text stringlengths 5 1.02k | source stringclasses 1
value |
|---|---|
i } i = 1 K {\\textstyle \\{\\mathbf {\\Gamma } _{i}\\}_{i=1}^{K}} satisfy the following: \u2016 \u0393 i \u2212 \u0393 ^ i \u2016 2 2 \u2264 \u03b5 i 2 {\\textstyle \\|\\mathbf {\\Gamma } _{i}-{\\hat {\\mathbf {\\Gamma } }}_{i}\\|_{2}^{2}\\leq \\varepsilon _{i}^{2}} ." | large_corpus_distillation |
"Sodium polyacrylate-Applications-Agriculture In the agricultural industry, sodium polyacrylate is used to help plants retain moisture in the soil. It can act as a water reservoir for plants and is commonly used by florists to keep flowers fresh. Furthermore, the use of sodium polyacrylate for growing domestic fruit an... | large_corpus_distillation |
"English determiners-Terminology-Words and phrases can be categorized by both their syntactic category and their syntactic function. In the clause the dog bit the man, for example, the dog belongs to the syntactic category of noun phrase and performs the syntactic function of subject. The distinction between category a... | large_corpus_distillation |
"Presentation-Visual elements-Images/videos Large images relevant to the presentation attract an audience\u2019s attention which in turn can clarify the topics within the presentation. Using pictures sparingly helps support other presentation elements (e.g. text). Short videos are used to help the presenter reinforce t... | large_corpus_distillation |
decided to allow security vendors access to the kernel by creating special API instructions." | large_corpus_distillation |
"Induced path-Algorithms and complexity-It is NP-complete to determine, for a graph G and parameter k, whether the graph has an induced path of length at least k. Garey & Johnson (1979) credit this result to an unpublished communication of Mihalis Yannakakis. However, this problem can be solved in polynomial time for c... | large_corpus_distillation |
"L\u00e9vy\u2013Prokhorov metric-Properties-If (M,d) is separable, convergence of measures in the L\u00e9vy\u2013Prokhorov metric is equivalent to weak convergence of measures. Thus, \u03c0 is a metrization of the topology of weak convergence on P(M) The metric space (P(M),\u03c0) is separable if and only if (M,d)... | large_corpus_distillation |
"Adjunct (grammar)-Representing adjuncts-The object argument each time is identified insofar as it is a sister of V that appears to the right of V, and the adjunct status of the adverb early and the PP before class is seen in the higher position to the right of and above the object argument. Other adjuncts, in contrast... | large_corpus_distillation |
"Gr\u00f6bner basis-Definition-Existence of Gr\u00f6bner bases. For every admissible monomial ordering and every finite set G of polynomials, there is a Gr\u00f6bner basis that contains G and generates the same ideal. Moreover, such a Gr\u00f6bner basis may be computed with Buchberger's algorithm." | large_corpus_distillation |
"Backpropagation through time-Advantages-BPTT tends to be significantly faster for training recurrent neural networks than general-purpose optimization techniques such as evolutionary optimization." | large_corpus_distillation |
"16.1E: Exercises for Section 16.1\n\u21c0 \u21c0 \u21c0\n1. The domain of vector field F=F(x,y) is a set of points (x,y) in a plane, and the range of F is a set of what in the plane?\nFor exercises 2 - 4, determine whether the statement is true or false.\n2. Vector field F \u21c0 =\u27e83x2,1\u27e9 is a gradient field... | large_corpus_distillation |
"Parity P-Parity P-In computational complexity theory, the complexity class \u2295P (pronounced \"parity P\") is the class of decision problems solvable by a nondeterministic Turing machine in polynomial time, where the acceptance condition is that the number of accepting computation paths is odd. An example of a \u229... | large_corpus_distillation |
"Transport Layer Security-Security-RC4 as a stream cipher is immune to BEAST attack. Therefore, RC4 was widely used as a way to mitigate BEAST attack on the server side. However, in 2013, researchers found more weaknesses in RC4. Thereafter enabling RC4 on server side was no longer recommended.Chrome and Firefox themse... | large_corpus_distillation |
"Management cybernetics-Syntegration-One of the great difficulties in managing the modern large organization is that many of the issues are far too complex for even small groups. The critical knowledge is often dispersed among a substantial number of people. Organizations are often faced with choosing between 1) very c... | large_corpus_distillation |
"VxWorks-Platform overview-VxWorks supports Intel architecture, Power architecture, and ARM architectures. The RTOS can be used in multi-core asymmetric multiprocessing (AMP), symmetric multiprocessing (SMP), mixed modes and multi-OS (via Type 1 hypervisor) designs on 32- and 64- bit processors." | large_corpus_distillation |
"Small-bias sample space-Application: almost k-wise independence-k-wise independent spaces A random variable Y over {0,1}n is a k-wise independent space if, for all index sets I\u2286{1,\u2026,n} of size k , the marginal distribution Y|I is exactly equal to the uniform distribution over {0,1}k That is, for all su... | large_corpus_distillation |
"Euler's theorem-Euler's theorem-In 1736, Leonhard Euler published a proof of Fermat's little theorem (stated by Fermat without proof), which is the restriction of Euler's theorem to the case where n is a prime number. Subsequently, Euler presented other proofs of the theorem, culminating with his paper of 1763, in whi... | large_corpus_distillation |
(including the public key) A is attacking, and hi would be the output of the random oracle on its ith distinct input. The forking lemma is of use when it would be possible, given two different random signatures of the same message, to solve some underlying hard problem. An adversary that forges once, however, gives ris... | large_corpus_distillation |
"Automata theory-Variant definitions of automata-Which class of formal languages is recognizable by some type of automata? (Recognizable languages) Are certain automata closed under union, intersection, or complementation of formal languages? (Closure properties) How expressive is a type of automata in terms of recogni... | large_corpus_distillation |
Cash 20 account that is\nincreasing.\n\u25b2 Note Receivable\nNote Receivable 1,000 is an asset account\nthat is increasing.\n\u25bc Note Receivable\nNote Receivable 1,000 is an asset account\nthat is decreasing.\n\u25b2 Interest Revenue\nis a revenue account\nthat is increasing.\nInterest Revenue 20 page138image193564... | large_corpus_distillation |
"Differential entropy-Relation to estimator error-The differential entropy yields a lower bound on the expected squared error of an estimator. For any random variable X and estimator X^ the following holds: E\u2061[(X\u2212X^)2]\u226512\u03c0ee2h(X) with equality if and only if X is a Gaussian random variable and X... | large_corpus_distillation |
paid storage, with an emphasis on privacy. Being three of the largest file hosting services, Google Drive, Dropbox, and Mega all represent the core ideas and values of these services." | large_corpus_distillation |
"Security parameter-Computational security-The security of cryptographic primitives relies on the hardness of some hard problems. One sets the computational security parameter \u03ba such that O(2\u03ba) computation is considered intractable.\nExamples If the security of a scheme depends on the secrecy of a key for a... | large_corpus_distillation |
"Tamperproofing-Tampering-Tampering involves the deliberate altering or adulteration of a product, package, or system. Solutions may involve all phases of product production, packaging, distribution, logistics, sale, and use. No single solution can be considered as \"tamper-proof\". Often multiple levels of security ne... | large_corpus_distillation |
"Ring (mathematics)-Basic concepts-To give a ring homomorphism from a commutative ring R to a ring A with image contained in the center of A is the same as to give a structure of an algebra over R to A (which in particular gives a structure of an A-module).\nQuotient ring The notion of quotient ring is analogous to the... | large_corpus_distillation |
"Combinatoriality-Hexachordal combinatoriality-Occasionally a hexachord may be combined with an inverted or transposed version of itself in a special case which will then result in the aggregate (complete set of 12 chromatic pitches)." | large_corpus_distillation |
"RACE encoding-Nomenclature-RACE is an acronym for its main purpose. R stands for Row-based A for ASCII C for Compatible E Encoding " | large_corpus_distillation |
by the approach using a normal linear model, most teachers emphasize the normal linear model approach. Few statisticians object to model-based analysis of balanced randomized experiments." | large_corpus_distillation |
"Signcryption-Scheme-Security: A signcryption scheme should simultaneously fulfill the security attributes of an encryption scheme and those of a digital signature. Such additional properties mainly include: Confidentiality, Unforgeability, Integrity, and Non-repudiation. Some signcryption schemes provide further attri... | large_corpus_distillation |
"Peano kernel theorem-Statement-Let V[a,b] be the space of all functions f that are differentiable on (a,b) that are of bounded variation on [a,b] , and let L be a linear functional on V[a,b] . Assume that that L annihilates all polynomials of degree \u2264\u03bd , i.e.Suppose further that for any bivariate fun... | large_corpus_distillation |
"Multiplication-Computation-The algorithm, also based on the fast Fourier transform, is conjectured to be asymptotically optimal. The algorithm is not practically useful, as it only becomes faster for multiplying extremely large numbers (having more than 2172912 bits)." | large_corpus_distillation |
"Exploration problem-Information gain-The key concept in the exploration problem is the notion of information gain, that is, the amount of knowledge acquired while pushing the frontiers. A probabilistic measure of information gain is defined by the entropy log \u2061p(x)dx.\nThe function Hp(x) is maximized if p is a u... | large_corpus_distillation |
"Straight-line program-Straight-line program-Intuitively, an SLP computing some g \u2208 G is an efficient way of storing g as a group word over S; observe that if g is constructed in i steps, the word length of g may be exponential in i, but the length of the corresponding SLP is linear in i. This has important applic... | large_corpus_distillation |
"Lottery scheduling-Lottery scheduling-Lottery scheduling solves the problem of starvation. Giving each process at least one lottery ticket guarantees that it has non-zero probability of being selected at each scheduling operation." | large_corpus_distillation |
"Lord's paradox-Responses-To this end, Pearl used a simplified version of Lord\u2019s Paradox, proposed by Wainer and Brown, in which gender differences are not considered. Instead, the quantity of interest is the effect of diet on weight gain, as shown in Figure 2(a). The two ellipses represent two dining halls, each... | large_corpus_distillation |
"Named-entity recognition-Problem definition-In academic conferences such as CoNLL, a variant of the F1 score has been defined as follows: Precision is the number of predicted entity name spans that line up exactly with spans in the gold standard evaluation data. I.e. when [Person Hans] [Person Blick] is predicted but ... | large_corpus_distillation |
"Self-XSS-History and mitigation-In the past, a very similar attack took place, in which users were tricked into pasting malicious JavaScript into their address bar. When browser vendors stopped this by preventing easily running JavaScript from the address bar, attackers started using Self-XSS in its current form. Web ... | large_corpus_distillation |
"Multiplicatively closed set-Multiplicatively closed set-In abstract algebra, a multiplicatively closed set (or multiplicative set) is a subset S of a ring R such that the following two conditions hold: 1\u2208S ,xy\u2208S for all x,y\u2208S .In other words, S is closed under taking finite products, including the empt... | large_corpus_distillation |
"Row echelon form-Row echelon form-The leading entry (that is the left-most nonzero entry) of every nonzero row is to the right of the leading entry of every row above.Some texts add the condition that the leading coefficient must be 1 while others regard this as reduced row echelon form.\nThese two conditions imply th... | large_corpus_distillation |
"Index\n1 https://eng.libretexts.org/@go/page/25446" | large_corpus_distillation |
"Grammatical particle-Modern meaning-In modern grammar, a particle is a function word that must be associated with another word or phrase to impart meaning, i.e., it does not have its own lexical definition. According to this definition, particles are a separate part of speech and are distinct from other classes of fun... | large_corpus_distillation |
"Geometric mean-Calculation-This is sometimes called the log-average (not to be confused with the logarithmic average). It is simply computing the arithmetic mean of the logarithm-transformed values of ai (i.e., the arithmetic mean on the log scale) and then using the exponentiation to return the computation to the or... | large_corpus_distillation |
"Explicitly parallel instruction computing-Other research and development-There have been other investigations into EPIC architectures that are not directly tied to the development of the Itanium architecture: The IMPACT project at University of Illinois at Urbana\u2013Champaign, led by Wen-mei Hwu, was the source of m... | large_corpus_distillation |
"Faceted search-Faceted search-Faceted search augments lexical search with a faceted navigation system, allowing users to narrow results by applying filters based on a faceted classification of the items. It is a parametric search technique. A faceted classification system classifies each information element along mult... | large_corpus_distillation |
"Multiplicative function-Examples-1C(n), the indicator function of the set C \u2282 Z, for certain sets C. The indicator function 1C(n) is multiplicative precisely when the set C has the following property for any coprime numbers a and b: the product ab is in C if and only if the numbers a and b are both themselves in ... | large_corpus_distillation |
"Wehrl entropy-Properties-The entropy for the tensor product of two systems is always greater than the entropy of one system. In other words, for a state \u03c1 on a Hilbert space H=H1\u2297H2 , we have SW(\u03c11)\u2264SW(\u03c1) , where \u03c11=Tr2\u03c1 . Note that the quantum von Neumann entropy, S(\u03c1) , d... | large_corpus_distillation |
"MemoQ-Configuration-As of 2018, all supported memoQ editions contained these principal modules: File statistics Word counts and comparisons with translation memory databases, internal content similarities and format tag frequency. memoQ was the first translation environment tool to enable the weighting of format tags ... | large_corpus_distillation |
"Interactive machine translation-Evaluation-Evaluation is a difficult issue in interactive machine translation. Ideally, evaluation should take place in experiments involving human users. However, given the high monetary cost this would imply, this is seldom the case." | large_corpus_distillation |
"Certified Server Validation-Principles of operation-Determines the level of trust to give to the sending SMTP client, based on the results of (3) and (4)If the level of trust is high enough, process all email from that session in the traditional manner, delivering or forwarding without the need for further validation.... | large_corpus_distillation |
"Least mean squares filter-Derivation-The idea behind LMS filters is to use steepest descent to find filter weights h^(n) which minimize a cost function. We start by defining the cost function as C(n)=E{|e(n)|2} where e(n) is the error at the current sample n and E{\u22c5} denotes the expected value." | large_corpus_distillation |
"Public key certificate-Website security-Usefulness versus unsecured web sites In spite of the limitations described above, certificate-authenticated TLS is considered mandatory by all security guidelines whenever a web site hosts confidential information or performs material transactions. This is because, in practice,... | large_corpus_distillation |
almost all the outstanding transactions. Thus, in the case of incompatible local (partial) commitment orders, no action is needed since the atomic commitment protocol resolves it automatically by aborting a transaction that is a cause of incompatibility. This means that the above vote ordering strategy is also a suffic... | large_corpus_distillation |
"B-tree-Definition-According to Knuth's definition, a B-tree of order m is a tree which satisfies the following properties: Every node has at most m children.\nEvery internal node has at least \u2308m/2\u2309 children.\nThe root node has at least two children unless it is a leaf.\nAll leaves appear on the same level." | large_corpus_distillation |
"Omnibus test-In logistic regression-The null hypothesis for the overall model fit: The overall model does not predict re-arrest. OR, the independent variables as a group are not related to being re-arrested. (And for the independent variables: any of the separate independent variables is not related to the likelihood ... | large_corpus_distillation |
"HITS algorithm-Algorithm-The algorithm performs a series of iterations, each consisting of two basic steps: Authority update: Update each node's authority score to be equal to the sum of the hub scores of each node that points to it. That is, a node is given a high authority score by being linked from pages that are r... | large_corpus_distillation |
"Inductive reasoning-Methods-The two principal methods used to reach inductive conclusions are enumerative induction and eliminative induction." | large_corpus_distillation |
"Text nailing-Text nailing-Text Nailing (TN) is an information extraction method of semi-automatically extracting structured information from unstructured documents. The method allows a human to interactively review small blobs of text out of a large collection of documents, to identify potentially informative expressi... | large_corpus_distillation |
"Central processing unit-Structure and implementation-It was later recognized that finer-grain parallelism existed with a single program. A single program might have several threads (or functions) that could be executed separately or in parallel. Some of the earliest examples of this technology implemented input/output... | large_corpus_distillation |
"\uf128 Exercise 26\n5a+ 3 b+ 1a+ 9 b\n6 10 6 10\n\uf128 Exercise 27\n6.8p+9.14q+(\u22124.37p)+(\u22120.88q)\nAnswer\n2.43p+8.26q\n\uf128 Exercise 28\n9.6m+7.22n+(\u22122.19m)+(\u22120.65n)\nUse the Identity and Inverse Properties of Addition and Multiplication\nIn the following exercises, find the additive inverse of ... | large_corpus_distillation |
"Set (mathematics)-Subsets-{1, 3} \u2282 {1, 2, 3, 4}.\n{1, 2, 3, 4} \u2286 {1, 2, 3, 4}.The empty set is a subset of every set, and every set is a subset of itself: \u2205 \u2286 A.\nA \u2286 A." | large_corpus_distillation |
parameter and note the location\nand shape of the distribution function. For various values of the scale parameter, compute selected values of the distribution\nfunction and the quantile function.\nX Fc Fc(x)=exp(\u2212x2 ) x\u2208[0,\u221e)\nhas reliability function given by for .\n2b2\nProof\nFc(x)=1\u2212F(x)\nRecal... | large_corpus_distillation |
non-convex set X has a subset Y\u2282X that is larger than 12K , whose pairwise differences belong to X . When this is the case, the larger size of Y relative to 12K leads to tighter bounds on how big X needs to be sure of containing a lattice point.For a centrally symmetric star domain, it is possible to use th... | large_corpus_distillation |
"Curse of dimensionality-Domains-In this sense when points are uniformly generated in a high-dimensional hypercube, almost all points are much farther than r units away from the centre. In high dimensions, the volume of the d-dimensional unit hypercube (with coordinates of the vertices \u00b11 ) is concentrated near ... | large_corpus_distillation |
"Hash function security summary-Attacks on hashed passwords-Hashes described here are designed for fast computation and have roughly similar speeds. Because most users typically choose short passwords formed in predictable ways, passwords can often be recovered from their hashed value if a fast hash is used. Searches o... | large_corpus_distillation |
"Cross product-Computing-Using cofactor expansion along the first row instead, it expands to a\u00d7b=|a2a3b2b3|i\u2212|a1a3b1b3|j+|a1a2b1b2|k=(a2b3\u2212a3b2)i\u2212(a1b3\u2212a3b1)j+(a1b2\u2212a2b1)k, which gives the components of the resulting vector directly.\nUsing Levi-Civita tensors In any basis, the cross-produ... | large_corpus_distillation |
"Interpretation (logic)-General properties of truth-functional interpretations-(\u03a6 \u2194 \u03a8) is True iff (\u03a6 \u2192 \u03a8) is True and (\u03a8 \u2192 \u03a6) is True.So under a given interpretation of all the sentence letters \u03a6 and \u03a8 (i.e., after assigning a truth-value to each sentence letter),... | large_corpus_distillation |
"Bit manipulation-Example of bit manipulation-To determine if a number is a power of two, conceptually we may repeatedly do integer divide by two until the number won't divide by 2 evenly; if the only factor left is 1, the original number was a power of 2. Using bit and logical operators, there is a simple expression w... | large_corpus_distillation |
"Mathematical statistics-Topics-Many techniques for carrying out regression analysis have been developed. Familiar methods, such as linear regression, are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data (e.g. using ordinary least ... | large_corpus_distillation |
kIng anD thIs VVhoLe LanD.\" The English sentence demonstrates that the origin of the letter w as a double v or u was recognised historically." | large_corpus_distillation |
"Alogia-Example-The following table shows an example of \"poverty of speech\" which shows replies to questions that are brief and concrete, with a reduction in spontaneous speech: The following example of \"poverty of content of speech\" is a response from a patient when asked why he was in a hospital. Speech is vague,... | large_corpus_distillation |
"Set intersection oracle-Maximum memory, minimum query time-Alternatively, we can pre-process the sets and create an n-by-n table where the intersection information is already entered. Then the query time is O(1) , but the memory required is O(n2) " | large_corpus_distillation |
"Earliest deadline first scheduling-Kernels implementing EDF scheduling-Although EDF implementations are not common in commercial real-time kernels, here are a few links of open-source and real-time kernels implementing EDF: SHARK The SHaRK RTOS, implementing various versions of EDF scheduling and resource reservation ... | large_corpus_distillation |
"Transitive closure-Algorithms-Efficient algorithms for computing the transitive closure of the adjacency relation of a graph can be found in Nuutila (1995). Reducing the problem to multiplications of adjacency matrices achieves the least time complexity, viz. that of matrix multiplication (Munro 1971, Fischer & Meyer ... | large_corpus_distillation |
"Furstenberg's proof of the infinitude of primes-Furstenberg's proof-Define a topology on the integers Z , called the evenly spaced integer topology, by declaring a subset U \u2286 Z to be an open set if and only if it is a union of arithmetic sequences S(a,\u2009b) for a \u2260 0, or is empty (which can be seen as a... | large_corpus_distillation |
case of intervals on the real number line), it is always considered open and adjoined to a parenthesis. The endpoint can be closed when considering intervals on the extended real number line." | large_corpus_distillation |
"Transshipment problem-Mathematical formulation of the problem-The goal is to minimize \u2211i=1m\u2211j=1nti,jxi,j subject to: xr,s\u22650 ; \u2200r=1\u2026m , s=1\u2026n \u2211s=1m+nxi,s\u2212\u2211r=1m+nxr,i=ai ; \u2200i=1\u2026m \u2211r=1m+nxr,m+j\u2212\u2211s=1m+nxm+j,s=bm+j ; \u2200j=1\u2026n \u2211i=1mai=\u... | large_corpus_distillation |
"Kernel principal component analysis-Large datasets-In practice, a large data set leads to a large K, and storing K may become a problem. One way to deal with this is to perform clustering on the dataset, and populate the kernel with the means of those clusters. Since even this method may yield a relatively large K, it... | large_corpus_distillation |
"Q Score-Forms-Other Q Scores are calculated to order for clients who want to research public perception of a brand or celebrity. For example, in 2000, IBM hired Marketing Evaluations to calculate the Q Score for Deep Blue, the supercomputer that defeated chess Grandmaster Garry Kasparov. Deep Blue\u2019s Q Score was 9... | large_corpus_distillation |
"Strobogrammatic number-Nonstandard systems-In duodecimal, the strobogrammatic numbers are (using inverted two and three for ten and eleven, respectively) 0, 1, 8, 11, 2\u218a, 3\u218b, 69, 88, 96, \u218a2, \u218b3, 101, 111, 181, 20\u218a, 21\u218a, 28\u218a, 30\u218b, 31\u218b, 38\u218b, 609, 619, 689, 808, 818, 888,... | large_corpus_distillation |
"GSM 03.48-Overview-If so indicated in the Command Header, the Receiving Entity shall create a (Secured) Response Packet. The Response Packet consists of a Security Header (the Response Header) and optionally, application specific data supplied by the Receiving Application. Both the Response Header and the application ... | large_corpus_distillation |
function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpol... | large_corpus_distillation |
"Sylow theorems-Example applications-Since Sylow's theorem ensures the existence of p-subgroups of a finite group, it's worthwhile to study groups of prime power order more closely. Most of the examples use Sylow's theorem to prove that a group of a particular order is not simple. For groups of small order, the congrue... | large_corpus_distillation |
If the dataset is not too large, the significance of the principal components can be tested using parametric bootstrap, as an aid in determining how many principal components to retain." | large_corpus_distillation |
"Comparative anatomy-Concepts-Analogous structures - structures similar in different organisms because, in convergent evolution, they evolved in a similar environment, rather than were inherited from a recent common ancestor. They usually serve the same or similar purposes. An example is the streamlined torpedo body sh... | large_corpus_distillation |
"Polynomials calculating sums of powers of arithmetic progressions-Generalization of Faulhaber's formula-The matrix G(h,d) can be expressed as a function of the Bernoulli polynomials in the following way which for m=5 becomes from which the generalized Faulhaber formula is derived: and also the well-known special ca... | large_corpus_distillation |
"Python syntax and semantics-Literals-For instance, all of these Python statements:are equivalent to the Perl statement:They build a string using the variables num and printer.\nMulti-line string literals There are also multi-line strings, which begin and end with a series of three single or double quotes and function ... | large_corpus_distillation |
"Coin collecting-Grade and value-By the mid 20th century, with the growing market for rare coins, the American Numismatic Association helps identify most coins in North America, numbering coins from 1 (poor) to 70 (mint state), and setting aside a separate category for proof coinage. This system is often shunned by coi... | large_corpus_distillation |
"Fermat primality test-Algorithm-The algorithm can be written as follows: Inputs: n: a value to test for primality, n>3; k: a parameter that determines the number of times to test for primality Output: composite if n is composite, otherwise probably prime Repeat k times: Pick a randomly in the range [2, n \u2212 2] If ... | large_corpus_distillation |
"Root of unity-Elementary properties-Every nth root of unity z is a primitive ath root of unity for some a \u2264 n, which is the smallest positive integer such that za = 1.\nAny integer power of an nth root of unity is also an nth root of unity, as 1.\nThis is also true for negative exponents. In particular, the recip... | large_corpus_distillation |
"Salt-Edible salt-Salt is essential to the health of humans and other animals, and it is one of the five basic taste sensations. Salt is used in many cuisines, and it is often found in salt shakers on diners' eating tables for their personal use on food. Salt is also an ingredient in many manufactured foodstuffs. Table... | large_corpus_distillation |
"Android KitKat-Features-Platform A new runtime environment known as the Android Runtime (ART), intended to replace the Dalvik virtual machine, was introduced as a technology preview in KitKat. ART is a cross-platform runtime which supports the x86, ARM, and MIPS architectures in both 32-bit and 64-bit environments. Un... | large_corpus_distillation |
"Wozencraft ensemble-Proof-Now the Lemma implies that we have at least |P| different y such that wt(y)<Hq\u22121(12\u2212\u03b5)\u22c52k (one such codeword y for each linear code). Here wt(y) denotes the weight of codeword y , which is the number of non-zero positions of y Denote S={y:wt(y)<Hq\u22121(12\u2212\u0... | large_corpus_distillation |
"Community network-Community network-A community network is a computer-based system that is intended to help support (usually geographical) communities by supporting, augmenting, and extending already existing social networks, by using networking technologies by, and for, a community." | large_corpus_distillation |
for the case under consideration. This is not a phenomenon that can be easily understood intuitively,\nbut Example 6.2.1 and Exercise 6.3 will help.\nSolving for the steady-state process probabilities directly\nLet us return to the case where \u2211 k \u03c0 k /\u03bd k <\u221e, which is the case of virtually all appli... | large_corpus_distillation |
"Three-dimensional losses and correlation in turbomachinery-Types of losses-Three-dimensional losses are generally classified as: " | large_corpus_distillation |
"Law of large numbers-Proof of the strong law-We give a relatively simple proof of the strong law under the assumptions that the Xi are iid, =: \u03bc<\u221e , Var \u2061(Xi)=\u03c32<\u221e , and =: \u03c4<\u221e Let us first note that without loss of generality we can assume that \u03bc=0 by centering. In this ca... | large_corpus_distillation |
"Language Integrated Query-Architecture of LINQ in the .NET Framework-Take / TakeWhile The Take operator selects the first n objects from a collection, while the TakeWhile operator, which takes a predicate, selects those objects that match the predicate (stopping at the first object that doesn't match it).\nSkip / Skip... | large_corpus_distillation |
and thus could not block. More broadly, unlike with conventional computer security, attempting to box a superintelligent AI would be intrinsically risky as there could be no certainty that the boxing plan will work. Additionally, scientific progress on boxing would be fundamentally difficult because there would be no w... | large_corpus_distillation |
"The Poisson Distribution\nX=(X ,X ,\u2026,X ) n \u03b8\u2208(0,\u221e)\nSuppose that 1 2 n is a random sample of size from the Poisson distribution with parameter .\nRecall that this distribution is often used to model the number of \u201crandom points\u201d in a region of time or space and is studied in\nmore detail ... | large_corpus_distillation |
"Bibliographic index-Bibliographic index-A bibliographic index is a bibliography intended to help find a publication. Citations are usually listed by author and subject in separate sections, or in a single alphabetical sequence under a system of authorized headings collectively known as controlled vocabulary, developed... | large_corpus_distillation |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.