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"Feature (linguistics)-In morphology and syntax-Different lexical categories realise or are specified for different grammatical features: for example, verbs in English are specified for tense, aspect and mood features, as well as person and number. The features that a category realises can also differ from language to ...
large_corpus_distillation
however, that RC4, being a stream cipher, was for a period of time the only common cipher that was immune to the 2011 BEAST attack on TLS 1.0. The attack exploits a known weakness in the way cipher-block chaining mode is used with all of the other ciphers supported by TLS 1.0, which are all block ciphers."
large_corpus_distillation
"Optimal asymmetric encryption padding-Optimal asymmetric encryption padding-Prevent partial decryption of ciphertexts (or other information leakage) by ensuring that an adversary cannot recover any portion of the plaintext without being able to invert the trapdoor one-way permutation f .The original version of OAEP (...
large_corpus_distillation
"Sparse PCA-Mathematical formulation-If one takes k=p, the problem reduces to the ordinary PCA, and the optimal value becomes the largest eigenvalue of covariance matrix \u03a3.\nAfter finding the optimal solution v, one deflates \u03a3 to obtain a new matrix \u03a31=\u03a3\u2212(vT\u03a3v)vvT, and iterate this process...
large_corpus_distillation
"Linux Trace Toolkit-Usage-Collecting trace data Data collection is Started by: trace 15 foo This command will cause the LTT tracedaemon to do a trace that lasts for 15 seconds, writing trace data to foo.trace and process information from the /proc filesystem to foo.proc.\nThe trace command is actually a script which r...
large_corpus_distillation
a banking institution could get the user's account information and provide them efficiently with extensive information such as transactions, account information entries etc."
large_corpus_distillation
"Boxicity-Algorithmic results-Many graph problems can be solved or approximated more efficiently for graphs with bounded boxicity than they can for other graphs; for instance, the maximum clique problem can be solved in polynomial time for graphs with bounded boxicity. For some other graph problems, an efficient soluti...
large_corpus_distillation
"Confidence distribution-Using confidence distributions for inference-(2) For the singleton test K0: \u03b8 = b vs. K1: \u03b8 \u2260 b, P{K0: \u03b8 = b}(2 min{ps(Clo), one can show from the CD definition that ps(Cup)} \u2264 \u03b1) = \u03b1. Thus, 2 min{ps(Clo), ps(Cup)} = 2 min{Hn(b), 1 \u2212 Hn(b)} is the corresp...
large_corpus_distillation
"Corpus of Contemporary American English-Related-The corpus of Global Web-based English (GloWbE; pronounced \"globe\") contains about 1.9 billion words of text from twenty different countries. This makes it about 100 times as large as other corpora like the International Corpus of English, and it allows for many types ...
large_corpus_distillation
"Min-conflicts algorithm-Algorithm-algorithm MIN-CONFLICTS is input: console.csp, A constraint satisfaction problem.\nmax_steps, The number of steps allowed before giving up.\ncurrent_state, An initial assignment of values for the variables in the csp.\noutput: A solution set of values for the variable or failure."
large_corpus_distillation
"Local-density approximation-Local-density approximation-Local-density approximations (LDA) are a class of approximations to the exchange\u2013correlation (XC) energy functional in density functional theory (DFT) that depend solely upon the value of the electronic density at each point in space (and not, for example, d...
large_corpus_distillation
"EMML (Motorola)-EMML profiles (EMMP)-Below is an example of an EMML profile page: EMML Profiles are stored in .emmp files; these can be linked to the HTML document using the import method of the EMMLProfile module. This is an example of how an EMMP file would be linked: Note: Each META tag is parsed from left to right...
large_corpus_distillation
"Balls into bins problem-Applications-Online Load Balancing: consider a set of n identical computers. There are n users who need computing services. The users are not coordinated - each users comes on his own and selects which computer to use. Each user would of course like to select the least loaded computer, but this...
large_corpus_distillation
"Object categorization from image search-OPTIMOL-Once an image is accepted by meeting the above criterion and incorporated into the dataset, however, it needs to meet another criterion before it is incorporated into the \u63f7ache set\u6546the set of images to be used for training. This set is intended to be a diverse ...
large_corpus_distillation
"128 (number)-128 (number)-128 (one hundred [and] twenty-eight) is the natural number following 127 and preceding 129."
large_corpus_distillation
"ISO 639-3-Code space-Since the code is three-letter alphabetic, one upper bound for the number of languages that can be represented is 26 \u00d7 26 \u00d7 26 = 17,576. Since ISO 639-2 defines special codes (4), a reserved range (520) and B-only codes (22), 546 codes cannot be used in part 3. Therefore, a stricter uppe...
large_corpus_distillation
"Factorization-Ideals-In algebraic number theory, the study of Diophantine equations led mathematicians, during 19th century, to introduce generalizations of the integers called algebraic integers. The first ring of algebraic integers that have been considered were Gaussian integers and Eisenstein integers, which share...
large_corpus_distillation
the probability distribution of the sum X + Y of two independent random variables X and Y whose respective distributions are \u03bc and \u03bd."
large_corpus_distillation
"Magic number (programming)-Debug values-Magic debug values are specific values written to memory during allocation or deallocation, so that it will later be possible to tell whether or not they have become corrupted, and to make it obvious when values taken from uninitialized memory are being used. Memory is usually v...
large_corpus_distillation
"Microarchitecture-Microarchitectural concepts-One technique of how this parallelism is achieved is through multiprocessing systems, computer systems with multiple CPUs. Once reserved for high-end mainframes and supercomputers, small-scale (2\u20138) multiprocessors servers have become commonplace for the small busines...
large_corpus_distillation
"PL/I-Special topics in PL/I-ON-units and exception handling When PL/I was designed, programs only ran in batch mode, with no possible intervention from the programmer at a terminal. An exceptional condition such as division by zero would abort the program yielding only a hexadecimal core dump. PL/I exception handling,...
large_corpus_distillation
"Queue (abstract data type)-Queue (abstract data type)-The operation of adding an element to the rear of the queue is known as enqueue, and the operation of removing an element from the front is known as dequeue. Other operations may also be allowed, often including a peek or front operation that returns the value of t...
large_corpus_distillation
"Compound probability distribution-Computation-Compound distributions derived from exponential family distributions often have a closed form.\nIf analytical integration is not possible, numerical methods may be necessary."
large_corpus_distillation
"Probability bounds analysis-Magnitude comparisons-Like arithmetic and logical operations, these magnitude comparisons generally depend on the stochastic dependence between A and B, and the subtraction in the encoding should reflect that dependence. If their dependence is unknown, the difference can be computed without...
large_corpus_distillation
"EuroCrypt-EuroCrypt-EuroCrypt is a conditional access system for Multiplexed Analogue Components-encoded analogue satellite television. It had several versions (M, S and S2). It supported receivers with card slots and those with embedded keys. Its most widespread use was in Scandinavia, where the only EuroCrypt protec...
large_corpus_distillation
"Probabilistic classification-Probabilistic classification-In machine learning, a probabilistic classifier is a classifier that is able to predict, given an observation of an input, a probability distribution over a set of classes, rather than only outputting the most likely class that the observation should belong to....
large_corpus_distillation
erroneous. Instead of looking for discrepancies wherever they might be found, theory should guide comparison between different sub-tests."
large_corpus_distillation
and b be the two data elements of t, where a<b . There are four cases: If d is equal to a or b, then d is in T and we're done.\nIf d<a , then set T to p and go back to step 2.\nIf a<d<b , then set T to q and go back to step 2.\nIf d>b , then set T to r and go back to step 2.\nInsertion Insertion maintains the balan...
large_corpus_distillation
"HTTP/2 Server Push-Basic concept-For example, in the case of a website with three resources: index.html, styles.css and script.js, when a user, through their browser, connects to Wikipedia webserver to get the home page, they automatically retrieve index.html. As the browser parses the HTML text in index.html, it find...
large_corpus_distillation
"Medical terminology-Morphology-Prefixes do not normally require further modification to be added to a word root because the prefix normally ends in a vowel or vowel sound, although in some cases they may assimilate slightly and an in- may change to im- or syn- to sym-.\nSuffixes are attached to the end of a word root ...
large_corpus_distillation
"Machine learning in bioinformatics-Machine learning approaches-Convolutional neural networks Convolutional neural networks (CNN) are a class of deep neural network whose architecture is based on shared weights of convolution kernels or filters that slide along input features, providing translation-equivariant response...
large_corpus_distillation
(3.6.5)\ni i ij j\nk\nj\nWe can also write this in vector form as\nv\u2217(n,u)=max(rk+[Pk]v\u2217(n\u22121,u)) (3.6.6)\nk\nHere k is a set (or vector) of decisions, k=(k 1 ,k 2 ,\u2026,k M )\u22a4 , where k i is the decision for state i. [Pk] denotes a matrix whose\n(i,j) element is P(ki) , and rk denotes a vector who...
large_corpus_distillation
"Symbol (formal)-Overview-Formal symbols are usually thought of as purely syntactic structures, composed into larger structures using a formal grammar, though sometimes they may be associated with an interpretation or model (a formal semantics)."
large_corpus_distillation
"Ukkonen's algorithm-Ukkonen's algorithm example-To better illustrate how a suffix tree using Ukkonen's algorithm is constructed, we can use the following example: S=xabxac Start with an empty root node.\nConstruct T1 for S[1] by adding the first character of the string. Rule 2 applies, which creates a new leaf node.\n...
large_corpus_distillation
"Table of divisors-Key to the tables-a prime number has only 1 and itself as divisors; that is, d(n) = 2 a composite number has more than just 1 and itself as divisors; that is, d(n) > 2 a highly composite number has more divisors than any lesser number; that is, d(n) > d(m) for every positive integer m < n. Counterint...
large_corpus_distillation
"Unix security-File systems-The set user ID and set group ID bits, commonly abbreviated set-UID and set-GID respectively, are used to change the identity of the process which executes a file having either or both of those bits set. A file having the set-UID permission bit set will cause a process which executes that fi...
large_corpus_distillation
"Buffer overflow-Protective countermeasures-Microsoft's implementation of Data Execution Prevention (DEP) mode explicitly protects the pointer to the Structured Exception Handler (SEH) from being overwritten.Stronger stack protection is possible by splitting the stack in two: one for data and one for function returns. ...
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group. The conjecture also holds if G is one of certain kinds of exceptional group."
large_corpus_distillation
"Common spatial pattern-Discussion-Relation between LDA and CSP Linear discriminant analysis (LDA) and CSP apply in different circumstances. LDA separates data that have different means, by finding a rotation that maximizes the (normalized) distance between the centers of the two sets of data. On the other hand, CSP i...
large_corpus_distillation
down 2G services so that carriers can re-use the frequencies for newer technologies (e.g. 4G, 5G).In 2022, Android 12 introduced a system setting to disable 2G connectivity for the device, as 2G is considered to be insecure. Specifically, there exist well known methods to attack weaknesses in GSM since 2009 with practi...
large_corpus_distillation
as a part of their official emblem.On 24 December 2010, Tao Xie and Dengguo Feng announced the first published single-block (512-bit) MD5 collision. (Previous collision discoveries had relied on multi-block attacks.) For \"security reasons\", Xie and Feng did not disclose the new attack method. They issued a challenge ...
large_corpus_distillation
"Property testing-Testing graph properties-To make precise the general notions of property testing in the context of graphs, we say a tester for graph property P should distinguish with at least \u2154 probability between the cases of G satisfying P and the cases where G is \u03b5-far in edit distance from satisfying P...
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"Reference (computer science)-Examples-An alternative representation of such a function is a directed graph called a reachability graph. Here, each datum is represented by a vertex and there is an edge from u to v if the datum in u refers to the datum in v. The maximum out-degree is one. These graphs are valuable in ga...
large_corpus_distillation
"Mutation (genetic algorithm)-Mutation (genetic algorithm)-there must be no preference for parts or directions in the search space (no drift).\nsmall mutations should be more probable than large ones.For different genome types, different mutation types are suitable. Some mutations are Gaussian, Uniform, Zigzag, Scrambl...
large_corpus_distillation
"FCCH-FCCH-FCCH stands for Frequency Correction Channel. It is a downlink-only control channel in the GSM Um air interface.\nThe FCCH burst, defined in GSM 05.02 section 5.2.4, is an all-zero sequence that produces a fixed tone in the GMSK modulator output.\nThis tone enables the Mobile to lock its local oscillator to ...
large_corpus_distillation
"User story-History-2004: Mike Cohn generalized the principles of user stories beyond the usage of cards in his book User Stories Applied: For Agile Software Development that is now considered the standard reference for the topic according to Martin Fowler. Cohn names Rachel Davies as the inventor of user stories. Whil...
large_corpus_distillation
"Cantor set-Properties-We know that there are N=2n intervals of size 1/3n present in the system at the n th step of its construction. Then if we label the surviving intervals as x1,x2,\u2026,x2n then the df th moment is x1df+x2df+\u22ef+x2ndf=1 since x1=x2=\u22ef=x2n=1/3n The Hausdorff dimension of the Cantor se...
large_corpus_distillation
the inverse document frequencies of the terms in the new document decrease while that of the remaining terms increase. In average, as documents are added, the region where documents lie expands regulating the density of the entire collection representation. This behavior models the original motivation of Salton and his...
large_corpus_distillation
"Multi-booting-Technical issues-Partitioning The basic concept involves partitioning a disk to accommodate each planned installation, usually including separate partitions for boot, root, data storage and backups.\nMBR loader An MBR loader, such as Air-Boot, replaces the standard boot code in track 0 with code that dis...
large_corpus_distillation
"Cache hierarchy-Properties-However, in the case of the write back policy, the changed cache block will be updated in the lower-level hierarchy only when the cache block is evicted. A \"dirty bit\" is attached to each cache block and set whenever the cache block is modified. During eviction, blocks with a set dirty bit...
large_corpus_distillation
"X + Y sorting-Number of orderings-A well-known lower bound for unstructured sorting, in the decision tree model, is based on the factorial number of sorted orders that an unstructured list may have. Because each comparison can at best reduce the number of possible orderings by a factor of two, sorting requires a numbe...
large_corpus_distillation
"MacArabic encoding-MacArabic encoding-MacArabic encoding is an obsolete encoding for Arabic (and English) text that was used in Apple Macintosh computers to texts.\nThe encoding is identical to MacFarsi encoding, except the numerals."
large_corpus_distillation
"Chart parser-Chart parser-In computer science, a chart parser is a type of parser suitable for ambiguous grammars (including grammars of natural languages). It uses the dynamic programming approach\u2014partial hypothesized results are stored in a structure called a chart and can be re-used. This eliminates backtracki...
large_corpus_distillation
entirely or partially on the same condition are merged."
large_corpus_distillation
"Kenneth Witwer-Scientific rigor, standardization, and advocacy-Witwer has contributed to scientific standardization and rigor efforts. He was corresponding author in 2013 of the first position paper of the International Society for Extracellular Vesicles, on standardization of isolation and characterization of EVs in ...
large_corpus_distillation
"Automated Insights-Natural Language Generation-Automated Insights provides natural language generation (NLG) technology in the form of their Wordsmith platform. Natural language generation is a software process that automatically turns data into human-friendly prose. Structured data is fed into NLG software and run th...
large_corpus_distillation
in memory. The prettyprinted output from LIST could be redirected to a file or a printer with a shell-like notation, e.g. LIST bob >/p. One could also SAVE and LOAD procedures from storage."
large_corpus_distillation
"Bowling machine-Mechanical bowling machines-Simulating different deliveries Fast bowling This is achieved by setting both wheels to the same speed, as fast as the batsman is able to deal with, although the machine itself would have to be tipped horizontally. The coach can move the machine around slightly to vary the l...
large_corpus_distillation
"Priority queue-Operations-More advanced implementations may support more complicated operations, such as pull_lowest_priority_element, inspecting the first few highest- or lowest-priority elements, clearing the queue, clearing subsets of the queue, performing a batch insert, merging two or more queues into one, increm...
large_corpus_distillation
"Swift (programming language)-Comparisons to other languages-The one-statement form of if and while, which allows for the omission of braces around the statement, is unsupported.\nC-style enumeration for (int i = 0; i < c; i++), which is prone to off-by-one errors, is unsupported (from Swift 3 onward).\nThe pre- and po...
large_corpus_distillation
"BASIC Programming-Details-The BASIC Programming display is divided into six regions: Program is where instructions are typed. It has a maximum of eleven lines of code.\nStack shows temporary results of what the program does.\nVariables stores the values of any variables that the program is using.\nOutput displays any ...
large_corpus_distillation
"Strahler number-Definition-Any node with Strahler number i must have at least two descendants with Strahler number i \u2212 1, at least four descendants with Strahler number i \u2212 2, etc., and at least 2i \u2212 1 leaf descendants. Therefore, in a tree with n nodes, the largest possible Strahler number is log2 n + ...
large_corpus_distillation
"False coverage rate-The problems addressed by FCR-Selection Selection causes reduced average coverage. Selection can be presented as conditioning on an event defined by the data and may affect the coverage probability of a CI for a single parameter. Equivalently, the problem of selection changes the basic sense of P-v...
large_corpus_distillation
"Blockmodeling-Definition-A network as a system is composed of (or defined by) two different sets: one set of units (nodes, vertices, actors) and one set of links between the units. Using both sets, it is possible to create a graph, describing the structure of the network.During blockmodeling, the researcher is faced w...
large_corpus_distillation
"Clique percolation method-Algorithms and software-There are a number of implementations of clique percolation. The clique percolation method was first implemented and popularized by CFinder [1] (freeware for non-commercial use) software for detecting and visualizing overlapping communities in networks. The program ena...
large_corpus_distillation
"Collective classification-Methods-There are several existing approaches to collective classification. The two major methods are iterative methods and methods based on probabilistic graphical models."
large_corpus_distillation
"Hyperparameter (machine learning)-Optimization-Hyperparameter optimization finds a tuple of hyperparameters that yields an optimal model which minimizes a predefined loss function on given test data. The objective function takes a tuple of hyperparameters and returns the associated loss."
large_corpus_distillation
"Web service-W3C Web services-Many organizations use multiple software systems for management. Different software systems often need to exchange data with each other, and a Web service is a method of communication that allows two software systems to exchange this data over the Internet. The software system that request...
large_corpus_distillation
"Mathematical induction-Transfinite induction-Proofs by transfinite induction typically distinguish three cases: when n is a minimal element, i.e. there is no element smaller than n; when n has a direct predecessor, i.e. the set of elements which are smaller than n has a largest element; when n has no direct predecesso...
large_corpus_distillation
"Matching (graph theory)-Algorithms and computational complexity-Finding all maximally matchable edges One of the basic problems in matching theory is to find in a given graph all edges that may be extended to a maximum matching in the graph (such edges are called maximally matchable edges, or allowed edges). Algorithm...
large_corpus_distillation
"Betweenness centrality-Definition-The betweenness centrality of a node v is given by the expression: g(v)=\u2211s\u2260v\u2260t\u03c3st(v)\u03c3st where \u03c3st is the total number of shortest paths from node s to node t and \u03c3st(v) is the number of those paths that pass through v (not where v is an end po...
large_corpus_distillation
"Barcan formula-The Barcan formula-The Barcan formula is: \u2200x\u25fbFx\u2192\u25fb\u2200xFx .In English, the schema reads: If every x is necessarily F, then it is necessary that every x is F. It is equivalent to \u25ca\u2203xFx\u2192\u2203x\u25caFx .The Barcan formula has generated some controversy because\u2014in t...
large_corpus_distillation
"Interrupt priority level-Overview-Of course, multiprocessor systems add their complications, which are not addressed here.\nRegardless of what the hardware might support, typical UNIX-type systems only use two levels: the minimum (all interrupts disabled) and the maximum (all interrupts enabled)."
large_corpus_distillation
"Robust collaborative filtering-Introduction-One of the biggest challenges to collaborative filtering is shilling attacks. That is, malicious users or a competitor may deliberately inject certain number of fake profiles to the system (typically 1~5%) in such a way that they can affect the recommendation quality or even...
large_corpus_distillation
correct). The Designer\u2019s score is twice the difference between the highest player\u2019s score and the lowest player\u2019s score (i.e., 2x(Highest-Lowest) ). This rewards a pattern that one player discovers easily and another player has great difficulty understanding."
large_corpus_distillation
"Spatial modulation-Example-The receiver must estimate the antenna index, as well as decode the symbol."
large_corpus_distillation
"Polynomial code-Polynomial code-In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length) that are divisible by a given fixed polynomial (of shorter length, called the generator polynomial)."
large_corpus_distillation
"Shared secret-Shared secret-The shared secret can be used for authentication (for instance when logging into a remote system) using methods such as challenge\u2013response or it can be fed to a key derivation function to produce one or more keys to use for encryption and/or MACing of messages.\nTo make unique session ...
large_corpus_distillation
"Off-the-Record Messaging-Implementation-In addition to providing encryption and authentication \u2014 features also provided by typical public-key cryptography suites, such as PGP, GnuPG, and X.509 (S/MIME) \u2014 OTR also offers some less common features: Forward secrecy Messages are only encrypted with temporary per...
large_corpus_distillation
"Random permutation statistics-Generalizations-Similar statistics are available for random endomorphisms on a finite set."
large_corpus_distillation
"Enterprise bookmarking-Differences-Tag management Enterprise bookmarking tools also differ from social bookmarking tools in the way that they often face an existing taxonomy. Some of these tools have evolved to provide Tag management which is the combination of uphill abilities (e.g. faceted classification, predefined...
large_corpus_distillation
it.\nWrite and test a big program in small pieces.\nUse recursive procedures for recursively-defined data structures.\nTest input for plausibility and validity.\nMake sure input doesn't violate the limits of the program.\nTerminate input by end-of-file marker, not by count.\nIdentify bad input; recover if possible.\nMa...
large_corpus_distillation
"Pascal MicroEngine-Other languages-A group led by David A. Fisher developed the third validated Ada compiler using the Modular MicroEngine.\nfor version 17.1 of the Ada verification system then in use."
large_corpus_distillation
"Natural number-Properties-No nonzero zero divisors: if a and b are natural numbers such that a \u00d7 b = 0, then a = 0 or b = 0 (or both).\nIf the natural numbers are taken as \"excluding 0\", and \"starting at 1\", the \"no nonzero zero divisors\" property is not satisfied."
large_corpus_distillation
"Infinite divisibility (probability)-Limit theorem-Infinitely divisible distributions appear in a broad generalization of the central limit theorem: the limit as n \u2192 +\u221e of the sum Sn = Xn1 + \u2026 + Xnn of independent uniformly asymptotically negligible (u.a.n.) random variables within a triangular array 11 ...
large_corpus_distillation
"Muller\u2013Schupp theorem-Remarks and further developments-At the time the 1983 paper of Muller and Schupp was published, accessibility of finitely presented groups has not yet been established. Therefore, the original formulation of the Muller\u2013Schupp theorem said that a finitely generated group is virtually fre...
large_corpus_distillation
"Maclisp-Name-Maclisp was named for Project MAC, and is unrelated to Apple's Macintosh (Mac) computer, which it predates by decades or to John McCarthy. The various Lisp systems for the Macintosh have no particular similarity to Maclisp."
large_corpus_distillation
"Injective tensor product-Definition-And if in addition Y is Banach then so is Lb(Xb\u2032;Y) (even if X is not complete)."
large_corpus_distillation
"System virtual machine-Techniques-Full virtualization is particularly helpful in operating system development, when experimental new code can be run at the same time as older, more stable, versions, each in a separate virtual machine. The process can even be recursive: IBM debugged new versions of its virtual machine ...
large_corpus_distillation
"Shortest common supersequence problem-Shortest common supersequence problem-There is no similar relationship between shortest common supersequences and longest common subsequences of three or more input sequences. (In particular, LCS and SCS are not dual problems.) However, both problems can be solved in O(nk) time u...
large_corpus_distillation
"No Silver Bullet-Related concepts-Brooks's paper has sometimes been cited in connection with Wirth's law, to argue that \"software systems grow faster in size and complexity than methods to handle complexity are invented\"."
large_corpus_distillation
re-sends it to all the other nodes in the network.NORM's NACK suppression mechanism, combined with its FEC mechanism, allows NORM multicast groups to scale to very large group sizes while maintaining reliability."
large_corpus_distillation
and success in such courses. The use of information and communication technologies have been found to improve student attitudes towards learning.By incorporating information technology into class projects, communication between lecturers and part-time students has improved, and students were able to better evaluate the...
large_corpus_distillation
"Program evaluation and review technique-Implementation-The ES for f is 10.33. The duration (4.5 work days) is added to the ES to get an EF of 14.83.\nThe ES for g is 14.34. The duration (5.17 work days) is added to the ES to get an EF of 19.51."
large_corpus_distillation
"Resistance distance-Definition-On a graph G, the resistance distance \u03a9i,j between two vertices vi and vj is := \u0393i,i+\u0393j,j\u2212\u0393i,j\u2212\u0393j,i, where \u0393=(L+1|V|\u03a6)+, with + denoting the Moore\u2013Penrose inverse, L the Laplacian matrix of G, |V| is the number of vertices in G, and \u03...
large_corpus_distillation
counterexample from Bondarenko's construction, giving the best bound up to now.Apart from finding the minimum number n of dimensions such that the number of pieces \u03b1(n) > n + 1, mathematicians are interested in finding the general behavior of the function \u03b1(n). Kahn and Kalai show that in general (that is, fo...
large_corpus_distillation
"Knuth's Algorithm X-Knuth's Algorithm X-Algorithm X works as follows: The nondeterministic choice of r means that the algorithm recurses over independent subalgorithms; each subalgorithm inherits the current matrix A, but reduces it with respect to a different row r.\nIf column c is entirely zero, there are no subalgo...
large_corpus_distillation
"Semi-Thue system-Definition-A string rewriting system or semi-Thue system is a tuple (\u03a3,R) where \u03a3 is an alphabet, usually assumed finite. The elements of the set \u03a3\u2217 (* is the Kleene star here) are finite (possibly empty) strings on \u03a3, sometimes called words in formal languages; we will sim...
large_corpus_distillation
"Rekursiv-Description-Microcode The processor's instruction set was stored in a dedicated area of static RAM known as the \"control store\". It was accessed via a dedicated 16-bit bus, organized as 16,384 words of 128-bits each. A separate \"control store map\" section of SRAM holds a numbered table of entry points int...
large_corpus_distillation
"Google Safe Browsing-Clients protected-Web browsers: Google Chrome, Safari, Firefox, Vivaldi, Brave and GNOME Web.\nAndroid: Google Play Protect, Verify Apps API Google Messages Google Search Google AdSense Gmail Instagram "
large_corpus_distillation