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, .\nSuppose that we have 3 coins. The coins are tossed, yielding the data in the following table:\nHeads Tails\nCoin 1 29 21\nCoin 2 23 17\nCoin 3 42 18\n1. Test the null hypothesis that all 3 coin are fair.\n3 2\n2. Test the null hypothesis that coin 1 has probability of heads ; coin 2 is fair; and coin 3 has probabi... | large_corpus_distillation |
"Defence in depth (non-military)-Examples-Nuclear In nuclear engineering and nuclear safety, all safety activities, whether organizational, behavioural or equipment related, are subject to layers of overlapping provisions, so that if a failure should occur it would be compensated for or corrected without causing harm t... | large_corpus_distillation |
"Linear independence-Linear independence-In the theory of vector spaces, a set of vectors is said to be linearly independent if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be linearly dependent. These concept... | large_corpus_distillation |
"Proof by contradiction-Relationship with other proof techniques-The laws of excluded middle and non-contradiction together mean that exactly one of P and \u00acP is true." | large_corpus_distillation |
Security\u201d Best Student Paper Award - Kexin Qiao, Lei Hu and Siwei Sun, \u201cDifferential Security Evaluation of Simeck with Dynamic Key-guessing Techniques\u201d ICISSP 2015 \u2013 ESEO, Angers, Loire Valley, France Proceedings of the 1st International Conference on Information Systems Security and Privacy . ISBN... | large_corpus_distillation |
"Information content-Relationship to entropy-The Shannon entropy of the random variable X above is defined as by definition equal to the expected information content of measurement of X .:\u200a11\u200a:\u200a19\u201320\u200a The expectation is taken over the discrete values over its support. Sometimes, the entropy ... | large_corpus_distillation |
source to be truly in the public domain, the proper rights must be granted by the individual or organization which digitized and edited the original source of the image." | large_corpus_distillation |
flattens a tree from left to right, and even sortBy :: (a -> a -> Bool) -> List a -> List a, which sorts a list based on a provided comparison function." | large_corpus_distillation |
"Bootstrapping (statistics)-Types of bootstrap scheme-Case resampling The bootstrap is generally useful for estimating the distribution of a statistic (e.g. mean, variance) without using normality assumptions (as required, e.g., for a z-statistic or a t-statistic). In particular, the bootstrap is useful when there is n... | large_corpus_distillation |
"Context-free grammar-Linguistic applications-Chomsky initially hoped to overcome the limitations of context-free grammars by adding transformation rules.Such rules are another standard device in traditional linguistics; e.g. passivization in English. Much of generative grammar has been devoted to finding ways of refin... | large_corpus_distillation |
during free recall is when subjects learn several different lists followed by recall tests, and then a final unexpected recall test at the end of the experiment where they are required to recall as many items as possible from all of the lists. Results show that participants tend to recall items from the more recent lis... | large_corpus_distillation |
to converge to Z with probability 1 (WP1) if\n}\nPr{\u03c9\u2208\u03a9: lim Z (\u03c9)=Z(\u03c9)} =1 (1.5.21)\nn\nn\u2192\u221e\nThe condition Pr{\u03c9\u2208\u03a9:lim n\u2192\u221e Z n (\u03c9)=Z(\u03c9)}=1 is often stated more compactly as Pr{lim n Z n =Z}=1, and even\nmore compactly as lim n Z n =Z WP1, but the for... | large_corpus_distillation |
"Dempster\u2013Shafer theory-Overview-Dempster\u2013Shafer theory is a generalization of the Bayesian theory of subjective probability. Belief functions base degrees of belief (or confidence, or trust) for one question on the subjective probabilities for a related question. The degrees of belief themselves may or may n... | large_corpus_distillation |
"Cluster analysis-Algorithms-For high-dimensional data, many of the existing methods fail due to the curse of dimensionality, which renders particular distance functions problematic in high-dimensional spaces. This led to new clustering algorithms for high-dimensional data that focus on subspace clustering (where only ... | large_corpus_distillation |
"Oblivious transfer-1\u20132 oblivious transfer-Alice combines v with both of her random values to produce: mod N and mod N . Now kb will be equal to k and the other will be a meaningless random value. However since Alice does not know the value of b that Bob chose, she cannot determine which of k0 and k1 is eq... | large_corpus_distillation |
"Ar (Unix)-File format details-System V ar uses the special filename \"/\" to denote that the following data entry contains a symbol lookup table, which is used in ar libraries to speed up access. This symbol table is built in three parts which are recorded together as contiguous data.\nA 32-bit big endian integer, giv... | large_corpus_distillation |
website. Many of them are also not supported by popular third-party implementations of PDF." | large_corpus_distillation |
"Boolean function-Analysis-Cryptographic analysis The Walsh transform of a Boolean function is a k-ary integer-valued function giving the coefficients of a decomposition into linear functions (Walsh functions), analogous to the decomposition of real-valued functions into harmonics by the Fourier transform. Its square i... | large_corpus_distillation |
"Robustification-Principles-This basic principle underlies all robustification, but in practice there are typically a number of inputs and it is the suitable point with the lowest gradient on a multi-dimensional surface that must be found.\nNon-constant variability Consider a case where an output Z is a function of two... | large_corpus_distillation |
"Random oracle-Random oracle-Random oracles as a mathematical abstraction were first used in rigorous cryptographic proofs in the 1993 publication by Mihir Bellare and Phillip Rogaway (1993). They are typically used when the proof cannot be carried out using weaker assumptions on the cryptographic hash function. A syst... | large_corpus_distillation |
"Long code (mathematics)-Definition-This string has length 2n=22k The Walsh-Hadamard code is a subcode of the long code, and can be obtained by only using functions fi that are linear functions when interpreted as functions F2k\u2192F2 on the finite field with two elements. Since there are only 2k such functions, t... | large_corpus_distillation |
"Groupoid-Definitions-Vertex groups and orbits Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G(x,x), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in ... | large_corpus_distillation |
List<int>> are valid types, however are advised against for member signatures in code analysis design rules..NET allows six varieties of generic type constraints using the where keyword including restricting generic types to be value types, to be classes, to have constructors, and to implement interfaces. Below is an e... | large_corpus_distillation |
"Sidorenko's conjecture-Statement-Equivalent formulation Sidorenko's property is equivalent to the following reformulation: For all graphs G , if G has n vertices and an average degree of pn , then t(H,G)\u2265p|E(H)| .This is equivalent because the number of homomorphisms from K2 to G is twice the number of edg... | large_corpus_distillation |
"Hamming code-History-Such codes cannot correctly repair all errors, however. In our example, if the channel flips two bits and the receiver gets 001, the system will detect the error, but conclude that the original bit is 0, which is incorrect. If we increase the size of the bit string to four, we can detect all two-b... | large_corpus_distillation |
"Secure messaging-Secure messaging-Secure messaging is a server-based approach to protect sensitive data when sent beyond the corporate borders, and it provides compliance with industry regulations such as HIPAA, GLBA and SOX. Advantages over classical secure e-mail are that confidential and authenticated exchanges can... | large_corpus_distillation |
distribution is symmetric, by considering the distribution of values above and below the median Zheng and Gastwirth have argued that 2n(m\u2212as) where n is the sample size, is distributed as a t distribution." | large_corpus_distillation |
"Ambiguous grammar-Inherently ambiguous languages-While some context-free languages (the set of strings that can be generated by a grammar) have both ambiguous and unambiguous grammars, there exist context-free languages for which no unambiguous context-free grammar can exist. Such languages are called inherently ambig... | large_corpus_distillation |
"P (complexity)-Relationships to other classes-Another generalization of P is P/poly, or Nonuniform Polynomial-Time. If a problem is in P/poly, then it can be solved in deterministic polynomial time provided that an advice string is given that depends only on the length of the input. Unlike for NP, however, the polynom... | large_corpus_distillation |
(NP over N' over N) to describe undetermined nominals that function as NPs, instead introducing a determination construction that requires ('asks for') a non-maximal nominal sister and a lexical 'maximality' feature for which plural and mass nouns are unmarked. BCG also offers a unification-based representation of 'arg... | large_corpus_distillation |
these ages are not exact to when every child will develop these skills." | large_corpus_distillation |
"Books on cryptography-List-Significant books Significant books on cryptography include: Aumasson, Jean-Philippe (2017), Serious Cryptography: A Practical Introduction to Modern Encryption. No Starch Press, 2017, ISBN 9781593278267.[1] Presents modern cryptography in a readable way, suitable for practitioners, software... | large_corpus_distillation |
"Software security assurance-Building in security-Security testing Software security testing, which includes penetration testing, confirms the results of design and code analysis, investigates software behaviour, and verifies that the software complies with security requirements. Special security testing, conducted in ... | large_corpus_distillation |
"Birthday problem-Approximations-According to the approximation, the same approach can be applied to any number of \"people\" and \"days\". If rather than 365 days there are d, if there are n persons, and if n \u226a d, then using the same approach as above we achieve the result that if p(n, d) is the probability that ... | large_corpus_distillation |
"Denotational semantics-Historical development-Things become more difficult in modelling programs with local variables. One approach is to no longer work with domains, but instead to interpret types as functors from some category of worlds to a category of domains. Programs are then denoted by natural continuous functi... | large_corpus_distillation |
"Jordan normal form-Overview-Notation Some textbooks have the ones on the subdiagonal; that is, immediately below the main diagonal instead of on the superdiagonal. The eigenvalues are still on the main diagonal.\nMotivation An n \u00d7 n matrix A is diagonalizable if and only if the sum of the dimensions of the eigens... | large_corpus_distillation |
"Factored language model-Factored language model-An FLM provides the probabilistic model P(f|f1,...,fN) where the prediction of a factor f is based on N parents {f1,...,fN} . For example, if w represents a word token and t represents a Part of speech tag for English, the expression P(wi|wi\u22122,wi\u22121,ti\u2... | large_corpus_distillation |
"Input enhancement (computer science)-String matching-Because of the necessity of more efficient string matching algorithms, several faster algorithms have been developed, with most of them utilizing the idea of input enhancement. The key is preprocessed to gather information about what to look for in the text and that... | large_corpus_distillation |
"Feedback arc set-Applications-Several problems involving finding rankings or orderings can be solved by finding a feedback arc set on a tournament graph, a directed graph with one edge between each pair of vertices. Reversing the edges of the feedback arc set produces a directed acyclic graph whose unique topological ... | large_corpus_distillation |
Z/4Z={0\u00af,1\u00af,2\u00af,3\u00af} with the following operations: The sum x\u00af+y\u00af in Z/4Z is the remainder when the integer x + y is divided by 4 (as x + y is always smaller than 8, this remainder is either x + y or x + y \u2212 4). For example, 2\u00af+3\u00af=1\u00af and 3\u00af+3\u00af=2\u00af.\nThe ... | large_corpus_distillation |
for with the help of the quadratic formula gives the result.\n1\u2212\u03b1 r= 1\nIn practice, the equal-tailed confidence interval in part (a) of (2), obtained by setting , is the one that is always used.\n2\nr\u21911 1\u2212\u03b1 r\u21930\nAs , the right enpoint converges to the confidence upper bound in part (b), a... | large_corpus_distillation |
"Honey encryption-Honey encryption-Honey encryption is a type of data encryption that \"produces a ciphertext, which, when decrypted with an incorrect key as guessed by the attacker, presents a plausible-looking yet incorrect plaintext password or encryption key.\" " | large_corpus_distillation |
"Pretail-Pretail as a competitive advantage-Supply chain and finance Product development costs are pushed down, more and more people can start their own business, create goods, and provide services to broader audiences. By being able to measure demand before mass production is started allows companies to forecast finan... | large_corpus_distillation |
"MICKEY-Protection in Scan Chain-He can SCAN-IN and SCAN-OUT vectors as per his choice.To hide the mapping between the scan cells and the actual variables of a cipher is what drove the previous single-feedback and Double-Feedback XOR-Chain schemes. As this is also falling prey to cryptanalysis, as shown in the previous... | large_corpus_distillation |
"Machinist square-Accuracy checking and calibration-The simplest method of checking a low grade square for accuracy is to draw a line across a board with a flat face and straight edge (illustrated). Then flip the square over 180 degrees and check if the blade aligns with the line just drawn. Any error is multiplied by ... | large_corpus_distillation |
it may be possible to sort a partial order using a number of comparisons that is better than this analysis would suggest, because it may not be possible for this worst-case behavior to occur at each step of a sorting algorithm. In this direction, it has been conjectured that log\u03c6E comparisons may suffice, where \u... | large_corpus_distillation |
"Polynomial regression-Alternative approaches-Polynomial regression is one example of regression analysis using basis functions to model a functional relationship between two quantities. More specifically, it replaces x\u2208Rdx in linear regression with polynomial basis \u03c6(x)\u2208Rd\u03c6 , e.g. [1,x]\u2192\u0... | large_corpus_distillation |
"RAMP Simulation Software for Modelling Reliability, Availability and Maintainability-RAMP Model Builder-Repair trades repair condition Repair trades can be specified for the repair of any element, and they represent manpower in the form of a set of skilled maintenance workers with a particular trade. A repair trade ca... | large_corpus_distillation |
"Singular value-Inequalities about singular values-See also.\nSingular values of sub-matrices For A\u2208Cm\u00d7n." | large_corpus_distillation |
"Abstract syntax tree-Application in compilers-An AST usually contains extra information about the program, due to the consecutive stages of analysis by the compiler. For example, it may store the position of each element in the source code, allowing the compiler to print useful error messages.ASTs are needed because o... | large_corpus_distillation |
sentences created using the artificial grammar. The control group is given a number of random strings made up of the same letters, but not following the rules of the artificial grammar. Both groups are told that they are doing a memory task, and must memorize the letter strings and then reproduce them. In the test phas... | large_corpus_distillation |
"Cheque-Cheque fraud-Embezzlement Taking advantage of the float period (cheque kiting) to delay the notice of non-existent funds. This often involves trying to convince a merchant or other recipient, hoping the recipient will not suspect that the cheque will not clear, giving time for the fraudster to disappear.\nForge... | large_corpus_distillation |
"Dedekind\u2013MacNeille completion-Algorithms-Several researchers have investigated algorithms for constructing the Dedekind\u2013MacNeille completion of a finite partially ordered set. The Dedekind\u2013MacNeille completion may be exponentially larger than the partial order it comes from, and the time bounds for such... | large_corpus_distillation |
"Mixture model-Structure-Mathematically, a basic parametric mixture model can be described as follows: number of mixture components number of observations parameter of distribution of observation associated with component mixture weight, i.e., prior probability of a particular component -dimensional vector composed o... | large_corpus_distillation |
"Riesel Sieve-Progress-At the start of the project in August 2003, there were 101 k less than 509,203 for which no prime k \u00d7 2n \u2212 1 was known. As of May 2018, 52 of these k had been eliminated by Riesel Sieve or outside persons; the largest prime found by this project is 502,573 \u00d7 27,181,987 \u2212 1 of ... | large_corpus_distillation |
"Kirkman's schoolgirl problem-Generalization-The problem can be generalized to n girls, where n must be an odd multiple of 3 (that is mod 6) ), walking in triplets for {\\textstyle {\\frac {1}{2}}(n-1)} days, with the requirement, again, that no pair of girls walk in the same row twice. The solution to this general... | large_corpus_distillation |
"Topographical code-Examples-Only the first of these is a system dedicated only to topography. The others are more generalized systems that contain topographic axes.\nNomina Anatomica (updated to Terminologia Anatomica) ICD-O SNOMED MeSH (the 'A' axis) " | large_corpus_distillation |
where n(\u03bb)=\u2211i(i\u22121)\u03bbi=\u2211i(\u03bbi\u20322) for the conjugate partition \u03bb\u2032 Skew shape formula There is a generalization of this formula for skew shapes, s\u03bb/\u03bc(1,t,t2,\u22ef)=\u2211S\u2208E(\u03bb/\u03bc)\u220f(i,j)\u2208\u03bb\u2216St\u03bbj\u2032\u2212i1\u2212th(i,j) where the... | large_corpus_distillation |
"Gilbert\u2013Varshamov bound for linear codes-Gilbert\u2013Varshamov bound theorem-Let \u0394(m1,m2) be a Hamming distance of two messages m1 and m2 . Then for any message m , we have: wt \u2061(m)=\u0394(0,m) . Therefore: Pr random G(mG=y) Due to the randomness of G , mG is a uniformly random vector from Fqn... | large_corpus_distillation |
"Unique sink orientation-In simple polytopes-A simple d-dimensional polytope is a polytope in which every vertex has exactly d incident edges. In a unique-sink orientation of a simple polytope, every subset of k incoming edges at a vertex v determines a k-dimensional face for which v is the unique sink. Therefore, the ... | large_corpus_distillation |
"Matroid-Examples-Other matroids on graphs were discovered subsequently: The bicircular matroid of a graph is defined by calling a set of edges independent if every connected subset contains at most one cycle." | large_corpus_distillation |
"Bayesian quadrature-Bayesian quadrature-Bayesian quadrature consists of specifying a prior distribution over f , conditioning this prior on f(x1),\u2026,f(xn) to obtain a posterior distribution f , then computing the implied posterior distribution on \u03bd[f] . The name \"quadrature\" comes from the fact that the... | large_corpus_distillation |
"Wasserstein GAN-Wasserstein GAN-The Wasserstein Generative Adversarial Network (WGAN) is a variant of generative adversarial network (GAN) proposed in 2017 that aims to \"improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperpara... | large_corpus_distillation |
"Cone (formal languages)-Cone (formal languages)-In formal language theory, a cone is a set of formal languages that has some desirable closure properties enjoyed by some well-known sets of languages, in particular by the families of regular languages, context-free languages and the recursively enumerable languages. Th... | large_corpus_distillation |
"XML framework-XML framework-An XML framework is a Software framework that implements features to aid the programmer in creating applications with all data produced in XML. The programmer defines and produces pure data in XML format and the framework transforms the document to any format desired. One code, one XML and ... | large_corpus_distillation |
"SHA-3-Design-In SHA-3, the state S consists of a 5 \u00d7 5 array of w-bit words (with w = 64), b = 5 \u00d7 5 \u00d7 w = 5 \u00d7 5 \u00d7 64 = 1600 bits total. Keccak is also defined for smaller power-of-2 word sizes w down to 1 bit (total state of 25 bits). Small state sizes can be used to test cryptanalytic attack... | large_corpus_distillation |
"5000 (number)-Selected numbers in the range 5001\u20135999-5281 \u2013 super-prime, twin prime with 5279 5282 - used in various paintings by Thomas Kinkade 5292 \u2013 Kaprekar number 5300 to 5399 5303 \u2013 Sophie Germain prime, balanced prime 5329 = 732, centered octagonal number 5333 \u2013 Sophie Germain prime 53... | large_corpus_distillation |
"Homoglyph-Multi-letter homoglyphs-Some other combinations of letters look similar, for instance rn looks similar to m, cl looks similar to d, and vv looks similar to w.\nIn certain narrow-spaced fonts (such as Tahoma), placing the letter c next to a letter such as j, l or i will create a homoglyph, such as cj cl ci (g... | large_corpus_distillation |
Let f:Rn\u2192R be a smooth function. We define the 1-form df on U for p\u2208U and vp\u2208Rpn by := Df|p(v) , where Df|p:Rn\u2192R is the total derivative of f at p . (Recall that the total derivative is a linear transformation.) Of particular interest are the projection maps (also known as coordinate functi... | large_corpus_distillation |
"Rectangle-Formulae-If a rectangle has length \u2113 and width w it has area A=\u2113w it has perimeter P=2\u2113+2w=2(\u2113+w) each diagonal has length d=\u21132+w2 and when \u2113=w , the rectangle is a square." | large_corpus_distillation |
"Address space layout randomization-Implementations-The randomization can be disabled for a specific process by changing its execution domain, using personality(2)." | large_corpus_distillation |
"Formal Aspects of Computing-Formal Aspects of Computing-Formal Aspects of Computing (FAOC) is a peer-reviewed scientific journal published by Springer Science+Business Media, covering the area of formal methods and associated topics in computer science. The editor-in-chief is Jim Woodcock. According to the Journal Cit... | large_corpus_distillation |
"P-group-Properties-Every p-group is periodic since by definition every element has finite order." | large_corpus_distillation |
"Handle leak-Causes-An example of this might be retrieving a handle to the display device. Programmers might use this handle to check some property (e.g. querying the supported resolutions), and then simply proceed on without ever releasing the handle. If the handle was just a pointer to some data structure with no add... | large_corpus_distillation |
"Recurrence relation-Applications-Economics Recurrence relations, especially linear recurrence relations, are used extensively in both theoretical and empirical economics. In particular, in macroeconomics one might develop a model of various broad sectors of the economy (the financial sector, the goods sector, the labo... | large_corpus_distillation |
ending -\u00f8 Fourth feminine declension (feminine i-/e-stem declension); ending -e, genitive plural ending -ihNeuter: First neuter declension; ending -a Neuter o-/e-stem declension Neuter n-stem declension Neuter s-stem declension Neuter t-stem declension Second neuter declension (neuter a-stem declension); ending -e... | large_corpus_distillation |
"Cycles per instruction-Explanation-Let us assume a classic RISC pipeline, with the following five stages: Instruction fetch cycle (IF).\nInstruction decode/Register fetch cycle (ID).\nExecution/Effective address cycle (EX).\nMemory access (MEM)." | large_corpus_distillation |
"Load (computing)-CPU load vs CPU utilization-The comparative study of different load indices carried out by Ferrari et al. reported that CPU load information based upon the CPU queue length does much better in load balancing compared to CPU utilization. The reason CPU queue length did better is probably because when a... | large_corpus_distillation |
"Bland's rule-Extensions to oriented matroids-In the abstract setting of oriented matroids, Bland's rule cycles on some examples. A restricted class of oriented matroids on which Bland's rule avoids cycling has been termed \"Bland oriented matroids\" by Jack Edmonds. Another pivoting rule, the criss-cross algorithm, av... | large_corpus_distillation |
"Block Truncation Coding-Compression procedure-x(i,j)={a,y(i,j)=0b,y(i,j)=1 This demonstrates that the algorithm is asymmetric in that the encoder has much more work to do than the decoder. This is because the decoder is simply replacing 1's and 0's with the estimated value whereas the encoder is also required to calcu... | large_corpus_distillation |
"F2FS-Features-Multi-head logging Multi-level hash table for directory entries Static/dynamic hot and cold data separation Adaptive logging scheme Configurable operational units Dual checkpoint Roll-back and roll-forward recovery Heap-style block allocation TRIM/FITRIM support Online fs defragmentation/file defragmenta... | large_corpus_distillation |
without using electricity to generate an air conditioned climate. Thus neither money nor electricity are spent to control the climate of the storage space, which stresses not only museum funds but increasingly scarce electricity too." | large_corpus_distillation |
"Chi-squared distribution-Properties-Cochran's theorem If Z1,...,Zn are independent identically distributed (i.i.d.), standard normal random variables, then \u2211t=1n(Zt\u2212Z\u00af)2\u223c\u03c7n\u221212 where Z\u00af=1n\u2211t=1nZt.\nA direct and elementary proof is as follows: Let Z\u223cN(0\u00af,11) be a vect... | large_corpus_distillation |
"Block suballocation-Suballocation schemes-Tail packing Some file systems have since been designed to take advantage of this unused space, and can pack the tails of several files in a single shared tail block. While this may, at first, seem like it would significantly increase file system fragmentation, the negative ef... | large_corpus_distillation |
"Query theory-Query theory-Query theory (QT) is a theory that proposes that preferences are constructed, rather than pre-stored and immediately retrievable (as assumed by many economic models) by individuals in accordance with the answers to one or more internally posed questions, or queries. Further, the order of such... | large_corpus_distillation |
"P versus NP problem-Sources-\"P vs NP Problem\". www.claymath.org (Cook, Levin). Retrieved 20 June 2021. Suppose that you are organizing housing accommodations for a group of four hundred university students. Space is limited and only one hundred of the students will receive places in the dormitory. To complicate matt... | large_corpus_distillation |
"ARRL Radiogram-Text part-An easy rule to remember about counting word groups: ANY GROUP OF ONE OR MORE CONSECUTIVE CHARACTERS WITH NO INTERRUPTING SPACES, WITH A SPACE BEFORE IT AND AFTER IT, IS COUNTED AS ONE GROUP. Such a group may be all letters, all numbers, or any mix of numbers, letters, or slashes (/), so long ... | large_corpus_distillation |
"Max-flow min-cut theorem-Linear program formulation-The equality in the max-flow min-cut theorem follows from the strong duality theorem in linear programming, which states that if the primal program has an optimal solution, x*, then the dual program also has an optimal solution, y*, such that the optimal values forme... | large_corpus_distillation |
"Medical image computing-Image-based physiological modelling-Cross-fertilization between imaging and modelling goes beyond interpretation of measurements in a way consistent with physiology. Image-based patient-specific modelling, combined with models of medical devices and pharmacological therapies, opens the way to p... | large_corpus_distillation |
"Memory safety-Memory safety-Memory safety is the state of being protected from various software bugs and security vulnerabilities when dealing with memory access, such as buffer overflows and dangling pointers. For example, Java is said to be memory-safe because its runtime error detection checks array bounds and poin... | large_corpus_distillation |
"Constant-recursive sequence-Examples-Arithmetic progressions For any a and any r\u22600 , the arithmetic progression a,a+r,a+2r,\u2026 is constant-recursive of order 2, because it satisfies sn=2sn\u22121\u2212sn\u22122 . Generalizing this, see polynomial sequences below.\nGeometric progressions For any a\u22600 a... | large_corpus_distillation |
the probability distribution that maximizes M is the\none with equal probability for each of the two input states.\nThis page titled 7.5: Capacity is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Paul Penfield, Jr. (MIT\nOpenCourseWare) via source content that was edited to the sty... | large_corpus_distillation |
"Hamming(7,4)-Channel coding-In the adjacent diagram, the seven bits of the encoded word are inserted into their respective locations; from inspection it is clear that the parity of the red, green, and blue circles are even: red circle has two 1's green circle has two 1's blue circle has four 1'sWhat will be shown shor... | large_corpus_distillation |
"Parasitic gap-History-Controversy Extraction gap versus proform The theoretical analysis of parasitic gaps is not a settled matter by any means, since accounts of the phenomenon vary drastically. In very broad terms, there are two lines of analysis that one can pursue: The extraction analysis assumes that parasitic ga... | large_corpus_distillation |
activation='softmax')\n])\n# Compile the model\nmodel.compile(optimizer='adam', loss='sparse_categorical_crossentropy',\nmetrics=['accuracy'])\n# Train the model\nhistory = model.fit(X_train_scaled, y_train, epochs=10, batch_size=32,\nvalidation_split=0.2)\n# Evaluate the model on test data\ntest_loss, test_accuracy = ... | large_corpus_distillation |
"Standard Singaporean Mandarin-Differences between standard and colloquial forms-Colloquial Singaporean Mandarin uses a variety of Southern Chinese exclamatory particles, in lieu of standard Mandarin equivalents. An example is the loan exclamatory final particle \u56c9 (lor) from Cantonese (analogous to Singlish usage)... | large_corpus_distillation |
"BPP (complexity)-Derandomization-Russell Impagliazzo and Avi Wigderson showed that if any problem in E, where E=DTIME(2O(n)), has circuit complexity 2\u03a9(n) then P = BPP." | large_corpus_distillation |
"Mutual exclusion-Enforcing mutual exclusion-Hardware solutions On uni-processor systems, the simplest solution to achieve mutual exclusion is to disable interrupts during a process's critical section. This will prevent any interrupt service routines from running (effectively preventing a process from being preempted).... | large_corpus_distillation |
"Metrical task system-Formal Definition-A task system is a pair (S,d) where S={s1,s2,\u2026,sn} is a set of states and d:S\u00d7S\u2192R is a distance function. If d is a metric, (S,d) is a metrical task system. An input to the task system is a sequence \u03c3=T1,T2,\u2026,Tl such that for each i , Ti is a vect... | large_corpus_distillation |
"Sequence container (C++)-Properties-array, vector and deque all support fast random access to the elements. list supports bidirectional iteration, whereas forward_list supports only unidirectional iteration." | large_corpus_distillation |
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