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"Kolmogorov complexity-Compression-Theorem: With the uniform probability distribution on the space of bitstrings of length n, the probability that a string is incompressible by c is at least 1 \u2212 2\u2212c+1 + 2\u2212n." | large_corpus_distillation |
"Reliability (computer networking)-Reliability (computer networking)-In computer networking, a reliable protocol is a communication protocol that notifies the sender whether or not the delivery of data to intended recipients was successful. Reliability is a synonym for assurance, which is the term used by the ITU and A... | large_corpus_distillation |
performance characteristics,\" one (Innova) had a sensitivity of 78.8% and a false positive rate of 0.32%." | large_corpus_distillation |
"Selfie-Origins and development of selfie-taking-The app shows a feed of public photos of everyone's selfies and from the people they follow. The app does not allow users to comment and users can only respond with selfies. The app soon gained popularity among teenagers." | large_corpus_distillation |
to provide expected performance benefits.Certain experimental page-level prefetching systems have been developed to further improve performance." | large_corpus_distillation |
"Array DBMS-Concepts-As iteration over an array is at the heart of array processing, declarativeness very much centers on this aspect. The requirement, then, is that conceptually all cells should be inspected simultaneously \u2013 in other words, the query does not enforce any explicit iteration sequence over the array... | large_corpus_distillation |
"Exam-Assessment formats-Performance tests A performance test is an assessment that requires an examinee to actually perform a task or activity, rather than simply answering questions referring to specific parts. The purpose is to ensure greater fidelity to what is being tested.\nAn example is a behind-the-wheel drivin... | large_corpus_distillation |
"Creative and productive sets-History-Deborah Joseph and Paul Young (1985) formulated an analogous concept, polynomial creativity, in computational complexity theory, and used it to provide potential counterexamples to the Berman\u2013Hartmanis conjecture on isomorphism of NP-complete sets." | large_corpus_distillation |
"Assisted GNSS-Operation-In A-GPS, the network operator deploys an A-GPS server, a cache server for GPS data. These A-GPS servers download the orbital information from the satellite and store it in the database. An A-GPS-capable device can connect to these servers and download this information using mobile-network radi... | large_corpus_distillation |
"Structured sparsity regularization-Structures and norms-Norms defined on grids If the structure assumed over variables is in the form of a 1D, 2D or 3D grid, then submodular functions based on overlapping groups can be considered as norms, leading to stable sets equal to rectangular or convex shapes. Such methods have... | large_corpus_distillation |
"Proofs of Fermat's little theorem-Proof as a particular case of Euler's theorem-This proof, discovered by James Ivory and rediscovered by Dirichlet requires some background in modular arithmetic.\nLet us assume that a is positive and not divisible by p.\nThe idea is that if we write down the sequence of numbers and re... | large_corpus_distillation |
probability 0 and lim t\u2192\u221e N(t)=\u221e WP1.\nNext, E[N(t)] is nondecreasing in t, and thus has either a finite or infinite limit as t\u2192\u221e. For each n,\nPr{N(t)\u2265n}\u22651/2 for large enough t, and therefore E[N(t)]\u2265n/2 for such t. Thus E[N(t)] can have no finite limit\n4.3.1 https://eng.libret... | large_corpus_distillation |
"RPE2-RPE2-RPE2, or Relative server Performance Estimate 2, is a computer benchmark developed by Ideas International to compare the relative performance of servers built on x86, IA-64, and RISC processor architectures. The benchmark is a composite of results, or estimated results, from the SAP SD Standard Application ... | large_corpus_distillation |
"Hypergeometric distribution-Related distributions-The properties of this distribution are given in the adjacent table, where c is the number of different colors and N=\u2211i=1cKi is the total number of marbles in the urn.\nExample Suppose there are 5 black, 10 white, and 15 red marbles in an urn. If six marbles are ... | large_corpus_distillation |
"Coding best practices-Coding best practices-The size of a project or program has a significant effect on error rates, programmer productivity, and the amount of management needed." | large_corpus_distillation |
"Virtual memory compression-Compression using quantization-First, the programmer has to manually implement conversions and the additional instructions that quantize and dequantize values, imposing a programmer's effort and performance overhead. Second, to cover outliers, the bitwidth of the quantized values often becom... | large_corpus_distillation |
"Rubik's family cubes of varying sizes-Reachable and unreachable states for cubes of all sizes-If a cube has at some previous time occupied the set state, then any state that can arise after legal moves is considered to be a reachable state. For small size cubes (size 2, 3, or 4), an unreachable state is one that canno... | large_corpus_distillation |
"Preference learning-Tasks-Object ranking Object ranking is similar to instance ranking except that no labels are associated with instances. Given a set of pairwise preference information in the form xi\u227bxj and the model should find out a ranking order among instances." | large_corpus_distillation |
"Bias\u2013variance tradeoff-Bias\u2013variance decomposition of mean squared error-The three terms represent: the square of the bias of the learning method, which can be thought of as the error caused by the simplifying assumptions built into the method. E.g., when approximating a non-linear function f(x) using a lea... | large_corpus_distillation |
"Discoverability-Applications-Services In a service delivery context, the application of this principle requires collecting information about the service during the service analysis phase as during this phase; maximum information is available about the service's functional context and the capabilities of the service. A... | large_corpus_distillation |
"Mutual exclusivity-Probability-In probability theory, events E1, E2, ..., En are said to be mutually exclusive if the occurrence of any one of them implies the non-occurrence of the remaining n \u2212 1 events. Therefore, two mutually exclusive events cannot both occur. Formally said, the intersection of each two of t... | large_corpus_distillation |
"Very long instruction word-Very long instruction word-Very long instruction word (VLIW) refers to instruction set architectures designed to exploit instruction level parallelism (ILP). Whereas conventional central processing units (CPU, processor) mostly allow programs to specify instructions to execute in sequence on... | large_corpus_distillation |
eigenvalues of the operator are also evaluated in the same way as for the square matrix, by solving the characteristic polynomial: det (A^\u2212aI^)=0, where I is the n \u00d7 n identity matrix, as an operator it corresponds to the identity operator. For a discrete basis: I^=\u2211i|\u03d5i\u27e9\u27e8\u03d5i| while fo... | large_corpus_distillation |
"Id (programming language)-Examples-Id supports algebraic datatypes, similar to ML, Haskell, or Miranda: type bool = False | True; Types are inferred by default, but may be annotated with a typeof declaration. Type variables use the syntax *0, *1, etc." | large_corpus_distillation |
"ZMODEM-Variations-The most notable ZMODEM implementations were from Chuck Forsberg's Omen Technology, Inc. These included DSZ (DOS Send ZMODEM), GSZ (Graphical Send ZMODEM), and the ubiquitous (l)rzsz for Unix variants." | large_corpus_distillation |
"Gifar-Examples-\"//\" is a comment in both PHP and C and the root directory in bash.\nShell redirection is used to eliminate undesirable outputs.\nEven on commented out lines, the \"<?php\" and \"?>\" PHP indicators still have effect.\nThe statement \"function main()\" is valid in both PHP and bash; C #defines are use... | large_corpus_distillation |
proceeds by multiplying the three selected branches by a common random amount, akin to stretching or shrinking the clothesline. Finally the leftmost of the two hanging sub-trees is disconnected and reattached to the clothesline at a location selected uniformly at random. This would be the candidate tree." | large_corpus_distillation |
by C9, which postulates that no individual has a topological boundary: C9. \u2200x\u2203y[Pyx\u2227(Czy\u2192Ozx)\u2227\u00ac(Pxy\u2227(Czx\u2192Ozy))].\nWhen the domain consists of geometric figures, the boundaries can be points, curves, and surfaces. What boundaries could mean, given other ontologies, is not an easy... | large_corpus_distillation |
"Random permutation statistics-Number of permutations containing an even number of even cycles-We may use the Flajolet\u2013Sedgewick fundamental theorem directly and compute more advanced permutation statistics. (Check that page for an explanation of how the operators we will use are computed.) For example, the set of... | large_corpus_distillation |
"Naive Bayes classifier-Parameter estimation and event models-This training algorithm is an instance of the more general expectation\u2013maximization algorithm (EM): the prediction step inside the loop is the E-step of EM, while the re-training of naive Bayes is the M-step. The algorithm is formally justified by the a... | large_corpus_distillation |
"SPARC-Architecture-There are a wide variety of conditional branches: BA (branch always, essentially a jmp), BN (branch never), BE (equals), BNE (not equals), BL (less than), BLE (less or equal), BLEU (less or equal, unsigned), BG (greater), BGE (greater or equal), BGU (greater unsigned), BPOS (positive), BNEG (negativ... | large_corpus_distillation |
"P versus NP problem-Polynomial-time algorithms-FOR K = 1...\u221e FOR M = 1...K Run program number M for K steps with input S IF the program outputs a list of distinct integers AND the integers are all in S AND the integers sum to 0 THEN OUTPUT \"yes\" and HALT If, and only if, P = NP, then this is a polynomial-time a... | large_corpus_distillation |
"Riffle shuffle permutation-Riffle shuffle permutation-As a special case of this, a (p,q) -shuffle, for numbers p and q with p+q=n , is a riffle in which the first packet has p cards and the second packet has q cards." | large_corpus_distillation |
"Neuroscience Information Framework-Data Via Web Services-Retrieve the registry items that match a search term: * http://nif-services.neuinfo.org/servicesv1/v1/federation/data/nlx_144509-1?q=miame The NIF Registry is a data source and this service will return all items in the registry that match the particular search t... | large_corpus_distillation |
"Software documentation-Documentation and agile development controversy-\"The resistance to documentation among developers is well known and needs no emphasis.\" This situation is particularly prevalent in agile software development because these methodologies try to avoid any unnecessary activities that do not direct... | large_corpus_distillation |
for each game; these methods can provide a constant approximation to the minimum-upset ranking." | large_corpus_distillation |
"Upper ontology-Table of formal upper ontologies-The following table contains data mainly from \"A Comparison of Upper Ontologies\" article by V Mascardi, V Cordi and P Rosso (2007). Please expand the table if you have an ongoing UO project. Note that the lack of fresh releases does not imply inactivity or uselessness.... | large_corpus_distillation |
"Bar recursion-Technical definition-The idea is that one extends the sequence arbitrarily, using the recursion term B to determine the effect, until a sufficiently long node of the tree of sequences over V is reached; then the base term L determines the final value of f. The well-definedness condition corresponds to th... | large_corpus_distillation |
of Code Snippet 1 to the default executable Java representation of Code Snippet 2." | large_corpus_distillation |
a variable is null to fix null pointer exception, or changing an integer constant by one to fix off-by-one errors." | large_corpus_distillation |
can only fail during avalanche breakdown due to extreme thermal stress." | large_corpus_distillation |
"McCarthy 91 function-History-It is easier to reason about tail-recursive control flow, this is an equivalent (extensionally equal) definition: Mt(n)=Mt\u2032(n,1) if 10 if 100 and 11 if 100 and c\u22600 As one of the examples used to demonstrate such reasoning, Manna's book includes a tail-recursive algorithm equ... | large_corpus_distillation |
parallel corpora. There are two main types of parallel corpora which contain texts in two languages. In a translation corpus, the texts in one language are translations of texts in the other language. In a comparable corpus, the texts are of the same kind and cover the same content, but they are not translations of eac... | large_corpus_distillation |
"Verb\u2013object\u2013subject word order-Occurrence-Subject-gapped RCs and object-gapped RCs in English: Subject-gapped RC: The head noun, \"mouse,\" is placed before the relative clause (postnominal RC) in a subject-gapped RC in English. That is not the case in Cantonese and Mandarin in which head nouns are always pl... | large_corpus_distillation |
"Exponential family-Role in statistics-As a counterexample if these conditions are relaxed, the family of uniform distributions (either discrete or continuous, with either or both bounds unknown) has a sufficient statistic, namely the sample maximum, sample minimum, and sample size, but does not form an exponential fam... | large_corpus_distillation |
"Accurizing-Determining accuracy-Determining accuracy is not always a straightforward task, as it depends on a large number of variables." | large_corpus_distillation |
"Jaro\u2013Winkler distance-Jaro\u2013Winkler distance-In computer science and statistics, the Jaro\u2013Winkler similarity is a string metric measuring an edit distance between two sequences. It is a variant of the Jaro distance metric metric (1989, Matthew A. Jaro) proposed in 1990 by William E. Winkler.The Jaro\u201... | large_corpus_distillation |
"Elliptic-curve cryptography-Security-Quantum computing attacks Shor's algorithm can be used to break elliptic curve cryptography by computing discrete logarithms on a hypothetical quantum computer. The latest quantum resource estimates for breaking a curve with a 256-bit modulus (128-bit security level) are 2330 qubit... | large_corpus_distillation |
"Software map-History-Software maps methods and techniques belong to the scientific discipline of software visualization and information visualization. They form a key concept and technique within the fields of software diagnosis. They also have applications in software mining and software analytics. Software maps have... | large_corpus_distillation |
"JScript.Encode-JScript.Encode-JScript.Encode is a method created by Microsoft used to encode both server and Client-side JavaScript or VB Script source code in order to protect the source code from copying. JavaScript code is used for creating dynamic web content on many websites, with the source code easily viewable,... | large_corpus_distillation |
along with the phone), and for the removal of optical image stabilization from the camera.The G Flex's curved display was praised for having good viewing angles and brightness levels, and as promised, having a lower level of glare than most smartphones. However, the display was criticized for having a significantly low... | large_corpus_distillation |
"Parkerian Hexad-Attributes from the CIA triad-Confidentiality Confidentiality refers to limits on who can get what kind of information. For example, executives concerned about protecting their enterprise's strategic plans from competitors; individuals are concerned about unauthorized access to their financial records.... | large_corpus_distillation |
"Even code-Even code-A binary code is called an even code if the Hamming weight of each of its codewords is even. An even code should have a generator polynomial that include (1+x) minimal polynomial as a product. Furthermore, a binary code is called doubly even if the Hamming weight of all its codewords is divisible b... | large_corpus_distillation |
"Multicast-Wireless networks-Wireless communications (with exception to point-to-point radio links using directional antennas) are inherently broadcasting media. However, the communication service provided may be unicast, multicast as well as broadcast, depending on if the data is addressed to one, to a group or to all... | large_corpus_distillation |
"Integer complexity-Algorithms and counterexamples-In particular, it is not necessarily the case that the optimal expression for a number n is obtained either by subtracting one from n or by expressing n as the product of two smaller factors. The smallest example of a number whose optimal expression is not of this form... | large_corpus_distillation |
(2008). A polynomial time algorithm for finding equitable colorings with this many colors was described by Kierstead and Kostochka; they credit Marcelo Mydlarz and Endre Szemer\u00e9di with a prior unpublished polynomial time algorithm. Kierstead and Kostochka also announce but do not prove a strengthening of the theor... | large_corpus_distillation |
"Security-Enhanced Linux-Overview-A Linux kernel integrating SELinux enforces mandatory access control policies that confine user programs and system services, as well as access to files and network resources. Limiting privilege to the minimum required to work reduces or eliminates the ability of these programs and dae... | large_corpus_distillation |
dots can be utilized in several applications that benefit from their unique properties, such as medical imaging and thermal destruction of malignant cancers." | large_corpus_distillation |
"Strategic voting-In particular methods-Score voting In score voting, strategic voters who expect all other voters to be strategic will exaggerate their true preferences and use the same quasi-compromising strategy as in approval voting, above. That is, they will give all candidates either the highest possible or the l... | large_corpus_distillation |
"Opposite ring-Examples-If the multiplication of H(a,b) is denoted \u22c5 , it has the multiplication table Then the opposite algebra op with multiplication denoted \u2217 has the table Commutative ring A commutative ring (R,\u22c5) is isomorphic to its opposite ring op since x\u22c5y=y\u22c5x=x\u2217y for all ... | large_corpus_distillation |
"Schreier's lemma-Example-Let us establish the evident fact that the group Z3 = Z/3Z is indeed cyclic. Via Cayley's theorem, Z3 is a subgroup of the symmetric group S3. Now, Z3={e,(123),(132)} S3={e,(12),(13),(23),(123),(132)} where e is the identity permutation. Note S3 = \u27e8 { s1=(1 2), s2 = (1 2 3) } \u27e9 Z3 ... | large_corpus_distillation |
"Bluetooth-Specifications and features-The main new feature is AMP (Alternative MAC/PHY), the addition of 802.11 as a high-speed transport. The high-speed part of the specification is not mandatory, and hence only devices that display the \"+HS\" logo actually support Bluetooth over 802.11 high-speed data transfer. A B... | large_corpus_distillation |
"Church encoding-Church numerals-Church numerals are the representations of natural numbers under Church encoding. The higher-order function that represents natural number n is a function that maps any function f to its n-fold composition. In simpler terms, the \"value\" of the numeral is equivalent to the number of t... | large_corpus_distillation |
"Primitive recursive functional-Background-For any two types \u03c3 and \u03c4, the type \u03c3\u2192\u03c4 represents a function that takes an input of type \u03c3 and returns an output of type \u03c4. Thus the function f(n) = n+1 is of type 0\u21920. The types (0\u21920)\u21920 and 0\u2192(0\u21920) are different; by... | large_corpus_distillation |
"Gazetteer-Types and organization-Gazetteers are often categorized by the type, and scope, of the information presented. World gazetteers usually consist of an alphabetical listing of countries, with pertinent statistics for each one, with some gazetteers listing information on individual cities, towns, villages, and o... | large_corpus_distillation |
adjacency diagram, the size of the node is easily represented in this model." | large_corpus_distillation |
"NTRUEncrypt-Security and performance improvements-In this case f has coefficients different from -1, 0 or 1, because of the multiplication by p. But because Bob multiplies by p to generate the public key h, and later on reduces the ciphertext modulo p, this will not have an effect on the encryption method.\nSecond, f ... | large_corpus_distillation |
"U-Prove-U-Prove-U-Prove is a free and open-source technology and accompanying SDK for user-centric identity management. The underlying cryptographic protocols were designed by Dr. Stefan Brands and further developed by Credentica and, subsequently, Microsoft. The technology was developed to allow internet users to dis... | large_corpus_distillation |
"Damerau\u2013Levenshtein distance-Definition-Each recursive call matches one of the cases covered by the Damerau\u2013Levenshtein distance: da,b(i\u22121,j)+1 corresponds to a deletion (from a to b), da,b(i,j\u22121)+1 corresponds to an insertion (from a to b), da,b(i\u22121,j\u22121)+1(ai\u2260bj) corresponds to a ma... | large_corpus_distillation |
"Robbed-bit signaling-Bit robbing-With Super Frame framing, the robbed bits are named A and B. With Extended Super Frame, the same stream is divided into four bits, named A, B, C, and D. The meanings of these bits depend on what type of signaling is provisioned on the channel. The most common types of signaling are loo... | large_corpus_distillation |
"Rewrite (programming)-Risks-Several software engineers, such as Joel Spolsky have warned against total rewrites, especially under schedule constraints or competitive pressures. While developers may initially welcome the chance to correct historical design mistakes, a rewrite also discards those parts of the design tha... | large_corpus_distillation |
"Function of several complex variables-Reinhardt domain-Logarithmically-convex A Reinhardt domain D is called logarithmically convex if the image \u03bb(D\u2217) of the set D\u2217={z=(z1,\u2026,zn)\u2208D;z1,\u2026,zn\u22600} under the mapping ln ln \u2061|zn|) is a convex set in the real coordinate space Rn Every s... | large_corpus_distillation |
"Multi-attribute utility-Additive independence-This result generalizes to any number of attributes: iff preferences over lotteries on attributes 1,...,n depend only on their marginal probability distributions, then the n-attribute utility function is additive::\u200a295\u200a u(x1,\u2026,xn)=\u2211i=1nkiui(xi) where u... | large_corpus_distillation |
"Huang's algorithm-Algorithm-Huang's algorithm can be described by the following: Initially all processes are idle.\nA distributed task is started by a process sending a computational message to another process. This initial process to send the message is the \"controlling agent\".\nThe initial weight of the controllin... | large_corpus_distillation |
"Token reconfiguration-Complexity-Consider an instance of set cover, where we wish to cover all elements v1,v2,\u2026,vn in a universe U using subsets S1,S2,\u2026,Sm of U using the minimum number of subsets. Construct a graph as follows: Make a vertex for each of the elements in the universe and each of the subset... | large_corpus_distillation |
"Firearm-Health hazards-Death From 1990 to 2015, global deaths from assault by firearm rose from 128,000 to 173,000, however this represents a drop in rate from 2.41/100,000 to 2.35/100,000, as world population has increased by more than two billion.In 2017, there were 39,773 gun-related deaths in the United States; ov... | large_corpus_distillation |
"S2 T2\nMean square errors of n and n.\nmse(T2)= 2n\u22121\u03c34\n1.\nn2\nmse(S2)= 2 \u03c34\n2.\nn\u22121\nmse(T2)<mse(S2) n\u2208{2,3,\u2026,}\n3. for\nProof\n\u03c3 =3\u03c34\nRecall that for the normal distribution, 4 . Substituting this into the general results gives parts (a) and (b). Part (c)\nfollows from (a) ... | large_corpus_distillation |
"Convex set-Properties-From what has just been said, it is clear that such intersections are convex, and they will also be closed sets. To prove the converse, i.e., every closed convex set may be represented as such intersection, one needs the supporting hyperplane theorem in the form that for a given closed convex set... | large_corpus_distillation |
"Axiom schema of replacement-Applications-Larger ordinals rely on replacement less directly. For example, \u03c91, the first uncountable ordinal, can be constructed as follows \u2013 the set of countable well orders exists as a subset of P(N\u00d7N) by separation and powerset (a relation on A is a subset of A\u00d7A ... | large_corpus_distillation |
"Design by contract-Description-Design by contract also defines criteria for correctness for a software module: If the class invariant AND precondition are true before a supplier is called by a client, then the invariant AND the postcondition will be true after the service has been completed.\nWhen making calls to a su... | large_corpus_distillation |
"NGSI-LD-Design-A type is an OWL class that is a subclass of either the NGSI-LD Entity, NGSI-LD Relationship, NGSI-LD Property or NGSI-LD Value classes defined in the NGSI-LD meta-model. NGSI-LD pre-defines a small number of types, but is otherwise open to any types defined by users.Complementing this metamodel, the NG... | large_corpus_distillation |
"Newton's method in optimization-Higher dimensions-The above iterative scheme can be generalized to d>1 dimensions by replacing the derivative with the gradient (different authors use different notation for the gradient, including f\u2032(x)=\u2207f(x)=gf(x)\u2208Rd ), and the reciprocal of the second derivative with... | large_corpus_distillation |
"Control table-Examples of control tables-* ------------------ interpreter --------------------------------------------* SR R14,R14 ********* Set R14=0 CALC IC R14,INPUT1 * calc * put EBCDIC byte into lo order bits (24\u201331) of R14 IC R14,CT1X(R14) * * use EBCDIC value as index on table 'CT1X' to get new index SLL R... | large_corpus_distillation |
"Exact division-Comparison with other criteria-A better truthful mechanism, which works for the case in which all weights are 1/n, can be built given any existing algorithm (or oracle) for finding a consensus division: Ask each partner to report his value measure.\nUse the existing algorithm/oracle to generate a partit... | large_corpus_distillation |
"Random self-reducibility-Examples-Given a generator g of a cyclic group G = { gi | 0 \u2264 i < |G| }, and an x \u2208 G, the discrete log of x to the base g is the integer k (0 \u2264 k < |G|) with x = gk. Take B to be distributed uniformly on {0,...,|G| \u2212 1}, then xgB = gk+B is also distributed uniformly on G. ... | large_corpus_distillation |
"True quantified Boolean formula-Notes and references-Fortnow & Homer (2003) provides some historical background for PSPACE and TQBF.\nZhang (2003) provides some historical background of Boolean formulas.\nArora, Sanjeev. (2001). COS 522: Computational Complexity. Lecture Notes, Princeton University. Retrieved October ... | large_corpus_distillation |
"Comparison of programming paradigms-Performance comparison-For other paradigms, where a mix of the above paradigms may be employed, subroutine use is less predictable." | large_corpus_distillation |
"Graph coloring-Properties-For planar graphs, vertex colorings are essentially dual to nowhere-zero flows.\nAbout infinite graphs, much less is known.\nThe following are two of the few results about infinite graph coloring: If all finite subgraphs of an infinite graph G are k-colorable, then so is G, under the assumpti... | large_corpus_distillation |
"SHA-2-Cryptanalysis and validation-As of December 2013, there are over 1300 validated implementations of SHA-256 and over 900 of SHA-512, with only 5 of them being capable of handling messages with a length in bits not a multiple of eight while supporting both variants." | large_corpus_distillation |
"Reification (computer science)-Reflective programming languages-The C programming language reifies the low-level detail of memory addresses.Many programming language designs encapsulate the details of memory allocation in the compiler and the run-time system. In the design of the C programming language, the memory add... | large_corpus_distillation |
"Noncentral chi distribution-Definition-If Xi are k independent, normally distributed random variables with means \u03bci and variances \u03c3i2 , then the statistic Z=\u2211i=1k(Xi\u03c3i)2 is distributed according to the noncentral chi distribution. The noncentral chi distribution has two parameters: k which spec... | large_corpus_distillation |
repetitive or nonsensical when generating long passages. It was superseded by GPT-3 and GPT-4 models, which are not open source anymore. GPT-2 has, like its predecessor GPT-1 and its successors GPT-3 and GPT-4, a generative pre-trained transformer architecture, implementing a deep neural network, specifically a transf... | large_corpus_distillation |
"Unit (ring theory)-Examples-Matrix rings The unit group of the ring Mn(R) of n\u2009\u00d7\u2009n matrices over a ring R is the group GLn(R) of invertible matrices. For a commutative ring R, an element A of Mn(R) is invertible if and only if the determinant of A is invertible in R. In that case, A\u22121 can be given ... | large_corpus_distillation |
"ProbLog-Semantics-A probabilistic fact is a pair (p,a) with a an atom and p\u2208[0,1] the probability of a being true. A rule is defined by an atom h , called the head, and a finite set of n literals {b1,b2,...,bn} , called the body." | large_corpus_distillation |
"3.2 \u2022 Domain and Range 239\nPractice Makes Perfect\nFind the domain and range of a function.\n1. For the relation {(1,3),(2,6),(3,9),(4,12),(5,15)}:\n\u24d0 Find the domain of the function, express using set notation.\n\u24d1 Find the range of the function, express using set notation.\n2. Use the graph of the fun... | large_corpus_distillation |
"Quantum teleportation-Logic gate teleportation-The success criterion for teleportation has the expression Tr Tr \u03c1\u22c5O." | large_corpus_distillation |
"GSM Radio Frequency optimization-Technical details-A mobile is informed on a paging channel (PCH) that it has a call or SMS, to which the mobile station responds with a Random Access Channel (RACH) request. The mobile station is notified on an Access Grant Channel (AGCH) that it may tune to a specific Stand-alone dedi... | large_corpus_distillation |
"XOR swap algorithm-Variations-The underlying principle of the XOR swap algorithm can be applied to any operation meeting criteria L1 through L4 above. Replacing XOR by addition and subtraction gives various slightly different, but largely equivalent, formulations. For example: Unlike the XOR swap, this variation requi... | large_corpus_distillation |
"Digital electronics-Design-Sequential systems divide into two further subcategories. \"Synchronous\" sequential systems change state all at once when a clock signal changes state. \"Asynchronous\" sequential systems propagate changes whenever inputs change. Synchronous sequential systems are made using flip flops that... | large_corpus_distillation |
"F-algebra-Examples-To put this in a categorical framework, first define the identity and inverse as functions (morphisms of the set G ) by e:1\u2192G with e(\u2217)=1 , and i:G\u2192G with i(x)=x\u22121 . Here 1 denotes the set with one element 1={\u2217} , which allows one to identify elements x\u2208G with m... | large_corpus_distillation |
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