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"Semi-structured data-Pros and cons-Advantages Programmers persisting objects from their application to a database do not need to worry about object-relational impedance mismatch, but can often serialize objects via a light-weight library.\nSupport for nested or hierarchical data often simplifies data models representi... | large_corpus_distillation |
"VEGA Microprocessors-VEGA Microprocessors-VEGA Microprocessors are a portfolio of indigenous processors developed by C-DAC. The portfolio includes several 32-bit/64-bit Single/Multi-core Superscalar In-order/Out-of-Order high performance processors based on the RISC-V ISA. Also features India's first indigenous 64-bit... | large_corpus_distillation |
"Endomorphism ring-Description-If the set A does not form an abelian group, then the above construction is not necessarily additive, as then the sum of two homomorphisms need not be a homomorphism. This set of endomorphisms is a canonical example of a near-ring that is not a ring." | large_corpus_distillation |
"Backpressure routing-How it works-Backpressure routing is designed to make decisions that (roughly) minimize the sum of squares of queue backlogs in the network from one timeslot to the next. The precise mathematical development of this technique is described in later sections. This section describes the general netwo... | large_corpus_distillation |
"Multivariate kernel density estimation-Alternative optimality criteria-The KL can be estimated using a cross-validation method, although KL cross-validation selectors can be sub-optimal even if it remains consistent for bounded density functions. MH selectors have been briefly examined in the literature.All these opti... | large_corpus_distillation |
"Hungarian algorithm-The algorithm in terms of bipartite graphs-During the algorithm we maintain a potential y and an orientation of Gy (denoted by Gy\u2192 ) which has the property that the edges oriented from T to S form a matching M. Initially, y is 0 everywhere, and all edges are oriented from S to T (so M is emp... | large_corpus_distillation |
"Cognitive models of information retrieval-Exploratory search-Researchers in the areas of human-computer interaction and cognitive science focus on how people explore for information when interacting with the WWW. This kind of search, sometimes called exploratory search, focuses on how people iteratively refine their s... | large_corpus_distillation |
"Hazard pointer-Hazard pointer-In a multithreaded computing environment, hazard pointers are one approach to solving the problems posed by dynamic memory management of the nodes in a lock-free data structure. These problems generally arise only in environments that don't have automatic garbage collection.Any lock-free ... | large_corpus_distillation |
"Lean IT-Complementary methodologies-Scrum is one of the more well known agile methods for project management, and has as one of its origins concepts from Lean Thinking. Scrum also organizes work in a cross-functional, multidisciplinary work cell. It uses some form of kanban system to visualize and limit work in progre... | large_corpus_distillation |
"Genera (operating system)-Features-Genera makes extensive use of the condition system (exception handling) to handle all kinds of runtime errors and is able to recover from many of these errors. For example, it allows retrying network operations if a network connection has a failure; the application code will keep run... | large_corpus_distillation |
"Code point-Code point-In character encoding terminology, a code point, codepoint or code position is a numerical value that maps to a specific character. Code points usually represent a single grapheme\u2014usually a letter, digit, punctuation mark, or whitespace\u2014but sometimes represent symbols, control character... | large_corpus_distillation |
"Flooding (computer networking)-Algorithms-There are several variants of flooding algorithms. Most work roughly as follows: Each node acts as both a transmitter and a receiver.\nEach node tries to forward every message to every one of its neighbors except the source node.This results in every message eventually being d... | large_corpus_distillation |
"Categorial grammar-Basics-Given a set of primitive types Prim , let Tp Prim ) be the set of types constructed from primitive types. In the basic case, this is the least set such that Prim Tp Prim ) and if Tp Prim ) then Tp Prim ) Think of these as purely formal expressions freely generated from the primitive type... | large_corpus_distillation |
"HNN extension-Key properties-Every element of finite order in G\u2217\u03b1 is conjugate to an element of G.\nEvery finite subgroup of G\u2217\u03b1 is conjugate to a finite subgroup of G.\nIf G contains an element g such that gk is contained in neither H nor K for any integer k , then G\u2217\u03b1 contains ... | large_corpus_distillation |
"Multiplication algorithm-Algorithms for multiplying by hand-As shown in the example, the multiplicand and multiplier are written above and to the right of a lattice, or a sieve. It is found in Muhammad ibn Musa al-Khwarizmi's \"Arithmetic\", one of Leonardo's sources mentioned by Sigler, author of \"Fibonacci's Liber ... | large_corpus_distillation |
"Enterprise release management-Influence of Continuous Delivery and DevOps-While continuous delivery and agile software development provide for faster execution on a project level, the accelerated pace made possible by continuous delivery creates challenges for less-agile components in an IT portfolio. ERM provides org... | large_corpus_distillation |
"Rabin cryptosystem-Evaluation of the algorithm-Efficiency For encryption, a square modulo n must be calculated. This is more efficient than RSA, which requires the calculation of at least a cube.\nFor decryption, the Chinese remainder theorem is applied, along with two modular exponentiations. Here the efficiency is c... | large_corpus_distillation |
"Unix-like-Unix-like-Some well-known examples of Unix-like operating systems include Linux and BSD. These systems are often used on servers, as well as on personal computers and other devices. Many popular applications, such as the Apache web server and the Bash shell, are also designed to be used on Unix-like systems.... | large_corpus_distillation |
"Diagonalizable matrix-Examples-The roots of the characteristic polynomial det (\u03bbI\u2212A) are the eigenvalues \u03bb1=1,\u03bb2=1,\u03bb3=2 . Solving the linear system (I\u2212A)v=0 gives the eigenvectors v1=(1,1,0) and v2=(0,2,1) , while (2I\u2212A)v=0 gives v3=(1,0,\u22121) ; that is, Avi=\u03bbivi for ... | large_corpus_distillation |
"Entropy (information theory)-Entropy for continuous random variables-Note; log(\u0394) \u2192 \u2212\u221e as \u0394 \u2192 0, requires a special definition of the differential or continuous entropy: lim log log \u2061f(x)dx, which is, as said before, referred to as the differential entropy. This means that the differ... | large_corpus_distillation |
the parent - increase its rank by increasing the rank-differences between it and each of its children - and continue rebalancing with the old parent as the new node." | large_corpus_distillation |
"Structured concurrency-Variations-A major point of variation is how an error in one member of a concurrent thread tree is handled. Simple implementations will merely wait until the children and siblings of the failing thread run to completion before propagating the error to the parent scope. However, that could take a... | large_corpus_distillation |
each other. Print-through on analog tape causes unintended pre- and post-echoes on playback and is generally cannot be removed once it has occurred. In professional half-track use, post-echo is considered less problematic than pre-echo, as the echo is largely masked by the signal itself, and therefore tapes stored for ... | large_corpus_distillation |
"Cache (computing)-Operation-During a cache miss, some other previously existing cache entry is removed in order to make room for the newly retrieved data. The heuristic used to select the entry to replace is known as the replacement policy. One popular replacement policy, \"least recently used\" (LRU), replaces the ol... | large_corpus_distillation |
"Aspects of the Theory of Syntax-Background-All of these activities aided to develop what is now known as the \"Standard Theory\" of TGG, in which the basic formulations of Syntactic Structures underwent considerable revision. In 1965, eight years after the publication of Syntactic Structures, Chomsky published Aspects... | large_corpus_distillation |
"DICT-Resources for free dictionaries from DICT protocol servers-Dictionaries of English Bouvier's Law Dictionary, Revised 6th Ed (1856) CIA World Factbook Easton's Bible Dictionary (1897) Elements database Free On-line Dictionary of Computing Hitchcock's Bible Names Dictionary Jargon File Moby Thesaurus Oxford Advance... | large_corpus_distillation |
"Gradient conjecture-Gradient conjecture-The conjecture states that given a real-valued analytic function f defined on Rn and a trajectory x(t) of the gradient vector field of f having a limit point x0 \u2208 Rn, where f has an isolated critical point at x0, there exists a limit (in the projective space PRn-1) for the ... | large_corpus_distillation |
"Approximations of \u03c0-Development of efficient formulae-15 3.1409 + accurate to four digits: 31 3.1413 + 63 23 3.14142 2+ 51 16 3.14142 8+ accurate to four digits (or five significant figures): 3.1416 + an approximation by Ramanujan, accurate to 4 digits (or five significant figures): 3.1416 + accurate to five digi... | large_corpus_distillation |
"Four glasses puzzle-Solution-An algorithm that guarantees the bell will ring in at most five turns is as follows: On the first turn choose a diagonally opposite pair of glasses and turn both glasses up.\nOn the second turn choose two adjacent glasses. At least one will be up as a result of the previous step. If the ot... | large_corpus_distillation |
"Block code-Error detection and correction properties-In order to decode in the presence of more than (d\u22121)/2 errors, list-decoding or maximum likelihood decoding can be used." | large_corpus_distillation |
"Monomorphism-Terminology-Another name for monomorphism is extension, although this has other uses too." | large_corpus_distillation |
"Stochastic optimization-Methods for stochastic functions-Partly random input data arise in such areas as real-time estimation and control, simulation-based optimization where Monte Carlo simulations are run as estimates of an actual system, and problems where there is experimental (random) error in the measurements of... | large_corpus_distillation |
"Addition-Addition of numbers-To prove the usual properties of addition, one must first define addition for the context in question. Addition is first defined on the natural numbers. In set theory, addition is then extended to progressively larger sets that include the natural numbers: the integers, the rational number... | large_corpus_distillation |
"Classic monolingual word-sense disambiguation-Task Description-For comparison purposes, known, yet simple, algorithms named baselines are used. These include different variants of Lesk algorithm or most frequent sense algorithm." | large_corpus_distillation |
"Search engine (computing)-How search engines work-Search engines provide an interface to a group of items that enables users to specify criteria about an item of interest and have the engine find the matching items. The criteria are referred to as a search query. In the case of text search engines, the search query is... | large_corpus_distillation |
"Determiner phrase-Arguments for DP over NP-Definite pronouns The fact that definite pronouns are in complementary distribution with determiners is taken as evidence in favor of DP. The important observation in this area is that definite pronouns cannot appear together with a determiner like the or a in one and the sam... | large_corpus_distillation |
"Quantifier (logic)-Quantifier (logic)-In a first-order logic statement, quantifications in the same type (either universal quantifications or existential quantifications) can be exchanged without changing the meaning of the statement, while the exchange of quantifications in different types changes the meaning. As an ... | large_corpus_distillation |
"3G-3G-A new generation of cellular standards has appeared approximately every tenth year since 1G systems were introduced in 1979 and the early to mid-1980s. Each generation is characterized by new frequency bands, higher data rates and non\u2013backward-compatible transmission technology. The first commercial 3G netw... | large_corpus_distillation |
"19 (number)-Mathematics-19 is the first number in an infinite sequence of numbers in decimal whose digits start with 1 and have trailing 9's, that form triangular numbers containing trailing zeroes in proportion to 9s present in the original number; i.e. 19900 is the 199th triangular number, and 1999000 is the 1999th.... | large_corpus_distillation |
"Independent component analysis-Independent component analysis-In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statisti... | large_corpus_distillation |
"Expected value-Definition-If one rolls the die n times and computes the average (arithmetic mean) of the results, then as n grows, the average will almost surely converge to the expected value, a fact known as the strong law of large numbers.The roulette game consists of a small ball and a wheel with 38 numbered poc... | large_corpus_distillation |
"Huffman coding-Basic technique-Enqueue all leaf nodes into the first queue (by probability in increasing order so that the least likely item is in the head of the queue).\nWhile there is more than one node in the queues: Dequeue the two nodes with the lowest weight by examining the fronts of both queues.\nCreate a new... | large_corpus_distillation |
IP address and mask. These are 0 for address requests.\nThe two-byte Reserved field is currently unused and undefined.\nSLARP Keep-Alive frame structure The following table shows the structure of a SLARP cHDLC keep-alive frame.\nThe op-code is 0x02 for keep-alives.\nThe sender sequence number increments with each keep-... | large_corpus_distillation |
"Conditional random field-Description-Notably, in contrast to HMMs, CRFs can contain any number of feature functions, the feature functions can inspect the entire input sequence X at any point during inference, and the range of the feature functions need not have a probabilistic interpretation." | large_corpus_distillation |
"Anagram-Methods of construction-The program or server carries out an exhaustive search of a database of words, to produce a list containing every possible combination of words or phrases from the input word or phrase using a jumble algorithm. Some programs (such as Lexpert) restrict to one-word answers. Many anagram s... | large_corpus_distillation |
"Cash on delivery-Cash on delivery order management-Upon successful delivery of the ordered item, the delivery personnel collects the payment in cash from the customer. The online retailer is then responsible for updating the payment status to \"Paid\" on the admin panel. This update confirms that the payment has been ... | large_corpus_distillation |
the prior distribution (beta distribution); hence hyperparameters.In principle, priors can be decomposed into many conditional levels of distributions, so-called hierarchical priors." | large_corpus_distillation |
either transient or null-recurrent. An example of this will arise in Exercise\n6.3.\nThis page titled 5.2: Birth-Death Markov chains is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by\nRobert Gallager (MIT OpenCourseWare) via source content that was edited to the style and standards ... | large_corpus_distillation |
"Web server-Technical overview-Dynamic cache Dynamic content, output by an internal module or an external program, may not always change very frequently (given a unique URL with keys / parameters) and so, maybe for a while (e.g. from 1 second to several hours or more), the resulting output can be cached in RAM or even ... | large_corpus_distillation |
"Van Emde Boas tree-Implementations-There is a verified implementation in Isabelle (proof assistant). Both functional correctness and time bounds are proved.\nEfficient imperative Standard ML code can be generated." | large_corpus_distillation |
of their nodes and edges to reflect attributes of interest.Social network analysis has emerged as a key technique in modern sociology. It has also gained significant popularity in the following - anthropology, biology, demography, communication studies, economics, geography, history, information science, organizational... | large_corpus_distillation |
"Closure (topology)-Examples-In topological space: In any space, cl \u2061\u2205 . In other words, the closure of the empty set \u2205 is \u2205 itself.\nIn any space X, cl \u2061X." | large_corpus_distillation |
securing information in storage devices. Thus, a deterministic algorithm called a key derivation function (KDF) uses a password to generate the secure cryptographic keying material to compensate for the password's weakness. Various methods such as adding a salt or key stretching may be used in the generation." | large_corpus_distillation |
"C-K theory-Central findings-Theory of designAt The Design Society's 2009 International Conference on Engineering Design, an awarded-paper links scientific discovery and design process using C-K theory as a formal framework. It is suggested that a science of design is possible, and complementary to the more traditional... | large_corpus_distillation |
"Ingleton's inequality-Importance of inequality-There are interesting connections between matroids, the entropy region and group theory. Some of those connections are revealed by Ingleton's Inequality.\nPerhaps, the more interesting application of Ingleton's inequality concerns the computation of network coding capacit... | large_corpus_distillation |
"Efficient cake-cutting-Efficient cake-cutting-Efficient cake-cutting is a problem in economics and computer science. It involves a heterogeneous resource, such as a cake with different toppings or a land with different coverings, that is assumed to be divisible - it is possible to cut arbitrarily small pieces of it wi... | large_corpus_distillation |
code (e.g., system@plt, execve@plt, sprintf@plt, strcpy@plt).Address space layout randomization (ASLR) makes this type of attack extremely unlikely to succeed on 64-bit machines as the memory locations of functions are random. For 32-bit systems, however, ASLR provides little benefit since there are only 16 bits availa... | large_corpus_distillation |
"Set cover problem-Greedy algorithm-Inapproximability results show that the greedy algorithm is essentially the best-possible polynomial time approximation algorithm for set cover up to lower order terms (see Inapproximability results below), under plausible complexity assumptions. A tighter analysis for the greedy alg... | large_corpus_distillation |
"MacChoro-Data Classification-The program stressed data classification, and implemented six methods including unclassed, equal interval, quantile, natural breaks, standard deviation and user-defined. The unclassed method was limited to 16 shadings. Each of the remaining methods could be made with between 2 and 16 categ... | large_corpus_distillation |
"Filter (mathematics)-Special cases-Isotony If A \u2208 F and A \u2286 B \u2286 S, then B \u2208 F.A proper/non-degenerate filter is one that does not contain \u2205, and these three conditions (including non-degeneracy) are Henri Cartan's original definition of a filter. It is common \u2014 though not universal \u2014... | large_corpus_distillation |
"Grunwald\u2013Wang theorem-Wang's counter-example-Grunwald's original claim that an element that is an nth power almost everywhere locally is an nth power globally can fail in two distinct ways: the element can be an nth power almost everywhere locally but not everywhere locally, or it can be an nth power everywhere l... | large_corpus_distillation |
the more accurate the ultimate model will be.Leo Breiman distinguished two statistical modeling paradigms: data model and algorithmic model, wherein \"algorithmic model\" means more or less the machine learning algorithms like Random Forest." | large_corpus_distillation |
"Connection (algebraic framework)-Commutative algebra-Second definition Let D(A) be the module of derivations of a ring A . A connection on an A-module M is defined as an A-module morphism \u2207:D(A)\u2192Diff1(M,M);u\u21a6\u2207u such that the first order differential operators \u2207u on M obey the Leibniz rule ... | large_corpus_distillation |
"Application portfolio management-Methods and measures for evaluating applications-There are many popular financial measures, and even more metrics of different (non-financial or complex) types that are used for evaluating applications or information systems." | large_corpus_distillation |
"Subtyping-Subtyping-The concept of subtyping is related to the linguistic notions of hyponymy and holonymy. It is also related to the concept of bounded quantification in mathematical logic (see Order-sorted logic). Subtyping should not be confused with the notion of (class or object) inheritance from object-oriented ... | large_corpus_distillation |
"International Securities Identification Number-Examples-Convert any letters to numbers by taking the ASCII code of the capital letter and subtracting 55: U = 30, S = 28. US037833100 -> 30 28 037833100 Collect odd and even characters: 3028037833100 = (3, 2, 0, 7, 3, 1, 0), (0, 8, 3, 8, 3, 0) Multiply the group containi... | large_corpus_distillation |
of security called entropic security, which assumes that the adversary knows almost nothing about the message being sent. The goal here is to hide all functions of the plaintext rather than all information about it.\nInformation-theoretic cryptography is quantum-safe." | large_corpus_distillation |
"Convolutional neural network-Building blocks-Intuitively, the exact location of a feature is less important than its rough location relative to other features. This is the idea behind the use of pooling in convolutional neural networks. The pooling layer serves to progressively reduce the spatial size of the represent... | large_corpus_distillation |
"Z-test-Example-Another way of stating things is that with probability 1 \u2212 0.014 = 0.986, a simple random sample of 55 students would have a mean test score within 4 units of the population mean. We could also say that with 98.6% confidence we reject the null hypothesis that the 55 test takers are comparable to a ... | large_corpus_distillation |
"IIf-Criticisms-Side effects Another issue with IIf arises because it is a library function: unlike the C-derived conditional operator, both truepart and the falsepart will be evaluated regardless of which one is actually returned. In the following code snippet: although TrueFunction is the function intended to be call... | large_corpus_distillation |
"Vigen\u00e8re cipher-Description-To encrypt, a table of alphabets can be used, termed a tabula recta, Vigen\u00e8re square or Vigen\u00e8re table. It has the alphabet written out 26 times in different rows, each alphabet shifted cyclically to the left compared to the previous alphabet, corresponding to the 26 possible... | large_corpus_distillation |
"Manual testing-Overview-Author a test report, detailing the findings of the testers. The report is used by managers to determine whether the software can be released, and if not, it is used by engineers to identify and correct the problems.A rigorous test case based approach is often traditional for large software eng... | large_corpus_distillation |
"Disjoint-set data structure-Operations-Disjoint-set data structures support three operations: Making a new set containing a new element; Finding the representative of the set containing a given element; and Merging two sets." | large_corpus_distillation |
"Contradiction-Outside formal logic-Colloquial usage can label actions or statements as contradicting each other when due (or perceived as due) to presuppositions which are contradictory in the logical sense.\nProof by contradiction is used in mathematics to construct proofs.\nThe scientific method uses contradiction t... | large_corpus_distillation |
"Google Data Protocol-Implementations-An implementation called libgdata written in C is available under the LGPL license." | large_corpus_distillation |
"\u00c9tale cohomology-\u2113-adic cohomology groups-In applications to algebraic geometry over a finite field Fq with characteristic p, the main objective was to find a replacement for the singular cohomology groups with integer (or rational) coefficients, which are not available in the same way as for geometry of an ... | large_corpus_distillation |
of the BA model was obtained by Klemm and Egu\u00edluz and proven by Bollob\u00e1s. A mean-field approach to study the clustering coefficient was applied by Fronczak, Fronczak and Holyst.This behavior is still distinct from the behavior of small-world networks where clustering is independent of system size.\nIn the cas... | large_corpus_distillation |
"Gensim-Gensim-Gensim is an open-source library for unsupervised topic modeling, document indexing, retrieval by similarity, and other natural language processing functionalities, using modern statistical machine learning.\nGensim is implemented in Python and Cython for performance. Gensim is designed to handle large t... | large_corpus_distillation |
"Buffer overflow protection-Canaries-In addition, random XOR canaries can protect against a certain type of attack involving overflowing a buffer in a structure into a pointer to change the pointer to point at a piece of control data. Because of the XOR encoding, the canary will be wrong if the control data or return v... | large_corpus_distillation |
\"GML\" data server (precursor of the WFS) at the first OGC Web Map Test Bed in September 1999. In October 1999, Galdos Systems rewrote the SFXML draft document into a Request for Comment, and changed the name of the language to GML (Geography Markup Language). This document introduced several key ideas that became the... | large_corpus_distillation |
"Graph removal lemma-Quantitative bounds-There is a large gap between upper and lower bounds for \u03b4 in the general case. The current best result true for all graphs H is due to Alon and states that for each nonbipartite H there exists constant c>0 such that log \u2061(c/\u03f5) is necessary for the graph remov... | large_corpus_distillation |
to a chosen feature map and then evaluate the inner products between the transformed inputs. As discussed above, this can be captured by a kernel function K(x,x\u2032) , since all kernel functions are inner products of feature-mapped inputs. This yields the ridgeless kernel regression estimator:If the kernel matrix K... | large_corpus_distillation |
"Comparison of version-control software-Comparison of version-control software-In software development, version control is a class of systems responsible for managing changes to computer programs or other collections of information such that revisions have a logical and consistent organization. The following tables inc... | large_corpus_distillation |
"SipHash-Overview-For example, suppose a network server is designed to be able to handle up to a million requests at once. It keeps track of incoming requests in a hash table with two million entries, using a hash function to map identifying information from each request to one of the two million possible table entries... | large_corpus_distillation |
"Van der Corput inequality-Statement of the inequality-Let V be a real or complex inner product space with inner product \u27e8\u22c5,\u22c5\u27e9 and induced norm \u2016\u22c5\u2016 . Suppose that v,u1,\u2026,un\u2208V and that \u2016v\u2016=1 . Then (\u2211i=1n|\u27e8v,ui\u27e9|)2\u2264\u2211i,j=1n|\u27e8ui,uj\u... | large_corpus_distillation |
p )P (x)+ p P (x|\u03b8 ) (25)\nm m m m\u22121 m m\nm\u22121\n\ufffd\n\u02c6 \u02c6\n= [(1 \u2212 p )P(j)]P (x|\u03b8 )+ p P (x|\u03b8 ) (26)\nm j m m\nj=1\n\u02c6\nNote that by scaling down P (x) with 1\u2212p we can keep the overall mixture proportions\nm\u22121 m\nto sum to one regardless of p \u2208 [0, 1]. We can ... | large_corpus_distillation |
"Library-Types-Library 2.0, a term coined in 2005, is the library's response to the challenge of Google and an attempt to meet the changing needs of users by using Web 2.0 technology. Some of the aspects of Library 2.0 include, commenting, tagging, bookmarking, discussions, use of online social networks by libraries, p... | large_corpus_distillation |
"LAN Manager-Security weaknesses-The hash value is sent to network servers without salting, making it susceptible to man-in-the-middle attacks such as replay the hash. Without salt, time\u2013memory tradeoff pre-computed dictionary attacks, such as a rainbow table, are feasible. In 2003, Ophcrack, an implementation of ... | large_corpus_distillation |
and pays .\nW\nLet denote the winnings on a unit straight bet. Then\nP(W =\u22121)= 37 P(W =35)= 1\n1. ,\n38 38\nE(W)=\u2212 1 \u2248\u22120.0526\n2.\n19\nsd(W)\u22485.7626\n3.\nIn the roulette experiment, select the single number bet. Run the simulation 1000 times and compare the empirical density\nW\nfunction and mom... | large_corpus_distillation |
"Cryptanalysis of the Enigma-Polish breakthroughs-There was a set of 26 of these sheets for each of the six possible sequences wheel orders. Each sheet was for the left (slowest-moving) rotor. The 51\u00d751 matrices on the sheets represented the 676 possible starting positions of the middle and right rotors. The sheet... | large_corpus_distillation |
"Chow\u2013Liu tree-The Chow\u2013Liu algorithm-Chow and Liu show how to select second-order terms for the product approximation so that, among all such second-order approximations (first-order dependency trees), the constructed approximation P\u2032 has the minimum Kullback\u2013Leibler divergence to the actual distr... | large_corpus_distillation |
that and are probability distributions on with distribution functions and , respectively. Then and are\na\u2208R b\u2208(0,\u221e)\nof the same type if there exist constants and such that\nx\u2212a\nF(x)=G( ), x\u2208R (5.1.12)\nb\nR P Q R\nBeing of the same type is an equivalence relation on the collection of probabil... | large_corpus_distillation |
"Gap buffer-Gap buffer-Text in a gap buffer is represented as two strings, which take very little extra space and which can be searched and displayed very quickly, compared to more sophisticated data structures such as linked lists. However, operations at different locations in the text and ones that fill the gap (requ... | large_corpus_distillation |
"Mode locking-Mode-locking theory-Using this equation, the minimum pulse duration can be calculated consistent with the measured laser spectral width. For the HeNe laser with a 1.5 GHz bandwidth, the shortest Gaussian pulse consistent with this spectral width would be around 300 picoseconds; for the 128 THz bandwidth T... | large_corpus_distillation |
"Distributed minimum spanning tree-GHS algorithm-Description of the algorithm The GHS algorithm assigns a level to each fragment, which is a non-decreasing integer with initial value 0. Furthermore, each fragment with a non-zero level has an ID, which is the ID of the core edge in the fragment, which is selected when t... | large_corpus_distillation |
always outperform random Monte Carlo. However, log \u2061(N)s grows exponentially quickly with the dimension, meaning a poorly-chosen sequence can be much worse than Monte Carlo in high dimensions. In practice, it is almost always possible to select an appropriate low-discrepancy sequence, or apply an appropriate tran... | large_corpus_distillation |
in which a backdoor could occur, since they filed a patent application in January 2005 on exactly how to insert or prevent the backdoor in DUAL_EC_DRBG. The working of the \"trap door\" mentioned in the patent is identical to the one later confirmed in Dual_EC_DRBG. Writing about the patent in 2014, commentator Matthew... | large_corpus_distillation |
"Enriched category-Definition-Note that there are several distinct notions of \"identity\" being referenced here: the monoidal identity object I of M, being an identity for \u2297 only in the monoid-theoretic sense, and even then only up to canonical isomorphism (\u03bb, \u03c1).\nthe identity morphism 1C(a, b) : C(a, ... | large_corpus_distillation |
JBW algebra with identity p.\nIf a is any element of a JBW algebra, the smallest weakly closed unital subalgebra it generates is associative and hence the self-adjoint part of an Abelian von Neumann algebra. In particular a can be approximated in norm by linear combinations of orthogonal projections.\nThe projections i... | large_corpus_distillation |
"Miwin's dice-Mathematical attributes-Probabilities 1/3 of the die-face values can be divided by three without carry over.\n1/3 of the die-face values can be divided by three having a carry over of one.\n1/3 of the die-face values can be divided by three having a carry over of two.The probability for a given number wit... | large_corpus_distillation |
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