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"Cox's theorem-Implications of Cox's postulates-It is important to note that the postulates imply only these general properties. We may recover the usual laws of probability by setting a new function, conventionally denoted P or Pr , equal to wm . Then we obtain the laws of probability in a more familiar form: Certa... | large_corpus_distillation |
"Raft (algorithm)-Basics-Timing and availability Timing is critical in Raft to elect and maintain a steady leader over time, in order to have a perfect availability of the cluster. Stability is ensured by respecting the timing requirement of the algorithm :broadcastTime << electionTimeout << MTBF broadcastTime is the a... | large_corpus_distillation |
"Multifit algorithm-Proof idea-Let s be the size of the smallest item. Then s>nn\u22121(p\u2212q) . Proof: Since s does not fit into the first n bundles, we have sum(Pi)+s>p , so \u2211i=1nsum(Pi)+n\u22c5s>n\u22c5p . On the other hand, since all items fit into n bins of capacity q, we have \u2211i=1nsum(Pi)+s\u2264... | large_corpus_distillation |
in the numeric system, flats and sharps can be represented either by the use of fractions (e.g. an A natural in the scale above becomes 4+1\u20442) or, more commonly in written text, by inserting an accidental before the number (e.g. the same note becomes \u266d5 or \u266f4)." | large_corpus_distillation |
"Supercomputer-Performance measurement-Performance metrics In general, the speed of supercomputers is measured and benchmarked in FLOPS (floating-point operations per second), and not in terms of MIPS (million instructions per second), as is the case with general-purpose computers. These measurements are commonly used ... | large_corpus_distillation |
"U-boot (cocktail)-Other names and variations-In Flanders and the Netherlands, it is called a \"Duikboot\", literally translated \"Submarine\". It is seen as a variant on the kopstoot (lit. \"headbutt\") in the Netherlands. The kopstoot is a shot of jenever followed by a beer as a chaser.\nIn North Macedonia it is call... | large_corpus_distillation |
"Cache coherence-Overview-In a shared memory multiprocessor system with a separate cache memory for each processor, it is possible to have many copies of shared data: one copy in the main memory and one in the local cache of each processor that requested it. When one of the copies of data is changed, the other copies m... | large_corpus_distillation |
"Bourne shell-Bourne shell-Developed by Stephen Bourne at Bell Labs, it was a replacement for the Thompson shell, whose executable file had the same name\u2014sh. It was released in 1979 in the Version 7 Unix release distributed to colleges and universities. Although it is used as an interactive command interpreter, it... | large_corpus_distillation |
"Root mean square-Uses-The term RMS power is sometimes erroneously used in the audio industry as a synonym for mean power or average power (it is proportional to the square of the RMS voltage or RMS current in a resistive load). For a discussion of audio power measurements and their shortcomings, see Audio power." | large_corpus_distillation |
"CPU Sim-Example program for the Wombat 1 CPU-This program reads in integers until a negative integer is read. It then outputs the sum of all the positive integers.\nStart: read // read n -> acc jmpn Done // jump to Done if acc < 0." | large_corpus_distillation |
"Function word-Overview-The following is a list of the kind of words considered to be function words with English examples. They are all uninflected in English unless marked otherwise: articles \u2014 the and a. In some inflected languages, the articles may take on the case of the declension of the following noun.\npro... | large_corpus_distillation |
"Syzkaller-Syzkaller-Syzkaller is a software fuzzing framework that has been used for fuzzing the Linux kernel. It also supports other kernels.As of 2021, the Syzkaller dashboard showed hundreds of bugs in the Linux kernel." | large_corpus_distillation |
"Intuitive criterion-Background-Intuitively, we can eliminate a PBE if there is exists a sender type who wants to deviate, assuming that the receiver has a reasonable belief. It is reasonable to believe that the deviating sender is of a type who would benefit from the deviation in at least the best-case scenario. If a ... | large_corpus_distillation |
are required to work with formulas involving the equality symbol.\nI8. x=x for every variable x.\nI9. := := y]) " | large_corpus_distillation |
"Hardware description language-History-Over the years, much effort has been invested in improving HDLs. The latest iteration of Verilog, formally known as IEEE 1800-2005 SystemVerilog, introduces many new features (classes, random variables, and properties/assertions) to address the growing need for better test bench r... | large_corpus_distillation |
tree path LRLRLLL... while the second corresponds to the different path LRLLRRR...." | large_corpus_distillation |
"Cryptomatte-Supported render engines-Cryptomatte images can be created by various 3D graphic programs like Blender, Autodesk Maya, Autodesk 3ds Max or Houdini and are usually exported using the OpenEXR file format." | large_corpus_distillation |
"Circular prime-Other bases-In base 2, only Mersenne primes can be circular primes, since any 0 permuted to the one's place results in an even number." | large_corpus_distillation |
"Tail call-Implementation methods-In assembly Tail calls are often optimized by interpreters and compilers of functional programming and logic programming languages to more efficient forms of iteration. For example, Scheme programmers commonly express while loops as calls to procedures in tail position and rely on the ... | large_corpus_distillation |
"Jiro-Overview-Jiro Implements an infrastructure for creating integrated and automated management software in a distributed, cross-platform environment. Jiro makes use of Jini technology for allowing services come and go in network.\nJiro introduces a middle tier of management between the client/GUI and other Java-base... | large_corpus_distillation |
"Grand Cru (cipher)-Grand Cru (cipher)-Grand Cru is designed on the principle of multiple layered security. It is equivalent to a chain of 4 subciphers with independent keys, such that if 3 of the keys are known, the remaining cipher should still be secure." | large_corpus_distillation |
"Multiparty communication complexity-Upper and lower bounds-The Generalized Inner Product function (GIP) is defined as follows: Let y1,y2,...,yk be n -bit vectors, and let Y be the n times k matrix, with k columns as the y1,y2,...,yk vectors. Then GIP(y1,y2,...,yk) is the number of the all-1 rows of matrix Y ,... | large_corpus_distillation |
"Foolscap folio-F4-F4 is a paper size 210 mm \u00d7 330 mm (8.27 in \u00d7 13.0 in). Although metric, based on the A4 paper size, and named to suggest that it is part of the official ISO 216 paper sizes, it is only a de facto standard.\nIt is often referred to as (metric) \"foolscap\" or \"folio\" because of its simila... | large_corpus_distillation |
"Race condition-In software-This is an extremely strong guarantee for programmers. Programmers do not need to reason about reorderings to determine that their code contains data races. Therefore they do not need to reason about reorderings when determining whether their code is correctly synchronized. Once the determin... | large_corpus_distillation |
"Multinomial distribution-Related distributions-When k = 2, the multinomial distribution is the binomial distribution.\nCategorical distribution, the distribution of each trial; for k = 2, this is the Bernoulli distribution.\nThe Dirichlet distribution is the conjugate prior of the multinomial in Bayesian statistics.\n... | large_corpus_distillation |
"Bluetooth-Technical information-Pairing mechanisms Pairing mechanisms changed significantly with the introduction of Secure Simple Pairing in Bluetooth v2.1. The following summarizes the pairing mechanisms: Legacy pairing: This is the only method available in Bluetooth v2.0 and before. Each device must enter a PIN cod... | large_corpus_distillation |
"Associative array-Operations-In an associative array, the association between a key and a value is often known as a \"mapping\", and the same word mapping may also be used to refer to the process of creating a new association.\nThe operations that are usually defined for an associative array are: Insert or put: add a ... | large_corpus_distillation |
"Eager learning-Eager learning-The main disadvantage with eager learning is that it is generally unable to provide good local approximations in the target function." | large_corpus_distillation |
"Barrier function-Motivation-A barrier function, now, is a continuous approximation g to c that tends to infinity as x approaches b from above. Using such a function, a new optimization problem is formulated, viz.\nminimize f(x) + \u03bc g(x)where \u03bc > 0 is a free parameter. This problem is not equivalent to the or... | large_corpus_distillation |
"178 (number)-178 (number)-178 (one hundred [and] seventy-eight) is the natural number following 177 and preceding 179." | large_corpus_distillation |
"PL/I-Language summary-Values are computed by expressions written using a specific set of operations and builtin functions, most of which may be applied to aggregates as well as to single values, together with user-defined procedures which, likewise, may operate on and return aggregate as well as single values. The ass... | large_corpus_distillation |
numbers (if they exist) are preferred for mail services." | large_corpus_distillation |
"Hidden subgroup problem-Hidden subgroup problem-The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. The framework captures problems such as factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. This makes it especially important in the ... | large_corpus_distillation |
"Discounted maximum loss-Definition-Given a finite state space S , let X be a portfolio with profit Xs for s\u2208S . If X1:S,...,XS:S is the order statistic the discounted maximum loss is simply \u2212\u03b4X1:S , where \u03b4 is the discount factor.\nGiven a general probability space (\u03a9,F,P) , let X be ... | large_corpus_distillation |
S1 and the j+1th element in S2. Here, c[j+1] in statement S2 is written to in one iteration. In the next iteration, c[j] in statement S2, which is the same memory location as c[j+1] in the previous iteration, is written to again. This output dependence can be represented as S1[j] \u2192O S2[j+1]." | large_corpus_distillation |
"Hidden Field Equations-HFE variations-For encryption, the situation is better with HFE+ since the decryption process takes the same amount of time, however the public key has more equations than variables." | large_corpus_distillation |
"Vanishing gradient problem-Solutions-Residual networks One of the newest and most effective ways to resolve the vanishing gradient problem is with residual neural networks, or ResNets (not to be confused with recurrent neural networks). ResNets refer to neural networks where skip connections or residual connections ar... | large_corpus_distillation |
"Cache performance measurement and metric-Power law of cache misses-The Power law of cache misses shows a trend in the capacity misses in a particular application of the program as affected by the cache size. This empirical observation led to the mathematical form of power law, which shows the relation between the miss... | large_corpus_distillation |
reader and ZoomText screen magnifier and the free and open source screen reader NVDA by NV Access are more popular for that operating system. Apple Inc.'s macOS, iOS, and tvOS include VoiceOver as a built-in screen reader, while Google's Android provides the Talkback screen reader and its ChromeOS can use ChromeVox. Si... | large_corpus_distillation |
"ZNF337-Transcripts-The ZNF337 gene contains two transcript variants (both encode the same protein); variant 1 represents the longer transcript (751 aa) while variant 2 differs in the 5\u2019 UTR. There are also three isoforms (X1, X2, and X3). These isoforms represent one of many splice variants of the gene (while the... | large_corpus_distillation |
"Polish grammar-Regular morphological alternation-Certain regular or common alternations apply across the Polish inflectional system, affecting the morphology of nouns, adjectives, verbs, and other parts of speech. Some of these result from the restricted distribution of the vowels i and y, and from the voicing rules f... | large_corpus_distillation |
"SIM lock-Unlocking technology-Unlock code generators There are online services that will provide an IMEI unlocking service for DCT4 and DCT3 Nokia mobile phones. This method of unlock requires the user to know which carrier the mobile phone is locked to, and also needs to provide an IMEI. Generally, older model Nokia ... | large_corpus_distillation |
fk be measurable functions for k=1,...,m . Then \u2016\u220fk=1nfk\u20161\u2265\u220fk=1n\u2016fk\u2016pk.\nThis follows from the symmetric form of the H\u00f6lder inequality (see below)." | large_corpus_distillation |
hold but the assumption that the metric is required to be Minkowski is dropped." | large_corpus_distillation |
"Signed graph-Coloring-The constraints on proper colorings come from the edges of the signed graph. The integers assigned to two vertices must be distinct if they are connected by a positive edge. The labels on adjacent vertices must not be additive inverses if the vertices are connected by a negative edge. There can b... | large_corpus_distillation |
the examples above are a snapshot of the multitude of conversion metrics that a campaign can achieve." | large_corpus_distillation |
"Unscented transform-Sigma points-To compute the unscented transform, one first has to choose a set of sigma points. Since the seminal work of Uhlmann, many different sets of sigma points have been proposed in the literature. A thoroughgoing review of these variants can be found in the work of Menegaz et al. In general... | large_corpus_distillation |
"Hall-type theorems for hypergraphs-Aharoni's conditions: largest matching-Em contains m \u2013 1 hyperedges of size r: {m,x1,1,1,\u2026,x1,r\u22121,r\u22121,},\u2026,{m,xm\u22121,1,1,\u2026,xm\u22121,r\u22121,1} Note that edge i in Em meets all edges in Ei.\nThis H does not admit a Y-perfect matching, since every hy... | large_corpus_distillation |
"Advantage (cryptography)-Description of concept-Let F be an oracle for the function being studied, and let G be an oracle for an idealized function of that type. The adversary A is a probabilistic algorithm, given F or G as input, and which outputs 1 or 0. A's job is to distinguish F from G, based on making queries to... | large_corpus_distillation |
"Initial value problem-Existence and uniqueness of solutions-In some situations, the function f is not of class C1, or even Lipschitz, so the usual result guaranteeing the local existence of a unique solution does not apply. The Peano existence theorem however proves that even for f merely continuous, solutions are gua... | large_corpus_distillation |
and loses \u20ac1 with probability . So n is the the gambler's total\nn X p= 1\nnet winnings after games. We showed in the Introduction that is a martingale if (the fair case), a sub-martingale if\n2\np> 1 p< 1 c\u2208Z\n(the favorable case), and a super-martingale if (the unfair case). Now, for , let\n2 2\n\u03c4 =inf... | large_corpus_distillation |
"Vigen\u00e8re cipher-Variants-If one uses a key that is truly random, is at least as long as the encrypted message, and is used only once, the Vigen\u00e8re cipher is theoretically unbreakable. However, in that case, the key, not the cipher, provides cryptographic strength, and such systems are properly referred to co... | large_corpus_distillation |
"Controlled vocabulary-Applications-To use machine-readable terms from any controlled vocabulary, web designers can choose from a variety of annotation formats, including RDFa, HTML5 Microdata, or JSON-LD in the markup, or RDF serializations (RDF/XML, Turtle, N3, TriG, TriX) in external files." | large_corpus_distillation |
"Dylan (programming language)-Classes-In Dylan, these sorts of visibility rules are not considered part of the code, but of the module/interface system. This adds considerable flexibility. For instance, one interface used during early development could declare everything public, whereas one used in testing and deployme... | large_corpus_distillation |
"Singular value decomposition-Applications of the SVD-One application of SVD to rather large matrices is in numerical weather prediction, where Lanczos methods are used to estimate the most linearly quickly growing few perturbations to the central numerical weather prediction over a given initial forward time period; i... | large_corpus_distillation |
"Accuracy and precision-In classification-In multiclass classification When computing accuracy in multiclass classification, accuracy is simply the fraction of correct classifications: This is usually expressed as a percentage. For example, if a classifier makes ten predictions and nine of them are correct, the accurac... | large_corpus_distillation |
"Tutte\u2013Berge formula-Explanation-The characterization of Tutte and Berge proves that this is the only obstacle to creating a large matching: the size of the optimal matching will be determined by the subset U with the biggest difference between its numbers of odd components outside U and vertices inside U . Tha... | large_corpus_distillation |
"IEEE 802.11w-2009-Protected frames-MPDU payload is TKIP or CCMP encrypted.\nMPDU payload and header are TKIP or CCMP integrity protected.\nProtected frame field of frame control field is set.\nOnly cipher suites already implemented are required.\nSender's pairwise temporal key (PTK) protects unicast management frame.B... | large_corpus_distillation |
"b) Use the Markov inequality to show that Pr{S n >4}\u22641/2 for all n. Show that the probability of an infinite number of\ntransitions by time 4 is at least 1/2.\nExercise 6.8.\na) Consider a Markov process with the set of states {0,1,...} in which the transition rates {q ij } between states are given by\nq i,i+1 =(... | large_corpus_distillation |
several\nproperties of square roots that allow us to simplify complicated radical expressions. The first rule we will look at is the\nproduct rule for simplifying square roots,which allows us to separate the square root of a product of two numbers into\nthe product of two separate rational expressions. For instance, we... | large_corpus_distillation |
"Laser engraving-Laser engraving machines-A laser can remove material very efficiently because the laser beam can be designed to deliver energy to the surface in a manner which converts a high percentage of the light energy into heat. The beam is highly focused and collimated\u2014in most non-reflective materials like ... | large_corpus_distillation |
"Permutable prime-Base 2-In base 2, only repunits can be permutable primes, because any 0 permuted to the ones place results in an even number. Therefore, the base 2 permutable primes are the Mersenne primes. The generalization can safely be made that for any positional number system, permutable primes with more than o... | large_corpus_distillation |
"Independent and identically distributed random variables-Examples-Independent \u2013 Each outcome of the card will not affect the next one, which means the 52 results are independent from each other. In contrast, if each card that is drawn is kept out of the deck, subsequent draws would be affected by it (drawing one ... | large_corpus_distillation |
"Glur2 RNA editing-RNA editing-Editing regulation Editing occurs in 100% of transcripts in human brain. Editing levels are lower in other tissues. Deletion analysis determined that editing requires 5' portion of intron B. The predicted minimum fragment required for editing to occur contains inverted repeat structure se... | large_corpus_distillation |
"SMASH (hash)-Definition-Input: 256/512-bit message blocks m1,m2,...,mt and \u03b8\u2208GF(2n) h0=f(iv)\u2295iv hi=h(hi\u22121,mi)=f(hi1\u2295mi)\u2295mi\u2295\u03b8mi ht+1=f(ht)\u2295ht The function f is a complex compression function consisting of H-Rounds and L-Rounds using S-boxes, linear diffusion and variable r... | large_corpus_distillation |
"CryptMix-CryptMix-CryptMix is a type of ransomware which claims that ransom fees will be donated to a children\u2019s charity. The CryptMix threat combines large portions of other open source ransomware code: CryptoWall 3.0, CryptoWall 4.0 and CryptXXX. CryptMix was created by a group calling themselves \u201cThe Char... | large_corpus_distillation |
"Digital security-Computer protection (countermeasures)-Vulnerabilities can be discovered with a vulnerability scanner, which analyzes a computer system in search of known vulnerabilities, such as open ports, insecure software configuration, and susceptibility to malware. In order for these tools to be effective, they ... | large_corpus_distillation |
"Bayesian network-Example-To predict the impact of turning the sprinkler on: Pr do Pr Pr (G\u2223R,S=T) with the term Pr (S=T\u2223R) removed, showing that the action affects the grass but not the rain." | large_corpus_distillation |
"Berkson's paradox-Statement-Note only two assumptions were used in the argument above: (i) 0<P(A)\u22641 which is sufficient to imply P(A)\u2264P(A\u2223A\u222aB) . And (ii) P(A\u222aB)<1 , which with (i) implies the strict inequality P(A)<P(A\u2223A\u222aB) , and so dependence of A and A\u222aB . It's not neces... | large_corpus_distillation |
"Vix-Places-Vix, C\u00f4te-d'Or Vix Grave of the Lady of Vix Vix, Vend\u00e9e " | large_corpus_distillation |
"ISO/IEC 27004-What does the standard establish?-This standard establishes: Monitoring and measuring of information security performance.\nMonitoring and measuring the effectiveness of an Information Security Management System (ISMS), including processes and controls.\nAnalysis and evaluating of monitoring and measurem... | large_corpus_distillation |
"Generalized assignment problem-Greedy approximation algorithm-The algorithm constructs a schedule in iterations, where during iteration j a tentative selection of items to bin bj is selected.\nThe selection for bin bj might change as items might be reselected in a later iteration for other bins." | large_corpus_distillation |
"Hellinger distance-Definition-Here, P(dx)=p(x)\u03bb(dx) and Q(dx)=q(x)\u03bb(dx) , i.e. p and q are the Radon\u2013Nikodym derivatives of P and Q respectively with respect to \u03bb . This definition does not depend on \u03bb , i.e. the Hellinger distance between P and Q does not change if \u03bb is replaced w... | large_corpus_distillation |
"Conditional sentence-Types of conditional sentence-There are various ways of classifying conditional sentences. Many of these categories are visible cross-linguistically." | large_corpus_distillation |
would like to select a random prior distribution G(\u03bc~i)=\u2211k=1\u221e\u03c0k\u03b4\u03bck(\u03bc~i) where the values of the clusters means \u03bck are again independently distributed according to H(\u03bb) and the distribution over \u03c0k is symmetric over the infinite set of clusters. This is exactly what ... | large_corpus_distillation |
"Context-free grammar-Decidable problems-Regularity and LL(k) checks It is decidable whether a given grammar is a regular grammar, as well as whether it is an LL(k) grammar for a given k\u22650.:\u200a233\u200a If k is not given, the latter problem is undecidable.:\u200a252\u200aGiven a context-free language, it is nei... | large_corpus_distillation |
"Test-driven development-Development style-Writing the tests first: The tests should be written before the functionality that is to be tested. This has been claimed to have many benefits. It helps ensure that the application is written for testability, as the developers must consider how to test the application from th... | large_corpus_distillation |
"Vigesimal-Cyclic numbers-The prime factorization of twenty is 22 \u00d7 5, so it is not a perfect power. However, its squarefree part, 5, is congruent to 1 (mod 4). Thus, according to Artin's conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not n... | large_corpus_distillation |
"Bayes' theorem-Forms-Events Simple form For events A and B, provided that P(B) \u2260 0, P(A|B)=P(B|A)P(A)P(B)." | large_corpus_distillation |
"Index\n1 https://eng.libretexts.org/@go/page/76906" | large_corpus_distillation |
"Fault tolerance-Fault tolerance techniques-One variant of DMR is pair-and-spare. Two replicated elements operate in lockstep as a pair, with a voting circuit that detects any mismatch between their operations and outputs a signal indicating that there is an error. Another pair operates exactly the same way. A final ci... | large_corpus_distillation |
"Dotted note-Triple dotting-A triple-dotted note is a note with three dots written after it; its duration is 1+7\u20448 times its basic note value. Use of a triple-dotted note value is not common in the Baroque and Classical periods, but quite common in the music of Richard Wagner and Anton Bruckner, especially in thei... | large_corpus_distillation |
"Set (card game)-Set (card game)-Set (stylized as SET or SET!) is a real-time card game designed by Marsha Falco in 1974 and published by Set Enterprises in 1991. The deck consists of 81 unique cards that vary in four features across three possibilities for each kind of feature: number of shapes (one, two, or three), s... | large_corpus_distillation |
"Commutative magma-Other examples-The bottom row in the Karnaugh diagram above gives more example operations, defined on the integers (or any commutative ring)." | large_corpus_distillation |
"Stream cipher-Security-For a stream cipher to be secure, its keystream must have a large period, and it must be impossible to recover the cipher's key or internal state from the keystream. Cryptographers also demand that the keystream be free of even subtle biases that would let attackers distinguish a stream from ran... | large_corpus_distillation |
"Texting while driving-Technology as a solution-In recent years, location-based technologies that detect potential texting while driving situations have been developed for both the Android operating system and the iPhone operating system (iOS). Other technologies have been developed for law enforcement. A search for \"... | large_corpus_distillation |
"Temporal Key Integrity Protocol-Security-TKIP uses the same underlying mechanism as WEP, and consequently is vulnerable to a number of similar attacks. The message integrity check, per-packet key hashing, broadcast key rotation, and a sequence counter discourage many attacks. The key mixing function also eliminates th... | large_corpus_distillation |
"C (programming language)-Syntax-Operators C supports a rich set of operators, which are symbols used within an expression to specify the manipulations to be performed while evaluating that expression. C has operators for: arithmetic: +, -, *, /, % assignment: = augmented assignment: +=, -=, *=, /=, %=, &=, |=, ^=, <<=... | large_corpus_distillation |
"Primitive recursive function-Examples-.That is, If (x,y,z) returns the then-part, y , if the if-part, x , is true, and the else-part, z , otherwise.\nJunctors Based on the If function, it is easy to define logical junctors. For example, defining If \u2218(P12,P22,C02) , one obtains If (x,y,0) , that is, And(x,... | large_corpus_distillation |
"Proof of Fermat's Last Theorem for specific exponents-n = 3-s = e2 + 3f2A short calculation shows that v = e (e2 \u2212 9f2) w = 3f (e2 \u2212 f2)Thus, e is odd and f is even, because v is odd. The expression for 18w then becomes r3 = 18w = 54f (e2 \u2212 f2) = 54f (e + f) (e \u2212 f) = 33\u00d72f (e + f) (e \u2212 f... | large_corpus_distillation |
"Grassmann number-Matrix representations-In general, a Grassmann algebra on n generators can be represented by 2n \u00d7 2n square matrices. Physically, these matrices can be thought of as raising operators acting on a Hilbert space of n identical fermions in the occupation number basis. Since the occupation number for... | large_corpus_distillation |
"Monoid (category theory)-Categories of monoids-Given two monoids (M, \u03bc, \u03b7) and (M', \u03bc', \u03b7') in a monoidal category C, a morphism f : M \u2192 M ' is a morphism of monoids when f o \u03bc = \u03bc' o (f \u2297 f), f o \u03b7 = \u03b7'.In other words, the following diagrams , commute.\nThe category ... | large_corpus_distillation |
"Shortest path problem-Single-source shortest paths-Undirected graphs Unweighted graphs Directed acyclic graphs (DAGs) An algorithm using topological sorting can solve the single-source shortest path problem in time \u0398(E + V) in arbitrarily-weighted DAGs.\nDirected graphs with nonnegative weights The following tabl... | large_corpus_distillation |
"Representer theorem-Generalizations-The Theorem stated above is a particular example of a family of results that are collectively referred to as \"representer theorems\"; here we describe several such.\nThe first statement of a representer theorem was due to Kimeldorf and Wahba for the special case in which E((x1,y1,f... | large_corpus_distillation |
but also on their annotation with textual labels which need to be analyzed. It was found that it results in better models in terms of understanding than alternative labelling styles." | large_corpus_distillation |
"Opaque data type-Opaque data type-Typical examples of opaque data types include handles for resources provided by an operating system to application software. For example, the POSIX standard for threads defines an application programming interface based on a number of opaque types that represent threads or synchroniza... | large_corpus_distillation |
"Ctrie-Advantages of Ctries-Ctries have been shown to be comparable in performance with concurrent skip lists, concurrent hash tables and similar data structures in terms of the lookup operation, being slightly slower than hash tables and faster than skip lists due to the lower level of indirections. However, they are ... | large_corpus_distillation |
"Seating plan-Transportation-Plans are also made for airplanes, where the objective is to differentiate passengers between the various travel classes and ensure everybody has a place." | large_corpus_distillation |
"Info-gap decision theory-Discussion-Satisficing and bounded rationality It is correct that the info-gap robustness function is local, and has restricted quantitative value in some cases. However, a major purpose of decision analysis is to provide focus for subjective judgments. That is, regardless of the formal analys... | large_corpus_distillation |
"Broken Picture Telephone-Similar games-Gartic Phone While Onrizon Social Games' Gartic.io website launched in 2017, the company found massive success upon launching Gartic Phone in December 2020. Like BPT and similar games, it combines elements of Pictionary and Broken Telephone. In Gartic Phone, players sketch a word... | large_corpus_distillation |
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