in order to implement a successful pat project, a combination of three main pat tools is essential : multivariate data acquisition and data analysis tools : usually advanced software packages which aid in design of experiments, collection of raw data and statistically analyzing this data in order to determine what parameters are cpp. process analytical chemistry ( pac ) tools : in - line and on - line analytical instruments used to measure those parameters that have been defined as cpp. these include mainly near infrared spectroscopy ( nirs ) ; but also include biosensors, raman spectroscopy, fiber optics and others. continuous improvement and / or knowledge management tools : paper systems or software packages which accumulate quality control data acquired over time for specific processes with the aim of defining process weaknesses and implementing and monitoring process improvement initiatives. these products may be the same or separated from the statistical analysis tools above.


in recent years, a number of commentators have called for legislative reforms to the state secrets privilege. these reforms center around several ideas : requiring judges to review each piece of evidence that the executive claims is subject to the privilege. requiring the executive to craft alternative evidence that is not subject to the privilege, for the opposing party to use in place of the original, privileged evidence. such substitute evidence should only be required when it is possible to do so without harming national security.


in the call center space, the following type of call transfers can be undertaken and take on a slightly different meaning : warm transfer : ( also known as a live or hot transfer ) the call center operator dials a number and talks to the person who has picked up the call before transferring the caller over to them. this could also be a three - way conference before the call center operator drops - off. one common example of a warm transfer is when a receptionist or virtual receptionist takes a call for the business and notifies the party attempting to be reached who the person is and the nature of their call. tepid transfer : this involves the call center operator dialing a number and transferring the caller on to the called number without conferencing or speaking to the third party.


each language had its own format for passing parameters into procedure calls, the file formats that they generated were often quite different. in general terms, it was not always possible to write different portions of a program in different languages, although doing so often has real utility.


in probability theory, the azuma – hoeffding inequality ( named after kazuoki azuma and wassily hoeffding ) gives a concentration result for the values of martingales that have bounded differences. suppose { x k : k = 0, 1, 2, 3, … } { \ displaystyle \ { x _ { k } : k = 0, 1, 2, 3, \ dots \ } } is a martingale ( or super - martingale ) and | x k − x k − 1 | ≤ c k, { \ displaystyle | x _ { k } - x _ { k - 1 } | \ leq c _ { k }, \, } almost surely. then for all positive integers n and all positive reals { \ displaystyle \ epsilon }, p ( x n − x 0 ≥ ) ≤ exp ( − 2 2 k = 1 n c k 2 ). { \ displaystyle { \ text { p } } ( x _ { n } - x _ { 0 } \ geq \ epsilon ) \ leq \ exp \ left ( { - \ epsilon ^ { 2 } \ over 2 \ sum _ { k = 1 } ^ { n } c _ { k } ^ { 2 } } \ right ). }


while there is ongoing debate on whether checkpointing is the dominating i / o workload on distributed computing systems, there is general consensus that checkpointing is one of the major i / o workloads. there are two main approaches for checkpointing in the distributed computing systems : coordinated checkpointing and uncoordinated checkpointing. in the coordinated checkpointing approach, processes must ensure that their checkpoints are consistent. this is usually achieved by some kind of two - phase commit protocol algorithm.


the driven exam can be completed in the class b bus the driver wishes to operate. it is common for restrictions to be issued on the driver's license disallowing them to operate higher classes of vehicles than they tested on. a common restriction is a driver with a class b cdl that performs their p endorsement test on a class b bus, resulting in their license bearing the " no class a passenger vehicle " restriction, which is notated with an'm ', in addition to their p endorsement.


in mathematics, economics, and computer science, the stable marriage problem ( also stable matching problem or smp ) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. a matching is a bijection from the elements of one set to the elements of the other set. a matching is not stable if : in other words, a matching is stable when there does not exist any pair ( a, b ) which both prefer each other to their current partner under the matching.


in quantum computing, the threshold theorem ( or quantum fault - tolerance theorem ) states that a quantum computer with a physical error rate below a certain threshold can, through application of quantum error correction schemes, suppress the logical error rate to arbitrarily low levels. this shows that quantum computers can be made fault - tolerant, as an analogue to von neumann's threshold theorem for classical computation. this result was proven ( for various error models ) by the groups of dorit aharanov and michael ben - or ; emanuel knill, raymond laflamme, and wojciech zurek ; and alexei kitaev independently. these results built off a paper of peter shor, which proved a weaker version of the threshold theorem.


in statistics, a symmetric probability distribution is a probability distribution — an assignment of probabilities to possible occurrences — which is unchanged when its probability density function ( for continuous probability distribution ) or probability mass function ( for discrete random variables ) is reflected around a vertical line at some value of the random variable represented by the distribution. this vertical line is the line of symmetry of the distribution. thus the probability of being any given distance on one side of the value about which symmetry occurs is the same as the probability of being the same distance on the other side of that value.


in project management ; risks that are external to the project and the project manager cannot control. good examples of external risks are changes in government legislation, changes in strategy from senior managers, and the economy.


in terms of representation scenarios, design knowledge can also be categorized into off - line and on - line knowledge. design process knowledge can be categorized into ontologies.


in mathematics, the drazin inverse, named after michael p. drazin, is a kind of generalized inverse of a matrix. let a be a square matrix. the index of a is the least nonnegative integer k such that rank ( ak + 1 ) = rank ( ak ).


this led mit technology review to name it'the machine that saved moore's law '. the first prototype in 2006 produced one wafer in 23 hours.


coin errors that occur on the die are generally more desirable than errors made at the time of the strike. for example, a doubled die, where a date or another device appears twice slightly offset, is often a highly desired error. strike errors are generally unique, whereas all coins struck with an error die will have the same characteristic.


in programming language design, there are a wide variety of factors to consider. some factors may be mutually exclusive ( e. g. security versus speed ). it may be necessary to consider whether a programming language will perform better interpreted, or compiled, if a language should be dynamically or statically typed, if inheritance will be in a language, and the general syntax of the language. many factors involved with the design of a language can be decided on by the goals behind the language.


for example, a client may receive an event stating that a given key has been pressed while the shift modifier was down. if this key would normally generate the character " a ", the client ( and not the server ) associates this event to the character " a ". while the translation from keycodes to keysyms is done by the client, the table that represents this association is maintained by the server.


{ \ displaystyle { \ sigma ^ { 2 } + \ left ( { \ frac { \ text { third central moment } } { 2 \ sigma ^ { 2 } } } \ right ) ^ { 2 } } \ leq { \ frac { 1 } { 4 } } ( m - m ) ^ { 2 }. } if one additionally assumes knowledge of the expectation, then the stronger bhatia – davis inequality holds σ 2 ≤ ( m − μ ) ( μ − m ) { \ displaystyle \ sigma ^ { 2 } \ leq ( m - \ mu ) ( \ mu - m ) } where μ is the expectation of the random variable. in the case of an independent sample of n observations from a bounded probability distribution, the von szokefalvi nagy inequality gives a lower bound to the variance of the sample mean : σ 2 ≥ ( m − m ) 2 2 n. { \ displaystyle \ sigma ^ { 2 } \ geq { \ frac { ( m - m ) ^ { 2 } } { 2n } }. }


in multi - processor systems ( more than one opteron on a single motherboard ), the cpus communicate using the direct connect architecture over high - speed hypertransport links. each cpu can access the main memory of another processor, transparent to the programmer. the opteron approach to multi - processing is not the same as standard symmetric multiprocessing ; instead of having one bank of memory for all cpus, each cpu has its own memory. thus the opteron is a non - uniform memory access ( numa ) architecture.


in order to extract the desired distortion information, at any given location in the spherical coordinate system, the values of k { \ displaystyle k } can be computed directly. the jacobian, j { \ displaystyle j }, can be computed analytically from the mapping function itself, but it is often simpler to numerically approximate the values at any location on the map using central differences. once these values are computed, svd can be applied to each transformation matrix to extract the local distortion information. remember that, because distortion is local, every location on the map will have its own transformation.


these probabilities are used to determine what the target is using a maximum likelihood decision. this method has been shown to be able to distinguish between vehicle types ( wheeled vs tracked vehicles for example ), and even decide how many people are present up to three people with a high probability of success. cnn - based target recognition convolutional neural network ( cnn ) - based target recognition is able to outperform the conventional methods.


for these reasons, constant interfaces may be considered an anti - pattern. use of this pattern has a few other downsides : it pollutes the class namespace with read - only variables that may not be of use. contrary to the compile - time tactical utility of implementing a constant interface, the incidental run - time artifacts have little practical purpose ( cf. marker interfaces which also have no methods but are useful at run - time ).


as x and y must be rational, the square of ± 2 x y { \ displaystyle \ pm 2 { \ sqrt { xy } } } must be rational. this implies that α = 0 { \ displaystyle \ alpha = 0 } in the expression of ± 2 x y { \ displaystyle \ pm 2 { \ sqrt { xy } } } as α + β c. { \ displaystyle \ alpha + \ beta { \ sqrt { c } }. }


in phrase structure grammars such as generative grammar, the verb phrase is one headed by a verb. it may be composed of only a single verb, but typically it consists of combinations of main and auxiliary verbs, plus optional specifiers, complements ( not including subject complements ), and adjuncts. for example : yankee batters hit the ball well enough to win their first world series since 2000. mary saw the man through the window.


however, to improve the usability and reliability of keys, many single - access keys incorporate reticulation, changing the tree structure into a directed acyclic graph. single - access keys have been in use for several hundred years. they may be printed in various styles ( e. g., linked, nested, indented, graphically branching ) or used as interactive, computer - aided keys.


the first two of these were to resolve the continuum hypothesis and prove the consistency of elementary arithmetic, respectively ; the tenth was to produce a method that could decide whether a multivariate polynomial equation over the integers has a solution. subsequent work to resolve these problems shaped the direction of mathematical logic, as did the effort to resolve hilbert's entscheidungsproblem, posed in 1928. this problem asked for a procedure that would decide, given a formalized mathematical statement, whether the statement is true or false.


in mathematics, the three classical pythagorean means are the arithmetic mean ( am ), the geometric mean ( gm ), and the harmonic mean ( hm ). these means were studied with proportions by pythagoreans and later generations of greek mathematicians because of their importance in geometry and music.


the cosets of inn ( g ) with respect to outer automorphisms are then the elements of out ( g ) ; this is an instance of the fact that quotients of groups are not, in general, ( isomorphic to ) subgroups. if the inner automorphism group is trivial ( when a group is abelian ), the automorphism group and outer automorphism group are naturally identified ; that is, the outer automorphism group does act on the group. for example, for the alternating group, an, the outer automorphism group is usually the group of order 2, with exceptions noted below. considering an as a subgroup of the symmetric group, sn, conjugation by any odd permutation is an outer automorphism of an or more precisely " represents the class of the ( non - trivial ) outer automorphism of an ", but the outer automorphism does not correspond to conjugation by any particular odd element, and all conjugations by odd elements are equivalent up to conjugation by an even element.


a second publication from 1968 described the theory and the technical details of the instrument and had hadravsky and robert galambos, the head of the group at yale, as additional authors. in 1970 the us patent was granted. it was filed in 1967.


as an example, given a postbqp algorithm a with success probability 2 / 3, we can construct another algorithm which runs three independent copies of a, outputs a postselection bit equal to the conjunction of the three " inner " ones, and outputs an output bit equal to the majority of the three " inner " ones ; the new algorithm will be correct with conditional probability ( 2 / 3 ) 3 + 3 ( 1 / 3 ) ( 2 / 3 ) 2 = 20 / 27 { \ displaystyle ( 2 / 3 ) ^ { 3 } + 3 ( 1 / 3 ) ( 2 / 3 ) ^ { 2 } = 20 / 27 }, greater than the original 2 / 3. postbqp is closed under intersection. suppose we have postbqp circuit families for two languages l 1 { \ displaystyle l _ { 1 } } and l 2 { \ displaystyle l _ { 2 } }, with respective postselection qubits and output qubits p 1, p 2, q 1, q 2 { \ displaystyle p _ { 1 }, p _ { 2 }, q _ { 1 }, q _ { 2 } }.


in number theory, the von staudt – clausen theorem is a result determining the fractional part of bernoulli numbers, found independently by karl von staudt ( 1840 ) and thomas clausen ( 1840 ). specifically, if n is a positive integer and we add 1 / p to the bernoulli number b2n for every prime p such that p − 1 divides 2n, we obtain an integer, i. e., b 2 n + ( p − 1 ) | 2 n 1 p ∈ z. { \ displaystyle b _ { 2n } + \ sum _ { ( p - 1 ) | 2n } { \ frac { 1 } { p } } \ in \ mathbb { z }. } this fact immediately allows us to characterize the denominators of the non - zero bernoulli numbers b2n as the product of all primes p such that p − 1 divides 2n ; consequently the denominators are square - free and divisible by 6. these denominators are 6, 30, 42, 30, 66, 2730, 6, 510, 798, 330, 138, 2730, 6, 870, 14322, 510, 6, 1919190, 6, 13530,... ( sequence a002445 in the oeis ). the sequence of integers b 2 n + ( p − 1 ) | 2 n 1 p { \ displaystyle b _ { 2n } + \ sum _ { ( p - 1 ) | 2n } { \ frac { 1 } { p } } } is 1, 1, 1, 1, 1, 1, 2, - 6, 56, - 528, 6193, - 86579, 1425518, - 27298230,... ( sequence a000146 in the oeis ).


let π ( x ) { \ displaystyle \ pi ( x ) }, the prime - counting function, denote the number of primes less than or equal to x { \ displaystyle x }. if q { \ displaystyle q } is a positive integer and a { \ displaystyle a } is coprime to q { \ displaystyle q }, we let π ( x ; q, a ) { \ displaystyle \ pi ( x ; q, a ) } denote the number of primes less than or equal to x { \ displaystyle x } which are equal to a { \ displaystyle a } modulo q { \ displaystyle q }. dirichlet's theorem on primes in arithmetic progressions then tells us that π ( x ; q, a ) ≈ π ( x ) φ ( q ) { \ displaystyle \ pi ( x ; q, a ) \ approx { \ frac { \ pi ( x ) } { \ varphi ( q ) } } } where φ { \ displaystyle \ varphi } is euler's totient function.


barzilai and borwein proved their method converges r - superlinearly for quadratic minimization in two dimensions. raydan demonstrates convergence in general for quadratic problems.


in mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e. g., a knot diagram. there are several types of unknotting algorithms. a major unresolved challenge is to determine if the problem admits a polynomial time algorithm ; that is, whether the problem lies in the complexity class p.


if portfolio weights are largely a function of estimation errors, then ex - post performance of a growth - optimal portfolio may differ fantastically from the ex - ante prediction. parameter uncertainty and estimation errors are a large topic in portfolio theory. an approach to counteract the unknown risk is to invest less than the kelly criterion ( e. g., half ).


every finite distributive lattice can be represented as a lattice of stable matchings. the number of elements in the lattice can vary from an average case of e − 1 n ln n { \ displaystyle e ^ { - 1 } n \ ln n } to a worst - case of exponential. computing the number of elements is # p - complete.


atlantis, is continued. ais and her crew face many other challenges, most notably internal problems, caused first by the rebellion of one of the deputies, and then by open warfare led by the non - delosiani dr. satham, a scrupulous scientist and his henchmen. while the uplift experiment seems to progress, eventually the great brain, the highest authority on des ( delos ), decides to stop and destroy the work of ais and her colleagues. however, ais and some of her subordinates questioned ( → reflection ) the strange order and refuse to abandon the uplift ( whether the command actually came directly from the great brain is not known.


in the heilbronn triangle problem, throw n { \ displaystyle n } points in the unit square and determine the maximum of the minimal area of a triangle formed by three of the points over all possible arrangements. this problem was solved for small arrangements, and much work was done on asymptotic expression as a function of n { \ displaystyle n }. the original conjecture of heilbronn was o ( 1 / n 2 ) { \ displaystyle o ( 1 / n ^ { 2 } ) } during the early 1950s. paul erdos proved that this bound is correct for n { \ displaystyle n }, a prime number.


he invented the adams operations in k - theory, which are derived from the exterior powers ; they are now also widely used in purely algebraic contexts. adams introduced them in a 1962 paper to solve the famous vector fields on spheres problem. subsequently he used them to investigate the adams conjecture, which is concerned ( in one instance ) with the image of the j - homomorphism in the stable homotopy groups of spheres.


in other projects the need to move into prolog was considered unnecessary because the printed logico - linguistic models provided an easy to use guide to decision making. for example, a system for mortgage loan approval


in the context of data race detection for programs using lock based synchronization, lockset - based techniques provide an unsound, yet lightweight mechanism for detecting data races. these techniques primarily detect violations of the lockset principle. which says that all accesses of a given memory location must be protected by a common lock. such techniques are also used to filter out candidate race reports in more expensive analyses.


seven dogs were missed ( false negatives ), and seven cats were correctly excluded ( true negatives ). the program's precision is then 5 / 8 ( true positives / selected elements ) while its recall is 5 / 12 ( true positives / relevant elements ). adopting a hypothesis - testing approach from statistics, in which, in this case, the null hypothesis is that a given item is irrelevant ( i. e., not a dog ), absence of type i and type ii errors ( i. e., perfect specificity and sensitivity of 100 % each ) corresponds respectively to perfect precision ( no false positive ) and perfect recall ( no false negative ).


and if you cannot do that, simplify your design until you can. ” at a sigplan symposium in 1973, tony hoare discussed various language aspects in some detail. he also identifies a number of shortcomings in ( then ) current programming languages. “ a programming language is a tool which should assist the programmer in the most difficult aspects of his art, namely program design, documentation, and debugging. ” “ objective criteria for good language design may be summarized in five catch phrases : simplicity, security, fast translation, efficient object code, and readability. ” " it is absurd to make elaborate security checks on debugging runs, when no trust is put in the results, and then remove them in production runs, when an erroneous result could be expensive or disastrous.


in probability theory and mathematical statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of total expectation, and the law of total variance. it has applications in the analysis of time series. it was introduced by david brillinger. it is most transparent when stated in its most general form, for joint cumulants, rather than for cumulants of a specified order for just one random variable. in general, we have κ ( x 1, …, x n ) = π κ ( κ ( x i : i ∈ b y ) : b ∈ π ), { \ displaystyle \ kappa ( x _ { 1 }, \ dots, x _ { n } ) = \ sum _ { \ pi } \ kappa ( \ kappa ( x _ { i } : i \ in b \ mid y ) : b \ in \ pi ), } where κ ( x1,..., xn ) is the joint cumulant of n random variables x1,..., xn, and the sum is over all partitions π { \ displaystyle \ pi } of the set { 1,..., n } of indices, and " b ∈ π ; " means b runs through the whole list of " blocks " of the partition π, and κ ( xi : i ∈ b | y ) is a conditional cumulant given the value of the random variable y. it is therefore a random variable in its own right — a function of the random variable y.


using a car as an analogy, if the user steps on the gas without first starting the engine, the car does not crash, fail, or throw an exception - it simply fails to accelerate. sequential coupling can be refactored with the template method pattern to overcome the problems posed by the usage of this anti - pattern. = = references = =


in mathematical optimization, dantzig's simplex algorithm ( or simplex method ) is a popular algorithm for linear programming. the name of the algorithm is derived from the concept of a simplex and was suggested by t. s. motzkin. simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial cones, and these become proper simplices with an additional constraint. the simplicial cones in question are the corners ( i. e., the neighborhoods of the vertices ) of a geometric object called a polytope. the shape of this polytope is defined by the constraints applied to the objective function.


in all page table formats supported by x86 and x86 - 64, the 12 least significant bits of the page table entry are either interpreted by the memory management unit or are reserved for operating system use. in processors that implement the " no - execute " or " execution disable " feature, the most significant bit ( bit 63 ) is the nx bit. the next eleven most significant bits ( bits 52 through 62 ) are reserved for operating system use by both intel and amd's architecture specifications.


in the united states, commercial truck classification is determined based on the vehicle's gross vehicle weight rating ( gvwr ). the classes are numbered 1 through 8. trucks are also classified more broadly by the federal highway administration ( fhwa ), which groups classes 1 and 2 as light duty, 3 through 6 as medium duty, and 7 and 8 as heavy duty. the environmental protection agency ( epa ) has a separate system of emissions classifications for trucks.


in any case, such definitions ( also called bridge laws or correspondence rules ) were held to serve three important purposes. in the first place, by connecting the uninterpreted formalism with the observation language, they permit the assignment of synthetic content to theories. in the second, according to whether they express a factual or a purely conventional content, they allow for the subdivision of science into two parts : one factual and independent of human conventions, the other non - empirical and conventional.


in contrast, a program where both stack and queue are subclasses of a type bag, whose specification for get is merely that it removes some element, does satisfy behavioral subtyping and allows clients to safely reason about correctness based on the presumed types of the objects they interact with. indeed, any object that satisfies the stack or queue specification also satisfies the bag specification. it is important to stress that whether a type s is a behavioral subtype of a type t depends only on the specification ( i. e. the documentation ) of type t ; the implementation of type t, if it has any, is completely irrelevant to this question.


in model checking, a subfield of computer science, a timed word is an extension of the notion of words, in a formal language, in which each letter is associated with a positive time tag. the sequence of time tags must be non - decreasing, which intuitively means that letters are received. for example, a system receiving a word over a network may associate to each letter the time at which the letter is received. the non - decreasing condition here means that the letters are received in the correct order. a timed language is a set of timed words.


fido is a dog. therefore fido is a mammal. " formally, the rule as an axiom schema is given as x a ⇒ a { x ↦ a }, { \ displaystyle \ forall x \, a \ rightarrow a \ { x \ mapsto a \ }, } for every formula a and every term a, where a { x ↦ a } { \ displaystyle a \ { x \ mapsto a \ } } is the result of substituting a for each free occurrence of x in a. a { x ↦ a } { \ displaystyle \, a \ { x \ mapsto a \ } } is an instance of x a.


in mathematical logic, focused proofs are a family of analytic proofs that arise through goal - directed proof - search, and are a topic of study in structural proof theory and reductive logic. they form the most general definition of goal - directed proof - search — in which someone chooses a formula and performs hereditary reductions until the result meets some condition. the extremal case where reduction only terminates when axioms are reached forms the sub - family of uniform proofs. a sequent calculus is said to have the focusing property when focused proofs are complete for some terminating condition. for system lk, system lj, and system ll, uniform proofs are focused proofs where all the atoms are assigned negative polarity. many other sequent calculi has been shown to have the focusing property, notably the nested sequent calculi of both the classical and intuitionistic variants of the modal logics in the s5 cube.


this is generally called roaming from a customer perspective, but also called visiting when describing the underlying technical process. each geographic area has a database called the visitor location register ( vlr ), which contains details of all the mobiles currently in that area. whenever a phone attaches, or visits, a new area, the visitor location register must contact the home location register to obtain the details for that phone.


in mathematical finite group theory, the brauer – fowler theorem, proved by brauer & fowler ( 1955 ), states that if a group g has even order g > 2 then it has a proper subgroup of order greater than g1 / 3. the technique of the proof is to count involutions ( elements of order 2 ) in g. perhaps more important is another result that the authors derive from the same count of involutions, namely that up to isomorphism there are only a finite number of finite simple groups with a given centralizer of an involution. this suggested that finite simple groups could be classified by studying their centralizers of involutions, and it led to the discovery of several sporadic groups. later it motivated a part of the classification of finite simple groups.


in statistics the mean squared prediction error ( mspe ), also known as mean squared error of the predictions, of a smoothing, curve fitting, or regression procedure is the expected value of the squared prediction errors ( pe ), the square difference between the fitted values implied by the predictive function g ^ { \ displaystyle { \ widehat { g } } } and the values of the ( unobservable ) true value g. it is an inverse measure of the explanatory power of g ^, { \ displaystyle { \ widehat { g } }, } and can be used in the process of cross - validation of an estimated model. knowledge of g would be required in order to calculate the mspe exactly ; in practice, mspe is estimated.


for example, under this assumption, a poset may be defined as a small posetal category, a distributive lattice as a small posetal distributive category, a heyting algebra as a small posetal finitely cocomplete cartesian closed category, and a boolean algebra as a small posetal finitely cocomplete * - autonomous category. conversely, categories, distributive categories, finitely cocomplete cartesian closed categories, and finitely cocomplete * - autonomous categories can be considered the respective categorifications of posets, distributive lattices, heyting algebras, and boolean algebras. = = references = =


in mathematics, the hardy – ramanujan – littlewood circle method is a technique of analytic number theory. it is named for g. h. hardy, s. ramanujan, and j. e. littlewood, who developed it in a series of papers on waring's problem.


unary relations can be viewed as a collection of members ( such as the collection of nobel laureates ) having some property ( such as that of having been awarded the nobel prize ). binary relations are the most commonly studied form of finitary relations. when x1 = x2 it is called a homogeneous relation, for example : equality and inequality, denoted by signs such as = and < in statements such as " 5 < 12 ", or divisibility, denoted by the sign | in statements such as " 13 | 143 ". otherwise it is a heterogeneous relation, for example : set membership, denoted by the sign ∈ in statements such as " 1 ∈ n ".


in mathematics, a complete boolean algebra is a boolean algebra in which every subset has a supremum ( least upper bound ). complete boolean algebras are used to construct boolean - valued models of set theory in the theory of forcing. every boolean algebra a has an essentially unique completion, which is a complete boolean algebra containing a such that every element is the supremum of some subset of a. as a partially ordered set, this completion of a is the dedekind – macneille completion. more generally, if κ is a cardinal then a boolean algebra is called κ - complete if every subset of cardinality less than κ has a supremum.


in qca's next step, inferential logic or boolean algebra is used to simplify or reduce the number of inferences to the minimum set of inferences supported by the data. this reduced set of inferences is termed the " prime implicates " by qca adherents. for instance, if the presence of conditions a and b is always associated with the presence of a particular value of d, regardless of the observed value of c, then the value that c takes is irrelevant.


in some languages, aspect and time are very clearly separated, making them much more distinct to their speakers. there are a number of languages that mark aspect much more saliently than time. prominent in this category are chinese and american sign language, which both differentiate many aspects but rely exclusively on optional time - indicating terms to pinpoint an action with respect to time. in other language groups, for example in most modern indo - european languages ( except slavic languages and some indo - aryan languages like hindi ), aspect has become almost entirely conflated, in the verbal morphological system, with time.


in telecommunications networks, a node ( latin : nodus, ‘ knot ’ ) is either a redistribution point or a communication endpoint. the definition of a node depends on the network and protocol layer referred to. a physical network node is an electronic device that is attached to a network, and is capable of creating, receiving, or transmitting information over a communication channel. a passive distribution point such as a distribution frame or patch panel is consequently not a node.


rete ii gives about a 100 to 1 order of magnitude performance improvement in more complex problems as shown by knowledgebased systems corporation benchmarks. rete ii can be characterized by two areas of improvement ; specific optimizations relating to the general performance of the rete network ( including the use of hashed memories in order to increase performance with larger sets of data ), and the inclusion of a backward chaining algorithm tailored to run on top of the rete network. backward chaining alone can account for the most extreme changes in benchmarks relating to rete vs. rete ii. rete ii is implemented in the commercial product advisor from fico, formerly called fair isaac jess ( at least versions 5. 0 and later ) also adds a commercial backward chaining algorithm on top of the rete network, but it cannot be said to fully implement rete ii, in part due to the fact that no full specification is publicly available.


in statistics and decision theory, a frequently used loss function is the 0 - 1 loss function l ( y ^, y ) = { \ displaystyle l ( { \ hat { y } }, y ) = \ left } using iverson bracket notation, i. e. it evaluates to 1 when y ^ = y { \ displaystyle { \ hat { y } } \ neq y }, and 0 otherwise.


in the following, fn is any of jn, yn, h ( 1 ) n, h ( 2 ) n for n = 0, ±1, ±2,...


{ \ displaystyle y ^ { 2 } = x ( x - a ^ { n } ) ( x + b ^ { n } ). \, } such an elliptic curve would enjoy very special properties, which are due to the appearance of high powers of integers in its equation and the fact that an + bn = cn is an nth power as well. in the summer of 1986, ken ribet demonstrated that, just as gerhard frey had anticipated, a special case of the taniyama – shimura conjecture ( still not proved at the time ), together with the now proved epsilon conjecture, implies fermat's last theorem. thus, if the taniyama – shimura conjecture is true for semistable elliptic curves, then fermat's last theorem would be true.


in most forth systems, the body of a code definition consists of either machine language, or some form of threaded code. the original forth which follows the informal fig standard ( forth interest group ), is a til ( threaded interpretive language ). this is also called indirect - threaded code, but direct - threaded and subroutine threaded forths have also become popular in modern times. the fastest modern forths, such as swiftforth, vfx forth, and iforth, compile forth to native machine code.


in mathematics, the schwartz kernel theorem is a foundational result in the theory of generalized functions, published by laurent schwartz in 1952. it states, in broad terms, that the generalized functions introduced by schwartz ( schwartz distributions ) have a two - variable theory that includes all reasonable bilinear forms on the space d { \ displaystyle { \ mathcal { d } } } of test functions. the space d { \ displaystyle { \ mathcal { d } } } itself consists of smooth functions of compact support.


different classification methods may have different percentages of error for a given classification project. it is important that the remote sensor chooses a classification method that works best with the number of classifications used while providing the least amount of error.


in prior versions of c + +, only functions, classes or type aliases could be templated. c + + 14 allows the creation of variables that are templated. an example given in the proposal is a variable pi that can be read to get the value of pi for various types ( e. g., 3 when read as an integral type ; the closest value possible with float, double or long double precision when read as float, double or long double, respectively ; etc. ). the usual rules of templates apply to such declarations and definitions, including specialization.


for almost all tournaments, the size is at least ( n 2 ) / 2 − 1. 73 n 3 / 2 { \ displaystyle { \ tbinom { n } { 2 } } / 2 - 1. 73n ^ { 3 / 2 } }. every directed acyclic graph d { \ displaystyle d } can be embedded as a subgraph of a larger tournament graph, in such a way that d { \ displaystyle d } is the unique minimum feedback arc set of the tournament. the size of this tournament has been defined as the " reversing number " of d { \ displaystyle d }, and among directed acyclic graphs with the same number of vertices it is largest when d { \ displaystyle d } is itself an ( acyclic ) tournament. a directed graph has an euler tour whenever it is strongly connected and each vertex has equal numbers of incoming and outgoing edges.


in mechanics, the eigenvectors of the moment of inertia tensor define the principal axes of a rigid body. the tensor of moment of inertia is a key quantity required to determine the rotation of a rigid body around its center of mass.


in some versions of ring - lwe there is a security reduction to the shortest - vector problem ( svp ) in a lattice as a lower bound on the security. the svp is known to be np - hard. specific ring - lwe systems that have provable security reductions include a variant of lyubashevsky's ring - lwe signatures defined in a paper by guneysu, lyubashevsky, and poppelmann.


in number theory, dirichlet's theorem, also called the dirichlet prime number 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 positive integer. in other words, there are infinitely many primes that are congruent to a modulo d. the numbers of the form a + nd form an arithmetic progression a, a + d, a + 2 d, a + 3 d, …, { \ displaystyle a, \ a + d, \ a + 2d, \ a + 3d, \ \ dots, \ } and dirichlet's theorem states that this sequence contains infinitely many prime numbers. the theorem, named after peter gustav lejeune dirichlet, extends euclid's theorem that there are infinitely many prime numbers. stronger forms of dirichlet's theorem state that for any such arithmetic progression, the sum of the reciprocals of the prime numbers in the progression diverges and that different such arithmetic progressions with the same modulus have approximately the same proportions of primes. equivalently, the primes are evenly distributed ( asymptotically ) among the congruence classes modulo d containing a's coprime to d.


when one processor is taken out then the other processor operates independently. when the faulty processor is repaired and brought in service then memory contents of the active processor are copied into its memory and the two are synchronized and comparator is enabled. it is possible that a comparator fault occurs only due to transient failure which is not shown even when check out program is run.


in mathematics, the erdos – ko – rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common. paul erdos, chao ko, and richard rado proved the theorem in 1938, but did not publish it until 1961. it is part of the field of combinatorics, and one of the central results of extremal set theory. the theorem applies to families of sets that all have the same size, r { \ displaystyle r }, and are all subsets of some larger set of size n { \ displaystyle n }.


in most modern operating systems ( oss ), a large body of reusable code is provided to simplify the programmer's job. this code is typically provided as a set of dynamically loadable libraries that applications can call at runtime. because the java platform is not dependent on any specific operating system, applications cannot rely on any of the pre - existing os libraries.


difficulties with such dependencies can be easily avoided if we reinsert the upper unit node η ′ { \ displaystyle \ eta ^ { \ prime } } after reinserting the unit node η { \ displaystyle \ eta } ( i. e. after reinsertion, η ′ { \ displaystyle \ eta ^ { \ prime } } must appear below η { \ displaystyle \ eta }, to cancel the extra literal ℓ { \ displaystyle { \ overline { \ ell } } } from η { \ displaystyle \ eta } ’ s clause ). this can be ensured by collecting the unit nodes in a queue during a bottom - up traversal of the proof and reinserting them in the order they were queued. the algorithm for fixing a proof containing many roots performs a top - down traversal of the proof, recomputing the resolvents and replacing broken nodes ( e. g. nodes having deletednodemarker as one of their parents ) by their surviving parents ( e. g. the other parent, in case one parent was deletednodemarker ). when unit nodes are collected and removed from a proof of a clause κ { \ displaystyle \ kappa } and the proof is fixed, the clause κ ′ { \ displaystyle \ kappa ^ { \ prime } } in the root node of the new proof is not equal to κ { \ displaystyle \ kappa } anymore, but contains ( some of ) the duals of the literals of the unit clauses that have been removed from the proof. the reinsertion of unit nodes at the bottom of the proof resolves κ ′ { \ displaystyle \ kappa ^ { \ prime } } with the clauses of ( some of ) the collected unit nodes, in order to obtain a proof of κ { \ displaystyle \ kappa } again.


then the new state is ( a 1, a 2, …, a r ; z ′ ) { \ displaystyle ( a _ { 1 }, a _ { 2 }, \ dots, a _ { r } ; z') }. by iterating the state change an fcsr generates an infinite, eventually periodic sequence of numbers in s { \ displaystyle s }. fcsrs have been used in the design of stream ciphers ( such as the f - fcsr generator ), in the cryptanalysis of the summation combiner stream cipher ( the reason goresky and klapper invented them ), and in generating pseudorandom numbers for quasi - monte carlo ( under the name multiply with carry ( mwc ) generator - invented by couture and l'ecuyer, ) generalizing work of marsaglia and zaman. fcsrs are analyzed using number theory.


in mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. it collects the various partial derivatives of a single function with respect to many variables, and / or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities. this greatly simplifies operations such as finding the maximum or minimum of a multivariate function and solving systems of differential equations. the notation used here is commonly used in statistics and engineering, while the tensor index notation is preferred in physics.


in most traditional pcrs the resulting products are analyzed after the pcr has been completed. this is called end - point analysis and is normally qualitative of nature rather than being quantitative. for this sort of analysis, products are mostly analyzed on an agarose gel and visualized using ethidium bromide as a fluorescent dye. direct correlation between signal strength and initial sample concentration is not possible using end - point analysis since pcr efficiency decreases as the reaction nears the plateau phase.


in the branch of abstract algebra known as ring theory, a left primitive ring is a ring which has a faithful simple left module. well known examples include endomorphism rings of vector spaces and weyl algebras over fields of characteristic zero.


+ 1 { \ displaystyle ( p - 1 )! + 1 }. both are named for 18th - century english mathematician john wilson ; in 1770, edward waring credited the theorem to wilson, although it had been stated centuries earlier by ibn al - haytham. the only known wilson primes are 5, 13, and 563 ( sequence a007540 in the oeis ).


as a result, the vast majority of a program's time was being spent in only five instructions. further, even when the program called one of those five instructions, the microcode required a finite time to decode it, even if it was just to call the internal hardware. on faster machines, this overhead was considerable.


this becomes important, for example, when the levene's test fails to satisfy the rather generous conditions for normality associated with that test and is a default alternative under those conditions for certain statistical software programs like the varianceequivalencetest routine in mathematica. in addition to levene's test, other parametric tests for equality of variance include the bartlett, brown - forsythe, and fisher ratio tests. = = references = =


this permits the existence of directory hierarchies, i. e., directories containing sub - directories. a name that refers to a file within a directory must be typically unique. in other words, there must be no identical names within a directory.


in number theory and combinatorics, a multipartition of a positive integer n is a way of writing n as a sum, each element of which is in turn a partition. the concept is also found in the theory of lie algebras.


{ \ displaystyle h _ { d } ( x, r ) = - \ sum _ { i \ in ( 1 \ dots r ) } p _ { d } ( d _ { i }, x, r ) \ log p _ { d } ( d _ { i }, x, r ). } using this entropy equation we can further calculate h d ( x, r ) { \ displaystyle h _ { d } ( x, r ) } for every point x { \ displaystyle x } and region shape r { \ displaystyle r }. a more complex region, like the eye region, has a more complex distributor and hence higher entropy.


it is essential in assuring that a transmission stays within its channel. an fm radio station, for example, must attenuate everything beyond ±75khz from the center frequency by a few decibels, and anything beyond ±100 khz ( the channel boundary ) by much more. emissions on further adjacent channels must be reduced to almost zero.


{ \ displaystyle k _ { 1 } k _ { 2 } \ cdots k _ { m }. } a conditional probability table can be put into matrix form.


in order to prevent adaptive - chosen - ciphertext attacks, it is necessary to use an encryption or encoding scheme that limits ciphertext malleability and a proof of security of the system. after the theoretical and foundation level development of cca secure systems, a number of systems have been proposed in the random oracle model : the most common standard for rsa encryption is optimal asymmetric encryption padding ( oaep ). unlike improvised schemes such as the padding used in the early versions of pkcs # 1, oaep has been proven secure in the random oracle model, oaep was incorporated into pkcs # 1 as of version 2. 0 published in 1998 as the now - recommended encoding scheme, with the older scheme still supported but not recommended for new applications. however, the golden standard for security is to show the system secure without relying on the random oracle idealization.


in mathematics, the root test is a criterion for the convergence ( a convergence test ) of an infinite series. it depends on the quantity lim sup n → ∞ | a n | n, { \ displaystyle \ limsup _ { n \ rightarrow \ infty } { \ sqrt { | a _ { n } | } }, } where a n { \ displaystyle a _ { n } } are the terms of the series, and states that the series converges absolutely if this quantity is less than one, but diverges if it is greater than one. it is particularly useful in connection with power series.


in music, a reduction is an arrangement or transcription of an existing score or composition in which complexity is lessened to make analysis, performance, or practice easier or clearer ; the number of parts may be reduced or rhythm may be simplified, such as through the use of block chords.


in order to avoid regressions being seen by the end - user after release, developers regularly run regression tests after changes are introduced to the software. these tests can include unit tests to catch local regressions as well as integration tests to catch remote regressions. regression testing techniques often leverage existing test cases to minimize the effort involved in creating them. however, due to the volume of these existing tests, it is often necessary to select a representative subset, using techniques such as test - case prioritization.


in terms of university records, authorities both on the state and federal level have shown an awareness about issues of privacy in education and a distaste for institutions'disclosure of information. the u. s. department of education has provided guidance about data discourse and identification, instructing educational institutions to be sensitive to the risk of re - identification of anonymous data by cross - referencing with auxiliary data, to minimize the amount of data in the public domain by decreasing publication of directory information about students and institutional personnel, and to be consistent in the processes of de - identification.


the statement is relative easy to prove by induction on the dimension of z ( even for y = z, x = 0, c = 1 ) with a k that depends only on n ; the point of the theorem is that k is independent of n. in fact, the constant c can be made arbitrarily close to 1, at the expense of the constant k becoming large. the original proof allowed c ( k ) ≈ 1 − const / log log k. { \ displaystyle c ( k ) \ approx 1 - { \ text { const } } / \ log \ log k. }


a porous barrier or ceramic disk may be used to separate the two solutions while allowing the flow of sulfate ions. when the half cells are placed in two entirely different and separate containers, a salt bridge is often used to connect the two cells. the salt bridge typically contains a high concentration of potassium nitrate ( a salt that will not interfere chemically with the reaction in either half - cell ).


in mathematical logic, minimal axioms for boolean algebra are assumptions which are equivalent to the axioms of boolean algebra ( or propositional calculus ), chosen to be as short as possible. for example, if one chooses to take commutativity for granted, an axiom with six nand operations and three variables is equivalent to boolean algebra : ( ( a b ) c ) ( a ( ( a c ) a ) ) = c { \ displaystyle ( ( a \ mid b ) \ mid c ) \ mid ( a \ mid ( ( a \ mid c ) \ mid a ) ) = c } where the vertical bar represents the nand logical operation ( also known as the sheffer stroke ). it is one of 25 candidate axioms for this property identified by stephen wolfram, by enumerating the sheffer identities of length less or equal to 15 elements ( excluding mirror images ) that have no noncommutative models with four or fewer variables, and was first proven equivalent by william mccune, branden fitelson, and larry wos. mathworld, a site associated with wolfram, has named the axiom the " wolfram axiom ".


in the case of a cache miss, the purpose of using such a structure will be rendered useless and the computer will have to go to the main memory to fetch the required data. however, with a multiple - level cache, if the computer misses the cache closest to the processor ( level - one cache or l1 ) it will then search through the next - closest level ( s ) of cache and go to main memory only if these methods fail. the general trend is to keep the l1 cache small and at a distance of 1 – 2 cpu clock cycles from the processor, with the lower levels of caches increasing in size to store more data than l1, hence being more distant but with a lower miss rate. this results in a better aat. the number of cache levels can be designed by architects according to their requirements after checking for trade - offs between cost, aats, and size.


in previous work, according to chi ( 2000 ), " researchers have attempted to construct taxonomies of information visualization techniques by examining the data domains that are compatible with these techniques. this is useful because implementers can quickly identify various techniques that can be applied to their domain of interest. however, these taxonomies do not help the implementers understand how to apply and implement these techniques ". according to chi ( 2000 ), he and j. t.


in order to treat very large problems, the structure of hierarchical matrices can be improved : h2 - matrices replace the general low - rank structure of the blocks by a hierarchical representation closely related to the fast multipole method in order to reduce the storage complexity to o ( n k ) { \ displaystyle o ( nk ) }. in the context of boundary integral operators, replacing the fixed rank k { \ displaystyle k } by block - dependent ranks leads to approximations that preserve the rate of convergence of the underlying boundary element method at a complexity of o ( n ). { \ displaystyle o ( n ). } arithmetic operations like multiplication, inversion, and cholesky or lr factorization of h2 - matrices can be implemented based on two fundamental operations : the matrix - vector multiplication with submatrices and the low - rank update of submatrices. while the matrix - vector multiplication is straightforward, implementing efficient low - rank updates with adaptively optimized cluster bases poses a significant challenge.


in the khoisan languages and the international phonetic alphabet, the vertical bar is used to write the dental click ( ). a double vertical bar is used to write the alveolar lateral click ( ). since these are technically letters, they have their own unicode code points in the latin extended - b range : u + 01c0 for the single bar and u + 01c1 for the double bar.


in the new memory layout, the ensemble dimension is added to the lowest dimension to reduce possible branch divergence. the impact of the unavoidable branch divergence from data irregularity, caused by the noise, is minimized via a regularization technique using the on - chip memory. moreover, the cache memory is utilized to amortize unavoidable uncoalesced memory accesses.


in mathematics, division by two or halving has also been called mediation or dimidiation. the treatment of this as a different operation from multiplication and division by other numbers goes back to the ancient egyptians, whose multiplication algorithm used division by two as one of its fundamental steps. some mathematicians as late as the sixteenth century continued to view halving as a separate operation, and it often continues to be treated separately in modern computer programming. performing this operation is simple in decimal arithmetic, in the binary numeral system used in computer programming, and in other even - numbered bases.


{ \ displaystyle x ^ { * } ( p _ { 1 }, p _ { 2 }, i ) = \ left ( { \ frac { ip _ { 1 } ^ { \ epsilon - 1 } } { p _ { 1 } ^ { \ epsilon } + p _ { 2 } ^ { \ epsilon } } }, { \ frac { ip _ { 2 } ^ { \ epsilon - 1 } } { p _ { 1 } ^ { \ epsilon } + p _ { 2 } ^ { \ epsilon } } } \ right ), \ quad { \ text { with } } \ quad \ epsilon = { \ frac { \ delta } { \ delta - 1 } }. } in both cases, the preferences are strictly convex, the demand is unique and the demand function is continuous. 3.


on the probability space we define the space x = { x } { \ displaystyle { \ mathcal { x } } = \ { x \ } } of random variables with values in measurable metric space ( u, d u ) { \ displaystyle ( u, d _ { u } ) } and the space y = { y } { \ displaystyle { \ mathcal { y } } = \ { y \ } } of random variables with values in measurable metric space ( v, d v ) { \ displaystyle ( v, d _ { v } ) }. by characterizations of probability distributions we understand general problems of description of some set c { \ displaystyle { \ mathcal { c } } } in the space x { \ displaystyle { \ mathcal { x } } } by extracting the sets a ⊆ x { \ displaystyle { \ mathcal { a } } \ subseteq { \ mathcal { x } } } and b ⊆ y { \ displaystyle { \ mathcal { b } } \ subseteq { \ mathcal { y } } } which describe the properties of random variables x ∈ a { \ displaystyle x \ in { \ mathcal { a } } } and their images y = f x ∈ b { \ displaystyle y = \ mathbf { f } x \ in { \ mathcal { b } } }, obtained by means of a specially chosen mapping f : x → y { \ displaystyle \ mathbf { f } : { \ mathcal { x } } \ to { \ mathcal { y } } }. the description of the properties of the random variables x { \ displaystyle x } and of their images y = f x { \ displaystyle y = \ mathbf { f } x } is equivalent to the indication of the set a ⊆ x { \ displaystyle { \ mathcal { a } } \ subseteq { \ mathcal { x } } } from which x { \ displaystyle x } must be taken and of the set b ⊆ y { \ displaystyle { \ mathcal { b } } \ subseteq { \ mathcal { y } } } into which its image must fall.


snippets are similar to having static preprocessing included in the editor, and do not require support by a compiler. on the flip side, this means that snippets cannot be invariably modified after the fact, and thus is vulnerable to all of the problems of copy and paste programming. for this reason snippets are primarily used for simple sections of code ( with little logic ), or for boilerplate, such as copyright notices, function prototypes, common control structures, or standard library imports.


a number of dimensional models have been produced, differing in the way in which they are constructed and the way in which they are intended to be interpreted. there are four broad types of dimensional representation, although others also exist : dimensional representation of the original dsm categories of personality disorders ; dimensional representation based on identification of latent traits with the dsm disorders ; dimensional representation based on the traits from normal personality research ; representation based on integration of dimensional modals, e. g. by using network analysis. the dimensional approach is included in section iii ( " emerging measures and models " ) of the fifth edition of the diagnostic and statistical manual of mental disorders ( dsm - 5 ), where it is described as an " alternative dsm - 5 model for personality disorders. " : p. 761 – 781 the decision to retain the old dsm - iv categorical model of personality disorders in dsm - 5 was controversial, and efforts continue to persuade the american psychiatric association to replace it with the dimensional model in dsm 5. 1.


in the u. s., the calculation and disclosure of apr is governed by the truth in lending act ( which is implemented by the consumer financial protection bureau ( cfpb ) in regulation z of the act ). in general, apr in the united states is expressed as the periodic ( for instance, monthly ) interest rate times the number of compounding periods in a year ( also known as the nominal interest rate ) ; since the apr must include certain non - interest charges and fees, it requires more detailed calculation. the apr must be disclosed to the borrower within 3 days of applying for a mortgage. this information is typically mailed to the borrower and the apr is found on the truth in lending disclosure statement, which also includes an amortization schedule.


if the content is deemed dangerous or inappropriate, its spread could be curbed immediately. understandably, methods for countering disinformation that involve algorithmic governance raise ethical concerns. the use of technologies that track and manipulate information raises questions about " who is accountable for their operation, whether they can create injustices and erode civic norms, and how we should resolve their ( un ) intended consequences ". a study from the pew research center reports that public support for restriction of disinformation by both technology companies and government increased among americans from 2018 - 2021. however, views on whether government and technology companies should take such steps became increasingly partisan and polarized during the same time period.


in object - oriented programming ( oop ), an instance is a concrete occurrence of any object, existing usually during the runtime of a computer program. formally, " instance " is synonymous with " object " as they are each a particular value ( realization ), and these may be called an instance object ; " instance " emphasizes the distinct identity of the object. the creation of an instance is called instantiation. an object may be varied in a number of ways.


in some hackathons, all work is on a single application, such as an operating system, programming language, or content management system. such events are often known as " code sprints ", and are especially popular for open source software projects, where such events are sometimes the only opportunity for developers to meet face - to - face. code sprints typically last from one week to three weeks and often take place near conferences at which most of the team attend. unlike other hackathons, these events rarely include a competitive element. the annual hackathon to work on the operating system openbsd, held since 1999, is one such event ; it may have originated the word " hackathon ".


η. { \ displaystyle \ eta ^ { \ prime } s. \ eta. } see : distributive law between monads. a generalized distributive law has also been proposed in the area of information theory.


other methods of defining the correspondence include a nondeterministic algorithm in terms of jeu de taquin. the bijective nature of the correspondence relates it to the enumerative identity λ ∈ p n ( t λ ) 2 = n! { \ displaystyle \ sum _ { \ lambda \ in { \ mathcal { p } } _ { n } } ( t _ { \ lambda } ) ^ { 2 } = n! } where p n { \ displaystyle { \ mathcal { p } } _ { n } } denotes the set of partitions of n ( or of young diagrams with n squares ), and tλ denotes the number of standard young tableaux of shape λ.


before virtual memory could be implemented in mainstream operating systems, many problems had to be addressed. dynamic address translation required expensive and difficult - to - build specialized hardware ; initial implementations slowed down access to memory slightly. there were worries that new system - wide algorithms utilizing secondary storage would be less effective than previously used application - specific algorithms.


0 k m, n = { \ displaystyle 0 _ { k _ { m, n } } = { \ begin { bmatrix } 0 _ { k } & 0 _ { k } & \ cdots & 0 _ { k } \ \ 0 _ { k } & 0 _ { k } & \ cdots & 0 _ { k } \ \ \ vdots & \ vdots & & \ vdots \ \ 0 _ { k } & 0 _ { k } & \ cdots & 0 _ { k } \ end { bmatrix } } } the zero matrix is the additive identity in k m, n { \ displaystyle k _ { m, n } }. that is, for all a ∈ k m, n { \ displaystyle a \ in k _ { m, n } } : 0 k m, n + a = a + 0 k m, n = a { \ displaystyle 0 _ { k _ { m, n } } + a = a + 0 _ { k _ { m, n } } = a } there is exactly one zero matrix of any given size m × n ( with entries from a given ring ), so when the context is clear, one often refers to the zero matrix.


the relative point of view is that much of algebraic geometry should be developed for a morphism x → y of schemes ( called a scheme x over y ), rather than for an individual scheme. for example, in studying algebraic surfaces, it can be useful to consider families of algebraic surfaces over any scheme y. in many cases, the family of all varieties of a given type can itself be viewed as a variety or scheme, known as a moduli space. for some of the detailed definitions in the theory of schemes, see the glossary of scheme theory.


additionally, mdp allowed the protocol to be optionally configured to send proactive repair packets in the original data transmission block. mdp was a direct predecessor to norm, with an initial ietf draft published in november 1996. the national aeronautics and space administration ( nasa ) adopted mdp for reliable file transfers during space missions., and the u. s.


in mathematics, hall's conjecture is an open question, as of 2015, on the differences between perfect squares and perfect cubes. it asserts that a perfect square y2 and a perfect cube x3 that are not equal must lie a substantial distance apart. this question arose from consideration of the mordell equation in the theory of integer points on elliptic curves.


in mathematics, a nonempty subset s of a group g is said to be symmetric if it contains the inverses of all of its elements.


in recent years, the term " algebraic statistics " has been used more restrictively, to label the use of algebraic geometry and commutative algebra to study problems related to discrete random variables with finite state spaces. commutative algebra and algebraic geometry have applications in statistics because many commonly used classes of discrete random variables can be viewed as algebraic varieties.


the load step becomes a separate instruction, and that instruction is statically scheduled much earlier in the code sequence. the compiler puts independent steps in between. scheduling memory accesses requires explicit, spare registers.


in predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as " there exists ", " there is at least one ", or " for some ". it is usually denoted by the logical operator symbol, which, when used together with a predicate variable, is called an existential quantifier ( " " or " ( x ) " or " ( ) " ). existential quantification is distinct from universal quantification ( " for all " ), which asserts that the property or relation holds for all members of the domain. some sources use the term existentialization to refer to existential quantification.


a surrogate key may be used as the primary key to avoid giving one candidate key artificial primacy over the others. since primary keys exist primarily as a convenience to the programmer, surrogate primary keys are often used, in many cases exclusively, in database application design. due to the popularity of surrogate primary keys, many developers and in some cases even theoreticians have come to regard surrogate primary keys as an inalienable part of the relational data model.


ammunition and canisters which replenish shields or oxygen can be found while exploring the game's environments, as well as various temporary power - ups. single - player level objectives can include exterminating all hostile creatures, rescuing civilians, retrieving certain items, or exploring certain locations. most levels contain platforms, stairs, doors, and liquids which players can control by activating switches.


in probability theory, cantelli's inequality ( also called the chebyshev - cantelli inequality and the one - sided chebyshev inequality ) is an improved version of chebyshev's inequality for one - sided tail bounds. the inequality states that, for λ > 0, { \ displaystyle \ lambda > 0, } pr ( x − e ≥ λ ) ≤ σ 2 σ 2 + λ 2, { \ displaystyle \ pr ( x - \ mathbb { e } \ geq \ lambda ) \ leq { \ frac { \ sigma ^ { 2 } } { \ sigma ^ { 2 } + \ lambda ^ { 2 } } }, } where x { \ displaystyle x } is a real - valued random variable, pr { \ displaystyle \ pr } is the probability measure, e { \ displaystyle \ mathbb { e } } is the expected value of x { \ displaystyle x }, σ 2 { \ displaystyle \ sigma ^ { 2 } } is the variance of x { \ displaystyle x }. applying the cantelli inequality to − x { \ displaystyle - x } gives a bound on the lower tail, pr ( x − e ≤ − λ ) ≤ σ 2 σ 2 + λ 2. { \ displaystyle \ pr ( x - \ mathbb { e } \ leq - \ lambda ) \ leq { \ frac { \ sigma ^ { 2 } } { \ sigma ^ { 2 } + \ lambda ^ { 2 } } }. }


rebol reifies code as data and vice versa. many languages, such as lisp, javascript, and curl, provide an eval or evaluate procedure that effectively reifies the language interpreter. the logtalk framework for prolog offers a means to explore reification in the context of logic programming. smalltalk and actor languages permit the reification of blocks and messages, which are equivalent of lambda expressions in lisp, and thiscontext in smallltalk, which is a reification of the current executing block. homoiconic languages reify the syntax of the language itself in the form of an abstract syntax tree, typically together with eval.


this was still a vast amount of memory at the time, but because of this limitation, architectures since have included various steps away from the original 26 - bit design. the arm architecture version 3 introduced a 32 - bit pc and separate psr, as well as a 32 - bit address bus, allowing 4 gib of memory to be addressed. the change in the pc / psr layout caused incompatibility with code written for previous architectures, so the processor also included a 26 - bit compatibility mode which used the old pc / psr combination.


in set notation a subset s { \ displaystyle s } of a group g { \ displaystyle g } is called symmetric if whenever s ∈ s { \ displaystyle s \ in s } then the inverse of s { \ displaystyle s } also belongs to s. { \ displaystyle s. } so if g { \ displaystyle g } is written multiplicatively then s { \ displaystyle s } is symmetric if and only if s = s − 1 { \ displaystyle s = s ^ { - 1 } } where s − 1 : = { s − 1 : s ∈ s }. { \ displaystyle s ^ { - 1 } : = \ left \ { s ^ { - 1 } : s \ in s \ right \ }. }


in mathematics, the concept of an inverse element generalises the concepts of opposite ( −x ) and reciprocal ( 1 / x ) of numbers. given an operation denoted here ∗, and an identity element denoted e, if x ∗ y = e, one says that x is a left inverse of y, and that y is a right inverse of x. ( an identity element is an element such that x * e = x and e * y = y for all x and y for which the left - hand sides are defined. ) when the operation ∗ is associative, if an element x has both a left inverse and a right inverse, then these two inverses are equal and unique ; they are called the inverse element or simply the inverse.


in nature, species do not evolve in isolation but in large networks of interacting species. one of the main goals in evolutionary ecology is to disentangle the evolutionary mechanisms that shape and are shaped by patterns of interaction between species. a particularly important question concerns how coevolution, the reciprocal evolutionary change in local populations of interacting species driven by natural selection, is shaped by the architecture of food webs, plant - animal mutualistic networks, and host - parasite communities. the concept of diffuse coevolution, where adaptation is in response to a suite of biotic interactions, was the first step towards a framework unifying relevant theories in community ecology and coevolution.


in the area of mathematical logic and computer science known as type theory, a type constructor is a feature of a typed formal language that builds new types from old ones. basic types are considered to be built using nullary type constructors. some type constructors take another type as an argument, e. g., the constructors for product types, function types, power types and list types. new types can be defined by recursively composing type constructors.


one can then also calculate the mean square of the model by dividing the sum of squares of the model minus the degrees of freedom, which is just the number of parameters. then the f value can be calculated by dividing the mean square of the model by the mean square of the error, and we can then determine significance ( which is why you want the mean squares to begin with. ). however, because of the behavior of the process of regression, the distributions of residuals at different data points ( of the input variable ) may vary even if the errors themselves are identically distributed.


in some countries, declining satisfaction with the urban environment is held to blame for continuing migration to smaller towns and rural areas ( so - called urban exodus ). successful urban planning supported regional planning can bring benefits to a much larger hinterland or city region and help to reduce both congestion along transport routes and the wastage of energy implied by excessive commuting.


it is widely used in a filipino youth subculture known as jejemons. kkkk : in somali and ethiopian languages spoken in the horn of africa, iterations of the letter " k ", usually ranging between 2 and 8 k's, are used as a variation of lol. these iterations are also used by shona, ndebele and other zimbabwean languages speakers, with the longer variant being " kikiki " ( emulating a laughing sound ).


the number of trailing zeros in a non - zero base - b integer n equals the exponent of the highest power of b that divides n. for example, 14000 has three trailing zeros and is therefore divisible by 1000 = 103, but not by 104. this property is useful when looking for small factors in integer factorization. some computer architectures have a count trailing zeros operation in their instruction set for efficiently determining the number of trailing zero bits in a machine word.


in matroid theory, an eulerian matroid is a matroid whose elements can be partitioned into a collection of disjoint circuits.


in mathematics, the geometric topology is a topology one can put on the set h of hyperbolic 3 - manifolds of finite volume.


in probability theory and statistics, the poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. it is named after french mathematician simeon denis poisson ( ; french pronunciation : ). the poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.


in stop / step mode debugging, the core / microcontroller is stopped through the use of breakpoints and then " single - stepped " through the code by executing instructions one at a time. if the other cores / microcontrollers of the soc have finished synchronously, the overall state of the system can be examined. stop / step mode debugging includes control / configure techniques, run control of a core / microcontroller, start / stop synchronization with other cores, memory and register access, and additional debug features such as performance counter and run - time memory access.


in the autumn of 1884, karoly zipernowsky, otto blathy and miksa deri ( zbd ), three hungarian engineers associated with the ganz works, had determined that open - core devices were impracticable, as they were incapable of reliably regulating voltage. in their joint 1885 patent applications for novel transformers ( later called zbd transformers ), they described two designs with closed magnetic circuits where copper windings were either wound around an iron wire ring core or surrounded by an iron wire core. the two designs were the first application of the two basic transformer constructions in common use to this day, termed " core form " or " shell form ". the ganz factory had also in the autumn of 1884 made delivery of the world's first five high - efficiency ac transformers, the first of these units having been shipped on september 16, 1884.


consider for example the random variable of the number of items in a shopper's basket at a supermarket checkout line. presumably a shopper does not stand in line with nothing to buy ( i. e., the minimum purchase is 1 item ), so this phenomenon may follow a ztp distribution. since the ztp is a truncated distribution with the truncation stipulated as k > 0, one can derive the probability mass function g ( k ; λ ) from a standard poisson distribution f ( k ; λ ) as follows : g ( k ; λ ) = p ( x = k x > 0 ) = f ( k ; λ ) 1 − f ( 0 ; λ ) = λ k e − λ k! ( 1 − e − λ ) = λ k ( e λ − 1 ) k! { \ displaystyle g ( k ; \ lambda ) = p ( x = k \ mid x > 0 ) = { \ frac { f ( k ; \ lambda ) } { 1 - f ( 0 ; \ lambda ) } } = { \ frac { \ lambda ^ { k } e ^ { - \ lambda } } { k! \ left ( 1 - e ^ { - \ lambda } \ right ) } } = { \ frac { \ lambda ^ { k } } { ( e ^ { \ lambda } - 1 ) k! } } } the mean is e = λ 1 − e − λ = λ e λ e λ − 1 { \ displaystyle \ operatorname { e } = { \ frac { \ lambda } { 1 - e ^ { - \ lambda } } } = { \ frac { \ lambda e ^ { \ lambda } } { e ^ { \ lambda } - 1 } } } and the variance is var = λ + λ 2 1 − e − λ − λ 2 ( 1 − e − λ ) 2 = e ( 1 + λ − e ) { \ displaystyle \ operatorname { var } = { \ frac { \ lambda + \ lambda ^ { 2 } } { 1 - e ^ { - \ lambda } } } - { \ frac { \ lambda ^ { 2 } } { ( 1 - e ^ { - \ lambda } ) ^ { 2 } } } = \ operatorname { e } ( 1 + \ lambda - \ operatorname { e } ) }


as a bracketing strategy, in each iteration the itp queries the value of the function on one point and discards the part of the interval between two points where the function value shares the same sign. the queried point is calculated with three steps : it interpolates finding the regula falsi estimate, then it perturbes / truncates the estimate ( similar to regula falsi § improvements in regula falsi ) and then projects the perturbed estimate onto an interval in the neighbourhood of the bisection midpoint. the neighbourhood around the bisection point is calculated in each iteration in order to guarantee minmax optimality ( theorem 2. 1 of ). the method depends on three hyper - parameters κ 1 ∈ ( 0, ∞ ), κ 2 ∈ [ 1, 1 + ) { \ displaystyle \ kappa _ { 1 } \ in ( 0, \ infty ), \ kappa _ { 2 } \ in \ left [ 1, 1 + \ phi \ right ) } and n 0 ∈ [ 0, ∞ ) { \ displaystyle n _ { 0 } \ in [ 0, \ infty ) } where { \ displaystyle \ phi } is the golden ratio 1 2 ( 1 + 5 ) { \ displaystyle { \ tfrac { 1 } { 2 } } ( 1 + { \ sqrt { 5 } } ) } : the first two control the size of the truncation and the third is a slack variable that controls the size of the interval for the projection step.


first, since the self - improvement through learning is more direct and rapid than the evolution process, the social learning algorithm can improve the efficiency of the algorithms mimicking natural evolution. second, compared with the interaction and learning behaviors in animal groups, the social learning process of human beings exhibits a higher level of intelligence. by emulating human learning behaviors, it is possible to arrive at more effective optimizers than existing swarm intelligence algorithms.


in physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. although the most common use of the word collision refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force. in physics, collisions can be classified by the change in the total kinetic energy of the system before and after the collision : if most or all of the total kinetic energy is lost ( dissipated as heat, sound, etc. or absorbed by the objects themselves ), the collision is said to be inelastic ; such collisions involve objects coming to a full stop. an example of such a collision is a car crash, as cars crumple inward when crashing, rather than bouncing off of each other. this is by design, for the safety of the occupants and bystanders should a crash occur - the frame of the car absorbs the energy of the crash instead.


these relations set strong limitations for the nonexistence of common eigenstates for incompatible observables. the maccone – pati uncertainty relations have been experimentally tested for qutrit systems. the new uncertainty relations not only capture the incompatibility of observables but also of quantities that are physically measurable ( as variances can be measured in the experiment ).


in order to run safely on multiprocessor machines, access to shared resources ( like files, data structures ) must be serialized so that threads or processes do not attempt to modify the same resource at the same time. in order to prevent multiple threads from accessing or modifying a shared resource simultaneously, dragonfly employs critical sections, and serializing tokens to prevent concurrent access. while both linux and freebsd 5 employ fine - grained mutex models to achieve higher performance on multiprocessor systems, dragonfly does not. until recently, dragonfly also employed spls, but these were replaced with critical sections.


in the united states, the modern demarcation point is a device defined by fcc rules ( 47 c. f. r. part 68 ) to allow safe connection of third - party telephone customer - premises equipment and wiring to the public switched telephone network ( pstn ). the modern demarcation point is the network interface device ( nid ) or intelligent network interface device ( inid ) also known as a " smartjack ". the nid is the telco's property.


when information is transferred across time, often to specific points in time, the process is known as forecasting. forecasting usually requires time series methods, while prediction is often performed on cross - sectional data. statistical techniques used for prediction include regression and its various sub - categories such as linear regression, generalized linear models ( logistic regression, poisson regression, probit regression ), etc. in case of forecasting, autoregressive moving average models and vector autoregression models can be utilized.


with no differing information to counter the untruths or the general agreement within isolated social clusters, some argue the outcome is an absence of a collective reality. although social media sites have changed their algorithms to prevent the spread of fake news, the problem still exists. furthermore, research has shown that while people may know what the scientific community has proved as a fact, they may still refuse to accept it as such. researchers fear that misinformation in social media is " becoming unstoppable. "


in microbiology, genes can move freely even between distantly related bacteria, possibly extending to the whole bacterial domain. as a rule of thumb, microbiologists have assumed that kinds of bacteria or archaea with 16s ribosomal rna gene sequences more similar than 97 % to each other need to be checked by dna - dna hybridisation to decide if they belong to the same species or not. this concept was narrowed in 2006 to a similarity of 98. 7 %. dna - dna hybridisation is outdated, and results have sometimes led to misleading conclusions about species, as with the pomarine and great skua. modern approaches compare sequence similarity using computational methods.


in the microsoft. net framework, xml literal allows a computer program to include xml directly in the code. it is currently only supported in vb. net 9. 0 and vb. net 10. 0. when a visual basic expression is embedded in an xml literal, the application creates a linq - to - xml object for each literal at run time.


in mathematics, the scalar projection of a vector a { \ displaystyle \ mathbf { a } } on ( or onto ) a vector b, { \ displaystyle \ mathbf { b }, } also known as the scalar resolute of a { \ displaystyle \ mathbf { a } } in the direction of b, { \ displaystyle \ mathbf { b }, } is given by : s = ‖ a ‖ cos θ = a ⋅ b ^, { \ displaystyle s = \ left \ | \ mathbf { a } \ right \ | \ cos \ theta = \ mathbf { a } \ cdot \ mathbf { \ hat { b } }, } where the operator ⋅ { \ displaystyle \ cdot } denotes a dot product, b ^ { \ displaystyle { \ hat { \ mathbf { b } } } } is the unit vector in the direction of b, { \ displaystyle \ mathbf { b }, } ‖ a ‖ { \ displaystyle \ left \ | \ mathbf { a } \ right \ | } is the length of a, { \ displaystyle \ mathbf { a }, } and θ { \ displaystyle \ theta } is the angle between a { \ displaystyle \ mathbf { a } } and b { \ displaystyle \ mathbf { b } }. the term scalar component refers sometimes to scalar projection, as, in cartesian coordinates, the components of a vector are the scalar projections in the directions of the coordinate axes. the scalar projection is a scalar, equal to the length of the orthogonal projection of a { \ displaystyle \ mathbf { a } } on b { \ displaystyle \ mathbf { b } }, with a negative sign if the projection has an opposite direction with respect to b { \ displaystyle \ mathbf { b } }. multiplying the scalar projection of a { \ displaystyle \ mathbf { a } } on b { \ displaystyle \ mathbf { b } } by b ^ { \ displaystyle \ mathbf { \ hat { b } } } converts it into the above - mentioned orthogonal projection, also called vector projection of a { \ displaystyle \ mathbf { a } } on b { \ displaystyle \ mathbf { b } }.


if k = r { \ displaystyle \ mathbb { k } = \ mathbb { r } }, then a ∗ = a t { \ displaystyle a ^ { * } = a ^ { \ textsf { t } } }. for a ∈ k m × n { \ displaystyle a \ in \ mathbb { k } ^ { m \ times n } }, ran ( a ) { \ displaystyle \ operatorname { ran } ( a ) } ( standing for " range " ) denotes the column space ( image ) of a { \ displaystyle a } ( the space spanned by the column vectors of a { \ displaystyle a } ) and ker ( a ) { \ displaystyle \ ker ( a ) } denotes the kernel ( null space ) of a { \ displaystyle a }. finally, for any positive integer n { \ displaystyle n }, i n ∈ k n × n { \ displaystyle i _ { n } \ in \ mathbb { k } ^ { n \ times n } } denotes the n × n { \ displaystyle n \ times n } identity matrix.


in some software originating on big - endian machines such as silicon graphics, colors were stored in 32 bits similar to argb32, but with the alpha in the bottom 8 bits rather than the top. for example, 808000ff would be red and green : 50. 2 %, blue : 0 % and alpha : 100 %, a brown. this is what you would get if rgba8888 data was read as words on these machines. it is used in portable arbitrary map and in fltk, but in general it is rare. the bytes are stored in memory on a little - endian machine in the order abgr.


the requirements for the united states are covered in title 47 of the code of federal regulations, part 97. 119. land mobile two - way ( including public safety and business mobile ) require station identifications by call sign. in the case of the gmrs service, this is to be done by each station in a similar manner to the amateur practice, though the time limit is fifteen minutes.


numerical semigroups are commutative monoids and are also known as numerical monoids. the definition of numerical semigroup is intimately related to the problem of determining nonnegative integers that can be expressed in the form x1n1 + x2 n2 +... + xr nr for a given set { n1, n2,..., nr } of positive integers and for arbitrary nonnegative integers x1, x2,..., xr. this problem had been considered by several mathematicians like frobenius ( 1849 – 1917 ) and sylvester ( 1814 – 1897 ) at the end of the 19th century. during the second half of the twentieth century, interest in the study of numerical semigroups resurfaced because of their applications in algebraic geometry.


schedule 1 drugs have little or no medical benefit, hence their limitations on prescribing. district nurses and health visitors have had limited prescribing rights since the mid - 1990s ; until then, prescriptions for dressings and simple medicines had to be signed by a doctor. once issued, a prescription is taken by the patient to a pharmacy, which dispenses the medicine.


with thirty diverse bidders unable to communicate about strategy except through their bids, forming such unanimous agreement is difficult at best. " nevertheless, federal communications commission ( fcc ) experimented with precautions for spectrum auctions like restricting visibility of bids, limiting the number of bids and anonymous bidding.


to have a lack - of - fit sum of squares that differs from the residual sum of squares, one must observe more than one y - value for each of one or more of the x - values. one then partitions the " sum of squares due to error ", i. e., the sum of squares of residuals, into two components : sum of squares due to error = ( sum of squares due to " pure " error ) + ( sum of squares due to lack of fit ). the sum of squares due to " pure " error is the sum of squares of the differences between each observed y - value and the average of all y - values corresponding to the same x - value. the sum of squares due to lack of fit is the weighted sum of squares of differences between each average of y - values corresponding to the same x - value and the corresponding fitted y - value, the weight in each case being simply the number of observed y - values for that x - value. because it is a property of least squares regression that the vector whose components are " pure errors " and the vector of lack - of - fit components are orthogonal to each other, the following equality holds : ( observed value − fitted value ) 2 ( error ) = ( observed value − local average ) 2 ( pure error ) + weight × ( local average − fitted value ) 2 ( lack of fit ) { \ displaystyle { \ begin { aligned } & \ sum ( { \ text { observed value } } - { \ text { fitted value } } ) ^ { 2 } & & { \ text { ( error ) } } \ \ & \ qquad = \ sum ( { \ text { observed value } } - { \ text { local average } } ) ^ { 2 } & & { \ text { ( pure error ) } } \ \ & \ qquad \ qquad { } + \ sum { \ text { weight } } \ times ( { \ text { local average } } - { \ text { fitted value } } ) ^ { 2 } & & { \ text { ( lack of fit ) } } \ end { aligned } } } hence the residual sum of squares has been completely decomposed into two components.


in practice, testing measures are never perfectly consistent. theories of test reliability have been developed to estimate the effects of inconsistency on the accuracy of measurement. the basic starting point for almost all theories of test reliability is the idea that test scores reflect the influence of two sorts of factors : 1. consistency factors : stable characteristics of the individual or the attribute that one is trying to measure.


in probability theory, the kelly criterion ( or kelly strategy or kelly bet ) is a formula for sizing a bet. the kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. it assumes that the expected returns are known and is optimal for a bettor who values their wealth logarithmically. j. l. kelly jr, a researcher at bell labs, described the criterion in 1956.


this technique was developed by c e wynn - williams at the cavendish laboratory and first published in 1932. the original counters used a cascade of " eccles - jordan " divide - by - two circuits, today known as flip flops. early count readings were therefore binary numbers and had to be manually re - calculated into decimal values. later, with the development of electronic indicators, which started with the introduction of the dekatron readout tube in the 1950s, and culminating in the modern digital indicator, totalised readings came to be directly indicated in decimal notation.


in mathematics, the euler numbers are a sequence en of integers ( sequence a122045 in the oeis ) defined by the taylor series expansion 1 cosh t = 2 e t + e − t = n = 0 ∞ e n n! ⋅ t n { \ displaystyle { \ frac { 1 } { \ cosh t } } = { \ frac { 2 } { e ^ { t } + e ^ { - t } } } = \ sum _ { n = 0 } ^ { \ infty } { \ frac { e _ { n } } { n! } } \ cdot t ^ { n } }, where cosh ( t ) { \ displaystyle \ cosh ( t ) } is the hyperbolic cosine function.


in the finding of a pathognomonic sign or symptom it is almost certain that the target condition is present, and in the absence of finding a sine qua non sign or symptom it is almost certain that the target condition is absent. in reality, however, the subjective probability of the presence of a condition is never exactly 100 % or 0 %, so tests are rather aimed at estimating a post - test probability of a condition or other entity. most diagnostic tests basically use a reference group to establish performance data such as predictive values, likelihood ratios and relative risks, which are then used to interpret the post - test probability for an individual. in monitoring tests of an individual, the test results from previous tests on that individual may be used as a reference to interpret subsequent tests.


in number theory, the positive remainder is always chosen, but in computing, programming languages choose depending on the language and the signs of a or n. standard pascal and algol 68, for example, give a positive remainder ( or 0 ) even for negative divisors, and some programming languages, such as c90, leave it to the implementation when either of n or a is negative ( see the table under § in programming languages for details ). a modulo 0 is undefined in most systems, although some do define it as a. as described by leijen, boute argues that euclidean division is superior to the other ones in terms of regularity and useful mathematical properties, although floored division, promoted by knuth, is also a good definition. despite its widespread use, truncated division is shown to be inferior to the other definitions. however, truncated division satisfies the identity ( − a ) / b = − ( a / b ) = a / ( − b ) { \ displaystyle ( { - a } ) / b = { - ( a / b ) } = a / ( { - b } ) }.


in scholarly writing, an important objective of classifying sources is to determine their independence and reliability. in contexts such as historical writing, it is almost always advisable to use primary sources and that " if none are available, it is only with great caution that may proceed to make use of secondary sources. " sreedharan believes that primary sources have the most direct connection to the past and that they " speak for themselves " in ways that cannot be captured through the filter of secondary sources.


in this sense the solution represents the unbounded μ operator that can, if necessary, hunt ad infinitum along the unbounded string of registers until it finds what it is looking for. the pointer register is exactly like any other register with one exception : under the circumstances called " indirect addressing " it provides its contents, rather than the address - operand in the state machine's table, to be the address of the target register ( including possibly itself! ).


most programming languages, even those with no explicit boolean type, have support for boolean algebraic operations such as conjunction ( and, &, * ), disjunction ( or, |, + ), equivalence ( eqv, =, = = ), exclusive or / non - equivalence ( xor, neqv, ^,! =, ¬ ), and negation ( not, ~,!, ¬ ). in some languages, like ruby, smalltalk, and alice the true and false values belong to separate classes, e. g., true and false, respectively, so there is no one boolean type. in sql, which uses a three - valued logic for explicit comparisons because of its special treatment of nulls, the boolean data type ( introduced in sql : 1999 ) is also defined to include more than two truth values, so that sql booleans can store all logical values resulting from the evaluation of predicates in sql. a column of boolean type can be restricted to just true and false though.


in marketing research, the most frequently used types of observational techniques are : personal observation observing products in use to detect usage patterns and problems observing license plates in store parking lots determining the socio - economic status of shoppers determining the level of package scrutiny determining the time it takes to make a purchase decision mechanical observationeye - tracking analysis while subjects watch advertisements oculometers – what the subject is looking at pupilometers – how interested is the viewer electronic checkout scanners – records purchase behaviour on - site cameras in stores people meters ( as in monitoring television viewing ) e. g. nielsen box voice pitch meters – measures emotional reactions psychogalvanometer – measures galvanic skin response auditsretail audits to determine the quality of service in stores inventory audits to determine product acceptance shelf space audits scanner based audits trace analysiscredit card records computer cookie records garbology – looking for traces of purchase patterns in garbage detecting store traffic patterns by observing the wear in the floor ( long term ) or the dirt on the floor ( short term ) exposure to advertisements content analysisobserve the content of magazines, television broadcasts, radio broadcasts, or newspapers, either articles, programs, or advertisements


in mathematics, a covering set for a sequence of integers refers to a set of prime numbers such that every term in the sequence is divisible by at least one member of the set. the term " covering set " is used only in conjunction with sequences possessing exponential growth.


in the c99 version of the c programming language and the c + + 11 version of c + +, a long long type is supported that has double the minimum capacity of the standard long. this type is not supported by compilers that require c code to be compliant with the previous c + + standard, c + + 03, because the long long type did not exist in c + + 03. for an ansi / iso compliant compiler, the minimum requirements for the specified ranges, that is, − ( 263−1 ) to 263−1 for signed and 0 to 264−1 for unsigned, must be fulfilled ; however, extending this range is permitted.


in practice, the above algorithm is typically iterated to produce a sequence x n { \ displaystyle \ mathbf { x } _ { n } }, n = 1, 2,...


in probability theory, the poisson scatter theorem describes a probability model of random scattering. it implies that the number of points in a fixed region will follow a poisson distribution.


in mathematics, the concept of graph dynamical systems can be used to capture a wide range of processes taking place on graphs or networks. a major theme in the mathematical and computational analysis of gdss is to relate their structural properties ( e. g. the network connectivity ) and the global dynamics that result. the work on gdss considers finite graphs and finite state spaces.


in mathematics, logic and computer science, a formal language is called recursively enumerable ( also recognizable, partially decidable, semidecidable, turing - acceptable or turing - recognizable ) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i. e., if there exists a turing machine which will enumerate all valid strings of the language. recursively enumerable languages are known as type - 0 languages in the chomsky hierarchy of formal languages. all regular, context - free, context - sensitive and recursive languages are recursively enumerable. the class of all recursively enumerable languages is called re.