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"Virtual private network-Security mechanisms-Authentication Tunnel endpoints must be authenticated before secure VPN tunnels can be established. User-created remote-access VPNs may use passwords, biometrics, two-factor authentication, or other cryptographic methods. Network-to-network tunnels often use passwords or dig... | large_corpus_distillation |
foreshadowing the New Testament Typology (urban planning and architecture), the classification of characteristics common to buildings or urban spaces Building typology, relating to buildings and architecture Farm typology, farm classification by the USDA Sociopolitical typology, four types, or levels, of a political or... | large_corpus_distillation |
"Dynamic software updating-Implementation-DSU systems must load new code into a running program, and transform existing state into a format that is understood by the new code. Since many motivational use-cases of DSU are time-critical (for example, deploying a security fix on a live and vulnerable system), DSU systems ... | large_corpus_distillation |
"Collection (abstract data type)-Associative collections-Sets In a set, the order of data items does not matter (or is undefined) but duplicate data items are not permitted. Examples of operations on sets are the addition and removal of data items and searching for a data item in the set. Some languages support sets di... | large_corpus_distillation |
"Base32-Disadvantages-Base32 representation takes roughly 20% more space than Base64. Also, because it encodes 5 bytes to 8 characters (rather than 3 bytes to 4 characters), padding to an 8-character boundary is a greater burden on short messages (which may be a reason to elide padding, which is an option in RFC 4648).... | large_corpus_distillation |
"NP/poly-Applications-The same computational hardness assumption that co-NP is not a subset of NP/poly also implies several other results in complexity such as the optimality of certain kernelization techniques." | large_corpus_distillation |
"Principal component analysis-Further considerations-PCA is a popular primary technique in pattern recognition. It is not, however, optimized for class separability. However, it has been used to quantify the distance between two or more classes by calculating center of mass for each class in principal component space a... | large_corpus_distillation |
"Sorting algorithm-Popular sorting algorithms-Heapsort Heapsort is a much more efficient version of selection sort. It also works by determining the largest (or smallest) element of the list, placing that at the end (or beginning) of the list, then continuing with the rest of the list, but accomplishes this task effici... | large_corpus_distillation |
in many other datasets could have induced overfitting).While the cost of training GPT-2 is known to have been $256 per hour, the amount of hours it took to complete training is unknown; therefore, the overall training cost cannot be estimated accurately. However, comparable large language models using transformer archi... | large_corpus_distillation |
structure rules, transformational rules and morphophonemic rules. The phrase structure rules are used for expanding grammatical categories and for substitutions. These yield a string of morphemes. A transformational rule \"operates on a given string ... with a given constituent structure and converts it into a new stri... | large_corpus_distillation |
"Covering problems-Rainbow covering and conflict-free covering-If the geometric cover problem admits an r-approximation algorithm, then the conflict-free geometric cover problem admits a similar approximation algorithm in FPT time." | large_corpus_distillation |
open rooms that function as multiple rooms within a single living space. The most common design is a great room that combines the kitchen, dining room, and living room into one shared space. Such floor plans usually work well in homes with a smaller area, while larger homes have more leeway to work with when integratin... | large_corpus_distillation |
"Btrfs-Design-Superblock All the file system's trees\u2014including the chunk tree itself\u2014are stored in chunks, creating a potential bootstrapping problem when mounting the file system. To bootstrap into a mount, a list of physical addresses of chunks belonging to the chunk and root trees are stored in the superbl... | large_corpus_distillation |
"Lustre (file system)-Architecture-A Lustre file system has three major functional units: One or more metadata servers (MDS) nodes that have one or more metadata target (MDT) devices per Lustre filesystem that stores namespace metadata, such as filenames, directories, access permissions, and file layout. The MDT data i... | large_corpus_distillation |
n\u2192\u221e \u03b8\u2208T\n1. is asymptotically unbiased if n as for each .\nU mse(U \u2223\u03b8)\u21920 n\u2192\u221e \u03b8\u2208T\n2. is mean-square consistent if n as for each .\nOften we cannot construct unbiased Bayesian estimators, but we do hope that our estimators are at least asymptotically unbiased\nU\nan... | large_corpus_distillation |
"Static single-assignment form-Extensions-Extensions to SSA form can be divided into two categories.\nRenaming scheme extensions alter the renaming criterion. Recall that SSA form renames each variable when it is assigned a value. Alternative schemes include static single use form (which renames each variable at each s... | large_corpus_distillation |
"Dirichlet-multinomial distribution-Likelihood function-For a set of individual outcomes Joint distribution For categorical variables Z=z1,\u2026,zN , the marginal joint distribution is obtained by integrating out p Pr Pr Pr (p\u2223\u03b1)dp which results in the following explicit formula: Pr (Z\u2223\u03b1)=\u0393(... | large_corpus_distillation |
"Foundations of mathematics-Historical context-Group theory For the first time, the limits of mathematics were explored. Niels Henrik Abel (1802\u20131829), a Norwegian, and \u00c9variste Galois, (1811\u20131832) a Frenchman, investigated the solutions of various polynomial equations, and proved that there is no genera... | large_corpus_distillation |
"Fiber (computer science)-Advantages and disadvantages-Because fibers multitask cooperatively, thread safety is less of an issue than with preemptively scheduled threads, and synchronization constructs including spinlocks and atomic operations are unnecessary when writing fibered code, as they are implicitly synchroniz... | large_corpus_distillation |
"Instruction scheduling-Data hazards-Write after Read (WAR or \"Anti\"): Instruction 1 reads a location that is later overwritten by Instruction 2. Instruction 1 must come first, or it will read the new value instead of the old.\nWrite after Write (WAW or \"Output\"): Two instructions both write the same location. They... | large_corpus_distillation |
IP address to the attacker's MAC address. Such an attack is commonly referred to as a \"man in the middle\" attack." | large_corpus_distillation |
node on FinFET silicon should show reduced power consumption and therefore heat over their 28 nm and 32 nm non-FinFET predecessors (for equivalent designs), or be more computationally powerful at equivalent heat output/power consumption.\nZen also uses clock gating, reducing the frequency of underutilized portions of t... | large_corpus_distillation |
"Content determination-Content determination-Content determination is the subtask of natural language generation (NLG) that involves deciding on the information to be communicated in a generated text. It is closely related to the task of document structuring." | large_corpus_distillation |
"H3 (classification)-Rankings-This classification has UCI rankings for elite competitors." | large_corpus_distillation |
variance. For the data which can be negative as well as positive, the null distribution for cosine similarity is the distribution of the dot product of two independent random unit vectors. This distribution has a mean of zero and a variance of 1/n. While Euclidean distance will be invariant to this correction." | large_corpus_distillation |
"Real hyperelliptic curve-Transformation from real hyperelliptic curve to imaginary hyperelliptic curve-A (finite or infinite) point is said to be ramified if it is equal to its own opposite. It means that P=(a,b)=P\u00af=(a,\u2212b\u2212h(a)) , i.e. that h(a)+2b=0 . If P is ramified then D=P\u2212\u221e1 is a rami... | large_corpus_distillation |
"Full reptend prime-Binary full reptend primes-Further, all safe primes congruent to 3 modulo 8 are full reptend primes in base 2. For example, 3, 11, 59, 83, 107, 179, 227, 347, 467, 563, 587, 1019, 1187, 1283, 1307, 1523, 1619, 1907, etc. (less than 2000)." | large_corpus_distillation |
of 10.\n2. Add zeros at the end of the number as needed.\n\uf128 Exercise 1.8.25\nMultiply 5.63\n1. by 10\n2. by 100\n3. by 1,000.\nAnswer\nBy looking at the number of zeros in the multiple of ten, we see the number of places we need to move the decimal to the right.\n\u24d0\n5.63(10)\nThere is 1 zero in 10, so move th... | large_corpus_distillation |
"Paravector-The three-dimensional Euclidean space-Every expression in the paravector space can be written in terms of the null basis. A paravector p is in general parametrized by two real scalars numbers {u,v} and a general scalar number w (including scalar and pseudoscalar numbers) p=uP\u00af3+vP3+we1P3+w\u2020P3e1... | large_corpus_distillation |
"Emoji domain-Availability and registration-The availability of an emoji domain can be verified by using an emoji domain search engine or by checking the WHOIS data of the punycoded domain." | large_corpus_distillation |
"Representation theory of finite groups-Decompositions-Let V\u03c0 be a nontrivial irreducible representation of G.\nThen the isotype to the trivial representation of \u03c0 is the null space. That means the following equation holds 0.\nLet e1,...,en be an orthonormal basis of V\u03c0.\nThen we have: Tr 0.\nTheref... | large_corpus_distillation |
"Perfect digital invariant-Programming example-The example below implements the perfect digital invariant function described in the definition above to search for perfect digital invariants and cycles in Python. This can be used to find happy numbers." | large_corpus_distillation |
"League Bowling-Modes-League Bowling has three types of modes, played up to 4 players.\nRegulation Played just like a normal game of bowling, with 300 being a perfect score.\nFlash Values of 100 to 300 will flash on a randomizer during the time the bowler throws his shot. A strike adds the bonus flash value to the scor... | large_corpus_distillation |
"Telegraph key-Types-Since its original inception, the telegraph key's design has developed such that there are now multiple types of keys." | large_corpus_distillation |
"Lambda calculus-Informal description-The following definitions are necessary in order to be able to define \u03b2-reduction: Free variables The free variables of a term are those variables not bound by an abstraction. The set of free variables of an expression is defined inductively: The free variables of x are just ... | large_corpus_distillation |
"Flow cytometry-Data analysis-Computational analysis Recent progress on automated population identification using computational methods has offered an alternative to traditional gating strategies. Automated identification systems could potentially help findings of rare and hidden populations. Representative automated m... | large_corpus_distillation |
"Pythagorean theorem-Other proofs of the theorem-Let A, B, C be the vertices of a right triangle, with a right angle at A. Drop a perpendicular from A to the side opposite the hypotenuse in the square on the hypotenuse. That line divides the square on the hypotenuse into two rectangles, each having the same area as one... | large_corpus_distillation |
irrelevance is that maximizing the expected value of utility u(c)=(1\u2212e\u2212ac)/a gives the same result for the choice variable as does maximizing the expected value of u(c)=\u2212e\u2212ac/a ; since expected values of utility (as opposed to the utility function itself) are interpreted ordinally instead of cardi... | large_corpus_distillation |
"Idempotence-Computer science meaning-A sequence of idempotent subroutines where at least one subroutine is different from the others, however, is not necessarily idempotent if a later subroutine in the sequence changes a value that an earlier subroutine depends on\u2014idempotence is not closed under sequential compos... | large_corpus_distillation |
"Agile software development-Experience and adoption-Public surveys One of the early studies reporting gains in quality, productivity, and business satisfaction by using agile software developments methods was a survey conducted by Shine Technologies from November 2002 to January 2003.A similar survey, the State of Agil... | large_corpus_distillation |
"Zinc Finger Protein 800-Transcript level regulation-Looking at the intron sequences next to the beginning and end of each exon and comparing those to favorable ones, it was found that all of the splice regions on ZNF800 are favorable. This explains why there are no shorter ZNF800 isoforms." | large_corpus_distillation |
"Set (mathematics)-Basic operations-their intersection A \u2229 B is the set of all things that are members of both A and B. If A \u2229 B = \u2205, then A and B are said to be disjoint." | large_corpus_distillation |
"COMMIT (SQL)-COMMIT (SQL)-In computer science and data management, a commit is the making of a set of tentative changes permanent, marking the end of a transaction and providing Durability to ACID transactions. A commit is an act of committing. The record of commits is called the commit log.\nIn terms of transactions,... | large_corpus_distillation |
"Doubly linked list-Advanced concepts-function insertBefore(Node node, Node newNode) if node.prev == null error \"The node is not in a list\" newNode.prev := node.prev atAddress(newNode.prev) := newNode newNode.next := node node.prev = addressOf(newNode.next) function insertAfter(Node node, Node newNode) newNode.next :... | large_corpus_distillation |
"Integer square root-Digit-by-digit algorithm-The traditional pen-and-paper algorithm for computing the square root n is based on working from higher digit places to lower, and as each new digit pick the largest that will still yield a square \u2264n . If stopping after the one's place, the result computed will be th... | large_corpus_distillation |
"Tree structure-Terminology and properties-Tree structures can depict all kinds of taxonomic knowledge, such as family trees, the biological evolutionary tree, the evolutionary tree of a language family, the grammatical structure of a language (a key example being S \u2192 NP VP, meaning a sentence is a noun phrase and... | large_corpus_distillation |
"Proof by example-Valid cases of proof by example-In certain circumstances, examples can suffice as logically valid proof.\nProofs of existential statements In some scenarios, an argument by example may be valid if it leads from a singular premise to an existential conclusion (i.e. proving that a claim is true for at l... | large_corpus_distillation |
:= T]\u2286T} Less formally, this means that, for a given transition system (S,R,V) :p holds in the set of states V(p) ;\u03d5\u2227\u03c8 holds in every state where \u03d5 and \u03c8 both hold; \u00ac\u03d5 holds in every state where \u03d5 does not hold." | large_corpus_distillation |
"IOS 12-App features-FaceTime FaceTime gains support for Animoji and Memoji, as well as new text and GIF effects similar to those found on other social media applications and in the Messages application.iOS 12.1, released on October 30, 2018, adds the ability to include up to 32 people in a FaceTime conversation. This ... | large_corpus_distillation |
"Test-driven development-Development style-To achieve some advanced design concept such as a design pattern, tests are written that generate that design. The code may remain simpler than the target pattern, but still pass all required tests. This can be unsettling at first but it allows the developer to focus only on w... | large_corpus_distillation |
"Gene nomenclature-Vertebrate gene and protein symbol conventions-Mouse and rat Gene symbols generally are italicised, with only the first letter in uppercase and the remaining letters in lowercase (Shh). Italics are not required on web pages. Protein designations are the same as the gene symbol, but are not italicised... | large_corpus_distillation |
models, the posterior distribution is given by: P(\u03b8,\u03d5,X\u2223Y)=P(Y\u2223\u03b8)P(\u03b8\u2223\u03d5)P(\u03d5\u2223X)P(X)P(Y) P(\u03b8,\u03d5,X\u2223Y)\u221dP(Y\u2223\u03b8)P(\u03b8\u2223\u03d5)P(\u03d5\u2223X)P(X) " | large_corpus_distillation |
"Key feedback mode-Key feedback mode-Historically, encryption modes have been studied extensively in regard to their error propagation properties under various scenarios of data modification. Later development regarded integrity protection as an entirely separate cryptographic goal. Some modern modes of operation combi... | large_corpus_distillation |
(to avoid overflows) and the RFC tag has been removed.\nThe eighth version of the scheduler has been submitted to LKML on October 14, 2013.\nThe ninth version of the scheduler has been submitted to LKML on November 7, 2013." | large_corpus_distillation |
"Isocost-The case of smooth isoquants convex to the origin-Now since the absolute value of the slope of the isocost line is the input cost ratio w/r , and the absolute value of the slope of an isoquant is the marginal rate of technical substitution (MRTS), we reach the following conclusion: If the isoquants are smooth... | large_corpus_distillation |
p\u2208(0,1) (7.4.7)\nB(a,b)\na/(a+b) p a=b=1\nand has mean . For example, if we know nothing about , we might let , so that the prior distribution is\n(0,1) p 2\nuniform on the parameter space (the non-informative prior). On the other hand, if we believe that is about , we might let\n3\na=4 b=2 2 X p\nand , so that th... | large_corpus_distillation |
"Modular programming-Modular programming-Modular programming is a software design technique that emphasizes separating the functionality of a program into independent, interchangeable modules, such that each contains everything necessary to execute only one aspect of the desired functionality." | large_corpus_distillation |
"Church encoding-Church pairs-Church pairs are the Church encoding of the pair (two-tuple) type. The pair is represented as a function that takes a function argument. When given its argument it will apply the argument to the two components of the pair. The definition in lambda calculus is, pair first second \u2261\u03b... | large_corpus_distillation |
"Large width limits of neural networks-Theoretical approaches based on a large width limit-The Neural Network Gaussian Process (NNGP) corresponds to the infinite width limit of Bayesian neural networks, and to the distribution over functions realized by non-Bayesian neural networks after random initialization.\nThe sam... | large_corpus_distillation |
"Biolinguistics-Recent Developments-Due to these limitations in each system, where both lexical and expressive categories can only be one layer deep, the recursive and unbounded hierarchical structure of human language is surprising. The Integration hypothesis posits that it is the combination of these two types of lay... | large_corpus_distillation |
"Decorator pattern-Common usecases-Obstacles of interfacing with decorators Applying combinations of decorators in diverse ways to a collection of objects introduces some problems interfacing with the collection in a way that takes full advantage of the functionality added by the decorators. The use of an Adapter or Vi... | large_corpus_distillation |
"Conditional loop-Types-The following types are written in C++, but apply to multiple languages.\nWhile loop Checks condition for truthfulness before executing any of the code in the loop. If condition is initially false, the code inside the loop will never be executed. In PL/I this is a DO WHILE... statement.\nDo-Whil... | large_corpus_distillation |
"Advanced Encryption Standard-Definitive standards-The Advanced Encryption Standard (AES) is defined in each of: FIPS PUB 197: Advanced Encryption Standard (AES) ISO/IEC 18033-3: Block ciphers " | large_corpus_distillation |
"Eulerian number-Basic properties-For fixed {\\textstyle n} there is a single permutation which has 0 ascents: {\\textstyle (n,n-1,n-2,\\ldots ,1)} . Indeed, as (n0)=1 for all n , {\\textstyle A(n,0)=1} . This formally includes the empty collection of numbers, {\\textstyle n=0} . And so {\\textstyle A_{0}(t)=A_{... | large_corpus_distillation |
"Multiplication algorithm-Computational complexity of multiplication-Although using more and more parts can reduce the time spent on recursive multiplications further, the overhead from additions and digit management also grows. For this reason, the method of Fourier transforms is typically faster for numbers with seve... | large_corpus_distillation |
"Logical address-Computer memory-The physical address of computer memory banks may be mapped to different logical addresses for various purposes." | large_corpus_distillation |
"Seed testing-Seed testing-Accuracy Properly conducted TZ and germination test results are generally in close agreement and within the range of normal sampling variation. Differences of 3% to 5% may be due to an unavoidable sampling variation error. Differences between TZ and germination test results are usually smalle... | large_corpus_distillation |
"Vop\u011bnka's principle-Definition-Many equivalent formulations are possible.\nFor example, Vop\u011bnka's principle is equivalent to each of the following statements. For every proper class of simple directed graphs, there are two members of the class with a homomorphism between them.\nFor any signature \u03a3 and ... | large_corpus_distillation |
"Simple group-Tests for nonsimplicity-Proof: If n is a prime-power, then a group of order n has a nontrivial center and, therefore, is not simple. If n is not a prime power, then every Sylow subgroup is proper, and, by Sylow's Third Theorem, we know that the number of Sylow p-subgroups of a group of order n is equal to... | large_corpus_distillation |
"Team programming-Modern trends: multiple programmers to one sub-task-It builds on principles of lean manufacturing, extreme programming, and lean software development. Early use of the phrase \"mob programming\" was made in Extreme Programming Perspectives.In addition to software coding, a mob programming team can wor... | large_corpus_distillation |
"Moufang loop-Definition-A Moufang loop is a loop Q that satisfies the four following equivalent identities for all x , y , z in Q (the binary operation in Q is denoted by juxtaposition): z(x(zy))=((zx)z)y x(z(yz))=((xz)y)z (zx)(yz)=(z(xy))z (zx)(yz)=z((xy)z) These identities are known as Moufang identities." | large_corpus_distillation |
is greater than 4, and so cannot be negative. As\n4\u2212x>0 x 4>x\nfor the first alternative, the condition can be rewritten (adding to both sides) as , so we\nx>0 4>x 4>x>0 0<x<4\nneed: and (this is sometimes combined in the form , or, equivalently, ). In\n(0,4)\ninterval notation, this says that the domain is the in... | large_corpus_distillation |
"Pseudorandom generator theorem-Existence of pseudorandom generators-PRG \u2192 OWF Consider a pseudorandom generator Gl: {0,1}l \u2192 {0,1}2l. Let's create the following one-way function \u0192: {0,1}n \u2192 {0,1}n that uses the first half of the output of Gl as its output. Formally, \u0192(x,y) \u2192 Gl(x) A key o... | large_corpus_distillation |
"Causative alternation-Theoretical approaches-The general consensus in the field is that there is a derivational relationship between verbs undergoing the causative alternation that share the same lexical entry. From this it follows that there is uncertainty surrounding which form, the intransitive or the transitive, i... | large_corpus_distillation |
"6.867 Machine learning, lecture 15 (Jaakkola) 5\nin terms of unidentified sub-groups. However, we can make use of them only if we can\nestimate such models easily from the available data.\nComplete data. The simplest way to understand how to estimate mixture models is\nto start by pretending that we knew all the sub-t... | large_corpus_distillation |
"Counting points on elliptic curves-Schoof\u2013Elkies\u2013Atkin algorithm-The status of a particular prime \u2113 depends on the elliptic curve E/Fq , and can be determined using the modular polynomial \u03a8\u2113(X,Y) . If the univariate polynomial \u03a8\u2113(X,j(E)) has a root in Fq , where j(E) denotes th... | large_corpus_distillation |
"Quicksort-Formal analysis-Best-case analysis In the most balanced case, each time we perform a partition we divide the list into two nearly equal pieces. This means each recursive call processes a list of half the size. Consequently, we can make only log2 n nested calls before we reach a list of size 1. This means tha... | large_corpus_distillation |
"Interactive Intelligence-Awards and recognition-The company was recognized as a \"market leader\" by industry analyst firms such as Datamonitor, Frost & Sullivan, and Gartner.The company was recognized on Software Magazine's Top 500 Software and Services Companies\" list for 12 consecutive years.In 2011, the company w... | large_corpus_distillation |
"Cache coherency protocols (examples)-Snoopy coherency protocol-\u2013 Write-broadcast (updating) is better when there is a single producer and many consumers of data, but it is worse when a cache is filled with data that will be not next read again (bus traffic increasing, cache interference increasing).- Invalidation... | large_corpus_distillation |
"Exponentiation-Exponentiation-Exponentiation is used extensively in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public-key cryptography." | large_corpus_distillation |
"Euclid's theorem-Stronger results-The theorems in this section simultaneously imply Euclid's theorem and other results.\nDirichlet's theorem on arithmetic progressions Dirichlet's theorem states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a p... | large_corpus_distillation |
square of the\n\u03b8\u2208T\nerror. Note that bias and mean square error are functions of . The following definitions are a natural complement to the\ndefinition of bias.\nU \u03b8 T \u2286R\nSuppose again that is a statistic used as an estimator of a parameter with values in .\nU bias(U)=0 E(U)=\u03b8 \u03b8\u2208T\n... | large_corpus_distillation |
"Set (mathematics)-Euler and Venn diagrams-An Euler diagram is a graphical representation of a collection of sets; each set is depicted as a planar region enclosed by a loop, with its elements inside. If A is a subset of B, then the region representing A is completely inside the region representing B. If two sets have ... | large_corpus_distillation |
"Davenport\u2013Schinzel sequence-Application to lower envelopes-In the original application of Davenport and Schinzel, the functions under consideration were a set of different solutions to the same homogeneous linear differential equation of order s. Any two distinct solutions can have at most s values in common, so ... | large_corpus_distillation |
must seek further detail within a record in order to correctly assign the correct diagnoses code. An inexperienced coder may simply just use the description from the discharge summary such as Infarction and may not use the correct detail which could be further found within the details of the medical record. This direct... | large_corpus_distillation |
"AddressSanitizer-AddressSanitizer-Google's ASan, introduced in 2012, uses a shadow memory scheme to detect memory bugs. It is available in: Clang (starting from version 3.1) GCC (starting from version 4.8) Xcode (starting from version 7.0) MSVC (widely available starting from version 16.9).On average, the instrumentat... | large_corpus_distillation |
"Language resource-Typology-As of May 2020, no widely used standard typology of language resources has been established (current proposals include the LREMap, METASHARE, and, for data, the LLOD classification). Important classes of language resources include data lexical resources, e.g., machine-readable dictionaries, ... | large_corpus_distillation |
correlation might reflect real changes in the attribute itself." | large_corpus_distillation |
"Noetherian topological space-Definition-A topological space X is called Noetherian if it satisfies the descending chain condition for closed subsets: for any sequence Y1\u2287Y2\u2287\u22ef of closed subsets Yi of X , there is an integer m such that Ym=Ym+1=\u22ef." | large_corpus_distillation |
either because it is granted by the hierarchy in contradiction with the industry's best practices, or because, though not granted, it is still enforced either because the system cannot manage it or because, by neglect, it has not been properly set up in that system; Finally, a capture error may arise in a system with w... | large_corpus_distillation |
"Stable matching polytope-Integrality-It is a theorem of Vande Vate (1989) that the polytope described by the facet constraints listed above has only the vertices described above. In particular it is an integral polytope. This can be seen as an analogue of the theorem of Garrett Birkhoff that an analogous polytope, the... | large_corpus_distillation |
and Function Notationthat the domain of a function can be read by observing the horizontal extent\nof its graph. We find the domain of the inverse function by observing theverticalextent of the graph of the original\nfunction, because this corresponds to the horizontal extent of the inverse function. Similarly, we find... | large_corpus_distillation |
"Tomasulo's algorithm-Instruction lifecycle-The three stages listed below are the stages through which each instruction passes from the time it is issued to the time its execution is complete." | large_corpus_distillation |
"Negative raising-NEG-raising in English-Consider the following example proposed by Paul Crowley, in which the verb \"say\" attempts to display negative raising: Mary didn't say it would snow Mary said it would not snow.As seen in this example, \"say\" is not a predicate that can be used for Neg-raising, as the raising... | large_corpus_distillation |
"Dutch grammar-Word order-In the following example, the SOV order in the subordinate clause causes the various noun phrases to be separated from the verbs that introduce them, creating a relatively deep \"nesting\" structure: Adjectives always come before the noun to which they belong.\nrode appels \u2013 red applesIn ... | large_corpus_distillation |
"Carmichael's totient function conjecture-Other results-Another way of stating Carmichael's conjecture is that, if A(f) denotes the number of positive integers n for which \u03c6(n) = f, then A(f) can never equal 1. Relatedly, Wac\u0142aw Sierpi\u0144ski conjectured that every positive integer other than 1 occurs as a ... | large_corpus_distillation |
0 or 1.The relation to the j-invariant is 256 256 (1\u2212\u03bb+\u03bb2)3\u03bb2(1\u2212\u03bb)2.\nwhich is the j-invariant of the elliptic curve of Legendre form y2=x(x\u22121)(x\u2212\u03bb) Given m\u2208C\u2216{0,1} , let \u03c4=iK{1\u2212m}K{m} where K is the complete elliptic integral of the first kind with pa... | large_corpus_distillation |
"Unimodality-Unimodal probability distribution-Skewness and kurtosis Rohatgi and Szekely claimed that the skewness and kurtosis of a unimodal distribution are related by the inequality: 1.2 where \u03ba is the kurtosis and \u03b3 is the skewness. Klaassen, Mokveld, and van Es showed that this only applies in certain se... | large_corpus_distillation |
"Form and document creation-The Structure and Organization-Standard expository models are: \"nonfiction print documents that (1) are primarily informational rather than expressive; (2) are intended to be read linearly (broadly speaking, from beginning to end); and (3) reveal structure explicitly with at least one headi... | large_corpus_distillation |
"Principle of maximum entropy-Justifications for the principle of maximum entropy-Proponents of the principle of maximum entropy justify its use in assigning probabilities in several ways, including the following two arguments. These arguments take the use of Bayesian probability as given, and are thus subject to the s... | large_corpus_distillation |
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