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h(x)=g(f(x)) is convex. For example, if f is convex, then so is ef(x) because ex is convex and monotonically increasing.\nIf f is concave and g is convex and non-increasing over a univariate domain, then h(x)=g(f(x)) is convex.\nConvexity is invariant under affine maps: that is, if f is convex with domain Df\u2... | large_corpus_distillation |
"Community informatics-Understanding communities-It is crucial to know how communities are formed and evolved and how the participation to a community occurs and differs while formation process. Understanding the nature of communities and the participation process will surely ensure designing and implementing a success... | large_corpus_distillation |
and compare the results to those for the previous problem\n(relevant section)\nQ10\n4\nYou have means, and you want to compare each mean to every other mean.\na. How many tests total are you going to compute?\n0.05\nb. What would be the chance of making at least one Type I error if the Type I error for each test was an... | large_corpus_distillation |
"C++-Language-Polymorphism Polymorphism enables one common interface for many implementations, and for objects to act differently under different circumstances.\nC++ supports several kinds of static (resolved at compile-time) and dynamic (resolved at run-time) polymorphisms, supported by the language features described... | large_corpus_distillation |
"EM algorithm and GMM model-EM algorithm in GMM-The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the z(i) can be randomly initialized. In the E-step, the algorithm tries to guess the value of z(i) based on the parameters, while in the M-step, the algorithm updates t... | large_corpus_distillation |
"Dynamic linker-Implementations-Unix-like systems using ELF, and Darwin-based systems In most Unix-like systems, most of the machine code that makes up the dynamic linker is actually an external executable that the operating system kernel loads and executes first in a process address space newly constructed as a result... | large_corpus_distillation |
"132 (number)-132 (number)-132 (one hundred [and] thirty-two) is the natural number following 131 and preceding 133." | large_corpus_distillation |
"Extravagant number-Mathematical definition-Let b>1 be a number base, and let log b\u2061n\u230b+1 be the number of digits in a natural number n for base b . A natural number n has the prime factorisation prime p\u2223npvp(n) where vp(n) is the p-adic valuation of n , and n is an extravagant number in base b i... | large_corpus_distillation |
"International Securities Identification Number-Examples-Collect odd and even characters: 103000003331163510 = (1, 3, 0, 0, 3, 3, 1, 3, 1), (0, 0, 0, 0, 3, 1, 6, 5, 0) Multiply the group containing the rightmost character (which is the SECOND group) by 2: (0, 0, 0, 0, 6, 2, 12, 10, 0) Add up the individual digits: (1 +... | large_corpus_distillation |
"Interpreter pattern-Example-This C++11 implementation is based on the pre C++98 sample code in the book.\nThe program output is: " | large_corpus_distillation |
"Least-squares support vector machine-Bayesian interpretation for LS-SVM-A general Bayesian evidence framework was developed by MacKay, and MacKay has used it to the problem of regression, forward neural network and classification network. Provided data set D , a model M with parameter vector w and a so-called hyper... | large_corpus_distillation |
"Rotem Commuter Cars-Types-BTC-5 (Blind Trailer Coach) - car coaches with 179 seats and capacity for 185 CTC-5 (Control Trailer Coach) - car coaches with 173 seats and capacity for 179 Bi-level rail set - rail set consisting of locomotive, coaches and cab car seating 233 passengers and capacity for 337 " | large_corpus_distillation |
"Method of conditional probabilities-Example using conditional expectations-Probabilistic proof. Color each vertex black or white by flipping a fair coin. By calculation, for any edge e in E, the probability that it is cut is 1/2. Thus, by linearity of expectation, the expected number of edges cut is |E|/2. Thus, there... | large_corpus_distillation |
"Slowly changing dimension-Type 2 / type 6 fact implementation-Here is the Supplier table using the pure Type 6 methodology: The following example shows how the query must be extended to ensure a single supplier record is retrieved for each transaction.\nA fact record with an effective date (Delivery_Date) of August 9,... | large_corpus_distillation |
is the Boltzmann entropy formula, where k is the Boltzmann constant, which may be interpreted as the thermodynamic entropy per nat. Some authors argue for dropping the word entropy for the H function of information theory and using Shannon's other term, \"uncertainty\", instead." | large_corpus_distillation |
"Pseudorandom graph-Pseudorandom graph-Pseudorandom properties were first formally considered by Andrew Thomason in 1987. He defined a condition called \"jumbledness\": a graph G=(V,E) is said to be (p,\u03b1) -jumbled for real p and \u03b1 with 0<p<1\u2264\u03b1 if |e(U)\u2212p(|U|2)|\u2264\u03b1|U| for every sub... | large_corpus_distillation |
Cantrill, an engineer of a competing OS, agrees that \"Linux wasn't designed, it evolved\", but considers this to be a limitation, proposing that some features, especially those related to security, cannot be evolved into, \"this is not a biological system at the end of the day, it's a software system.\"A Linux-based s... | large_corpus_distillation |
"IOS jailbreaking-IOS jailbreaking-On Apple devices running iOS and iOS-based operating systems, jailbreaking is the use of a privilege escalation exploit to remove software restrictions imposed by the manufacturer. Typically it is done through a series of kernel patches. A jailbroken device permits root access within ... | large_corpus_distillation |
"Email spam-Related vocabulary-Final, Ultimate Solution for the Spam Problem (FUSSP) An ironic reference to na\u00efve developers who believe they have invented the perfect spam filter, which will stop all spam from reaching users' inboxes while deleting no legitimate email accidentally." | large_corpus_distillation |
"Normally distributed and uncorrelated does not imply independent-Examples-A symmetric example Suppose X has a normal distribution with expected value 0 and variance 1. Let W have the Rademacher distribution, so that W=1 or W=\u22121 , each with probability 1/2, and assume W is independent of X . Let Y=WX . Then... | large_corpus_distillation |
"Gradient descent-Comments-Methods based on Newton's method and inversion of the Hessian using conjugate gradient techniques can be better alternatives. Generally, such methods converge in fewer iterations, but the cost of each iteration is higher. An example is the BFGS method which consists in calculating on every st... | large_corpus_distillation |
(x2+y2)3/2\n\u21c0\n=F(x,y).\n\uf128 Exercise 16.3.7\nFind a potential function f for the three-dimensional gravitational force\n\u21c0 \u2212Gx \u2212Gy \u2212Gz\nF(x,y,z)=\u27e8 , , \u27e9.\n(x2+y2+z2) 3/2 (x2+y2+z2) 3/2 (x2+y2+z2) 3/2\nHint\nFollow the Problem-Solving Strategy.\nAnswer\nG\nf(x,y,z)= \u2212\u2212\u22... | large_corpus_distillation |
"Primality certificate-Primality certificate-Producing certificates for the complement problem, to establish that a number is composite, is straightforward: it suffices to give a nontrivial divisor. Standard probabilistic primality tests such as the Baillie\u2013PSW primality test, the Fermat primality test, and the Mi... | large_corpus_distillation |
"Linux kernel-Architecture and features-In-kernel API There are several kernel internal APIs utilized between the different subsystems. Some are available only within the kernel subsystems, while a somewhat limited set of in-kernel symbols (i.e., variables, data structures, and functions) is exposed also to dynamically... | large_corpus_distillation |
"Linux namespaces-Implementation details-The kernel assigns each process a symbolic link per namespace kind in /proc/<pid>/ns/. The inode number pointed to by this symlink is the same for each process in this namespace. This uniquely identifies each namespace by the inode number pointed to by one of its symlinks.\nRead... | large_corpus_distillation |
"Covariance-Examples-Suppose that X and Y have the following joint probability mass function, in which the six central cells give the discrete joint probabilities f(x,y) of the six hypothetical realizations (x,y)\u2208S={(5,8),(6,8),(7,8),(5,9),(6,9),(7,9)} :X can take on three values (5, 6 and 7) while Y can take... | large_corpus_distillation |
= ((x+y)+y)+y. An example for non-commuting substitutions is { x \u21a6 y } { y \u21a6 z } = { x \u21a6 z, y \u21a6 z }, but { y \u21a6 z} { x \u21a6 y} = { x \u21a6 y, y \u21a6 z }." | large_corpus_distillation |
"Partial derivative-Example-Once a value of y is chosen, say a, then f(x,y) determines a function fa which traces a curve x2 + ax + a2 on the xz-plane: In this expression, a is a constant, not a variable, so fa is a function of only one real variable, that being x. Consequently, the definition of the derivative for a f... | large_corpus_distillation |
"Man-in-the-middle attack-Defense and detection-Tamper detection Latency examination can potentially detect the attack in certain situations, such as with long calculations that lead into tens of seconds like hash functions. To detect potential attacks, parties check for discrepancies in response times. For example: Sa... | large_corpus_distillation |
"MD2 (hash function)-MD2 (hash function)-The MD2 Message-Digest Algorithm is a cryptographic hash function developed by Ronald Rivest in 1989. The algorithm is optimized for 8-bit computers. MD2 is specified in IETF RFC 1319. The \"MD\" in MD2 stands for \"Message Digest\".\nEven though MD2 is not yet fully compromised... | large_corpus_distillation |
sequence of independent random variables with n + identically distributed. We assume\nE(|V |)<\u221e n\u2208N a {V :n\u2208N } X={X :n\u2208N}\nthat n for and we let denote the common mean of n + . Let n be the partial sum\nV\nprocess associated with so that\n17.1.4 https://stats.libretexts.org/@go/page/10299" | large_corpus_distillation |
share ideas with one another. An opinion leader has constructed this network, but the ability to influence others lies in the network itself. In order to effectively influence the opinion of followers, they must find the leader to be above them." | large_corpus_distillation |
"Set (mathematics)-Principle of inclusion and exclusion-The inclusion\u2013exclusion principle is a technique for counting the elements in a union of two finite sets in terms of the sizes of the two sets and their intersection. It can be expressed symbolically as A more general form of the principle gives the cardinali... | large_corpus_distillation |
"Transient execution CPU vulnerability-Overview-In October 2021 for the first time ever a vulnerability similar to Meltdown was disclosed to be affecting all AMD CPUs however the company doesn't think any new mitigations have to be applied and the existing ones are already sufficient.In March 2022, a new variant of the... | large_corpus_distillation |
words are embedded into meaningful text. This is because meaningful texts are stored better in memory and are more deeply processed." | large_corpus_distillation |
"Active SETI-Transmissions-Below is a table of messages sent and target/destination stars, ordered chronologically by date of sending: " | large_corpus_distillation |
"Monadic second-order logic-Computational complexity of evaluation-By contrast, when we wish to check whether a Boolean MSO formula is satisfied by an input finite tree, this problem can be solved in linear time in the tree, by translating the Boolean MSO formula to a tree automaton and evaluating the automaton on the ... | large_corpus_distillation |
"Paving matroid-History-Paving matroids were initially studied by Hartmanis (1959), in their equivalent formulation in terms of d -partitions; Hartmanis called them generalized partition lattices. In their 1970 book Combinatorial Geometries, Henry Crapo and Gian-Carlo Rota observed that these structures were matroidal... | large_corpus_distillation |
"ISO 25178-New features-Nesting index: index corresponding to the cut-off wavelength of a linear filter, or to the scale of the structuring element of a morphological filter. Under 25178, industry-specific taxonomies such as roughness vs waviness are replaced by the more general concept of \"scale limited surface\" and... | large_corpus_distillation |
"Fundamental theorems of welfare economics-Proof of the first fundamental theorem-An allocation is a pair (X,Y) where X\u2208\u03a0i\u2208IRG and Y\u2208\u03a0j\u2208JRG , i.e. X is the 'matrix' (allowing potentially infinite rows/columns) whose ith column is the bundle of goods allocated to consumer i and Y is th... | large_corpus_distillation |
"Page replacement algorithm-Page replacement algorithms-The not frequently used page-replacement algorithm generates fewer page faults than the least recently used page replacement algorithm when the page table contains null pointer values." | large_corpus_distillation |
"Pointer (computer programming)-Making pointers safer-As a pointer allows a program to attempt to access an object that may not be defined, pointers can be the origin of a variety of programming errors. However, the usefulness of pointers is so great that it can be difficult to perform programming tasks without them. C... | large_corpus_distillation |
"Semigroup with involution-Semigroup with involution-In mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which\u2014roughly speaking\u2014brings it closer to a group because this involution, considered as unary oper... | large_corpus_distillation |
"Computer-Hardware-A key component common to all CPUs is the program counter, a special memory cell (a register) that keeps track of which location in memory the next instruction is to be read from.The control system's function is as follows\u2014 this is a simplified description, and some of these steps may be perform... | large_corpus_distillation |
"Numeric precision in Microsoft Excel-Accuracy and binary storage-With this option, depending upon circumstance, accuracy may turn out to be better or worse, but you will know exactly what Excel is doing. (Only the selected precision is retained, and one cannot recover extra digits by reversing this option.) Some simil... | large_corpus_distillation |
"Chinese remainder theorem-Applications-Dedekind's theorem Dedekind's theorem on the linear independence of characters. Let M be a monoid and k an integral domain, viewed as a monoid by considering the multiplication on k. Then any finite family ( fi )i\u2208I of distinct monoid homomorphisms fi : M \u2192 k is linearl... | large_corpus_distillation |
"Self-stabilization-Overview-Efficiency improvements More recently, researchers have presented newer methods for light-weight error detection for self-stabilizing systems using local checking. and for general tasks.The term local refers to a part of a computer network. When local detection is used, a computer in a netw... | large_corpus_distillation |
"Pathfinding-Multi-agent pathfinding-Multi-agent pathfinding is to find the paths for multiple agents from their current locations to their target locations without colliding with each other, while at the same time optimizing a cost function, such as the sum of the path lengths of all agents. It is a generalization of ... | large_corpus_distillation |
"Random binary tree-Binary trees from random permutations-The longest path Although not as easy to analyze as the average path length, there has also been much research on determining the expectation (or high probability bounds) of the length of the longest path in a binary search tree generated from a random insertion... | large_corpus_distillation |
rev3. This document emphasizes the importance of self-assessments as well as risk assessments. [4] Special publication 800-37, updated in 2010 provides a new risk approach: \"Guide for Applying the Risk Management Framework to Federal Information Systems\" Special publication 800-53 rev4, \"Security and Privacy Control... | large_corpus_distillation |
"Software security assurance-Software security assurance activities-There are two basic types of Software Security Assurance activities.\nSome focus on ensuring that information processed by an information system is assigned a proper sensitivity category, and that the appropriate protection requirements have been devel... | large_corpus_distillation |
"Dynamic site acceleration-Techniques-Prefetching If personalized content cannot be cached, it might be queued on an edge device. This means that the system will store a list of possible responses that might needed in the future, allowing them to be readily served. This differs from caching as prefetched responses are ... | large_corpus_distillation |
"Matching polytope-The matching polytopes in a bipartite graph-If K has a column with a single 1, then det K can be expanded about this column and it equals either +1 or -1 times a determinant of a (k \u2212 1) by (k \u2212 1) matrix, which by the induction assumption is 0 or +1 or \u22121." | large_corpus_distillation |
"Ring learning with errors key exchange-Parameter choices-Also in their November 2015 paper, Alkim, Ducas, P\u00f6ppelmann and Schwabe recommend that the choice of the base polynomial for the key exchange ( a(x) above ) be either generated randomly from a secure random number generator for each exchange or created in a... | large_corpus_distillation |
08.BB With only medium-sized cations, (OH, etc.):RO4 \u00a31:1: 15 Sarkinite; 30 Zincolivenite, 30 Eveite, 30 Olivenite, 30 Adamite, 30 Auriacusite; 35 Paradamite, 40 Wilhelmkleinite, 50 Namibite, 60 Urusovite, 65 Theoparacelsite, 70 Turanite, 75 Stoiberite, 80 Fingerite, 85 Averievite 08.BC With only medium-sized cati... | large_corpus_distillation |
"XOR gate-Alternatives-For the NAND constructions, the upper arrangement requires fewer gates. For the NOR constructions, the lower arrangement offers the advantage of a shorter propagation delay (the time delay between an input changing and the output changing)." | large_corpus_distillation |
"Information-theoretic security-Physical layer encryption-The basic idea of the information theoretic approach to securely transmit confidential messages (without using an encryption key) to a legitimate receiver is to use the inherent randomness of the physical medium (including noises and channel fluctuations due to ... | large_corpus_distillation |
this, software packages can then simply request a component that has a particular major version, and any minor version (greater than or equal to a particular minor version). As such, they will continue to work, and dependencies will be resolved successfully, even if the minor version changes. Semantic Versioning (aka \... | large_corpus_distillation |
"Emergency position-indicating radiobeacon-Search-and-rescue response-Responsible agencies RCCs are responsible for a geographic area, known as a \"search-and-rescue region of responsibility\" (SRR). SRRs are designated by the International Maritime Organization and the International Civil Aviation Organization. RCCs a... | large_corpus_distillation |
"Probability distribution fitting-Selection of distribution-Skew distributions to the left When the smaller values tend to be farther away from the mean than the larger values, one has a skew distribution to the left (i.e. there is negative skewness), one may for example select the square-normal distribution (i.e. the ... | large_corpus_distillation |
"Field (mathematics)-Elementary notions-A field may thus be defined as set F equipped with two operations denoted as an addition and a multiplication such that F is an abelian group under addition, F \\ {0} is an abelian group under multiplication (where 0 is the identity element of the addition), and multiplication is... | large_corpus_distillation |
"Ext2-History-On Linux kernels prior to 2.6.17, restrictions in the block driver mean that ext2 filesystems have a maximum file size of 2 TiB." | large_corpus_distillation |
"7.7: Normal Approximation Demonstration\nLearning Objectives\nState the relationship between sample size and the accuracy of normal approximation of\nthe binomial distribution\nInstructions\nThe normal distribution can be used to approximate the binomial distribution. This demonstration allows you to explore the\naccu... | large_corpus_distillation |
"Matching polytope-Integral matching polytope-The integral matching polytope (usually called just the matching polytope) of a graph G, denoted MP(G), is a polytope whose corners are the incidence vectors of the integral matchings in G.\nMP(G) is always contained in FMP(G). In the above examples: The MP of the triangle ... | large_corpus_distillation |
"190 (number)-In mathematics-190 is a triangular number, a hexagonal number, and a centered nonagonal number, the fourth figurate number (after 1, 28, and 91) with that combination of properties. It is also a truncated square pyramid number." | large_corpus_distillation |
"Smart File System-Features-SFS uses block sizes ranging from 512 (29) to 32768 (215) bytes with a maximum partition size of 128 GB." | large_corpus_distillation |
"Distributed point function-Distributed point function-Given any two values a and b one can define a point function Pa,b(x) (a variant of the Kronecker delta function) by for for x\u2260a That is, it is zero everywhere except at a , where its value is b A distributed point function consists of a family of functi... | large_corpus_distillation |
"Quantum logic gate-Circuit composition-Serially wired gates Assume that we have two gates A and B that both act on n qubits. When B is put after A in a series circuit, then the effect of the two gates can be described as a single gate C." | large_corpus_distillation |
it is computationally infeasible to retrieve the entire list and operate on it (the initial 'entire list' may be an entire XML database).\nIn XPath, the expression: is conceptually evaluated as a series of \"steps\" where each step produces a list and the next step applies a filter function to each element in the previ... | large_corpus_distillation |
"Statistica (journal)-Abstracting and indexing-The journal is abstracted and indexed in Web of Science Core Collection \u2013 Emerging Sources Citation Index, a Clarivate Analytics database and Repec." | large_corpus_distillation |
"Sub-Gaussian distribution-More equivalent definitions-Laplace transform condition: for some B, b > 0, E\u2061e\u03bb(X\u2212E\u2061[X])\u2264Be\u03bb2b holds for all \u03bb Moment condition: for some K > 0, E\u2061|X|p\u2264Kppp/2 for all p\u22651 Moment generating function condition: for some L>0 , exp exp \u20... | large_corpus_distillation |
"Adiabatic accessibility-Thermodynamic entropy-A definition of thermodynamic entropy can be based entirely on certain properties of the relation \u227a of adiabatic accessibility that are taken as axioms in the Lieb-Yngvason approach. In the following list of properties of the \u227a operator, a system is represented... | large_corpus_distillation |
"Memory safety-History-Memory errors were first considered in the context of resource management (computing) and time-sharing systems, in an effort to avoid problems such as fork bombs. Developments were mostly theoretical until the Morris worm, which exploited a buffer overflow in fingerd. The field of computer securi... | large_corpus_distillation |
U \u2208T f\n1. Trivially, if , then for so is continuous.\nf :T \u2192S x f {x} S f\u22121{x}\n2. Suppose that is continuous and that is in the range of . Then is open and closed in , so is open\nT T f\u22121{x}=T\nand closed in . If is connected, this means that .\nEuclidean Spaces\nThe standard topologies used in th... | large_corpus_distillation |
"Wildmat-Pattern matching operations-There are five pattern matching operations other than a strict one-to-one match between the pattern and the source to be checked for a match.\nAsterisk (*) to match any sequence of zero or more characters.\nQuestion mark (?) to match any single character." | large_corpus_distillation |
"Bernoulli process-Randomness extraction-Von Neumann (classical) main operation pseudocode: Iterated von Neumann extractor This decrease in efficiency, or waste of randomness present in the input stream, can be mitigated by iterating the algorithm over the input data. This way the output can be made to be \"arbitrarily... | large_corpus_distillation |
"Orthogonal frequency-division multiple access-Usage-the Qualcomm Flarion Technologies Mobile Flash-OFDM the now defunct Qualcomm/3GPP2 Ultra Mobile Broadband (UMB) project, intended as a successor of CDMA2000, but replaced by LTE.OFDMA is also a candidate access method for the IEEE 802.22 Wireless Regional Area Networ... | large_corpus_distillation |
"First-class function-Language support-The C family allowed both passing functions as arguments and returning them as results, but avoided any problems by not supporting nested functions. (The gcc compiler allows them as an extension.) As the usefulness of returning functions primarily lies in the ability to return nes... | large_corpus_distillation |
"Fault tolerance-Fault tolerance techniques-Replication Spare components address the first fundamental characteristic of fault tolerance in three ways: Replication: Providing multiple identical instances of the same system or subsystem, directing tasks or requests to all of them in parallel, and choosing the correct re... | large_corpus_distillation |
"Doob's martingale convergence theorems-Doob's upcrossing inequality-The following result, called Doob's upcrossing inequality or, sometimes, Doob's upcrossing lemma, is used in proving Doob's martingale convergence theorems. A \"gambling\" argument shows that for uniformly bounded supermartingales, the number of upcro... | large_corpus_distillation |
"Transformer (machine learning model)-Architecture-All transformers have the same primary components: Tokenizers, which convert text into tokens Embedding layers, which convert tokens into semantically meaningful representations Transformer layers, which carry out the reasoning capabilities, and consist of Attention an... | large_corpus_distillation |
"Package cushioning-Evaluation of finished package-Verification and validation of prototype designs are required. The design of a package and its cushioning is often an iterative process involving several designs, evaluations, redesigns, etc. Several (ASTM, ISTA, and others) published package testing protocols are avai... | large_corpus_distillation |
then switch between various gates (\"patterns\") exponentially fast." | large_corpus_distillation |
"Reliable multicast-Other existing or proposed protocols-Pragmatic General Multicast (PGM) Tibco Software's TRDP (part of RV). Note: when Tibco acquired Talarian, they inherited a PGM implementation with SmartSockets (SmartPGM). TRDP pre-dates the development of SmartPGM OpenDDS as an open source implementation since t... | large_corpus_distillation |
"Defense Message System-Defense Message System-The Defense Message System or Defense Messaging System (DMS) is a deployment of secure electronic mail and directory services in the United States Department of Defense. DMS was intended to replace the AUTODIN network, and is based on implementations of the OSI X.400 mail,... | large_corpus_distillation |
"Negative log predictive density-Example-Calculating the NLPD for a simple classification example We have a method that classifies images as dogs or cats. Importantly it assigns probabilities to the two classes.\nWe show it a picture of three dogs and three cats. It predicts that the probability of the first three bein... | large_corpus_distillation |
"Document clustering-Document clustering-Document clustering (or text clustering) is the application of cluster analysis to textual documents. It has applications in automatic document organization, topic extraction and fast information retrieval or filtering." | large_corpus_distillation |
"Space (mathematics)-Taxonomy of spaces-Such topology is non-unique in general, but unique when the real linear space is finite-dimensional. For these spaces the transition is both injective and surjective, that is, bijective; see the arrow from \"finite-dim real linear topological\" to \"finite-dim real linear\" on Fi... | large_corpus_distillation |
"Three utilities problem-Properties of the utility graph-Generalizations Two important characterizations of planar graphs, Kuratowski's theorem that the planar graphs are exactly the graphs that contain neither K3,3 nor the complete graph K5 as a subdivision, and Wagner's theorem that the planar graphs are exactly th... | large_corpus_distillation |
"Cure-Statistical model-The Berkson and Gage equation is S(t)=p+[(1\u2212p)\u00d7S\u2217(t)] where S(t) is the proportion of people surviving at any given point in time, p is the proportion that are permanently cured, and S\u2217(t) is an exponential curve that represents the survival of the non-cured people." | large_corpus_distillation |
"8-8-8 (eight) is the natural number following 7 and preceding 9." | large_corpus_distillation |
"Sorting algorithm-Comparison of algorithms-Non-comparison sorts The following table describes integer sorting algorithms and other sorting algorithms that are not comparison sorts. As such, they are not limited to \u03a9(n log n). Complexities below assume n items to be sorted, with keys of size k, digit size d, and r... | large_corpus_distillation |
"Polygon partition-Partition a polygon into convex polygons-Equalizing the area and perimeter The fair polygon partitioning problem is to partition a (convex) polygon into (convex) pieces with an equal perimeter and equal area (this is a special case of fair cake-cutting). Any convex polygon can be easily cut into any ... | large_corpus_distillation |
"Covariance matrix-Properties-The matrix KYX\u2061KXX\u22121 is known as the matrix of regression coefficients, while in linear algebra KY|X is the Schur complement of KXX in \u03a3 The matrix of regression coefficients may often be given in transpose form, KXX\u22121\u2061KXY , suitable for post-multiplying a row... | large_corpus_distillation |
"Generalized method of moments-Properties-Relative Efficiency So far we have said nothing about the choice of matrix W, except that it must be positive semi-definite. In fact any such matrix will produce a consistent and asymptotically normal GMM estimator, the only difference will be in the asymptotic variance of that... | large_corpus_distillation |
"Conceptual dependency theory-Conceptual dependency theory-Schank developed the model to represent knowledge for natural language input into computers. Partly influenced by the work of Sydney Lamb, his goal was to make the meaning independent of the words used in the input, i.e. two sentences identical in meaning, woul... | large_corpus_distillation |
"K\u0151nig's lemma-Computability aspects-The computability aspects of K\u0151nig's lemma have been thoroughly investigated. For this purpose it is convenient to state K\u0151nig's lemma in the form that any infinite finitely branching subtree of \u03c9<\u03c9 has an infinite path. Here \u03c9 denotes the set of natu... | large_corpus_distillation |
to be executed out of order, improving performance." | large_corpus_distillation |
digits in length.\nNigeria Codes are four to five digits in length.\nNorway Codes are four to five digits in length.\nPakistan Codes are three and four digits in length. Users are charged PKR 5 - PKR 25 per SMS sent on short codes. Mobile operators charge a setup fee, monthly fee and fee per keyword for short codes. Sh... | large_corpus_distillation |
"Plural-POS tagging-In part-of-speech tagging notation, tags are used to distinguish different types of plurals based on their grammatical and semantic context. Resolution varies, for example the Penn-Treebank tagset (~36 tags) has two tags: NNS - noun, plural, and NPS - Proper noun, plural, while the CLAWS 7 tagset (~... | large_corpus_distillation |
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