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"Poisson distribution-Computational methods-Some computing languages provide built-in functions to evaluate the Poisson distribution, namely R: function dpois(x, lambda); Excel: function POISSON( x, mean, cumulative), with a flag to specify the cumulative distribution; Mathematica: univariate Poisson distribution as Po... | large_corpus_distillation |
"__add__(self, other)\n__sub__(self, other)\n__mul__(self, other)\n__truediv__(self, other)\n__mod__(self, other)\n__pow__(self, other)\nother\nAccount.__add__()\nacct_a = Account(\"Ashe\", 6492)\nacct_b = Account(\"Bevins\", 5210)\nacct_ab = acct_a + acct_b\nacct_a\nacct_b\nacct_ab" | large_corpus_distillation |
Luhn & Gerd Lamprecht improved the record to 6,701 digits in October 2019: p = 22582235875\u00d7222224+1.Serge Batalov improved the record to 15,004 digits in April 2022: p = 2494779036241x249800+1." | large_corpus_distillation |
"Sentence (linguistics)-Length-The 1980s saw a renewed surge in interest in sentence length, primarily in relation to \"other syntactic phenomena\".One definition of the average sentence length of a prose passage is the ratio of the number of words to the number of sentences.\nThe textbook Mathematical Linguistics, by ... | large_corpus_distillation |
for all employees to use (their technical skills have to be taken under consideration), as well as containing the ability to cater to all of the necessary business needs. Another point to be considered is to not only look at the text side of things, but employ video and image capturing techniques as well. With this poi... | large_corpus_distillation |
a 256-bit key (which is already in use in some systems) would take about two minutes to crack. Using a 512-bit key would increase the cracking time to approaching 1072 years, without increasing the time for encryption by more than a constant factor (depending on the encryption algorithms used)." | large_corpus_distillation |
"Proximal gradient methods for learning-Lasso regularization-The \u21131 regularization problem is sometimes referred to as lasso (least absolute shrinkage and selection operator). Such \u21131 regularization problems are interesting because they induce sparse solutions, that is, solutions w to the minimization prob... | large_corpus_distillation |
information obtained from the monitoring is used for illegal or malicious purposes." | large_corpus_distillation |
"\uf128 Exercise 9.2.6\na. Let \\((a,b)\\) and \\((c,d)\\0 be two open intervals of real numbers. Show that these two sets\nhave the same cardinality by constructing a one-to-one onto function between them.\nHint\nA linear function should do the trick.\nR\nb. Show that any open interval of real numbers has the same car... | large_corpus_distillation |
"ITunes-Music library-iTunes features a music library. Each track has attributes, called metadata, that can be edited by the user, including changing the name of the artist, album, and genre, year of release, artwork, among other additional settings. The software supports importing digital audio tracks that can then be... | large_corpus_distillation |
"Space\u2013time tradeoff-Types of tradeoff-Lookup tables vs. recalculation A common situation is an algorithm involving a lookup table: an implementation can include the entire table, which reduces computing time, but increases the amount of memory needed, or it can compute table entries as needed, increasing computin... | large_corpus_distillation |
"260 (number)-Integers from 261 to 269-261 261 = 32\u00b729, lucky number, nonagonal number, unique period in base 2, number of possible unfolded tesseract patterns.\n262 262 = 2\u00b7131, meandric number, open meandric number, untouchable number, happy number, palindrome number, semiprime.\n263 263 is a prime, safe pr... | large_corpus_distillation |
"Heterogeneous earliest finish time-Heterogeneous earliest finish time-Heterogeneous earliest finish time (or HEFT) is a heuristic to schedule a set of dependent tasks onto a network of heterogenous workers taking communication time into account. For inputs HEFT takes a set of tasks, represented as a directed acyclic ... | large_corpus_distillation |
"Release consistency-Lazy release consistency-Drawback LRC requires performing write propagation in bulk at the release point of synchronization. Propagating such a large number of writes altogether will slow down the release access and the subsequent acquire access. Hence it can hardly improve the performance of a har... | large_corpus_distillation |
"Glossary of engineering: M\u2013Z-M-In probability and statistics, the population mean, or expected value, is a measure of the central tendency either of a probability distribution or of a random variable characterized by that distribution. In a discrete probability distribution of a random variable X, the mean is equ... | large_corpus_distillation |
number) match the first prize number, you still get a prize. Sports Toto also offers three lottery games, similar to those seen in Western countries. These are Mega Toto 6/52, Power Toto 6/55 & Supreme Toto 6/58. The last number indicates the highest number \u2013 Mega Toto 6/52 requires the player to pick 6 numbers fr... | large_corpus_distillation |
"Sparsity matroid-General (k,l)-sparse multigraphs-Theorem. There exists an n0 such that for all n\u2265n0 , there exist s -uniform hypergraphs on n vertices that are (k,l) -tight.\nThe next result extends the Tutte and Nash-Williams theorem to hypergraphs.\nTheorem. If G is a (k,l) -tight hypergraph, for l\u22... | large_corpus_distillation |
"Significant figures-Identifying significant figures-\u03c0 is a specific real number with several equivalent definitions. All of the digits in its exact decimal expansion 3.14159265358979323... are significant. Although many properties of these digits are known \u2014 for example, they do not repeat, because \u03c0 is... | large_corpus_distillation |
"Suffixaufnahme-Significance and debates on case-stacking-Theoretical issues in morphology and syntax Regarding the phenomenon of Suffixaufnahme, Frans Plank (1995) has proposed several theoretical issues in morphology and syntax in his influential work as following: Suffixaufnahme represents an oddity in case and agre... | large_corpus_distillation |
"Control-flow integrity-Implementations-LLVM/Clang LLVM/Clang provides a \"CFI\" option that works in the forward edge by checking for errors in virtual tables and type casts. It depends on link-time optimization (LTO) to know what functions are supposed to be called in normal cases. There is a separate \"shadow call s... | large_corpus_distillation |
"Fractional approval voting-Rules-The random priority rule selects a permutation of the voters uniformly at random, and then implements the priority rule for that permutation. It is anonymous, neutral, and satisfies the following additional properties::\u200aProp.5\u200a Ex-post PE, but not (ex-ante) PE.\nWith the anal... | large_corpus_distillation |
"Design sprint-Possible uses-Claimed uses of the approach include Launching a new product or a service.\nExtending an existing experience to a new platform.\nExisting MVP needing revised User experience design and/or UI Design.\nAdding new features and functionality to a digital product.\nOpportunities for improvement ... | large_corpus_distillation |
"Kullback\u2013Leibler divergence-Interpretations-Coding In the context of coding theory, KL (P\u2225Q) can be constructed by measuring the expected number of extra bits required to code samples from P using a code optimized for Q rather than the code optimized for P Inference In the context of machine learning, K... | large_corpus_distillation |
"Fisher kernel-Derivation-Fisher score The Fisher kernel makes use of the Fisher score, defined as log \u2061P(X|\u03b8) with \u03b8 being a set (vector) of parameters. The function taking \u03b8 to log P(X|\u03b8) is the log-likelihood of the probabilistic model.\nFisher kernel The Fisher kernel is defined as K(Xi,Xj)... | large_corpus_distillation |
"Distributed agile software development-Distributed agile software development-Distributed agile software development is a research area that considers the effects of applying the principles of agile software development to a globally distributed development setting, with the goal of overcoming challenges in projects w... | large_corpus_distillation |
"Kahn process networks-Properties-FIFO bounds can be grown on demand.\nBlocking writes can be used so that a process blocks if a FIFO is full. This approach may unfortunately lead to an artificial deadlock unless the designer properly derives safe bounds for FIFOs (Parks, 1995). Local artificial detection at run-time m... | large_corpus_distillation |
"Erd\u0151s\u2013P\u00f3sa theorem-Motivation and statement-Unfortunately, in general, this bound is not tight: if the largest collection of vertex-disjoint cycles in a graph contains k cycles, then it does not necessarily follow that there is a feedback vertex set of size k. The graph in Figure 1 is an example of this... | large_corpus_distillation |
"Overdetermined system-Overdetermined linear systems of equations-K = N. This case yields either a single solution or no solution, the latter occurring when the coefficient vector of one equation can be replicated by a weighted sum of the coefficient vectors of the other equations but that weighted sum applied to the c... | large_corpus_distillation |
"Quadratic sieve-Multiple polynomials-This approach (called MPQS, Multiple Polynomial Quadratic Sieve) is ideally suited for parallelization, since each processor involved in the factorization can be given n, the factor base and a collection of polynomials, and it will have no need to communicate with the central proce... | large_corpus_distillation |
"Stein's unbiased risk estimate-Proof-We wish to show that SURE \u2061(h)}.\nWe start by expanding the MSE as E\u03bc\u2061\u2016h(x)\u2212\u03bc\u20162=E\u03bc\u2061\u2016g(x)+x\u2212\u03bc\u20162=E\u03bc\u2061\u2016g(x)\u20162+E\u03bc\u2061\u2016x\u2212\u03bc\u20162+2E\u03bc\u2061g(x)T(x\u2212\u03bc)=E\u03bc\u2061\u... | large_corpus_distillation |
"Dihedral group of order 6-Permutations of a set of three objects-By inspection, we can also determine associativity and closure (two of the necessary group axioms); note for example that (ab)a = a(ba) = aba, and (ba)b = b(ab) = bab.The group is non-abelian since, for example, ab \u2260 ba. Since it is built up from th... | large_corpus_distillation |
"Spelling suggestion-Algorithms-Logs of human text input, such as from a popular search engine. This is essentially a crowdsourced corpus, but it is assumed there will be some spelling mistakes. Data might be included about when people click on a spelling suggestion or make a second, very similar query; this creates a ... | large_corpus_distillation |
"Hopf algebra-Hopf algebras in braided monoidal categories-Groups. In the monoidal category Set ,\u00d7,1) of sets (with the cartesian product \u00d7 as the tensor product, and an arbitrary singletone, say, 1={\u2205} , as the unit object) a triple (H,\u2207,\u03b7) is a monoid in the categorical sense if and only ... | large_corpus_distillation |
"CHFS-Structure-Similar to UBIFS, the CHFS file system utilizes a separate layer for handling Flash aging and bad blocks, called EBH (erase block handler). The file system itself is modelled after JFFS2, thus the internal structure is very similar." | large_corpus_distillation |
"Messaging spam-In opinion-based recommender systems-Current approach of spam detection methods includes analyzing the spam text and identifying the spam reviewers by their reviews and activities. For the first kind, a machine learning application on review text has been developed. For the second kind, researchers use ... | large_corpus_distillation |
"Boyer\u2013Moore majority vote algorithm-Analysis-Similarly, on a random access machine the algorithm takes time O(n) (linear time) on an input sequence of n items, because it performs only a constant number of operations per input item. The algorithm can also be implemented on a Turing machine in time linear in the i... | large_corpus_distillation |
"Fermi (microarchitecture)-Warp scheduling-Most instructions can be dual issued; two integer instructions, two floating instructions, or a mix of integer, floating point, load, store, and SFU instructions can be issued concurrently.\nDouble precision instructions do not support dual dispatch with any other operation." | large_corpus_distillation |
"Intraclass correlation-Relationship to Pearson's correlation coefficient-In terms of its algebraic form, Fisher's original ICC is the ICC that most resembles the Pearson correlation coefficient. One key difference between the two statistics is that in the ICC, the data are centered and scaled using a pooled mean and s... | large_corpus_distillation |
"JavaScript library-Libraries-With the expanded demands for JavaScript, an easier means for programmers to develop such dynamic interfaces was needed. Thus, JavaScript libraries and JavaScript widget libraries were developed, allowing for developers to concentrate more upon more distinctive applications of Ajax. This h... | large_corpus_distillation |
"Modular arithmetic-Applications-In music, arithmetic modulo 12 is used in the consideration of the system of twelve-tone equal temperament, where octave and enharmonic equivalency occurs (that is, pitches in a 1:2 or 2:1 ratio are equivalent, and C-sharp is considered the same as D-flat).\nThe method of casting out ni... | large_corpus_distillation |
4. \u0393\u22a2A:K\u0393,x:A\u22a2N:B\u0393\u22a2(\u03bbx:A.N):(\u2200x:A.B) 5. := N] 6. \u0393\u22a2M:AA=\u03b2B\u0393\u22a2B:K\u0393\u22a2M:B Defining logical operators The calculus of constructions has very few basic operators: the only logical operator for forming propositions is \u2200 . However, this one oper... | large_corpus_distillation |
"Arrowhead matrix-Real symmetric arrowhead matrices-Let A be a real symmetric (permuted) arrowhead matrix of the form A=[DzzT\u03b1], where D=diag\u2061(d1,d2,\u2026,dn\u22121) is diagonal matrix of order n\u22121, z=[\u03b61\u03b62\u22ef\u03b6n\u22121]T is a vector and \u03b1 is a scalar. Let A=V\u039bVT be the eige... | large_corpus_distillation |
"Camellia (cipher)-Performance-The S-boxes used by Camellia share a similar structure to AES's S-box. As a result, it is possible to accelerate Camellia software implementations using CPU instruction sets designed for AES, such as x86 AES-NI or x86 GFNI, by affine isomorphism." | large_corpus_distillation |
"Vigen\u00e8re cipher-Cryptanalysis-Kasiski examination In 1863, Friedrich Kasiski was the first to publish a successful general attack on the Vigen\u00e8re cipher. Earlier attacks relied on knowledge of the plaintext or the use of a recognizable word as a key. Kasiski's method had no such dependencies. Although Kasisk... | large_corpus_distillation |
"Defective coloring-Defective coloring-In graph theory, a mathematical discipline, coloring refers to an assignment of colours or labels to vertices, edges and faces of a graph. Defective coloring is a variant of proper vertex coloring. In a proper vertex coloring, the vertices are coloured such that no adjacent vertic... | large_corpus_distillation |
"Task parallelism-Description-Task parallelism emphasizes the distributed (parallelized) nature of the processing (i.e. threads), as opposed to the data (data parallelism). Most real programs fall somewhere on a continuum between task parallelism and data parallelism.Thread-level parallelism (TLP) is the parallelism in... | large_corpus_distillation |
"CHAPTER OVERVIEW\n11: Energy\nIn Chapter 9 of these notes we introduced the Principle of Maximum Entropy as a technique for estimating probability distributions\nconsistent with constraints.\nA simple case that can be done analytically is that in which there are three probabilities, one constraint in the form of an av... | large_corpus_distillation |
"Polynomial ring-Univariate polynomials over a field-The unique factorization property results from Euclid's lemma. In the case of integers, this is the fundamental theorem of arithmetic. In the case of K[X], it may be stated as: every non-constant polynomial can be expressed in a unique way as the product of a constan... | large_corpus_distillation |
read the same book 52 times, and by reading this often, their mind will process the information quicker when they see the same words and will share a deeper understanding and meaning of the same book." | large_corpus_distillation |
"HyperTalk-Description-Referring to containers A key concept in HyperTalk was the way it referred to containers through a navigational system based on the visual hierarchy of the stack. Every container in the stack was given a unique ID number when created and could also be given an optional name. Scripts could refer t... | large_corpus_distillation |
with their own chipsets at its heart, with capabilities far beyond what two-socket \"commodity servers\" could offer. Development of a chipset costs tens of millions of dollars and so represented a major commitment to the use of Itanium." | large_corpus_distillation |
supports either the given hypothesis or a more specific one, thus forming a lower bound on its probability. Belief (usually denoted Bel) measures the strength of the evidence in favor of a proposition p. It ranges from 0 (indicating no evidence) to 1 (denoting certainty). Plausibility is 1 minus the sum of the masses o... | large_corpus_distillation |
"Transformation semigroup-Transformation semigroups and monoids-A transformation semigroup is a pair (X,S), where X is a set and S is a semigroup of transformations of X. Here a transformation of X is just a function from a subset of X to X, not necessarily invertible, and therefore S is simply a set of transformations... | large_corpus_distillation |
"Hall-type theorems for hypergraphs-Preliminaries-3. Neighbors: Given a bipartite hypergraph H = (X + Y, E) and a subset Y0 of Y, the neighbors of Y0 are the subsets of X that share hyperedges with vertices of Y0. Formally: := {X0\u2286X|\u2203y0\u2208Y0:{y0}\u222aX0\u2208E}." | large_corpus_distillation |
"\u039b X =(X ,X ,\u2026,X ) k+Y\nThe posterior distribution of given n 1 2 n is gamma with shape parameter n and rate parameter\nr+n\n.\nProof\nn\u2208N x=(x ,x ,\u2026,x )\u2208Nn y=\u2211n x\nFix +. Let 1 2 n and i=1 i. Then\n\u03bby\nf(x\u2223\u03bb)=g(x \u2223\u03bb)g(x \u2223\u03bb)\u22efg(x \u2223\u03bb)=e\u2212... | large_corpus_distillation |
"Abelian group-Relation to other mathematical topics-There are still many areas of current research: Amongst torsion-free abelian groups of finite rank, only the finitely generated case and the rank 1 case are well understood; There are many unsolved problems in the theory of infinite-rank torsion-free abelian groups; ... | large_corpus_distillation |
"Stable group-The Cherlin\u2013Zilber conjecture-The Cherlin\u2013Zilber conjecture (also called the algebraicity conjecture), due to Gregory Cherlin (1979) and Boris Zil'ber (1977), suggests that infinite (\u03c9-stable) simple groups are simple algebraic groups over algebraically closed fields. The conjecture would h... | large_corpus_distillation |
"Huber loss-Huber loss-In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used." | large_corpus_distillation |
"Theoretical neuromorphology-History-Theoretical tools General morphology The classic traditional forms were emanating from and could be described by using Euclidean geometry for instance in relation to the cartesian triedre (one perpendicular axe for three \"dimensions\"). These forms can have material realisations (c... | large_corpus_distillation |
"Diffie\u2013Hellman key exchange-Ephemeral and/or static keys-static, static: Would generate a long term shared secret. Does not provide forward secrecy, but implicit authenticity. Since the keys are static it would for example not protect against replay-attacks." | large_corpus_distillation |
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