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mean .\nProof\nlng(x)=\u2212r+xlnr\u2212ln(x!) x\u2208N\nNote that for . Hence the log-likelihood function corresponding to\nx=(x ,x ,\u2026,x )\u2208Nn\n1 2 n is\nlnL (r)=\u2212nr+ylnr\u2212C, r\u2208(0,\u221e) (7.3.25)\nx\ny=\u2211n x C =\u2211n ln(x !) d lnL (r)=\u2212n+y/r r=y/n=m\nwhere i=1 i and i=1 i . Hence dr ... | large_corpus_distillation |
"Tripling-oriented Doche\u2013Icart\u2013Kohel curve-Definition-An elliptic curve in tripling oriented Doche\u2013Icart\u2013Kohel form is defined by the equation: Ta:y2=x3+3a(x+1)2 with a\u2208K A general point P on Ta has affine coordinates (x,y) . The \"point at infinity\" represents the neutral element for the g... | large_corpus_distillation |
"Data Coding Scheme-Message character sets-A special 7-bit encoding called the GSM 7 bit default alphabet was designed for the Short Message System in GSM. The alphabet contains the most-often used symbols from most Western-European languages (and some Greek uppercase letters). Some ASCII characters and the Euro sign d... | large_corpus_distillation |
"Survival analysis-Fitting parameters to data-Survival models can be usefully viewed as ordinary regression models in which the response variable is time. However, computing the likelihood function (needed for fitting parameters or making other kinds of inferences) is complicated by the censoring. The likelihood functi... | large_corpus_distillation |
"O(1) scheduler-Overview-The Linux scheduler was overhauled completely with the release of kernel 2.6 in 2003. The new scheduler was called the O(1) scheduler. The algorithm used by the O(1) scheduler relies on active and expired arrays of processes to achieve constant scheduling time. Each process is given a fixed tim... | large_corpus_distillation |
"Market intelligence-Gathering market intelligence data-Internal intelligence gathering Sources of internal intelligence gathering is include but is not limited to, gathering data from customers, manufacturers, through research and development (R&D), employees, also known as salesforce, physical evidence, sales quotes,... | large_corpus_distillation |
"Quotient group-Examples-The real numbers modulo the integers Consider the group of real numbers R under addition, and the subgroup Z of integers. Each coset of Z in R is a set of the form a+Z , where a is a real number. Since a1+Z and a2+Z are identical sets when the non-integer parts of a1 and a2 are equal,... | large_corpus_distillation |
"Fermat's little theorem-Generalizations-The basic idea of RSA cryptosystem is thus: if a message x is encrypted as y = xe (mod n), using public values of n and e, then, with the current knowledge, it cannot be decrypted without finding the (secret) factors p and q of n.\nFermat's little theorem is also related to the ... | large_corpus_distillation |
"Descendant tree (group theory)-Pro-p groups and coclass trees-For a sound understanding of coclass trees as a particular instance of descendant trees, it is necessary to summarize some facts concerning infinite topological pro-p groups.\nThe members \u03b3j(S) , with j\u22651 , of the lower central series of a pro-p... | large_corpus_distillation |
matrix, we can find the inverse of a matrix by setting" | large_corpus_distillation |
"Family of sets-Examples-The set of all subsets of a given set S is called the power set of S and is denoted by \u2118(S).\nThe power set \u2118(S) of a given set S is a family of sets over S.\nA subset of S having k elements is called a k -subset of S.\nThe k -subsets S(k) of a set S form a family of sets... | large_corpus_distillation |
"Semigroup with involution-Notions of regularity-Semigroups that satisfy only x** = x = xx*x (but not necessarily the antidistributivity of * over multiplication) have also been studied under the name of I-semigroups." | large_corpus_distillation |
"Libcwd-Run-time access to memory allocation administration-The library also provides a few global functions that can be called from within a debugger, like gdb, allowing the developer to quickly find out which allocation a given pointer is pointing at. For example, (gdb) call cwdebug_alloc(0x8a19450) 0x8a19450 points ... | large_corpus_distillation |
"Dirichlet-multinomial distribution-Likelihood function-The conditional probability for a given word is almost identical to the LDA case. Once again, all words generated by the same Dirichlet prior are interdependent. In this case, this means the words of all documents having a given label \u2014 again, this can vary d... | large_corpus_distillation |
"Open Semantic Framework-Open Semantic Framework-OSF is a platform-independent Web services framework for accessing and exposing structured data, semi-structured data, and unstructured data using ontologies to reconcile semantic heterogeneities within the contributing data and schema. Internal to OSF, all data is conve... | large_corpus_distillation |
"Key stretching-History-The first deliberately slow password-based key derivation function \"CRYPT\" was described in 1978 by Robert Morris for encrypting Unix passwords. It used an iteration count of 25, a 12-bit salt and a variant of DES as the sub-function. (DES proper was avoided in an attempt to frustrate attacks ... | large_corpus_distillation |
"Accuracy and precision-Common technical definition-Quantification In industrial instrumentation, accuracy is the measurement tolerance, or transmission of the instrument and defines the limits of the errors made when the instrument is used in normal operating conditions.Ideally a measurement device is both accurate an... | large_corpus_distillation |
"Mobile security-Countermeasures-An example of a defense mechanism against this is the chain of trust (such as in iOS). This mechanism relies on signatures from applications required to start the operating system, and a certificate signed by the manufacturer (Apple). In the event that the signature checks are inconclus... | large_corpus_distillation |
"Interactive electronic technical manual-Classes-Class 5 - In this class the documentation is now integrated with expert systems that may influence the display of content. For example, the IETM system may aggregate data from a large number of users input, feed that to the expert system that analyzes it and then the res... | large_corpus_distillation |
"Generation effect-Causes-Lexical activation hypothesis According to the lexical activation hypothesis, the participant must search his or her semantic memory during the process of generation. The search activates semantic features in memory that are related to the target item. During the retrieval of the target item a... | large_corpus_distillation |
means to find all of the values for the variables that make the two expressions on either side of the equation\nequal to each other.\n4.2.1 https://math.libretexts.org/@go/page/7119" | large_corpus_distillation |
"SimRank-SimRank-SimRank is a general similarity measure, based on a simple and intuitive graph-theoretic model.\nSimRank is applicable in any domain with object-to-object relationships, that measures similarity of the structural context in which objects occur, based on their relationships with other objects." | large_corpus_distillation |
"Pseudoforest-Graphs of functions-Cycle detection, the problem of following a path in a functional graph to find a cycle in it, has applications in cryptography and computational number theory, as part of Pollard's rho algorithm for integer factorization and as a method for finding collisions in cryptographic hash func... | large_corpus_distillation |
"Entity\u2013relationship model-Entity\u2013relationship model-The model's linguistic aspect described above is utilized in the declarative database query language ERROL, which mimics natural language constructs. ERROL's semantics and implementation are based on reshaped relational algebra (RRA), a relational algebra t... | large_corpus_distillation |
"Argon2-Algorithm-Initial block is generated from message V1 \u2190 Blake2b(digestSize \u2225 message, 64); Subsequent blocks are generated from previous blocks for i \u2190 2 to r do Vi \u2190 Blake2b(Vi-1, 64) Generate the final (possibly partial) block partialBytesNeeded \u2190 digestSize \u2013 32*r; Vr+1 \u2190 Bl... | large_corpus_distillation |
n, given X 0 =i. This is\nnot a renewal counting process, but, as with Markov processes, it provides a way to combine the time-average results for all states\nj. The following theorem is the same as that for Markov processes, except for the omission of ensemble average results.\nTheorem 6.8.1. Consider a semi Markov pr... | large_corpus_distillation |
differs from t (given random weights). A loss function L(t,y) is used for measuring the discrepancy between the target output t and the computed output y. For regression analysis problems the squared error can be used as a loss function, for classification the categorical cross-entropy can be used." | large_corpus_distillation |
"Internet traffic-Traffic classification-Bayesian analysis techniques Work involving supervised machine learning to classify network traffic. Data are hand-classified (based upon flow content) to one of a number of categories. A combination of data set (hand-assigned) category and descriptions of the classified flows (... | large_corpus_distillation |
W. (1992). Linguistic Semantics. Hillsdale, NJ: Lawrence Erlbaum Associates. ISBN 0805810749. (Chapter V. Thematic Roles, pp. 197\u2013249) Angela D. Friederici, Anja Hahne, Axel Mecklinger: Temporal structure of syntactic parsing. Early and late event-related potential effects. In: Journal of Experimental Psychology: ... | large_corpus_distillation |
"Residuated Boolean algebra-Definition-A residuated Boolean algebra is an algebraic structure (L, \u2227, \u2228, \u00ac, 0, 1, \u2022, I, \\, /) such that An equivalent signature better suited to the relation algebra application is (L, \u2227, \u2228, \u00ac, 0, 1, \u2022, I, \u25b7, \u25c1) where the unary operations... | large_corpus_distillation |
"Linux kernel-Architecture and features-Linux provides both user preemption as well as full kernel preemption.:\u200a62\u201363\u200a Preemption reduces latency, increases responsiveness, and makes Linux more suitable for desktop and real-time applications." | large_corpus_distillation |
"MaxiCode-Modes-Mode 2 - Formatted data containing a structured Carrier Message with a numeric postal code. (Primary use is US domestic destinations.) Mode 3 - Formatted data containing a structured Carrier Message with an alphanumeric postal code. (Primary use is international destinations.) Mode 4 - Unformatted data ... | large_corpus_distillation |
"Statistical potential-Explanation-In order to combine the two distributions, such that the local structure will be distributed according to Q(X) , while the pairwise distances will be distributed according to P(Y) , the following expression is needed: P(X,Y)=P(Y)Q(Y)Q(X) where Q(Y) is the distribution over Y impli... | large_corpus_distillation |
"Machine learning-Approaches-Anomaly detection In data mining, anomaly detection, also known as outlier detection, is the identification of rare items, events or observations which raise suspicions by differing significantly from the majority of the data. Typically, the anomalous items represent an issue such as bank f... | large_corpus_distillation |
PHI-base has been cited in over 350 peer-reviewed publications. Details on all these publications are cited in the \u2018about us\u2019 section of the database." | large_corpus_distillation |
"Proof by contrapositive-Proof by contrapositive-Logically, the validity of proof by contrapositive can be demonstrated by the use of the following truth table, where it is shown that p \u2192 q and \u00ac q \u2192 \u00ac p share the same truth values in all scenarios: " | large_corpus_distillation |
relevancy. Each thumbnail is a link back to the original web site where that image is located. Using an advanced search option the user can typically adjust the search criteria to fit their own needs, choosing to search only images or animations, color or black and white, and setting preferences on image size." | large_corpus_distillation |
"Linear prediction-Linear prediction-Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples.\nIn digital signal processing, linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of f... | large_corpus_distillation |
to use 53- as a classification. Either 53 on its own or, better yet, a more specific code should be used." | large_corpus_distillation |
"Deepfake-Responses-Social media platforms Twitter Twitter is taking active measures to handle synthetic and manipulated media on their platform. In order to prevent disinformation from spreading, Twitter is placing a notice on tweets that contain manipulated media and/or deepfakes that signal to viewers that the media... | large_corpus_distillation |
"Polynomial greatest common divisor-GCD over a ring and its field of fractions-For univariate polynomials over the rational numbers, one may think that Euclid's algorithm is a convenient method for computing the GCD. However, it involves simplifying a large number of fractions of integers, and the resulting algorithm i... | large_corpus_distillation |
"Errors-in-variables models-Motivating example-It is this coefficient, rather than \u03b2 , that would be required for constructing a predictor of y based on an observed x which is subject to noise.\nIt can be argued that almost all existing data sets contain errors of different nature and magnitude, so that attenua... | large_corpus_distillation |
"Bayesian multivariate linear regression-Details-First, let us apply sum-of-squares to obtain new expression for the likelihood: We would like to develop a conditional form for the priors: where \u03c1(\u03a3\u03f5) is an inverse-Wishart distribution and \u03c1(B|\u03a3\u03f5) is some form of normal distribution in t... | large_corpus_distillation |
"Cepstral mean and variance normalization-Cepstral Normalization Techniques-Fixed codeword-dependent cepstral normalization (FCDCN) FCDCN was developed to provide a form of compensation that provides greater recognition accuracy than SDCN but in a more computationally-efficient manner than the CDCN algorithm. The FCDCN... | large_corpus_distillation |
"Word-Word-A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no consensus among linguists on its definition and numerous attempts to find ... | large_corpus_distillation |
"Cache replacement policies-Policies-Adaptive replacement cache (ARC) Constantly balances between LRU and LFU, to improve the combined result. ARC improves on SLRU by using information about recently evicted cache items to dynamically adjust the size of the protected segment and the probationary segment to make the bes... | large_corpus_distillation |
monotonically with each boosting iteration. The exponential loss of the ensemble\ndoes, however, decrease monotonically. This should be evident since it is exactly the loss\nwe are sequentially minimizing by adding the base learners. We can also quantify, based on\nthe weighted error achieved by each base learner, how ... | large_corpus_distillation |
"Local independence-Example-Local independence can be explained by an example of Lazarsfeld and Henry (1968). Suppose that a sample of 1000 people was asked whether they read journals A and B. Their responses were as follows: One can easily see that the two variables (reading A and reading B) are strongly related, and ... | large_corpus_distillation |
and physical capabilities. More specifically, some studies indicate it could be the higher levels of inactivity within older adults that may have significant ramifications on their health and well-being.With attention to these hypotheses, research shows play and activity tend to decline with age which may result in neg... | large_corpus_distillation |
"Second derivative-Example-Given the function f(x)=x3, the derivative of f is the function f\u2032(x)=3x2.\nThe second derivative of f is the derivative of f\u2032 , namely f\u2032\u2032(x)=6x." | large_corpus_distillation |
"Logical equivalence-Examples-If Lisa is not in Europe, then she is not in Denmark (a statement of the form \u00ace\u27f9\u00acd ).Syntactically, (1) and (2) are derivable from each other via the rules of contraposition and double negation. Semantically, (1) and (2) are true in exactly the same models (interpretations... | large_corpus_distillation |
"Eigendecomposition of a matrix-Eigendecomposition of a matrix-Let A be a square n \u00d7 n matrix with n linearly independent eigenvectors qi (where i = 1, ..., n). Then A can be factorized as A=Q\u039bQ\u22121 where Q is the square n \u00d7 n matrix whose ith column is the eigenvector qi of A, and \u039b is the diago... | large_corpus_distillation |
of IID rv\u2019s, each of mean X\u00af . If J is a stopping trial for {X n ;n\u22651} and if E[J]<\u221e, then\nthe sum S J =X 1 +X 2 +\u22ef+X J at the stopping trial J satisfies\nE[S ]=X\u00afE[J] (4.5.1)\nJ\nProof\nNote that X n is included in S J =\u2211J n=1 X n whenever n\u2264J, i.e., whenever the n=1 indicator ... | large_corpus_distillation |
"E6 (mathematics)-Algebra-1 generator which is their chirality generator, and is the sixth Cartan generator.One choice of simple roots for E6 is given by the rows of the following matrix, indexed in the order : [1\u22121000001\u22121000001\u2212100000110\u221212\u221212\u221212\u221212\u221212320001\u221210] Weyl group... | large_corpus_distillation |
"Covariance matrix-Properties-Equivalently, the correlation matrix can be seen as the covariance matrix of the standardized random variables Xi/\u03c3(Xi) for i=1,\u2026,n corr \u2061(X)=[1E\u2061[(X1\u2212\u03bc1)(X2\u2212\u03bc2)]\u03c3(X1)\u03c3(X2)\u22efE\u2061[(X1\u2212\u03bc1)(Xn\u2212\u03bcn)]\u03c3(X1)\u03c3(... | large_corpus_distillation |
"Monus-Definition-Let (M,+,0) be a commutative monoid. Define a binary relation \u2264 on this monoid as follows: for any two elements a and b , define a\u2264b if there exists an element c such that a+c=b . It is easy to check that \u2264 is reflexive and that it is transitive. M is called naturally ordered i... | large_corpus_distillation |
"Convolutional neural network-History-It was inspired by the above-mentioned work of Hubel and Wiesel. The neocognitron introduced the two basic types of layers in CNNs: convolutional layers, and downsampling layers. A convolutional layer contains units whose receptive fields cover a patch of the previous layer. The we... | large_corpus_distillation |
a logarithm of a product by rewriting it as a sum of\nindividual logarithms." | large_corpus_distillation |
"Highway-Road traffic safety-The report also noted that the problem was most severe in developing countries and that simple prevention measures could halve the number of deaths. For reasons of clear data collection, only harm involving a road vehicle is included. A person tripping with fatal consequences or dying for s... | large_corpus_distillation |
lists by combinatorics tools start first value of range.\nstep increment of range.\ncount number of items in range.\nlast inclusive last value of range.\nend exclusive last value of range." | large_corpus_distillation |
1 and dt 2 0 2 . The vector x y is very\n\u2207f f\nuseful, so it has its own symbol, , pronounced \"del f''; it is also called the gradient of .\n\uf00c Example 14.5.1\nz=x2+y2 (1,2) \u27e83,4\u27e9\nFind the slope of at in the direction of the vector .\nSolution\n(1,2) \u2207f =\u27e82x,2y\u27e9 \u27e82,4\u27e9 (1,2)... | large_corpus_distillation |
"W^X-W^X-W^X (\"write xor execute\", pronounced W xor X) is a security feature in operating systems and virtual machines. It is a memory protection policy whereby every page in a process's or kernel's address space may be either writable or executable, but not both. Without such protection, a program can write (as data... | large_corpus_distillation |
"Motorcycle-Safety-Motorcycles have a higher rate of fatal accidents than automobiles or trucks and buses. United States Department of Transportation data for 2005 from the Fatality Analysis Reporting System show that for passenger cars, 18.62 fatal crashes occur per 100,000 registered vehicles. For motorcycles this fi... | large_corpus_distillation |
"Entry point-Programming languages-The main() function is special; normally every C and C++ program must define it exactly once.\nIf declared, main() must be declared as if it has external linkage; it cannot be declared static or inline.\nIn C++, main() must be in the global namespace (i.e. ::main), cannot be overloade... | large_corpus_distillation |
"Algebraic fraction-Irrational fractions-An irrational fraction is one that contains the variable under a fractional exponent. An example of an irrational fraction is x1/2\u221213ax1/3\u2212x1/2." | large_corpus_distillation |
"Sweep account-Mechanics-Larger corporate bank accounts are charged numerous fees for each of the services the bank offers (such as a charge per every check deposited), however the bank rebates these fees based on the companies account balances in a process known as account analysis.\nHow it actually works In a sweep a... | large_corpus_distillation |
"Translation lookaside buffer-Overview-A TLB has a fixed number of slots containing page-table entries and segment-table entries; page-table entries map virtual addresses to physical addresses and intermediate-table addresses, while segment-table entries map virtual addresses to segment addresses, intermediate-table ad... | large_corpus_distillation |
"Support vector machine-History-The original SVM algorithm was invented by Vladimir N. Vapnik and Alexey Ya. Chervonenkis in 1964. In 1992, Bernhard Boser, Isabelle Guyon and Vladimir Vapnik suggested a way to create nonlinear classifiers by applying the kernel trick to maximum-margin hyperplanes. The \"soft margin\" i... | large_corpus_distillation |
"Neighbourhood (graph theory)-Local properties in graphs-For example: Any complete graph Kn is locally Kn-1. The only graphs that are locally complete are disjoint unions of complete graphs.\nA Tur\u00e1n graph T(rs,r) is locally T((r-1)s,r-1). More generally any Tur\u00e1n graph is locally Tur\u00e1n.\nEvery planar gr... | large_corpus_distillation |
"Closure (computer programming)-Anonymous functions-For example, in the following Python code: the values of a and b are closures, in both cases produced by returning a nested function with a free variable from the enclosing function, so that the free variable binds to the value of parameter x of the enclosing function... | large_corpus_distillation |
"Author-level metrics-List of metrics-Field-weighted Citation Impact Field-weighted Citation Impact (FWCI) is an author-level metric introduced and applied by Scopus SciVal. FWCI equals to the total citations actually received divided by the total citations that would be expected based on the average of the considered ... | large_corpus_distillation |
"Multidimensional discrete convolution-The helix transform-X\u2032=[X000] and Y\u2032=[Y000] where each of the input matrices are now of dimensions (M+K\u22121) \u00d7 (N+L\u22121) . It is then possible to implement column-wise lexicographic ordering in order to convert the modified matrices into vectors, X\u2033 an... | large_corpus_distillation |
"Buffer overflow-Exploitation-NOP sled technique A NOP-sled is the oldest and most widely known technique for exploiting stack buffer overflows. It solves the problem of finding the exact address of the buffer by effectively increasing the size of the target area. To do this, much larger sections of the stack are corru... | large_corpus_distillation |
"Cold start (recommender systems)-Systems affected-This of course assumes that a new item will be already described by its attributes, which is not always the case. Consider the case of so-called editorial features (e.g. director, cast, title, year), those are always known when the item, in this case movie, is added to... | large_corpus_distillation |
"Error exponent-Error exponent in source coding-Thus, as an example of when an error occurs, supposed that the source sequence X1n(1) was mapped to message 1 as was the source sequence X1n(2) . If X1n(1) was generated at the source, but P(X1n(2))>P(X1n(1)) then an error occurs.\nLet Si denote the event that the s... | large_corpus_distillation |
"Branching (version control)-Merging-Branching generally implies the ability to later merge or integrate changes back onto the parent branch. Often the changes are merged back to the trunk, even if this is not the parent branch. A branch not intended to be merged (e.g. because it has been relicensed under an incompatib... | large_corpus_distillation |
"Distributed morphology-Distributed morphology approach to core theoretical issues-Featural specification derives allomorphy in featural paradigms. Allomorphy in which different phonological exponents of the same feature bundle are idiosyncratically realized depending on the morphological or phonological environment is... | large_corpus_distillation |
"Uno Flip!-Gameplay-Both sides contain two \"Flip\" cards in each of their respective colors. Whenever a Flip is played, both the stockpile and the discard pile are immediately turned over and all players must turn their hands around to play the other side of their cards.\nLight Side Colors for this side are red, blue,... | large_corpus_distillation |
"Ruby (programming language)-Syntax-The syntax of Ruby is broadly similar to that of Perl and Python. Class and method definitions are signaled by keywords, whereas code blocks can be defined by either keywords or braces. In contrast to Perl, variables are not obligatorily prefixed with a sigil. When used, the sigil ch... | large_corpus_distillation |
"Book-Identification and classification-One of the earliest and most widely known systems of cataloguing books is the Dewey Decimal System. Another widely known system is the Library of Congress Classification system. Both systems are biased towards subjects which were well represented in US libraries when they were de... | large_corpus_distillation |
"Lagrange's identity-Proof of algebraic form-The second term on the left side of Lagrange's identity can be expanded as: which means that a symmetric square can be broken up into its diagonal and a pair of equal triangles on either side of the diagonal." | large_corpus_distillation |
"Support vector machine-Implementation-The parameters of the maximum-margin hyperplane are derived by solving the optimization. There exist several specialized algorithms for quickly solving the quadratic programming (QP) problem that arises from SVMs, mostly relying on heuristics for breaking the problem down into sma... | large_corpus_distillation |
"Variable elimination-Basic Operations-Factor Multiplication Computing a product between multiple factors results in a factor compatible with a single instantiation in each factor.Algorithm 2 mult-factors( v ,\u03d5 )Z = Union of all variables between product of factors f1(X1),...,fm(Xm) f = a factor over f where f ... | large_corpus_distillation |
"Longest path problem-Parameterized complexity-The longest path problem is fixed-parameter tractable when parameterized by the length of the path. For instance, it can be solved in time linear in the size of the input graph (but exponential in the length of the path), by an algorithm that performs the following steps: ... | large_corpus_distillation |
"Next-fit bin packing-Next-fit bin packing-When an item arrives, it checks whether the item fits into the current bin.\nIf it fits, it is placed inside it.\nOtherwise, the current bin is closed, a new bin is opened and the coming item is placed inside this new bin.Next-Fit is a bounded space algorithm - it requires onl... | large_corpus_distillation |
"Expected return-Discrete scenarios-In gambling and probability theory, there is usually a discrete set of possible outcomes. In this case, expected return is a measure of the relative balance of win or loss weighted by their chances of occurring.\nFor example, if a fair die is thrown and numbers 1 and 2 win $1, but 3-... | large_corpus_distillation |
"Inverse element-In groups-A group is a set with an associative operation that has an identity element, and for which every element has an inverse. Thus, the inverse is a function from the group to itself that may also be considered as an operation of arity one. It is also an involution, since the inverse of the inver... | large_corpus_distillation |
"Schur multiplier-Examples and properties-The Schur multiplier M\u2061(G) of a finite group G is a finite abelian group whose exponent divides the order of G. If a Sylow p-subgroup of G is cyclic for some p, then the order of M\u2061(G) is not divisible by p. In particular, if all Sylow p-subgroups of G are cyclic, t... | large_corpus_distillation |
"Beck\u2013Fiala theorem-Proof sketch-Consider only sets with |Sj|>t . Since each element appears at most t times in a set, there are less than n such sets. Now, enforce linear constraints \u2211i\u2208Sjxi=0 for them. Since it is a non-trivial linear subspace of Rn with fewer constraints than variables, there is ... | large_corpus_distillation |
"Shallow minor-Separator theorems-As Plotkin, Rao & Smith (1994) showed, graphs with excluded shallow minors can be partitioned analogously to the planar separator theorem for planar graphs. In particular, if the complete graph Kh is not a d-shallow minor of an n-vertex graph G, then there exists a subset S of G, with ... | large_corpus_distillation |
"Wi-Fi Protected Access-Security issues-Weak password Pre-shared key WPA and WPA2 remain vulnerable to password cracking attacks if users rely on a weak password or passphrase. WPA passphrase hashes are seeded from the SSID name and its length; rainbow tables exist for the top 1,000 network SSIDs and a multitude of com... | large_corpus_distillation |
"Intransitive dice-Intransitive 12-sided dice-In analogy to the intransitive six-sided dice, there are also dodecahedra which serve as intransitive twelve-sided dice. The points on each of the dice result in the sum of 114. There are no repetitive numbers on each of the dodecahedra.\nMiwin\u2019s dodecahedra (set 1) wi... | large_corpus_distillation |
"Asynchronous I/O-Forms-The select loop does not reach the ultimate system efficiency possible with, say, the completion queues method, because the semantics of the select call, allowing as it does for per-call tuning of the acceptable event set, consumes some amount of time per invocation traversing the selection arra... | large_corpus_distillation |
and show that a variant on Trivium which made no change except to increase the key length beyond the 80 bits mandated by eSTREAM Profile 2 would not be secure. Using optimised solving strategy, it is further possible to reduce the state-recovery complexity to 2132 steps.A detailed justification of the design of Trivium... | large_corpus_distillation |
"Type safety-Type safety issues in specific languages-In addition, C, like Ada, provides unspecified or undefined explicit conversions; and unlike in Ada, idioms that use these conversions are very common, and have helped to give C a type-unsafe reputation. For example, the standard way to allocate memory on the heap i... | large_corpus_distillation |
"To define the composition g\u2218f, the range of f must be contained in the domain of g.\nEven functions are symmetric about the y-axis whereas odd functions are symmetric about the origin.\nKey Equations\nComposition of two functions\n(g\u2218f)(x)=g(f(x))\nAbsolute value function\n\u2212x, if x<0\nf(x)={\nx, if x\u2... | large_corpus_distillation |
agree with Wald\u2019s equality. In particular, since S J is 1 with probability 1, we also\nhave E[S J ]=1. Since X\u00af=2p\u22121 and E[J]=1/(2p\u22121), Wald\u2019s equality is satisfied (which of course it has to be).\nFor p=1/2, we still have S J =1 with probability 1 and thus E[S J ]=1. However X\u00af=0 so X\u00... | large_corpus_distillation |
2003 Nissan Jikoo - 1935 Datsun Type 14 Roadster 2003 Peugeot 4002 - Various historic Peugeot models 2004 Fiat Trepi\u00f9no \u2013 Fiat 500 2004 Chevrolet Nomad - 1954 Chevrolet Nomad \"Dream Car\" 2004 Ford Shelby Cobra Concept - AC Cobra 2004 Ford Bronco - 1966 Ford Bronco 2005 Holden Efijy \u2013 Holden FJ 2005 Vol... | large_corpus_distillation |
"Laplacian matrix-Definitions for simple graphs-Symmetric Laplacian for a directed graph The Laplacian matrix of a directed graph is by definition generally non-symmetric, while, e.g., traditional spectral clustering is primarily developed for undirected graphs with symmetric adjacency and Laplacian matrices. A trivial... | large_corpus_distillation |
"Congruence subgroup-The congruence subgroup problem-There is a surjection \u0393(2)\u2192Z ; for m large enough the kernel of \u0393(2)\u2192Z\u2192Z/mZ must be non-congruence (one way to see this is that the Cheeger constant of the Schreier graph goes to 0; there is also a simple algebraic proof in the spirit of t... | large_corpus_distillation |
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