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prime ideals, but the converse is not true. For example, the zero ideal in the ring of n\u2009\u00d7\u2009n matrices over a field is a prime ideal, but it is not completely prime." | large_corpus_distillation |
"Annotation-Software and engineering-Digital imaging In the digital imaging community the term annotation is commonly used for visible metadata superimposed on an image without changing the underlying master image, such as sticky notes, virtual laser pointers, circles, arrows, and black-outs (cf. redaction).In the medi... | large_corpus_distillation |
"Kernel adaptive filter-Kernel adaptive filter-Kernel adaptive filters implement a nonlinear transfer function using kernel methods. In these methods, the signal is mapped to a high-dimensional linear feature space and a nonlinear function is approximated as a sum over kernels, whose domain is the feature space. If thi... | large_corpus_distillation |
"Supercharger-Supercharging versus turbocharging-A disadvantage of supercharging is that the engine must withstand the net power output of the engine plus the power to drive the supercharger.\nTurbocharged engines are more prone to heat soak of the intake air (since turbocharging can place the hot exhaust components ne... | large_corpus_distillation |
and Arrows block (U+2B00\u2013U+2BFF Arrows) contains arrows and geometric shapes with various fills.\nThe math subset of this block is U+2B30\u2013U+2B44, U+2B47\u2013U+2B4C.\nCombining Diacritical Marks for Symbols block The Combining Diacritical Marks for Symbols block contains arrows, dots, enclosures, and overlays... | large_corpus_distillation |
"Decision tree learning-General-A tree is built by splitting the source set, constituting the root node of the tree, into subsets\u2014which constitute the successor children. The splitting is based on a set of splitting rules based on classification features. This process is repeated on each derived subset in a recurs... | large_corpus_distillation |
"Workshop on Logic, Language, Information and Computation-Ranking-According to Computer Science Conference Ranking 2010, the conference is ranked \"B\" among over 1900 international conferences across the world. It is also ranked \"B\" on The CORE Conference Ranking Exercise - CORE Portal (2021). It is currently ranked... | large_corpus_distillation |
"Integer-valued function-Algebraic properties-On an arbitrary set X, integer-valued functions form a ring with pointwise operations of addition and multiplication, and also an algebra over the ring Z of integers. Since the latter is an ordered ring, the functions form a partially ordered ring: f\u2264g\u27fa\u2200x:f(x... | large_corpus_distillation |
"Methods of computing square roots-Initial estimate-An estimate for a good to 8 bits can be obtained by table lookup on the high 8 bits of a , remembering that the high bit is implicit in most floating point representations, and the bottom bit of the 8 should be rounded. The table is 256 bytes of precomputed 8-bit sq... | large_corpus_distillation |
"Atomic commit-Usage-Atomic commits are essential for multi-step updates to data. This can be clearly shown in a simple example of a money transfer between two checking accounts.This example is complicated by a transaction to check the balance of account Y during a transaction for transferring 100 dollars from account ... | large_corpus_distillation |
"Strict conditional-Constructive logic-In a constructive setting, the symmetry between \u297d and \u25fb is broken, and the two connectives can be studied independently. Constructive strict implication can be used to investigate interpretability of Heyting arithmetic and to model arrows and guarded recursion in comput... | large_corpus_distillation |
"Rectangle-Rectangle-The word rectangle comes from the Latin rectangulus, which is a combination of rectus (as an adjective, right, proper) and angulus (angle)." | large_corpus_distillation |
"Clique problem-Algorithms-Approximation algorithms Several authors have considered approximation algorithms that attempt to find a clique or independent set that, although not maximum, has size as close to the maximum as can be found in polynomial time. Although much of this work has focused on independent sets in spa... | large_corpus_distillation |
High-School GPA ( ) and their total SAT score (verbal + math). The basic idea is to find\nHSGPA SAT UGPA\na linear combination of and that best predicts University GPA ( ). That is, the problem is to find the values\nb b UGPA\nof 1 and 2 in the equation shown below that give the best predictions of . As in the case of ... | large_corpus_distillation |
"Unimodality-Unimodal probability distribution-It is worth noting that the maximum distance is minimized at 0.5 (i.e., when the symmetric quantile average is equal to 0.5 =\u03bd ), which indeed motivates the common choice of the median as a robust estimator for the mean. Moreover, when 0.5 , the bound is equal to ... | large_corpus_distillation |
"Structured sparsity regularization-Connections to Other Areas of Machine Learning-For simplicity, the case in which there are only two dictionaries A={aj:X\u2192R,j=1,...,p} and B={bt:X\u2192R,t=1,...,q} where q and p are integers, will be considered. The atoms in A as well as the atoms in B are assumed to be li... | large_corpus_distillation |
"Ontology language-Classification of ontology languages-DAML+OIL Ontology Inference Layer (OIL) Web Ontology Language (OWL) Resource Description Framework (RDF) RDF Schema (RDFS) SHOE Controlled natural languages Attempto Controlled English Open vocabulary natural languages Executable English Classification by structur... | large_corpus_distillation |
"Sequential access memory-Sequential access memory-In computing, sequential access memory (SAM) is a class of data storage devices that read stored data in a sequence. This is in contrast to random access memory (RAM) where data can be accessed in any order. Sequential access devices are usually a form of magnetic stor... | large_corpus_distillation |
"Uninflected word-Uninflected word-Only words that cannot be inflected at all are called \"invariable\". In the strict sense of the term \"uninflected\", only invariable words are uninflected, but in broader linguistic usage, these terms are extended to be inflectable words that appear in their basic form. For example,... | large_corpus_distillation |
"Vocabulary-Vocabulary in an individual-Some words cannot be easily linked through association or other methods. When a word in the second language is phonologically or visually similar to a word in the native language, one often assumes they also share similar meanings. Though this is frequently the case, it is not al... | large_corpus_distillation |
"Computational social choice-Other topics-Tournament solutions A tournament solution is a rule that assigns to every tournament a set of winners. Since a preference profile induces a tournament through its majority relation, every tournament solution can also be seen as a voting rule which only uses information about t... | large_corpus_distillation |
"Collatz conjecture-Syracuse function-If k is an odd integer, then 3k + 1 is even, so 3k + 1 = 2ak\u2032 with k\u2032 odd and a \u2265 1. The Syracuse function is the function f from the set I of odd integers into itself, for which f(k) = k\u2032 (sequence A075677 in the OEIS)." | large_corpus_distillation |
"SCHED DEADLINE-Operation-This is not sufficient to guarantee temporal isolation. A task suspending itself shortly after its activation, and then waking up close to its current deadline or even beyond, would wake up with nearly the whole of its configured budget, with a current deadline that is very close to expire, or... | large_corpus_distillation |
"Associative classifier-Metrics-The rules of an AC inherit some of the metrics of association rules, like the support or the confidence. Metrics can be used to order or filter the rules in the model and to evaluate their quality." | large_corpus_distillation |
"Monad (category theory)-Algebras for a monad-Algebras over the distribution monad Another example is the distribution monad D on the category of sets. It is defined by sending a set X to the set of functions f:X\u2192[0,1] with finite support and such that their sum is equal to 1 . In set-builder notation, this is... | large_corpus_distillation |
"Diffie\u2013Hellman problem-Problem description-The Diffie\u2013Hellman problem is stated informally as follows: Given an element g and the values of gx and gy, what is the value of gxy?Formally, g is a generator of some group (typically the multiplicative group of a finite field or an elliptic curve group) and x and ... | large_corpus_distillation |
"Public-key cryptography-Description-Before the mid-1970s, all cipher systems used symmetric key algorithms, in which the same cryptographic key is used with the underlying algorithm by both the sender and the recipient, who must both keep it secret. Of necessity, the key in every such system had to be exchanged betwee... | large_corpus_distillation |
"Home network-Network management-Microsoft ecosystem devices Microsoft offers simple access control features built into their Windows operating system. Homegroup is a feature that allows shared disk access, shared printer access and shared scanner access among all computers and users (typically family members) in a hom... | large_corpus_distillation |
"Geometrical Product Specification and Verification-Form, orientation, location and run-out specifications-The content of each cell can be either: a single datum identified by a capital letter such as 'A' (or several capital letters without separators like 'AA' or 'AAA') or a common datum identified by a sequence of ca... | large_corpus_distillation |
picking up grocery items, and remembering times of meetings." | large_corpus_distillation |
"Range tree-Data structure-A range tree on a set of 1-dimensional points is a balanced binary search tree on those points. The points stored in the tree are stored in the leaves of the tree; each internal node stores the largest value of its left subtree.\nA range tree on a set of points in d-dimensions is a recursivel... | large_corpus_distillation |
"Information asymmetry-Solutions-Mandatory information disclosure Both signaling and screening resemble voluntary information disclosure, where the party having more information, for their own best interest, use various measures to inform the other party. However, voluntary information disclosure is not always feasible... | large_corpus_distillation |
"Universal Decimal Classification-UDC structure-=...\nCommon auxiliaries of language. Table 1c (0...) Common auxiliaries of form. Table 1d (1/9) Common auxiliaries of place. Table 1e (=...) Common auxiliaries of human ancestry, ethnic grouping and nationality. Table 1f \"...\" Common auxiliaries of time. Table 1g helps... | large_corpus_distillation |
"Hamiltonian path-Properties-The number of different Hamiltonian cycles in a complete undirected graph on n vertices is (n \u2013 1)!/2 and in a complete directed graph on n vertices is (n \u2013 1)!. These counts assume that cycles that are the same apart from their starting point are not counted separately." | large_corpus_distillation |
"Omnibus test-In logistic regression-Omnibus tests of model coefficients The table shows the \"Omnibus Test of Model Coefficients\" based on Chi-Square test, which implies that the overall model is predictive of re-arrest (focus is on row three\u2014\"Model\"): (4 degrees of freedom) = 41.15, p < .001, and the null can... | large_corpus_distillation |
"Probability distribution fitting-Uncertainty of prediction-With the binomial distribution one can obtain a prediction interval. Such an interval also estimates the risk of failure, i.e. the chance that the predicted event still remains outside the confidence interval. The confidence or risk analysis may include the re... | large_corpus_distillation |
is blocked until a fix is made. Depending on the nature of the failure, this could be a quick procedure, or could take longer." | large_corpus_distillation |
"Transformational grammar-Basic mechanisms-Deep structure and surface structure While Chomsky's 1957 book Syntactic Structures followed Harris's distributionalistic practice of excluding semantics from structural analysis, his 1965 book Aspects of the Theory of Syntax developed the idea that each sentence in a language... | large_corpus_distillation |
"Intermittent fault-Troubleshooting techniques-Some techniques to resolve intermittent faults are: Automatic logging of relevant parameters over a long enough time for the fault to manifest can help; parameter values at the time of the fault may identify the cause so that appropriate remedial action can be taken.\nChan... | large_corpus_distillation |
isomorphic to each other and have the largest possible order: if |G|=pnm with n>0 where p does not divide m, then every Sylow p-subgroup P has order |P|=pn . That is, P is a p-group and gcd (|G:P|,p)=1 . These properties can be exploited to further analyze the structure of G." | large_corpus_distillation |
"Statistical classification-Algorithms-Since no single form of classification is appropriate for all data sets, a large toolkit of classification algorithms has been developed. The most commonly used include: Artificial neural networks \u2013 Computational model used in machine learning, based on connected, hierarchica... | large_corpus_distillation |
aV\n4.\n1a\n2\n5. NV(1\u2212V)\n6.\n1a2+1a\n12 2\nMixtures of Distributions\nSuppose that X=(X 1 ,X 2 ,\u2026) is a sequence of real-valued random variables. Denote the mean, variance, and moment generating function of X i by \u03bc i =E(X i ),\n\u03c3 i 2=var(X i ), and M i (t)=E(etXi), for i\u2208N +. Suppose also th... | large_corpus_distillation |
"Discrete Fourier transform-Applications-Multiplication of large integers The fastest known algorithms for the multiplication of very large integers use the polynomial multiplication method outlined above. Integers can be treated as the value of a polynomial evaluated specifically at the number base, with the coefficie... | large_corpus_distillation |
"Probabilistic method-Two examples due to Erd\u0151s-Second example A 1959 paper of Erd\u0151s (see reference cited below) addressed the following problem in graph theory: given positive integers g and k, does there exist a graph G containing only cycles of length at least g, such that the chromatic number of G is at l... | large_corpus_distillation |
"Uncorrelatedness (probability theory)-Examples of dependence without correlation-Example 2 If X is a continuous random variable uniformly distributed on [\u22121,1] and Y=X2 , then X and Y are uncorrelated even though X determines Y and a particular value of Y can be produced by only one or two values of X :f... | large_corpus_distillation |
"Forecasting-Forecasting accuracy-Compute the forecast accuracy measures based on the errors obtained.This makes efficient use of the available data, as only one observation is omitted at each step For time series data, the training set can only include observations prior to the test set. Therefore, no future observati... | large_corpus_distillation |
"Spacer GIF-Usage-It was recognised early on that although the size of table cells could not be set directly, each cell could contain an image through an IMG tag. The size of image tags could be set independently, with their WIDTH and HEIGHT attributes. The table cell would then resize itself automatically to just cont... | large_corpus_distillation |
"Assumed mean-Example using class ranges-The mean is then estimated to be 175.5 55 100 173.85 which is very close to the actual mean of 173.846.\nThe standard deviation is estimated as 5.57 " | large_corpus_distillation |
"Ciphertext stealing-Ciphertext stealing mode description-The following steps describe how to handle the last two blocks of the plaintext, called Pn\u22121 and Pn, where the length of Pn\u22121 equals the block size of the cipher in bits, B; the length of the last block, Pn, is M bits; and K is the key that is in use. ... | large_corpus_distillation |
"Terminology-Terminology-Terminology is a discipline that systematically studies the \"labelling or designating of concepts\" particular to one or more subject fields or domains of human activity. It does this through the research and analysis of terms in context for the purpose of documenting and promoting consistent ... | large_corpus_distillation |
"Biconvex optimization-Biconvex optimization-A function f(x1,\u2026,xK)\u2192R is block multi-convex iff it is convex with respect to each of the individual arguments while holding all others fixed." | large_corpus_distillation |
"Slepian\u2013Wolf coding-Theorem-The bound for the lossless coding rates as shown below: RX\u2265H(X|Y), RY\u2265H(Y|X), RX+RY\u2265H(X,Y)." | large_corpus_distillation |
"CMA-ES-Theoretical foundations-This means that on average the distance to the optimum decreases in each iteration by a \"constant\" factor, namely by exp \u2061(\u2212c) . The convergence rate c is roughly 0.1 \u03bb/n , given \u03bb is not much larger than the dimension n . Even with optimal \u03c3 and C , the... | large_corpus_distillation |
"Acyclic orientation-Special cases-Every orientation of a tree is acyclic. The directed acyclic graph resulting from such an orientation is called a polytree.An acyclic orientation of a complete graph is called a transitive tournament, and is equivalent to a total ordering of the graph's vertices. In such an orientatio... | large_corpus_distillation |
"Photograph manipulation-Retouching human subjects-On social media Not only are photos being manipulated by professionals for the media but with the rise of social media, everyone has easy access to editing photos they post online. Social media filters have become a major part of photo manipulation. Through apps like S... | large_corpus_distillation |
"Avalanche (blockchain platform)-Design-Termination (or liveness) If network resumes synchronous operation, then all nodes will achieve agreement.Avalanche, like other asynchronous networks, is not guaranteed to terminate and thus does not have the liveness property, during asynchrony. Like Paxos, Avalanche's goal is t... | large_corpus_distillation |
"Flash memory-Principles of operation-The architecture of NAND flash means that data can be read and programmed (written) in pages, typically between 4 KiB and 16 KiB in size, but can only be erased at the level of entire blocks consisting of multiple pages. When a block is erased, all the cells are logically set to 1.... | large_corpus_distillation |
"Life and death-Status of a group-The unsettled status is therefore most worthy of attention. By playing first, the attacking player can kill such a group. By playing first, the defending player can save such a group. There is an enormous range of formations that are unsettled." | large_corpus_distillation |
"Error exponent-Error exponent in source coding-A simple upper bound for the term on the left can be established as [P(P(X1n(i\u2032))\u2265P(X1n(i)))]\u2264(P(X1n(i\u2032))P(X1n(i)))s for some arbitrary real number s>0." | large_corpus_distillation |
Optional fields: volume/number, series, type, address, edition, month, note, key incollection A part of a book having its own title.\nRequired fields: author, title, booktitle, publisher, year Optional fields: editor, volume/number, series, type, chapter, pages, address, edition, month, note, key inproceedings An artic... | large_corpus_distillation |
"Netlib-Other projects-GNU Scientific Library (GSL), written in C and distributed under the GNU General Public License " | large_corpus_distillation |
"Miller\u2013Rabin primality test-Deterministic variants-Testing against small sets of bases When the number n to be tested is small, trying all a < 2(ln n)2 is not necessary, as much smaller sets of potential witnesses are known to suffice. For example, Pomerance, Selfridge, Wagstaff and Jaeschke have verified that if... | large_corpus_distillation |
"Rapidly-exploring random tree-Algorithm-For a general configuration space C, the algorithm in pseudocode is as follows: In the algorithm above, \"RAND_CONF\" grabs a random configuration qrand in C. This may be replaced with a function \"RAND_FREE_CONF\" that uses samples in Cfree, while rejecting those in Cobs using ... | large_corpus_distillation |
overcome) is their susceptibility to noise in the outline. Likewise, neither compares homologous points, and global change is always given more weight than local variation (which may have large biological consequences)." | large_corpus_distillation |
"Scheme (programming language)-Review of standard forms and procedures-The language is formally defined in the standards R5RS (1998) and R6RS (2007). They describe standard \"forms\": keywords and accompanying syntax, which provide the control structure of the language, and standard procedures which perform common task... | large_corpus_distillation |
"Non-extensive self-consistent thermodynamical theory-Non-extensive entropy for ideal quantum gas-The starting point of the theory is entropy for a non-extensive quantum gas of bosons and fermions, as proposed by Conroy, Miller and Plastino, which is given by Sq=SqFD+SqBE where SqFD is the non-extended version of the... | large_corpus_distillation |
representing a copy of data within different iteration bodies accordingly to the tagged-token dataflow architecture. This allows the dynamic scheduler to handle several iterations in parallel." | large_corpus_distillation |
"Selection (linguistics)-Selection (linguistics)-In linguistics, selection denotes the ability of predicates to determine the semantic content of their arguments. Predicates select their arguments, which means they limit the semantic content of their arguments. One sometimes draws a distinction between types of selecti... | large_corpus_distillation |
x86 exceptions and may be prefetch aborts (failed instruction fetches) or data aborts (failed data accesses), and may be synchronous or asynchronous. Asynchronous aborts may be precise or imprecise. MMU aborts (page faults) are synchronous." | large_corpus_distillation |
"Differential argument marking-Patterns of differential marking-Differential marking is known to be affected by a range of semantic and information structure factors. These include semantic properties of the argument such as animacy, definiteness and referentiality. It also includes properties related to the event sema... | large_corpus_distillation |
"Transitive reduction-Computational complexity-As Aho et al. show, when the time complexity of graph algorithms is measured only as a function of the number n of vertices in the graph, and not as a function of the number of edges, transitive closure and transitive reduction of directed acyclic graphs have the same comp... | large_corpus_distillation |
"Wagner\u2013Fischer algorithm-Calculating distance-Possible modifications Possible modifications to this algorithm include: We can adapt the algorithm to use less space, O(m) instead of O(mn), since it only requires that the previous row and current row be stored at any one time.\nWe can store the number of insertions... | large_corpus_distillation |
"Classical definition of probability-Classical definition of probability-The classical definition or interpretation of probability is identified with the works of Jacob Bernoulli and Pierre-Simon Laplace. As stated in Laplace's Th\u00e9orie analytique des probabilit\u00e9s, The probability of an event is the ratio of t... | large_corpus_distillation |
"Everything2-Messaging-The message system lets users send private messages to other users. The messages are stored in the user's mailbox to be read when he or she next logs in. The main use for the message system is giving constructive criticism to the author of a writeup; however, it can be and is used like any medium... | large_corpus_distillation |
"Intransitive dice-Variations-P(C>D) can be calculated by summing conditional probabilities for two events: C rolls 6 (probability 1/3); wins regardless of D (probability 1) C rolls 2 (probability 2/3); wins only if D rolls 1 (probability 1/2)The total probability of win for C is therefore (13\u00d71)+(23\u00d712)=23 W... | large_corpus_distillation |
"English verbs-Inflected forms-Archaic forms Formerly, particularly in the Old English period, the English language had a far greater degree of verb inflection than it does now (some other Germanic languages retain a greater variety of inflected forms than English does). Some of the forms used in Early Modern English h... | large_corpus_distillation |
"Betweenness centrality-Betweenness centrality-In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph, there exists at least one shortest path between the vertices such that either the number of edges that the path passes th... | large_corpus_distillation |
"Malware-Risks-Malware can exploit recently discovered vulnerabilities before developers have had time to release a suitable patch. Even when new patches addressing the vulnerability have been released, they may not necessarily be installed immediately, allowing malware to take advantage of systems lacking patches. Som... | large_corpus_distillation |
have to be retrained every time a new person is added to the face database. This can be avoided by posing the problem as a similarity learning problem instead of a classification problem. Here the network is trained (using a contrastive loss) to output a distance which is small if the image belongs to a known person an... | large_corpus_distillation |
and only if it is linearly independent.\nA subset of V with n elements is a basis if and only if it is a spanning set of V." | large_corpus_distillation |
"Public key infrastructure-Uses-PKIs of one type or another, and from any of several vendors, have many uses, including providing public keys and bindings to user identities which are used for: Encryption and/or sender authentication of e-mail messages (e.g., using OpenPGP or S/MIME); Encryption and/or authentication o... | large_corpus_distillation |
"Everyone's a Critic-Lists-EaC critics can also see Adjustable Movie Rankings by applying filters to the lists. Critics can filter by year, genre, My Critics, movies the critic has rated and movies the critic has not rated.\nCritic List EaC critics can view a list of all other EaC critics with links to each critic's pe... | large_corpus_distillation |
nth derivative of f(x), and y=f(n\u22121)(x) , assuming for 0<i\u2264n+1 :d(f(n))\u22121(z)dz=1f(n+1)(x) " | large_corpus_distillation |
"Connected-component labeling-Algorithms-The pseudocode is : algorithm OneComponentAtAtime(data) input : imageData[xDim][yDim] initialization : label = 0, labelArray[xDim][yDim] = 0, statusArray[xDim][yDim] = false, queue1, queue2; for i = 0 to xDim do for j = 0 to yDim do if imageData[i][j] has not been processed do ... | large_corpus_distillation |
"Medoid-Medoids in text and natural language processing (NLP)-Jaccard similarity Jaccard similarity, also known as the Jaccard coefficient, measures the similarity between two sets by comparing the ratio of their intersection to their union. In the context of text data, each document is represented as a set of words, a... | large_corpus_distillation |
"Reliable multicast-Virtual synchrony-Other such systems include the Horus system the Transis system, the Totem system, an IBM system called Phoenix, a distributed security key management system called Rampart, the \"Ensemble system\", the Quicksilver system, \"The OpenAIS project\", its derivative the Corosync Cluster... | large_corpus_distillation |
15.603265\u202fT2Note that this gives an average cycle length now of 25,676 years." | large_corpus_distillation |
"Parallel Extensions-Parallel LINQ-PLINQ, or Parallel LINQ, parallelizing the execution of queries on objects (LINQ to Objects) and XML data (LINQ to XML). PLINQ is intended for exposing data parallelism by use of queries. Any computation on objects that has been implemented as queries can be parallelized by PLINQ. How... | large_corpus_distillation |
"Robust regression-Methods for robust regression-In the 1980s, several alternatives to M-estimation were proposed as attempts to overcome the lack of resistance. See the book by Rousseeuw and Leroy for a very practical review. Least trimmed squares (LTS) is a viable alternative and is currently (2007) the preferred cho... | large_corpus_distillation |
"Automotive security-Threat model-Spoofing Spoofing attacks comprise all cases in which an attacker, by falsifying data, sends messages pretending to be another node of the network. In automotive security usually spoofing attacks are divided into masquerade and replay attacks. Replay attacks are defined as all those wh... | large_corpus_distillation |
while also preventing errors wherever possible by tolerating varied inputs and sequences and by interpreting all reasonable actions reasonable." | large_corpus_distillation |
"Index (publishing)-Index quality-Some principles of good indexing include: Ensuring each topic/section includes a variety of relevant index entries; use two or three entries per topic Understanding the audience and understand what kind of index entries they're likely to look for Use the same form throughout (singular ... | large_corpus_distillation |
"Chi-squared distribution-Related distributions-If Y is a k -dimensional Gaussian random vector with mean vector \u03bc and rank k covariance matrix C , then X=(Y\u2212\u03bc)TC\u22121(Y\u2212\u03bc) is chi-squared distributed with k degrees of freedom.\nThe sum of squares of statistically independent unit-varia... | large_corpus_distillation |
"Matrix chain multiplication-More efficient algorithms-Other O(n log n) algorithms Wang, Zhu and Tian have published a simplified O(n log m) algorithm, where n is the number of matrices in the chain and m is the number of local minimums in the dimension sequence of the given matrix chain.Nimbark, Gohel, and Doshi have ... | large_corpus_distillation |
schemes, this is still a bad choice and is not considered to be best practice among cryptographers any more." | large_corpus_distillation |
"Native resolution-Native resolution-The native resolution of an liquid crystal display (LCD), liquid crystal on silicon (LCoS) or other flat panel display refers to its single fixed resolution. As an LCD consists of a fixed raster, it cannot change resolution to match the signal being displayed as a cathode-ray tube (... | large_corpus_distillation |
"Software versioning-Significance-Versioning is also a required practice to enable many schemes of patching and upgrading software, especially to automatically decide what and where to upgrade to." | large_corpus_distillation |
"Gauss\u2013Markov theorem-Statement-Remark Proof that the OLS indeed minimizes the sum of squares of residuals may proceed as follows with a calculation of the Hessian matrix and showing that it is positive definite. The MSE function we want to minimize is for a multiple regression model with p variables. The first ... | large_corpus_distillation |
announced the computation of a discrete logarithm modulo a 232-digit (768-bit) safe prime, using the number field sieve. The computation was started in February 2015 and took approximately 6600 core years scaled to an Intel Xeon E5-2660 at 2.2 GHz." | large_corpus_distillation |
"Simplex algorithm-Algorithm-Columns 2, 3, and 4 can be selected as pivot columns, for this example column 4 is selected. The values of z resulting from the choice of rows 2 and 3 as pivot rows are 10/1 = 10 and 15/3 = 5 respectively. Of these the minimum is 5, so row 3 must be the pivot row. Performing the pivot produ... | large_corpus_distillation |
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