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r and s Reduction to a finite class: We can now restrict the function class H to a fixed joint sample and hence, if H has finite VC Dimension, it reduces to the problem to one involving a finite function class.We present the technical details of the proof." | large_corpus_distillation |
"Device driver synthesis and verification-Verification of Device Drivers-Compiler Techniques The rules that have a straightforward mapping to source code can be checked using a compiler. Rule violations can be found by checking if the source operation does not make sense. For example, rules like \"enabling an interrupt... | large_corpus_distillation |
"R10000-Description-Integer unit The integer unit consists of the integer register file and three pipelines, two integer, one load store. The integer register file is 64 bits wide and contains 64 entries, of which 32 are architectural registers and 32 are rename registers which implement register renaming. The register... | large_corpus_distillation |
"Yahalom (protocol)-Protocol description-B\u2192S:B,{A,NA,NB}KBS Bob sends a message to the Server encrypted under KBS .S\u2192A:{B,KAB,NA,NB}KAS,{A,KAB}KBS The Server sends to Alice a message containing the generated session key KAB and a message to be forwarded to Bob.\nA\u2192B:{A,KAB}KBS,{NB}KAB Alice forwards th... | large_corpus_distillation |
"Torus-based cryptography-Torus-based cryptography-Torus-based cryptography involves using algebraic tori to construct a group for use in ciphers based on the discrete logarithm problem. This idea was first introduced by Alice Silverberg and Karl Rubin in 2003 in the form of a public key algorithm by the name of CEILID... | large_corpus_distillation |
"Indirect tests of memory-Artificial grammar learning (AGL)-Similarity The specific similarity theory states that learning occurs by encoding each letter string in the learning phase as a whole. Grammaticality judgments in the test phase are made by comparing novel letter string to the ones already in memory. The more ... | large_corpus_distillation |
the web context, such as standalone graphical applications and robotic drone control. PHP code can also be directly executed from the command line." | large_corpus_distillation |
would survey 4 times as many females as males, so that in the final sample, both genders will be represented equally. (See also Stratified Sampling.) Under-representation of one class in the outcome (dependent) variable. Suppose we want to predict, from a large clinical dataset, which patients are likely to develop a p... | large_corpus_distillation |
"Mobile operating system-Mobile operating system-A mobile operating system is an operating system for smartphones, tablets, smartwatches, smartglasses, or other non-laptop personal mobile computing devices. While computers such as typical/mobile laptops are \"mobile\", the operating systems used on them are generally n... | large_corpus_distillation |
example provided, were two additional tasks to be assessed e.g. A and B, which had HEP values of 0.5 and 10 -4 respectively and SLIs respectively of 4.00 and 6.00, respectively, then the formulation would be: log HEP 1.85 SLI 7.1 The final HEP values would thus be determined as V0204 = 0.0007 Alarm mis-set = 0.14 Alarm... | large_corpus_distillation |
"Cutting-plane method-Gomory's cut-Step 1: solving the relaxed linear program Using the simplex method to solve a linear program produces a set of equations of the form xi+\u2211ja\u00afi,jxj=b\u00afi where xi is a basic variable and the xj's are the nonbasic variables (i.e. the basic solution which is an optimal solut... | large_corpus_distillation |
"OllyDbg-Related software-Interactive Disassembler (IDA Pro) Radare2 Ghidra Cheat Engine Debuggers for reverse-engineering software x64dbg Syser Debugger Syser Debugger by reversecode x32/x64 (reverse engineering & improvement) " | large_corpus_distillation |
"Diffie\u2013Hellman key exchange-Description-If a third party listened to the exchange, they would only know the common color (yellow) and the first mixed colors (orange-tan and light-blue), but it would be very hard for them to find out the final secret color (yellow-brown). Bringing the analogy back to a real-life e... | large_corpus_distillation |
"Sequential coupling-Sequential coupling-In object-oriented programming, sequential coupling (also known as temporal coupling) is a form of coupling where a class requires its methods to be called in a particular sequence. This may be an anti-pattern, depending on context.\nMethods whose name starts with Init, Begin, S... | large_corpus_distillation |
"ODRL-ODRL Vocabulary-The ODRL Core Vocabulary defines the semantics for the concepts and terms from the ODRL Information Model. The ODRL Core Vocabulary represents the minimally supported terms for ODRL Policies.\nIn addition, the ODRL Common Vocabulary defines semantics for generic terms that may be optionally used i... | large_corpus_distillation |
"Rayleigh\u2013Ritz method-For matrix singular value problems-Let us take with the column-space that is spanned by the two exact right singular vectors corresponding to the singular values 1 and 2." | large_corpus_distillation |
"Language Integrated Query-Architecture of LINQ in the .NET Framework-OrderBy / ThenBy The OrderBy operator is used to specify the primary sort ordering of the elements in a collection according to some key. The default ordering is in ascending order, to reverse the order, the OrderByDescending operator is to be used. ... | large_corpus_distillation |
"Graph power-Computational complexity-The kth powers of trees can be recognized in time linear in the size of the input graph.\nGiven a graph, deciding whether it is the square of another graph is NP-complete.\nMoreover, it is NP-complete to determine whether a graph is a kth power of another graph, for a given number ... | large_corpus_distillation |
"Proofs of Fermat's little theorem-Proofs using group theory-For instance, if a = 5 and p = 13, then, since 52 = 25 \u2261 12 (mod 13), 53 = 125 \u2261 8 (mod 13), 54 = 625 \u2261 1 (mod 13),we have k = 4 and A = {1, 5, 8, 12}. Clearly, A \u2260 G = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let b1 be an element of G\\A;... | large_corpus_distillation |
"Multislice-Available software-MacTempas This software is specifically developed to run in Mac OS X by Dr. Roar Kilaas of Lawrence Berkeley National Laboratory. It is designed to have a user-friendly user interface and has been well-maintained relative to many other codes (last update May 2013). It is available (for a ... | large_corpus_distillation |
"Regularized least squares-Kernel formulation-Complexity The complexity of training is basically the cost of computing the kernel matrix plus the cost of solving the linear system which is roughly O(n3) . The computation of the kernel matrix for the linear or Gaussian kernel is O(n2D) . The complexity of testing is ... | large_corpus_distillation |
"Recursion (computer science)-Implementation issues-Depth-first search A basic example of short-circuiting is given in depth-first search (DFS) of a binary tree; see binary trees section for standard recursive discussion." | large_corpus_distillation |
"Unix file types-Device file (block, character)-In Unix, almost all things are handled as files and have a location in the file system, even hardware devices like hard drives. The great exception is network devices, which do not turn up in the file system but are handled separately.\nDevice files are used to apply acce... | large_corpus_distillation |
"Recommender system-Overview-Recommender systems usually make use of either or both collaborative filtering and content-based filtering (also known as the personality-based approach), as well as other systems such as knowledge-based systems. Collaborative filtering approaches build a model from a user's past behavior (... | large_corpus_distillation |
our discussion of dice. Recall that the mean for a\nE(X)=\u2211n x P(x )\ndiscrete random variable is i=1 i i . In the more general context we use an integral in place of the sum.\n9.8.3 https://math.libretexts.org/@go/page/489" | large_corpus_distillation |
"Audio deepfake-Categories-This method is often confused with the previous Synthetic-based method, as there is no clear separation between the two approaches regarding the generation process. Indeed, both methods modify acoustic-spectral and style characteristics of the speech audio signal, but the Imitation-based usua... | large_corpus_distillation |
"SM9 (cryptography standard)-Further Information-The following links provide more detailed information on the SM9 algorithms in English: The SM9 Cryptographic Schemes Using Identity as Raw Public Key in Transport Layer Security (TLS) and Datagram Transport Layer Security (DTLS) " | large_corpus_distillation |
"Sentence extraction-Sentence extraction-Sentence extraction is a technique used for automatic summarization of a text.\nIn this shallow approach, statistical heuristics are used to identify the most salient sentences of a text. Sentence extraction is a low-cost approach compared to more knowledge-intensive deeper appr... | large_corpus_distillation |
frequent. In this way, the cipher can be distinguished from random. More sophisticated variations allow the key to be recovered faster than exhaustive search." | large_corpus_distillation |
inverse of this matrix is given by Lij(m)\u22121=Lij(\u2212m).\nThe matrix and its inverse are triangular matrices.\ndet 1.\nTherefore, for a square matrix A (of the correct size) we have det det (A).\nRow-addition transforms satisfy the Steinberg relations." | large_corpus_distillation |
"Opaque set-Bounds-When the region to be covered is a convex set, the length of its shortest opaque set must be at least half its perimeter and at most its perimeter. For some regions, additional improvements to these bounds can be made." | large_corpus_distillation |
"General Leibniz rule-Proof-The proof of the general Leibniz rule proceeds by induction. Let f and g be n -times differentiable functions. The base case when n=1 claims that: (fg)\u2032=f\u2032g+fg\u2032, which is the usual product rule and is known to be true. Next, assume that the statement holds for a fixed n\u... | large_corpus_distillation |
"Proximity search (text)-Usage in commercial search engines-In regards to implicit/automatic versus explicit proximity search, as of November 2008, most Internet search engines only implement an implicit proximity search functionality. That is, they automatically rank those search results higher where the user keywords... | large_corpus_distillation |
"Parsing-Types of parsers-The task of the parser is essentially to determine if and how the input can be derived from the start symbol of the grammar. This can be done in essentially two ways: Top-down parsing Top-down parsing can be viewed as an attempt to find left-most derivations of an input-stream by searching for... | large_corpus_distillation |
"Loss functions for classification-Loss functions for classification-Within classification, several commonly used loss functions are written solely in terms of the product of the true label y and the predicted label f(x\u2192) . Therefore, they can be defined as functions of only one variable \u03c5=yf(x\u2192) , so... | large_corpus_distillation |
the algorithm need only search for prime divisors less than / equal to n For another example, consider how this algorithm determines the primality of 17. One has 17 <5 , and the only primes 17 are 2 and 3. Neither divides 17, proving that 17 is prime. For a last example, consider 221. One has 14 221 15 , and the pr... | large_corpus_distillation |
"ISO/IEC 2022-Code structure-Character set designations Escape sequences to designate character sets take the form ESC I [I...] F. As mentioned above, the intermediate (I) bytes are from the range 0x20\u20130x2F, and the final (F) byte is from the range 0x30\u20130x7E. The first I byte (or, for a multi-byte set, the fi... | large_corpus_distillation |
"Poisson distribution-Related distributions-Weibull and Stable count Poisson's probability mass function f(k;\u03bb) can be expressed in a form similar to the product distribution of a Weibull distribution and a variant form of the stable count distribution. The variable (k+1) can be regarded as inverse of L\u00e9vy... | large_corpus_distillation |
"Literature-based discovery-Text mining-The automation of literature-based discovery relies heavily on text mining.The language in scientific articles often include ambiguities, and an important step for coeherent parsing of the literature is the extraction of the sense of each term in the context they are used, a task... | large_corpus_distillation |
"Stable Diffusion-Technology-A \"hypernetwork\" is a small pretrained neural network that is applied to various points within a larger neural network, and refers to the technique created by NovelAI developer Kurumuz in 2021, originally intended for text-generation transformer models. Hypernetworks steer results towards... | large_corpus_distillation |
"Integrated development environment-Overview-One aim of the IDE is to reduce the configuration necessary to piece together multiple development utilities. Instead, it provides the same set of capabilities as one cohesive unit. Reducing setup time can increase developer productivity, especially in cases where learning t... | large_corpus_distillation |
"Transformer (machine learning model)-Subsequent work-Sub-quadratic transformers Training transformer-based architectures can be expensive, especially for long inputs. Alternative architectures include the Reformer (which reduces the computational load from O(N2) to ln \u2061N) ), or models like ETC/BigBird (which ca... | large_corpus_distillation |
"Bias of an estimator-Median-unbiased estimators-There are methods of construction median-unbiased estimators for probability distributions that have monotone likelihood-functions, such as one-parameter exponential families, to ensure that they are optimal (in a sense analogous to minimum-variance property considered f... | large_corpus_distillation |
inverted sentences and question tags as described above." | large_corpus_distillation |
"CudaText-Add-on system and Python-Plug-in: Text_Statistics The text statistics plug-in is a tool for linguists. It displays the number of lines, words, letters and all characters as well as the 30 most common words and the sentences with n words, i.e. a short statistic of the number of sentences with 1 to 9 elements." | large_corpus_distillation |
"Decision Linear assumption-Formal definition-Let G be a cyclic group of prime order p . Let u , v , and h be uniformly random generators of G . Let a,b be uniformly random elements of {1,2,\u2026,p\u22121} . Define a distribution D1=(u,v,h,ua,vb,ha+b).\nLet \u03b7 be another uniformly random element of G . D... | large_corpus_distillation |
a sender without using a The Onion Router (Tor) or Virtual Private Network (VPN). In November 2018, Zcoin conducted the world's first large-scale party elections in Thailand Democrat Party using InterPlanetary File System (IPFS). In December 2018, Zcoin implemented Merkle tree proof, a mining algorithm that deters the ... | large_corpus_distillation |
"Google Pay Send-Business model-Google does not charge users for access to Google Wallet. Sending and receiving money is free, as is adding money to a Wallet Card through a linked bank account. There are limits on how much money users can add to their Wallet Balance, withdraw from the linked account or card, or send an... | large_corpus_distillation |
"Augmented matrix-Existence and number of solutions-Consider the system of equations The coefficient matrix is and the augmented matrix is Since both of these have the same rank, namely 2, there exists at least one solution; and since their rank is less than the number of unknowns, the latter being 3, there are an inf... | large_corpus_distillation |
"Covariance-Calculating the sample covariance-The sample covariances among K variables based on N observations of each, drawn from an otherwise unobserved population, are given by the K\u00d7K matrix q\u00af=[qjk] with the entries qjk=1N\u22121\u2211i=1N(Xij\u2212X\u00afj)(Xik\u2212X\u00afk), which is an estimate o... | large_corpus_distillation |
"Extensible Authentication Protocol-Methods-EAP Encrypted Key Exchange (EAP-EKE) EAP with the encrypted key exchange, or EAP-EKE, is one of the few EAP methods that provide secure mutual authentication using short passwords and no need for public key certificates. It is a three-round exchange, based on the Diffie-Hellm... | large_corpus_distillation |
"Generation of primes-Generation of primes-In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications, for example hashing, public-key cryptography, and search of prime factors in large numbers." | large_corpus_distillation |
communication of large amounts of data over long distances." | large_corpus_distillation |
"Linux kernel-Architecture and features-Scheduling and preemption The Linux scheduler is modular, in the sense that it enables different scheduling classes and policies. Scheduler classes are plugable scheduler algorithms that can be registered with the base scheduler code. Each class schedules different types of proce... | large_corpus_distillation |
to give the correct answer of 0010 (2.). Overflow checks still must exist to catch operations such as summing 0100 and 0100." | large_corpus_distillation |
in his robot form. He finishes this journey down memory lane by going to his wife's grave. He digs her corpse out and rips it into two, shouting that all he wants is not to be with her, but for these memories to fade.Meanwhile, the Manhunters begin an assault on the JLA satellite. Hawkgirl, Black Lightning, and Red Arr... | large_corpus_distillation |
"Trace scheduling-Trace scheduling-Trace scheduling was originally developed for Very Long Instruction Word, or VLIW machines, and is a form of global code motion. It works by converting a loop to long straight-line code sequence using loop unrolling and static branch prediction. This process separates out \"unlikely\"... | large_corpus_distillation |
"Time complexity-Quasilinear time-Comparison sorts require at least log \u2061n) comparisons in the worst case because log log \u2061n) , by Stirling's approximation. They also frequently arise from the recurrence relation {\\textstyle T(n)=2T\\left({\\frac {n}{2}}\\right)+O(n)} " | large_corpus_distillation |
"AVL tree-Operations-To split an AVL tree into two smaller trees, those smaller than key k, and those larger than key k, first draw a path from the root by inserting k into the AVL. After this insertion, all values less than k will be found on the left of the path, and all values greater than k will be found on the rig... | large_corpus_distillation |
"128-bit computing-Software-Increasing the word size can speed up multiple precision mathematical libraries, with applications to cryptography, and potentially speed up algorithms used in complex mathematical processing (numerical analysis, signal processing, complex photo editing and audio and video processing).\nMD5 ... | large_corpus_distillation |
"Edge coloring-Relation to degree-Vizing's theorem The edge chromatic number of a graph G is very closely related to the maximum degree \u0394(G), the largest number of edges incident to any single vertex of G. Clearly, \u03c7\u2032(G) \u2265 \u0394(G), for if \u0394 different edges all meet at the same vertex v, then ... | large_corpus_distillation |
"Django (web framework)-Version history-The Django team will occasionally designate certain releases to be \"long-term support\" (LTS) releases. LTS releases will get security and data loss fixes applied for a guaranteed period of time, typically 3+ years, regardless of the pace of releases afterwards." | large_corpus_distillation |
"Index calculus algorithm-Index calculus algorithm-In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms." | large_corpus_distillation |
"FASTA format-Sequence representation-Following the header line, the actual sequence is represented. Sequences may be protein sequences or nucleic acid sequences, and they can contain gaps or alignment characters (see sequence alignment). Sequences are expected to be represented in the standard IUB/IUPAC amino acid and... | large_corpus_distillation |
to some external stimulus or event (that can occur asynchronously), rather than execution of an in-line control flow statement.\nAt the level of machine language or assembly language, control flow instructions usually work by altering the program counter. For some central processing units (CPUs), the only control flow ... | large_corpus_distillation |
respectively, we have that the CDF of the sum is: H(z)=\u222b\u2212\u221e\u221eF(z\u2212t)g(t)dt=\u222b\u2212\u221e\u221eG(t)f(z\u2212t)dt If we start with random variables X and Y , related by Z=X+Y , and with no information about their possible independence, then: fZ(z)=\u222b\u2212\u221e\u221efXY(x,z\u2212x)dx Ho... | large_corpus_distillation |
"Polish grammar-Prepositions-Polish uses prepositions, which form phrases by preceding a noun or noun phrase. Different prepositions take different cases (all cases are possible except nominative and vocative); some prepositions can take different cases depending on meaning." | large_corpus_distillation |
"Transformational grammar-Core concepts-Innate linguistic knowledge Using a term such as \"transformation\" may give the impression that theories of transformational generative grammar are intended as a model of the processes by which the human mind constructs and understands sentences, but Chomsky clearly stated that ... | large_corpus_distillation |
"ARM big.LITTLE-The problem that big.LITTLE solves-For a given library of CMOS logic, active power increases as the logic switches more per second, while leakage increases with the number of transistors. So, CPUs designed to run fast are different from CPUs designed to save power. When a very fast out-of-order CPU is i... | large_corpus_distillation |
"Convolutional code-Free distance and error distribution-The free distance (d) is the minimal Hamming distance between different encoded sequences. The correcting capability (t) of a convolutional code is the number of errors that can be corrected by the code. It can be calculated as t=\u230ad\u221212\u230b.\nSince a c... | large_corpus_distillation |
"Itaconic anhydride-Reactions-Itaconic anhydride can react with aromatics such as benzene via Friedel-Crafts acylation. This always happens in such a way that the ring opening occurs at the carbonyl group, which is further away from the methylene group (3-position).\nNucleophiles such as thiols can easily be added to t... | large_corpus_distillation |
"Delta modulation-Delta modulation-A delta modulation (DM or \u0394-modulation) is an analog-to-digital and digital-to-analog signal conversion technique used for transmission of voice information where quality is not of primary importance. DM is the simplest form of differential pulse-code modulation (DPCM) where the ... | large_corpus_distillation |
"B*-Details-Expansion B* is a best-first process, which means that it is very efficient to traverse the tree, repeatedly descending to find a leaf to expand. This section describes how to choose the node to expand. (Note: Whether or not the tree is memory-resident, is a function of the overall implementation efficiency... | large_corpus_distillation |
"Normal-exponential-gamma distribution-Probability density function-The probability density function (pdf) of the normal-exponential-gamma distribution is proportional to exp \u2061((x\u2212\u03bc)24\u03b82)D\u22122k\u22121(|x\u2212\u03bc|\u03b8) ,where D is a parabolic cylinder function.As for the Laplace distributio... | large_corpus_distillation |
"Isotopes of zirconium-Zirconium-93-Nuclear fission produces it at a fission yield of 6.3% (thermal neutron fission of 235U), on a par with the other most abundant fission products. Nuclear reactors usually contain large amounts of zirconium as fuel rod cladding (see zircaloy), and neutron irradiation of 92Zr also prod... | large_corpus_distillation |
"Semantic similarity-Sources-Veksler, V.D. & Gray, W.D. (2006). \"Test Case Selection for Evaluating Measures of Semantic Distance\" (PDF). Proceedings of the 28th Annual Meeting of the Cognitive Science Society, CogSci2006.\nWong, W., Liu, W. & Bennamoun, M. (2008) Featureless Data Clustering. In: M. Song and Y. Wu; H... | large_corpus_distillation |
"Root directory-Unix-like systems-Unix abstracts the nature of this tree hierarchy entirely and in Unix and Unix-like systems the root directory is denoted by the / (slash) sign. Though the root directory is conventionally referred to as /, the directory entry itself has no name \u2013 its path is the \"empty\" part be... | large_corpus_distillation |
"Answer\n41\n1.\n72\n15 8 18\n2. that the coin is fair, that the coin is biased, that the coin is two-headed\n41 41 41\nCompare die-coin experiment and bag of coins experiment. In the die-coin experiment, we toss a coin with a fixed probability of\nheads a random number of times. In the bag of coins experiment, we effe... | large_corpus_distillation |
factors of with a sum of\n3. Write the factored expression\nEXAMPLE2\nFactoring a Trinomial with Leading Coefficient 1\nFactor\nSolution\nWe have a trinomial with leading coefficient and We need to find two numbers with a product of\nand a sum of In the table below, we list factors until we find a pair with the desired... | large_corpus_distillation |
"Exponentiation-Irrationality and transcendence-In other words, if x is irrational and b\u2209{0,1}, then at least one of b, x and bx is transcendental." | large_corpus_distillation |
"Affix grammar-Example-We can describe an extremely simple fragment of English in the following manner: Sentence \u2192 Subject Predicate Subject \u2192 Noun Predicate \u2192 Verb Object Object \u2192 Noun Noun \u2192 John Noun \u2192 Mary Noun \u2192 children Noun \u2192 parents Verb \u2192 like Verb \u2192 likes Verb... | large_corpus_distillation |
to the right of the zero,enter), then guess (move your cursor between\nthe bounds near the zero, enter). Round your answers to the nearest thousandth.\n44. 45. 46." | large_corpus_distillation |
"Similarity learning-Learning setup-Locality sensitive hashing (LSH) Hashes input items so that similar items map to the same \"buckets\" in memory with high probability (the number of buckets being much smaller than the universe of possible input items). It is often applied in nearest neighbor search on large-scale hi... | large_corpus_distillation |
"Fuzzy retrieval-Recent work-Zadrozny revisited the fuzzy information retrieval model. He further extends the fuzzy extended Boolean model by: assuming linguistic terms as importance weights of keywords also in documents taking into account the uncertainty concerning the representation of documents and queries interpre... | large_corpus_distillation |
"Binary icosahedral group-Binary icosahedral group-It is an extension of the icosahedral group I or (2,3,5) of order 60 by the cyclic group of order 2, and is the preimage of the icosahedral group under the 2:1 covering homomorphism Spin SO \u2061(3) of the special orthogonal group by the spin group. It follows that th... | large_corpus_distillation |
"One-time pad-One-time pad-There is some ambiguity to the term \"Vernam cipher\" because some sources use \"Vernam cipher\" and \"one-time pad\" synonymously, while others refer to any additive stream cipher as a \"Vernam cipher\", including those based on a cryptographically secure pseudorandom number generator (CSPRN... | large_corpus_distillation |
"Ford\u2013Fulkerson algorithm-Algorithm-Let G(V,E) be a graph, and for each edge from u to v, let c(u,v) be the capacity and f(u,v) be the flow. We want to find the maximum flow from the source s to the sink t. After every step in the algorithm the following is maintained: This means that the flow through the netwo... | large_corpus_distillation |
"Item (game terminology)-Types-Items often come in various types and in most games where items are collected, they are sorted by these types. In RPGs, an item inventory is a common UI feature where one can view all the items that have been collected thus far. Often, these are sorted by categories, such as \"equipment\"... | large_corpus_distillation |
Markov Models\nHidden Markov Models (HMMs) extend Markov models by assuming that the states of the\nMarkov chain are not observed directly, i.e., the Markov chain itself remains hidden. We\ntherefore also model how the states relate to the actual observations. This assumption of a\nsimple Markov model underlying a sequ... | large_corpus_distillation |
"Classical orthogonal polynomials-Definition-In general, the orthogonal polynomials Pn with respect to a weight W:R\u2192R+ satisfy deg \u2061Pn=n,n=0,1,2,\u2026\u222bPm(x)Pn(x)W(x)dx=0,m\u2260n.\nThe relations above define Pn up to multiplication by a number. Various normalisations are used to fix the constant, e.g... | large_corpus_distillation |
"Collective operation-Broadcast-Since an implementation by means of a sequential for-loop with p\u22121 iterations becomes a bottleneck, divide-and-conquer approaches are common. One possibility is to utilize a binomial tree structure with the requirement that p has to be a power of two. When a processing unit is res... | large_corpus_distillation |
"Chernoff bound-Applications-The set balancing problem arises while designing statistical experiments. Typically while designing a statistical experiment, given the features of each participant in the experiment, we need to know how to divide the participants into 2 disjoint groups such that each feature is roughly as ... | large_corpus_distillation |
wiring of the core of each rotor provided an electrical pathway from the pins on one side to different connection points on the other. The left hand side of each rotor made electrical connection with the rotor to its left. The leftmost rotor then made contact with the reflector (German: Umkehrwalze). The reflector prov... | large_corpus_distillation |
"Pr\u00fcfer sequence-Algorithm to convert a tree into a Pr\u00fcfer sequence-Example Consider the above algorithm run on the tree shown to the right. Initially, vertex 1 is the leaf with the smallest label, so it is removed first and 4 is put in the Pr\u00fcfer sequence. Vertices 2 and 3 are removed next, so 4 is add... | large_corpus_distillation |
"Tree measurement-Height-A third remote method is called the sine-height method or ENTS method. It requires the use of a laser rangefinder and clinometer. In this method the distance to the top of a tree is directly measured by the surveyor using the laser rangefinder. The angle to the top is measured with the clinomet... | large_corpus_distillation |
"Simmons\u2013Su protocols-Multi-cake cutting-A solution to this problem for the case of 2 partners and 2 or 3 cakes was published in 2009. If the number of cakes is m, and each cake is divided to k pieces, then the space of partitions can be represented by an n-vertex d-dimensional polytope, where d=m(k \u2212 1) and ... | large_corpus_distillation |
"Bitwise operations in C-Logical equivalents-Example: The output of the above program will be " | large_corpus_distillation |
and Lemma 7.8.1 all carry over to martingales (submartingales or supermartingales) relative to a joint\nprocess. These theorems are stated more precisely in Exercises 7.23 to 7.26. To summarize them here, assume that {Z n ;n\u22651} is\na martingale (submartingale or supermartingale) relative to a joint process {Z n ,X... | large_corpus_distillation |
"Intermittent fault-Intermittent fault-Intermittent faults are notoriously difficult to identify and repair (\"troubleshoot\") because each individual factor does not create the problem alone, so the factors can only be identified while the malfunction is actually occurring. The person capable of identifying and solvin... | large_corpus_distillation |
"Goldwasser\u2013Micali cryptosystem-Basis-The GM cryptosystem is semantically secure based on the assumed intractability of the quadratic residuosity problem modulo a composite N = pq where p, q are large primes. This assumption states that given (x, N) it is difficult to determine whether x is a quadratic residue mod... | large_corpus_distillation |
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