed by conclusions and discussions in Section 4. ## Method and Data EIT (Delaboudinière et al., 1995), an instrument onboard SOHO, has provided 14 years of nearly continuous EUV observations over the span of Solar Cycle 23. SDO was launched in 2010, continuing the role of a provider of synoptic EUV observations through the EUV telescope Atmospheric Imaging Assembly (AIA, Lemen et al., 2012). Having launched a few years before, the twin spacecraft Solar Terrestrial Relations Observatory (STEREO) A and B have swept out a significant portion of vantage points on the far side of the Sun. Employing the Extreme Ultraviolet Imager (EUVI, Howard et al., 2008) on each of the STEREO spacecraft, additional viewpoints are available in the EUV. The particular combination of EUV data from SDO/AIA and STEREO/EUVI A/B allows for a unique observational opportunity. As the STEREO spacecraft have swept out in their orbits, expanded heliographic longitude coverage in EUV has been made possible. Additionally, polar EUV coverage was expanded by the more staggered $$B$$-angle for each of the spacecraft in use. Joint observations by the three spacecraft complement one another to provide better coverage of the polar areas, important regions contributing to the evolution of solar open magnetic flux. The joint AIA/EUVI coverage makes possible continuous, consistent, and nearly full solar surface observations of coronal hole boundaries over Solar Cycle 24. Table 1 displays the relevant datasets used in this study and the corresponding availability ranges. Using these data ranges, we characterize coronal hole boundaries over one and a half solar activity cycles, and compare the results between Cycles 23 and 24. To provide context for the solar cycle dependence of coronal hole properties, Figure 1 displays the observational spacecraft $$B$$-angle in comparison with the position in the solar activity cycle. Part of this dataset was featured in our previous study. However, here the range is extended to cover through August 2014 (Lowder et al., 2014, Figure 13). The upper panel displays the monthly hemispheric sunspot number (WDC-SILSO, Royal Observatory of Belgium, Brussels), with the northern and southern sunspot counts in red and blue, respectively, and with the dominant pole shade filling between. The middle panel displays the spacecraft $$B$$-angle for SOHO/EIT (black), SDO/AIA (green), STEREO/EUVI A (red), and STEREO/EUVI B (blue). Using the single vantage point of SOHO/EIT, our polar observations are limited by this angle. This will become apparent in subsequent figures. Rather than attempting a convoluted method to correct for or estimate this lack of coverage, results are displayed unmodified. With the combination of SDO/AIA and STEREO/EUVI A/B, this polar coverage gap is greatly reduced. When we compare this with our gauge of the solar activity cycle, we note that our EIT observations span over the entire first solar cycle under consideration. Our improved polar coverage from STEREO begins conveniently just as the next solar cycle begins. The bottom panel displays a butterfly diagram of the mean radial magnetic field strength, taken from measurements from the Michelson Doppler Imager (MDI, Scherrer et al., 1995) and the Helioseismic and Magnetic Imager (HMI, Scherrer et al., 2012), with a vertical dot-dashed red line to indicate the transition. This dataset is scaled to $${\pm}\,5~\mbox{G}$$ to highlight trends in dominant magnetic field sign throughout the solar cycle. With these data, techniques have been developed and documented for the automated detection of coronal hole boundaries, detailed in the literature (Lowder et al., 2014). In brief, each frame of EUV data is analyzed via an instrument-independent intensity thresholding method to mark out coronal hole boundaries. Boolean maps of suspected coronal hole regions are generated and mapped into a Carrington Equal Area (CEA) projection, and then segmented and cataloged into individual regions through a watershed method. For our SOHO-era (solar activity Cycle 23) data, this process is repeated for each time-step, with half of the solar surface not visible. Full rotation maps are built by summing these individual EIT hole maps over each Carrington rotation, and then flattening into a boolean map. For the SDO-era (solar activity Cycle 24) data, thresholded projections are made individually for each of our three datasets (SDO/AIA and STEREO/EUVI A/B), and then summed and flattened into one resulting boolean map. This initial mapping detects both coronal holes and filament channels, which both appear as dark features in EUV. Here we use the underlying magnetic flux density information to distinguish the two. Filament channels straddle magnetic polarity inversion lines, encompassing roughly equal distributions of positive and negative flux. In the encompassed area of a coronal hole, a single magnetic polarity dominates (Cranmer, 2009). Therefore, we calculate the skew of magnetic flux density in each candidate coronal hole region, using magnetograms from SOHO/MDI in conjunction with SOHO/EIT, or SDO/HMI with SDO/AIA and STEREO/EUVI A/B. Regions with a relatively small skew are considered to be filament channels and are therefore ‘sieved’ out, leaving behind a boolean CEA map of coronal hole pixel locations. For the current application of this routine for long-duration coronal hole evolution, the EUV data cadence is as follows. SOHO/EIT data are assimilated daily, with a resulting daily coronal hole map. These daily maps are then summed and flattened to provide an upper estimate over an entire solar rotation, to account for missing far-side data. SDO/AIA and STEREO/EUVI A/B data are gathered at a cadence of 12 hours, providing two full-surface coronal hole maps per day. Note that with the expanded longitudinal and polar coverage, these maps are considered individually, without the requirement of summing over an entire solar rotation. For more details and intermediate results on this process, see Lowder et al. (2014). For the sake of brevity, this code and existing methodology are referred to as the Global Automated Coronal Hole Detection routine (GACHD). Here the techniques have been further refined, and applied to the complete data range from 31 May 1996 to 19 August 2014, the furthest data available until the recent communication loss with one of the STEREO spacecraft. These data cover the entire past Cycle 23 as well as a large portion of the current Solar Cycle 24. ## Coronal Hole Properties in Solar Cycles 23 and 24 Using this dataset of coronal hole boundaries, spanning over one and a half solar cycles in length, we can consider several interesting quantities. These include the area as well as the signed and unsigned magnetic flux enclosed by coronal hole boundaries. Rather than considering just the polar coronal hole properties, our data extend across all latitudes to characterize the latitude-dependence of these properties and their evolution. In this section, we first present the time-latitude maps of coronal hole properties. The total magnetic flux in the holes is then presented by comparing the polar regions with low latitudes, and the past Cycle 23 with the current cycle. For the following set of figures, there are two notes of importance. Figures 2, 3, 4, and 5 display quantities over the full time span from May 1996 to August 2014, illustrating the solar cycle dependence of the measured properties. Figures 6, 7, 8, and 9 provide a zoomed-in display of identical quantities from 2010 May onward, over the SDO and STEREO-era data for Solar Cycle 24. Over all of these plots, panel a displays the monthly hemispheric sunspot number in red and blue for the northern and southern sunspot counts, respectively. This panel will lead some of the following figures for an easily markable solar activity cycle cross-reference tool. It should be noted that a partial overlap with the results in Lowder et al. (2014) exists within Figures 3, 4, and 5. However, results contained here use an alternative latitudinal definition of polar regions. Additional data extend the range of results to cover a more significant fraction of Cycle 24. ### Latitude Coronal Hole Profiles We consider Figure 2, which displays the full latitude dependence of our coronal hole quantities over the full time span of our datasets. Of immediate note, the distributions of the coronal hole area (panel b), the mean magnetic field (panel c), and the total unsigned magnetic flux (panel d) in the holes all exhibit distinctive evolution patterns near $${\pm}\,55~\mbox{degrees}$$ latitude, which are marked by two horizontal lines in the figures. Other authors have arrived at slightly different limiting latitudes for polar coronal hole boundaries. Wang and Sheeley (2002) considered the formation and evolution of a polar field as beginning at far lower latitudes. In this formalism, remnants of active-region flux are transported toward the poles, where shearing and diffusion work to reduce the nonaxisymmetric component of this field. The remaining field component continues toward the poles, establishing a dominant polarity. In this manner, coronal holes begin their formation in lower latitudes, $${\pm}\,30\,\mbox{--}\,60~\mbox{degrees}$$, before establishing themselves above $${\pm}\,60~\mbox{degrees}$$, with boundaries somewhat maintained by a balance between meridional flow and diffusion. Similarly, from observations of polar coronal holes in He i 10,830 Å spectroheliograms, Harvey and Recely (2002) found that most held positions above $${\pm}\,60~\mbox{degrees}$$, with some exceptions. Taking the mean polar coronal hole latitude, Harvey and Recely (2002) found dips in the northern and southern poles to 58 – 59 degrees and 54 – 55 degrees, respectively, during the minimum between Cycles 22 and 23. In the following analysis, the $${\pm}\,55~\mbox{degree}$$ latitude is therefore chosen as the division between polar and low-latitude regions. While lower than the $${\pm}\,60~\mbox{degree}$$ boundary, this provides a clear distinction of polar regions, without misattributing open magnetic flux. Note that this distinction of polar regions differs from the previous study by Lowder et al. (2014), which used the $${\pm}\,65~\mbox{degree}$$ latitude as a separator. Appendix A works through a more detailed analysis of the effects of shifting this polar latitude boundary, with further justification for this boundary choice. Note that the selection here of a polar latitude is useful for comparative purposes. These particular latitudes at $${\pm}\,55$$-degrees have been noted previously as a demarcation of certain other aspects of solar activity, coincidentally. Thompson et al. (1996), using the Global Oscillation Network Group (GONG) set of observations, considered the internal rotation rate of the Sun from the surface deep into the convection zone. A slice through the convection zone reveals the internal structure of the differential rotation, beneath the photospheric surface flow. At $${\pm}\,55~\mbox{degree}$$ latitude, there is a distinct change in the behavior of these subsurface flows. Spruit (2011), in an effort to sketch out a few theories of internal solar dynamo processes, devised a simple model. Starting with a uniform poloidal field, a differential rotation profile from observations was applied. This resulted in a shearing of the field, which can eventually lead to a buildup of an azimuthal field and an instability. From this simple model, the azimuthal field builds as $$\partial_{t} B_{\phi} \sim\sin2 \lambda(1+ 1.51 \sin^{2} \lambda )$$. As a function of latitude, the maximum shearing occurs around $${\pm}\,55~\mbox{degrees}$$. Snodgrass (1983) finds this same latitude as a peak of differential rotation shearing. This latitude was further revealed as a zone of interest by McIntosh et al. (2014, 2015), who found a scarcity of EUV bright points above this latitude, as well as a distinct evolution pattern of the magnetic range of influence (MRoI) divided by this latitude. While the coronal hole polar boundary is determined by properties of the polar field itself, several other quantities show variation nearby. Panel b of Figure 2 displays for each time frame and bin of sine latitude the fraction of longitude bins that are characterized as coronal holes, with the color mapping truncated at 0.2 for display purposes. Note that this fraction varies from 0 (no coronal holes at any longitudes at that particular latitude) to 1.0 (complete coronal hole coverage at every longitude for that particular latitude). From 1996 to 1998, and from 2006 through 2012, coronal holes are concentrated in the polar regions above $${\pm}\,55$$-degrees. Note here that the polar hole extensions from 1996 to 1998 extend further equatorward, pushing toward our boundaries at $${\pm}\,55~\mbox{degrees}$$. The apparent annual variation in the polar hole area is not a physical result, but rather a consequence of the solar $$B$$-angle modulation of the SOHO spacecraft (see Figure 1). The single vantage point of these observations results in alternating reduced polar coverage. From 2010, with the combination of the AIA/EUVI suite of data, staggered spacecraft $$B$$-angles allow for more comprehensive polar measurements. During the solar maximum from 1999 to 2003, and then from 2012 through 2014, coronal holes extend to low latitudes below $${\pm}\,55~\mbox{degrees}$$, and are diminished in polar regions. Figure 2, panel c, displays the mean magnetic field strength encompassed by coronal hole boundaries, averaged over all longitude bins for each bin of sine latitude. Using synoptic magnetograms from SOHO/MDI and SDO/HMI, coronal hole enclosed magnetic flux (signed and unsigned) is integrated over all longitudes. To avoid the contribution of noise for both signed and unsigned flux calculations, instrument-specific noise levels are used to remove magnetic flux density measurements below this noise threshold. For MDI synoptic chart measurements of radial magnetic flux density, this noise level is measured as $${\pm}\,5.0~\mbox{G}$$, while for similar synoptic measurements from HMI, this noise level is measured as $${\pm}\,2.3~\mbox{G}$$ (Liu et al., 2012). While the range of integrated values extends from −8.4 to 14.3 G, here the map is displayed truncated at $${\pm}\,0.5~\mbox{G}$$ to illustrate the frequently weak polarity dominance at lower latitudes. The resulting map displays the distribution of the dominant polarity of coronal hole-enclosed magnetic flux and its evolution over the solar cycle. These distributions of dominant coronal hole polarity exhibit a hemispheric pattern over the course of the solar cycle. In the rise of the previous cycle before 1999, the northern polar coronal hole distribution is dominated by positive magnetic field, with the southern polar coronal hole dominated by negative field. At lower latitudes, this same general polarity trend is observed, although at a much lower strength, usually below 1 G, and the trend is not as spatially uniform across latitudes and time. During the solar activity maximum in 2001 – 2003, the hemispheric field reversal is observed in the swap of the polar coronal hole dominant polarity, persisting until 2012. For the current cycle, the reversal of the dominant polarity in polar regions begins in 2012 and 2013 for the northern and southern hemisphere, respectively. However, the resulting polar coronal hole coverage and polarity dominance have been very weak in comparison with the previous cycle. In lower latitudes during the current cycle, the distribution of coronal hole polarity dominance is much weaker and spatially mixed. Figure 2, panel d, displays the fractional unsigned open flux, collected by summing all coronal-hole-encompassed-flux over longitude bins for each time and sine-latitude bin. An identical noise cutoff of the synoptic magnetogram is used for this calculation to avoid including instrument noise. Note that the range of calculated open flux extends from $$0 \mbox{ to } 4.7\times 10^{20}~\mbox{Mx}$$, with the displayed data being represented as a fraction of the maximum measured. With a sine-latitude coordinate system, broken into 1440 pixel latitude bins, each pixel represents an equal solar surface area. This allows a comparison of the relative strength of open flux sources at polar and low-latitude regions. From 1997 – 1999, the polar coronal holes contain the majority of the open magnetic flux. As the poles reverse as solar activity increases, larger concentrations of open flux appear at lower latitudes between 1999 and 2003. Past the maximum of Cycle 23, this pattern quickly returns to larger concentrations of open flux in the poles, until the next reversal around 2013. In the southern pole, the concentration of coronal hole flux persists for the extended deep minimum until the next reversal around 2013. This particular cycle from 2009 onward has shown unique behavior in the early drop-off of the northern polar coronal hole signature. This in turn has resulted in almost nonexistent open flux from the northern polar region. In concluding this portion of the analysis, we note that McIntosh et al. (2014, 2015) have also reported the solar-cycle dependence of coronal holes observed in much the same time range. However, their study only captured coronal holes with area greater than $$20{,}000~\mbox{Mm}^{2}$$ at low latitudes (below $${\pm}\,55~\mbox{degree}$$). By employing joint observations by AIA/EUVI, our study not only provides a more complete coverage of polar holes from May 2010, but also allows the assessment of polar hole measurements by EIT in the past cycle through comparison of measurements by different instruments, as we discuss further in Sections 3.2 and 3.3. ### Coronal Hole Area Figure 3 breaks down the latitude dependence of the coronal hole areas in Figure 2 into the distinct ranges of northern polar (NP; 55:90 degrees), low latitudinal (LL; −55:55 degrees), and southern polar (SP; −90:−55 degrees). Results from EIT and the combination of results from AIA/EUVI are displayed in red and blue, respectively. Note here that EIT measurements of coronal hole area are integrated over each solar rotation, providing a measurement within observable regions. The brief overlap of EIT and AIA/EUVI observations in the second half of 2010 demonstrates that as also discussed in Lowder et al. (2014), the joint AIA/EUVI observational coverage allows better estimates of polar coronal hole areas and fluxes. Figure 3, panel b, displays results for the entire range of latitudes, from −90:90 degrees. The total area of coronal holes over the course of this study varies between $$1\,\mbox{--}\,7\times 10^{21}~\mbox{cm}^{2}$$, or from 2 % to 12 % of the total solar surface area. Figure 3, panels c – e, displays the latitude zones under consideration, where we can note several observations. The northern coronal hole has dropped from 2011 onward, hovering around zero area, and has never recovered to the pre-2009 level. The southern pole area was still rising from 2011, and suffered a drop in the middle of 2012, but recovered from 2014 onward. Compared with the previous cycle drop in polar coronal hole area from 1999 – 2001, this behavior is highly asymmetric, reflecting the asymmetries in sunspot activity that are visible in Figure 1. In both cycles, low-latitude coronal holes cover a large area during the solar maximum, and consequently are a source of a significant amount of total open flux on the Sun during the solar maximum. In the current Cycle 24, the low-latitude coronal hole area is notably smaller than in the last cycle. ### Unsigned Magnetic Flux In a similar manner, Figure 4 breaks down the latitude dependence of the unsigned open magnetic flux encompassed by our coronal hole boundaries. Figure 4, panel b, displays the total unsigned open flux, with several datasets in place. EIT and AIA/EUVI results for coronal hole-encompassed unsigned flux are plotted in red and blue, respectively. These direct measurements are compared with the open flux calculated by the potential field source surface (PFSS) model (Schatten, Wilcox, and Ness, 1969; Wang and Sheeley, 1992). This model calculates the magnetic potential field using spherical harmonics of photospheric radial magnetic field determinations from the Wilcox Solar Observatory (WSO), and with the source-surface defined at $$2.5R_{\odot}$$, where field lines are assumed to be open. An array of field lines is traced down from this source-surface to their photospheric origin, and is mapped out as the boundaries of the open magnetic field. Magnetic fluxes are then computed by integrating the photospheric radial magnetic field within these open footpoint boundaries. Note that while WSO observations are used as a boundary condition, the calculated open flux is a PFSS model output using this observational input. For the purposes of comparison with other model results, this dataset may be referred to as ‘observational,’ referring to the observational basis of the model input. The resulting unsigned open magnetic flux from this PFSS model is displayed in black. The measured open flux from the EIT coronal holes undershoots the values predicted by the PFSS model, which is partially due to a contrast issue with SOHO/EIT (Lowder et al., 2014). This issue is most prevalent in lower-latitude regions during periods of higher solar activity. AIA/EUVI measurements reveal more open flux than EIT alone during the overlapping period in the second half of 2010, as a result of the more complete coverage of the polar regions by the AIA/EUVI dataset. This additional flux sets the AIA/EUVI dataset more in line with the PFSS model. Finally, the OMNI dataset is used to compute an equivalent open magnetic flux. In situ (Lagrange point L1) measurements of the $$B_{x}$$ component (Geocentric Solar Ecliptic; GSE) of the magnetic field extend backward for decades through a cross-spacecraft calibrated dataset (King and Papitashvili, 2005). The OMNI data are obtained from the GSFC/SPDF OMNIWeb interface at http://omniweb.gsfc.nasa.gov . For this study we focus on data for the previous two decades. When we assume that our long-term interplanetary magnetic field is uniform and radial, the equivalent OMNI unsigned open magnetic flux can be computed as $$\Phi_{\mathrm{OMNI}} = 4 \pi R_{L1}^{2} \|B_{x}\|$$ (Lockwood, 2002). During solar minimum periods, the OMNI data and PFSS model are in better agreement than in periods of higher solar activity. Figure 4, panels c – e, displays the coronal hole unsigned open flux for the latitude zones demarcated by $${\pm}\,55~\mbox{degrees}$$ latitude. Similar evolution patterns are observed with regard to cyclic variation and latitudinal dependence, as compared with measurements of coronal hole areas. In the polar regions, the lack of coverage during the EIT-era dataset is apparent, and is a consequence of the $$B$$-angle variation. However, the peak values of the EIT coronal hole area and unsigned open flux provide an upper bound on this value for each pole during optimal angling. Considering the upper bounds of the EIT data, good agreement is found with the PFSS open flux in polar regions. This trend continues with AIA/EUVI data, although with more complete coverage of the polar regions. These comparisons allow us to state that the magnetic open flux in polar regions computed with the PFSS model is generally consistent with direct measurements in both solar cycles. In terms of the solar cycle dependence of open flux in the poles, the unsigned open flux in the northern and southern poles in Solar Cycle 23 evolved in a mostly symmetric manner. An asymmetry presented itself in Solar Cycle 24, however, in the same way as with the evolution of the coronal hole areas. Once again, this is a consequence of asymmetric sunspot emergence. For this cycle, the northern polar unsigned open flux drops off to nearly zero around 2011 and continues at this level. Slight signs of the beginning of a recovery are apparent in 2014, but with no clear recovery trend. The southern pole open flux drops to zero in 2013, two years later than the northern poles, and then begins to rise once again. Consideration of the low-latitude open flux reveals the discrepancy during periods of maximum solar activity, when low-latitude coronal holes closely border larger concentrations of magnetic flux. ### Signed Magnetic Flux Figure 5, panels b – d, displays the signed open magnetic flux from each of the latitude zones demarcated by $${\pm}\,55~\mbox{degrees}$$. When we consider the northern and southern low-latitude regions of panel c in Figure 5, we see that the signed open flux undergoes a few variations throughout the cycle. During solar minima, the signed open fluxes are relatively weaker because of a reduced low-latitude area during these phases. As the areas increase during Cycle 23, each low-latitude hemisphere begins to exhibit a dominant signed polarity, positive in the south and negative in the north. This behavior decreases during the decline to solar minimum between Cycles 23 and 24. As Cycle 24 begins to increase, observations of low-latitude hemispheric signed flux remain relatively weak. For the northern and southern polar regions, shown in Figure 5, panels b – d, the polarity dominance is more apparent. During the lull in solar activity around 1997 before Cycle 23 began, each polar region is strongly dominated. The northern pole shows a strong dominance of positive magnetic polarity, while the southern pole shows a strong negative dominance. Our EIT coronal hole and the WSO computed open field measurements agree. As solar maximum for Cycle 23 is reached, this polarity dominance decreases, and each pole becomes neutral around 2000. Throughout this next phase of minimal activity between Cycles 23 and 24, a different picture emerges. Here, the WSO computed open field shows a much weaker polarity dominance, this time of the opposite sign, as expected. This is also reflected in a weaker polar unsigned flux. Our EIT measurements of coronal hole open flux show an even weaker polarity dominance. This stands in stark contrast with the heavy polarity dominance of the previous minimum. As Cycle 24 reaches something resembling a peak around 2014, both poles once again have reverted to a neutral state. Here our AIA/EUVI observations fall more in line with the computed WSO open field measurements. ### A Close Look at Cycle 24 To better illustrate details for Solar Cycle 24, we consider only data from 13 May 2010 – 19 August 2014, that is, Carrington Rotations 2096 – 2154. Here, many of the same trends and conclusions are evident, with some new details visible with scaling. Figures 6, 7, 8, and 9 display identical values to the larger dataset discussed above, but with a retracted viewpoint to only cover the range of data available from AIA/EUVI. Figure 6 shows maps of the latitude distribution of the coronal hole, the mean magnetic field, and the total unsigned flux in the holes. Figures 7, 8, and 9 represent the measured coronal hole area, the unsigned open magnetic flux, and the signed open magnetic flux, respectively. These plots are identical in labeling to those spanning the entire dataset, with the addition of AIA/EUVI raw data displayed in a lighter shade of blue, compared with a 27-day running average in darker blue. Figure 6, panels b – d, displays the SDO-era data available using our coronal hole detection routine. While our SOHO-era coronal hole data was gathered at a 24-hour cadence, the results were stacked and binned over a full solar rotation. This method allows for the calculation of an upper bound of the coronal hole area and the enclosed unsigned magnetic flux, capturing the location of each Earth-facing coronal hole location throughout that rotation. Our SDO-era method is slightly different, with the inclusion of STEREO/EUVI data. With the inclusion of EUVI data, far-side (opposite of Earth) coronal hole observations are possible. This allows for our coronal hole mappings to be presented at full 12-hour cadence, without binning. This is immediately apparent with the coronal hole area latitude profiles in Figure 6, panel b. In May 2010, the beginning of our dataset, a regular gap in the data appears, coinciding with the solar rotation rate. At the beginning of our SDO-era data, 13 May 2010, the STEREO spacecraft had achieved an orbital separation of roughly 70 degrees ahead and behind, each with respect to Earth. This left a roughly 40-degree range of longitudes that were unobservable in EUV. As the STEREO spacecraft continued in their orbital separation, this gap continued to shrink. With near-limb data truncated from each data source, higher frequency gaps appear further in the dataset as large holes that rotate through these small blind-spots. SDO-era latitude profiles of coronal hole area and signed/unsigned flux displayed in Figure 6 reveal that a few items are noteworthy. From May 2010 until January 2014, the latitude demarcation of $${\pm}\,55~\mbox{degrees}$$ continues to divide our polar and low-latitude coronal holes. From January 2014 until August 2014, two large coronal holes develop at the upper edge of our low-latitude region, then drift and extend beyond $${\pm}\,55~\mbox{degrees}$$, with the northern polar extension of this hole developing much weaker and diminishing earlier than the extension found in the southern pole. Referring back to Figure 2, panel b, this same pattern of expansion into the pole is apparent with EIT data from 2001 until 2003. Here, however, this expansion occurs with much greater symmetry and nearly in phase; both the northern and southern extensions into the polar regions evolve and persist. The asymmetric coronal hole distribution within polar regions in Cycle 24 is apparent in the total coronal hole area displayed in Figure 7. The mean coronal hole field in Figure 6 shows the dominant polarity of each of our major coronal hole distributions. From May 2010 until August 2012, the northern polar coronal hole distribution is dominated by negative magnetic flux, with the southern polar coronal holes dominated by positive flux. Note that the northern polar coronal hole distribution has decreased in area and resulting signed/unsigned flux as of February 2011, with lingering traces thereafter, until it completely vanishes in February 2012. Once again, this particular lead-in to a polar polarity inversion behaves in a much more asymmetric manner than the reversal observed with SOHO-era data in mid-1999. The unsigned open flux latitude distribution in Figure 6, panel d, results from previous noted trends in the coronal hole area latitude profile. Here we see that the southern polar coronal hole distribution dominates the density of unsigned open magnetic flux, with smaller distributions at the northern pole and lower latitudes. The measured total flux is plotted in Figure 8. As described in Lowder et al. (2014), as a whole, the AIA/EUVI measured total flux is much closer to the model computed total flux, but there are variations in the latitude-dependent comparison. The AIA/EUVI measured flux is comparable to or higher than the model computed flux within the polar regions. However, at lower latitudes, the computed flux overshoots the measured flux. ## Conclusions and Discussions Through the use of SOHO/EIT, SDO/AIA, and STEREO/EUVI A/B EUV data from May 1996 until August 2014, coronal hole boundaries have been tracked over the entirety of Solar Cycle 23 and a good portion of Cycle 24. This extensive range allows for a detailed analysis of coronal hole evolution in all latitudes, and for a comparison of the magnetic open flux, which is directly measured from the coronal holes, from the past cycle to the current cycle. The addition of STEREO/EUVI data allows for improved polar coverage in the current cycle, and also provides a reference to assess the polar hole and open flux measurements by EIT in the past cycle. A few trends in this dataset are apparent. These data show that coronal holes, and the signed and unsigned magnetic flux measured inside the holes, exhibit distinct evolution patterns as a function of latitude near the polar regions. We also observed an asymmetry in the evolution of coronal holes in the northern and southern polar regions, consistent with observations by McIntosh et al. (2014). This asymmetry manifests itself in both the rising of the polar coronal hole coverage during Solar Cycle 23, and more distinctively in the decline and rise of polar coronal holes in Solar Cycle 24. By tracking the evolution of coronal holes across all latitudes, we see the appearance of large dominant-polarity coronal hole structures at lower latitudes, migrating toward the polar regions. While these low-latitude signatures appear at roughly identical times, their push into the polar regions occurs at differing speeds, which causes the northern polar coronal hole to establish itself much earlier. When the two cycles are compared in their early stages, the current cycle has a similar coronal hole extent and total open flux. Most significantly, in Cycle 24, the polar flux reversal exhibits a stark asymmetry compared with the last cycle. The northern polar holes have dropped off from 2009, two years ahead of the southern polar holes, and the open flux there has remained at a very low level since then, whereas the southern polar holes have recovered from the drop-off in 2013 with the open flux rising again in 2014. It remains to be seen how the differences of Cycle 24 will affect the peak distribution of coronal holes and open magnetic flux during the declining phase of Cycle 24. Finally, the observed coronal holes, directly measured open flux in these holes, and their latitude dependence have been compared with the calculation by the PFSS model using the synoptic WSO data. We showed that on the one hand, this model reproduces polar coronal holes and open flux in general agreement with observations in both cycles. On the other hand, the clear discrepancy at low latitudes confirms the results in our earlier study (Lowder et al., 2014). This discrepancy significantly contributes to the total open flux, particularly during the solar maximum. The potential field model appears to produce more open flux than observed at the low latitudes in both cycles, even though these regions are presumably better captured by the AIA/EUVI instruments in the current cycle. This comparison therefore indicates the importance of the latitude-dependent evolution of coronal hole boundaries, which provide an observational constraint to help advance models of the Sun’s global magnetic field. ## References 1. Broussard, R.M., Tousey, R., Underwood, J.H., Sheeley, N.R. Jr.: 1978, A survey of coronal holes and their solar wind associations throughout sunspot cycle 20. Solar Phys. 56, 161. DOI . ADS . 2. Cranmer, S.R.: 2009, Coronal Holes. Living Rev. Solar Phys. 6, 3. DOI . ADS . 3. Delaboudinière, J.-P., Artzner, G.E., Brunaud, J., Gabriel, A.H., Hochedez, J.F., Millier, F., Song, X.Y., Au, B., Dere, K.P., Howard, R.A., Kreplin, R., Michels, D.J., Moses, J.D., Defise, J.M., Jamar, C., Rochus, P., Chauvineau, J.P., Marioge, J.P., Catura, R.C., Lemen, J.R., Shing, L., Stern, R.A., Gurman, J.B., Neupert, W.M., Maucherat, A., Clette, F., Cugnon, P., van Dessel, E.L.: 1995, EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO mission. Solar Phys. 162, 291. DOI . ADS . 4. Harvey, K.L., Recely, F.: 2002, Polar coronal holes during cycles 22 and 23. Solar Phys. 211, 31. DOI . ADS . 5. Howard, R.A., Moses, J.D., Vourlidas, A., Newmark, J.S., Socker, D.G., Plunkett, S.P., Korendyke, C.M., Cook, J.W., Hurley, A., Davila, J.M., Thompson, W.T., St Cyr, O.C., Mentzell, E., Mehalick, K., Lemen, J.R., Wuelser, J.P., Duncan, D.W., Tarbell, T.D., Wolfson, C.J., Moore, A., Harrison, R.A., Waltham, N.R., Lang, J., Davis, C.J., Eyles, C.J., Mapson-Menard, H., Simnett, G.M., Halain, J.P., Defise, J.M., Mazy, E., Rochus, P., Mercier, R., Ravet, M.F., Delmotte, F., Auchere, F., Delaboudiniere, J.P., Bothmer, V., Deutsch, W., Wang, D., Rich, N., Cooper, S., Stephens, V., Maahs, G., Baugh, R., McMullin, D., Carter, T.: 2008, Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI). Space Sci. Rev. 136, 67. DOI . ADS . 6. Kahler, S.W., Davis, J.M., Harvey, J.W.: 1983, Comparison of coronal holes observed in soft X-ray and He i 10 830 Å spectroheliograms. Solar Phys. 87, 47. DOI . ADS . 7. King, J.H., Papitashvili, N.E.: 2005, Solar wind spatial scales in and comparisons of hourly Wind and ACE plasma and magnetic field data. J. Geophys. Res. 110, A02104. DOI . ADS . 8. Lemen, J.R., Title, A.M., Akin, D.J., Boerner, P.F., Chou, C., Drake, J.F., Duncan, D.W., Edwards, C.G., Friedlaender, F.M., Heyman, G.F., Hurlburt, N.E., Katz, N.L., Kushner, G.D., Levay, M., Lindgren, R.W., Mathur, D.P., McFeaters, E.L., Mitchell, S., Rehse, R.A., Schrijver, C.J., Springer, L.A., Stern, R.A., Tarbell, T.D., Wuelser, J.-P., Wolfson, C.J., Yanari, C., Bookbinder, J.A., Cheimets, P.N., Caldwell, D., Deluca, E.E., Gates, R., Golub, L., Park, S., Podgorski, W.A., Bush, R.I., Scherrer, P.H., Gummin, M.A., Smith, P., Auker, G., Jerram, P., Pool, P., Soufli, R., Windt, D.L., Beardsley, S., Clapp, M., Lang, J., Waltham, N.: 2012, The Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Solar Phys. 275, 17. DOI . ADS . 9. Liu, Y., Hoeksema, J.T., Scherrer, P.H., Schou, J., Couvidat, S., Bush, R.I., Duvall, T.L., Hayashi, K., Sun, X., Zhao, X.: 2012, Comparison of line-of-sight magnetograms taken by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager and Solar and Heliospheric Observatory/Michelson Doppler Imager. Solar Phys. 279, 295. DOI . ADS . 10. Lockwood, M.: 2002, Long-term variations in the open solar flux and possible links to Earth’s climate. In: Wilson, A. (ed.) From Solar Min to Max: Half a Solar Cycle with SOHO, ESA Special Publication 508, 507. ADS . 11. Lowder, C., Qiu, J., Leamon, R., Liu, Y.: 2014, Measurements of EUV coronal holes and open magnetic flux. Astrophys. J. 783, 142. DOI . ADS . 12. Mackay, D.H., Priest, E.R., Lockwood, M.: 2002a, The evolution of the Sun’s open magnetic flux—I. A single bipole. Solar Phys. 207, 291. DOI . ADS . 13. Mackay, D.H., Priest, E.R., Lockwood, M.: 2002b, The evolution of the Sun’s open magnetic flux—II. Full solar cycle simulations. Solar Phys. 209, 287. DOI . ADS . 14. Malanushenko, O.V., Jones, H.P.: 2005, Differentiating coronal holes from the quiet sun by He 1083 nm imaging spectroscopy. Solar Phys. 226, 3. DOI . ADS . 15. McIntosh, S.W., Leamon, R.J., Gurman, J.B., Olive, J.-P., Cirtain, J.W., Hathaway, D.H., Burkepile, J., Miesch, M., Markel, R.S., Sitongia, L.: 2013, Hemispheric asymmetries of solar photospheric magnetism: Radiative, particulate, and heliospheric impacts. Astrophys. J. 765, 146. DOI . ADS . 16. McIntosh, S.W., Wang, X., Leamon, R.J., Davey, A.R., Howe, R., Krista, L.D., Malanushenko, A.V., Markel, R.S., Cirtain, J.W., Gurman, J.B., Pesnell, W.D., Thompson, M.J.: 2014, Deciphering solar magnetic activity. I. On the relationship between the sunspot cycle and the evolution of small magnetic features. Astrophys. J. 792, 12. DOI . ADS . 17. McIntosh, S.W., Leamon, R.J., Krista, L.D., Title, A.M., Hudson, H.S., Riley, P., Harder, J.W., Kopp, G., Snow, M., Woods, T.N., Kasper, J.C., Stevens, M.L., Ulrich, R.K.: 2015, The solar magnetic activity band interaction and instabilities that shape quasi-periodic variability. Nat. Commun. 6, 6491. DOI . ADS . 18. Robbrecht, E., Wang, Y.-M., Sheeley, N.R. Jr., Rich, N.B.: 2010, On the “extended” solar cycle in coronal emission. Astrophys. J. 716, 693. DOI . ADS . 19. Schatten, K.H., Wilcox, J.M., Ness, N.F.: 1969, A model of interplanetary and coronal magnetic fields. Solar Phys. 6, 442. DOI . ADS . 20. Scherrer, P.H., Bogart, R.S., Bush, R.I., Hoeksema, J.T., Kosovichev, A.G., Schou, J., Rosenberg, W., Springer, L., Tarbell, T.D., Title, A., Wolfson, C.J., Zayer, I. (MDI Engineering Team): 1995, The solar oscillations investigation—Michelson Doppler Imager. Solar Phys. 162, 129. DOI . ADS . 21. Scherrer, P.H., Schou, J., Bush, R.I., Kosovichev, A.G., Bogart, R.S., Hoeksema, J.T., Liu, Y., Duvall, T.L., Zhao, J., Title, A.M., Schrijver, C.J., Tarbell, T.D., Tomczyk, S.: 2012, The Helioseismic and Magnetic Imager (HMI) investigation for the Solar Dynamics Observatory (SDO). Solar Phys. 275, 207. DOI . ADS . 22. Schrijver, C.J., De Rosa, M.L.: 2003, Photospheric and heliospheric magnetic fields. Solar Phys. 212, 165. DOI . ADS . 23. Sheeley, N.R. Jr.: 1980, The evolution of the polar coronal holes. Solar Phys. 65, 229. DOI . ADS . 24. Snodgrass, H.B.: 1983, Magnetic rotation of the solar photosphere. Astrophys. J. 270, 288. DOI . ADS . 25. Spruit, H.C.: 2011, In: Miralles, M.P., Sánchez Almeida, J. (eds.) Theories of the Solar Cycle: A Critical View, 39. ADS . 26. Thompson, M.J., Toomre, J., Anderson, E.R., Antia, H.M., Berthomieu, G., Burtonclay, D., Chitre, S.M., Christensen-Dalsgaard, J., Corbard, T., De Rosa, M., Genovese, C.R., Gough, D.O., Haber, D.A., Harvey, J.W., Hill, F., Howe, R., Korzennik, S.G., Kosovichev, A.G., Leibacher, J.W., Pijpers, F.P., Provost, J., Rhodes, E.J. Jr., Schou, J., Sekii, T., Stark, P.B., Wilson, P.R.: 1996, Differential rotation and dynamics of the solar interior. Science 272, 1300. DOI . ADS . 27. Tousey, R., Sandlin, G.D., Purcell, J.D.: 1968, On some aspects of XUV spectroheliograms. In: Kiepenheuer, K.O. (ed.) Structure and Development of Solar Active Regions, IAU Symposium 35, 411. ADS . 28. Upton, L., Hathaway, D.H.: 2014, Predicting the Sun’s polar magnetic fields with a surface flux transport model. Astrophys. J. 780, 5. DOI . ADS . 29. Wang, Y.-M.: 2009, Coronal holes and open magnetic flux. Space Sci. Rev. 144, 383. DOI . ADS . 30. Wang, Y.-M., Sheeley, N.R. Jr.: 1992, On potential field models of the solar corona. Astrophys. J. 392, 310. DOI . ADS . 31. Wang, Y.-M., Sheeley, N.R.: 2002, Sunspot activity and the long-term variation of the Sun’s open magnetic flux. J. Geophys. Res. 107, 1302. DOI . ADS . 32. Webb, D.F., Davis, J.M., McIntosh, P.S.: 1984, Observations of the reappearance of polar coronal holes and the reversal of the polar magnetic field. Solar Phys. 92, 109. DOI . ADS . 33. Yeates, A.R., Mackay, D.H., van Ballegooijen, A.A., Constable, J.A.: 2010, A nonpotential model for the Sun’s open magnetic flux. J. Geophys. Res. 115, A09112. DOI . ADS . ## Acknowledgements This work was supported by the NASA Living with a Star (LWS) program. This work uses datasets available from the SDO, STEREO, and SOHO missions. Particular thanks to Dana Longcope and Richard Canfield for discussion of this project. We also thank the referee for constructive questions and comments, which have clarified and improved this work. ## Author information Authors ### Corresponding author Correspondence to Chris Lowder. ## Ethics declarations ### Conflict of interest The authors declare that they have no conflicts of interest. ## Appendix A: Polar Latitude Determination ### Appendix A: Polar Latitude Determination In the preceding analysis, a polar boundary latitude was chosen at $${\pm}\,55~\mbox{degrees}$$. While the latitude-time profiles display variation over a continuum of latitude bins, a polar boundary value was necessary to quantify the coronal hole area and enclosed flux across specified ranges of latitudes. This appendix works through an analysis of the effects of the shifting polar boundary, providing justification for the choice of boundary. Figure 10 displays the mean radial magnetic field strength, capped at $${\pm}\,5~\mbox{G}$$. Measurements from SOHO/MDI are plotted until 22 April 2010 (marked with a dot-dashed red line), after which SDO/HMI data are mapped. To study a range of latitude values, latitudes of $${\pm}\,\{45, 50, 55, 60, 65\}~\mbox{degrees}$$ were chosen as boundaries for study, to give a wide range of values for comparison. These latitude values are marked here by blue dotted lines. During the period from 2001 – 2014, the distribution of strong polar magnetic flux remains above $${\approx}\,60~\mbox{degree}$$ latitude. However, a difference in this distribution appears for available data before 2001. Here, the distribution of polar flux appears to dip further equatorward. This difference in the extent of the polar magnetic field manifests itself in changes of the distribution of the polar open magnetic field. Figure 11 maps out the latitudinal distribution of coronal hole boundaries and the flux enclosed therein throughout the span of observed data. For comparison, latitudes of $${\pm}\,\{45, 50, 55, 60, 65\}~\mbox{degrees}$$ are plotted in dotted styles in both panels. Note that the remainder of the data here is identical to the associated panels in Figure 2. From the period 2001 – 2014, the resulting coronal hole distribution remains relatively above $${\pm}\,60~\mbox{degrees}$$ latitude. However, in the time spans 1996 – 1998 and 2011 – 2012, extensions of coronal holes dip below this, encroaching closer to $${\pm}\,55~\mbox{degrees}$$. The lower panel displays the corresponding coronal hole enclosed unsigned open magnetic flux. These extensions to lower latitudes carry a significant corresponding amount of open magnetic flux. To quantify the effects of this boundary shift, a profile of open magnetic flux was created for each polar region as defined by the ranges of boundary latitudes previously defined. From each of these profiles, the peak value of the open magnetic flux was separately computed for the range of Solar Cycles 23 and 24. Figure 12 plots these peak values of the polar open magnetic flux as a function of the choice of the polar latitude boundary. The northern and southern polar regions are plotted in red and blue, respectively. Solar Cycle 23 peaks are plotted in solid curves, with Cycle 24 shown by dashed curves. As the polar boundary is pushed further poleward, the peak polar open fluxes decline as more enclosed flux is reclassified as low-latitude flux. For both the northern and southern hemispheres of Solar Cycle 23, a more significant drop in the peak polar open magnetic flux occurs as the polar boundary pushes beyond $${\pm}\,55~\mbox{degree}$$ latitude toward the poles. This same trend does not appear for the portion of Cycle 24 data we gathered. For the coronal hole distributions of Cycle 23, moving poleward from $${\pm}\,55~\mbox{degree}$$ latitude begins a significant drop in the peak open magnetic flux. These analyses suggest that a polar boundary of $${\pm}\,55~\mbox{degree}$$ latitude provides a balanced choice. It allows for capture of polar open flux during more standard periods of coronal hole activity, while also providing a buffer to capture extensions into slightly lower latitudes without being integrated into lower latitude profiles. ## Rights and permissions Reprints and Permissions Lowder, C., Qiu, J. & Leamon, R. Coronal Holes and Open Magnetic Flux over Cycles 23 and 24. Sol Phys 292, 18 (2017). https://doi.org/10.1007/s11207-016-1041-8	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8708111047744751, "perplexity": 3792.5997697330645}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991650.73/warc/CC-MAIN-20210518002309-20210518032309-00085.warc.gz"}
http://math.stackexchange.com/questions/34842/name-of-formula-x3y3-z31/34844	# Name of Formula $x^3+y^3=z^3+1$ I encountered the formula $$x^3+y^3=z^3+1$$ with the condition, that $$x<y<z$$ and wonder, whether it has got a specific name or whether it can be easily transformed into another well-known (family of) formula(s). - Hi T.K.. How did you come upon this formula? The set of $(x,y,z)$ which satisfy your conditions is some subset of $\mathbb{R}^3$. Your condition is cone-like, so the set $\{(x,y,z):x^3+y^3 = z^3 + 1\}$ is contained in a kind of cone. – Glen Wheeler Apr 24 '11 at 20:10 In a programming class this formula was part of the task: Write a program, that calculates the first 18 sets of $(x,y,z)\in\mathbb{R}^+$, which satisfy the formula and the condition, ordered by increasing $x$. – Torbjoern Apr 25 '11 at 10:19 @T.K.: I am not sure because I have yet to encounter equations personally yet, but I do run across things from time to time and this looked familiar when I seen it. I am thinking that this could be an example of a Diophantine equations, but like I said not sure so don't take that as a for sure. Might want to give this a look. [1] (en.wikipedia.org/wiki/Diophantine_equation) – night owl Apr 26 '11 at 7:20 It looks like the equation for a one-sheet hyperboloid. – please delete me Apr 26 '11 at 7:23 @nightowl: I think, the term Diphantine equations is the thing I was looking for. Thank you very much for this answer/comment. – Torbjoern Apr 26 '11 at 15:35 Have a look at http://www.mathpages.com/home/kmath071.htm There you will find $$(1\pm9m^3)^3+(9m^4)^3+(-9m^4\pm3m)^3=1$$ and another similar-but-more-complicated formula, also it says it is known that there are infinitely many such formulas, and it is not known whether every solution is part of such an infinite family. - Thank you for this link and for the formula. All elements of the set $\{(x,y,z), x<y<z:x3+y3=z3+1\}$ I already found, satisfy this equation. – Torbjoern Apr 26 '11 at 15:40 $$X^3+ Y^3+ Z^3=1$$ is the formula which is known as harder factor and yours is a distorted and conditional form of harder factor If $X+Y+Z=0$ then $X^3+ Y^3+ Z^3=1$. In your question $X$ is less than $Y$ and $Y$ is less than $Z$ means the minimum possible difference between $X$ and $Y$, $Y$ and $Z$ is $1$. At the same time the minimum possible difference between $X$ and $Z$ will be $2$. So there will in all the cases except $X=-2$, $Y=-1$, $Z=3$ where $X+Y+Z$ is not equal to zero then it must be that $X^3+ Y^3+ Z^3$ is not equal to $1$. So $X^3+ Y^3+ Z^3$ must be greater/less than $1$. As it is given that $Z>Y>X$ then $X^3+ Y^3$ must be unequal to $Z^3$. It means $X^3+ Y^3$ may be equal to $Z^3+1$. In this way $X^3+ Y^3+ Z^3=1$ is related to the question asked by the poster - Maybe you want to give any reference to this? Searching for "harder factor" doesn't yield anything interesting on google & co. – Listing Apr 24 '11 at 10:28 I don't see how this is related to the original question. Could you please elaborate? – t.b. Apr 24 '11 at 13:16 This is very wrong. Among other issues, $X$,$Y$, and $Z$ are not integers! – Glen Wheeler Apr 24 '11 at 19:58 @GlenWheeler: He's right, that $X$, $Y$ and $Z$ are integers --- at least in the formula I encountered. – Torbjoern Apr 25 '11 at 10:22 @T.K. Ok, but then you should mention this in the question and should not use $\mathbb{R}$. This is the set of real numbers. – Glen Wheeler Apr 25 '11 at 10:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8749140501022339, "perplexity": 200.70240536722292}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398453805.6/warc/CC-MAIN-20151124205413-00257-ip-10-71-132-137.ec2.internal.warc.gz"}
http://www.computer.org/csdl/trans/tc/2009/02/ttc2009020287.html	Correction to "Reduced Length Checking Sequences" FEBRUARY 2009 (Vol. 58, No. 2) pp. 287-287 Correction to "Reduced Length Checking Sequences" R.M. Hierons, IEEE Member H. Ural The paper [ 1 ] describes improvements on the algorithm from [ 2 ], which produces a checking sequence from a finite state machine that has a known distinguishing sequence . However, while the improvements described in [ 1 ] are valid, the final step of the checking sequence generation algorithm was not included and we outline this step here. The algorithm in [ 1 ] produces a directed graph and then generates a tour of such that contains certain edges. Checking sequence generation is thus represented in terms of the rural Chinese postman problem. The checking sequence is produced by starting at vertex . However, in contrast to [ 2 ], in doing this we may fail to check the final transition in the tour and, if this is the case, then we need to add a distinguishing sequence to the end of the sequence produced by [ 1 ]. We can thus produce a checking sequence from in the following way: We choose an edge from such that represents a transition test for a transition that ends at the initial state of . We replace by the corresponding sequence of edges from to form a tour . Let denote a walk produced by starting with and let be the label of . We return the input/output sequence that forms our checking sequence. Although both [ 1 ] and [ 2 ] correctly state that the algorithm of [ 2 ] should start a tour at the vertex , instead, in the examples, [ 1 ] started it at . As a result, [ 1 ] did not apply the algorithm of [ 2 ] correctly to the example and should have given the checking sequence The corrected algorithm of [ 1 ] returns the checking sequence of length 64 (rather than one of length 61 reported). R.M. Hierons is with the School of Information Systems, Computing, and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK. E-mail: rob.hierons@brunel.ac.uk. H. Ural is with the School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada. E-mail: ural@site.uottawa.ca, ural@sci.uottawa.ca. Manuscript received 13 Nov. 2006; accepted 23 Jan. 2007; published online 15 Sept. 2008. Recommended for acceptance by B. Bose. For information on obtaining reprints of this article, please send e-mail to: tc@computer.org, and reference IEEECS Log Number TC-0432-1106. Digital Object Identifier no. 10.1109/TC.2008.173. x	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.884644627571106, "perplexity": 1092.1390467370002}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657118950.27/warc/CC-MAIN-20140914011158-00332-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}
https://alanzed.wordpress.com/2009/03/10/limits/	## Limits Tonight, I was reading about the fundamental definition of limits of functions, and for the first time, really understood it. The context was a limit in multiple variables, as $\displaystyle\lim_{(x,y)\to (0,0)}f(x,y) = L$ The interesting issue is that in two dimensions like this, showing the limit exists is harder than one dimensions, since there are infinitely many ways to approach (a,b). The definition for continuity becomes, $f(x,y)$ is continuous at the point $(a,b)$ if the limit exists and is $f(a,b)$, or $\displaystyle\lim_{(x,y)\to (a,b)}f(x,y) = f(a,b)$ Somehow, I never fully understood the 1D case until I saw the explaination and example in 2D.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9929900765419006, "perplexity": 254.90015610390898}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423785.29/warc/CC-MAIN-20170721142410-20170721162410-00123.warc.gz"}
http://groupprops.subwiki.org/wiki/Verbal_subgroup	Verbal subgroup This article defines a subgroup property related to (or which arises in the context of): geometric group theory View other subgroup properties related to geometric group theory\|View other terms related to geometric group theory \| View all subgroup properties This article defines a subgroup property related to (or which arises in the context of): combinatorial group theory \|View other terms related to combinatorial group theory \| View all subgroup properties History The notion of verbal subgroup was introduced in the study of free groups in combinatorial group theory. Definition Definition in terms of words and word maps Let be a collection of words (or expressions in terms of the group operations, in unknown variables). Define the span of in a group as the collection of elements of which are realized from words in by substituting, for the variables, elements of . In other words, the span of is defined as the union of the images of the word maps for every word in . A subgroup of is termed verbal if it satisfies the following equivalent conditions: • It is generated by the span of a collection of words • It is itself the span of a collection of words Definition in terms of varieties Let be a subvariety of the variety of groups. The verbal subgroup corresponding to is the unique smallest normal subgroup of such that . is a verbal subgroup of if it is a verbal subgroup corresponding to some subvariety of the variety of groups. Equivalence of definitions Further information: equivalence of definitions of verbal subgroup Examples Extreme examples • The trivial subgroup is a verbal subgroup corresponding to the word that just gives the identity element. • The whole group is a verbal subgroup corresponding to the word in one letter that's just that letter, i.e., the word . Typical examples of verbal subgroups Verbal subgroup Corresponding word or words Corresponding variety of groups derived subgroup (also called abelianization) commutator of two elements, i.e., (if using left action convention) abelian groups member of lower central series the member corresponds to the word nilpotent groups of class at most member of derived series commutator of two words, each of which is a commutator of two words, and so on, done times. Total of variables. solvable groups of derived length at most . Subgroups generated by powers, for fixed , are also examples of verbal subgroups. all products of powers Since every word is essentially a combination of commutator and power operations, these are somewhat representative examples of verbal subgroups. In an abelian group In an abelian group, the only verbal subgroups are the sets of powers for different integer values of . Note that gives the trivial subgroup and gives the whole group. For full proof, refer: Verbal subgroup equals power subgroup in abelian group Examples of subgroups satisfying the property Here are some examples of subgroups in basic/important groups satisfying the property: Here are some examples of subgroups in relatively less basic/important groups satisfying the property: Here are some examples of subgroups in even more complicated/less basic groups satisfying the property: Examples of subgroups not satisfying the property Here are some examples of subgroups in basic/important groups not satisfying the property: Here are some some examples of subgroups in relatively less basic/important groups not satisfying the property: Here are some examples of subgroups in even more complicated/less basic groups not satisfying the property: Metaproperties Metaproperty name Satisfied? Proof Statement with symbols transitive subgroup property Yes verbality is transitive If are groups such that is a verbal subgroup of and is a verbal subgroup of , then is a verbal subgroup of . quotient-transitive subgroup property Yes verbality is quotient-transitive If are groups such that is a verbal subgroup of and is a verbal subgroup of , then is a verbal subgroup of . finite direct power-closed subgroup property Yes verbality is finite direct power-closed If is a verbal subgroup of and is a positive integer, then in the direct power , the subgroup is verbal. direct power-closed subgroup property No verbality is not direct power-closed It is possible to have a group , a verbal subgroup of , and a cardinal such that the direct power is not verbal in . finite-intersection-closed subgroup property No verbality is not finite-intersection-closed it is possible to have a group and verbal subgroups of such that the intersection is not verbal. strongly join-closed subgroup property Yes verbality is strongly join-closed Suppose is a group and are all verbal subgroups of . Then, the join of subgroups is also a verbal subgroup of . image condition Yes verbality satisfies image condition Suppose is a group and is a verbal subgroup. Suppose is a homomorphism of groups. Then, is a verbal subgroup of . Relation with other properties Stronger properties Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions commutator-verbal subgroup a verbal subgroup where all the words are described in terms of the commutator symbol \| verbal subgroup of finite group the whole group is a finite group Verbal subgroup of finite type\|FULL LIST, MORE INFO verbal subgroup of finite type it is a union of the images of finitely many word maps Template:Inermediate notions short verbal subgroup of finitely generated type it is generated by the union of the images of finitely many word maps \| member of the lower central series (finite part) member of the derived series (finite part) Weaker properties Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions intersection of finitely many verbal subgroups can be expressed as an intersection of a finite number of verbal subgroups \| quasiverbal subgroup similar definition, replacing "variety" with "quasivariety" (see quasivarietal group property) \| pseudoverbal subgroup similar definition, replacing "variety" with "pseudovariety" (see pseudovarietal group property) \| existentially bound-word subgroup subgroup described by a set of equations quantified existentially in all other variables verbal implies existentially bound-word existentially bound-word not implies verbal image-closed fully invariant subgroup under any surjective homomorphism from the whole group, the image of the subgroup is fully invariant in the target group verbal implies image-closed fully invariant image-closed fully invariant not implies verbal \| fully invariant subgroup (also called fully characteristic subgroup) invariant under all endomorphisms verbal implies fully invariant fully invariant not implies verbal (see also list of examples) Existentially bound-word subgroup, Image-closed fully invariant subgroup, Intersection of finitely many verbal subgroups, Pseudoverbal subgroup, Quasiverbal subgroup, Quotient-subisomorph-containing subgroup, Weakly image-closed fully invariant subgroup\|FULL LIST, MORE INFO image-closed characteristic subgroup under any surjective homomorphism from the whole group, the image of the subgroup is characteristic in the target group (via image-closed fully invariant) (via image-closed fully invariant) Image-closed fully invariant subgroup\|FULL LIST, MORE INFO characteristic subgroup invariant under all automorphisms (via fully invariant) (via fully invariant) Bound-word subgroup, Finite direct power-closed characteristic subgroup, Fully invariant subgroup, Image-closed characteristic subgroup, Image-closed fully invariant subgroup, Intersection of finitely many verbal subgroups, Pseudoverbal subgroup, Quasiverbal subgroup, Quotient-subisomorph-containing subgroup, Weakly image-closed characteristic subgroup, Weakly image-closed fully invariant subgroup\|FULL LIST, MORE INFO strictly characteristic subgroup invariant under all surjective endomorphisms (via fully invariant) (via fully invariant) Bound-word subgroup, Existentially bound-word subgroup, Fully invariant subgroup, Quotient-subisomorph-containing subgroup\|FULL LIST, MORE INFO normal subgroup invariant under all inner automorphisms (via characteristic) (via characteristic) Bound-word subgroup, Characteristic subgroup, Finite direct power-closed characteristic subgroup, Fully invariant subgroup, Image-closed characteristic subgroup, Intersection of finitely many verbal subgroups, Normal-potentially verbal subgroup, Potentially fully invariant subgroup, Weakly image-closed characteristic subgroup, Weakly image-closed fully invariant subgroup\|FULL LIST, MORE INFO	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 73, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8690080046653748, "perplexity": 1979.4465714830746}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721174.97/warc/CC-MAIN-20161020183841-00162-ip-10-171-6-4.ec2.internal.warc.gz"}
https://calculator.academy/gross-distribution-calculator/	Enter the net distribution and the tax rate into the calculator to determine a gross distribution. ## Gross Distribution Formula The following formula is used to calculate a gross distribution. GD = ND / (1 - T) • Where GD is the gross distribution • ND is the net distribution • T is the tax rate To calculate the gross distribution, divide the net distribution by 1 minus the tax rate. ## Gross Distribution Definition A gross distribution is defined as the total value of distribution before taxes have been paid. ## Are gross distribution taxable? Yes, all gross distribution is subject to tax. The tax that is paid on a gross distribution depends on several factors including the total amount and the length that the distribution has been held. ## Gross Distribution Example How to calculate a gross distribution? 1. First, determine the net distribution. Calculate the net distribution that was taken home after taxes. 2. Next, determine the tax rate. Calculate or determine the total percentage tax rate. 3. Finally, calculate the gross distribution. Using the formula above, calculate the gross distribution. ## FAQ What is a gross distribution? A gross distribution is a measure of the total distribution paid out to an investor before taxes have been withdrawn.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9648821353912354, "perplexity": 2810.3129785716396}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499713.50/warc/CC-MAIN-20230129112153-20230129142153-00060.warc.gz"}