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"Modular arithmetic-Advanced properties-Another simple consequence is that if a \u2261 b (mod \u03c6(n)), where \u03c6 is Euler's totient function, then ka \u2261 kb (mod n) provided k is coprime with n.\nWilson's theorem: p is prime if and only if (p \u2212 1)! \u2261 \u22121 (mod p)." | large_corpus_distillation |
have a different subunit compared to the other. Representing these differing sub-sequences as gaps will allow us to treat these cases as \u201cgood matches\u201d even though there are long consecutive runs with indel operations in the sequence. Therefore, using a good gap penalty model will avoid low scores in alignmen... | large_corpus_distillation |
"Archival image-Archival image-An archival image is an image meant to have lasting utility. Archival images are usually kept off-line on a cheaper storage medium such as CD-ROM or magnetic tape, in a secure environment. Archival images are usually of a higher resolution and quality than the digital image delivered to t... | large_corpus_distillation |
"User experience evaluation-Constructs-Scale (metrics): Indicators that show effectiveness, efficiency and satisfaction.\nOther Factors: Conditions of use, the surrounding environment and other human factors." | large_corpus_distillation |
sentence is always true. If interpretations are understood in terms of possible worlds, logically true sentences can be seen as sentences that are true in every possible world. Expressed in terms of valid arguments: an argument is valid if and only if its conclusion is true in all possible worlds in which its premises ... | large_corpus_distillation |
"Baumslag\u2013Gersten group-Properties of the Baumslag\u2013Gersten group G-The conjugacy problem in G is known to be decidable, but the only known worst-case upper bound estimate for the complexity of the conjugacy problem, due to Janis Beese, is elementary recursive. It is conjectured that this estimate is sharp, ba... | large_corpus_distillation |
"Avant Browser-History and development-The Avant Browser's default search engine is a version of the Yahoo! search engine renamed Avantfind and is given a custom look. Other search engines are available via the address bar's \"Quick Search\" facility, and instructions on how to change the default to an engine of the us... | large_corpus_distillation |
"Spaces of test functions and distributions-Spaces of distributions-Compactly supported Lp-spaces Given 1\u2264p\u2264\u221e, the vector space Lcp(U) of compactly supported Lp functions on U and its topology are defined as direct limits of the spaces Lcp(K) in a manner analogous to how the canonical LF-topologies ... | large_corpus_distillation |
1715 = k such that geometric mean of phi(k) and sigma(k) is an integer 1716 = 857 + 859: sum of twin prime pair 1717 = pentagonal number 1718 = 12 12 d) 1719 = composite de Polignac number 1720 = sum of the first 31 primes 1721 = twin prime; number of squares between 422 and 424." | large_corpus_distillation |
"Log-linear model-Log-linear model-Poisson regression for contingency tables, a type of generalized linear model.The specific applications of log-linear models are where the output quantity lies in the range 0 to \u221e, for values of the independent variables X, or more immediately, the transformed quantities fi(X) in... | large_corpus_distillation |
"Multi-armed bandit-Bandit strategies-A major breakthrough was the construction of optimal population selection strategies, or policies (that possess uniformly maximum convergence rate to the population with highest mean) in the work described below." | large_corpus_distillation |
"Christine Shoemaker-Research Interest-Prof. Shoemaker\u2019s research focuses on finding cost-effective, robust solutions for engineering problems by using computational mathematics for optimization, modeling, deep learning and statistical analyses. Her application areas include lake PDE model parameter calibration, p... | large_corpus_distillation |
"Mura (Japanese term)-Limitations, critiques and improvements-Some processes have asymmetric cost. In such situations, it may be better to err away from the higher cost error. In this case, there appears to be waste and higher average error, but the waste or errors are smaller ones and in aggregate leads to lower costs... | large_corpus_distillation |
the different terms and definitions for improved forest statistics." | large_corpus_distillation |
"Proof of impossibility-Richard's paradox-Kurt G\u00f6del considered his proof to be \u201can analogy\u201d of Richard's paradox, which he called \u201cRichard's antinomy\u201d (see below).\nAlan Turing constructed this paradox with a machine and proved that this machine could not answer a simple question: will this ma... | large_corpus_distillation |
"Prompt engineering-Text-to-text-Automatic prompt generation Retrieval-augmented generation Prompts often contain a few examples (thus \"few-shot\"). Examples can be automatically retrieved from a database with document retrieval, sometimes using a vector database. Given a query, a document retriever is called to retri... | large_corpus_distillation |
"Revision Control System-Behavior-Advantages Simple structure and easy to work with Revision saving is not dependent on a central repository Disadvantages There is little security, in the sense that the version history can be edited by the users.\nOnly one user can work on a file at a time." | large_corpus_distillation |
"Standard of Good Practice for Information Security-Organization-The Principles and Objectives part of the Standard provides a high-level version of the Standard, by bringing together just the principles (which provide an overview of what needs to be performed to meet the Standard) and objectives (which outline the rea... | large_corpus_distillation |
and connections in the industry, as well as advantages in specialization and high quality of work. In other words, manufacturers produce large quantity of goods and products but are limited in its assortment and merchandise. Consumers seek a wider variety in lesser quantities. Therefore, it is highly essential to distr... | large_corpus_distillation |
"my_list = [2, 2 3, 23]\nmy_list = [\"Jimmy\", 2, \"times\"]\nmy_list = [\"C\", \"C++\", \"Python\", \"Java\", \"Rust\", \"Scala\"]\n[]\nnew_list[3] new_list\nlen()\nlen()\nlen()\n1 # Setup a list of numbers\n2 num_list = [2, 3, 5, 9, 11]\n3 print(num_list)\n4\n5 # Print the length of the list\n6 print(\"Length: \", le... | large_corpus_distillation |
"Concurrent data structure-Design and implementation-The primary source of this additional difficulty is concurrency, exacerbated by the fact that threads must be thought of as being completely asynchronous: they are subject to operating system preemption, page faults, interrupts, and so on. On today's machines, the ... | large_corpus_distillation |
"Database journalism-History and development of database journalism-Beginning with the early years of the 21st century, some researchers expanded the conceptual dimension for databases in journalism, and in digital journalism or cyberjournalism. A conceptual approach begins to consider databases as a specificity of dig... | large_corpus_distillation |
"Self-modifying code-Usage-Self-modifying code can be used for various purposes: Semi-automatic optimizing of a state-dependent loop.\nDynamic in-place code optimization for speed depending on load environment.\nRun-time code generation, or specialization of an algorithm in runtime or loadtime (which is popular, for ex... | large_corpus_distillation |
"Structural vulnerability (computing)-Structural vulnerability (computing)-In computing, a structural vulnerability is an IT system weakness that consists of several so-called component vulnerabilities. This type of weakness generally emerges due to several system architecture flaws.\nAn example of a structural vulnera... | large_corpus_distillation |
"Semantic desktop-General description-A definition of Semantic Desktop was given (Sauermann et al. 2005): A Semantic Desktop is a device in which an individual stores all her digital information like documents, multimedia and messages. These are interpreted as Semantic Web resources, each is identified by a Uniform Re... | large_corpus_distillation |
"Legendre symbol-Properties of the Legendre symbol-There are a number of useful properties of the Legendre symbol which, together with the law of quadratic reciprocity, can be used to compute it efficiently.\nGiven a generator g\u2208Fp\u2217 , if x=gr , then x is a quadratic residue if and only if r is even. This ... | large_corpus_distillation |
"Common Intermediate Language-Execution-Just-in-time compilation Just-in-time compilation (JIT) involves turning the byte-code into code immediately executable by the CPU. The conversion is performed gradually during the program's execution. JIT compilation provides environment-specific optimization, runtime type safet... | large_corpus_distillation |
"Vulnerabilities Equities Process-Vulnerabilities Equities Process-The Vulnerabilities Equities Process (VEP) is a process used by the U.S. federal government to determine on a case-by-case basis how it should treat zero-day computer security vulnerabilities; whether to disclose them to the public to help improve gener... | large_corpus_distillation |
"Label propagation algorithm-Functioning of the algorithm-At initial condition, the nodes carry a label that denotes the community they belong to. Membership in a community changes based on the labels that the neighboring nodes possess. This change is subject to the maximum number of labels within one degree of the nod... | large_corpus_distillation |
"Dedekind zeta function-Arithmetically equivalent fields-Perlis (1977) showed that two number fields K and L are arithmetically equivalent if and only if all but finitely many prime numbers p have the same inertia degrees in the two fields, i.e., if pi are the prime ideals in K lying over p, then the tuples dim Z/p\u... | large_corpus_distillation |
\ufffd\nn\nJ(\u03b8,\u03b8 ; \u03b1) = \u2212 \u03b1 y = 0 (7)\n0 t t\nd\u03b8\n0\nt=1\nd \ufffd\nn\nJ(\u03b8,\u03b8 ; \u03b1) = \u03b8 \u2212 \u03b1 y \u03c6(x ) = 0 (8)\n0 t t t\nd\u03b8\nt=1\nSo, again the solution for \u03b8 is in the span of the feature vectors corresponding to the training\nexamples. Substituting... | large_corpus_distillation |
and interpreter. Then, the Forth system's code is compiled, but this version is stored in the buffer. The buffer in memory is written to disk, and ways are provided to load it temporarily into memory for testing. When the new version appears to work, it is written over the previous version." | large_corpus_distillation |
"Bounding volume hierarchy-Construction-There are three primary categories of tree construction methods: top-down, bottom-up, and insertion methods. Top-down methods proceed by partitioning the input set into two (or more) subsets, bounding them in the chosen bounding volume, then keep partitioning (and bounding) recu... | large_corpus_distillation |
"Signature (logic)-Many-sorted signatures-For many-sorted logic and for many-sorted structures, signatures must encode information about the sorts. The most straightforward way of doing this is via symbol types that play the role of generalized arities.\nSymbol types Let S be a set (of sorts) not containing the symbol... | large_corpus_distillation |
"Memory confusion protocol-Memory confusion protocol-The subjects then see a set of sentences, each of which is paired with a photograph of the individual who said it." | large_corpus_distillation |
"HP Time-Shared BASIC-String handling-The main advantage to this style of string access is that it eliminates the need for complex memory management that is otherwise required when string lengths change. MS BASIC had a lengthy library to handle the compression of memory by removing dead space in the string heap when th... | large_corpus_distillation |
"Batcher odd\u2013even mergesort-Batcher odd\u2013even mergesort-Batcher's odd\u2013even mergesort is a generic construction devised by Ken Batcher for sorting networks of size O(n (log n)2) and depth O((log n)2), where n is the number of items to be sorted. Although it is not asymptotically optimal, Knuth concluded in... | large_corpus_distillation |
density function f defined by f(x,y)=6x2y for 0\u2264x\u22641, 0\u2264y\u22641. Find each of the following:\n1. E(X,Y)\n2. vc(X,Y)\nAnswer\nNote that X and Y are independent.\n1. (3 4 ,2 3 )\n3 0\n2. [80 ]\n0 1\n18\nSuppose that (X,Y) has probability density function f defined by f(x,y)=15x2y for 0\u2264x\u2264y\u22641... | large_corpus_distillation |
"Flajolet\u2013Martin algorithm-The algorithm-Assume that we are given a hash function hash(x) that maps input x to integers in the range [0;2L\u22121] , and where the outputs are sufficiently uniformly distributed. Note that the set of integers from 0 to 2L\u22121 corresponds to the set of binary strings of length... | large_corpus_distillation |
"Quartic reciprocity-Integers-Gauss The first thing to notice when working within the ring Z of integers is that if the prime number q is \u2261 3 (mod 4) then a residue r is a quadratic residue (mod q) if and only if it is a biquadratic residue (mod q). Indeed, the first supplement of quadratic reciprocity states that... | large_corpus_distillation |
"Spatial Archive and Interchange Format-Schema definition-SAIF defines 285 classes (including enumerations) in the Class Syntax Notation, covering the definitions of high-level features, geometric types, topological relationships, temporal coordinates and relationships, geodetic coordinate system components and metadat... | large_corpus_distillation |
"Destination routing-Description-The telephone network comprises various classes of switching systems. An end office switch connects directly to the stations. It knows which circuit to activate (ring) when given a destination number. Other switches in the network are for transport only. These are sometimes called tande... | large_corpus_distillation |
"Emergency Alert System-Technical concept-EAS header Because the header lacks error detection codes, it is repeated three times for redundancy. EAS decoders compare the received headers against one another, looking for an exact match between any two, eliminating most errors which can cause an activation to fail. The de... | large_corpus_distillation |
"Simple Knowledge Organization System-Overview-Concept collections The concept collections (Collection, orderedCollection) are labeled and/or ordered (orderedCollection) groups of SKOS concepts. Collections can be nested, and can have defined URIs or not (which is known as a blank node). Neither a SKOS Concept nor a Co... | large_corpus_distillation |
"Secure by design-Secure by design-Secure by design, in software engineering, means that software products and capabilities have been designed to be foundationally secure." | large_corpus_distillation |
"Hildebrand solubility parameter-Units-The conventional units for the solubility parameter are (calories per cm3)1/2, or cal1/2 cm\u22123/2. The SI units are J1/2 m\u22123/2, equivalent to the pascal1/2. 1 calorie is equal to 4.184 J.\n1 cal1/2 cm\u22123/2 = (523/125 J)1/2 (10\u22122 m)\u22123/2 = (4.184 J)1/2 (0.01 m)... | large_corpus_distillation |
"Traffic classification-Traffic classification-Traffic classification is an automated process which categorises computer network traffic according to various parameters (for example, based on port number or protocol) into a number of traffic classes. Each resulting traffic class can be treated differently in order to d... | large_corpus_distillation |
"Pacenotes-Typical notes-When pacenotes are read, the co-driver will not translate into the fully worded text given above, but instead will keep some abbreviations, such as 'K' for a bend or kink. Distances are just given, the units are understood. The above notes might be read as: 100 K left 2, 100 K right 2, 200 squa... | large_corpus_distillation |
"Google Assistant-Reception-PC World's Mark Hachman gave a favorable review of the Google Assistant, saying that it was a \"step up on Cortana and Siri.\" Digital Trends called it \"smarter than Google Now ever was\"." | large_corpus_distillation |
"Relational model-Topics-The fundamental assumption behind a relational model is that all data is represented as mathematical n-ary relations, an n-ary relation being a subset of the Cartesian product of n domains. In the mathematical model, reasoning about such data is done in two-valued predicate logic, meaning there... | large_corpus_distillation |
"Quadratic pair-Quadratic pair-In mathematical finite group theory, a quadratic pair for the odd prime p, introduced by Thompson (1971), is a finite group G together with a quadratic module, a faithful representation M on a vector space over the finite field with p elements such that G is generated by elements with min... | large_corpus_distillation |
"Junction Grammar-Advent of Junction Grammar-J-rules The base/junction rules (J-rules) of junction grammars are a set of algebraic formulas which generate for natural language what is akin to the Periodic Table of elements in chemistry, namely, an enumeration of well-formed linguistic structures sometimes referred to a... | large_corpus_distillation |
"Arity-Examples-The Forth language also contains a ternary operator, */, which multiplies the first two (one-cell) numbers, dividing by the third, with the intermediate result being a double cell number. This is used when the intermediate result would overflow a single cell.\nThe Unix dc calculator has several ternary ... | large_corpus_distillation |
"Monotone comparative statics-Monotone comparative statics under uncertainty-Note that {u^(\u22c5;s)}s\u2208S , where := u(wR+x(s\u2212R)) , obeys single crossing (though not necessarily increasing) differences. By Theorem 6, {V(\u22c5;t)}t\u2208T obeys single crossing differences, and hence arg max x\u22650V(x;t) ... | large_corpus_distillation |
"Password-Factors in the security of a password system-Password security architecture Common techniques used to improve the security of computer systems protected by a password include: Not displaying the password on the display screen as it is being entered or obscuring it as it is typed by using asterisks (*) or bull... | large_corpus_distillation |
of \u22122\u221a \u2212 1 \u2212 1 at the point (\u22122\u221a11, \u22126\u221a11, 2\u221a11) and a relative\n11 11 11\n\u2212\u2212 2\u221a11 6\u221a11 2\u221a11\nmaximum of 2\u221a11 at the point ( , , \u2212 ).\n11 11 11\n1 1 1\n12) Objective function: f(x,y,z)=x+y+z Constraint: + + =1\nx y z\n13) Objective function... | large_corpus_distillation |
"U-Net-Description-The U-Net architecture stems from the so-called \u201cfully convolutional network\u201d proposed by Long, Shelhamer, and Darrell in 2014.The main idea is to supplement a usual contracting network by successive layers, where pooling operations are replaced by upsampling operators. Hence these layers i... | large_corpus_distillation |
"Cryptanalysis of the Enigma-Polish breakthroughs-Polish bomba After Rejewski's characteristics method became useless, he invented an electro-mechanical device that was dubbed the bomba kryptologiczna, 'cryptologic bomb'. Each machine contained six sets of Enigma rotors for the six positions of the repeated three-lette... | large_corpus_distillation |
"Prototype JavaScript Framework-Problems-Unlike other JavaScript libraries like jQuery, Prototype extends the DOM. There are plans to change this in the next major version of the library.In April 2010, blogger Juriy 'kangax' Zaytsev (of Prototype Core) described at length the problems that can follow from monkey patchi... | large_corpus_distillation |
"Mixing patterns-Types of Mixing Patterns-Mixing patterns are a characteristic of an entire network, referring to the extent for nodes to connect to other similar or different nodes. Mixing, therefore, can be classified broadly as assortative or disassortative. Assortative mixing is the tendency for nodes to connect to... | large_corpus_distillation |
"IPA number-900: transcription delimiters-Brackets and other punctuation that mark linguistic transcription " | large_corpus_distillation |
the measures inside specific applications such as information retrieval, recommender systems, natural language processing, etc." | large_corpus_distillation |
"Polar decomposition-Construction and proofs of existence-General derivation The SVD of a squared matrix A reads A=WD12V\u2217 , with W,V unitary matrices, and D a diagonal, positive semi-definite matrix. By simply inserting an additional pair of W s or V s, we obtain the two forms of the polar decomposition of ... | large_corpus_distillation |
"Natural language processing-Common NLP tasks-Semantic role labelling (see also implicit semantic role labelling below) Given a single sentence, identify and disambiguate semantic predicates (e.g., verbal frames), then identify and classify the frame elements (semantic roles)." | large_corpus_distillation |
"Bogosort-Related algorithms-Bozosort Another sorting algorithm based on random numbers. If the list is not in order, it picks two items at random and swaps them, then checks to see if the list is sorted. The running time analysis of a bozosort is more difficult, but some estimates are found in H. Gruber's analysis of ... | large_corpus_distillation |
"Advanced learner's dictionary-Advanced learner's dictionary-Although these advanced dictionaries have been produced for learners of several languages (including Chinese, Dutch, German, and Spanish), the majority are written for learners of English." | large_corpus_distillation |
"Max-flow min-cut theorem-Application-Let P be the set of pixels assigned to foreground and Q be the set of points assigned to background, then the problem can be formulated as, max {g}=\u2211i\u2208Pfi+\u2211i\u2208Qbi\u2212\u2211i\u2208P,j\u2208Q\u2228j\u2208P,i\u2208Qpij.\nThis maximization problem can be formulated... | large_corpus_distillation |
"Code 128-Specification-Despite its name, Code 128 does not have 128 distinct symbols, so it cannot represent 128 code points directly. To represent all 128 ASCII values, it shifts among three code sets (A, B, C). Together, code sets A and B cover all 128 ASCII characters. Code set C is used to efficiently encode digit... | large_corpus_distillation |
"Anonymous P2P-Arguments for and against anonymous P2P communication-Freedom of speech Some claim that true freedom of speech, especially on controversial subjects, is difficult or impossible unless individuals can speak anonymously. If anonymity is not possible, one could be subjected to threats or reprisals for voici... | large_corpus_distillation |
"Secure Communications Interoperability Protocol-Key Management (120)-To set up a secure call, a new Traffic Encryption Key (TEK) must be negotiated. For Type 1 security (classified calls), the SCIP signalling plan uses an enhanced FIREFLY messaging system for key exchange. FIREFLY is an NSA key management system based... | large_corpus_distillation |
"Havel\u2013Hakimi algorithm-The algorithm-If the given list A is graphic, then the theorem will be applied at most n\u22121 times setting in each further step := A\u2032 . Note that it can be necessary to sort this list again. This process ends when the whole list A\u2032 consists of zeros. Let G be a simple grap... | large_corpus_distillation |
"XOR swap algorithm-Proof of correctness-Linear algebra interpretation As XOR can be interpreted as binary addition and a pair of bits can be interpreted as a vector in a two-dimensional vector space over the field with two elements, the steps in the algorithm can be interpreted as multiplication by 2\u00d72 matrices o... | large_corpus_distillation |
"Fragile base class-Solutions-Objective-C has categories as well as non-fragile instance variables.\nComponent Pascal deprecates superclass calls.\nJava, C++ (Since C++11) and D allow inheritance or overriding a class method to be prohibited by labeling a declaration of a class or method, respectively, with the keyword... | large_corpus_distillation |
down) with a minimum node size of 5 as the default.:\u200a592\u200a In practice, the best values for these parameters should be tuned on a case-to-case basis for every problem.:\u200a592 ExtraTrees Adding one further step of randomization yields extremely randomized trees, or ExtraTrees. While similar to ordinary rando... | large_corpus_distillation |
"Damerau\u2013Levenshtein distance-Algorithm-for i := 0 to length(a) inclusive do d[i, 0] := i for j := 0 to length(b) inclusive do d[0, j] := j for i := 1 to length(a) inclusive do for j := 1 to length(b) inclusive do if a[i] = b[j] then cost := 0 else cost := 1 d[i, j] := minimum(d[i-1, j] + 1, // deletion d[i, j-1] ... | large_corpus_distillation |
"Edge coloring-Definitions-As with its vertex counterpart, an edge coloring of a graph, when mentioned without any qualification, is always assumed to be a proper coloring of the edges, meaning no two adjacent edges are assigned the same color. Here, two distinct edges are considered to be adjacent when they share a co... | large_corpus_distillation |
"Dual space-Algebraic dual space-The annihilator of a subset is itself a vector space.\nThe annihilator of the zero vector is the whole dual space: {0}0=V\u2217 , and the annihilator of the whole space is just the zero covector: V0={0}\u2286V\u2217 Furthermore, the assignment of an annihilator to a subset of V rever... | large_corpus_distillation |
running example, the set {x,y,z} is the greatest element, and {} is the least.\nMaximal elements and minimal elements: An element g\u2208P is a maximal element if there is no element a\u2208P such that a>g.\nSimilarly, an element m\u2208P is a minimal element if there is no element a\u2208P such that a<m.\nIf a... | large_corpus_distillation |
"Language model-Evaluation and benchmarks-Evaluation of the quality of language models is mostly done by comparison to human created sample benchmarks created from typical language-oriented tasks. Other, less established, quality tests examine the intrinsic character of a language model or compare two such models. Sinc... | large_corpus_distillation |
"Chinese remainder theorem-Chinese remainder theorem-In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the conditi... | large_corpus_distillation |
"Statistical hypothesis testing-The testing process-In the statistics literature, statistical hypothesis testing plays a fundamental role. There are two mathematically equivalent processes that can be used.The usual line of reasoning is as follows: There is an initial research hypothesis of which the truth is unknown.\... | large_corpus_distillation |
"Nervos Network-Publications-Sun, Meng; Lu, Yuteng; Feng, Yichun; Zhang, Qi; Liu, Shaoying (November 2021). \"Modeling and Verifying the CKB Blockchain Consensus Protocol\". Mathematics. 9 (22): 2954. doi:10.3390/math9222954. ISSN 2227-7390.\nSzepieniec, Alan; Ashur, Tomer (2020). \"Eaglesong: An ARX hash with fast dif... | large_corpus_distillation |
"Nearest-neighbor chain algorithm-Application to specific clustering distances-If d(A,B) is the smallest of the three distances on the right hand side (as would necessarily be true if A and B are mutual nearest-neighbors) then the negative contribution from its term is cancelled by the nC coefficient of one of the ... | large_corpus_distillation |
"Gang scheduling-Types-Response time Rj of jth Bag of Gangs is defined as the time interval from the arrival of the BoG at the grid dispatcher to the completion of jobs of all of the sub-gangs which belong to the BoG. The average response time is defined as follows: Response Time (RT)= 1N\u2211j\u22121NRj .The respon... | large_corpus_distillation |
"Spectre (security vulnerability)-Mitigation-Since Spectre represents a whole class of attacks, most likely, there cannot be a single patch for it. While work is already being done to address special cases of the vulnerability, the original website devoted to Spectre and Meltdown states: \"As [Spectre] is not easy to f... | large_corpus_distillation |
"Polynomial code-Example-Consider the polynomial code over GF(2)={0,1} with n=5 , m=2 , and generator polynomial g(x)=x2+x+1 . This code consists of the following code words: 0\u22c5g(x),1\u22c5g(x),x\u22c5g(x),(x+1)\u22c5g(x), x2\u22c5g(x),(x2+1)\u22c5g(x),(x2+x)\u22c5g(x),(x2+x+1)\u22c5g(x).\nOr written explicitl... | large_corpus_distillation |
"Convolutional neural network-Building blocks-Loss layer The \"loss layer\", or \"loss function\", specifies how training penalizes the deviation between the predicted output of the network, and the true data labels (during supervised learning). Various loss functions can be used, depending on the specific task.\nThe S... | large_corpus_distillation |
true value of the objective) is lower than the current best sampled function value." | large_corpus_distillation |
"Mercer's theorem-Generalizations-Mercer's theorem itself is a generalization of the result that any symmetric positive-semidefinite matrix is the Gramian matrix of a set of vectors.\nThe first generalization replaces the interval [a, b] with any compact Hausdorff space and Lebesgue measure on [a, b] is replaced by a f... | large_corpus_distillation |
"Deductive lambda calculus-Intensional versus extensional equality-mult plus plus mult mult \u20612s)\u03bbr.\u03bbs.(\u03bbm.\u03bbn.\u03bbf.m(nf))(\u03bbf.\u03bbx.f(fx))((\u03bbm.\u03bbn.\u03bbf.\u03bbx.mf(nfx))rs)=\u03bbr.\u03bbs.(\u03bbm.\u03bbn.\u03bbf.\u03bbx.mf(nfx))((\u03bbm.\u03bbn.\u03bbf.m(nf))(\u03bbf.\u03b... | large_corpus_distillation |
"Minimum-weight triangulation-Heuristics-Because of the difficulty of finding the exact solutions of the minimum-weight triangulation, many authors have studied heuristics that may in some cases find the solution although they cannot be proven to work in all cases. In particular, much of this research has focused on th... | large_corpus_distillation |
"Jensen's inequality-Proofs-It is easily seen that the subdifferential is linear in y (that is false and the assertion requires Hahn-Banach theorem to be proved) and, since the infimum taken in the right-hand side of the previous formula is smaller than the value of the same term for \u03b8 = 1, one gets \u03c6(x)\u226... | large_corpus_distillation |
"Rootkit-Defenses-System hardening represents one of the first layers of defence against a rootkit, to prevent it from being able to install. Applying security patches, implementing the principle of least privilege, reducing the attack surface and installing antivirus software are some standard security best practices ... | large_corpus_distillation |
"Ultrasonic transducer-Applications and performance-This technology, as well, can detect approaching objects and track their positions.Ultrasound can also be used to make point-to-point distance measurements by transmitting and receiving discrete bursts of ultrasound between transducers. This technique is known as Sono... | large_corpus_distillation |
"Redintegration-Models of Redintegration-Criticism The main criticism of Schweickert model concerns its discrete nature. The model treats memory in a binomial manner, where trace can be either intact, leading to correct recall, or partially decayed, with subsequent successful or unsuccessful redintegration. It does not... | large_corpus_distillation |
is as follows:\nX >0.742\n1. Select candidate 1 if 1 ; otherwise,\nX >0.695\n2. select candidate 2 if 2 ; otherwise,\nX >0.625\n3. select candidate 3 if 3 ; otherwise,\nX >0.5\n4. select candidate 4 if 4 ; otherwise,\n5. select candidate 5.\nThe expected value of our chosen candidate is 0.775.\nIn our original version ... | large_corpus_distillation |
AES-256 would have the same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search (see Key size)." | large_corpus_distillation |
"Covering code-Applications-The standard work on covering codes lists the following applications.\nCompression with distortion Data compression Decoding errors and erasures Broadcasting in interconnection networks Football pools Write-once memories Berlekamp-Gale game Speech coding Cellular telecommunications Subset su... | large_corpus_distillation |
"Socio-hydrology-Flood risk management-Levee effect Floods can be mild, severe, or catastrophic. Human societies cope with flooding with a combination of structural (e.g. levees) and non-structural measures (e.g. resettlements). Structural measures, such as levees, change the frequency and magnitude of flooding. In are... | large_corpus_distillation |
"Quantifier elimination-Basic ideas-Finally, to eliminate a universal quantifier \u2200x.F where F is quantifier-free, we transform \u00acF into disjunctive normal form, and use the fact that \u2200x.F is equivalent to \u00ac\u2203x.\u00acF." | large_corpus_distillation |
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