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We say that a k -graph H(k) is (\u03b4k,r) -regular with respect to a family of partitions P if all but at most \u03b4knk k\u2212 edges K of H(k) have the property that K\u2208Kk(G(1)) and if P={P(j)}j=1k\u22121 is unique (k,k\u22121) -complex for which K\u2208Kk(P(k\u22121)) , then H(k) is (\u03b4k,d(H(k)...
large_corpus_distillation
receives these broadcasts exchanges the time that each reference broadcast was received locally with its neighbors. Nodes then calculate phase shifts relative to each other as the average of the difference of the timestamps of the node's local clocks for the M reference broadcasts. In multihop networks, time synchroniz...
large_corpus_distillation
the risk of further conflicts. Some of them also actively helped to maintain software dealing with partitions to work with the updated lists, indicated conflicts, devised additional detection methods and work-arounds for vendors, or engaged in coordinating new non-conflictive partition type assignments as well."
large_corpus_distillation
rules. Assume and\ng(x,y)\nare differentiable functions.\n\u2207(fg)=f\u2207(g)+g\u2207(f)\na.\n\u2207(f/g)=(g\u2207f\u2212f\u2207g)/g2\nb.\n\u2207((f(x,y))n)=nf(x,y)n\u22121\u2207f\nc.\n14.6: Higher order Derivatives\nf =xy/(x2+y2) f f f\nQ14.6.1 Let ; compute xx, yx, and yy. (answer)\nx3y2+y5\nQ14.6.2 Find all first ...
large_corpus_distillation
"Static cast-Static cast-In the C++ programming language, static_cast is an operator that performs an explicit type conversion."
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"Multitrait-multimethod matrix-Example-Ideally, the trait should matter more than the specific method chosen for measurement. For example, if a person is measured as being highly depressed by one measure, then another depression measure should also yield high scores. On the other hand, people who appear highly depresse...
large_corpus_distillation
viewdata services to post or read messages, or to download or upload software. Some enthusiasts with computers equipped with large storage capacity and a dedicated phone line operated bulletin boards of their own. This capability anticipated the internet by nearly 20 years."
large_corpus_distillation
"Quotient group-Quotient group-For a congruence relation on a group, the equivalence class of the identity element is always a normal subgroup of the original group, and the other equivalence classes are precisely the cosets of that normal subgroup. The resulting quotient is written G/N , where G is the original grou...
large_corpus_distillation
"XOR linked list-Features-Two XOR operations suffice to do the traversal from one item to the next, the same instructions sufficing in both cases. Consider a list with items {\u2026B C D\u2026} and with R1 and R2 being registers containing, respectively, the address of the current (say C) list item and a work register ...
large_corpus_distillation
"Rubber-hose cryptanalysis-Details-Although the term is used tongue-in-cheek, its implications are serious: in modern cryptosystems, the weakest link is often the human user. A direct attack on a cipher algorithm, or the cryptographic protocols used, is likely to be much more expensive and difficult than targeting the ...
large_corpus_distillation
"Hough transform-Variations and extensions-Carefully chosen parameter space A high-dimensional parameter space for the Hough transform is not only slow, but if implemented without forethought can easily overrun the available memory. Even if the programming environment allows the allocation of an array larger than the a...
large_corpus_distillation
"Hilbert's tenth problem-Applications-\u03a010 sentences have the special property that if they are false, that fact will be provable in any of the usual formal systems. This is because the falsity amounts to the existence of a counter-example which can be verified by simple arithmetic. So if a \u03a010 sentence is su...
large_corpus_distillation
"Moore's law-Moore's law-Industry experts have not reached a consensus on exactly when Moore's law will cease to apply. Microprocessor architects report that semiconductor advancement has slowed industry-wide since around 2010, slightly below the pace predicted by Moore's law. In September 2022 Nvidia CEO Jensen Huang ...
large_corpus_distillation
"Fano's inequality-Fano's inequality-In information theory, Fano's inequality (also known as the Fano converse and the Fano lemma) relates the average information lost in a noisy channel to the probability of the categorization error. It was derived by Robert Fano in the early 1950s while teaching a Ph.D. seminar in in...
large_corpus_distillation
"Cipolla's algorithm-Example-Step 1: Find an a such that a2\u2212n is not a square. As stated, this has to be done by trial and error. Choose a=2 . Then a2\u2212n becomes 7. The Legendre symbol 13 ) has to be \u22121. Again this can be computed using Euler's criterion: 343 25 mod 13 {\\textstyle 7^{6}=343^{2}\\equ...
large_corpus_distillation
"Influence diagrams approach-IDA Methodology-Describe all relevant conditioning events Experts who have sufficient knowledge of the situation under evaluation form a group; in depth knowledge is essential for the technique to be used to its optimal potential. The chosen individuals include a range of experts - typicall...
large_corpus_distillation
"Physics beyond the Standard Model-Problems with the Standard Model-At any given moment there are several experimental results standing that significantly differ from a Standard Model-based prediction. In the past, many of these discrepancies have been found to be statistical flukes or experimental errors that vanish a...
large_corpus_distillation
"C8orf82-mRNA-The mRNA produced by the C8orf82 gene is 1,979 base pairs long with coding sequence that starts at base 159 and ends at base 809. According to NCBI Gene there are no alternative transcripts or isoforms. AceView lists several alternative transcripts and isoforms, the existence of which is uncertain."
large_corpus_distillation
"Lychrel number-Other bases-Lychrel numbers have been proven to exist in the following bases: 11, 17, 20, 26 and all powers of 2.No base contains any Lychrel numbers smaller than the base. In fact, in any given base b, no single-digit number takes more than two iterations to form a palindrome. For b > 4, if k < b/2 the...
large_corpus_distillation
"Mental calculation-Methods and techniques-Finally, another unique aspect of using this method is that the user is able to choose one of several different \u201croutes of multiplication\u201d to the specific multiplication problem at hand based on their subjective preferences or strengths and weaknesses with particular...
large_corpus_distillation
"Van Hiele model-Properties of the levels-4. Separation: a teacher who is reasoning at one level speaks a different \"language\" from a student at a lower level, preventing understanding. When a teacher speaks of a \"square\" she or he means a special type of rectangle. A student at Level 0 or 1 will not have the same ...
large_corpus_distillation
any reason, stating that any system updating from them will \"unquestionably break.\"There are also two other repositories that include the newest version of certain desktop environments.\ngnome-unstable, which contains packages of a new version of the software from GNOME before being released into testing."
large_corpus_distillation
"Index (publishing)-Purpose-Sample back-of-the-book index excerpt: sage, 41\u201342. See also Herbs \u2190 directing the reader to related terms Scarlet Sages. See Salvia coccinea \u2190 redirecting the reader to term used in the text shade plants \u2190 grouping term (may not appear in the text; may be generated by in...
large_corpus_distillation
"Internet Protocol-Reliability-All fault conditions in the network must be detected and compensated by the participating end nodes. The upper layer protocols of the Internet protocol suite are responsible for resolving reliability issues. For example, a host may buffer network data to ensure correct ordering before the...
large_corpus_distillation
"Set cover problem-Set cover problem-The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 1972. Given a set of elements {1, 2, \u2026, n} (called the universe) and a collectio...
large_corpus_distillation
frequency-rank relation can be modeled more accurately as by separate Zipf\u2013Mandelbrot laws distributions for different subsets or subtypes of words. This is the case for the frequency-rank plot of the first 10 million words of the English Wikipedia. In particular, the frequencies of the closed class of function wo...
large_corpus_distillation
"Lexis (linguistics)-Lexis (linguistics)-In linguistics, the term lexis (from Ancient Greek: \u03bb\u03ad\u03be\u03b9\u03c2 / word) designates the complete set of all possible words in a language, or a particular subset of words that are grouped by some specific linguistic criteria. For example, the general term Englis...
large_corpus_distillation
"Seminorm-Topologies of seminormed spaces-A TVS is normable if and only if it is a T1 space and admits a bounded convex neighborhood of the origin.\nIf X is a Hausdorff locally convex TVS then the following are equivalent: X is normable.\nX is seminormable.\nX has a bounded neighborhood of the origin.\nThe strong dua...
large_corpus_distillation
"Additive category-Matrix representation of morphisms-This may be confusing in the special case where m or n is zero, because we usually don't think of matrices with 0 rows or 0 columns. This concept makes sense, however: such matrices have no entries and so are completely determined by their size. While these matrices...
large_corpus_distillation
"Info-gap decision theory-Classical decision theory perspective-Sniedovich raises two points to info-gap, from the point of view of classical decision theory, one substantive, one scholarly: the info-gap uncertainty model is flawed and oversold Under severe uncertainty, one should use global decision theory , not local...
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"Stacki-Stacki-Stacki is a computer cluster software product from the company StackIQ, released as open-source software."
large_corpus_distillation
"Linear congruential generator-Advantages and disadvantages-Nevertheless, for some applications LCGs may be a good option. For instance, in an embedded system, the amount of memory available is often severely limited. Similarly, in an environment such as a video game console taking a small number of high-order bits of ...
large_corpus_distillation
"Suffix tree-Implementation-An important choice when making a suffix tree implementation is the parent-child relationships between nodes. The most common is using linked lists called sibling lists. Each node has a pointer to its first child, and to the next node in the child list it is a part of. Other implementations ...
large_corpus_distillation
"Automorphisms of the symmetric and alternating groups-The exceptional outer automorphism of S6-Structure of outer automorphism On cycles, it exchanges permutations of type (12) with (12)(34)(56) (class 21 with class 23), and of type (123) with (145)(263) (class 31 with class 32). The outer automorphism also exchanges ...
large_corpus_distillation
"Data Encryption Standard-Description-The key schedule for decryption is similar\u2014the subkeys are in reverse order compared to encryption. Apart from that change, the process is the same as for encryption. The same 28 bits are passed to all rotation boxes.\nPseudocode Pseudocode for the DES algorithm follows."
large_corpus_distillation
"Operad-Examples-Rooted trees In graph theory, rooted trees form a natural operad. Here, P(n) is the set of all rooted trees with n leaves, where the leaves are numbered from 1 to n. The group Sn operates on this set by permuting the leaf labels. Operadic composition T\u2218(S1,\u2026,Sn) is given by replacing the i...
large_corpus_distillation
"Go ranks and ratings-Rating systems-Elo ratings as used in Go The European Go Federation (EGF) implementation of the Elo rating system attempts to establish rough correspondence between ratings and kyu/dan ranks. This is done by varying some of the components of the Elo formula to achieve a close match to the adjacent...
large_corpus_distillation
"Monad (functional programming)-Variations-At a mathematical level, some monads have particularly nice properties and are uniquely fitted to certain problems.\nAdditive monads An additive monad is a monad endowed with an additional closed, associative, binary operator mplus and an identity element under mplus, called m...
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+, adds a variable to the left of any argument list.\n+Fn=def{x0x1\u22efxn:Fnx1\u22efxn}.\n+Fx1\u22efxn\u2194Fx2\u22efxn.\nCropping, \u2203, erases the leftmost variable in any argument list.\n\u2203Fn=def{x2\u22efxn:\u2203x1Fnx1\u22efxn}.\nFx1\u22efxn\u2192\u2203Fx2\u22efxn.\nCropping enables two useful defined functo...
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"Head-directionality parameter-Mixed word-order languages-[AP [PP auf seine Kinder] [A stolze]]However, when essentially the same adjective phrase is used predicatively rather than attributively, it can also be head-initial: [AP [A stolz] [PP auf seine Kinder]]Most adpositional phrases are head-initial (as German has m...
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"Mertens' theorems-Third theorem-Merten's third theorem is lim log 0.561459483566885 , where \u03b3 is the Euler\u2013Mascheroni constant (A001620).\nRelation to sieve theory An estimate of the probability of X (X\u226bn ) having no factor \u2264n is given by \u220fp\u2264n(1\u22121p) This is closely related to Merte...
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non-noticeable actions or noticeable actions. Non-noticeable responses can be storing their information in memory and noticeable responses are immediate action such as dialing the commercials number to order a product advertised on television. One of the main goals of communication is receiving appropriate receiver res...
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"Premium pricing-Premium pricing-Premium pricing (also called image pricing or prestige pricing) is the practice of keeping the price of one of the products or service artificially high in order to encourage favorable perceptions among buyers, based solely on the price. Premium refers to a segment of a company's brands...
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particular frequency can only be evaluated for a brief fraction of a millisecond, as the fast downward sweep of the call does not remain at any one frequency for long."
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"Thomas precession-Mathematical explanation-Corresponding to the boost is the (small change in the) boost vector \u0394b, with magnitude and direction of the relative velocity of the boost (divided by c). The boost B(\u0394b) and rotation R(\u0394\u03b8) here are infinitesimal transformations because \u0394b and rotati...
large_corpus_distillation
"Weight pulling-Objectives-Weight pull matches start with either an empty cart or sled or at low weights. Carts may be placed on dirt, carpet or even rails. Dogs are sorted into classes by weight and then fitted with a specially constructed freighting harness designed to distribute the weight and minimize the chance of...
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"Vysochanskij\u2013Petunin inequality-One-sided version-An improved version of the Vysochanskij-Petunin inequality for one-sided tail bounds exists. For a unimodal random variable X with mean \u03bc and variance \u03c32 , and r\u22650 , the one-sided Vysochanskij-Petunin inequality holds as follows: for otherwise....
large_corpus_distillation
"Send Me To Heaven-Gameplay-Petr Svarovsky, a Czech-born Norwegian artist who founded Carrot Pop to develop transgressive smartphone apps, indicated during an interview with WIRED magazine that he hoped to have people destroy as many iPhones as possible while playing his game. \"The original idea was to have very expen...
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"Normalization (statistics)-Examples-Note that some other ratios, such as the variance-to-mean ratio ( \u03c3 2 \u03bc ) {\\textstyle \\left({\\frac {\\sigma ^{2}}{\\mu }}\\right)} , are also done for normalization, but are not nondimensional: the units do not cancel, and thus the ratio has units, and is not scale-inv...
large_corpus_distillation
"Parts cleaning-Elements and their interactions-Cleaning media plays an important role as it removes the contaminants from the substrate."
large_corpus_distillation
"Md5deep-Md5deep-md5deep is a software package used in the computer security, system administration and computer forensics communities to run large numbers of files through any of several different cryptographic digests. It was originally authored by Jesse Kornblum, at the time a special agent of the Air Force Office o...
large_corpus_distillation
"Snark (graph theory)-Snark (graph theory)-In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three colors. In order to avoid trivial cases, snarks are often restricted to have additional requirements on their connectivit...
large_corpus_distillation
"Universal algebra-Basic idea-In universal algebra, an algebra (or algebraic structure) is a set A together with a collection of operations on A. An n-ary operation on A is a function that takes n elements of A and returns a single element of A. Thus, a 0-ary operation (or nullary operation) can be represented simply a...
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"GNOME Archive Manager-File formats-Supporting the archive formats requires external back-end programs and libraries, it supports: "
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"Monoid ring-Monoid ring-In abstract algebra, a monoid ring is a ring constructed from a ring and a monoid, just as a group ring is constructed from a ring and a group."
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"Regular expression-Syntax-POSIX basic and extended In the POSIX standard, Basic Regular Syntax (BRE) requires that the metacharacters ( ) and { } be designated \\(\\) and \\{\\}, whereas Extended Regular Syntax (ERE) does not.\nExamples: .at matches any three-character string ending with \"at\", including \"hat\", \"c...
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"Berman\u2013Hartmanis conjecture-Evidence-And Fenner, Fortnow & Kurtz (1992) found an oracle machine model in which the analogue to the isomorphism conjecture is true.Evidence against the conjecture was provided by Joseph & Young (1985) and Kurtz, Mahaney & Royer (1995). Joseph and Young introduced a class of NP-compl...
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"Eigenvalues and eigenvectors-Eigenvalues and eigenvectors of matrices-The determinant of A is the product of all its eigenvalues, det (A)=\u220fi=1n\u03bbi=\u03bb1\u03bb2\u22ef\u03bbn.\nThe eigenvalues of the k th power of A ; i.e., the eigenvalues of Ak , for any positive integer k , are \u03bb1k,\u2026,\u03bbn...
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"ZPP (complexity)-Witness and proof-The classes NP, RP and ZPP can be thought of in terms of proof of membership in a set."
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"Bedspace apartment-Environment-Limited space Since cage homes are often located within older urban districts, they are usually extremely small, the same size as a parking space in the U.S. Such space is only suitable for people to take a rest, thus preventing any additional recreational activities. It is observed that...
large_corpus_distillation
like Listaller to find the components a new application needs to run in the distribution's package database. Additionally, the new metadata allows easier installation of prerequisites needed to build software in the first place, as well as matching upstream applications with distribution packages and matching packages ...
large_corpus_distillation
decrease in terrorist groups trying to use the platform owing to its \"zero-tolerance policy enforcement\". According to Vijaya Gadde, Legal, Policy and Trust and Safety Lead at Twitter, there was a reduction of 19% terror related tweets from the previous reporting period (January\u2013June 2018).As of July 30, 2020, T...
large_corpus_distillation
"Similarity (philosophy)-Conceptions of similarity-Metric The problem of quantitative properties is better handled by the metric conception of similarity, which posits that there are certain dimensions of similarity concerning different respects, e.g. color, shape or weight, which constitute the axes of one unified met...
large_corpus_distillation
"Web shell-Delivery of web shells-Web shells are installed through vulnerabilities in web application or weak server security configuration including the following: SQL injection; Vulnerabilities in applications and services (e.g. web server software such as NGINX or content management system applications such as WordP...
large_corpus_distillation
"Diffusing update algorithm-Operation-Topology table contains the metric (cost information) of all routes to any destination within the autonomous system. This information is received from neighboring routers contained in the Neighbor table. The primary (successor) and secondary (feasible successor) routes to a destina...
large_corpus_distillation
"Cantor's first set theory article-The development of Cantor's ideas-On December 2, Cantor responded that his question does have interest: \"It would be nice if it could be answered; for example, provided that it could be answered no, one would have a new proof of Liouville's theorem that there are transcendental numbe...
large_corpus_distillation
"Nielsen\u2013Schreier theorem-Example-Let G be the free group with two generators a,b , and let H be the subgroup consisting of all reduced words of even length (products of an even number of letters a,b,a\u22121,b\u22121 ). Then H is generated by its six elements p=aa,q=ab,r=ba,s=bb,t=ab\u22121,u=a\u22121b."
large_corpus_distillation
"Left-child right-sibling binary tree-Left-child right-sibling binary tree-1 / / / 2---3---4 / / 5---6 7 / 8---9 We can transform this tree to a binary tree by turning each sibling 45\u00b0 clockwise.\n1 / 2 / \\ 5 3 \\ \\ 6 4 / 7 / 8 \\ 9 "
large_corpus_distillation
"Haswell (microarchitecture)-Technology-Haswell-EP models with ten and more cores support cluster on die (COD) operation mode, allowing CPU's multiple columns of cores and last level cache (LLC) slices to be logically divided into what is presented as two non-uniform memory access (NUMA) CPUs to the operating system. B...
large_corpus_distillation
"Fast Infoset-Structure-An index table is built for most strings, which includes element and attribute names, and their values. This means that the text of repeated tags and values only appears once per document."
large_corpus_distillation
"Queap-Queap-In computer science, a queap is a priority queue data structure. The data structure allows insertions and deletions of arbitrary elements, as well as retrieval of the highest-priority element. Each deletion takes amortized time logarithmic in the number of items that have been in the structure for a longer...
large_corpus_distillation
"Intel 8051-Related processors-The 80C537 (ROM-less) and 80C517 (8 KB ROM) are CMOS versions, designed for the automotive industry. Enhancements mostly include new and enhanced peripherals. The 80C5x7 has fail-safe mechanisms, analog signal processing facilities, enhanced timer capabilities, and a 32-bit arithmetic per...
large_corpus_distillation
"Covariance and contravariance (computer science)-Arrays-Likewise, the contravariant rule would be safe for write-only arrays.\nCovariant arrays in Java and C# Early versions of Java and C# did not include generics, also termed parametric polymorphism. In such a setting, making arrays invariant rules out useful polymor...
large_corpus_distillation
"Definite clause grammar-Parsing with DCGs-The main practical use of a DCG is to parse sentences of the given grammar, i.e. to construct a parse tree. This can be done by providing \"extra arguments\" to the functors in the DCG, like in the following rules: One can now query the interpreter to yield a parse tree of any...
large_corpus_distillation
"Authorization certificate-Contents of a typical attribute certificate-Version: the version of the certificate.\nHolder: the holder of the certificate.\nIssuer: the issuer of the certificate.\nSignature algorithm: the algorithm by which the certificate is signed.\nSerial number: the unique issuance number given by the ...
large_corpus_distillation
In that case the Poisson process is no longer stationary, according to some definitions of stationarity."
large_corpus_distillation
"Logjam (computer security)-Logjam (computer security)-Logjam is a security vulnerability in systems that use Diffie\u2013Hellman key exchange with the same prime number. It was discovered by a team of computer scientists and publicly reported on May 20, 2015. The discoverers were able to demonstrate their attack on 51...
large_corpus_distillation
"Page (computer memory)-Page size-Starting with the Pentium Pro, and the AMD Athlon, x86 processors support 4 MiB pages (called Page Size Extension) (2 MiB pages if using PAE) in addition to their standard 4 KiB pages; newer x86-64 processors, such as AMD's newer AMD64 processors and Intel's Westmere and later Xeon pro...
large_corpus_distillation
"Average-Miscellaneous types-Other more sophisticated averages are: trimean, trimedian, and normalized mean, with their generalizations.One can create one's own average metric using the generalized f-mean: y=f\u22121(1n[f(x1)+f(x2)+\u22ef+f(xn)]) where f is any invertible function. The harmonic mean is an example of th...
large_corpus_distillation
"Information criterion (information technology)-Information criterion (information technology)-Efficiency concerns the provision of information through the optimal (most productive and economical) use of resources.\nConfidentiality concerns the protection of sensitive information from unauthorised disclosure.\nIntegrit...
large_corpus_distillation
"The actual mean square error when we use L(Y \u2223X) to approximate Y, namely E(\u2225Y\u2212L(Y \u2223X)\u22252), is the trace (sum of the diagonal entries) of the variance-\ncovariance matrix above. The function of x given by\nL(Y \u2223X=x)=E(Y)+cov(Y,X)vc\u22121(X)[x\u2212E(X)] (4.8.16)\nis known as the (distribu...
large_corpus_distillation
"Shamir's Secret Sharing-Example calculation-This yields coefficients 1234 166 94 ), where a0 is the secretThe polynomial to produce secret shares (points) is therefore: 1234 166 94 x2 Six points Dx\u22121=(x,f(x)) from the polynomial are constructed as: 1494 1942 2578 3402 4414 5614 ) Each participant in the scheme...
large_corpus_distillation
"Automated theorem proving-First-order theorem proving-In the late 1960s agencies funding research in automated deduction began to emphasize the need for practical applications. One of the first fruitful areas was that of program verification whereby first-order theorem provers were applied to the problem of verifying ...
large_corpus_distillation
that the problems were originally raised in 1995, before the WEP standard was available. The attack presented in the paper exploits the fact that WEP splits the data into smaller fragments, which are reassembled by the receiver. Taking advantage of the fact that at least part of the plaintext of some packets may be kno...
large_corpus_distillation
"World War I cryptography-France-The Tableau de Concordance was the main French diplomatic cipher."
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"B*-Details-When transpositions are possible, then the back-up operation might need to alter the values of nodes that did not lie on the selection path. In this case, the algorithm needs pointers from children to all parents so that changes can be propagated. Note that propagation can cease when a backup operation does...
large_corpus_distillation
"Collective classification-Methods-Collective classification with graphical models Another approach to collective classification is to represent the problem with a graphical model and use learning and inference techniques for the graphical modeling approach to arrive at the correct classifications. Graphical models are...
large_corpus_distillation
as discussed in the following section.\n3This is not intended as criticism, since we will see that there are good reasons to concentrate initially on such idealized\nexperiments. However, readers should always be aware that modeling errors are the major cause of misleading results in\napplications of probability, and t...
large_corpus_distillation
"Smalltalk-Syntax-Symbols are written as # followed by a string literal. For example: If the sequence does not include whitespace or punctuation characters, this can also be written as: Arrays: defines an array of four integers.\nMany implementations support the following literal syntax for ByteArrays: defines a ByteAr...
large_corpus_distillation
"Decompiler-Design-Loader The first decompilation phase loads and parses the input machine code or intermediate language program's binary file format. It should be able to discover basic facts about the input program, such as the architecture (Pentium, PowerPC, etc.) and the entry point. In many cases, it should be abl...
large_corpus_distillation
"(N ,N )\nExplicitly compute the values of the joint probability density function of 1 2 .\nAnswer\nP(N\n1\n=n\n1\n,Nn\n21\n==n1\n2\n)\n2 3 4 5 6 7 8 9\nn 2 =0 0.0414 0.0212 0.0142 0.0107 0.0086 0.0072 0.0062 0.0054 0.0048\n1 0.0378 0.0202 0.0138 0.0105 0.0084 0.0071 0.0061 0.0053 0.0047\n2 0.0348 0.0193 0.0134 0.0102 ...
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in which l appears as either the first or second index."
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"Softmax function-Applications-The softmax function is used in various multiclass classification methods, such as multinomial logistic regression (also known as softmax regression):\u200a206\u2013209\u200a [1], multiclass linear discriminant analysis, naive Bayes classifiers, and artificial neural networks. Specificall...
large_corpus_distillation
"Structured concurrency-History-The fork\u2013join model from the 1960s, embodied by multiprocessing tools like OpenMP, is an early example of a system ensuring all threads have completed before exit. However, Smith argues that this model is not true structured concurrency as the programming language is unaware of the ...
large_corpus_distillation
into two triangles by one of the diagonals of the rectangle. The last construction we use here is truncation of both corners and edges. Ignoring scaling, expansion can also be viewed as the rectification of the rectification. Likewise, the cantitruncation can be viewed as the truncation of the rectification."
large_corpus_distillation
"Expected value-Definition-Examples Suppose xi=i and pi=ci2i for i=1,2,3,\u2026, where ln \u20612 is the scaling factor which makes the probabilities sum to 1. Then, using the direct definition for non-negative random variables, we have Random variables with density Now consider a random variable X which has a prob...
large_corpus_distillation
"Morse code for non-Latin alphabets-Morse code for non-Latin alphabets-This is a summary of the use of Morse code to represent alphabets other than Latin."
large_corpus_distillation
"Flix (programming language)-Notable features-For example, the following program fragment does not type check: because in p1 the type of the Edge predicate is Edge(Int, Int) whereas in p2 it has type Edge(String, String). The Flix compiler rejects such programs as ill-typed."
large_corpus_distillation
"Newline-Representation-Recognizing and using the newline codes greater than 0x7F (NEL, LS and PS) is not often done. They are multiple bytes in UTF-8, and the code for NEL has been used as the ellipsis (\u2026) character in Windows-1252. For instance: ECMAScript accepts LS and PS as line-breaks, but considers U+0085 (...
large_corpus_distillation
"Dick pic-Prevalence-According to a 2016 U.S. survey, 49 percent of women had received at least one unsolicited photo of male sex organs. In a late-2017 survey, 78 percent of women aged 18 to 34 and 69 percent of women aged 35 to 54 said that they had received at least one dick pic without prior consent. Seventeen perc...
large_corpus_distillation