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"Stochastic ordering-Usual stochastic order-A\u2aafB if and only if for all non-decreasing functions u , E[u(A)]\u2264E[u(B)] If u is non-decreasing and A\u2aafB then u(A)\u2aafu(B) If u:Rn\u2192R is increasing in each variable and Ai and Bi are independent sets of random variables with Ai\u2aafBi for each i ... | large_corpus_distillation |
"Biclustering-Algorithms-Several approaches have been proposed based on the information contents of the resulting blocks: matrix-based approaches such as SVD and BVD, and graph-based approaches. Information-theoretic algorithms iteratively assign each row to a cluster of documents and each column to a cluster of words ... | large_corpus_distillation |
"Chandy\u2013Lamport algorithm-Definition-The assumptions of the algorithm are as follows: There are no failures and all messages arrive intact and only once The communication channels are unidirectional and FIFO ordered There is a communication path between any two processes in the system Any process may initiate the ... | large_corpus_distillation |
"Stochastic cellular automaton-PCA as Markov stochastic processes-As discrete-time Markov process, PCA are defined on a product space E=\u220fk\u2208GSk (cartesian product) where G is a finite or infinite graph, like Z and where Sk is a finite space, like for instance Sk={\u22121,+1} or Sk={0,1} . The transition p... | large_corpus_distillation |
"Memory span-Factors-Rate of presentation: The speed with which the stimuli are presented has an effect on memory span score. When listening to auditory stimuli, the impact of speed is mediated by whether the subject is actively or passively listening. Active listeners score better with faster stimuli presentation. Pas... | large_corpus_distillation |
"Bluetooth-Specifications and features-Bluetooth Low Energy, previously known as Wibree, is a subset of Bluetooth v4.0 with an entirely new protocol stack for rapid build-up of simple links. As an alternative to the Bluetooth standard protocols that were introduced in Bluetooth v1.0 to v3.0, it is aimed at very low pow... | large_corpus_distillation |
"Euclid\u2013Mullin sequence-Related sequences-A related sequence of numbers determined by the largest prime factor of one plus the product of the previous numbers (rather than the smallest prime factor) is also known as the Euclid\u2013Mullin sequence. It grows more quickly, but is not monotonic. The numbers in this s... | large_corpus_distillation |
"Shannon's source coding theorem-Statements-Source coding theorem In information theory, the source coding theorem (Shannon 1948) informally states that (MacKay 2003, pg. 81, Cover 2006, Chapter 5): N i.i.d. random variables each with entropy H(X) can be compressed into more than N\u2009H(X) bits with negligible risk o... | large_corpus_distillation |
"Algorithm-Formalization-Gurevich: \"\u2026 Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine \u2026 according to Savage [1987], an algorithm is a computational process defined by a Turing machine\".Turing machines can define computationa... | large_corpus_distillation |
"6.867 Machine learning, lecture 13 (Jaakkola) 1\nLecture topics:\n\u2022 Boosting, margin, and gradient descent\n\u2022 complexity of classifiers, generalization\nBoosting\nLast time we arrived at a boosting algorithm for sequentially creating an ensemble of\nbase classifiers. Our base classifiers were decision stumps... | large_corpus_distillation |
"HTML element-Concepts-SGML vs. XML SGML is complex, which has limited its widespread understanding and adoption. XML was developed as a simpler alternative. Although both can use the DTD to specify the supported elements and their permitted combinations as document structure, XML parsing is simpler. The relation from ... | large_corpus_distillation |
probability that a single prisoner finds their number is 50%. Therefore, the probability that all prisoners find their numbers is the product of the single probabilities, which is (1/2)100 \u2248 0.0000000000000000000000000000008, a vanishingly small number. The situation appears hopeless." | large_corpus_distillation |
and early Broadwell CPUs, which resulted in disabling the TSX/TSX-NI feature on affected CPUs via a microcode update.In 2016, a side-channel timing attack was found by abusing the way TSX/TSX-NI handles transactional faults (i.e. page faults) in order to break kernel address space layout randomization (KASLR) on all ma... | large_corpus_distillation |
"Adjunct (grammar)-Predicates vs. adjuncts-That made him tired.The resultative adjective tired can be viewed as an argument of the matrix predicate made. But it is also definitely a predicate over him. Such examples illustrate that distinguishing predicates, arguments, and adjuncts can become difficult and there are ma... | large_corpus_distillation |
"Calibrated probability assessment-Calibrated probability assessment-Alternatively, the trainee will be asked to provide a numeric range for a question like, \"In what year did Napoleon invade Russia?\", with the instruction that the provided range is to represent a 90% confidence interval. That is, the test-taker shou... | large_corpus_distillation |
"Minimax Condorcet method-Examples-Example without Condorcet winner Assume four candidates A, B, C and D. Voters are allowed to not consider some candidates (denoting an n/a in the table), so that their ballots are not taken into account for pairwise scores of that candidates." | large_corpus_distillation |
"Independence Theory in Combinatorics-Topics-A major theme of Independence Theory in Combinatorics is the unifying nature of abstraction, and in particular the way that matroid theory can unify the concept of independence coming from different areas of mathematics. It has five chapters, the first of which provides basi... | large_corpus_distillation |
"Maass wave form-Automorphic representations of the adele group-The subgroup := \u220fp<\u221eKp is a maximal compact, open subgroup of fin and can be thought of as a subgroup of GA , when we consider the embedding fin fin ,1\u221e) We define ZR as the center of G\u221e , that means ZR is the group of all diagona... | large_corpus_distillation |
"Statistical data type-Simple data types-The following table classifies the various simple data types, associated distributions, permissible operations, etc. Regardless of the logical possible values, all of these data types are generally coded using real numbers, because the theory of random variables often explicitly... | large_corpus_distillation |
and (i,j) will be an inversion, which shows that this number is indeed L(\u03c3)i.) This number to encode each object can be found by direct counting, in several ways (directly counting inversions, or correcting the total number of objects smaller than a given one, which is its sequence number starting from 0 in the se... | large_corpus_distillation |
"Linear programming relaxation-Branch and bound for exact solutions-Otherwise, let xj be any variable that is set to a fractional value in the relaxed solution. Form two subproblems, one in which xj is set to 0 and the other in which xj is set to 1; in both subproblems, the existing assignments of values to some of the... | large_corpus_distillation |
as [a] and finite lists x1:x2:...:xn:[] are written as [x1,x2,...,xn]. We can define operations on recursive types by inductive definitions where pattern matching supports the convenient separation of the different cases. For instance, the concatenation operation \u201c++\u201d on polymorphic lists can be defined as fo... | large_corpus_distillation |
operating systems (for example Berkeley UNIX 4.3BSD), computer algebra systems and programming languages (for example C99) provide a special natural logarithm plus 1 function, alternatively named LNP1, or log1p to give more accurate results for logarithms close to zero by passing arguments x, also close to zero, to a f... | large_corpus_distillation |
"Story Workshop-Main features-The Story Workshop method \"focuses on helping you hear your own individual voice and provides a supportive, interactive, and challenging environment for developing your reading, writing, listening, speaking, critical thinking, and imaginative problem-solving capacities.\"The Story Worksho... | large_corpus_distillation |
we cannot use any of the information gained by specific\noutcomes, because we would not know which to use. Instead, we have to average over all possible outcomes, i.e., over all events in\nthe partition with nonzero probability. The average information per event is found by multiplying the information for each event A ... | large_corpus_distillation |
"Orlicz space-Orlicz norm of a random variable-Similarly, the Orlicz norm of a random variable characterizes it as follows: inf {k\u2208(0,\u221e)\u2223E\u2061[\u03a8(|X|/k)]\u22641}.\nThis norm is homogeneous and is defined only when this set is non-empty." | large_corpus_distillation |
"Carmichael number-Overview-Arnault gives a 397-digit Carmichael number N that is a strong pseudoprime to all prime bases less than 307: 313 353 (p\u22121)+1) where p= 29674495668685510550154174642905332730771991799853043350995075531276838753171770199594238596428121188033664754218345562493168782883is a 131-digit prime... | large_corpus_distillation |
"Rademacher complexity-Bounding the Rademacher complexity-5. The Rademacher complexity of the convex hull of A equals Rad(A)." | large_corpus_distillation |
"X86 debug register-DR6 - Debug status-The debug status register permits the debugger to determine which debug conditions have occurred. When the processor detects an enabled debug exception, it will set the corresponding bits of this register before entering the debug exception handler." | large_corpus_distillation |
"Grammaticality-Use of grammaticality judgments-Computer-assisted language instruction Catt and Catt & Hirst created a model of grammaticality based around a computer program developed for computer-assisted language instruction which was designed to perform automatic error diagnosis and correction of ungrammaticalities... | large_corpus_distillation |
of all subsets E of X\u00d7X such that {(x,y)\u2208E:d(x,y)\u2265\u03b5} is compact.\nThe discrete coarse structure on a set X consists of the diagonal \u0394 together with subsets E of X\u00d7X which contain only a finite number of points (x,y) off the diagonal.\nIf X is a topological space then the indiscret... | large_corpus_distillation |
any natural number, and the quotient = 1 if and only if n is a prime or a Carmichael number (561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, ... A002997), the quotient = 2 if and only if n is in the sequence: 4, 6, 15, 91, 703, 1891, 2701, 11305, 12403, 13981, 18721, ... A191311) The least number with n values o... | large_corpus_distillation |
"Funarg problem-Upwards funarg problem-Example The following Haskell-like pseudocode defines function composition: compose f g = \u03bbx \u2192 f (g x) \u03bb is the operator for constructing a new function, which in this case has one argument, x, and returns the result of first applying g to x, then applying f to that... | large_corpus_distillation |
"Mobile harassment-Mobile harassment-Mobile harassment refers to the act of sending any type of text message, sext, photo message, video message, or voicemail from a mobile phone that causes the receiver to feel harassed, threatened, tormented, humiliated, embarrassed or otherwise victimized. It is recognized as a form... | large_corpus_distillation |
"Kitchen-Domestic kitchen planning-The double-file kitchen (or two-way galley) has two rows of cabinets on opposite walls, one containing the stove and the sink, the other the refrigerator. This is the classical work kitchen and makes efficient use of space.\nIn the L-kitchen, the cabinets occupy two adjacent walls. Ag... | large_corpus_distillation |
"Storage violation-Detection of storage violations-In systems such as CICS, storage violations are sometimes detected (by the CICS kernel) by the use of \"signatures\", which can be tested to see if they have been overlaid.\nAn alternative runtime library may be used to better detect storage violations, at the cost of ... | large_corpus_distillation |
density function is 1.\ng g S g g g \u2260g\nWe assume that 0 and 1 are positive on . Also, it makes no sense for 0 and 1 to be the same, so we assume that 0 1 on a\nset of positive measure. The test is based on the likelihood ratio test statistic\nn g (X )\nL =\u220f 0 i , n\u2208N (17.5.12)\nn\ng (X )\ni=1 1 i\nH L={... | large_corpus_distillation |
"RP (complexity)-Connection to P and NP-An alternative characterization of RP that is sometimes easier to use is the set of problems recognizable by nondeterministic Turing machines where the machine accepts if and only if at least some constant fraction of the computation paths, independent of the input size, accept. ... | large_corpus_distillation |
"Asymmetric multiprocessing-DECsystem-10-Digital Equipment Corporation (DEC) offered a dual-processor version of its DECsystem-1050 which used two KA10 processors; all peripherals were attached to one processor, the primary processor, and the primary processor ran the operating system code. This offering was extended t... | large_corpus_distillation |
"Obfuscation (software)-Obfuscation (software)-In software development, obfuscation is the act of creating source or machine code that is difficult for humans or computers to understand. Like obfuscation in natural language, it may use needlessly roundabout expressions to compose statements. Programmers may deliberatel... | large_corpus_distillation |
more\nthan one ball; sampling without replacement means that a cell may contain at most one ball.\nSuppose that 5 balls are distributed into 10 cells (with no restrictions). Find each of the following:\n1. The probability that the balls are all in different cells.\n2. The probability that the balls are all in the same ... | large_corpus_distillation |
"Mirror descent-Mirror descent-In mathematics, mirror descent is an iterative optimization algorithm for finding a local minimum of a differentiable function.\nIt generalizes algorithms such as gradient descent and multiplicative weights." | large_corpus_distillation |
"Rate-monotonic scheduling-Resource sharing-In many practical applications, resources are shared and the unmodified RMS will be subject to priority inversion and deadlock hazards. In practice, this is solved by disabling preemption or by priority inheritance. Alternative methods are to use lock-free algorithms or avoid... | large_corpus_distillation |
V, W, X, Y, Z. All were broadcast at 100 kHz, a much lower frequency than earlier systems. The result was a signal that offered a daytime ground wave range of 2,250 miles, nighttime ground wave of 1,650 miles and skywaves out to 3,000 miles. Timing accuracy was estimated at 0.15 microseconds, offering accuracies on the... | large_corpus_distillation |
"Memory confusion protocol-Memory confusion protocol-Subjects are not forewarned of the final step, a surprise recall task: the sentences are presented in random order, and the subjects must attribute each to the correct individual.The subjects' mistakes in the recall task reveal how they categorize the individuals: th... | large_corpus_distillation |
"Primality test-Number-theoretic methods-Certain number-theoretic methods exist for testing whether a number is prime, such as the Lucas test and Proth's test. These tests typically require factorization of n + 1, n \u2212 1, or a similar quantity, which means that they are not useful for general-purpose primality test... | large_corpus_distillation |
at most d iterations, each of which performs n violation tests and makes a single recursive call to a subproblem of size O(d\u221an)." | large_corpus_distillation |
"Entropy in thermodynamics and information theory-Theoretical relationship-A direct and physically real relationship between h and S can be found by assigning a symbol to each microstate that occurs per mole, kilogram, volume, or particle of a homogeneous substance, then calculating the 'h' of these symbols. By theory ... | large_corpus_distillation |
proceeding with the standard k-means optimization iterations.\nWith the k-means++ initialization, the algorithm is guaranteed to find a solution that is O(log k) competitive to the optimal k-means solution." | large_corpus_distillation |
"Bottom type-In programming languages-In Scala, the bottom type is denoted as Nothing. Besides its use for functions that just throw exceptions or otherwise don't return normally, it's also used for covariant parameterized types. For example, Scala's List is a covariant type constructor, so List[Nothing] is a subtype o... | large_corpus_distillation |
"Directory structure-Directory structure-In computing, a directory structure is the way an operating system arranges files that are accessible to the user. Files are typically displayed in a hierarchical tree structure." | large_corpus_distillation |
"Shortest path problem-Related problems-Strategic shortest paths Sometimes, the edges in a graph have personalities: each edge has its own selfish interest. An example is a communication network, in which each edge is a computer that possibly belongs to a different person. Different computers have different transmissio... | large_corpus_distillation |
"# import the libraries\nimport tensorflow as tf\nfrom sklearn.datasets import fetch_openml\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.preprocessing import StandardScaler\n# Load MNIST Digits dataset\nmnist = fetch_openml('mnist_784', version=1)\n# Split the dataset into training and testing se... | large_corpus_distillation |
upload fields in the Browser application.\nThe browser now shows all frames of animated GIFs instead of just the first frame.\nSupport for installing applications to the expandable memory.\nAdobe Flash support.\nSupport for high-PPI displays (up to 320 ppi), such as four-inch 720p screens.\nIntroduced .asec file extens... | large_corpus_distillation |
"Freivalds' algorithm-Ramifications-Simple algorithmic analysis shows that the running time of this algorithm is O(n2) (in big O notation). This beats the classical deterministic algorithm's runtime of O(n3) (or 2.373 ) if using fast matrix multiplication). The error analysis also shows that if the algorithm is run ... | large_corpus_distillation |
"EMI (protocol)-Syntax-The subsequent fields are dependent on the operation. In the first line above, '66677789' is the recipient's address (telephone number) and '68656C6C6F' is the content of the message, in this case the ASCII string \"hello\". The second line is the response with a matching transaction reference nu... | large_corpus_distillation |
"Test method-Validation-Test methods are often scrutinized for their validity, applicability, and accuracy. It is very important that the scope of the test method be clearly defined, and any aspect included in the scope is shown to be accurate and repeatable through validation.Test method validations often encompass th... | large_corpus_distillation |
"Shell (computing)-Graphical shells-In the case of macOS, Quartz Compositor acts as the windowing system, and the shell consists of the Finder, the Dock, SystemUIServer, and Mission Control." | large_corpus_distillation |
"Feedback loop (email)-Reporting formats-The Abuse Reporting Format (ARF) is the standard format for FBL reports. Much like bounce messages, whose design is inherited by ARF, an abuse report consists of a human readable part, followed by a machine readable part, and the original message. The report is characterized by ... | large_corpus_distillation |
"Visual research-Participant generated visual methodologies-Photovoice Caroline C. Wang and Mary Anne Burris conceptualized the visual methodology called photovoice. Participants are provided with a camera and asked to produce an image-based account of their experiences and/or those things that are important to them in... | large_corpus_distillation |
"Direction cosine-General meaning-More generally, direction cosine refers to the cosine of the angle between any two vectors. They are useful for forming direction cosine matrices that express one set of orthonormal basis vectors in terms of another set, or for expressing a known vector in a different basis." | large_corpus_distillation |
"Coaching psychology-Applications-Athlete coaching Coaching psychology influences training methods for athlete development. It aims not only to improve performance in sports, but also to develop athletes holistically. Thus, factors affecting development such as athlete motivation have been studied through cognitive, so... | large_corpus_distillation |
"Hexacode-Hexacode-In coding theory, the hexacode is a length 6 linear code of dimension 3 over the Galois field GF(4)={0,1,\u03c9,\u03c92} of 4 elements defined by := ax2+bx+c;a,b,c\u2208GF(4)}.\nIt is a 3-dimensional subspace of the vector space of dimension 6 over GF(4) Then H contains 45 codewords of weight 4, ... | large_corpus_distillation |
"Ahead-of-time compilation-Reduced runtime overhead-Some programming languages with a managed code runtime that can be compiled to an intermediate representation, use just-in-time (JIT) compiling. This, briefly, compiles intermediate code into machine code for a native run while the intermediate code is executing, whic... | large_corpus_distillation |
"One-way function-Candidates for one-way functions-Popular choices for the group G in discrete logarithm cryptography are the cyclic groups (Zp)\u00d7 (e.g. ElGamal encryption, Diffie\u2013Hellman key exchange, and the Digital Signature Algorithm) and cyclic subgroups of elliptic curves over finite fields (see elliptic... | large_corpus_distillation |
"National Institutes of Health Stroke Scale-Performing the scale-Notes If patients scores a 3 in this factor, the default coma scores should be used when applicable B) LOC questions Patient is verbally asked his or her age and for the name of the current month." | large_corpus_distillation |
"Alpha 21064-Description-Store instructions result in data buffered in a 4-entry by 32-byte write buffer. The write buffer improved performance by reducing the number of writes on the system bus by merging data from adjacent stores and by temporarily delaying stores, enabling loads to be serviced quicker as the system ... | large_corpus_distillation |
"Braille pattern dots-12345-Unified Braille-In unified international braille, the braille pattern dots-12345 is used to represent double consonants, such as /kw/ or /k\u0283/ or otherwise as needed.\nTable of unified braille values" | large_corpus_distillation |
"24 Chapter 1 | Functions and Graphs\n1\nx= \u00b1 .\ny\u22121\nSince 1/ y\u22121 is a real number if and only if y>1, the range of f is the set \u23a7 \u23a8y|y>1\u23ab \u23ac.\n\u23a9 \u23ad\n2\nd. (f\u2218g)(4)= f(g(4))= f \u239b1\u239e = \u239b1\u239e +1= 17\n\u239d4\u23a0 \u239d4\u23a0 16\n\u239b 1\u239e \u239b \u... | large_corpus_distillation |
"Formal proof-Background-Formal language A formal language is a set of finite sequences of symbols. Such a language can be defined without reference to any meanings of any of its expressions; it can exist before any interpretation is assigned to it \u2013 that is, before it has any meaning. Formal proofs are expressed ... | large_corpus_distillation |
"Market equilibrium computation-Main results-When the utilities are PLC (not necessarily separable) and m is constant, their algorithm is polynomial in n. When both m and n are variable, finding a CE is PPAD-hard even for Leontief utilities, which are a special case of PLC utilities (when n is constant but m is variabl... | large_corpus_distillation |
"Object composition-Aggregation-Composition is usually implemented such that an object contains another object. For example, in C++: In aggregation, the object may only contain a reference or pointer to the object (and not have lifetime responsibility for it).\nSometimes aggregation is referred to as composition when t... | large_corpus_distillation |
a recent app called Snapchat allows users to post videos, pictures, or even live streams of exactly what they're doing when they're doing it, strong indicators of behaviors and interactions with the world. In 2004, MIT conducted the Reality Mining Project which gave 100 MIT students a Nokia 6600 which was tracked in a ... | large_corpus_distillation |
"Basque verbs-Synthetic conjugation-Plural marking Plural number is marked in finite verbs in various ways, depending on the arguments whose plurality is being indexed. One set of plural forms are 'primary', that is, once again they refer to either the 'intransitive subject' or the 'transitive object' (the absolutive c... | large_corpus_distillation |
This a class of customers that is Moore's law driven and as price performance gains continue, IDC believes that these organizations will accelerate their consumption of IT infrastructure.\u201d " | large_corpus_distillation |
"Matrix representation-In 3D graphics-Column major With column-major order, a \"matrix \u00d7 vector\" multiply can be implemented with vectorized multiply-add operations, if the vector's components are broadcast to each SIMD lane. It is also easy to access the basis vectors represented by a transformation matrix as in... | large_corpus_distillation |
"IT risk management-Risk assessment-An analysis of system assets and vulnerabilities to establish an expected loss from certain events based on estimated probabilities of the occurrence of those events. The purpose of a risk assessment is to determine if countermeasures are adequate to reduce the probability of loss or... | large_corpus_distillation |
"Escape analysis-Examples (Scheme)-In the following example, the vector p does not escape into g, so it can be allocated on the stack and then removed from the stack before calling g.\nIf, however, we had then either p would need to be allocated on the heap or (if g is known to the compiler when f is compiled, and beha... | large_corpus_distillation |
"SMS hubbing-SMS hubbing-The GSM Association (GSMA) found in SMS Hubbing the solution to a problem that limits the continuing growth of international SMS, culminating to the development of the SMS Hubbing trials in 2006, part of the Open Connectivity project. This initiative created a new structure for international SM... | large_corpus_distillation |
"Existential quantification-Existential quantification-In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as \"there exists\", \"there is at least one\", or \"for some\". It is usually denoted by the logical operator symbol \u2203, which, when used togethe... | large_corpus_distillation |
"Location arithmetic-Division-Martin Gardner presented a slightly easier to understand version [2] of Napier's division method, which is what is shown here.\nDivision works pretty much the reverse of multiplication. Say we want to divide 485 by 13. First place counters for 485 (= 111100101) along the bottom edge and ma... | large_corpus_distillation |
2) Edmonds\u2013Karp algorithm. Specific variants of the algorithms achieve even lower time complexities. The variant based on the highest label node selection rule has O(V 2\u221aE) time complexity and is generally regarded as the benchmark for maximum flow algorithms. Subcubic O(VElog(V 2/E)) time complexity can be a... | large_corpus_distillation |
"Region Based Convolutional Neural Networks-History-April 2015: Fast R-CNN. While the original R-CNN independently computed the neural network features on each of as many as two thousand regions of interest, Fast R-CNN runs the neural network once on the whole image. At the end of the network is a novel method called R... | large_corpus_distillation |
"SAML 1.1-SAML 1.1 Profiles-Respond with a SAML Assertion The identity provider completes the back-channel exchange by responding with a SAML assertion bound to a SAML SOAP message: In this case, the authentication statement includes a NameIdentifier containing the principal's e-mail address.\nRespond to the principal'... | large_corpus_distillation |
"Crypt (C)-Key derivation functions supported by crypt-First the passphrase and salt are hashed together, yielding an MD5 message digest. Then a new digest is constructed, hashing together the passphrase, the salt, and the first digest, all in a rather complex form. Then this digest is passed through a thousand iterati... | large_corpus_distillation |
Annelies De Corte, Kenneth S\u00f6rensen and Gunther Steenackers. \"The Air Distribution Network Design Problem - A Complex Non-linear Combinatorial Optimization Problem \" ICORES 2014 - ESEO, Angers, Loire Valley, France Proceedings - Proceedings of the 3rd International Conference on Operations Research and Enterpris... | large_corpus_distillation |
"Invertible matrix-Methods of matrix inversion-The inversion procedure that led to Equation (1) performed matrix block operations that operated on C and D first. Instead, if A and B are operated on first, and provided D and A \u2212 BD\u22121C are nonsingular, the result is Equating Equations (1) and (2) leads to where... | large_corpus_distillation |
"Piecewise-Notation and interpretation-The following table documents the absolute value function at certain values of x In order to evaluate a piecewise-defined function at a given input value, the appropriate subdomain needs to be chosen in order to select the correct sub-function\u2014and produce the correct output ... | large_corpus_distillation |
"Merge sort-Parallel merge sort-Multi-sequence selection In its simplest form, given p sorted sequences S1,...,Sp distributed evenly on p processors and a rank k , the task is to find an element x with a global rank k in the union of the sequences. Hence, this can be used to divide each Si in two parts at a spli... | large_corpus_distillation |
"Terminal and nonterminal symbols-Production rules-A grammar is defined by production rules (or just 'productions') that specify which symbols may replace which other symbols; these rules may be used to generate strings, or to parse them. Each such rule has a head, or left-hand side, which consists of the string that m... | large_corpus_distillation |
"Assumptions\nX Y\nIt may surprise you, but the calculations shown in this section are assumption-free. Of course, if the relationship between and\nwere not linear, a different shaped function could fit the data better. Inferential statistics in regression are based on several\nassumptions, and these assumptions are pr... | large_corpus_distillation |
"Mean directional accuracy-Mean directional accuracy-Mean directional accuracy (MDA), also known as mean direction accuracy, is a measure of prediction accuracy of a forecasting method in statistics. It compares the forecast direction (upward or downward) to the actual realized direction. It is defined by the following... | large_corpus_distillation |
"Configuration graph-Use of this object-For example, since reachability is in NL when we can represent configurations in space which is logarithmic in the size of the input, and since the configuration of a Turing Machine in NL is indeed of logarithmic size, it follows that graph-reachability is complete for NL.In the ... | large_corpus_distillation |
"Core Multiplexing Technology-Details-A subset of traditional applications are often difficult to parallelize and make use of additional CPU hardware available on the platform, restraining applications to use only one CPU. Core Multiplexing Technology would allow for a process to be split into multiple threads at compi... | large_corpus_distillation |
"X86-Basic properties of the architecture-The presence of wide SIMD registers means that existing x86 processors can load or store up to 128 bits of memory data in a single instruction and also perform bitwise operations (although not integer arithmetic) on full 128-bits quantities in parallel. Intel's Sandy Bridge pro... | large_corpus_distillation |
"Permutation group-Neutral element and inverses-To obtain the inverse of a single cycle, we reverse the order of its elements. Thus, 125 521 152 ).\nTo obtain the inverse of a product of cycles, we first reverse the order of the cycles, and then we take the inverse of each as above. Thus, 125 34 34 125 43 521 34 152 ).... | large_corpus_distillation |
"Perceptron-Variants-The \u03b1 -perceptron further used a pre-processing layer of fixed random weights, with thresholded output units. This enabled the perceptron to classify analogue patterns, by projecting them into a binary space. In fact, for a projection space of sufficiently high dimension, patterns can become ... | large_corpus_distillation |
"Regression toward the mean-Importance-Although extreme individual measurements regress toward the mean, the second sample of measurements will be no closer to the mean than the first. Consider the students again. Suppose the tendency of extreme individuals is to regress 10% of the way toward the mean of 80, so a stude... | large_corpus_distillation |
"Mixture distribution-Mixture distribution-Mixture distributions arise in many contexts in the literature and arise naturally where a statistical population contains two or more subpopulations. They are also sometimes used as a means of representing non-normal distributions. Data analysis concerning statistical models ... | large_corpus_distillation |
"Scaled correlation-Scaled correlation-In statistics, scaled correlation is a form of a coefficient of correlation applicable to data that have a temporal component such as time series. It is the average short-term correlation. If the signals have multiple components (slow and fast), scaled coefficient of correlation c... | large_corpus_distillation |
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