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"Syntactic bootstrapping-Basis of bootstrapping-The syntactic-semantic link There are a number of hypotheses that attempt to explain how children acquire various aspects of language, such as syntax and word meanings. Even within the community of those who believe in bootstrapping, there are various hypotheses that atte... | large_corpus_distillation |
"Cohen's kappa-Related statistics-Fleiss' kappa Note that Cohen's kappa measures agreement between two raters only. For a similar measure of agreement (Fleiss' kappa) used when there are more than two raters, see Fleiss (1971). The Fleiss kappa, however, is a multi-rater generalization of Scott's pi statistic, not Cohe... | large_corpus_distillation |
"Kempner function-Computational complexity-For a number of the form n=px , where p is prime and x is less than p , the Kempner function of n is p . It follows from this that computing the Kempner function of a semiprime (a product of two primes) is computationally equivalent to finding its prime factorization, be... | large_corpus_distillation |
leads directly to the 4-gigabyte limit on main memory.\nMathematics: 4,294,967,297 is a Fermat number and semiprime. It is the smallest number of the form 22n+1 which is not a prime number.\nDemographics \u2013 world population: 8,300,000,000 \u2013 Estimated population for the world as of April 2023." | large_corpus_distillation |
"Digital signature forgery-Types-Existential forgery Existential forgery (existential unforgeability, EUF) is the creation (by an adversary) of at least one message/signature pair, (m,\u03c3) , where m has never been signed by the legitimate signer. The adversary can choose m freely; m need not have any particular ... | large_corpus_distillation |
"Backtracking line search-Time efficiency-Return \u03b3j for the learning rate \u03b1n .(In Nocedal & Wright (2000) one can find a description of an algorithm with 1), 3) and 4) above, which was not tested in deep neural networks before the cited paper.) One can save time further by a hybrid mixture between two-way b... | large_corpus_distillation |
"Extended memory-Extended memory-Extended memory can also be accessed directly by DOS programs running in protected mode using VCPI or DPMI, two (different and incompatible) methods of using protected mode under DOS." | large_corpus_distillation |
"Ring (mathematics)-History-Hilbert The term \"Zahlring\" (number ring) was coined by David Hilbert in 1892 and published in 1897. In 19th century German, the word \"Ring\" could mean \"association\", which is still used today in English in a limited sense (for example, spy ring), so if that were the etymology then it ... | large_corpus_distillation |
"Morphosyntactic alignment-Morphosyntactic alignment-In linguistics, morphosyntactic alignment is the grammatical relationship between arguments\u2014specifically, between the two arguments (in English, subject and object) of transitive verbs like the dog chased the cat, and the single argument of intransitive verbs li... | large_corpus_distillation |
Y \u2192Y n\u2192\u221e\nthat n has the same distribution as n for +, and n \u221e as with probability 1. Since\n3.8.4 https://stats.libretexts.org/@go/page/10148" | large_corpus_distillation |
"Data transformation (computing)-Transformational languages-Another advantage to using regular expressions is that they will not fail the null transform test. That is, using your transformational language of choice, run a sample program through a transformation that doesn't perform any transformations. Many transformat... | large_corpus_distillation |
"Active\u2013stative alignment-Argument marking-Additionally, active languages differ from ergative languages in how split case marking intersects with Silverstein's (1976) nominal hierarchy: pronouns (1st>2nd>3rd person) > proper nouns > common nouns (human > animate > inanimate)Specifically, ergative languages with s... | large_corpus_distillation |
"Cache (computing)-In-network cache-In the TLRU algorithm, when a piece of content arrives, a cache node calculates the local TTU value based on the TTU value assigned by the content publisher. The local TTU value is calculated by using a locally defined function. Once the local TTU value is calculated the replacement ... | large_corpus_distillation |
"Adherent point-Adherent point-In mathematics, an adherent point (also closure point or point of closure or contact point) of a subset A of a topological space X, is a point x in X such that every neighbourhood of x (or equivalently, every open neighborhood of x ) contains at least one point of A.\nA point x\u2... | large_corpus_distillation |
"Distance-Metaphorical distances-Many abstract notions of distance used in mathematics, science and engineering represent a degree of difference or separation between similar objects. This page gives a few examples." | large_corpus_distillation |
are the most common use cases, this feature is not specifically restricted to those filesystem types.\nuid=n, gid=n Sets the user identifier (uid), and group identifier (gid) for all files on the filesystem.\numask=nnn, dmask=nnn, fmask=nnn Controls masking of filesystem nodes. umask - user file creation dmask - direct... | large_corpus_distillation |
"Geometric mean-Applications-This has the effect of understating movements in the index compared to using the arithmetic mean." | large_corpus_distillation |
enumerable relative to \u03a3n; \u03a31 contains the computably enumerable sets. The index sets given here are even complete for their levels, that is, all the sets in these levels can be many-one reduced to the given index sets." | large_corpus_distillation |
"Singular value-Singular value-In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator T:X\u2192Y acting between Hilbert spaces X and Y , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator T\u2217T (where T\u2217 denote... | large_corpus_distillation |
"Thematic apperception test-Psychometric characteristics-Reliability Internal consistency, a reliability estimate focusing on how highly test items correlate to each other, is often quite low for TAT scoring systems. Some authors have argued that internal consistency measures do not apply to the TAT. In contrast to tra... | large_corpus_distillation |
"Cluster analysis-Algorithms-Most k-means-type algorithms require the number of clusters \u2013 k \u2013 to be specified in advance, which is considered to be one of the biggest drawbacks of these algorithms. Furthermore, the algorithms prefer clusters of approximately similar size, as they will always assign an object... | large_corpus_distillation |
"Hedge (finance)-Examples-On the second day, a favorable news story about the widgets industry is published and the value of all widgets stock goes up. Company A, however, because it is a stronger company, increases by 10%, while Company B increases by just 5%: Long 1,000 shares of Company A at $1.10 each: $100 gain Sh... | large_corpus_distillation |
in the 1940s This global expansion provides economic points of comparison like the Big Mac Index, by which one can compare the purchasing power of different countries where the Big Mac hamburger is sold." | large_corpus_distillation |
"Maximum disjoint set-Geometric separator algorithms-Consider all possible non-overlapping subsets of Cint. There are at most 2O(r\u22c5n) such subsets. For each such subset, recursively compute the MDS of Cleft and the MDS of Cright, and return the largest combined set.The run time of this algorithm satisfies the fol... | large_corpus_distillation |
"Strong subadditivity of quantum entropy-Relationship among inequalities-All of the above important inequalities are equivalent to each other, and can also be proved directly. The following are equivalent: Monotonicity of quantum relative entropy (MONO); Monotonicity of quantum relative entropy under partial trace (MPT... | large_corpus_distillation |
"Imprecise Dirichlet process-Imprecise Dirichlet process-The question is: how should we choose the prior parameters (s,G0) of the DP, in particular the infinite dimensional one G0 , in case of lack of prior information? To address this issue, the only prior that has been proposed so far is the limiting DP obtained fo... | large_corpus_distillation |
"File system-File systems and operating systems-An automounter will automatically mount a file system when a reference is made to the directory atop which it should be mounted. This is usually used for file systems on network servers, rather than relying on events such as the insertion of media, as would be appropriate... | large_corpus_distillation |
"Universal approximation theorem-History-The bounded depth and bounded width case was first studied by Maiorov and Pinkus in 1999. They showed that there exists an analytic sigmoidal activation function such that two hidden layer neural networks with bounded number of units in hidden layers are universal approximators.... | large_corpus_distillation |
"Integer-Cardinality-The cardinality of the set of integers is equal to \u21350 (aleph-null). This is readily demonstrated by the construction of a bijection, that is, a function that is injective and surjective from Z to N={0,1,2,...}.\nSuch a function may be defined as if if x>0, with graph (set of the pairs (x,... | large_corpus_distillation |
"Alternating decision tree-Alternating decision tree structure-An alternating decision tree consists of decision nodes and prediction nodes. Decision nodes specify a predicate condition. Prediction nodes contain a single number. ADTrees always have prediction nodes as both root and leaves. An instance is classified by ... | large_corpus_distillation |
"Minimum cut-With terminal nodes-In a weighted, undirected network, it is possible to calculate the cut that separates a particular pair of vertices from each other and has minimum possible weight. A system of cuts that solves this problem for every possible vertex pair can be collected into a structure known as the Go... | large_corpus_distillation |
"Kinetic minimum spanning tree-H-minor-free graphs-Agarwal et al. developed a data structure that maintains the MST for a graph belonging to a minor closed family. It uses the idea of a \"swap\", calculating the amount by which the weight of the MST would increase if some edge in the tree e was replaced by an edge f ou... | large_corpus_distillation |
"Data Encryption Standard-Description-The key is nominally stored or transmitted as 8 bytes, each with odd parity. According to ANSI X3.92-1981 (Now, known as ANSI INCITS 92\u20131981), section 3.5: One bit in each 8-bit byte of the KEY may be utilized for error detection in key generation, distribution, and storage. B... | large_corpus_distillation |
"Glossary of engineering: M\u2013Z-M-MedianIn statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as \"the middle\" value. The basic feature of the median in describi... | large_corpus_distillation |
plaques, inflammation, APOE, neurotransmitter receptors, neurogenesis, growth factors or hormones.Machine learning algorithms with electronic health records are being studied as a way to predict AD earlier." | large_corpus_distillation |
order batching. Any improvements in these areas will automatically improve both availability and inventory turns, thanks to the adaptive nature of Buffer Management." | large_corpus_distillation |
"Induced matching-Strong coloring and neighborhoods-The minimum number of induced matchings into which the edges of a graph can be partitioned is called its strong chromatic index, by analogy with the chromatic index of the graph, the minimum number of matchings into which its edges can be partitioned. It equals the ch... | large_corpus_distillation |
"Service refactoring-Rationale-It is natural for a service to undergo changes for various reasons. The change could be required because the underlying implementation e.g. databases, legacy systems, etc. needs to be upgraded or simply because the original service logic was not making efficient use of memory. In other ca... | large_corpus_distillation |
by Seaborg. Although models from Pyykk\u00f6 and Fricke generally place element 172 as the next noble gas, there is no clear consensus on the electron configurations of elements beyond 120 and thus their placement in an extended periodic table. It is now thought that because of relativistic effects, such an extension w... | large_corpus_distillation |
"Cluster graph-Related graph classes-Every cluster graph is a block graph, a cograph, and a claw-free graph. Every maximal independent set in a cluster graph chooses a single vertex from each cluster, so the size of such a set always equals the number of clusters; because all maximal independent sets have the same size... | large_corpus_distillation |
"Learning standards-Learning standards-Learning standards (also called academic standards, content standards and curricula) are elements of declarative, procedural, schematic, and strategic knowledge that, as a body, define the specific content of an educational program. Standards are usually composed of statements tha... | large_corpus_distillation |
not responding to the extra stimulus as much and increases the magnitude of the conditioned response (faster latent time)." | large_corpus_distillation |
"BCH code-Encoding-s(x)=p(x)g(x) As an example, consider the generator polynomial 10 +x9+x8+x6+x5+x3+1 , chosen for use in the (31, 21) binary BCH code used by POCSAG and others. To encode the 21-bit message {101101110111101111101}, we first represent it as a polynomial over GF(2) 20 18 17 15 14 13 11 10 +x9+x8+x6+x5... | large_corpus_distillation |
"Hidden Markov model-Extensions-Yet another variant is the factorial hidden Markov model, which allows for a single observation to be conditioned on the corresponding hidden variables of a set of K independent Markov chains, rather than a single Markov chain. It is equivalent to a single HMM, with NK states (assuming... | large_corpus_distillation |
"Euler's totient function-Computing Euler's totient function-This gives both versions of Euler's product formula.\nAn alternative proof that does not require the multiplicative property instead uses the inclusion-exclusion principle applied to the set {1,2,\u2026,n} , excluding the sets of integers divisible by the pr... | large_corpus_distillation |
"NSA Suite B Cryptography-NSA Suite B Cryptography-Suite B was announced on 16 February 2005. A corresponding set of unpublished algorithms, Suite A, is \"used in applications where Suite B may not be appropriate. Both Suite A and Suite B can be used to protect foreign releasable information, US-Only information, and S... | large_corpus_distillation |
"Data masking-Techniques-Recently, the problem of encrypting data while preserving the properties of the entities got recognition and a newly acquired interest among the vendors and academia. New challenge gave birth to algorithms performing format-preserving encryption. These are based on the accepted Advanced Encrypt... | large_corpus_distillation |
"Naming convention (programming)-Common elements-Multiple-word identifiers A common recommendation is \"Use meaningful identifiers.\" A single word may not be as meaningful, or specific, as multiple words. Consequently, some naming conventions specify rules for the treatment of \"compound\" identifiers containing more ... | large_corpus_distillation |
"6.867 Machine learning, lecture 6 (Jaakkola) 5\n5\n0\n\u22125\n\u22122 \u22121 0 1 2\na) x\ny\n5\n0\n\u22125\n\u22122 \u22121 0 1 2\nb) x\ny\n5\n0\n\u22125\n\u22122 \u22121 0 1 2\nc) x\ny\n5\n0\n\u22125\n\u22122 \u22121 0 1 2\nd) x\ny\nFigure 2: a) a linear model fit; b) a third order polynomial model fit to the same ... | large_corpus_distillation |
"Ideal (ring theory)-Radical of a ring-Indeed, if M is a simple module and x is a nonzero element in M, then Rx=M and Ann Ann \u2061(x)\u2243M , meaning Ann \u2061(M) is a maximal ideal. Conversely, if m is a maximal ideal, then m is the annihilator of the simple R-module R/m . There is also another characteriza... | large_corpus_distillation |
"Lexeme-Description-The notion of the lexeme is central to morphology, the basis for defining other concepts in that field. For example, the difference between inflection and derivation can be stated in terms of lexemes: Inflectional rules relate a lexeme to its forms." | large_corpus_distillation |
"Statistical inference-Models and assumptions-Many statisticians prefer randomization-based analysis of data that was generated by well-defined randomization procedures. (However, it is true that in fields of science with developed theoretical knowledge and experimental control, randomized experiments may increase the ... | large_corpus_distillation |
"Nonlinear dimensionality reduction-Other algorithms-For example, the graph K = (X,E) can be constructed using a Gaussian kernel." | large_corpus_distillation |
"Cipolla's algorithm-Cipolla's algorithm-Apart from prime moduli, Cipolla's algorithm is also able to take square roots modulo prime powers." | large_corpus_distillation |
as most dramas and art films, the influence of reviews is important. Poor reviews from leading critics at major papers and magazines will often reduce audience interest and attendance." | large_corpus_distillation |
"Samsung Galaxy S6-Reception-Critical reception The Galaxy S6 received a generally positive reaction from early reviewers, noting its higher quality design over previous Samsung devices, along with refinements to its camera, the high quality of its display, and the significantly smaller amount of \"bloat\" in the devic... | large_corpus_distillation |
"Rectifier (neural networks)-Advantages-Scale-invariant: max max for a\u22650 .Rectifying activation functions were used to separate specific excitation and unspecific inhibition in the neural abstraction pyramid, which was trained in a supervised way to learn several computer vision tasks. In 2011, the use of the re... | large_corpus_distillation |
"Witness (mathematics)-Relation to game semantics-The notion of witness leads to the more general idea of game semantics. In the case of sentence \u2203x\u03c6(x) the winning strategy for the verifier is to pick a witness for \u03c6 . For more complex formulas involving universal quantifiers, the existence of a winni... | large_corpus_distillation |
"Order statistic-Probabilistic analysis-We assume throughout this section that X1,X2,\u2026,Xn is a random sample drawn from a continuous distribution with cdf FX . Denoting Ui=FX(Xi) we obtain the corresponding random sample U1,\u2026,Un from the standard uniform distribution. Note that the order statistics also s... | large_corpus_distillation |
output such as low or high price.Since NNs require training and can have a large parameter space; it is useful to optimize the network for optimal predictive ability." | large_corpus_distillation |
"Lexical analysis-Lexical grammar-The specification of a programming language often includes a set of rules, the lexical grammar, which defines the lexical syntax. The lexical syntax is usually a regular language, with the grammar rules consisting of regular expressions; they define the set of possible character sequen... | large_corpus_distillation |
"Difference bound matrix-Definition-DBMs Given a set of n variables, x1,\u2026,xn , a DBM is a matrix with column and rows indexed by 0,x1,\u2026,xn and the entries are constraints. Intuitively, for a column C and a row R , the value m at position (C,R) represents C\u227aR+m . Thus, the zone defined by a matrix... | large_corpus_distillation |
"Uncountable set-Examples-The Cantor set is an uncountable subset of R. The Cantor set is a fractal and has Hausdorff dimension greater than zero but less than one (R has dimension one). This is an example of the following fact: any subset of R of Hausdorff dimension strictly greater than zero must be uncountable." | large_corpus_distillation |
"Dining cryptographers problem-Limitations-The DC-net protocol is simple and elegant. It has several limitations, however, some solutions to which have been explored in follow-up research (see the References section below)." | large_corpus_distillation |
"End-of-file-Details-In the C standard library, the character reading functions such as getchar return a value equal to the symbolic value (macro) EOF to indicate that an end-of-file condition has occurred. The actual value of EOF is implementation-dependent and must be negative (but is commonly \u22121, such as in gli... | large_corpus_distillation |
"Logistic distribution-Applications-Logistic regression One of the most common applications is in logistic regression, which is used for modeling categorical dependent variables (e.g., yes-no choices or a choice of 3 or 4 possibilities), much as standard linear regression is used for modeling continuous variables (e.g.... | large_corpus_distillation |
"Random permutation-Generating random permutations-Note that if the uniform() function is implemented simply as random() % (m) then a bias in the results is introduced if the number of return values of random() is not a multiple of m, but this becomes insignificant if the number of return values of random() is orders o... | large_corpus_distillation |
"Tutte theorem-Equivalence to the Tutte-Berge formula-The Tutte\u2013Berge formula says that the size of a maximum matching of a graph G=(V,E) equals min odd \u2061(G\u2212U)+|V|)/2 . Equivalently, the number of unmatched vertices in a maximum matching equals max odd \u2061(G\u2212U)\u2212|U|) This formula follows f... | large_corpus_distillation |
Gt, it is also possible to find the total lengths of the shortest pairs of paths from a given source vertex s to every other vertex in the graph, in an amount of time that is proportional to a single instance of Dijkstra's algorithm." | large_corpus_distillation |
"VxWorks-Features-A list of some of the features of the OS are: Multitasking kernel with preemptive and round-robin scheduling and fast interrupt response Native 64-bit operating system (only one 64-bit architecture supported: x86-64). Data model: LP64 User-mode applications (\"Real-Time Processes\", or RTP) isolated f... | large_corpus_distillation |
"LibreOffice-Versions-Since March 2014 and version 4.2.2, two different major \"released\" versions of LibreOffice are available at any time in addition to development versions (numbered release candidates and dated nightly builds). The versions are designated to signal their appropriateness for differing user requirem... | large_corpus_distillation |
"Linear cryptanalysis-Overview-The procedure for constructing approximations is different for each cipher. In the most basic type of block cipher, a substitution\u2013permutation network, analysis is concentrated primarily on the S-boxes, the only nonlinear part of the cipher (i.e. the operation of an S-box cannot be e... | large_corpus_distillation |
"Relational algebra-Joins and join-like operators-In SQL implementations, joining on a predicate is usually called an inner join, and the on keyword allows one to specify the predicate used to filter the rows. It is important to note: forming the flattened Cartesian product then filtering the rows is conceptually corre... | large_corpus_distillation |
"DevOps toolchain-Stages of DevOps-Version Control Version Control is an important link in a DevOps toolchain and a component of software configuration management. Version Control is the management of changes to documents, computer programs, large web sites, and other collections of information. A summary of Version Co... | large_corpus_distillation |
features of the Internet, which among other things results in spam e-mail messages filling networks and computers with unsolicited commercial content. With those threats in mind, privacy-invasive software may be defined as: " | large_corpus_distillation |
"ZRTP-Authentication-Key continuity ZRTP provides a second layer of authentication against a MitM attack, based on a form of key continuity. It does this by caching some hashed key information for use in the next call, to be mixed in with the next call's DH shared secret, giving it key continuity properties analogous t... | large_corpus_distillation |
"Cantor\u2013Zassenhaus algorithm-Overview-Now, each bi(x)+\u27e8pi(x)\u27e9 is an element of a field of order qd , as noted earlier. The multiplicative subgroup of this field has order qd\u22121 and so, unless bi(x)=0 , we have bi(x)qd\u22121=1 for each i and hence bi(x)m=\u00b11 for each i. If bi(x)=0 , then o... | large_corpus_distillation |
"Polynomial regression-Polynomial regression-The explanatory (independent) variables resulting from the polynomial expansion of the \"baseline\" variables are known as higher-degree terms. Such variables are also used in classification settings." | large_corpus_distillation |
"Skewness-Relationship of mean and median-A 2005 journal article points out:Many textbooks teach a rule of thumb stating that the mean is right of the median under right skew, and left of the median under left skew. This rule fails with surprising frequency. It can fail in multimodal distributions, or in distributions ... | large_corpus_distillation |
"Proportional cake-cutting-Procedures-Thanks to the divide-and-conquer strategy, the number of iterations is only O(log n), in contrast to O(n) in the Last Diminisher procedure. In each iteration, each partner is required to make a single mark. Hence, the total number of marks required is O(n log n).\nThis algorithm ha... | large_corpus_distillation |
"Digital radio-Two-way digital radio standards-Digital cellular telephony (2G systems and later generations): GSM UMTS (sometimes called W-CDMA) TETRA IS-95 (cdmaOne) IS-136 (D-AMPS, sometimes called TDMA) IS-2000 (CDMA2000) iDEN Digital Mobile Radio: Project 25 a.k.a. \"P25\" or \"APCO-25\" TETRA TETRAPOL NXDN/dPMR DM... | large_corpus_distillation |
"Numerical digit-Numerical digit-For a given numeral system with an integer base, the number of different digits required is given by the absolute value of the base. For example, the decimal system (base 10) requires ten digits (0 through to 9), whereas the binary system (base 2) requires two digits (0 and 1)." | large_corpus_distillation |
"Sampling frame-Sampling frame-In statistics, a sampling frame is the source material or device from which a sample is drawn. It is a list of all those within a population who can be sampled, and may include individuals, households or institutions.Importance of the sampling frame is stressed by Jessen and Salant and Di... | large_corpus_distillation |
"EXPRESS (data modeling language)-EXPRESS Building blocks-Constructed datatypes can be defined within an EXPRESS schema. They are mainly used to define entities, and to specify the type of entity attributes and aggregate members.\nDatatypes can be used in a recursive way to build up more and more complex data types. E.... | large_corpus_distillation |
"Longman Dictionary of Contemporary English-Longman Defining Vocabulary-A key feature of the LDOCE is its utilization of the Longman Defining Vocabulary, a 2000-word controlled defining vocabulary used to write all of the definitions in the dictionary. This defining vocabulary was developed from Michael West's General ... | large_corpus_distillation |
"Gaussian integer-Unique factorization-As for every unique factorization domain, every Gaussian integer may be factored as a product of a unit and Gaussian primes, and this factorization is unique up to the order of the factors, and the replacement of any prime by any of its associates (together with a corresponding ch... | large_corpus_distillation |
"Binary search algorithm-Variations-Interpolation search Instead of calculating the midpoint, interpolation search estimates the position of the target value, taking into account the lowest and highest elements in the array as well as length of the array. It works on the basis that the midpoint is not the best guess in... | large_corpus_distillation |
"Additive inverse-Formal definition-If + is associative, i.e., (x\u2009+\u2009y) + z = x + (y\u2009+\u2009z) for all x,\u2009y,\u2009z, then an additive inverse is unique. To see this, let x\u2032 and x\u2033 each be additive inverses of x; then x\u2032 = x\u2032 + o = x\u2032 + (x + x\u2033) = (x\u2032 + x) + x\u2033 ... | large_corpus_distillation |
"Google I/O-Evolution-Android Pay Android Wear \"Always on\" extension to apps Wrist gestures Chrome Custom tabs Gmail Inbox availability for everyone Maps Offline mode Nanodegree, an Android course on Udacity Now Reduction in voice error Context improvements Photos Play \"About\" tabs for developer pages A/B listings ... | large_corpus_distillation |
"Sequential pattern mining-Itemset mining-Some problems in sequence mining lend themselves to discovering frequent itemsets and the order they appear, for example, one is seeking rules of the form \"if a {customer buys a car}, he or she is likely to {buy insurance} within 1 week\", or in the context of stock prices, \"... | large_corpus_distillation |
"Factorization of polynomials over finite fields-Factoring algorithms-Square-free factorization The algorithm determines a square-free factorization for polynomials whose coefficients come from the finite field Fq of order q = pm with p a prime. This algorithm firstly determines the derivative and then computes the gcd... | large_corpus_distillation |
1A denote the indicator function of an event A, then E[1A] is given by the probability of A. This is nothing but a different way of stating the expectation of a Bernoulli random variable, as calculated in the table above." | large_corpus_distillation |
"Syntactic parsing (computational linguistics)-Constituency parsing-Transition-based Following the success of O(n) transition-based parsing for dependency grammars, work began on adapting the approach to constituency parsing. The first such work was by Kenji Sagae and Alon Lavie in 2005, which relied on a feature-base... | large_corpus_distillation |
value. Let N be the submanifold of M defined by G(x)=0.\nx is a stationary point of f|N if and only if ker \u2061(d\u2061fx) contains ker \u2061(d\u2061Gx).\nFor convenience let Lx=d\u2061fx and Kx=d\u2061Gx, where d\u2061G denotes the tangent map or Jacobian TM\u2192TRp.\nThe subspace ker \u2061(Kx) has dim... | large_corpus_distillation |
"Regularization (mathematics)-Regularizers for multitask learning-Nuclear norm regularization R(w)=\u2016\u03c3(W)\u20161 where \u03c3(W) is the eigenvalues in the singular value decomposition of W Mean-constrained regularization R(f1\u22effT)=\u2211t=1T\u2016ft\u22121T\u2211s=1Tfs\u2016Hk2 This regularizer constrain... | large_corpus_distillation |
"Coppersmith's attack-H\u00e5stad's broadcast attack-Generalizations H\u00e5stad also showed that applying a linear padding to M prior to encryption does not protect against this attack. Assume the attacker learns that Ci=fi(M)e for 1\u2264i\u2264k and some linear function fi , i.e., Bob applies a pad to the messag... | large_corpus_distillation |
"Weak supervision-Assumptions-Cluster assumption The data tend to form discrete clusters, and points in the same cluster are more likely to share a label (although data that shares a label may spread across multiple clusters). This is a special case of the smoothness assumption and gives rise to feature learning with c... | large_corpus_distillation |
"SM4 (cipher)-Cipher detail-The SM4 cipher has a key size and a block size of 128 bits each. Encryption or decryption of one block of data is composed of 32 rounds. A non-linear key schedule is used to produce the round keys and the decryption uses the same round keys as for encryption, except that they are in reversed... | large_corpus_distillation |
"Software testing controversies-Oversight-Finally, there is the analysis of historical find-rates. By measuring how many bugs are found and comparing them to predicted numbers (based on past experience with similar projects), certain assumptions regarding the effectiveness of testing can be made. While not an absolute ... | large_corpus_distillation |
"Mahalanobis distance-Intuitive explanation-Putting this on a mathematical basis, the ellipsoid that best represents the set's probability distribution can be estimated by building the covariance matrix of the samples. The Mahalanobis distance is the distance of the test point from the center of mass divided by the wid... | large_corpus_distillation |
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