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"Heterogeneous random walk in one dimension-Results for random walks in one dimension-Heterogeneous systems The solution for the Green's function Gij(t;L) for a semi-Markovian random walk in an arbitrarily heterogeneous environment in 1D was recently given using the path representation. (The function Gij(t;L) is the ... | large_corpus_distillation |
"Universal approximation theorem-History-The question of minimal possible width for universality was first studied in 2021, Park et al obtained the minimum width required for the universal approximation of Lp functions using feed-forward neural networks with ReLU as activation functions. Similar results that can be dir... | large_corpus_distillation |
"StaDyn (programming language)-Runtime performance-The type information gathered by StaDyn is used to perform significant optimizations in the generated code: the number of type inspections and type casts are reduced, reflection is avoided, frequent types are cached, and methods with constraints are specialized. The po... | large_corpus_distillation |
"Semantic Web-Standards-Components The term \"Semantic Web\" is often used more specifically to refer to the formats and technologies that enable it. The collection, structuring and recovery of linked data are enabled by technologies that provide a formal description of concepts, terms, and relationships within a given... | large_corpus_distillation |
"47 (number)-In mathematics-Forty-seven is the fifteenth prime number, a safe prime, the thirteenth supersingular prime, the fourth isolated prime, and the sixth Lucas prime. Forty-seven is a highly cototient number. It is an Eisenstein prime with no imaginary part and real part of the form 3n \u2212 1." | large_corpus_distillation |
b is a purchased for $432,000. In 35 years it is worth $60,500.\nreal valued constant, is an exponential function. Find the rate of depreciation.\n102. The domain of an even root function is all real 109. [T] The total cost C (in thousands of dollars) to\nnumbers. produce a certain item is modeled by the function\nC(x)... | large_corpus_distillation |
"Discrete logarithm-Examples-Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents. For example, the equation log10\u200953 = 1.724276\u2026 means that 101.724276\u2026 = 53. While integer exponents can be defined in any group using ... | large_corpus_distillation |
"Relational frame theory-Overview-Notice that the relations between A and C were never given. They can be derived from the other relations.\nTransfer and transformation of stimulus function A stimulus can have different functions depending on contextual cues. However a stimulus function can change based on the arbitrar... | large_corpus_distillation |
"Maximum subarray problem-Kadane's algorithm-The algorithm can be adapted to the case which disallows empty subarrays or to keep track of the starting and ending indices of the maximum subarray.\nThis algorithm calculates the maximum subarray ending at each position from the maximum subarray ending at the previous posi... | large_corpus_distillation |
"Worst-case execution time-Calculation-manual static analysis techniques such as counting assembler instructions for each function, loop etc. and then combining them.Both of these techniques have limitations. End to end measurements place a high burden on software testing to achieve the longest path; counting instructi... | large_corpus_distillation |
"Guruswami\u2013Sudan list decoding algorithm-Algorithm 2 (Guruswami\u2013Sudan list decoding algorithm)-D=knr(r\u22121) Therefore, t=\u2308kn(1\u22121r)\u2309 Substitute r=2kn ,t>\u2308kn\u221212\u2309>\u2308kn\u2309 Hence proved, that Guruswami\u2013Sudan List Decoding Algorithm can list decode Reed-Solomon codes u... | large_corpus_distillation |
"Full disclosure (computer security)-Full disclosure (computer security)-In the field of computer security, independent researchers often discover flaws in software that can be abused to cause unintended behaviour; these flaws are called vulnerabilities. The process by which the analysis of these vulnerabilities is sha... | large_corpus_distillation |
"Hedge (finance)-Hedge (finance)-A hedge is an investment position intended to offset potential losses or gains that may be incurred by a companion investment. A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, gamb... | large_corpus_distillation |
"Conversational user interface-Text-based interfaces-A chatbot is a web- or mobile-based interface that allows the user to ask questions and retrieve information. This information can be generic in nature such as the Google Assistant chat window that allows for internet searches, or it can be a specific brand or servic... | large_corpus_distillation |
"Constraint grammar-Constraint grammar-The CG concept was launched by Fred Karlsson in 1990 (Karlsson 1990; Karlsson et al., eds, 1995), and CG taggers and parsers have since been written for a large variety of languages, routinely achieving accuracy F-scores for part of speech (word class) of over 99%. A number of syn... | large_corpus_distillation |
"Subderivative-Subderivative-Let f:I\u2192R be a real-valued convex function defined on an open interval of the real line. Such a function need not be differentiable at all points: For example, the absolute value function f(x)=|x| is non-differentiable when x=0 . However, as seen in the graph on the right (where f(... | large_corpus_distillation |
"Game testing-Process-A typical bug report progression of testing process is seen below: Identification. Incorrect program behavior is analyzed and identified as a bug.\nReporting. The bug is reported to the developers using a defect tracking system. The circumstances of the bug and steps to reproduce are included in t... | large_corpus_distillation |
"Scott\u2013Potter set theory-Discussion-Includes no equivalents of Choice or the axiom schema of Replacement.Hence ZU is closer to the Zermelo set theory of 1908, namely ZFC minus Choice, Replacement, and Foundation. It is stronger than this theory, however, since cardinals and ordinals can be defined, despite the abs... | large_corpus_distillation |
"Overfitting-Machine learning-Generally, a learning algorithm is said to overfit relative to a simpler one if it is more accurate in fitting known data (hindsight) but less accurate in predicting new data (foresight). One can intuitively understand overfitting from the fact that information from all past experience can... | large_corpus_distillation |
"Reductive group-Lattices and arithmetic groups-Let G be a linear algebraic group over the rational numbers Q. Then G can be extended to an affine group scheme G over Z, and this determines an abstract group G(Z). An arithmetic group means any subgroup of G(Q) that is commensurable with G(Z). (Arithmeticity of a subgro... | large_corpus_distillation |
error on a test set of 100 exemplars is 0.084, smaller than the unnormalized error. Normalization yields accuracy improvement. Typically accuracy with normalized basis functions increases even more over unnormalized functions as input dimensionality increases." | large_corpus_distillation |
the right time window after most tonic-clonic or complex partial epileptic seizures. However, due to false positives and variability in results, this test is relied upon less frequently." | large_corpus_distillation |
"Megabyte-Megabyte-In the computer and information technology fields, other definitions have been used that arose for historical reasons of convenience. A common usage has been to designate one megabyte as 1048576bytes (220 B), a quantity that conveniently expresses the binary architecture of digital computer memory. T... | large_corpus_distillation |
"Support vector machine-Empirical risk minimization-Risk minimization In supervised learning, one is given a set of training examples X1\u2026Xn with labels y1\u2026yn , and wishes to predict yn+1 given Xn+1 . To do so one forms a hypothesis, f , such that f(Xn+1) is a \"good\" approximation of yn+1 . A \"good\"... | large_corpus_distillation |
"Conditional entropy-Conditional differential entropy-As in the discrete case there is a chain rule for differential entropy: h(Y|X)=h(X,Y)\u2212h(X) :\u200a253\u200aNotice however that this rule may not be true if the involved differential entropies do not exist or are infinite." | large_corpus_distillation |
"Index (economics)-Index numbers-Index number problem The index number problem is the term used by economists to describe the limitation of statistical indexing, when used as a measurement for cost-of-living increases.For example, in the Consumer Price Index, a reference year's \"market basket\" is assigned an index nu... | large_corpus_distillation |
"BIRCH-Problem with previous methods-Previous clustering algorithms performed less effectively over very large databases and did not adequately consider the case wherein a data-set was too large to fit in main memory. As a result, there was a lot of overhead maintaining high clustering quality while minimizing the cost... | large_corpus_distillation |
"Stochastic gradient descent-Extensions and variants-RMSProp RMSProp (for Root Mean Square Propagation) is a method invented by Geoffrey Hinton in 2012 in which the learning rate is, like in Adagrad, adapted for each of the parameters. The idea is to divide the learning rate for a weight by a running average of the mag... | large_corpus_distillation |
"Pollard's kangaroo algorithm-Algorithm-4. Begin computing a second sequence of group elements {y0,y1,\u2026} according to: y0=\u03b2 for i=0,1,\u2026,N\u22121 and a corresponding sequence of integers {d0,d1,\u2026} according to: dn=\u2211i=0n\u22121f(yi) .Observe that: for i=0,1,\u2026,N\u22121 5. Stop computing t... | large_corpus_distillation |
"Land-use forecasting-Penn-Jersey model-The P-J region was divided into u small areas recognizing n household groups and m residential bundles. Each residential bundle was defined on the house of apartment, the amenity level in the neighborhood (parks, schools, etc.), and the trip set associated with the site. There is... | large_corpus_distillation |
"Principle of maximum entropy-Testable information-The principle of maximum entropy is useful explicitly only when applied to testable information. Testable information is a statement about a probability distribution whose truth or falsity is well-defined. For example, the statements the expectation of the variable x ... | large_corpus_distillation |
"Data corruption-Countermeasures-Some file systems, such as Btrfs, HAMMER, ReFS, and ZFS, use internal data and metadata checksumming to detect silent data corruption. In addition, if a corruption is detected and the file system uses integrated RAID mechanisms that provide data redundancy, such file systems can also re... | large_corpus_distillation |
"Ratio estimator-Ratio estimator-The ratio estimator is a statistical estimator for the ratio of means of two random variables. Ratio estimates are biased and corrections must be made when they are used in experimental or survey work. The ratio estimates are asymmetrical and symmetrical tests such as the t test should ... | large_corpus_distillation |
"Primorial-Definition for natural numbers-In general, for a positive integer n, its primorial, n#, is the product of the primes that are not greater than n; that is, prime p=\u220fi=1\u03c0(n)pi=p\u03c0(n)# ,where \u03c0(n) is the prime-counting function (sequence A000720 in the OEIS), which gives the number of primes ... | large_corpus_distillation |
"Inter-rater reliability-Statistics-Kappa statistics Kappa is a way of measuring agreement or reliability, correcting for how often ratings might agree by chance. Cohen's kappa, which works for two raters, and Fleiss' kappa, an adaptation that works for any fixed number of raters, improve upon the joint probability in ... | large_corpus_distillation |
"International Corpus of English-Description-Each corpus contains one million words in 500 texts of 2000 words, following the sampling methodology used for the Brown Corpus. Unlike Brown or the Lancaster-Oslo-Bergen (LOB) Corpus (or indeed mega-corpora such as the British National Corpus), however, the majority of text... | large_corpus_distillation |
"En passant-Chess problems-Or Black can play 1... cxd3 e.p.and now White exploits the newly opened a2\u2013g8 diagonal with 2.Qa2+ d5 3.cxd6 e.p.#.\nThe diagrammed composition by Sommerfeldt shows the effect of pins on en passant captures.\nThe key 1. d4!threatens 2.Qf2#. The moves of the black e-pawn are restricted i... | large_corpus_distillation |
"Concept mining-Methods-Traditionally, the conversion of words to concepts has been performed using a thesaurus, and for computational techniques the tendency is to do the same. The thesauri used are either specially created for the task, or a pre-existing language model, usually related to Princeton's WordNet.\nThe ma... | large_corpus_distillation |
"Linear grammar-Relationship with regular grammars-Observe that by inserting new nonterminals, any linear grammar can be replaced by an equivalent one where some of the rules are left-linear and some are right-linear. For instance, the rules of G above can be replaced with S \u2192 aA A \u2192 Sb S \u2192 \u03b5However... | large_corpus_distillation |
"Trace field of a representation-Fuchsian and Kleinian groups-The invariant trace field is equal to the trace field of the subgroup \u0393(2) generated by all squares of elements of \u0393 (a finite-index subgroup of \u0393 ).The invariant trace field of Fuchsian groups is stable under taking commensurable groups. T... | large_corpus_distillation |
the mathematics of fuzzy sets to establish the output of each rule, with the help of an inference mechanism. If there are M rules then the fuzzy input sets to the Inference block will activate only a subset of those rules, where the subset contains at least one rule and usually way fewer than M rules. The inference is ... | large_corpus_distillation |
"Bogosort-Running time and termination-The best case occurs if the list as given is already sorted; in this case the expected number of comparisons is n \u2212 1, and no swaps at all are carried out.For any collection of fixed size, the expected running time of the algorithm is finite for much the same reason that the ... | large_corpus_distillation |
"Recursive tree-Recursive tree-In graph theory, a recursive tree (i.e., unordered tree) is a labeled, rooted tree. A size-n recursive tree's vertices are labeled by distinct positive integers 1, 2, \u2026, n, where the labels are strictly increasing starting at the root labeled 1. Recursive trees are non-planar, which ... | large_corpus_distillation |
"Statistical learning in language acquisition-Syntactical acquisition-Experimental results Evidence from a series of four experiments conducted by Gomez and Gerken suggests that children are able to generalize grammatical structures with less than two minutes of exposure to an artificial grammar. In the first experimen... | large_corpus_distillation |
"Kernelization-Kernelizability and fixed-parameter tractability are equivalent-The other direction, that a fixed-parameter tractable problem is kernelizable and decidable is a bit more involved. Assume that the question is non-trivial, meaning that there is at least one instance that is in the language, called Iyes , ... | large_corpus_distillation |
at most 12. Building on this work, in 2016, Aaron Landesman, Peter Ruhm, and Robin Zhang showed that the same bounds hold for the full ring (all weights), with the improved bounds of 5 and 10 when \u0393 has some nonzero odd weight modular form." | large_corpus_distillation |
this method need more preparation, it is a good opportunity to improve the engineers' individual abilities." | large_corpus_distillation |
"Centrality-Closeness centrality-In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes." | large_corpus_distillation |
"MapReduce-Logical view-It is necessary but not sufficient to have implementations of the map and reduce abstractions in order to implement MapReduce. Distributed implementations of MapReduce require a means of connecting the processes performing the Map and Reduce phases. This may be a distributed file system. Other o... | large_corpus_distillation |
"Okishio's theorem-Sraffa model-The argument of Nobuo Okishio, a Japanese economist, is based on a Sraffa-model. The economy consists of two departments I and II, where I is the investments goods department (means of production) and II is the consumption goods department, where the consumption goods for workers are pro... | large_corpus_distillation |
feature is useful, it should be deleted. This is the assumption behind feature selection algorithms." | large_corpus_distillation |
"Intensity measure-Definition-Let \u03b6 be a random measure on the measurable space (S,A) and denote the expected value of a random element Y with E\u2061[Y] The intensity measure E\u2061\u03b6:A\u2192[0,\u221e] of \u03b6 is defined as E\u2061\u03b6(A)=E\u2061[\u03b6(A)] for all A\u2208A . Note the difference i... | large_corpus_distillation |
"Weighted constraint satisfaction problem-Formal definition-A Weighted Constraint Network (WCN), aka Cost Function Network (CFN), is a triplet \u27e8X,C,k\u27e9 where X is a finite set of discrete variables, C is a finite set of soft constraints and k>0 is either a natural integer or \u221e Each soft constraint c... | large_corpus_distillation |
"Four-gradient-Definition-The 4-gradient covariant components compactly written in four-vector and Ricci calculus notation are::\u200a16\u200a The comma in the last part above ,\u03bc implies the partial differentiation with respect to 4-position X\u03bc The contravariant components are::\u200a16\u200a Alternative sy... | large_corpus_distillation |
distribution of scores on a psychology test. This distribution is not symmetric: the tail in the positive\ndirection extends further than the tail in the negative direction. A distribution with the longer tail extending in the positive direction\nis said to have a positive skew. It is also described as \"skewed to the ... | large_corpus_distillation |
"Complete graph-Properties-If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament." | large_corpus_distillation |
"Salt-Non-dietary uses-Only a small percentage of the salt manufactured in the world is used in food. The remainder is used in agriculture, water treatment, chemical production, de-icing, and other industrial use cases. Sodium chloride is one of the largest volume inorganic raw materials. It is a feedstock in the produ... | large_corpus_distillation |
"Earley parser-The algorithm-Completion: For every state in S(k) of the form (Y \u2192 \u03b3 \u2022, j), find all states in S(j) of the form (X \u2192 \u03b1 \u2022 Y \u03b2, i) and add (X \u2192 \u03b1 Y \u2022 \u03b2, i) to S(k).Duplicate states are not added to the state set, only new ones. These three operations a... | large_corpus_distillation |
"Counting points on elliptic curves-Naive approach-Example Let E be the curve y2 = x3 + x + 1 over F5 . To count points on E, we make a list of the possible values of x, then of the quadratic residues of x mod 5 (for lookup purpose only), then of x3 + x + 1 mod 5, then of y of x3 + x + 1 mod 5. This yields the points ... | large_corpus_distillation |
the check digit is 8). If the summed value of the digits is a number ending in zero, then the check digit is also zero." | large_corpus_distillation |
"Silver machine-Preliminaries-\u2200i,hi is a partial function from Xk(i) to X, for some integer k(i).If N=\u27e8X,<,(hi)i<\u03c9\u27e9 is an eligible structure then N\u03bb is defined to be as before but with all occurrences of X replaced with X\u2229\u03bb Let N1,N2 be two eligible structures which have the same... | large_corpus_distillation |
"Statistical hypothesis testing-The testing process-\"The probability of rejecting the null hypothesis is a function of five factors: whether the test is one- or two-tailed, the level of significance, the standard deviation, the amount of deviation from the null hypothesis, and the number of observations.\" Use and imp... | large_corpus_distillation |
"Cryptographic primitive-Combining cryptographic primitives-Cryptographic primitives, on their own, are quite limited. They cannot be considered, properly, to be a cryptographic system. For instance, a bare encryption algorithm will provide no authentication mechanism, nor any explicit message integrity checking. Only ... | large_corpus_distillation |
"Computational anatomy-Shapes and forms-The central objects are shapes or forms in computational anatomy, one set of examples being the 0,1,2,3-dimensional submanifolds of R3 , a second set of examples being images generated via medical imaging such as via magnetic resonance imaging (MRI) and functional magnetic reson... | large_corpus_distillation |
"Legendre transformation-Behavior of differentials under Legendre transforms-Let f(x,y) be a function of two independent variables x and y, with the differential Assume that the function f is convex in x for all y, so that one may perform the Legendre transform on f in x, with p the variable conjugate to x (for informa... | large_corpus_distillation |
"Digital enhanced cordless telecommunications-Technical features-DECT also provides frequency-hopping spread spectrum over TDMA/TDD structure for ISM band applications. If frequency-hopping is avoided, each base station can provide up to 120 channels in the DECT spectrum before frequency reuse. Each timeslot can be ass... | large_corpus_distillation |
"Domain Name System Security Extensions-Overview-It is widely believed that securing the DNS is critically important for securing the Internet as a whole, but deployment of DNSSEC specifically has been hampered (As of 22 January 2010) by several difficulties: The need to design a backward-compatible standard that can s... | large_corpus_distillation |
"Total coloring-Total coloring-In graph theory, total coloring is a type of graph coloring on the vertices and edges of a graph. When used without any qualification, a total coloring is always assumed to be proper in the sense that no adjacent edges, no adjacent vertices and no edge and either endvertex are assigned th... | large_corpus_distillation |
"Worst-case complexity-Ways of speaking-Very frequently, the complexity tA of an algorithm A is given in asymptotic Big-O Notation, which gives its growth rate in the form tA=O(g(n)) with a certain real valued comparison function g(n) and the meaning: There exists a positive real number M and a natural number n0 ... | large_corpus_distillation |
"Author-level metrics-List of metrics-L-index L-index combines the number of citations, the number of coauthors, the age of publications into a single value, which is independent of the number of publications and conveniently ranges from 0.0 to 9.9. With c as number of citations, a as number of authors and y as number ... | large_corpus_distillation |
"6.867 Machine learning, lecture 5 (Jaakkola) 8\nwhere again the estimation of \u03b8 and \u03b8 separates from setting the noise variance \u03c32 . Note\n0\nthat this separation is achieved because we tied the prior and noise variance parameters.\n\u02c6 \u02c6\nThe above regularized problem of finding the parameter e... | large_corpus_distillation |
"Telegraph key-Electronic keyers and paddle keys-When a single-paddle key is used with an electronic keyer, continuous dits are created by holding the dit-side paddle ( \u2584 \u2584 \u2584 \u2584 \u2584 \u2584 \u2584 \u2584 ...); likewise, continuous dahs are created by holding the dah paddle ( \u2584\u2584\u2584 \u25... | large_corpus_distillation |
"Loadable kernel module-Security-macOS In OS X Yosemite and later releases, a kernel extension has to be code-signed with a developer certificate that holds a particular \"entitlement\" for this. Such a developer certificate is only provided by Apple on request and not automatically given to Apple Developer members. Th... | large_corpus_distillation |
"Train speed optimization-Advantages using train speed optimization-If the train slows down much earlier, given the right timing, it reaches the distant signal just when the home signal switches to green, and so does not need to stop. Thus, wear on the brakes is reduced and the train uses less energy. But the main reas... | large_corpus_distillation |
simple geometric series, and the polylogarithm of order 1 is the standard power series for the natural\nX\nlogarithm. Note that the probability density function of can be written in terms of the polylogarithms of orders 0 and 1:\nLi [(1\u2212p)e\u2212x] Li [(1\u2212p)e\u2212x]\ng(x)=\u2212 0 = 0 , x\u2208[0,\u221e) (5.... | large_corpus_distillation |
these registers was one of the challenges of programming the operating system (OS) kernel." | large_corpus_distillation |
"Group (periodic table)-Group names-List of group names ^f Coinage metals: authors differ on whether roentgenium (Rg) is considered a coinage metal. It is in group 11, like the other coinage metals, and is expected to be chemically similar to gold. On the other hand, being extremely radioactive and short-lived, it cann... | large_corpus_distillation |
"Phylogenetic tree-Properties-Rooted tree A rooted phylogenetic tree (see two graphics at top) is a directed tree with a unique node \u2014 the root \u2014 corresponding to the (usually imputed) most recent common ancestor of all the entities at the leaves of the tree. The root node does not have a parent node, but ser... | large_corpus_distillation |
"Multivariate normal distribution-Properties-Correlations and independence In general, random variables may be uncorrelated but statistically dependent. But if a random vector has a multivariate normal distribution then any two or more of its components that are uncorrelated are independent. This implies that any two o... | large_corpus_distillation |
repeats and forms a free-running oscillator or an astable multivibrator." | large_corpus_distillation |
of a set standard of congeners, the ingested alcoholic beverage type is proposed." | large_corpus_distillation |
"Graded ring-Graded monoid-Assuming the gradations of non-identity elements are non-zero, the number of elements of gradation n is at most gn where g is the cardinality of a generating set G of the monoid. Therefore the number of elements of gradation n or less is at most n+1 (for g=1 ) or gn+1\u22121g\u22121 else.... | large_corpus_distillation |
"Stack buffer overflow-Stack buffer overflow-Stack buffer overflow bugs are caused when a program writes more data to a buffer located on the stack than what is actually allocated for that buffer. This almost always results in corruption of adjacent data on the stack, and in cases where the overflow was triggered by mi... | large_corpus_distillation |
Definition: SQUARE ROOT PROPERTY\n\u2212\u2212 \u2212\u2212\nIf x2=k, and k\u22650, then x=\u221ak or x=\u2212\u221ak.\nNotice that the Square Root Property gives two solutions to an equation of the form\nx2=k:\nthe principal square root of k and its\n\u2212\u2212\nopposite. We could also write the solution as x=\u00b1... | large_corpus_distillation |
"Matrix (mathematics)-Computational aspects-Determining the complexity of an algorithm means finding upper bounds or estimates of how many elementary operations such as additions and multiplications of scalars are necessary to perform some algorithm, for example, multiplication of matrices. Calculating the matrix produ... | large_corpus_distillation |
dropped in favour of treatment of presumed cases, the daily updates of laboratory confirmed cases were stopped. A weekly epidemiological update and pandemic flu update are published each Tuesday, with much detailed information including regional information and breakdown by age." | large_corpus_distillation |
"Float (money supply)-Definition-\"Float is money in the banking system that is counted twice, for a brief time, because of delays in processing checks or any transfer of cash\", as defined by the Federal Reserve Banks of United States. It is most obvious in the time delay between a cheque being written and the funds ... | large_corpus_distillation |
"Social navigation-Tag-based social navigation-Navigation is considered to have advantages over searching, since recognizing what users are looking for is easier than formulating and describing the information people need, which refers to the \"vocabulary problem\". Social tagging serves as a new social way of organizi... | large_corpus_distillation |
"Logarithmic integral function-Asymptotic expansion-The asymptotic behavior for x \u2192 \u221e is li ln \u2061x).\nwhere O is the big O notation. The full asymptotic expansion is li ln ln \u2061x)k or li ln ln ln ln \u2061x)3+\u22ef.\nThis gives the following more accurate asymptotic behaviour: li ln ln \u2061x)2).\n... | large_corpus_distillation |
"Shell script-Interoperability among scripting languages-One example of this is Bash, which offers the same grammar and syntax as the Bourne shell, and which also provides a POSIX-compliant mode. As such, most shell scripts written for the Bourne shell can be run in BASH, but the reverse may not be true since BASH has ... | large_corpus_distillation |
"Traveling library-Traveling library-A traveling library is a collection of books lent for stated periods by a central library to a branch library, club, or other organization or, in some instances, to an individual. The chief characteristics from which it derives its name are its temporary location in the place to whi... | large_corpus_distillation |
"Bookbinding-Bookbinding-The trade of binding books is in two parts: The first is stationery binding (vellum) for books planned to be written in. These include: accounting ledgers, business journals, blank-page books, guest logbooks, notebooks, manifold books, day books, diaries, and portfolios. The second is letterpre... | large_corpus_distillation |
"Information content-Derivation-By definition, information is transferred from an originating entity possessing the information to a receiving entity only when the receiver had not known the information a priori. If the receiving entity had previously known the content of a message with certainty before receiving the m... | large_corpus_distillation |
"Circuit satisfiability problem-Proof of NP-Completeness-Given a circuit and a satisfying set of inputs, one can compute the output of each gate in constant time. Hence, the output of the circuit is verifiable in polynomial time. Thus Circuit SAT belongs to complexity class NP. To show NP-hardness, it is possible to co... | large_corpus_distillation |
"Pseudopolynomial time number partitioning-Pseudopolynomial time number partitioning-Suppose the input to the algorithm is a multiset S of cardinality N S = {x1, ..., xN}Let K be the sum of all elements in S. That is: K = x1 + ... + xN. We will build an algorithm that determines whether there is a subset of S that su... | large_corpus_distillation |
"Parallel breadth-first search-Serial breadth-first search-1 define bfs_sequential(graph(V,E), source s): 2 for all v in V do 3 d[v] = -1; 4 d[s] = 0; level = 1; FS = {}; NS = {}; 5 push(s, FS); 6 while FS !empty do 7 for u in FS do 8 for each neighbour v of u do 9 if d[v] = -1 then 10 push(v, NS); 11 d[v] = level; 1... | large_corpus_distillation |
methods. Application techniques constitute the \"use\" component of the method which continues to evolve and grow throughout the life of the method. The method procedure, language constructs, and application techniques are reviewed and tested to iteratively refine the method." | large_corpus_distillation |
"Memory disambiguation-Memory disambiguation mechanisms-Avoiding WAR and WAW dependencies Values from store instructions are not committed to the memory system (in modern microprocessors, CPU cache) when they execute. Instead, the store instructions, including the memory address and store data, are buffered in a store ... | large_corpus_distillation |
"Digital electronics-Design-In register transfer logic, binary numbers are stored in groups of flip flops called registers. A sequential state machine controls when each register accepts new data from its input. The outputs of each register are a bundle of wires called a bus that carries that number to other calculatio... | large_corpus_distillation |
"Shapley\u2013Folkman lemma-Statements of the three main results-The converse of Shapley\u2013Folkman lemma In particular, the Shapley\u2013Folkman lemma requires the vector space to be finite-dimensional.\nShapley\u2013Folkman theorem Shapley and Folkman used their lemma to prove the following theorem, which quantifie... | large_corpus_distillation |
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