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"Anytime algorithm-Goals-This is often used for large decision set problems. This would generally not provide useful information unless it is allowed to finish. While this may sound similar to dynamic programming, the difference is that it is fine-tuned through random adjustments, rather than sequential." | large_corpus_distillation |
"CN2 algorithm-Description of algorithm-routine CN2(TrainingSet) let the ClassificationRuleList be empty repeat let the BestConditionExpression be Find_BestConditionExpression(TrainingSet) if the BestConditionExpression is not nil then let the TrainingSubset be the examples covered by the BestConditionExpression remove... | large_corpus_distillation |
"Bhargava factorial-Example: Factorials using set of prime numbers-Let S be the set of all prime numbers P = {2, 3, 5, 7, 11, \u2026 }.\nChoose p = 2 and form a p-ordering of P.Choose a0 = 19 arbitrarily from P." | large_corpus_distillation |
"Cramfs-Design-Files on cramfs file systems are zlib-compressed one page at a time to allow random read access. The metadata is not compressed, but is expressed in a terse representation that is more space-efficient than conventional file systems.\nThe file system is intentionally read-only to simplify its design; rand... | large_corpus_distillation |
"Double Ratchet Algorithm-Overview-The Double Ratchet Algorithm features properties that have been commonly available in end-to-end encryption systems for a long time: encryption of contents on the entire way of transport as well as authentication of the remote peer and protection against manipulation of messages. As a... | large_corpus_distillation |
of the Legendre symbol, (\u0394\u03d6) . When a prime p divides a but not b there is one root modulo p. Consequently, such primes do not contribute to the product." | large_corpus_distillation |
\u2261 1 mod n). For other numbers, the algorithm only returns \u201ccomposite\u201d with no further information." | large_corpus_distillation |
special circumstances where satellites and other long-distance communication channels cannot be relied on, such as in military communications." | large_corpus_distillation |
to reciprocate an answer.) 5.) Similarity(-)- The higher the initial POV, the more likely it is that people feel similar to one another. (And as two people feel more similar to one another, uncertainty decreases." | large_corpus_distillation |
"Fractional programming-Concave fractional programs-A fractional program in which f is nonnegative and concave, g is positive and convex, and S is a convex set is called a concave fractional program. If g is affine, f does not have to be restricted in sign. The linear fractional program is a special case of a concave f... | large_corpus_distillation |
(m) time for some \u03f5<1 , where n and m are the number of elements and the number of sets, respectively, of the instance of the set cover problem. Furthermore, it is known that the problem does not admit a polynomial kernel unless coNP NP/poly , even parameterized by the number of edges of the optimal Steiner tr... | large_corpus_distillation |
"6.8: Semi-Markov Processes\nSemi-Markov processes are generalizations of Markov processes in which the time intervals between transitions have an arbitrary\ndistribution rather than an exponential distribution. To be specific, there is an embedded Markov chain, {X n ;n\u22650} with a finite\nor count ably infinite sta... | large_corpus_distillation |
"Compound (linguistics)-Examples from different languages-Russian language In the Russian language compounding is a common type of word formation, and several types of compounds exist, both in terms of compounded parts of speech and of the way of the formation of a compound.Compound nouns may be agglutinative compounds... | large_corpus_distillation |
"Digit sum-Digit sum-In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number 9045 would be 18." | large_corpus_distillation |
"Key size-Asymmetric algorithm key lengths-Since 2015, NIST recommends a minimum of 2048-bit keys for RSA, an update to the widely-accepted recommendation of a 1024-bit minimum since at least 2002.1024-bit RSA keys are equivalent in strength to 80-bit symmetric keys, 2048-bit RSA keys to 112-bit symmetric keys, 3072-bi... | large_corpus_distillation |
"Proof by contradiction-Proof by contradiction in intuitionistic logic-In intuitionistic logic proof by contradiction is not generally valid, although some particular instances can be derived. In contrast, proof of negation and principle of noncontradiction are both intuitionistically valid." | large_corpus_distillation |
process as above, we get the sequence: 13333, 44801, 486157, 1615681, 3125281, 4219129, 9006401, 12589081, 13404751, 15576571, 16719781, \u2026.Notice there are only 3 such pseudoprimes below 500000, while there are many Frobenius (1, \u22121) and (3, \u22121) pseudoprimes below 500000." | large_corpus_distillation |
"Baire space-Properties-Every nonempty Baire space is nonmeagre. In terms of countable intersections of dense open sets, being a Baire space is equivalent to such intersections being dense, while being a nonmeagre space is equivalent to the weaker condition that such intersections are nonempty.\nEvery open subspace of ... | large_corpus_distillation |
"Corecursion-Discussion-This can be done in Python as well: The definition of zipWith can be inlined, leading to this: This example employs a self-referential data structure. Ordinary recursion makes use of self-referential functions, but does not accommodate self-referential data. However, this is not essential to the... | large_corpus_distillation |
"Emulator-Structure and organization-The following example illustrates how CPU simulation can be accomplished by an interpreter. In this case, interrupts are checked-for before every instruction executed, though this behavior is rare in real emulators for performance reasons (it is generally faster to use a subroutine ... | large_corpus_distillation |
"Type safety-Type safety in object oriented languages-In object oriented languages type safety is usually intrinsic in the fact that a type system is in place. This is expressed in terms of class definitions.\nA class essentially defines the structure of the objects derived from it and an API as a contract for handling... | large_corpus_distillation |
"Golden ratio-Golden ratio-In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a>b>0 where the Greek letter phi ( \u03c6 or \u03d5 ) denotes the golden ratio. The constan... | large_corpus_distillation |
"Secondary vector bundle structure-Construction of the secondary vector bundle structure-Proof Let (U, \u03c6) be a local coordinate system on the base manifold M with \u03c6(x) = (x1, ..., xn) and let := (x1,\u2026,xn,v1,\u2026,vN) be a coordinate system on := p\u22121(U)\u2282E adapted to it. Then p\u2217(Xk\u2202\u... | large_corpus_distillation |
"Nontotient-Nontotient-If a natural number n is a totient, it can be shown that n \u00b7 2k is a totient for all natural number k.\nThere are infinitely many even nontotient numbers: indeed, there are infinitely many distinct primes p (such as 78557 and 271129, see Sierpinski number) such that all numbers of the form 2... | large_corpus_distillation |
"Megaprime-Megaprime-As of 11 July 2023, there are 2171 known megaprimes and 104 further probable primes (PRPs) which have more than 1,000,000 digits. The first to be found was the Mersenne prime 26972593\u22121 with 2,098,960 digits, discovered in 1999 by Nayan Hajratwala, a participant in the distributed computing pr... | large_corpus_distillation |
"Protected mode-Features-386 The segment address inside the descriptor table entry is expanded to 32 bits so every byte of the physical memory can be defined as bound of the segment. The limit value inside the descriptor table entry is expanded to 20 bits and completed with a granularity flag (G-bit, for short): If G-b... | large_corpus_distillation |
"User interface-History-Just as importantly, the existence of an accessible screen \u2014 a two-dimensional display of text that could be rapidly and reversibly modified \u2014 made it economical for software designers to deploy interfaces that could be described as visual rather than textual. The pioneering applicatio... | large_corpus_distillation |
"English nouns-The syntax of nouns and noun phrases-Predeterminatives Inside the NP, but outside the nominal, there are also predeterminatives, as exemplified by all in the tree diagram above. In this case, all has a specifying role rather than a modifying role in the noun phrase, much like the determinative the, but t... | large_corpus_distillation |
"Dual linear program-Examples-Similarly, the minimum of the dual LP is attained when y1 is minimized to its lower bound under the constraints: the first constraint gives a lower bound of 3/5 while the second constraint gives a stricter lower bound of 4/6, so the actual lower bound is 4/6 and the minimum is 7 \u00b7 4/6... | large_corpus_distillation |
"Aircraft-Methods of lift-A powered, steerable aerostat is called a dirigible. Sometimes this term is applied only to non-rigid balloons, and sometimes dirigible balloon is regarded as the definition of an airship (which may then be rigid or non-rigid). Non-rigid dirigibles are characterized by a moderately aerodynamic... | large_corpus_distillation |
blocks more economically, by dynamically assigning blocks of a partition to a file as needed. To achieve this, the file system had to keep track of which blocks were used or unused by data files in a catalog or file allocation table. Though this made better use of the disc data space, it resulted in fragmentation of fi... | large_corpus_distillation |
"Binary relation-Special types of binary relations-Some important types of binary relations R over sets X and Y are listed below." | large_corpus_distillation |
"Secret sharing-Trivial secret sharing-t = n There are several (t, n) secret-sharing schemes for t = n, when all shares are necessary to recover the secret: Encode the secret as a binary number s of any length. Give to each player i aside from the last a random binary number pi of the same length as s. Give to the last... | large_corpus_distillation |
"Difference of two squares-Proof-The proof of the factorization identity is straightforward. Starting from the left-hand side, apply the distributive law to get (a+b)(a\u2212b)=a2+ba\u2212ab\u2212b2 By the commutative law, the middle two terms cancel: ba\u2212ab=0 leaving (a+b)(a\u2212b)=a2\u2212b2 The resulting ident... | large_corpus_distillation |
"General-purpose computing on graphics processing units-Stream processing-Stream filtering Stream filtering is essentially a non-uniform reduction. Filtering involves removing items from the stream based on some criteria." | large_corpus_distillation |
"Launch Pad (card game)-Card Types-Component Components consist of Metal and Fuel cards. A certain number of each is required by each Rocket in order to be eligible for advancement to the next zone: Observer - 1 Metal, 1 Fuel Explorer - 1 Metal, 2 Fuel Intrepid - 2 Metal, 2 Fuel Galactic - 3 Metal, 2 Fuel Expert Expert... | large_corpus_distillation |
"Backpropagation through time-Pseudocode-Update all the weights in f and g.\nx := f(x, a[t]); // compute the context for the next time-step " | large_corpus_distillation |
"Circle group-Elementary introduction-Another description is in terms of ordinary (real) addition, where only numbers between 0 and 1 are allowed (with 1 corresponding to a full rotation: 360\u00b0 or 2\u03c0 ), i.e. the real numbers modulo the integers: T\u2245R/Z . This can be achieved by throwing away the digits o... | large_corpus_distillation |
"Axiom of extensionality-In set theory with ur-elements-An ur-element is a member of a set that is not itself a set.\nIn the Zermelo\u2013Fraenkel axioms, there are no ur-elements, but they are included in some alternative axiomatisations of set theory.\nUr-elements can be treated as a different logical type from sets;... | large_corpus_distillation |
"Common mode current-Definitions-Differential mode (DM) is where the signal or power propagation through a conductor and return using the intended path by the designer or flowing differently in opposition to each other. Meanwhile common mode (CM) is where the parasitic circuit (unwanted) is formed between the desired c... | large_corpus_distillation |
"Generative art-History-Around the 2020s, generative AI models learned to imitate the distinct style of particular authors. For example, a generative image model such as Stable Diffusion is able to model the stylistic characteristics of an artist like Pablo Picasso (including his particular brush strokes, use of colour... | large_corpus_distillation |
Communications that this exemption is a potential security hole that could be exploited by malicious or compromised add-ons or extensions." | large_corpus_distillation |
"Bound variable pronoun-Syntax-Syntax is the branch of linguistics that deals with the formation and structure of a sentence in natural language. It is descriptive, meaning it is concerned with how language is actually used, spoken, or written by its users, unlike prescriptive grammar/prescription which is concerned wi... | large_corpus_distillation |
"Risk measure-Relation to acceptance set-There is a one-to-one correspondence between an acceptance set and a corresponding risk measure. As defined below it can be shown that RAR(X)=R(X) and ARA=A Risk measure to acceptance set If \u03c1 is a (scalar) risk measure then A\u03c1={X\u2208Lp:\u03c1(X)\u22640} is an ac... | large_corpus_distillation |
"10.1: Introduction to Estimation\nLearning Objectives\nDefine statistic\nDefine parameter\nDefine point estimate\nDefine interval estimate\nDefine margin of error\nOne of the major applications of statistics is estimating population parameters from sample statistics. For example, a poll may seek\nto estimate the propo... | large_corpus_distillation |
"Glossary of motorsport terms-K-KERS (kinetic energy recovery system) A device which recovers energy when brakes are applied and stores it until required to add power. In 2008 KERS systems started to appear in the World Rally Championship. Formula One followed soon after; its application is limited to a push to pass sy... | large_corpus_distillation |
"Books on cryptography-List-Overview of cryptography Bertram, Linda A. / Dooble, Gunther van / et al. (Eds.): Nomenclatura: Encyclopedia of modern Cryptography and Internet Security - From AutoCrypt and Exponential Encryption to Zero-Knowledge-Proof Keys, 2019, ISBN 9783746066684.\nPiper, Fred and Sean Murphy, Cryptogr... | large_corpus_distillation |
"Constructive set theory-Subtheories of ZF-Now consider the case A=\u03c9 . If \u03c7B(0)=0 , say, then the range {0}\u2282R\u2282{0,1} of \u03c7B is an inhabited, counted set, by Replacement. However, the R need not be again a decidable set itself, since the claim R={0} is equivalent to the rather strong \u2200... | large_corpus_distillation |
"Divisor sum identities-The Dirichlet inverse of an arithmetic function-For a fixed function f, let the function := if if n>1 Next, define the following two multiple, or nested, convolution variants for any fixed arithmetic function f: ds := times ds := if ds if 1.\nThe function Df(n) by the equivalent pair of su... | large_corpus_distillation |
"Symmetric algebra-Construction-From tensor algebra It is possible to use the tensor algebra T(V) to describe the symmetric algebra S(V). In fact, S(V) can be defined as the quotient algebra of T(V) by the two-sided ideal generated by the commutators v\u2297w\u2212w\u2297v." | large_corpus_distillation |
had the high bit set to allow them to be easily distinguished at runtime. Everything else on a line was left in its original format, so for instance, the line: 10 FOR I=1 TO 10 would be tokenized as: $64$81 I$B211$A410 Note that the space between FOR and I remains in the tokenized line, and the variable names and const... | large_corpus_distillation |
"Dirichlet process-Use in Dirichlet mixture models-To understand what Dirichlet processes are and the problem they solve we consider the example of data clustering. It is a common situation that data points are assumed to be distributed in a hierarchical fashion where each data point belongs to a (randomly chosen) clus... | large_corpus_distillation |
of a normal distribution required to contain of the\n\u03c3\narea and M is the standard error of the mean.\n\u03c3\nIf you look closely at this formula for a confidence interval, you will notice that you need to know the standard deviation ( ) in\n\u03c3\norder to estimate the mean. This may sound unrealistic, and it i... | large_corpus_distillation |
deviation.\nRelated Distributions\nY\nThe most important relation is the one between the folded normal distribution and the normal distribution in the definition: If has\nX=|Y|\na normal distribution then has a folded normal distribution. The folded normal distribution is also related to itself through\na symmetry prop... | large_corpus_distillation |
the identity pX,Y(x,y)=pY|X(y|x)pX(x) which, in turn, induces a mutual information I(X;Y) . The channel capacity is defined as sup pX(x)I(X;Y) where the supremum is taken over all possible choices of pX(x) " | large_corpus_distillation |
"Java syntax-Reference types-A method is called using . notation on an object, or in the case of a static method, also on the name of a class.\nThe throws keyword indicates that a method throws an exception. All checked exceptions must be listed in a comma-separated list.\nModifiers abstract - Abstract methods can be p... | large_corpus_distillation |
"Church encoding-List encodings-An (immutable) list is constructed from list nodes. The basic operations on the list are; We give four different representations of lists below: Build each list node from two pairs (to allow for empty lists).\nBuild each list node from one pair.\nRepresent the list using the right fold f... | large_corpus_distillation |
"Elliptic-curve cryptography-Elliptic curve theory-This set of points, together with the group operation of elliptic curves, is an abelian group, with the point at infinity as an identity element. The structure of the group is inherited from the divisor group of the underlying algebraic variety: Div0(E)\u2192Pic0(E)\u2... | large_corpus_distillation |
"Two-phase locking-Data-access locks-A lock is a system object associated with a shared resource such as a data item of an elementary type, a row in a database, or a page of memory. In a database, a lock on a database object (a data-access lock) may need to be acquired by a transaction before accessing the object. Corr... | large_corpus_distillation |
"Enigma rotor details-Ring setting-The ring setting will rotate the wiring. Where rotor I in the A-position normally encodes an A into an E, with a ring setting offset B-02 it will be encoded into K As mentioned before these encodings only happen after the key is pressed and the rotor has turned. Tracing the signal on ... | large_corpus_distillation |
"K-nearest neighbors algorithm-The weighted nearest neighbour classifier-The k-nearest neighbour classifier can be viewed as assigning the k nearest neighbours a weight 1/k and all others 0 weight. This can be generalised to weighted nearest neighbour classifiers. That is, where the ith nearest neighbour is assigned a... | large_corpus_distillation |
"Longest path problem-Special classes of graphs-A simple model of a directed acyclic graph is the Price model, developed by Derek J. de Solla Price to represent citation networks. This is simple enough to allow for analytic results to be found for some properties. For instance, the length of the longest path, from the ... | large_corpus_distillation |
"Algebraic K-theory-Lower K-groups-One can compute that K2 is zero for any finite field. The computation of K2(Q) is complicated: Tate proved odd prime (Z/p)\u2217 and remarked that the proof followed Gauss's first proof of the Law of Quadratic Reciprocity.For non-Archimedean local fields, the group K2(F) is the direct... | large_corpus_distillation |
"Finite field arithmetic-Multiplication-Multiplication in a finite field is multiplication modulo an irreducible reducing polynomial used to define the finite field. (I.e., it is multiplication followed by division using the reducing polynomial as the divisor\u2014the remainder is the product.) The symbol \"\u2022\" ma... | large_corpus_distillation |
bounding the complexity of k th order Voronoi diagrams.For the case when k=n/2 (halving lines), the maximum number of combinatorially distinct lines through two points of S that bisect the remaining points when k=1,2,\u2026 is Bounds have also been proven on the number of \u2264k -sets, where a \u2264k -set is a ... | large_corpus_distillation |
"Merge window-Merge window-The Linux kernel has used the merge window process since July 2005 with the release of version 2.6.14. Since then, every 2.6.*, 3.* and 4.* release has been followed by a two-week merge window.This causes much work for the project maintainers who have to merge all the patches. The process may... | large_corpus_distillation |
standard exponential distributions are related as follows:\nX V =\u2212lnX\n1. If has the standard exponential distribution then has the standard Gumbel distribution.\nV X=e\u2212V\n2. If has the standard Gumbel distribution then has the standard exponential distribution.\nProof\nv=\u2212lnx x=e\u2212v\nThese results f... | large_corpus_distillation |
"S\u00f8rensen\u2013Dice coefficient-Formula-Inserting these numbers into the formula, we calculate, s = (2 \u00b7 1) / (4 + 4) = 0.25.\nContinuous Dice Coefficient For a discrete ground truth and continuous measures the following formula can be used: cDC=2|X\u2229Y|c\u2217|X|+|Y| where c can be computed as follows: si... | large_corpus_distillation |
"Stack (C++)-Applications of stacks-Expression evaluation and syntax parsing Calculators employing reverse Polish notation use a stack structure to hold values. Expressions can be represented in prefix, postfix or infix notations and conversion from one form to another may be accomplished using a stack. Many compilers ... | large_corpus_distillation |
"Minimum description length-Statistical MDL learning-Furthermore, one is often not directly interested in specific parameters values, but just, for example, the degree of the polynomial. In that case, one sets H to be H={H0,H1,\u2026} where each Hj represents the hypothesis that the data is best described as a j-th ... | large_corpus_distillation |
"Carbon (API)-History-Classic Mac OS programming The original Mac OS used Pascal as its primary development platform, and the APIs were heavily based on Pascal's call semantics. Much of the Macintosh Toolbox consisted of procedure calls, passing information back and forth between the API and program using a variety of ... | large_corpus_distillation |
tested independently. One common testing scheme provides a test mode that forces some part of the logic machine to enter a test cycle. The test cycle usually exercises large independent parts of the machine." | large_corpus_distillation |
"E6 (mathematics)-E6 as an algebraic group-Over finite fields, the Lang\u2013Steinberg theorem implies that H1(k, E6) = 0, meaning that E6 has exactly one twisted form, known as 2E6: see below.\nAutomorphisms of an Albert Algebra Similar to how the algebraic group G2 is the automorphism group of the octonions and the a... | large_corpus_distillation |
"Deep learning-History-In 2015, Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used LSTM principles to create the Highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks. 7 months later, Kaiming He, Xiangyu Zhang; Shaoqing Ren, and Jian Sun won the ImageNet 2015 ... | large_corpus_distillation |
"Hash table-Hash table-Ideally, the hash function will assign each key to a unique bucket, but most hash table designs employ an imperfect hash function, which might cause hash collisions where the hash function generates the same index for more than one key. Such collisions are typically accommodated in some way." | large_corpus_distillation |
"Rounding-Rounding in other contexts-Some programming packages offer correct rounding. The GNU MPFR package gives correctly rounded arbitrary precision results. Some other libraries implement elementary functions with correct rounding in double precision: IBM's ml4j, which stands for Mathematical Library for Java, writ... | large_corpus_distillation |
"Adaptive Huffman coding-Algorithms-Since the FGK Algorithm has some drawbacks about the node-or-subtree swapping, Vitter proposed another algorithm to improve it.\nVitter algorithm Some important terminologies & constraints :- Implicit Numbering : It simply means that nodes are numbered in increasing order by level an... | large_corpus_distillation |
"Document-oriented database-Documents-It is here that the document store varies most from the key-value store. In theory, the values in a key-value store are opaque to the store, they are essentially black boxes. They may offer search systems similar to those of a document store, but may have less understanding about t... | large_corpus_distillation |
"Gprof-Implementation-GPROF output consists of two parts: the flat profile and the call graph. The flat profile gives the total execution time spent in each function and its percentage of the total running time. Function call counts are also reported. Output is sorted by percentage, with hot spots at the top of the lis... | large_corpus_distillation |
the argument. For example, Resnik has offered a pragmatic indispensability argument that \"claims that the justification for doing science ... also justifies our accepting as true such mathematics as science uses\"." | large_corpus_distillation |
"KCDSA-User parameters-z : the lower B bits of y." | large_corpus_distillation |
"Tag soup-Evolving specifications to solve tag soup-XML allows parsers to separate the process of interpreting the document syntax and its structure. In HTML and SGML, a parser needed to know certain rules about elements during parsing, such as what elements could be contained within other elements and which elements i... | large_corpus_distillation |
"E8 lattice-Other constructions-Hamming code The E8 lattice is very closely related to the (extended) Hamming code H(8,4) and can, in fact, be constructed from it. The Hamming code H(8,4) is a binary code of length 8 and rank 4; that is, it is a 4-dimensional subspace of the finite vector space (F2)8. Writing elements ... | large_corpus_distillation |
"Free abelian group-Properties-Rank Every two bases of the same free abelian group have the same cardinality, so the cardinality of a basis forms an invariant of the group known as its rank. Two free abelian groups are isomorphic if and only if they have the same rank. A free abelian group is finitely generated if and ... | large_corpus_distillation |
"True and false (commands)-Usage-The commands are usually employed in conditional statements and loops of shell scripts. For example, the following shell script repeats the echo hello loop until interrupted: The commands can be used to ignore the success or failure of a sequence of other commands, as in the example: Se... | large_corpus_distillation |
"Software transactional memory-Transactional locking-With CO the desired serializability property is achieved by committing transactions only in chronological order that is compatible with the precedence order (as determined by chronological orders of operations in conflicts) of the respective transactions. To enforce ... | large_corpus_distillation |
"TeraScale (microarchitecture)-TeraScale 1 (VLIW)-Ultra-threaded dispatch processor Although the R600 is a significant departure from previous designs, it still shares many features with its predecessor, the Radeon R520. The Ultra-Threaded Dispatch Processor is a major architectural component of the R600 core, just as ... | large_corpus_distillation |
"Bitap algorithm-Bitap algorithm-The bitap algorithm for exact string searching was invented by B\u00e1lint D\u00f6m\u00f6lki in 1964[1][2] and extended by R. K. Shyamasundar in 1977[3], before being reinvented by Ricardo Baeza-Yates and Gaston Gonnet[4] in 1989 (one chapter of first author's PhD thesis[5]) which also ... | large_corpus_distillation |
84 47 36 11 13 108 23 25 180 35 37 252 47 49 324 \u2212\u22f1.\nExample 4 Equal temperament's perfect fifth (27/12 or 12\u221a27 \u2248 1.498307...), with m = 7: With \"standard notation\": 12 12 19 36 17 31 60 29 43 84 41 36 19 108 17 31 180 29 43 252 41 55 324 \u2212\u22f1." | large_corpus_distillation |
d(A \u222a B, C) \u2265 min(d(A,C), d(B,C)).If a distance function has the reducibility property, then merging two clusters C and D can only cause the nearest neighbor of E to change if that nearest neighbor was one of C and D. This has two important consequences for the nearest neighbor chain algorithm. First, it can ... | large_corpus_distillation |
"Adele ring-The adele ring-For a tower of fields M/L/K, the result is: Tr Tr Tr M/K\u2061(\u03b1)\u2200\u03b1\u2208AMNL/K(NM/L(\u03b1))=NM/K(\u03b1)\u2200\u03b1\u2208AM Moreover, it can be proven that: Tr Tr Lw/Kv\u2061(\u03b1w))v\u2200\u03b1\u2208ALNL/K(\u03b1)=(\u220fw|vNLw/Kv(\u03b1w))v\u2200\u03b1\u2208AL Properti... | large_corpus_distillation |
"Lempel\u2013Ziv\u2013Welch-Algorithm-The decoder is always one code behind the encoder in building the table, so when it sees the code for \u03c9, it generates an entry for code 2p \u2212 1. Since this is the point where the encoder increases the code width, the decoder must increase the width here as well\u2014at the... | large_corpus_distillation |
"Stack-oriented programming-PostScript stacks-Procedures A procedure in a stack-based programming language is treated as a data object in its own right. In PostScript, procedures are denoted between { and }. For example, in PostScript syntax, { dup mul } represents an anonymous procedure to duplicate what is on the to... | large_corpus_distillation |
"Novelist-Process, publication and profession-Novelists apply a number of different methods to writing their novels, relying on a variety of approaches to inspire creativity. Some communities actively encourage amateurs to practice writing novels to develop these unique practices, that vary from author to author. For e... | large_corpus_distillation |
"Agent (grammar)-Theory-Typically, the situation is denoted by a sentence, the action by a verb in the sentence, and the agent by a noun phrase." | large_corpus_distillation |
"Disk buffer-Uses-Alternatively, the caching can simply be turned off when the integrity of data is deemed more important than write performance. Another option is to send data to disk in a carefully managed order and to issue \"cache flush\" commands in the right places, which is usually referred to as the implementat... | large_corpus_distillation |
"Bhattacharyya distance-Applications-A common task in classification is estimating the separability of classes. Up to a multiplicative factor, the squared Mahalanobis distance is a special case of the Bhattacharyya distance when the two classes are normally distributed with the same variances. When two classes have sim... | large_corpus_distillation |
"XHarbour-Control structures-In FOR EACH, the Var variable will have the value (scalar, or complex) of the respective element in the collection value. The collection expression, may be an Array (of any type or combinations of types), an Hash Table, or an Object type.\nIF statements IF CondExp ...\n[ELSEIF] CondExp ...\... | large_corpus_distillation |
"Code refactoring-Motivation-For a long routine, one or more smaller subroutines can be extracted; or for duplicate routines, the duplication can be removed and replaced with one shared function. Failure to perform refactoring can result in accumulating technical debt; on the other hand, refactoring is one of the prima... | large_corpus_distillation |
"Diffie\u2013Hellman key exchange-Description-Alice picks a random natural number a with 1 < a < n, and sends the element ga of G to Bob.\nBob picks a random natural number b with 1 < b < n, and sends the element gb of G to Alice.\nAlice computes the element (gb)a = gba of G.\nBob computes the element (ga)b = gab of G.... | large_corpus_distillation |
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