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"IEEE P1363-IEEE P1363-IEEE P1363 is an Institute of Electrical and Electronics Engineers (IEEE) standardization project for public-key cryptography. It includes specifications for: " | large_corpus_distillation |
"Polyphase merge sort-Ordinary merge sort-If there are only three working files, then an ordinary merge sort merges sorted runs from two working files onto a single working file, then distributes the runs evenly between the two output files. The merge iteration reduces run count by a factor of 2, the redistribute itera... | large_corpus_distillation |
"D\u00e9j\u00e0 vu-Explanations-Split perception explanation D\u00e9j\u00e0 vu may happen if a person experienced the current sensory experience twice successively. The first input experience is brief, degraded, occluded, or distracted. Immediately following that, the second perception might be familiar because the per... | large_corpus_distillation |
"Inversion (discrete mathematics)-Example: All permutations of four elements-The following sortable table shows the 24 permutations of four elements (in the \u03c0 column) with their place-based inversion sets (in the p-b column), inversion related vectors (in the v , l , and r columns), and inversion numbers (in t... | large_corpus_distillation |
"Multiple-vehicle collision-Korea-On Korean expressways, chain crashes represent 10.7% of crashes with injuries involving truck drivers. On Korean rural roads, chain crashes represent 0.6% of crashes with injuries involving truck drivers." | large_corpus_distillation |
"Clock rate-Research-Engineers continue to find new ways to design CPUs that settle a little more quickly or use slightly less energy per transition, pushing back those limits, producing new CPUs that can run at slightly higher clock rates. The ultimate limits to energy per transition are explored in reversible computi... | large_corpus_distillation |
"Multiplicative number theory-Scope-The distribution of primes numbers among residue classes modulo an integer is an area of active research. Dirichlet's theorem on primes in arithmetic progressions shows that there are an infinity of primes in each co-prime residue class, and the prime number theorem for arithmetic pr... | large_corpus_distillation |
1 2 is a sequence of independent, identically distributed random variables, and that is\nU \u03bb\u2208(0,\u221e) V =\u2211N U\nindependent of and has the Poisson distribution with parameter . Then i=1 i has a compound Poisson\ndistribution.\nBut in fact, compound Poisson variables usually do arise in the context of an... | large_corpus_distillation |
"Variable splitting-Details-This was first introduced by Kurt O. J\u00f6rnsten, Mikael N\u00e4sberg, Per A. Smeds in 1985. At the same time, M. Guignard and S. Kim introduced the same idea under the name Lagrangean Decomposition (their papers appeared in 1987). The original references are (1) Variable Splitting: A New... | large_corpus_distillation |
"String-searching algorithm-Overview-The most basic case of string searching involves one (often very long) string, sometimes called the haystack, and one (often very short) string, sometimes called the needle. The goal is to find one or more occurrences of the needle within the haystack. For example, one might search ... | large_corpus_distillation |
"Early stopping-Background-Regularization Regularization, in the context of machine learning, refers to the process of modifying a learning algorithm so as to prevent overfitting. This generally involves imposing some sort of smoothness constraint on the learned model." | large_corpus_distillation |
"Morpheme-Morpheme-These sample English words have the following morphological analyses: \"Unbreakable\" is composed of three morphemes: un- (a bound morpheme signifying \"not\"), break (the root, a free morpheme), and -able (a bound morpheme signifying \"an ability to be done\").\nThe plural morpheme for regular nouns... | large_corpus_distillation |
every r in R gives rise to a morphism of A: right multiplication by r. It is in fact true that this association of any element of R, to a morphism of A, as a function from R to EndR(A), is an isomorphism of rings. In this sense, therefore, any ring can be viewed as the endomorphism ring of some abelian X-group (by X-gr... | large_corpus_distillation |
"Email filtering-Email filtering-Email filtering is the processing of email to organize it according to specified criteria. The term can apply to the intervention of human intelligence, but most often refers to the automatic processing of messages at an SMTP server, possibly applying anti-spam techniques. Filtering can... | large_corpus_distillation |
"Network Information Service-Successor technologies-Sun introduced NIS+ as part of Solaris 2 in 1992, with the intention for it to eventually supersede NIS. NIS+ features much stronger security and authentication features, as well as a hierarchical design intended to provide greater scalability and flexibility. However... | large_corpus_distillation |
"Patience sorting-Overview-Analysis The first phase of patience sort, the card game simulation, can be implemented to take O(n log n) comparisons in the worst case for an n-element input array: there will be at most n piles, and by construction, the top cards of the piles form an increasing sequence from left to right,... | large_corpus_distillation |
"Honorifics (linguistics)-Other examples of honorifics-Pohnpeian In Pohnpeian, honorific speech is especially important when interacting with chiefs and during Christian church services. Even radio announcements use honorifics, specifically bystander honorifics, because a chief or someone of higher status could potenti... | large_corpus_distillation |
"Delay insensitive circuit-Delay insensitive circuit-The Delay-Insensitive (DI) class is the most robust of all asynchronous circuit delay models. It makes no assumptions on the delay of wires or gates. In this model all transitions on gates or wires must be acknowledged before transitioning again. This condition stops... | large_corpus_distillation |
"Speedrunning-Cheating-Modifying the timer or playback speed Modifying game timers, especially on computer games, is another common method to improve one's recorded times. However, this is a very noticeable manipulation, especially in highly competitive areas, since the speedruns in the upper area of leaderboards are r... | large_corpus_distillation |
"Assortativity-Measurement-Respectively, local assortativity for directed networks is a node's contribution to the directed assortativity of a network. A node's contribution to the assortativity of a directed network rd is defined as, \u03c1d=jout2(k\u00afin\u2212\u03bcqin)+jin2(k\u00afout\u2212\u03bcqout)2M\u03c3qin\... | large_corpus_distillation |
"Demand paging-Advantages-Demand paging, as opposed to loading all pages immediately: Only loads pages that are demanded by the executing process.\nAs there is more space in main memory, more processes can be loaded, reducing the context switching time, which utilizes large amounts of resources.\nLess loading latency o... | large_corpus_distillation |
"Parity of a permutation-Example-There are many other ways of writing \u03c3 as a composition of transpositions, for instance \u03c3 = (1 5)(3 4)(2 4)(1 2)(2 3),but it is impossible to write it as a product of an even number of transpositions." | large_corpus_distillation |
"Completely Fair Scheduler-History-(Task groups are tied to sessions created via the setsid() system call.) This solved the problem of slow interactive response times on multi-core and multi-CPU (SMP) systems when they were performing other tasks that use many CPU-intensive threads in those tasks. A simple explanation ... | large_corpus_distillation |
"HMAC-based one-time password-Algorithm-The recommendation is made that persistent throttling of HOTP value verification take place, to address their relatively small size and thus vulnerability to brute-force attacks. It is suggested that verification be locked out after a small number of failed attempts or that each ... | large_corpus_distillation |
"SPEKE-Description-In general, SPEKE can use any prime order group that is suitable for public key cryptography, including elliptic-curve cryptography. However, when SPEKE is realized by using Elliptic-curve cryptography, the protocol is essentially changed by requiring an additional primitive that must securely map a ... | large_corpus_distillation |
"Peano kernel theorem-Peano kernel theorem-In numerical analysis, the Peano kernel theorem is a general result on error bounds for a wide class of numerical approximations (such as numerical quadratures), defined in terms of linear functionals. It is attributed to Giuseppe Peano." | large_corpus_distillation |
"Consensus (computer science)-Models of computation-The FLP impossibility result for asynchronous deterministic consensus In a fully asynchronous message-passing distributed system, in which at least one process may have a crash failure, it has been proven in the famous 1985 FLP impossibility result by Fischer, Lynch a... | large_corpus_distillation |
holds true if Eij are generators of the universal enveloping algebra of Lie algebra gln, or its images in any representation.\nFor example, one can take Eij=xi\u2202\u2202xj;Eij=\u2211a=1nxia\u2202\u2202xja;Eij=\u03c8i\u2202\u2202\u03c8j.\nHere \u03c8 are Grassmann variables.\nObservation. zn\u22121detcol(d/dz\u2212E/... | large_corpus_distillation |
"Kind (type theory)-Kind (type theory)-A kind is sometimes confusingly described as the \"type of a (data) type\", but it is actually more of an arity specifier. Syntactically, it is natural to consider polymorphic types to be type constructors, thus non-polymorphic types to be nullary type constructors. But all nullar... | large_corpus_distillation |
number of matrices to t/D and the same for the preprocessing time P=N/D . The realtime required for the attack is T=(t/D)\u22c5t\u22c5D=t2 which is the product of the number of matrices, length of each iteration and number of available data points at attack time." | large_corpus_distillation |
"Cold start (recommender systems)-Mitigation strategies-One example of this approaches is called attribute to feature mapping which is tailored to matrix factorization algorithms. The basic idea is the following. A matrix factorization model represents the user-item interactions as the product of two rectangular matric... | large_corpus_distillation |
"Base-orderable matroid-Completeness-The class of base-orderable matroids is complete. This means that it is closed under the operations of minors, duals, direct sums, truncations, and induction by directed graphs.:\u200a2\u200a It is also closed under restriction, union and truncation.:\u200a410\u200aThe same is true ... | large_corpus_distillation |
the x and y data.\nThe sample covariance is defined to be\n1 n\ns(x,y)= \u2211[x \u2212m(x)][y \u2212m(y)] (6.7.3)\nn\u22121 i i\ni=1\nAssuming that the data vectors are not constant, so that the standard deviations are positive, the sample correlation is defined to be\ns(x,y)\nr(x,y)= (6.7.4)\ns(x)s(y)\nNote that the ... | large_corpus_distillation |
"Unavoidable pattern-Definitions-k -avoidable / k -unavoidable A pattern p is k -avoidable if p is avoidable on an alphabet \u03a3 of size k . Otherwise, p is k -unavoidable, which means p is unavoidable on every alphabet of size k .If pattern p is k -avoidable, then p is g -avoidable for all g\u2265k Gi... | large_corpus_distillation |
"Byzantine fault-Formal definition-Setting: Given a system of n components, t of which are dishonest, and assuming only point-to-point channels between all the components.\nWhenever a component A tries to broadcast a value x, the other components are allowed to discuss with each other and verify the consistency of A's ... | large_corpus_distillation |
"Chan's algorithm-Implementation-Chan's paper contains several suggestions that may improve the practical performance of the algorithm, for example: When computing the convex hulls of the subsets, eliminate the points that are not in the convex hull from consideration in subsequent executions.\nThe convex hulls of larg... | large_corpus_distillation |
using the following formula:\nX\u2212\u03bc\nZ= (17)\n\u03c3\nX\nTransforming a variable in this way is called \"standardizing\" the variable. It should be kept in mind that if is not normally\ndistributed then the transformed variable will not be normally distributed either.\nStandardize / Standard Score\n0 1 X\nA var... | large_corpus_distillation |
values are generally calculated from a protein structure, for example with the software DSSP. However, there is also an extensive literature attempting to predict RSA values from sequence data, using machine-learning approaches." | large_corpus_distillation |
some degree of inflection sometimes occurs; for example Latin has distinct active and passive infinitives." | large_corpus_distillation |
"Database caching-Potential design elements-Multiple cache granularity - Database level, Table level and Result-set caching: Major portions of corporate databases are historical and infrequently accessed. But, there is some information that should be instantly accessible like premium customer's data, etc.\nRecovery for... | large_corpus_distillation |
"Bag-of-words model-n-gram model-The Bag-of-words model is an orderless document representation \u2014 only the counts of words matter. For instance, in the above example \"John likes to watch movies. Mary likes movies too\", the bag-of-words representation will not reveal that the verb \"likes\" always follows a perso... | large_corpus_distillation |
"Sorites paradox-Proposed resolutions-Luce defined semi-orders and investigated their mathematical properties;Amartya Sen performed a similar task for quasitransitive relations.\nAbbreviating \"Peggy likes cx more than cy\" as \"cx > cy\", and abbreviating \"cx > cy or cx \u2248 cy\" by \"cx \u2265 cy\", it is reasonab... | large_corpus_distillation |
"Indexed grammar-Linear indexed grammars-Example Letting \u03c3 denote an arbitrary sequence of stack symbols, we can define a grammar for the language L = {an bn cn | n \u2265 1 } as To derive the string abc we have the steps: S[] \u21d2 aS[f]c \u21d2 aT[f]c \u21d2 aT[]bc \u21d2 abcSimilarly: S[] \u21d2 aS[f]c \u21d2 ... | large_corpus_distillation |
"Structure and Interpretation of Computer Programs-Content-Topics in the books are: Chapter 1: Building Abstractions with Procedures The Elements of Programming Procedures and the Processes They Generate Formulating Abstractions with Higher-Order Procedures Chapter 2: Building Abstractions with Data Introduction to Dat... | large_corpus_distillation |
"Signals intelligence in modern history-World War II-Messages were sent to and fro across the Atlantic by enciphered teleprinter links.\nSIGINT played a most important role for the Royal Navy, in its protection of merchant ships during the Battle of the Atlantic. While Ultra cryptanalysis certainly played a role in dea... | large_corpus_distillation |
"Control-flow graph-Reachability-Reachability is a graph property useful in optimization.\nIf a subgraph is not connected from the subgraph containing the entry block, that subgraph is unreachable during any execution, and so is unreachable code; under normal conditions it can be safely removed.\nIf the exit block is u... | large_corpus_distillation |
"Cumulative quantities (logistics)-Counting points-Target-actual-control-loop uses exactly defined counting points that demarcate the next-following intervals along the supply chain. The cumulative differences of next-following counting points show the quantities of material items which traverse the Interval and theref... | large_corpus_distillation |
"Secure Shell-Architecture-publickey: a method for public-key-based authentication, usually supporting at least DSA, ECDSA or RSA keypairs, with other implementations also supporting X.509 certificates." | large_corpus_distillation |
"TestOps-TestOps Features-Enhanced test planning \u2014 Automation is not effective if the entire codebase has to get tested every time a line of code is changed. TestOps provides a centralized platform that makes it easier for testers and developers to plan what tests to write, as well as identify what tests to run an... | large_corpus_distillation |
file read operations.\nAutomatic connection of program header files to command line names program copy(source, destination);var source, destination: text; c: char;begin reset(source); rewrite(destination); while not eof(source) do begin while not eoln(source) do begin read(source, c); write(destination, c) end; readln(... | large_corpus_distillation |
"Testing high-performance computing applications-Verification strategies-Test calculations Input is given to the system to generate a known result. This input-result pair can be obtained from previous empirical results and/or manual calculations. This is a system-level test that can be performed only when all relevant ... | large_corpus_distillation |
the heads of state of 125 countries and 139 other leading politicians have Twitter accounts that have between them sent more than 350,000 tweets and have almost 52 million followers. However, only 30 of these do their own tweeting, more than 80 do not subscribe to other politicians and many do not follow any accounts." | large_corpus_distillation |
"Draft horse showing-Types of classes-Unicorn\u2014Three horses hitched as a team with one horse in front of the team, driven by a man or woman Four\u2014Four horses hitched as two teams, one pair in front of the other, driven by a man or woman Six [1]\u2014Six horses hitched as three teams, one in front of another, dr... | large_corpus_distillation |
"Skewness-Other measures of skewness-A more general formulation of a skewness function was described by Groeneveld, R. A. and Meeden, G. (1984): \u03b3(u)=Q(u)+Q(1\u2212u)\u22122Q(1/2)Q(u)\u2212Q(1\u2212u) The function \u03b3(u) satisfies \u22121 \u2264 \u03b3(u) \u2264 1 and is well defined without requiring the exist... | large_corpus_distillation |
in a serialization format of the Resource Description Framework (RDF) and have relevance for Semantic Web and linked data content. This use of the 303 HTTP status code is conformant with the http-range-14 finding of the Technical Architecture Group of the World Wide Web Consortium." | large_corpus_distillation |
"Musical syntax-Comparison to linguistic syntax-Linguistic syntax \u2013 three principles Linguistic syntax is especially marked by its structural richness, which becomes apparent in its multi layered organization as well as in the strong relationship between syntax and meaning. That is that there are special linguisti... | large_corpus_distillation |
Entscheidungsproblem ('decision problem').When Turing returned to the UK he ultimately became jointly responsible for breaking the German secret codes created by encryption machines called \"The Enigma\"; he also became involved in the design of the ACE (Automatic Computing Engine), \"[Turing's] ACE proposal was effect... | large_corpus_distillation |
"Read-copy-update-Detailed description-A key property of RCU is that readers can access a data structure even when it is in the process of being updated: RCU updaters cannot block readers or force them to retry their accesses. This overview starts by showing how data can be safely inserted into and deleted from linked ... | large_corpus_distillation |
"Hutchinson metric-Formal definition-Consider only nonempty, compact, and finite metric spaces. For such a space X , let P(X) denote the space of Borel probability measures on X , with \u03b4:X\u2192P(X) the embedding associating to x\u2208X the point measure \u03b4x . The support |\u03bc| of a measure in P(X) i... | large_corpus_distillation |
"Library classification-Description-Library classification is an important and crucial aspect in library and information science. It is distinct from scientific classification in that it has as its goal to provide a useful ordering of documents rather than a theoretical organization of knowledge. Although it has the pr... | large_corpus_distillation |
"Fixed-point arithmetic-Operations-Addition and subtraction To add or subtract two values with the same implicit scaling factor, it is sufficient to add or subtract the underlying integers; the result will have their common implicit scaling factor, can thus can be stored in the same program variables as the operands. T... | large_corpus_distillation |
"Multihull-Multihull types-Catamaran (double-hull) A catamaran is a vessel with twin hulls. Commercial catamarans began in 17th century England. Separate attempts at steam-powered catamarans were carried out by the middle of the 20th century. However, success required better materials and more developed hydrodynamic te... | large_corpus_distillation |
"ND812-Programming facilities-/ /Input and store values for A & B *200 Start, TIF /Clear TTY flag JPS Input /Get value for A STJ A JPS Input /Get value for B STJ B / /Determine which of the two values is larger LDJ A SBJ B /Subtract B from A SIP J /Test for A positive JMP BRAN /No! B > A LDJ ABCST /Yes! A > B SKIP /Ski... | large_corpus_distillation |
as m bit elements 0 or 1 of GF(2m), and there will be m primitive factors of degree n, any of which can be used as the reducing polynomial for GF((2m)n). Mapping to a composite field can be generalized to map GF(pk) to a composite field such as GF((pm)n), for p any prime." | large_corpus_distillation |
"Vitali\u2013Hahn\u2013Saks theorem-Preliminaries-Proof: Let Then This means that the metric space B0~ can be identified with a subset of the Banach space L1(S,B,m) Let Bn\u2208B0 , with Then we can choose a sub-sequence \u03c7Bn\u2032 such that lim n\u2032\u2192\u221e\u03c7Bn\u2032(x)=\u03c7(x) exists almost eve... | large_corpus_distillation |
"Concurrent data structure-Basic principles-Safety properties usually state that something bad never happens, while liveness properties state that something good keeps happening.\nThese properties can be expressed, for example, using Linear Temporal Logic.\nThe type of liveness requirements tend to define the data stru... | large_corpus_distillation |
"Binary relation-Sets versus classes-In most mathematical contexts, references to the relations of equality, membership and subset are harmless because they can be understood implicitly to be restricted to some set in the context. The usual work-around to this problem is to select a \"large enough\" set A, that contain... | large_corpus_distillation |
"Co-NP-complete-Co-NP-complete-In complexity theory, computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that any problem in co-NP can be reformulated as a special case of any co-NP-complete problem with only polynomial overhead. If P is different from co-NP, th... | large_corpus_distillation |
"Modular multiplicative inverse-Modular multiplicative inverse-Finding modular multiplicative inverses also has practical applications in the field of cryptography, i.e. public-key cryptography and the RSA algorithm. A benefit for the computer implementation of these applications is that there exists a very fast algori... | large_corpus_distillation |
"FIFO (computing and electronics)-FIFO (computing and electronics)-In computing and in systems theory, first in, first out (the first in is the first out), acronymized as FIFO, is a method for organizing the manipulation of a data structure (often, specifically a data buffer) where the oldest (first) entry, or \"head\"... | large_corpus_distillation |
"Transistor tester-Types of tester-Laboratory-standard transistor tester or Analyser This type of tester is used for measuring transistor parameters dynamically under various operating conditions. The readings they give are absolute. Among the important characteristics measured are: Icbo collector current with emitter ... | large_corpus_distillation |
The term \"softmax\" derives from the amplifying effects of the exponential on any maxima in the input vector. For example, the standard softmax of (1,2,8) is approximately 0.001 0.002 0.997 ) , which amounts to assigning almost all of the total unit weight in the result to the position of the vector's maximal elemen... | large_corpus_distillation |
"Computational hardness assumption-Non-cryptographic hardness assumptions-Small Set Expansion Closely related to the Unique Label Cover problem is the Small Set Expansion (SSE) problem: Given a graph G=(V,E) , find a small set of vertices (of size log \u2061(n) ) whose edge expansion is minimal. It is known that if ... | large_corpus_distillation |
"Bias\u2013variance tradeoff-Motivation-The bias\u2013variance tradeoff is a central problem in supervised learning. Ideally, one wants to choose a model that both accurately captures the regularities in its training data, but also generalizes well to unseen data. Unfortunately, it is typically impossible to do both si... | large_corpus_distillation |
"Double-checked locking-Usage in C++11-For the singleton pattern, double-checked locking is not needed: If control enters the declaration concurrently while the variable is being initialized, the concurrent execution shall wait for completion of the initialization." | large_corpus_distillation |
"Structured English-Elements-Advanced English Structure is a limited-form \"pseudocode\" and consists of the following elements: Operation statements written as English phrases executed from the top down Conditional blocks indicated by keywords such as IF, THEN, and ELSE Repetition blocks indicated by keywords such as ... | large_corpus_distillation |
"\uf303 Definition: Total Differential\nLet z=f(x,y) be a function of two variables with (x 0 ,y 0 ) in the domain of f, and let \u0394x and \u0394y be chosen so that\n(x 0 +\u0394x,y 0 +\u0394y) is also in the domain of f. If f is differentiable at the point (x 0 ,y 0 ), then the differentials dx and dy are\ndefined a... | large_corpus_distillation |
"HITS algorithm-In detail-To begin the ranking, we let auth(p)=1 and hub(p)=1 for each page p . We consider two types of updates: Authority Update Rule and Hub Update Rule. In order to calculate the hub/authority scores of each node, repeated iterations of the Authority Update Rule and the Hub Update Rule are applie... | large_corpus_distillation |
"K-nearest neighbors algorithm-Dimension reduction-For high-dimensional data (e.g., with number of dimensions more than 10) dimension reduction is usually performed prior to applying the k-NN algorithm in order to avoid the effects of the curse of dimensionality.The curse of dimensionality in the k-NN context basically... | large_corpus_distillation |
"Incidence matrix-Graph theory-The incidence matrix of a directed graph is a n\u00d7m matrix B where n and m are the number of vertices and edges respectively, such that if edge leaves vertex if edge enters vertex otherwise." | large_corpus_distillation |
"Sigil (computer programming)-Sigil use in some languages-In CLIPS, scalar variables are prefixed with a \"?\" sigil, while multifield (e.g., a 1-level list) variables are prefixed with \"$?\".\nIn Common Lisp, special variables (with dynamic scope) are typically surrounded with * in what is called the \"earmuff conven... | large_corpus_distillation |
"Intel Core (microarchitecture)-Processor cores-Penryn/Wolfdale (45 nm) In Intel's Tick-Tock cycle, the 2007/2008 \"Tick\" was the shrink of the Core microarchitecture to 45 nanometers as CPUID model 23. In Core 2 processors, it is used with the code names Penryn (Socket P), Wolfdale (LGA 775) and Yorkfield (MCM, LGA 7... | large_corpus_distillation |
"Uncertainty quantification-Sources-Structural uncertainty Also known as model inadequacy, model bias, or model discrepancy, this comes from the lack of knowledge of the underlying physics in the problem. It depends on how accurately a mathematical model describes the true system for a real-life situation, considering ... | large_corpus_distillation |
"Late-life mortality deceleration-History-A brief historical review is given in Gavrilov & Gavrilova (2011, 2. Mortality at Advanced Ages: A Historical Review (pp. 433\u2013435)); a detailed survey is given in Olshansky (1998)." | large_corpus_distillation |
"Correlation-Other measures of dependence among random variables-The correlation ratio, entropy-based mutual information, total correlation, dual total correlation and polychoric correlation are all also capable of detecting more general dependencies, as is consideration of the copula between them, while the coefficien... | large_corpus_distillation |
"Ring theory-Ring theory-In algebra, ring theory is the study of rings\u2014algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, module... | large_corpus_distillation |
displacement vector with respect to the material coordinates yields the material displacement gradient tensor \u2207Xu. Thus we have: or where F is the deformation gradient tensor." | large_corpus_distillation |
"Quantities of information-Entropy-The entropy of a discrete message space M is a measure of the amount of uncertainty one has about which message will be chosen. It is defined as the average self-information of a message m from that message space: log \u2061p(m).\nwhere E[\u2212] denotes the expected value operation... | large_corpus_distillation |
"Fibonacci heap-Implementation of operations-Operation extract minimum (same as delete minimum) operates in three phases. First we take the root containing the minimum element and remove it. Its children will become roots of new trees. If the number of children was d, it takes time O(d) to process all new roots and the... | large_corpus_distillation |
"Phone hacking-Victims of phone hacking-Although any mobile phone users may be targeted, \"for those who are famous, rich or powerful or whose prize is important enough (for whatever reason) to devote time and resources to make a concerted attack, it is usually more common, there are real risks to face.\" " | large_corpus_distillation |
"Cross-validation (statistics)-Using prior information-When users apply cross-validation to select a good configuration \u03bb , then they might want to balance the cross-validated choice with their own estimate of the configuration. In this way, they can attempt to counter the volatility of cross-validation when the ... | large_corpus_distillation |
"6.867 Machine learning, lecture 10 (Jaakkola) 6\nIn many cases we cannot normalize this distribution, however. Suppose, as an extreme\nexample, that we have no data. The likelihood function in this case is just one for all\nthe parameter values. As a result the \u201cposterior\u201d after seeing no data is not well de... | large_corpus_distillation |
"Stabilizer code-Mathematical background-The stabilizer formalism exploits elements of the Pauli group \u03a0 in formulating quantum error-correcting codes. The set \u03a0={I,X,Y,Z} consists of the Pauli operators: I\u2261[1001],X\u2261[0110],Y\u2261[0\u2212ii0],Z\u2261[100\u22121].\nThe above operators act on a singl... | large_corpus_distillation |
in component form,\n\u21c0v=\u27e8x \u2212x ,y \u2212y \u27e9=\u27e81\u2212(\u22123),2\u22124\u27e9=\u27e84,\u22122\u27e9.\nt i t i\n\uf128 Exercise 12.1.4\nVector w\u21c0 has initial point (\u22124,\u22125) and terminal point (\u22121,2). Express w\u21c0 in component form.\nHint\nYou may use either geometric or algebr... | large_corpus_distillation |
"P-value-Example-In the above example: Null hypothesis (H0): The coin is fair, with Pr(heads) = 0.5 Test statistic: Number of heads Alpha level (designated threshold of significance): 0.05 Observation O: 14 heads out of 20 flips; and Two-tailed p-value of observation O given H0 = 2 \u00d7 min(Pr(no. of heads \u2265 14 ... | large_corpus_distillation |
"Probability space-Related concepts-Probability distribution Any probability distribution defines a probability measure.\nRandom variables A random variable X is a measurable function X: \u03a9 \u2192 S from the sample space \u03a9 to another measurable space S called the state space." | large_corpus_distillation |
"12 (number)-Mathematical properties-12 is the sixth composite number and the superfactorial of 3. It is the fourth pronic number (equal to 3 \u00d7 4), whose digits in decimal are also successive. It is the smallest abundant number, since it is the smallest integer for which the sum of its proper divisors (1 + 2 + 3 +... | large_corpus_distillation |
"Universal Character Set characters-Types of code point-Isolated surrogate code points have no general interpretation; consequently, no character code charts or names lists are provided for this range. In the Python programming language, individual surrogate codes are used to embed undecodable bytes in Unicode strings.... | large_corpus_distillation |
variable techniques are commonly used to address this problem.\nFull rank The sample data matrix X must have full column rank.\nrank \u2061(X)=k Otherwise X\u2032X is not invertible and the OLS estimator cannot be computed." | large_corpus_distillation |
actually measure a voltage. The accuracy of the measurement will, however, depend on the sensitivity of the instrument since this will affect the resolution of the bridge." | large_corpus_distillation |
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