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"Data model-Types-Semantic data model A semantic data model in software engineering is a technique to define the meaning of data within the context of its interrelationships with other data. A semantic data model is an abstraction that defines how the stored symbols relate to the real world. A semantic data model is so... | large_corpus_distillation |
"Concentration dimension-Examples-If B is n-dimensional Euclidean space Rn with its usual Euclidean norm, and X is a standard Gaussian random variable, then \u03c3(X) = 1 and E[||X||2] = n, so d(X) = n.\nIf B is Rn with the supremum norm, then \u03c3(X) = 1 but E[||X||2] (and hence d(X)) is of the order of log(n)." | large_corpus_distillation |
"Relational model-Set-theoretic formulation-Basic notions in the relational model are relation names and attribute names. We will represent these as strings such as \"Person\" and \"name\" and we will usually use the variables r,s,t,\u2026 and a,b,c to range over them. Another basic notion is the set of atomic values... | large_corpus_distillation |
"Engel's theorem-Proof-Step 1: Find an ideal h of codimension one in g This is the most difficult step. Let h be a maximal (proper) subalgebra of g , which exists by finite-dimensionality. We claim it is an ideal of codimension one. For each X\u2208h , it is easy to check that (1) ad \u2061(X) induces a linear en... | large_corpus_distillation |
"Whirlpool (hash function)-Whirlpool hashes-The following demonstrates a 43-byte ASCII input (not including quotes) and the corresponding Whirlpool hashes: Even a small change in the message will (with an extremely high probability of 10 154 ) result in a different hash, which will usually look completely different ju... | large_corpus_distillation |
"Side effect (computer science)-Referential transparency-Absence of side effects is a necessary, but not sufficient, condition for referential transparency. Referential transparency means that an expression (such as a function call) can be replaced with its value. This requires that the expression is pure, that is to s... | large_corpus_distillation |
"Doomsday rule-Finding a year's anchor day-Extending this to get the anchor day, the procedure is often described as accumulating a running total T in six steps, as follows: Let T be the year's last two digits.\nIf T is odd, add 11.\nNow let T = T/2.\nIf T is odd, add 11.\nNow let T = 7 \u2212 (T mod 7)." | large_corpus_distillation |
"Salman A. Avestimehr-Selected publications-C. He, M. Annavaram, and A. S. Avestimehr, \u201cGroup Knowledge Transfer: Federated Learning of Large CNNs at the Edge,\u201d in NeurIPS, 2020.\nC. He, et al, A. S. Avestimehr, \u201cFedML: A research library and benchmark for federated machine learning\u201d.\nQ. Yu, S. Li,... | large_corpus_distillation |
"\u0160id\u00e1k correction-Proof-The \u0160id\u00e1k correction is derived by assuming that the individual tests are independent. Let the significance threshold for each test be \u03b11 ; then the probability that at least one of the tests is significant under this threshold is (1 - the probability that none of them ... | large_corpus_distillation |
"Integrated master plan-Rationale-The event focus asks and answers the question what does done look like? rather than what work has been done. Certainly work must be done to complete a task, but a focus solely on the work hides the more important metric of are we meeting our commitments? While meeting commitments is cr... | large_corpus_distillation |
"Jun'ichi Tsujii-Selected publications-Tsujii, J.; Ananiadou, S. (2005). \"Thesaurus or Logical Ontology, Which One Do We Need for Text Mining?\". Language Resources and Evaluation. 39: 77\u201390. doi:10.1007/s10579-005-2697-0. S2CID 3204827.\nKazama, J. I.; Tsujii, J. I. (2005). \"Maximum Entropy Models with Inequali... | large_corpus_distillation |
"Grunwald\u2013Wang theorem-Wang's counter-example-Thus, 16 is an 8th power in K if and only if 2, \u22122 or \u22121 is a square in K. Let p be any odd prime. It follows from the multiplicativity of the Legendre symbol that 2, \u22122 or \u22121 is a square modulo p. Hence, by Hensel's lemma, 2, \u22122 or \u22121 is ... | large_corpus_distillation |
property of XAdES is that electronically signed documents can remain valid for long periods, even if underlying cryptographic algorithms are broken." | large_corpus_distillation |
"Work systems-Work system life cycle model-The work system life cycle model is iterative and includes both planned and unplanned change. It is fundamentally different from the frequently cited Systems Development Life Cycle (SDLC), which actually describes projects that attempt to produce software or produce changes in... | large_corpus_distillation |
"Fixed-point combinator-Fixed-point combinators in lambda calculus-The let expression may be regarded as the definition of the function y, where z is the parameter. Instantiation z as y in the call gives let in \u2061yy.\nAnd, because the parameter z always passes the function y, let in \u2061yy.\nUsing the eta reducti... | large_corpus_distillation |
"Edit distance-Formal definition and properties-For the task of correcting OCR output, merge and split operations have been used which replace a single character into a pair of them or vice versa.Other variants of edit distance are obtained by restricting the set of operations. Longest common subsequence (LCS) distance... | large_corpus_distillation |
"Glossary of group theory-G-generating set A generating set of a group G is a subset S of G such that every element of G can be expressed as a combination (under the group operation) of finitely many elements of S and inverses of elements of S.\ngroup automorphism See automorphism.\ngroup homomorphism See homomorphism.... | large_corpus_distillation |
"Wpa supplicant-Vulnerability to KRACK-wpa_supplicant was especially susceptible to KRACK, as it can be manipulated to install an all-zeros encryption key, effectively nullifying WPA2 protection in a man-in-the-middle attack. Version 2.7 fixed KRACK and several other vulnerabilities." | large_corpus_distillation |
"Glossary of category theory-M-monadic 1. An adjunction is said to be monadic if it comes from the monad that it determines by means of the Eilenberg\u2013Moore category (the category of algebras for the monad).\n2. A functor is said to be monadic if it is a constituent of a monadic adjunction.\nmonoidal category A mon... | large_corpus_distillation |
"LEA (cipher)-KCMVP-LEA is one of the cryptographic algorithms approved by the Korean Cryptographic Module Validation Program (KCMVP)." | large_corpus_distillation |
"Algorithmic efficiency-Measures of resource usage-Virtual memory is most often implemented in terms of secondary storage such as a hard disk, and is an extension to the memory hierarchy that has much larger storage space but much larger latency, typically around 1000 times slower than a cache miss for a value in RAM. ... | large_corpus_distillation |
"Multiset-Basic properties and operations-There is an inclusion\u2013exclusion principle for finite multisets (similar to the one for sets), stating that a finite union of finite multisets is the difference of two sums of multisets: in the first sum we consider all possible intersections of an odd number of the given m... | large_corpus_distillation |
"Filter (set theory)-Filters and prefilters-Many of the properties of B defined above and below, such as \"proper\" and \"directed downward,\" do not depend on X, so mentioning the set X is optional when using such terms. Definitions involving being \"upward closed in X, \" such as that of \"filter on X, \" do dep... | large_corpus_distillation |
after 10 years?\nSimplify the expression, to show Jamal\u2019s salary in dollars.\nYear Salary\n1 $35,000(1.03)\n2\n$35,000(1.03)2\n3\n$35,000(1.03)3\n... ...\n10 ?\n\uf128 Exercise 80\nClearance A department store is clearing out merchandise in order to make room for new inventory. The plan is to mark down\nitems by 3... | large_corpus_distillation |
"Mutual authentication-Password-based schemes-In mutual authentication schemes that require a user's input password as part of the verification process, there is a higher vulnerability to hackers because the password is human-made rather than a computer-generated certificate. While applications could simply require use... | large_corpus_distillation |
perspective). Also, if a process terminates without acquiring its maximum resource it only makes it easier on the system." | large_corpus_distillation |
"Coherent risk measure-Set-valued-In a situation with Rd -valued portfolios such that risk can be measured in n\u2264d of the assets, then a set of portfolios is the proper way to depict risk. Set-valued risk measures are useful for markets with transaction costs.\nProperties A set-valued coherent risk measure is a f... | large_corpus_distillation |
"Magnetic-tape data storage-Technical details-Encryption Standards exist to encrypt tapes. Encryption is used so that even if a tape is stolen, the thieves cannot use the data on the tape. Key management is crucial to maintain security. Compression is more efficient if done before encryption, as encrypted data cannot b... | large_corpus_distillation |
"Generator (computer programming)-Timeline-Haskell In Haskell, with its lazy evaluation model, every datum created with a non-strict data constructor is generated on demand. For example, where (:) is a non-strict list constructor, cons, and $ is just a \"called-with\" operator, used for parenthesization. This uses the ... | large_corpus_distillation |
variation of the GANs is used in training a network to generate optimal control inputs to nonlinear dynamical systems. Where the discriminatory network is known as a critic that checks the optimality of the solution and the generative network is known as an Adaptive network that generates the optimal control. The criti... | large_corpus_distillation |
for variations in how it presents itself. This is particularly useful for conservation because it allows future users to examine the document in a system that works for multiple different pieces of art. If the software or materials for one piece of art becomes obsolete, future researchers will be able to examine the ne... | large_corpus_distillation |
to use FST for morphological analysis, especially for languages for which there is a lot of available training data. For such languages, it is possible to build character-level language models without explicit use of a morphological parser." | large_corpus_distillation |
"SemEval-SemEval-This series of evaluations is providing a mechanism to characterize in more precise terms exactly what is necessary to compute in meaning. As such, the evaluations provide an emergent mechanism to identify the problems and solutions for computations with meaning. These exercises have evolved to articul... | large_corpus_distillation |
"Priority ceiling protocol-Priority ceiling protocol-In real-time computing, the priority ceiling protocol is a synchronization protocol for shared resources to avoid unbounded priority inversion and mutual deadlock due to wrong nesting of critical sections. In this protocol each resource is assigned a priority ceiling... | large_corpus_distillation |
"P-group-Examples-Unitriangular matrix groups The Sylow subgroups of general linear groups are another fundamental family of examples. Let V be a vector space of dimension n with basis { e1, e2, ..., en } and define Vi to be the vector space generated by { ei, ei+1, ..., en } for 1 \u2264 i \u2264 n, and define Vi = 0 ... | large_corpus_distillation |
"Additive function-Examples-a0(n) \u2013 the sum of primes dividing n counting multiplicity, sometimes called sopfr(n), the potency of n or the integer logarithm of n (sequence A001414 in the OEIS). For example:a0(4) = 2 + 2 = 4 a0(20) = a0(22 \u00b7 5) = 2 + 2 + 5 = 9 a0(27) = 3 + 3 + 3 = 9 a0(144) = a0(24 \u00b7 32) ... | large_corpus_distillation |
resistance offered by SHA2-384 and SHA2-512. The authors stated that \"claiming or relying on security strength levels above 256 bits is meaningless\"." | large_corpus_distillation |
"Monad (category theory)-Monads and adjunctions-Monadic adjunctions Given any adjunction (F:C\u2192D,G:D\u2192C,\u03b7,\u03b5) with associated monad T, the functor G can be factored as forget C, i.e., G(Y) can be naturally endowed with a T-algebra structure for any Y in D. The adjunction is called a monadic adjunction... | large_corpus_distillation |
"Regular language-The number of words in a regular language-Let sL(n) denote the number of words of length n in L . The ordinary generating function for L is the formal power series SL(z)=\u2211n\u22650sL(n)zn." | large_corpus_distillation |
International SAT Solver Competition has a parallel track reflecting recent advances in parallel SAT solving. In 2016, 2017 and 2018, the benchmarks were run on a shared-memory system with 24 processing cores, therefore solvers intended for distributed memory or manycore processors might have fallen short." | large_corpus_distillation |
"Mathematical induction-Variants-Example: forming dollar amounts by coins Assume an infinite supply of 4- and 5-dollar coins. Induction can be used to prove that any whole amount of dollars greater than or equal to 12 can be formed by a combination of such coins. Let S(k) denote the statement \"k dollars can be formed ... | large_corpus_distillation |
64 family of processors (except for Athlon X2 7000 series which is based on K10)." | large_corpus_distillation |
"FourQ-Cryptographic properties-Security The currently best known discrete logarithm attack is the generic Pollard's rho algorithm, requiring about 122.5 group operations on average. Therefore, it typically belongs to the 128 bit security level.\nIn order to prevent timing attacks, all group operations are done in con... | large_corpus_distillation |
"Data pre-processing-Applications-Data preprocessing allows for the removal of unwanted data with the use of data cleaning, this allows the user to have a dataset to contain more valuable information after the preprocessing stage for data manipulation later in the data mining process. Editing such dataset to either cor... | large_corpus_distillation |
"Covariance matrix-Applications-This is called principal component analysis (PCA) and the Karhunen\u2013Lo\u00e8ve transform (KL-transform)." | large_corpus_distillation |
exactly once, and so the solution that moves all tokens exactly once must be optimal." | large_corpus_distillation |
languages is closed under a particular operation when the operation, applied to languages in the class, always produces a language in the same class again. For instance, the context-free languages are known to be closed under union, concatenation, and intersection with regular languages, but not closed under intersecti... | large_corpus_distillation |
"Permutation-Other uses of the term permutation-For example, the number of distinct anagrams of the word MISSISSIPPI is: 11 34650 .A k-permutation of a multiset M is a sequence of length k of elements of M in which each element appears a number of times less than or equal to its multiplicity in M (an element's repetiti... | large_corpus_distillation |
"File-system permissions-POSIX permissions-Permissions on Unix-like file systems are defined in the POSIX.1-2017 standard, which uses three scopes or classes known as user, group, and others. When a file is created its permissions are restricted by the umask of the process that created it.\nClasses Files and directorie... | large_corpus_distillation |
"Aggregation (linguistics)-Examples-A simple example of syntactic aggregation is merging the two sentences John went to the shop and John bought an apple into the single sentence John went to the shop and bought an apple.\nSyntactic aggregation can be much more complex than this. For example, aggregation can embed one ... | large_corpus_distillation |
"Visual search engine-Visual information searchers-https://www.3dfindit.com/ Mobile visual search A mobile image searcher is a type of search engine designed exclusively for mobile phones, through which you can find any information on Internet, through an image made with the own mobile phone or using certain words (key... | large_corpus_distillation |
"Morphological pattern-Note-It is important to distinguish the paradigm of a lexeme from a morphological pattern. In the context of an inflecting language, an inflectional morphological pattern is not the explicit list of inflected forms. A morphological pattern usually references a prototypical class of inflectional f... | large_corpus_distillation |
"Crash test-Crash test-A crash test is a form of destructive testing usually performed in order to ensure safe design standards in crashworthiness and crash compatibility for various modes of transportation (see automobile safety) or related systems and components." | large_corpus_distillation |
"Tracy\u2013Widom distribution-Asymptotics-Probability density function Let f\u03b2(x)=F\u03b2\u2032(x) be the probability density function for the distribution, thenIn particular, we see that it is severely skewed to the right: it is much more likely for \u03bbmax to be much larger than 2\u03c3N than to be much sma... | large_corpus_distillation |
to also calculate tips and split bills, show how to prepare dishes from a recipe and can use text-to-speech." | large_corpus_distillation |
"Square number-Properties-All fourth powers, sixth powers, eighth powers and so on are perfect squares.\nA unique relationship with triangular numbers Tn is: " | large_corpus_distillation |
"Numerical methods for linear least squares-Orthogonal decomposition methods-Orthogonal decomposition methods of solving the least squares problem are slower than the normal equations method but are more numerically stable because they avoid forming the product XTX.\nThe residuals are written in matrix notation as r=y\... | large_corpus_distillation |
"Scale-free network-Characteristics-Clustering Another important characteristic of scale-free networks is the clustering coefficient distribution, which decreases as the node degree increases. This distribution also follows a power law. This implies that the low-degree nodes belong to very dense sub-graphs and those su... | large_corpus_distillation |
"Asymptotic theory (statistics)-Asymptotic theorems-Central limit theorem Continuous mapping theorem Glivenko\u2013Cantelli theorem Law of large numbers Law of the iterated logarithm Slutsky's theorem Delta method " | large_corpus_distillation |
"Job Control Language-OS JCL-Run STEP05, even if STEP03 abnormally ended.This translates to the following pseudocode: run STEP01 if STEP01's return code is greater than or equal to 4 then run STEP02 end if if any previous return code is less than 8 then run STEP03 end if if STEP01 abnormally ended then run STEP04 end i... | large_corpus_distillation |
"Train station-Train station-A train station, railway station, railroad station, or railway depot is a railway facility where trains stop to load or unload passengers, freight, or both. It generally consists of at least one platform, one track, and a station building providing such ancillary services as ticket sales, w... | large_corpus_distillation |
"Culling-Pedigreed animals-For example, a breeder is willing to make a smaller improvement in muzzle length and muzzle shape in order to have a moderate gain in improvement of eye placement and a more dramatic improvement in eye shape. Suppose the breeder determines that she would like to see 40% improvement in eye sha... | large_corpus_distillation |
"Predicate transformer semantics-Other predicate transformers-Weakest liberal precondition An important variant of the weakest precondition is the weakest liberal precondition wlp(S,R) , which yields the weakest condition under which S either does not terminate or establishes R. It therefore differs from wp in not gua... | large_corpus_distillation |
"Intersection (set theory)-Notation and terminology-Intersection is written using the symbol \" \u2229 \" between the terms; that is, in infix notation. For example: The intersection of more than two sets (generalized intersection) can be written as: which is similar to capital-sigma notation. For an explanation of th... | large_corpus_distillation |
the product (Equation 1.5.1) and power (Equation 1.5.3) properties of logarithmic functions, rewrite the left-hand\nside of the equation as\n1.5.8 https://math.libretexts.org/@go/page/2480" | large_corpus_distillation |
"Matrix calculus-Scope-Notice that we could also talk about the derivative of a vector with respect to a matrix, or any of the other unfilled cells in our table. However, these derivatives are most naturally organized in a tensor of rank higher than 2, so that they do not fit neatly into a matrix. In the following thre... | large_corpus_distillation |
"Item-item collaborative filtering-Method-First, the system executes a model-building stage by finding the similarity between all pairs of items. This similarity function can take many forms, such as correlation between ratings or cosine of those rating vectors. As in user-user systems, similarity functions can use nor... | large_corpus_distillation |
"Nonparametric regression-Examples-Kernel regression Kernel regression estimates the continuous dependent variable from a limited set of data points by convolving the data points' locations with a kernel function\u2014approximately speaking, the kernel function specifies how to \"blur\" the influence of the data points... | large_corpus_distillation |
"Computer memory-Management-Bugs Improper management of memory is a common cause of bugs, including the following types: A memory leak occurs when a program requests memory from the operating system and never returns the memory when it's done with it. A program with this bug will gradually require more and more memory ... | large_corpus_distillation |
transform. For n \u2265 1, there are isomorphisms Hn(U,M~)\u2192\u2245HIn+1(M)." | large_corpus_distillation |
"386 Chapter 4 | Applications of Derivatives\nCorollaries of the Mean Value Theorem\nLet\u2019snowlookatthreecorollariesoftheMeanValueTheorem.Theseresultshaveimportantconsequences,whichweuse\nin upcoming sections.\nAt this point, we know the derivative of any constant function is zero. The Mean Value Theorem allows us ... | large_corpus_distillation |
"Ontology engineering-Ontology engineering-A large-scale representation of abstract concepts such as actions, time, physical objects and beliefs would be an example of ontological engineering. Ontology engineering is one of the areas of applied ontology, and can be seen as an application of philosophical ontology. Core... | large_corpus_distillation |
hypothesis, the probability distribution of the test statistic is approximately a chi-squared distribution with degrees of freedom equal to alt null , respectively the number of free parameters of models alternative and null." | large_corpus_distillation |
"Best, worst and average case-Practical consequences-On the other hand, some data structures like hash tables have very poor worst-case behaviors, but a well written hash table of sufficient size will statistically never give the worst case; the average number of operations performed follows an exponential decay curve,... | large_corpus_distillation |
"Predication (computer architecture)-History-Predicated instructions were popular in European computer designs of the 1950s, including the Mail\u00fcfterl (1955), the Zuse Z22 (1955), the ZEBRA (1958), and the Electrologica X1 (1958). The IBM ACS-1 design of 1967 allocated a \"skip\" bit in its instruction formats, and... | large_corpus_distillation |
"Fermat's little theorem-History-Pierre de Fermat first stated the theorem in a letter dated October 18, 1640, to his friend and confidant Fr\u00e9nicle de Bessy. His formulation is equivalent to the following: If p is a prime and a is any integer not divisible by p, then a p \u2212 1 \u2212 1 is divisible by p." | large_corpus_distillation |
the equivalent of about 235 evaluations, it is considered to be a significant theoretical break. Their attack was extended further to 73 rounds (of 80) in 2010 by Grechnikov. In order to find an actual collision in the full 80 rounds of the hash function, however, tremendous amounts of computer time are required. To th... | large_corpus_distillation |
the statement that the conditional probability of one\nevent given the other is the same as the unconditional probability of the event:\nP(A\u2223B)=P(A) \u27fa P(B\u2223A)=P(B) \u27fa P(A\u2229B)=P(A)P(B) (2.5.2)\nThis is how you should think of independence: knowledge that one event has occurred does not change the p... | large_corpus_distillation |
"Whitehead's lemma-Whitehead's lemma-Here, eij(s) indicates a matrix whose diagonal block is 1 and ijth entry is s The name \"Whitehead's lemma\" also refers to the closely related result that the derived group of the stable general linear group is the group generated by elementary matrices. In symbols, GL GL \u20... | large_corpus_distillation |
"Strong and weak typing-Definitions of \"strong\" or \"weak\"-A number of different language design decisions have been referred to as evidence of \"strong\" or \"weak\" typing. Many of these are more accurately understood as the presence or absence of type safety, memory safety, static type-checking, or dynamic type-c... | large_corpus_distillation |
"MacMag-Operation of the virus-The virus infects classic Macintosh computers, and the intention was that on 2 March 1988 all infected computers would show the message \"RICHARD BRANDOW, publisher of MacMag, and its entire staff would like to take this opportunity to convey their UNIVERSAL MESSAGE OF PEACE to all Macint... | large_corpus_distillation |
"BRL-CAD-History-The BRL-CAD source code repository is the oldest known public version-controlled codebase in the world that's still under active development, dating back to 1983-12-16 00:10:31 UTC." | large_corpus_distillation |
"Whitespace character-Computing applications-Programming languages In programming language syntax, spaces are frequently used to explicitly separate tokens. In most languages multiple whitespace characters are treated the same as a single whitespace character (outside of quoted strings); such languages are called free-... | large_corpus_distillation |
"Function composition-Generalizations-Considering a function as a special case of a binary relation (namely functional relations), function composition satisfies the definition for relation composition. A small circle R\u2218S has been used for the infix notation of composition of relations, as well as functions. When ... | large_corpus_distillation |
rings) that motivated Hensel's choice. Now the representatives are the q solutions in the field to xq\u2212x=0 . Call the field Zp(\u03b7) , with \u03b7 an appropriate primitive th root of unity (over Zp ). The representatives are then 0 and \u03b7i for 0\u2264i\u2264q\u22122 . Since these representatives form... | large_corpus_distillation |
"Bijection-More mathematical examples-The exponential function, g: R \u2192 R, g(x) = ex, is not bijective: for instance, there is no x in R such that g(x) = \u22121, showing that g is not onto (surjective). However, if the codomain is restricted to the positive real numbers R+\u2261(0,\u221e) , then g would be biject... | large_corpus_distillation |
block, whether it be from the main memory or another processor\u2019s cache.\nFlush: This happens when a processor places an entire cache block on the bus. This is to reflect the changes made by the processor to the cached block in the main memory." | large_corpus_distillation |
versions both in Exercise 4.5 and Exercise 4.6. Exercise 4.6 has the added merit of\nexpressing the set {\u03c9:lim n Y n (\u03c9)=0} explicitly in terms of countable unions and intersections of simple events\ninvolving finite sets of the Y n. This representation is valid whether or not the conditions of the lemma are ... | large_corpus_distillation |
"General formal ontology-Categories-Conceptual structures are mental representations of entities or universals, and they exist in an agent's mind. For example, the individual representation of the (linguistic) term \"apple\" inside an agent's mind (determined by the agent's experience, knowledge and belief, etc.).\nSym... | large_corpus_distillation |
"Polyphase merge sort-Perfect 3 file polyphase merge sort-It is easiest to look at the polyphase merge starting from its ending conditions and working backwards. At the start of each iteration, there will be two input files and one output file. At the end of the iteration, one input file will have been completely consu... | large_corpus_distillation |
"Direction-preserving function-Basic concepts-We focus on functions f:X\u2192Rn , where the domain X is a finite subset of the Euclidean space Rn . ch(X) denotes the convex hull of X." | large_corpus_distillation |
"Inequality of arithmetic and geometric means-Inequality of arithmetic and geometric means-Extensions of the AM\u2013GM inequality are available to include weights or generalized means." | large_corpus_distillation |
"Classical cipher-Types of classical ciphers-A dot or pinprick null cipher is a common classical encryption method in which dot or pinprick is placed above or below certain letters in a piece of writing. An early reference to this was when Aeneas Tacticus wrote about it in his book On the Defense of Fortifications." | large_corpus_distillation |
"Geodemographic segmentation-Clustering algorithms-The use of different algorithms leads to different results, but there is no single best approach for selecting the best algorithm, just as no algorithm offers any theoretical proof of its certainty. One of the most frequently used techniques in geodemographic segmentat... | large_corpus_distillation |
class number of a number field is finite so let a1,\u2026,ah be the ideals, representing the classes in Cl K.\nThese ideals are generated by a finite number of prime ideals p1,\u2026,pn.\nLet S be a finite set of places containing P\u221e and the finite places corresponding to p1,\u2026,pn.\nConsider the isomorph... | large_corpus_distillation |
"Binary relation-Operations-Converse If R is a binary relation over sets X and Y then RT={(y,x):xRy} is the converse relation of R over Y and X.\nFor example, = is the converse of itself, as is \u2260, and < and > are each other's converse, as are \u2264 and \u2265.\nA binary relation is equal to its converse if... | large_corpus_distillation |
"Lagrangian relaxation-The LR solution as a bound-Of particular use is the property that for any fixed set of \u03bb~\u2ab00 values, the optimal result to the Lagrangian relaxation problem will be no smaller than the optimal result to the original problem. To see this, let x^ be the optimal solution to the original p... | large_corpus_distillation |
of a program intended to run on that profile, while allowing for unspecified behavior from programs written specifically for that implementation." | large_corpus_distillation |
"Unstructured data-Dealing with unstructured data-Approaches in natural language processing Specific computational workflows have been developed to impose structure upon the unstructured data contained within text documents. These workflows are generally designed to handle sets of thousands or even millions of document... | large_corpus_distillation |
"Linear algebra-Linear algebra-Linear algebra is also used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approxim... | large_corpus_distillation |
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