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density function for if and only if has the form\nf(x)=\u2211p f (x), x\u2208S (16.6.22)\ni i\ni\u2208I\n(p :i\u2208I) I f(x)=p f (x) i\u2208I x\u2208A\nwhere i is a probability density function on the index set . That is, i i for and i, and\nf(x)=0\notherwise.\nProof\nA=\u22c3 A f f(x)=0\nLet i\u2208I i, the set of po... | large_corpus_distillation |
atomically. In Haskell, locking is accomplished with MVars: Using such procedures will ensure that money will never be lost or gained due to improper interleaving of reads and writes to any individual account. However, if one tries to compose them together to create a procedure like transfer: a race condition still exi... | large_corpus_distillation |
"IA-64-History-Itanium 2: 2002\u20132010 The Itanium 2 processor was released in 2002. It relieved many of the performance problems of the original Itanium processor, which were mostly caused by an inefficient memory subsystem." | large_corpus_distillation |
"Map-Design-The design and production of maps is a craft that has developed over thousands of years, from clay tablets to Geographic information systems. As a form of Design, particularly closely related to Graphic design, map making incorporates scientific knowledge about how maps are used, integrated with principles ... | large_corpus_distillation |
"Church encoding-Church numerals-Starting with 0 not applying the function at all, proceed with 1 applying the function once, 2 applying the function twice, 3 applying the function three times, etc.: Number Function definition Lambda expression 00fx=x0=\u03bbf.\u03bbx.x11fx=fx1=\u03bbf.\u03bbx.fx22fx=f(fx)2=\u03bbf.\u0... | large_corpus_distillation |
law and associative law: Commutative law for OR: ( a \u2228 b ) \u2261 ( b \u2228 a ) Commutative law for AND: ( a & b ) \u2261 ( b & a ) Associative law for OR: (( a \u2228 b ) \u2228 c ) \u2261 ( a \u2228 (b \u2228 c) ) Associative law for AND: (( a & b ) & c ) \u2261 ( a & (b & c) )Omitting parentheses in strings of... | large_corpus_distillation |
"Root (linguistics)-Root (linguistics)-Content words in nearly all languages contain, and may consist only of, root morphemes. However, sometimes the term \"root\" is also used to describe the word without its inflectional endings, but with its lexical endings in place. For example, chatters has the inflectional root o... | large_corpus_distillation |
"Automatic vehicle location-Applications-Automatic vehicle locating is a powerful tool for managing fleets of vehicles such as service vehicles, emergency vehicles, and public transport vehicles such as buses and trains. It is also used to track mobile assets, such as non wheeled construction equipment, non motorized t... | large_corpus_distillation |
"Random self-reducibility-Examples-If we do so, we run the risk of being wrong 1/3 of the time, but by picking multiple random Xs and repeating the above procedure many times, and only providing the majority winner as an answer, we can drive the error rate down very low." | large_corpus_distillation |
the same is true for all the period p points, for any integer p." | large_corpus_distillation |
in a mathematically sound and coherent way\". He stresses out that \"one significant goal of a geometry course is to teach logic, and this program fails on that account\".Overall, the \"unacceptable nature of geometry\" and the fashion in which the program downplays \"algebraic structure and skills\" make the Core-Plus... | large_corpus_distillation |
"Joint spectral radius-Related notions-The Lyapunov exponent of the set of matrices characterizes the rate of growth of the geometric average." | large_corpus_distillation |
"Algorithmically random sequence-Properties and examples of Martin-L\u00f6f random sequences-There is a random sequence which is \u039420 , that is, computable relative to an oracle for the Halting problem. (Schnorr 1971) Chaitin's \u03a9 is an example of such a sequence.\nNo random sequence is decidable, computably e... | large_corpus_distillation |
"Symmetric derivative-Generalizations-The second symmetric derivative The second symmetric derivative is defined as:\u200a1\u200a If the (usual) second derivative exists, then the second symmetric derivative exists and is equal to it. The second symmetric derivative may exist, however, even when the (ordinary) second d... | large_corpus_distillation |
3 (mod 4) then \u22121 is a nonresidue modulo p. This implies the following: If p \u2261 1 (mod 4) the negative of a residue modulo p is a residue and the negative of a nonresidue is a nonresidue." | large_corpus_distillation |
"Exchange operator-Construction-In three or higher dimensions, the exchange operator can represent a literal exchange of the positions of the pair of particles by motion of the particles in an adiabatic process, with all other particles held fixed. Such motion is often not carried out in practice. Rather, the operation... | large_corpus_distillation |
"Heapsort-Algorithm-procedure heapify(a,count) is (end is assigned the index of the first (left) child of the root) end := 1 while end < count (sift up the node at index end to the proper place such that all nodes above the end index are in heap order) siftUp(a, 0, end) end := end + 1 (after sifting up the last node al... | large_corpus_distillation |
"Huffman coding-Problem definition-In general, a Huffman code need not be unique. Thus the set of Huffman codes for a given probability distribution is a non-empty subset of the codes minimizing L(C) for that probability distribution. (However, for each minimizing codeword length assignment, there exists at least one ... | large_corpus_distillation |
random variables in which each variable is conditioned on only a small number of other variables, as is the case in most typical hierarchical models. The individual variables are then sampled one at a time, with each variable conditioned on the most recent values of all the others. Various algorithms can be used to cho... | large_corpus_distillation |
checked at least once.From its inception until 2018, the project relied primarily on the Lucas\u2013Lehmer primality test as it is an algorithm that is both specialized for testing Mersenne primes and particularly efficient on binary computer architectures. Before applying it to a given Mersenne number, there was a tri... | large_corpus_distillation |
down, participants would encourage themselves and ultimately cultivate hope in upcoming exams. As a result of this, those who journaled immediately before these tests reported a lower amount of anxiety, and a better test result." | large_corpus_distillation |
"Multiplicative weight update method-Algorithm analysis-The very first algorithm that makes choice based on majority vote every iteration does not work since the majority of the experts can be wrong consistently every time. The weighted majority algorithm corrects above trivial algorithm by keeping a weight of experts ... | large_corpus_distillation |
by assuming the identity of another principal that has the appropriate authorizations.\nMessage stream modification \u2013 Protection against messages getting maliciously re-ordered, delayed, or replayed to affect unauthorized management operations.\nDisclosure \u2013 Protection against eavesdropping on the exchanges b... | large_corpus_distillation |
execution; the Pentium Pro and AMD K5 are early examples of this. It allows a fairly simple superscalar design to be located after the (fairly complex) decoders (and buffers), giving, so to speak, the best of both worlds in many respects. This technique is also used in IBM z196 and later z/Architecture microprocessors.... | large_corpus_distillation |
"Snowball sampling-Advantages and disadvantages-Lack of control over sampling method: As the subjects locate the hidden population, the research has very little control over the sampling method, which becomes mainly dependent on the original and subsequent subjects, who may add to the known sampling pool using a method... | large_corpus_distillation |
"Restricted randomization-Split-plot designs-In many industrial experiments, three situations often occur: some of the factors of interest may be 'hard to vary' while the remaining factors are easy to vary. As a result, the order in which the treatment combinations for the experiment are run is determined by the orderi... | large_corpus_distillation |
Bronze (1864\u20131909). A list of all members of a Type Set are listed below." | large_corpus_distillation |
"UMTS-Air interfaces-Vodafone launched several UMTS networks in Europe in February 2004. MobileOne of Singapore commercially launched its 3G (W-CDMA) services in February 2005. New Zealand in August 2005 and Australia in October 2005.\nAT&T Mobility utilized a UMTS network, with HSPA+, from 2005 until its shutdown in F... | large_corpus_distillation |
"Trial division-Speed-In the worst case, trial division is a laborious algorithm. For a base-2 n digit number a, if it starts from two and works up only to the square root of a, the algorithm requires ln \u20612 trial divisions, where \u03c0(x) denotes the prime-counting function, the number of primes less than x. Thi... | large_corpus_distillation |
"Subtyping-Subtyping-In programming language theory, subtyping (also subtype polymorphism or inclusion polymorphism) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements, typically subroutine... | large_corpus_distillation |
"Definitive software library-Scope-records (metadata) are kept in a configuration management database about where the software is installed and deployed from the DML and into the production environment. Each installation or deployment should be authorised by a corresponding production change request and the resulting c... | large_corpus_distillation |
"Function composition (computer science)-First-class composition-Python In Python, a way to define the composition for any group of functions, is using reduce function (use functools.reduce in Python 3): JavaScript In JavaScript we can define it as a function which takes two functions f and g, and produces a function: ... | large_corpus_distillation |
"Computers are social actors-Attributes-Specialist versus generalist: When a technology is labeled as 'specialist', this triggers a mindless response by influencing people's perceptions of the content the labeled technology presents. For example, a 2000 study revealed when people watched a television labeled 'News Tele... | large_corpus_distillation |
as many classes and activities are crammed into each day." | large_corpus_distillation |
"Clique (graph theory)-Computer science-In computer science, the clique problem is the computational problem of finding a maximum clique, or all cliques, in a given graph. It is NP-complete, one of Karp's 21 NP-complete problems. It is also fixed-parameter intractable, and hard to approximate. Nevertheless, many algori... | large_corpus_distillation |
"Simplified Spelling Board-First 300 words-The board's initial list of 300 words was published on April 1, 1906. Much of the list included words ending with -ed changed to end -t (\"addressed\", \"caressed\", \"missed\", \"possessed\" and \"wished\", becoming \"addresst\", \"carest\", \"mist\", \"possest\" and \"wisht\... | large_corpus_distillation |
"Streaming media-Use by the general public-As of 2019 Spotify has over 207 million users in 78 countries, As of 2018 Apple Music has about 60 million, and SoundCloud has 175 million. All platforms provide varying degrees of accessibility. Apple Music and Prime Music only offer their services for paid subscribers, where... | large_corpus_distillation |
"CryptoGraf-CryptoGraf-CryptoGraf is a secure messaging application for smartphones running Symbian OS and Windows Mobile. It allows the user to compose and send SMS and MMS messages that are encrypted and digitally signed using methods that are based on the S/MIME standard. Secure e-mail messaging is not supported.\nT... | large_corpus_distillation |
would be overkill for the application from an engineering perspective." | large_corpus_distillation |
"Instruction pipelining-Concept and motivation-Number of steps The number of dependent steps varies with the machine architecture. For example: The 1956\u201361 IBM Stretch project proposed the terms Fetch, Decode, and Execute that have become common.\nThe classic RISC pipeline comprises: Instruction fetch Instruction ... | large_corpus_distillation |
"Model organism-Disease models-Animal models serving in research may have an existing, inbred or induced disease or injury that is similar to a human condition. These test conditions are often termed as animal models of disease. The use of animal models allows researchers to investigate disease states in ways which wou... | large_corpus_distillation |
"Sequential pattern mining-Sequential pattern mining-There are several key traditional computational problems addressed within this field. These include building efficient databases and indexes for sequence information, extracting the frequently occurring patterns, comparing sequences for similarity, and recovering mis... | large_corpus_distillation |
"Depth-first search-Complexity-The computational complexity of DFS was investigated by John Reif. More precisely, given a graph G , let O=(v1,\u2026,vn) be the ordering computed by the standard recursive DFS algorithm. This ordering is called the lexicographic depth-first search ordering. John Reif considered the com... | large_corpus_distillation |
"Simplex algorithm-Standard form-Third, each unrestricted variable is eliminated from the linear program. This can be done in two ways, one is by solving for the variable in one of the equations in which it appears and then eliminating the variable by substitution. The other is to replace the variable with the differen... | large_corpus_distillation |
"Physical configuration audit-Physical configuration audit-A physical configuration audit (PCA) is the formal examination of the \"as-built\" configuration of a configuration item against its technical documentation to establish or verify the configuration item's product baseline." | large_corpus_distillation |
"ID/LP grammar-ID/LP grammar-Current work in the Minimalist Program also attempts to distinguish between dominance and ordering. For instance, recent papers by Noam Chomsky have proposed that, while hierarchical structure is the result of the syntactic structure-building operation Merge, linear order is not determined ... | large_corpus_distillation |
"Uncontrolled format string-Details-Format bugs arise because C's argument passing conventions are not type-safe. In particular, the varargs mechanism allows functions to accept any number of arguments (e.g. printf) by \"popping\" as many arguments off the call stack as they wish, trusting the early arguments to indica... | large_corpus_distillation |
Talagrand's concentration inequality for product probability spaces). Data separability by classical linear discriminants simplifies the problem of error correction for artificial intelligence systems in high dimension." | large_corpus_distillation |
"Word-sense disambiguation-Difficulties-Most research in the field of WSD is performed by using WordNet as a reference sense inventory for English. WordNet is a computational lexicon that encodes concepts as synonym sets (e.g. the concept of car is encoded as { car, auto, automobile, machine, motorcar }). Other resourc... | large_corpus_distillation |
"AI-complete-Software brittleness-Current AI systems can solve very simple and/or restricted versions of AI-complete problems, but never in their full generality. When AI researchers attempt to \"scale up\" their systems to handle more complicated, real-world situations, the programs tend to become excessively brittle ... | large_corpus_distillation |
"P-adic number-Cardinality-Both Zp and Qp are uncountable and have the cardinality of the continuum. For Zp, this results from the p-adic representation, which defines a bijection of Zp on the power set {0,\u2026,p\u22121}N.\nFor Qp this results from its expression as a countably infinite union of copies of Zp :... | large_corpus_distillation |
a Mach-O loader, then you want to dump the sections to the defined RAM addresses plus a base address to keep applications spaced apart so they do not write over one another.\nThe segment names and section names can be renamed to anything you like and there link will be no problems locating the appropriate sections by s... | large_corpus_distillation |
"Permutation test-Method-For paired samples the paired permutation test needs to be applied." | large_corpus_distillation |
"RSA numbers-RSA-340-RSA-340 has 340 decimal digits (1,128 bits), and has not been factored so far.\nRSA-340 = 2690987062294695111996484658008361875931308730357496490239672429933215694995 2758588771223263308836649715112756731997946779608413232406934433532048898585 9176676580752231563884394807622076177586625973975236127... | large_corpus_distillation |
"Pointer analysis-Flow-Insensitive Approaches-Many flow-insensitive algorithms are specified in Datalog, including those in the Soot analysis framework for Java.Context-sensitive, flow-sensitive algorithms achieve higher precision, generally at the cost of some performance, by analyzing each procedure several times, on... | large_corpus_distillation |
"NumPy-Features-Limitations Inserting or appending entries to an array is not as trivially possible as it is with Python's lists.\nThe np.pad(...) routine to extend arrays actually creates new arrays of the desired shape and padding values, copies the given array into the new one and returns it.\nNumPy's np.concatenate... | large_corpus_distillation |
"Access Linux Platform-Base frameworks-Several components from ALP were released under the Mozilla Public License as The Hiker Project. These components addressed issues of application life-cycle, intertask communication, exchange and use of structured data, security, time and event-based notifications, and other areas... | large_corpus_distillation |
"Amiga Old File System-Amiga Old File System-On the Amiga, the Old File System was the filesystem for AmigaOS before the Amiga Fast File System. Even though it used 512-byte blocks, it reserved the first small portion of each block for metadata, leaving an actual data block capacity of 488 bytes per block. It wasn't ve... | large_corpus_distillation |
"Supervised learning-Steps to follow-To solve a given problem of supervised learning, one has to perform the following steps: Determine the type of training examples. Before doing anything else, the user should decide what kind of data is to be used as a training set. In the case of handwriting analysis, for example, t... | large_corpus_distillation |
"Honeywell ARGUS-Modes of Addressing Memory-Indexed Addressing This applies only to 8 registers, called index registers. It takes 3 bits to specify the index register and another 7 to specify an offset of 0 to 127. So the offset is added to a full-length main memory address. This is a powerful tool. It is helpful for p... | large_corpus_distillation |
"Samplesort-Algorithm-function sampleSort(A[1..n], k, p) // if average bucket size is below a threshold switch to e.g. quicksort if n / k < threshold then smallSort(A) /* Step 1 */ select S = [S1, ..., S(p\u22121)k] randomly from // select samples sort S // sort sample [s0, s1, ..., sp\u22121, sp] <- [-\u221e, Sk, S2k... | large_corpus_distillation |
"Analytic hierarchy process-Non-monotonicity of some weight extraction methods-Within a comparison matrix one may replace a judgement with a less favorable judgment and then check to see if the indication of the new priority becomes less favorable than the original priority. In the context of tournament matrices, it ha... | large_corpus_distillation |
"Funnel (concurrent computing)-Funnel (concurrent computing)-Because a funnel is automatically dropped when a thread blocks, care must be taken to ensure that synchronized resources are acquired again after any blocking operation. Specifically, acquiring a funnel can be a blocking operation, so if multiple funnels are ... | large_corpus_distillation |
"RDRAND-Security issues-Intel refers to the CrossTalk vulnerability as Special Register Buffer Data Sampling (SRBDS). In response to the research, Intel released microcode updates to mitigate the issue. The updated microcode ensures that off-core accesses are delayed until sensitive operations \u2013 specifically the R... | large_corpus_distillation |
gives very different\nresults from weighing to weighing. However, it is just as likely to underestimate as overestimate your weight. Sometimes it vastly\noverestimates it and sometimes it vastly underestimates it. However, the average of a large number of measurements would be your\n1 2\nactual weight. Scale is biased ... | large_corpus_distillation |
"Reference work-Reference book-In contrast to books that are loaned, a reference book or reference-only book in a library is one that may only be used in the library and may not be borrowed from the library. Many such books are reference works (in the first sense), which are, usually, used briefly or photocopied from, ... | large_corpus_distillation |
"K-graph C*-algebra-Examples-It can be shown that a 1-graph is precisely the path category of a directed graph.\nThe category Tk consisting of a single object and k commuting morphisms f1,...,fk , together with the map d:Tk\u2192Nk defined by d(f1n1...fknk)=(n1,\u2026,nk) is a k-graph.\nLet \u03a9k={(m,n):m,n\u220... | large_corpus_distillation |
"Stirling's approximation-Stirling's approximation-In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of n . It is named after James Stirling, though a related but less precise result was fir... | large_corpus_distillation |
"Behrens\u2013Fisher problem-Variants-A minor variant of the Behrens\u2013Fisher problem has been studied. In this instance the problem is, assuming that the two population-means are in fact the same, to make inferences about the common mean: for example, one could require a confidence interval for the common mean." | large_corpus_distillation |
"Arithmetic-Arithmetic operations-Multiplication is commutative and associative; further, it is distributive over addition and subtraction. The multiplicative identity is 1, since multiplying any number by 1 yields that same number. The multiplicative inverse for any number except 0 is the reciprocal of this number, be... | large_corpus_distillation |
"Bianconi\u2013Barab\u00e1si model-Algorithm-Preferential attachment The probability \u03a0i that a new node connects to one of the existing links to a node i in the network depends on the number of edges, ki , and on the fitness \u03b7i of node i , such that, \u03a0i=\u03b7iki\u2211j\u03b7jkj." | large_corpus_distillation |
p\u2208(0,\u221e) \u222b |f|pd\u03bc [0,\u221e] \u2225f\u2225\nSince is a nonnegative, measurable function for ,\nS\nexists in , and hence so does p. Clearly\n\u2225f\u2225 [0,\u221e] f b\u2208[0,\u221e] |f|\u2264b\n\u221e also exists in and is known as the essential supremum of . A number such that almost\nS f f\never... | large_corpus_distillation |
"Principal component analysis-Relation with other methods-Non-negative matrix factorization Non-negative matrix factorization (NMF) is a dimension reduction method where only non-negative elements in the matrices are used, which is therefore a promising method in astronomy, in the sense that astrophysical signals are n... | large_corpus_distillation |
"Hash table-Collision resolution-Other collision resolution techniques based on open addressing Coalesced hashing Coalesced hashing is a hybrid of both separate chaining and open addressing in which the buckets or nodes link within the table.:\u200a6\u20138\u200a The algorithm is ideally suited for fixed memory allocat... | large_corpus_distillation |
"Turbocharger-Turbo lag and boost threshold-The boost threshold causes delays in the power delivery at low rpm (since the unboosted engine must accelerate the vehicle to increase the rpm above the boost threshold), while turbo lag causes delay in the power delivery at higher rpm." | large_corpus_distillation |
"S L=L L \u22ef\nIn this discussion, we interpret as an alphabet, and we write the sequence of variables in concatenation form, 1 2\nS\nrather than standard sequence form. Thus the sequence is an infinite string of letters from our alphabet . We are interested in the\nfirst occurrence of a particular finite substring o... | large_corpus_distillation |
"Radio coloring-Computational complexity-Finding a radio coloring with a given (or minimum) span is NP-complete, even when restricted to planar graphs, split graphs, or the complements of bipartite graphs. However it is solvable in polynomial time for trees and cographs. For arbitrary graphs, it can be solved in singly... | large_corpus_distillation |
"Integrated Encryption Scheme-Formal description of ECIES-Bob's public key KB , which Bob generates it as follows: KB=kBG , where kB\u2208[1,n\u22121] is the private key he chooses at random.\nSome optional shared information: S1 and S2 O which denotes the point at infinity." | large_corpus_distillation |
"Anticommutative property-Anticommutative property-In mathematics, anticommutativity is a specific property of some non-commutative mathematical operations. Swapping the position of two arguments of an antisymmetric operation yields a result which is the inverse of the result with unswapped arguments. The notion invers... | large_corpus_distillation |
"Symbol of a differential operator-Properties of differential operators-Differentiation is linear, i.e.\nD(f+g)=(Df)+(Dg), D(af)=a(Df), where f and g are functions, and a is a constant.\nAny polynomial in D with function coefficients is also a differential operator. We may also compose differential operators by the rul... | large_corpus_distillation |
"Graphic matroid-Representation-If a set of edges contains a cycle, then the corresponding columns (multiplied by \u22121 if necessary to reorient the edges consistently around the cycle) sum to zero, and is not independent. Conversely, if a set of edges forms a forest, then by repeatedly removing leaves from this for... | large_corpus_distillation |
"SemEval-Semantic evaluation tasks-Senseval-1 & Senseval-2 focused on evaluation WSD systems on major languages that were available corpus and computerized dictionary. Senseval-3 looked beyond the lexemes and started to evaluate systems that looked into wider areas of semantics, such as Semantic Roles (technically know... | large_corpus_distillation |
"Adaptive quadrature-Adaptive quadrature-Adaptive quadrature is a numerical integration method in which the integral of a function f(x) is approximated using static quadrature rules on adaptively refined subintervals of the region of integration. Generally, adaptive algorithms are just as efficient and effective as tr... | large_corpus_distillation |
"86 (number)-In science-86 is the atomic number of radon.\nThere are 86 metals on the modern periodic table." | large_corpus_distillation |
g(\u03b8) , and that T is a complete sufficient statistic for the family of densities. Then \u03b7(X1,X2,\u2026,Xn)=E\u2061(\u03b4(X1,X2,\u2026,Xn)\u2223T) is the MVUE for g(\u03b8).\nA Bayesian analog is a Bayes estimator, particularly with minimum mean square error (MMSE)." | large_corpus_distillation |
"Postage stamp design error-Postage stamp design error-A postage stamp design error is a mistake made during the design phase of the postage stamp production process. Design errors most commonly occur as minor mistakes, such as a missing letter in the binomial name of an organism depicted on the stamp, but some have be... | large_corpus_distillation |
"Phase detector-Types-Digital phase detector A phase detector suitable for square wave signals can be made from an exclusive-OR (XOR) logic gate. When the two signals being compared are completely in-phase, the XOR gate's output will have a constant level of zero. When the two signals differ in phase by 1\u00b0, the XO... | large_corpus_distillation |
root mod 5, so if n \u2265 5, then either 5 divides x (in this case, x = 5, since x \u2208 {1, 5, 7, 11}) or |x \u2212 y| (in this case, either x = y = 1 (That is, the prime is a repunit) or x = 1, y = 11 or x = 11, y = 1, since x, y \u2208 {1, 5, 7, 11}.) or n is a multiple of 5 \u2212 1 = 4. Similarly, since 12 is a ... | large_corpus_distillation |
"Speed of light-Practical effects of finiteness-Small scales In computers, the speed of light imposes a limit on how quickly data can be sent between processors. If a processor operates at 1 gigahertz, a signal can travel only a maximum of about 30 centimetres (1 ft) in a single clock cycle \u2014 in practice, this dis... | large_corpus_distillation |
"Real-time operating system-Scheduling-The critical response time, sometimes called the flyback time, is the time it takes to queue a new ready task and restore the state of the highest priority task to running. In a well-designed RTOS, readying a new task will take 3 to 20 instructions per ready-queue entry, and resto... | large_corpus_distillation |
"\u2212\u2212\u2212\u2212\u2212\n2. Since Z and W are independent and each has the standard normal distribution, Y =\u03bd+\u03c4\u03c1Z+\u03c4\u221a1\u2212\u03c12W is normally distributed by\nanother basic property. Because Z and W have mean 0, it follows from the linear property of expected value that E(Y)=\u03bd. Si... | large_corpus_distillation |
"Logical volume management-Disadvantages-With implementations that are solely volume management, such as Core Storage and Linux LVM, separating and abstracting away volume management from the file system loses the ability to easily make storage decisions for particular files or directories. For example, if a certain di... | large_corpus_distillation |
"Small-bias sample space-Definition-The size s of an \u03f5 -biased set X is the size of the multiset that generates the sample space.\n\u03f5-biased generator An \u03f5 -biased generator G:{0,1}\u2113\u2192{0,1}n is a function that maps strings of length \u2113 to strings of length n such that the multiset XG=... | large_corpus_distillation |
"Divine equilibrium-Example-If we look again at the payoff matrix under the low settlement case, then regardless of how the plaintiff assigns his probability of choosing \"accept\" or \"reject\", the payoff for type t1 is higher than type t2 (for example, if the plaintiff plays a strategy of choosing equally between \"... | large_corpus_distillation |
In particular, the posterior left parameter is deterministic and depends on the data only through the sample\nn\nsize .\np X\nThe Bayesian estimator of based on nis\na+n\nV = (7.4.32)\nn a+b+Y\nn\nProof\nBy definition, the Bayesian estimator is the mean of the posterior distribution. Recall again that the mean of the b... | large_corpus_distillation |
can also be considered important examples of this type." | large_corpus_distillation |
"WIPI2-WIPI2-WD repeat domain phosphoinositide-interacting protein 2 is a protein that in humans is encoded by the WIPI2 gene." | large_corpus_distillation |
"Tensor product-Definitions and constructions-As a quotient space A construction of the tensor product that is basis independent can be obtained in the following way.\nLet V and W be two vector spaces over a field F. One considers first a vector space L that has the Cartesian product V\u00d7W as a basis. That is, the... | large_corpus_distillation |
"Grammar induction-Methodologies-Grammatical inference by trial-and-error The method proposed in Section 8.7 of Duda, Hart & Stork (2001) suggests successively guessing grammar rules (productions) and testing them against positive and negative observations. The rule set is expanded so as to be able to generate each pos... | large_corpus_distillation |
"Salt (cryptography)-Common mistakes-Salt re-use Using the same salt for all passwords is dangerous because a precomputed table which simply accounts for the salt will render the salt useless. Generation of precomputed tables for databases with unique salts for every password is not viable because of the computational... | large_corpus_distillation |
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