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"Network switching subsystem-Visitor location register (VLR)-Description The Visitor Location Register (VLR) is a database of the MSs (Mobile stations) that have roamed into the jurisdiction of the Mobile Switching Center (MSC) which it serves. Each main base transceiver station in the network is served by exactly one ... | large_corpus_distillation |
"Comparison of file transfer protocols-Serial protocols-The following protocols were designed for serial communication, mostly for the RS-232 standard. They are used for uploading and downloading computer files via modem or serial cable (e.g., by null modem or direct cable connection). UUCP is one protocol that can ope... | large_corpus_distillation |
queue up data entries for fast retrieval by other jobs).\n*MSGQ: Message queue (used to send message to users, can also be used like a data queue).\n*OUTQ: Output queue (used to queue up output to a printer).\n*USRSPC: User space - a generic data-containing object of arbitrary size (up to 16T)." | large_corpus_distillation |
"Systems Programming Language-Language-Data types Where SPL differs most noticeably from ALGOL is that its data types are very machine specific, based on the 3000's 16-bit big endian word format.The INTEGER type is a 16-bit signed type, with 15 bits of value and the least significant bit as the sign. DOUBLE is a 32-bit... | large_corpus_distillation |
"Wiener's attack-Small private key-Using the Chinese Remainder Theorem: Suppose one chooses d such that both mod (p\u22121) and mod (q\u22121) are small but d itself is not, then a fast decryption of C can be done as follows: 1. First compute mod p and mod q . 2. Use the Chinese Remainder Theorem to compute the ... | large_corpus_distillation |
"Computational learning theory-Overview-Negative results \u2013 Showing that certain classes cannot be learned in polynomial time.Negative results often rely on commonly believed, but yet unproven assumptions, such as: Computational complexity \u2013 P \u2260 NP (the P versus NP problem); Cryptographic \u2013 One-way f... | large_corpus_distillation |
"Texting while driving-Technology as a solution-Android operating system: In addition to Android Auto, there are apps that utilize the GPS and Network Location services of Android mobile phones to estimate the speed that the cell phone is travelling at the time text messages are sent. As noted before, some of these app... | large_corpus_distillation |
"Functional programming-Concepts-Referential transparency Functional programs do not have assignment statements, that is, the value of a variable in a functional program never changes once defined. This eliminates any chances of side effects because any variable can be replaced with its actual value at any point of exe... | large_corpus_distillation |
"Feedback arc set-Theory-In planar directed graphs, the feedback arc set problem obeys a min-max theorem: the minimum size of a feedback arc set equals the maximum number of edge-disjoint directed cycles that can be found in the graph. This is not true for some other graphs; for instance the first illustration shows a ... | large_corpus_distillation |
"Tomasulo's algorithm-Implementation concepts-Register renaming Tomasulo's algorithm uses register renaming to correctly perform out-of-order execution. All general-purpose and reservation station registers hold either a real value or a placeholder value. If a real value is unavailable to a destination register during ... | large_corpus_distillation |
"Hardware-based encryption-Advantages-Implementing cryptography in hardware means that part of the processor is dedicated to the task. This can lead to a large increase in speed. In particular, modern processor architectures that support pipelining can often perform other instructions concurrently with the execution of... | large_corpus_distillation |
"Maximal ideal-Maximal ideal-In mathematics, more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other ideals contained between I and R.\nMaximal ideals are important bec... | large_corpus_distillation |
"Bertrand's postulate-Prime number theorem-The prime number theorem (PNT) implies that the number of primes up to x is roughly x/ln(x), so if we replace x with 2x then we see the number of primes up to 2x is asymptotically twice the number of primes up to x (the terms ln(2x) and ln(x) are asymptotically equivalent). Th... | large_corpus_distillation |
"Argument (linguistics)-Distinguishing between arguments and adjuncts-a. She cleaned the kitchen.\nb. She cleaned. \u2013 the kitchen is an optional argument.a. We are waiting for Larry.\nb. We are waiting. \u2013 for Larry is an optional argument.a. Susan was working on the model." | large_corpus_distillation |
"Merge sort-Use with tape drives-Naming the four tape drives as A, B, C, D, with the original data on A, and using only two record buffers, the algorithm is similar to the bottom-up implementation, using pairs of tape drives instead of arrays in memory. The basic algorithm can be described as follows: Merge pairs of re... | large_corpus_distillation |
"Expurgation-Examples-Cursing Many Internet message boards and forums use automatic wordfiltering to block offensive words and phrases from being published or automatically amend them to more innocuous substitutes such as asterisks or nonsense. This often catches innocent words, in a scenario referred to as the Scuntho... | large_corpus_distillation |
"Normal basis-Case of finite fields-For example, in the field K=GF(23)=F8 above, we may represent elements as bit-strings: where the coefficients are bits ai\u2208GF(2)={0,1}.\nNow we can square elements by doing a left circular shift, \u03b12=\u03a6(a2,a1,a0)=(a1,a0,a2) , since squaring \u03b24 gives \u03b28 = \u03... | large_corpus_distillation |
"Regular open set-Examples-If R has its usual Euclidean topology then the open set S=(0,1)\u222a(1,2) is not a regular open set, since Int \u2061(S\u00af)=(0,2)\u2260S.\nEvery open interval in R is a regular open set and every non-degenerate closed interval (that is, a closed interval containing at least two distin... | large_corpus_distillation |
"Ideal lattice-Use in cryptography-Let f(x)=xn+1\u2208Z[x] , where the security parameter n is a power of 2, making f(x) irreducible over the rationals. (This particular f(x) comes from the family of cyclotomic polynomials, which play a special role in this work)." | large_corpus_distillation |
"Probability axioms-Further consequences-Another important property is: P(A\u222aB)=P(A)+P(B)\u2212P(A\u2229B).\nThis is called the addition law of probability, or the sum rule." | large_corpus_distillation |
"Pedersen index-Countries-The Pedersen indices for individual countries are listed below, only the last available index is shown. The Pedersen index tends to decrease for some countries with increasing number of consecutive elections." | large_corpus_distillation |
"Boy or Girl paradox-First question-Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?Under the aforementioned assumptions, in this problem, a random family is selected. In this sample space, there are four equally probable events: Only two of these possible eve... | large_corpus_distillation |
"Chauvenet's criterion-Derivation-where Z is the Z -score, x is the sample value, \u03bc=0 is the mean of standard normal distribution, and \u03c3=1 is the standard deviation of standard normal distribution.Based on Eq.4, to find the Dmax (Eq.1) find the z-score corresponding to Pz in a Z -score table. Dmax is equ... | large_corpus_distillation |
"Elementary arithmetic-Multiplication-Example of multiplication for a single-digit factor Multiplying 729 and 3, starting on the ones-column, the product of 9 and 3 is 27. 7 is written under the ones column and 2 is written above the tens column as a carry digit.\nThe product of 2 and 3 is 6, and the carry digit adds 2... | large_corpus_distillation |
"Grammar checker-Technical issues-True grammar checking is more complex. While a programming language has a very specific syntax and grammar, this is not so for natural languages. One can write a somewhat complete formal grammar for a natural language, but there are usually so many exceptions in real usage that a forma... | large_corpus_distillation |
"Statistical classification-Relation to other problems-Correspondingly, it can abstain when its confidence of choosing any particular output is too low.\nBecause of the probabilities which are generated, probabilistic classifiers can be more effectively incorporated into larger machine-learning tasks, in a way that par... | large_corpus_distillation |
"Parsing-Human languages-Computational methods In some machine translation and natural language processing systems, written texts in human languages are parsed by computer programs. Human sentences are not easily parsed by programs, as there is substantial ambiguity in the structure of human language, whose usage is to... | large_corpus_distillation |
"Link prediction-Problem definition-Link prediction task can also be formulated as an instance of missing value estimation task.\nHere, the graph is represented as an adjacency matrix with missing values. The task is to complete the matrix by identifying the missing values.\nMatrix factorization based methods commonly... | large_corpus_distillation |
"MP3 blog-Aggregators-Aggregators such as The Hype Machine and Music Blogtrotter track MP3 blog posts and display the most recently updated posts on its front page. The services are meant to provide a snapshot of what's going on in music blogging and make it easier to search through recently posted MP3s. The Hype Machi... | large_corpus_distillation |
"Empty category-Null DPs-In example 4), the null object must be referring to the matrix clause subject [Zhangsan] but not the embedded subject [Lisi], since condition C of the Binding Theory states that it must be free. (Square brackets indicate that an element is covert (not pronounced), as in the second English trans... | large_corpus_distillation |
"Natural evolution strategy-Method-Replacing fitness with utility, the gradient estimate becomes log \u2061\u03c0(xk|\u03b8) .The choice of utility function is a free parameter of the algorithm." | large_corpus_distillation |
"Generalized normal distribution-Symmetric version-This family includes the normal distribution when \u03b2=2 (with mean \u03bc and variance \u03b122 ) and it includes the Laplace distribution when \u03b2=1 . As \u03b2\u2192\u221e , the density converges pointwise to a uniform density on (\u03bc\u2212\u03b1,\u03b... | large_corpus_distillation |
"IBM 3270-Technical Information-Example The following data stream writes an attribute in row 24, column 1, writes the (protected) characters '> ' in row 24, columns 2 and 3, and creates an unprotected field on row 24 from columns 5-79. Because the buffer wraps around an attribute is placed on row 24, column 80 to termi... | large_corpus_distillation |
"Arithmetic derivative-Elementary properties-The Leibniz rule implies that D(0) = 0 (take m = n = 0) and D(1) = 0 (take m = n = 1).\nThe power rule is also valid for the arithmetic derivative. For any integers k and n \u2265 0: D(kn)=nkn\u22121D(k).\nThis allows one to compute the derivative from the prime factorizatio... | large_corpus_distillation |
benefit of early CVE candidacy is that all future correspondence can refer to the CVE number. Information on getting CVE identifiers for issues with open source projects is available from Red Hat and GitHub.CVEs are for software that has been publicly released; this can include betas and other pre-release versions if t... | large_corpus_distillation |
"Instruction scheduling-Phase order-If the architecture being scheduled has instruction sequences that have potentially illegal combinations (due to a lack of instruction interlocks), the instructions must be scheduled after register allocation. This second scheduling pass will also improve the placement of the spill/f... | large_corpus_distillation |
the original program, potentially via its abstract syntax tree representation, or a more coarse-grained representation such as operating at the statement-level or block-level. Earlier genetic improvement approaches operate at the statement level and carry out simple delete/replace operations such as deleting an existin... | large_corpus_distillation |
a power of a prime, the orthogonal Latin squares produce error detecting codes that are as efficient as possible." | large_corpus_distillation |
"Local search (constraint satisfaction)-Local search on a cycle cutset-The cost of variable evaluations can be used by local search for computing the cost of a solution. The cost of values of the roots of the forest is indeed the minimal number of violated constraints in the forest for these given values. These costs c... | large_corpus_distillation |
"Minimum spanning tree-Properties-By a similar argument, if more than one edge is of minimum weight across a cut, then each such edge is contained in some minimum spanning tree.\nMinimum-cost edge If the minimum cost edge e of a graph is unique, then this edge is included in any MST.\nProof: if e was not included in th... | large_corpus_distillation |
algorithm in the face of processor failures and unreliable communications links. The choice of an appropriate distributed algorithm to solve a given problem depends on both the characteristics of the problem, and characteristics of the system the algorithm will run on such as the type and probability of processor or li... | large_corpus_distillation |
"Inflection-In various languages-English Old English was a moderately inflected language, using an extensive case system similar to that of modern Icelandic or German. Middle and Modern English lost progressively more of the Old English inflectional system. Modern English is considered a weakly inflected language, sinc... | large_corpus_distillation |
dominates the time spent on other computation, further parallelization (that is, splitting the workload over even more threads) increases rather than decreases the amount of time required to finish. This problem, known as parallel slowdown, can be improved in some cases by software analysis and redesign." | large_corpus_distillation |
"Kolmogorov extension theorem-General form of the theorem-The Kolmogorov extension theorem gives us conditions for a collection of measures on Euclidean spaces to be the finite-dimensional distributions of some Rn -valued stochastic process, but the assumption that the state space be Rn is unnecessary. In fact, any c... | large_corpus_distillation |
"3G adoption-3G adoption-In December 2007, 190 3G networks were operating in 40 countries and 154 HSDPA networks were operating in 71 countries, according to the Global Mobile Suppliers Association (GSA). In Asia, Europe, Canada and the US, telecommunication companies use W-CDMA technology with the support of around 10... | large_corpus_distillation |
(scaled by the factor \u03c32 ), with n \u2212 1 degrees of freedom. The degrees-of-freedom, here a parameter of the distribution, can still be interpreted as the dimension of an underlying vector subspace.\nLikewise, the one-sample t-test statistic, n(X\u00af\u2212\u03bc0)\u2211i=1n(Xi\u2212X\u00af)2/(n\u22121) follo... | large_corpus_distillation |
"Nuclear operator-Nuclear operators between locally convex spaces-Sufficient conditions for nuclearity Let W, X, Y, and Z be Hausdorff locally convex spaces, N:X\u2192Y a nuclear map, and M:W\u2192X and P:Y\u2192Z be continuous linear maps. Then N\u2218M:W\u2192Y , P\u2218N:X\u2192Z , and P\u2218N\u2218M:W\u2192Z... | large_corpus_distillation |
the idf's log function is always greater than or equal to 1, the value of idf (and tf\u2013idf) is greater than or equal to 0. As a term appears in more documents, the ratio inside the logarithm approaches 1, bringing the idf and tf\u2013idf closer to 0." | large_corpus_distillation |
"Pseudo-order-Discussion-Relation to other properties This section assumes classical logic. At least then, following properties can be proven: If R is a co-transitive relation, then R is also quasitransitive; R satisfies axiom 3 of semiorders; incomparability w.r.t. R is a transitive relation; and R is connex iff it is... | large_corpus_distillation |
"Google Books-Content issues and criticism-Google Books versus Google Scholar While Google Books has digitized large numbers of journal back issues, its scans do not include the metadata required for identifying specific articles in specific issues. This has led the makers of Google Scholar to start their own program t... | large_corpus_distillation |
"Separation oracle-Usage-If the oracle says that xt is infeasible, then it typically returns a specific constraint that is violated by xt , that is, a row aj in the matrix A, such that aj\u22c5xt>bj . Since aj\u22c5x\u2264bj for all feasible x, this implies that aj\u22c5xt>aj\u22c5x for all feasible x. Then, we d... | large_corpus_distillation |
"{{X=x}:x\u2208S} \u03a9\nNote that is a countable partition of the sample space . That is, these events are disjoint and their union\n\u03a9\nis the entire sample space . Hence\nP(E)=\u2211P(E\u2229{X=x})=\u2211P(X=x)P(E\u2223X=x)=\u2211f(x)P(E\u2223X=x) (3.1.9)\nx\u2208S x\u2208S x\u2208S\nX E X\nThis result is usefu... | large_corpus_distillation |
"Braille pattern dots-345-Braille pattern dots-345-The Braille pattern dots-345 ( \u281c ) is a 6-dot braille cell with the top and middle right and bottom left dots raised, or an 8-dot braille cell with the top and upper-middle right, and lower-middle left dots raised. It is represented by the Unicode code point U+281... | large_corpus_distillation |
"Formal grammar-Formal definition-Example For these examples, formal languages are specified using set-builder notation." | large_corpus_distillation |
"Arabic Speech Corpus-Purpose-The corpus was mainly built for speech synthesis purposes, specifically Speech Synthesis, but the corpus has been used for building HMM based voices in Arabic. It was also used to automatically align other speech corpora with their phonetic transcript and could be used as part of a larger ... | large_corpus_distillation |
integer1 integer2) -> product: ARITH integer1 * integer2.\nFN MULT_234 = ([2][3]element:matrix1, [3][4]element:matrix2) -> [2][4]product: MATRIX_MULT{MULT,PLUS}(matrix1, matrix2).\nFN TEST = () -> [2][4]product: ( LET m1 = ((elt/2, elt/1, elt/1), (elt/3, elt/6, elt/9)), m2 = ((elt/6, elt/1, elt/3, elt/4), (elt/9, el... | large_corpus_distillation |
assume also that the steepness of the hill is not immediately obvious with simple observation, but rather it requires a sophisticated instrument to measure, which the person happens to have at the moment. It takes quite some time to measure the steepness of the hill with the instrument, thus they should minimize their ... | large_corpus_distillation |
"Processor design-Markets-The 8-bit 6502 architecture and the first MOS Technology 6502 chip were designed in 13 months by a group of about 9 people.\nResearch and educational CPU design The 32-bit Berkeley RISC I and RISC II processors were mostly designed by a series of students as part of a four quarter sequence of ... | large_corpus_distillation |
"Geometric hashing-Geometric hashing in computer vision-Describe feature locations with respect to that basis, i.e. compute the projections to the new coordinate axes. The coordinates should be discretised to make recognition robust to noise, we take the bin size 0.25. We thus get the coordinates 0.75 1.25 ); 1.00 0.0... | large_corpus_distillation |
"Shadow (OS/2)-Shadow (OS/2)-A shadow is a stand-in for any other object on the desktop, such as a document, an application, a folder, a hard disk, a network share or removable medium, or a printer. A target object can have an arbitrary number of shadows. When double-clicked, the desktop acts the same way as if the ori... | large_corpus_distillation |
"Minimum mean square error-Examples-The cross correlation matrix CYX is defined as 10 ].\nWe now solve the equation CYWT=CYX by inverting CY and pre-multiplying to get 4.85 1.71 0.142 1.71 0.428 0.2857 0.142 0.2857 0.1429 10 2.57 0.142 0.5714 ]=WT." | large_corpus_distillation |
"Saturation attack-Theoretical calculations-Taking the design of an anti-ship missile as a theoretical example, one can begin with the goal of creating a missile which will get through and destroy its target 100% of the time. It is also understood, however, that an opponent will develop counter measures if given enough... | large_corpus_distillation |
"Affine cipher-Description-It can be shown as follows that decryption function is the inverse of the encryption function, mod mod mod mod mod mod m " | large_corpus_distillation |
"Minimum spanning tree-Algorithms-For every integer r, it is possible to find optimal decision trees for all graphs on r vertices by brute-force search. This search proceeds in two steps.\nA. Generating all potential DTs There are 2(r2) different graphs on r vertices.\nFor each graph, an MST can always be found using ... | large_corpus_distillation |
"RSA numbers-RSA-170-RSA-170 has 170 decimal digits (563 bits) and was first factored on December 29, 2009, by D. Bonenberger and M. Krone from Fachhochschule Braunschweig/Wolfenb\u00fcttel. An independent factorization was completed by S. A. Danilov and I. A. Popovyan two days later.The value and factorization are as ... | large_corpus_distillation |
avoiding spurious modes from out-of-distribution samples.\nCompositionality\u2013Individual models are unnormalized probability distributions, allowing models to be combined through product of experts or other hierarchical techniques." | large_corpus_distillation |
"Iterative deepening depth-first search-Related algorithms-When the depth will reach two hops along the arcs, the forward search will proceed to v from u , and the backward search will proceed from v to u . Pictorially, the search frontiers will go through each other, and instead a suboptimal path consisting of an ... | large_corpus_distillation |
"Graphics display resolution-Unsystematic resolutions-Other manufacturers have also introduced phones with irregular display resolutions and aspect ratios, such as Samsung's various \"Infinity\" displays with 37:18 = 18+1/2:9 aspect ratios (Galaxy S8/S9 and A8/Samsung Galaxy A9 (2018)) at resolutions of 2960\u2009\u00d... | large_corpus_distillation |
"Gaussian integral-Generalizations-The integral of a Gaussian function The integral of an arbitrary Gaussian function is An alternative form is This form is useful for calculating expectations of some continuous probability distributions related to the normal distribution, such as the log-normal distribution, for examp... | large_corpus_distillation |
"Sequential estimation-Sequential estimation-In statistics, sequential estimation refers to estimation methods in sequential analysis where the sample size is not fixed in advance. Instead, data is evaluated as it is collected, and further sampling is stopped in accordance with a predefined stopping rule as soon as sig... | large_corpus_distillation |
"Elo rating system-Elo rating system-Elo ratings are comparative only, and are valid only within the rating pool in which they were calculated, rather than being an absolute measure of a player's strength." | large_corpus_distillation |
"TeXML-Application-TeXML is used to generate Technical Documentation from XML data.\nAfter the transformation TeXML \u2192 TeX, the entire LaTeX-defined range of TeX macros is available.\nBy means of using TeX macros, it is possible to publish XML data having configurable layout options." | large_corpus_distillation |
"Line number-Line number-In the C programming language the line number of a source code line is one greater than the number of new-line characters read or introduced up to that point.Programmers could also assign line numbers to statements in older programming languages, such as Fortran, JOSS, and BASIC. In Fortran, no... | large_corpus_distillation |
"Training, validation, and test data sets-Validation data set-An application of this process is in early stopping, where the candidate models are successive iterations of the same network, and training stops when the error on the validation set grows, choosing the previous model (the one with minimum error)." | large_corpus_distillation |
"Time-utility function-Utility Accrual Scheduling-The TUF/UA paradigm resolves each instance of this contention using an application-specific algorithmic technique that creates (or updates) a schedule at scheduling events\u2014e.g., times (such as action arrival or completion) or states. The instance's contending actio... | large_corpus_distillation |
"Instruction pipelining-Illustrated example-To the right is a generic pipeline with four stages: fetch, decode, execute and write-back. The top gray box is the list of instructions waiting to be executed, the bottom gray box is the list of instructions that have had their execution completed, and the middle white box i... | large_corpus_distillation |
is compared to has a similar form as before, decreasing with the margin \u03c1. See\nSchapire et al. (1998) for details. The paper is available from the course website as optional\nreading.\nMixture models\nThere are many problems in machine learning that are not simple classification problems\nbut rather modeling prob... | large_corpus_distillation |
in conjunction with mapping\nexamples to higher dimensional feature vectors. The regularized least squares objective to\nbe minimized, with parameter \u03bb, is given by\nJ(\u03b8) = \ufffd\nn\n\ufffd y \u2212 \u03b8T \u03c6(x ) \ufffd 2 + \u03bb\ufffd\u03b8\ufffd2 (23)\nt t\nt=1\nCite as: Tommi Jaakkola, course materi... | large_corpus_distillation |
"-onym-Words that end in -onym-limnonym: a name of a lake or a pond.\nlogonym: a polysemic term, with several meanings.\nlinguonym: a name of a language macrotoponym: a type of toponym that designates an important toponymic feature, that has a wider (regional, national, continental, global) significance.\nmeronym: a wo... | large_corpus_distillation |
"Hamming code-[7,4] Hamming code-Construction of G and H The matrix := (Ik\u2212AT) is called a (canonical) generator matrix of a linear (n,k) code, and := (AIn\u2212k) is called a parity-check matrix." | large_corpus_distillation |
same as . The function to maximize is . The two gradient vectors are and\n\u27e8yz,xz,xy\u27e9\n, so the equations to be solved are\nyz=2x\u03bb\nxz=2y\u03bb\nxy =2z\u03bb\n1 =x2+y2+z2\n\u03bb=0 x y z\nIf then at least two of , , must be 0, giving a volume of 0, which will not be the maximum. If we multiply the first\n... | large_corpus_distillation |
"Forcing (mathematics)-Generic filters-For G to be \"generic relative to M \" means: If D\u2208M is a \"dense\" subset of P (that is, for each p\u2208P , there exists a q\u2208D such that q\u2264p ), then G\u2229D\u2260\u2205 .Given that M is a countable model, the existence of a generic filter G follows from... | large_corpus_distillation |
"VAX 8000-VAX 8600-The VAX 8600 has a CPU with an 80 ns cycle time (12.5 MHz) implemented with emitter coupled logic (ECL) macrocell arrays (MCAs). The CPU consists of four major logical sections, the E Box, F Box, I Box and M Box. The E Box executes all instructions, including floating-point instructions through micro... | large_corpus_distillation |
"Glossary of artificial intelligence-R-Resource Description Framework (RDF) A family of World Wide Web Consortium (W3C) specifications originally designed as a metadata data model. It has come to be used as a general method for conceptual description or modeling of information that is implemented in web resources, usin... | large_corpus_distillation |
holds if and only if P[U=E(X\u2223G)]=1, so U and E(X\u2223G) are equivalent.\nProof\n1. Note that\nE[(X\u2212U)2] =E([X\u2212E(X\u2223G)+E(X\u2223G)\u2212U]2) (4.10.24)\n=E([X\u2212E(X\u2223G)]2)+2E([X\u2212E(X\u2223G)][E(X\u2223G)\u2212U])+E([E(X\u2223G)\u2212U]2) (4.10.25)\nBy mean property, X\u2212E(X\u2223G) has m... | large_corpus_distillation |
"Divisor summatory function-Piltz divisor problem-In the generalized case, one has log \u2061x)+\u0394k(x) where Pk is a polynomial of degree k\u22121 . Using simple estimates, it is readily shown that log k\u22122\u2061x) for integer k\u22652 . As in the k=2 case, the infimum of the bound is not known for any valu... | large_corpus_distillation |
objects, a sphere and a cube. Fr\u00f6bel called this gift \"the child's delight\", since he observed the joy of each child discovering the differences between the sphere and cube." | large_corpus_distillation |
size of p is the key security parameter, not the smoothness of p-1." | large_corpus_distillation |
"Lp space-The p-norm in infinite dimensions and \u2113p spaces-This contains as special cases: \u21131, the space of sequences whose series is absolutely convergent, \u21132, the space of square-summable sequences, which is a Hilbert space, and \u2113\u221e, the space of bounded sequences.The space of sequences has a n... | large_corpus_distillation |
"Flooding algorithm-Flooding algorithm-Different flooding algorithms can be applied for different problems, and run with different time complexities. For example, the flood fill algorithm is a simple but relatively robust algorithm that works for intricate geometries and can determine which part of the (target) area th... | large_corpus_distillation |
"Linear map-Applications-Another application of these transformations is in compiler optimizations of nested-loop code, and in parallelizing compiler techniques." | large_corpus_distillation |
"Floating-point arithmetic-Accuracy problems-A detailed treatment of the techniques for writing high-quality floating-point software is beyond the scope of this article, and the reader is referred to, and the other references at the bottom of this article. Kahan suggests several rules of thumb that can substantially de... | large_corpus_distillation |
"Greatest element and least element-Definitions-Contrast to maximal elements and local/absolute maximums A greatest element of a subset of a preordered set should not be confused with a maximal element of the set, which are elements that are not strictly smaller than any other element in the set. Let (P,\u2264) be a ... | large_corpus_distillation |
"Two-hybrid screening-One-, three- and one-two-hybrid variants-One-two-hybrid Simultaneous use of the one- and two-hybrid methods (that is, simultaneous protein\u2013protein and protein\u2013DNA interaction) is known as a one-two-hybrid approach and expected to increase the stringency of the screen." | large_corpus_distillation |
"Quasinormal operator-Definition and some properties-So UP = PU on the range of P. On the other hand, if h \u2208 H lies in kernel of P, clearly UP h = 0. But PU h = 0 as well. because U is a partial isometry whose initial space is closure of range P. Finally, the self-adjointness of P implies that H is the direct sum ... | large_corpus_distillation |
"Regression testing-Uses-Regression tests can be broadly categorized as functional tests or unit tests. Functional tests exercise the complete program with various inputs. Unit tests exercise individual functions, subroutines, or object methods. Both functional testing tools and unit-testing tools tend to be automated ... | large_corpus_distillation |
"Turning point test-Statement of test-Test statistic We say i is a turning point if the vector X1, X2, ..., Xi, ..., Xn is not monotonic at index i. The number of turning points is the number of maxima and minima in the series.Letting T be the number of turning points then for large n, T is approximately normally distr... | large_corpus_distillation |
"Matrix calculus-Matrix calculus-In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single var... | large_corpus_distillation |
"Fuzzing-Early random testing-In 1991, the crashme tool was released, which was intended to test the robustness of Unix and Unix-like operating systems by randomly executing systems calls with randomly chosen parameters." | large_corpus_distillation |
\u03b7 = R\u221a ,\ns\nL k\nLR\nIE[f(x\u00af )]\u2212f(x\u2217)\u2264 \u221a\nk\nk\nProof.\nf(x )\u2212f(x\u2217) \u2264g \u22a4(x \u2212x\u2217)\ns s s\n=IE[g\u02dc\u22a4(x \u2212x\u2217)|x ]\ns s s\n1\n= IE[(y \u2212x )\u22a4(x \u2212x\u2217)|x ]\ns+1 s s s\n\u03b7\n1\n= IE[kx \u2212y k2+kx \u2212x\u2217k2\u2212ky \u... | large_corpus_distillation |
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