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Theposterior probabilityis a type ofconditional probabilitythat results fromupdatingtheprior probabilitywith information summarized by thelikelihoodvia an application ofBayes' rule.[1]From anepistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time.[2]After the arrival of new information, the current posterior probability may serve as the prior in another round of Bayesian updating.[3]
In the context ofBayesian statistics, theposteriorprobability distributionusually describes the epistemic uncertainty aboutstatistical parametersconditional on a collection of observed data. From a given posterior distribution, variouspointandinterval estimatescan be derived, such as themaximum a posteriori(MAP) or thehighest posterior density interval(HPDI).[4]But while conceptually simple, the posterior distribution is generally not tractable and therefore needs to be either analytically or numerically approximated.[5]
In Bayesian statistics, the posterior probability is the probability of the parametersθ{\displaystyle \theta }given the evidenceX{\displaystyle X}, and is denotedp(θ|X){\displaystyle p(\theta |X)}.
It contrasts with thelikelihood function, which is the probability of the evidence given the parameters:p(X|θ){\displaystyle p(X|\theta )}.
The two are related as follows:
Given apriorbelief that aprobability distribution functionisp(θ){\displaystyle p(\theta )}and that the observationsx{\displaystyle x}have a likelihoodp(x|θ){\displaystyle p(x|\theta )}, then the posterior probability is defined as
wherep(x){\displaystyle p(x)}is the normalizing constant and is calculated as
for continuousθ{\displaystyle \theta },
or by summingp(x|θ)p(θ){\displaystyle p(x|\theta )p(\theta )}over all possible values ofθ{\displaystyle \theta }for discreteθ{\displaystyle \theta }.[7]
The posterior probability is thereforeproportional tothe productLikelihood · Prior probability.[8]
Suppose there is a school with 60% boys and 40% girls as students. The girls wear trousers or skirts in equal numbers; all boys wear trousers. An observer sees a (random) student from a distance; all the observer can see is that this student is wearing trousers. What is the probability this student is a girl? The correct answer can be computed using Bayes' theorem.
The eventGis that the student observed is a girl, and the eventTis that the student observed is wearing trousers. To compute the posterior probabilityP(G|T){\displaystyle P(G|T)}, we first need to know:
Given all this information, theposterior probabilityof the observer having spotted a girl given that the observed student is wearing trousers can be computed by substituting these values in the formula:
An intuitive way to solve this is to assume the school hasNstudents. Number of boys = 0.6Nand number of girls = 0.4N. IfNis sufficiently large, total number of trouser wearers = 0.6N+ 50% of 0.4N. And number of girl trouser wearers = 50% of 0.4N. Therefore, in the population of trousers, girls are (50% of 0.4N)/(0.6N+ 50% of 0.4N) = 25%. In other words, if you separated out the group of trouser wearers, a quarter of that group will be girls. Therefore, if you see trousers, the most you can deduce is that you are looking at a single sample from a subset of students where 25% are girls. And by definition, chance of this random student being a girl is 25%. Every Bayes-theorem problem can be solved in this way.[9]
The posterior probability distribution of onerandom variablegiven the value of another can be calculated withBayes' theoremby multiplying theprior probability distributionby thelikelihood function, and then dividing by thenormalizing constant, as follows:
gives the posteriorprobability density functionfor a random variableX{\displaystyle X}given the dataY=y{\displaystyle Y=y}, where
Posterior probability is a conditional probability conditioned on randomly observed data. Hence it is a random variable. For a random variable, it is important to summarize its amount of uncertainty. One way to achieve this goal is to provide acredible intervalof the posterior probability.[11]
Inclassification, posterior probabilities reflect the uncertainty of assessing an observation to particular class, see alsoclass-membership probabilities.
Whilestatistical classificationmethods by definition generate posterior probabilities, Machine Learners usually supply membership values which do not induce any probabilistic confidence. It is desirable to transform or rescale membership values to class-membership probabilities, since they are comparable and additionally more easily applicable for post-processing.[12]
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Speaker diarisation(ordiarization) is the process of partitioning an audio stream containing human speech into homogeneous segments according to the identity of each speaker.[1]It can enhance the readability of anautomatic speech transcriptionby structuring the audio stream into speaker turns and, when used together withspeaker recognitionsystems, by providing the speaker’s true identity.[2]It is used to answer the question "who spoke when?"[3]Speaker diarisation is a combination of speaker segmentation and speaker clustering. The first aims at finding speaker change points in an audio stream. The second aims at grouping together speech segments on the basis of speaker characteristics.
With the increasing number of broadcasts, meeting recordings and voice mail collected every year, speaker diarisation has received much attention by the speech community, as is manifested by the specific evaluations devoted to it under the auspices of theNational Institute of Standards and Technologyfor telephone speech, broadcast news and meetings.[4]A leading list tracker of speaker diarization research can be found at Quan Wang's github repo.[5]
In speaker diarisation, one of the most popular methods is to use aGaussian mixture modelto model each of the speakers, and assign the corresponding frames for each speaker with the help of aHidden Markov Model. There are two main kinds of clustering strategies. The first one is by far the most popular and is called Bottom-Up. The algorithm starts in splitting the full audio content in a succession of clusters and progressively tries to merge the redundant clusters in order to reach a situation where each cluster corresponds to a real speaker. The second clustering strategy is calledtop-downand starts with one single cluster for all the audio data and tries to split it iteratively until reaching a number of clusters equal to the number of speakers.
A 2010 review can be found at[1].
More recently, speaker diarisation is performed vianeural networksleveraging large-scaleGPUcomputing and methodological developments indeep learning.[6]
There are some open source initiatives for speaker diarisation (in alphabetical order):
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Constraint satisfaction problems(CSPs) are mathematical questions defined as a set of objects whosestatemust satisfy a number ofconstraintsorlimitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints overvariables, which is solved byconstraint satisfactionmethods. CSPs are the subject of research in bothartificial intelligenceandoperations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families.CSPs often exhibit high complexity, requiring a combination ofheuristicsandcombinatorial searchmethods to be solved in a reasonable time.Constraint programming(CP) is the field of research that specifically focuses on tackling these kinds of problems.[1][2]Additionally, theBoolean satisfiability problem(SAT),satisfiability modulo theories(SMT),mixed integer programming(MIP) andanswer set programming(ASP) are all fields of research focusing on the resolution of particular forms of the constraint satisfaction problem.
Examples of problems that can be modeled as a constraint satisfaction problem include:
These are often provided with tutorials ofCP, ASP, Boolean SAT and SMT solvers. In the general case, constraint problems can be much harder, and may not be expressible in some of these simpler systems. "Real life" examples includeautomated planning,[6][7]lexical disambiguation,[8][9]musicology,[10]product configuration[11]andresource allocation.[12]
The existence of a solution to a CSP can be viewed as adecision problem. This can be decided by finding a solution, or failing to find a solution after exhaustive search (stochastic algorithmstypically never reach an exhaustive conclusion, while directed searches often do, on sufficiently small problems). In some cases the CSP might be known to have solutions beforehand, through some other mathematical inference process.
Formally, a constraint satisfaction problem is defined as a triple⟨X,D,C⟩{\displaystyle \langle X,D,C\rangle }, where[13]
Each variableXi{\displaystyle X_{i}}can take on the values in the nonempty domainDi{\displaystyle D_{i}}.
Every constraintCj∈C{\displaystyle C_{j}\in C}is in turn a pair⟨tj,Rj⟩{\displaystyle \langle t_{j},R_{j}\rangle }, wheretj⊆{1,2,…,n}{\displaystyle t_{j}\subseteq \{1,2,\ldots ,n\}}is a set ofk{\displaystyle k}indices andRj{\displaystyle R_{j}}is ak{\displaystyle k}-aryrelationon the corresponding product of domains×i∈tjDi{\displaystyle \times _{i\in t_{j}}D_{i}}where the product is taken with indices in ascending order. Anevaluationof the variables is a function from a subset of variables to a particular set of values in the corresponding subset of domains. An evaluationv{\displaystyle v}satisfies a constraint⟨tj,Rj⟩{\displaystyle \langle t_{j},R_{j}\rangle }if the values assigned to the variablestj{\displaystyle t_{j}}satisfy the relationRj{\displaystyle R_{j}}.
An evaluation isconsistentif it does not violate any of the constraints. An evaluation iscompleteif it includes all variables. An evaluation is asolutionif it is consistent and complete; such an evaluation is said tosolvethe constraint satisfaction problem.
Constraint satisfaction problems on finite domains are typically solved using a form ofsearch. The most used techniques are variants ofbacktracking,constraint propagation, andlocal search. These techniques are also often combined, as in theVLNSmethod, and current research involves other technologies such aslinear programming.[14]
Backtrackingis a recursive algorithm. It maintains a partial assignment of the variables. Initially, all variables are unassigned. At each step, a variable is chosen, and all possible values are assigned to it in turn. For each value, the consistency of the partial assignment with the constraints is checked; in case of consistency, arecursivecall is performed. When all values have been tried, the algorithm backtracks. In this basic backtracking algorithm, consistency is defined as the satisfaction of all constraints whose variables are all assigned. Several variants of backtracking exist.Backmarkingimproves the efficiency of checking consistency.Backjumpingallows saving part of the search by backtracking "more than one variable" in some cases.Constraint learninginfers and saves new constraints that can be later used to avoid part of the search.Look-aheadis also often used in backtracking to attempt to foresee the effects of choosing a variable or a value, thus sometimes determining in advance when a subproblem is satisfiable or unsatisfiable.
Constraint propagationtechniques are methods used to modify a constraint satisfaction problem. More precisely, they are methods that enforce a form oflocal consistency, which are conditions related to the consistency of a group of variables and/or constraints. Constraint propagation has various uses. First, it turns a problem into one that is equivalent but is usually simpler to solve. Second, it may prove satisfiability or unsatisfiability of problems. This is not guaranteed to happen in general; however, it always happens for some forms of constraint propagation and/or for certain kinds of problems. The most known and used forms of local consistency arearc consistency,hyper-arc consistency, andpath consistency. The most popular constraint propagation method is theAC-3 algorithm, which enforces arc consistency.
Local searchmethods are incomplete satisfiability algorithms. They may find a solution of a problem, but they may fail even if the problem is satisfiable. They work by iteratively improving a complete assignment over the variables. At each step, a small number of variables are changed in value, with the overall aim of increasing the number of constraints satisfied by this assignment. Themin-conflicts algorithmis a local search algorithm specific for CSPs and is based on that principle. In practice, local search appears to work well when these changes are also affected by random choices. An integration of search with local search has been developed, leading tohybrid algorithms.
CSPs are also studied incomputational complexity theory,finite model theoryanduniversal algebra. It turned out that questions about the complexity of CSPs translate into important universal-algebraic questions about underlying algebras. This approach is known as thealgebraic approachto CSPs.[15]
Since every computational decision problem ispolynomial-time equivalentto a CSP with an infinite template,[16]general CSPs can have arbitrary complexity. In particular, there are also CSPs within the class ofNP-intermediateproblems, whose existence was demonstrated byLadner, under the assumption thatP ≠ NP.
However, a large class of CSPs arising from natural applications satisfy a complexity dichotomy, meaning that every CSP within that class is either inPorNP-triology math complete. These CSPs thus provide one of the largest known subsets ofNPwhich avoidsNP-intermediateproblems. A complexity dichotomy was first proven bySchaeferfor Boolean CSPs, i.e. CSPs over a 2-element domain and where all the available relations areBoolean operators. This result has been generalized for various classes of CSPs, most notably for all CSPs over finite domains. Thisfinite-domain dichotomy conjecturewas first formulated by Tomás Feder and Moshe Vardi,[17]and finally proven independently by Andrei Bulatov[18]and Dmitriy Zhuk in 2017.[19]
Other classes for which a complexity dichotomy has been confirmed are
Most classes of CSPs that are known to be tractable are those where thehypergraphof constraints has boundedtreewidth,[27]or where the constraints have arbitrary form but there exist equationally non-trivial polymorphisms of the set of constraint relations.[28]
Aninfinite-domain dichotomy conjecture[29]has been formulated for all CSPs of reducts of finitely bounded homogenous structures, stating that the CSP of such a structure is in P if and only if itspolymorphism cloneis equationally non-trivial, and NP-hard otherwise.
The complexity of such infinite-domain CSPs as well as of other generalisations (Valued CSPs, Quantified CSPs, Promise CSPs) is still an area of active research.[30][1][2]
Every CSP can also be considered as aconjunctive querycontainment problem.[31]
A similar situation exists between the functional classesFPand#P. By a generalization ofLadner's theorem, there are also problems in neither FP nor#P-completeas long as FP ≠ #P. As in the decision case, a problem in the #CSP is defined by a set of relations. Each problem takes aBooleanformula as input and the task is to compute the number of satisfying assignments. This can be further generalized by using larger domain sizes and attaching a weight to each satisfying assignment and computing the sum of these weights. It is known that any complex weighted #CSP problem is either in FP or #P-hard.[32]
The classic model of Constraint Satisfaction Problem defines a model of static, inflexible constraints. This rigid model is a shortcoming that makes it difficult to represent problems easily.[33]Several modifications of the basic CSP definition have been proposed to adapt the model to a wide variety of problems.
Dynamic CSPs[34](DCSPs) are useful when the original formulation of a problem is altered in some way, typically because the set of constraints to consider evolves because of the environment.[35]DCSPs are viewed as a sequence of static CSPs, each one a transformation of the previous one in which variables and constraints can be added (restriction) or removed (relaxation). Information found in the initial formulations of the problem can be used to refine the next ones. The solving method can be classified according to the way in which information is transferred:
Classic CSPs treat constraints as hard, meaning that they areimperative(each solution must satisfy all of them) andinflexible(in the sense that they must be completely satisfied or else they are completely violated).Flexible CSPs relax those assumptions, partiallyrelaxingthe constraints and allowing the solution to not comply with all of them. This is similar to preferences inpreference-based planning. Some types of flexible CSPs include:
In DCSPs[36]each constraint variable is thought of as having a separate geographic location. Strong constraints are placed on information exchange between variables, requiring the use of fully distributed algorithms to solve the constraint satisfaction problem.
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VoxForgeis afreespeech corpusandacoustic modelrepository foropen sourcespeech recognitionengines.
VoxForge was set up to collect transcribed speech to create a freeGPLspeech corpus in order to be uses with open source speech recognition engines. The speech audio files will be 'compiled' into acoustic models for use with open source speech recognition engines such asJulius,ISIP, andSphinxandHTK(note: HTK has distribution restrictions).
VoxForge has[1]usedLibriVoxas a source of audio data since 2007.
This article about adigital libraryis astub. You can help Wikipedia byexpanding it.
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In mathematics, asemigroupis analgebraic structureconsisting of asettogether with anassociativeinternalbinary operationon it.
The binary operation of a semigroup is most often denoted multiplicatively (just notation, not necessarily the elementary arithmeticmultiplication):x⋅y, or simplyxy, denotes the result of applying the semigroup operation to theordered pair(x,y). Associativity is formally expressed as that(x⋅y) ⋅z=x⋅ (y⋅z)for allx,yandzin the semigroup.
Semigroups may be considered a special case ofmagmas, where the operation is associative, or as a generalization ofgroups, without requiring the existence of an identity element or inverses.[a]As in the case of groups or magmas, the semigroup operation need not becommutative, sox⋅yis not necessarily equal toy⋅x; a well-known example of an operation that is associative but non-commutative ismatrix multiplication. If the semigroup operation is commutative, then the semigroup is called acommutative semigroupor (less often than in theanalogous case of groups) it may be called anabelian semigroup.
Amonoidis an algebraic structure intermediate between semigroups and groups, and is a semigroup having anidentity element, thus obeying all but one of the axioms of a group: existence of inverses is not required of a monoid. A natural example isstringswithconcatenationas the binary operation, and the empty string as the identity element. Restricting to non-emptystringsgives an example of a semigroup that is not a monoid. Positiveintegerswith addition form a commutative semigroup that is not a monoid, whereas the non-negativeintegersdo form a monoid. A semigroup without an identity element can be easily turned into a monoid by just adding an identity element. Consequently, monoids are studied in the theory of semigroups rather than in group theory. Semigroups should not be confused withquasigroups, which are generalization of groups in a different direction; the operation in a quasigroup need not be associative but quasigroupspreserve from groupsthe notion ofdivision. Division in semigroups (or in monoids) is not possible in general.
The formal study of semigroups began in the early 20th century. Early results includea Cayley theorem for semigroupsrealizing any semigroup as atransformation semigroup, in which arbitrary functions replace the role of bijections in group theory. A deep result in the classification of finite semigroups isKrohn–Rhodes theory, analogous to theJordan–Hölder decompositionfor finite groups. Some other techniques for studying semigroups, likeGreen's relations, do not resemble anything in group theory.
The theory of finite semigroups has been of particular importance intheoretical computer sciencesince the 1950s because of the natural link between finite semigroups andfinite automatavia thesyntactic monoid. Inprobability theory, semigroups are associated withMarkov processes.[1]In other areas ofapplied mathematics, semigroups are fundamental models forlinear time-invariant systems. Inpartial differential equations, a semigroup is associated to any equation whose spatial evolution is independent of time.
There are numerousspecial classes of semigroups, semigroups with additional properties, which appear in particular applications. Some of these classes are even closer to groups by exhibiting some additional but not all properties of a group. Of these we mention:regular semigroups,orthodox semigroups,semigroups with involution,inverse semigroupsandcancellative semigroups. There are also interesting classes of semigroups that do not contain any groups except thetrivial group; examples of the latter kind arebandsand their commutative subclass –semilattices, which are alsoordered algebraic structures.
A semigroup is asetStogether with abinary operation⋅ (that is, afunction⋅ :S×S→S) that satisfies theassociative property:
More succinctly, a semigroup is an associativemagma.
Aleft identityof a semigroupS(or more generally,magma) is an elementesuch that for allxinS,e⋅x=x. Similarly, aright identityis an elementfsuch that for allxinS,x⋅f=x. Left and right identities are both calledone-sided identities. A semigroup may have one or more left identities but no right identity, and vice versa.
Atwo-sided identity(or justidentity) is an element that is both a left and right identity. Semigroups with a two-sided identity are calledmonoids. A semigroup may have at most one two-sided identity. If a semigroup has a two-sided identity, then the two-sided identity is the only one-sided identity in the semigroup. If a semigroup has both a left identity and a right identity, then it has a two-sided identity (which is therefore the unique one-sided identity).
A semigroupSwithout identity may beembeddedin a monoid formed by adjoining an elemente∉StoSand defininge⋅s=s⋅e=sfor alls∈S∪ {e}.[2][3]The notationS1denotes a monoid obtained fromSby adjoining an identityif necessary(S1=Sfor a monoid).[3]
Similarly, every magma has at most oneabsorbing element, which in semigroup theory is called azero. Analogous to the above construction, for every semigroupS, one can defineS0, a semigroup with 0 that embedsS.
The semigroup operation induces an operation on the collection of its subsets: given subsetsAandBof a semigroupS, their productA·B, written commonly asAB, is the set{ab|a∈Aandb∈B}.(This notion is defined identically asit is for groups.) In terms of this operation, a subsetAis called
IfAis both a left ideal and a right ideal then it is called anideal(or atwo-sided ideal).
IfSis a semigroup, then the intersection of any collection of subsemigroups ofSis also a subsemigroup ofS.
So the subsemigroups ofSform acomplete lattice.
An example of a semigroup with no minimal ideal is the set of positive integers under addition. The minimal ideal of acommutativesemigroup, when it exists, is a group.
Green's relations, a set of fiveequivalence relationsthat characterise the elements in terms of theprincipal idealsthey generate, are important tools for analysing the ideals of a semigroup and related notions of structure.
The subset with the property that every element commutes with any other element of the semigroup is called thecenterof the semigroup.[4]The center of a semigroup is actually a subsemigroup.[5]
Asemigrouphomomorphismis a function that preserves semigroup structure. A functionf:S→Tbetween two semigroups is a homomorphism if the equation
holds for all elementsa,binS, i.e. the result is the same when performing the semigroup operation after or before applying the mapf.
A semigroup homomorphism between monoids preserves identity if it is amonoid homomorphism. But there are semigroup homomorphisms that are not monoid homomorphisms, e.g. the canonical embedding of a semigroupSwithout identity intoS1. Conditions characterizing monoid homomorphisms are discussed further. Letf:S0→S1be a semigroup homomorphism. The image offis also a semigroup. IfS0is a monoid with an identity elemente0, thenf(e0) is the identity element in the image off. IfS1is also a monoid with an identity elemente1ande1belongs to the image off, thenf(e0) =e1, i.e.fis a monoid homomorphism. Particularly, iffissurjective, then it is a monoid homomorphism.
Two semigroupsSandTare said to beisomorphicif there exists abijectivesemigroup homomorphismf:S→T. Isomorphic semigroups have the same structure.
Asemigroup congruence~ is anequivalence relationthat is compatible with the semigroup operation. That is, a subset~ ⊆S×Sthat is an equivalence relation andx~yandu~vimpliesxu~yvfor everyx,y,u,vinS. Like any equivalence relation, a semigroup congruence ~ inducescongruence classes
and the semigroup operation induces a binary operation ∘ on the congruence classes:
Because ~ is a congruence, the set of all congruence classes of ~ forms a semigroup with ∘, called thequotient semigrouporfactor semigroup, and denotedS/ ~. The mappingx↦ [x]~is a semigroup homomorphism, called thequotient map,canonicalsurjectionorprojection; ifSis a monoid then quotient semigroup is a monoid with identity [1]~. Conversely, thekernelof any semigroup homomorphism is a semigroup congruence. These results are nothing more than a particularization of thefirst isomorphism theorem in universal algebra. Congruence classes and factor monoids are the objects of study instring rewriting systems.
Anuclear congruenceonSis one that is the kernel of an endomorphism ofS.[6]
A semigroupSsatisfies themaximal condition on congruencesif any family of congruences onS, ordered by inclusion, has a maximal element. ByZorn's lemma, this is equivalent to saying that theascending chain conditionholds: there is no infinite strictly ascending chain of congruences onS.[7]
Every idealIof a semigroup induces a factor semigroup, theRees factor semigroup, via the congruence ρ defined byxρyif eitherx=y, or bothxandyare inI.
The following notions[8]introduce the idea that a semigroup is contained in another one.
A semigroupTis a quotient of a semigroupSif there is a surjective semigroup morphism fromStoT. For example,(Z/2Z, +)is a quotient of(Z/4Z, +), using the morphism consisting of taking the remainder modulo 2 of an integer.
A semigroupTdivides a semigroupS, denotedT≼SifTis a quotient of a subsemigroupS. In particular, subsemigroups ofSdividesT, while it is not necessarily the case that there are a quotient ofS.
Both of those relations are transitive.
For any subsetAofSthere is a smallest subsemigroupTofSthat containsA, and we say thatAgeneratesT. A single elementxofSgenerates the subsemigroup{xn|n∈Z+}. If this is finite, thenxis said to be offinite order, otherwise it is ofinfinite order.
A semigroup is said to beperiodicif all of its elements are of finite order.
A semigroup generated by a single element is said to bemonogenic(orcyclic). If a monogenic semigroup is infinite then it is isomorphic to the semigroup of positiveintegerswith the operation of addition.
If it is finite and nonempty, then it must contain at least oneidempotent.
It follows that every nonempty periodic semigroup has at least one idempotent.
A subsemigroup that is also a group is called asubgroup. There is a close relationship between the subgroups of a semigroup and its idempotents. Each subgroup contains exactly one idempotent, namely the identity element of the subgroup. For each idempotenteof the semigroup there is a unique maximal subgroup containinge. Each maximal subgroup arises in this way, so there is a one-to-one correspondence between idempotents and maximal subgroups. Here the termmaximal subgroupdiffers from its standard use in group theory.
More can often be said when the order is finite. For example, every nonempty finite semigroup is periodic, and has a minimalidealand at least one idempotent. The number of finite semigroups of a given size (greater than 1) is (obviously) larger than the number of groups of the same size. For example, of the sixteen possible "multiplication tables" for a set of two elements{a,b}, eight form semigroups[b]whereas only four of these are monoids and only two form groups. For more on the structure of finite semigroups, seeKrohn–Rhodes theory.
There is a structure theorem for commutative semigroups in terms ofsemilattices.[10]A semilattice (or more precisely a meet-semilattice)(L, ≤)is apartially ordered setwhere every pair of elementsa,b∈Lhas agreatest lower bound, denoteda∧b. The operation ∧ makesLinto a semigroup that satisfies the additionalidempotencelawa∧a=a.
Given a homomorphismf:S→Lfrom an arbitrary semigroup to a semilattice, each inverse imageSa=f−1{a}is a (possibly empty) semigroup. Moreover,SbecomesgradedbyL, in the sense thatSaSb⊆Sa∧b.
Iffis onto, the semilatticeLis isomorphic to thequotientofSby the equivalence relation ~ such thatx~yif and only iff(x) =f(y). This equivalence relation is a semigroup congruence, as defined above.
Whenever we take the quotient of a commutative semigroup by a congruence, we get another commutative semigroup. The structure theorem says that for any commutative semigroupS, there is a finest congruence ~ such that the quotient ofSby this equivalence relation is a semilattice. Denoting this semilattice byL, we get a homomorphismffromSontoL. As mentioned,Sbecomes graded by this semilattice.
Furthermore, the componentsSaare allArchimedean semigroups. An Archimedean semigroup is one where given any pair of elementsx,y, there exists an elementzandn> 0such thatxn=yz.
The Archimedean property follows immediately from the ordering in the semilatticeL, since with this ordering we havef(x) ≤f(y)if and only ifxn=yzfor somezandn> 0.
Thegroup of fractionsorgroup completionof a semigroupSis thegroupG=G(S)generated by the elements ofSas generators and all equationsxy=zthat hold true inSasrelations.[11]There is an obvious semigroup homomorphismj:S→G(S)that sends each element ofSto the corresponding generator. This has auniversal propertyfor morphisms fromSto a group:[12]given any groupHand any semigroup homomorphismk:S→H, there exists a uniquegroup homomorphismf:G→Hwithk=fj. We may think ofGas the "most general" group that contains a homomorphic image ofS.
An important question is to characterize those semigroups for which this map is an embedding. This need not always be the case: for example, takeSto be the semigroup of subsets of some setXwithset-theoretic intersectionas the binary operation (this is an example of a semilattice). SinceA.A=Aholds for all elements ofS, this must be true for all generators ofG(S) as well, which is therefore thetrivial group. It is clearly necessary for embeddability thatShave thecancellation property. WhenSis commutative this condition is also sufficient[13]and theGrothendieck groupof the semigroup provides a construction of the group of fractions. The problem for non-commutative semigroups can be traced to the first substantial paper on semigroups.[14][15]Anatoly Maltsevgave necessary and sufficient conditions for embeddability in 1937.[16]
Semigroup theory can be used to study some problems in the field ofpartial differential equations. Roughly speaking, the semigroup approach is to regard a time-dependent partial differential equation as anordinary differential equationon a function space. For example, consider the following initial/boundary value problem for theheat equationon the spatialinterval(0, 1) ⊂Rand timest≥ 0:
LetX=L2((0, 1)R)be theLpspaceof square-integrable real-valued functions with domain the interval(0, 1)and letAbe the second-derivative operator withdomain
whereH2{\displaystyle H^{2}}is aSobolev space. Then the above initial/boundary value problem can be interpreted as an initial value problem for an ordinary differential equation on the spaceX:
On an heuristic level, the solution to this problem "ought" to beu(t)=exp(tA)u0.{\displaystyle u(t)=\exp(tA)u_{0}.}However, for a rigorous treatment, a meaning must be given to theexponentialoftA. As a function oft, exp(tA) is a semigroup of operators fromXto itself, taking the initial stateu0at timet= 0to the stateu(t) = exp(tA)u0at timet. The operatorAis said to be theinfinitesimal generatorof the semigroup.
The study of semigroups trailed behind that of other algebraic structures with more complex axioms such asgroupsorrings. A number of sources[17][18]attribute the first use of the term (in French) to J.-A. de Séguier inÉlements de la Théorie des Groupes Abstraits(Elements of the Theory of Abstract Groups) in 1904. The term is used in English in 1908 in Harold Hinton'sTheory of Groups of Finite Order.
Anton Sushkevichobtained the first non-trivial results about semigroups. His 1928 paper "Über die endlichen Gruppen ohne das Gesetz der eindeutigen Umkehrbarkeit" ("On finite groups without the rule of unique invertibility") determined the structure of finitesimple semigroupsand showed that the minimal ideal (orGreen's relationsJ-class) of a finite semigroup is simple.[18]From that point on, the foundations of semigroup theory were further laid byDavid Rees,James Alexander Green,Evgenii Sergeevich Lyapin[fr],Alfred H. CliffordandGordon Preston. The latter two published a two-volume monograph on semigroup theory in 1961 and 1967 respectively. In 1970, a new periodical calledSemigroup Forum(currently published bySpringer Verlag) became one of the few mathematical journals devoted entirely to semigroup theory.
Therepresentation theoryof semigroups was developed in 1963 byBoris Scheinusingbinary relationson a setAandcomposition of relationsfor the semigroup product.[19]At an algebraic conference in 1972 Schein surveyed the literature on BA, the semigroup of relations onA.[20]In 1997 Schein andRalph McKenzieproved that every semigroup is isomorphic to a transitive semigroup of binary relations.[21]
In recent years researchers in the field have become more specialized with dedicated monographs appearing on important classes of semigroups, likeinverse semigroups, as well as monographs focusing on applications inalgebraic automata theory, particularly for finite automata, and also infunctional analysis.
If the associativity axiom of a semigroup is dropped, the result is amagma, which is nothing more than a setMequipped with abinary operationthat is closedM×M→M.
Generalizing in a different direction, ann-ary semigroup(alson-semigroup,polyadic semigroupormultiary semigroup) is a generalization of a semigroup to a setGwith an-ary operationinstead of a binary operation.[22]The associative law is generalized as follows: ternary associativity is(abc)de=a(bcd)e=ab(cde), i.e. the stringabcdewith any three adjacent elements bracketed.n-ary associativity is a string of lengthn+ (n− 1)with anynadjacent elements bracketed. A 2-ary semigroup is just a semigroup. Further axioms lead to ann-ary group.
A third generalization is thesemigroupoid, in which the requirement that the binary relation be total is lifted. As categories generalize monoids in the same way, a semigroupoid behaves much like a category but lacks identities.
Infinitary generalizations of commutative semigroups have sometimes been considered by various authors.[c]
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https://en.wikipedia.org/wiki/Semigroup_ideal
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Netzwerkis theGermanword for "network".
It may also refer to:
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https://en.wikipedia.org/wiki/Netzwerk_(disambiguation)
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Incomputing,input/output(I/O,i/o, or informallyioorIO) is the communication between an information processing system, such as acomputer, and the outside world, such as another computer system, peripherals, or a human operator.Inputsare the signals or data received by the system and outputs are the signals ordatasent from it. The term can also be used as part of an action; to "perform I/O" is to perform aninput or output operation.
I/O devicesare the pieces ofhardwareused by a human (or other system) to communicate with a computer. For instance, akeyboardorcomputer mouseis aninput devicefor a computer, whilemonitorsandprintersareoutput devices. Devices for communication between computers, such asmodemsandnetwork cards, typically perform both input and output operations. Any interaction with the system by an interactor is aninputand the reaction the system responds is called the output.
The designation of a device as either input or output depends on perspective. Mice and keyboards take physical movements that the human user outputs and convert them into input signals that a computer can understand; the output from these devices is the computer's input. Similarly, printers and monitors take signals that computers output as input, and they convert these signals into a representation that human users can understand. From the humanuser's perspective, the process of reading or seeing these representations is receiving output; this type of interaction between computers and humans is studied in the field ofhuman–computer interaction. A further complication is that a device traditionally considered an input device, e.g., card reader, keyboard, may accept control commands to, e.g., select stacker, display keyboard lights, while a device traditionally considered as an output device may provide status data (e.g., low toner, out of paper, paper jam).
In computer architecture, the combination of theCPUandmain memory, to which the CPU can read or write directly using individualinstructions, is considered the brain of a computer. Any transfer of information to or from the CPU/memory combo, for example by reading data from adisk drive, is considered I/O.[1]The CPU and its supporting circuitry may providememory-mapped I/Othat is used in low-levelcomputer programming, such as in the implementation ofdevice drivers, or may provide access toI/O channels. AnI/O algorithmis one designed to exploit locality and perform efficiently when exchanging data with a secondary storage device, such as a disk drive.
An I/O interface is required whenever the I/O device is driven by a processor. Typically a CPU communicates with devices via abus. The interface must have the necessary logic to interpret the device address generated by the processor.Handshakingshould be implemented by the interface using appropriate commands (like BUSY, READY, and WAIT), and the processor can communicate with an I/O device through the interface. If different data formats are being exchanged, the interface must be able to convert serial data to parallel form and vice versa. Because it would be a waste for a processor to be idle while it waits for data from an input device there must be provision for generatinginterrupts[2]and the corresponding type numbers for further processing by the processor if required.[clarification needed]
A computer that usesmemory-mapped I/Oaccesses hardware by reading and writing to specific memory locations, using the same assembly language instructions that computer would normally use to access memory. An alternative method is via instruction-based I/O which requires that a CPU have specialized instructions for I/O.[1]Both input and output devices have adata processingrate that can vary greatly.[2]With some devices able to exchange data at very high speedsdirect accessto memory (DMA) without the continuous aid of a CPU is required.[2]
Higher-leveloperating systemand programming facilities employ separate, more abstract I/O concepts andprimitives. For example, most operating systems provide application programs with the concept offiles. Most programming languages provide I/O facilities either as statements in the language or asfunctionsin a standard library for the language.
An alternative to special primitive functions is theI/O monad, which permits programs to just describe I/O, and the actions are carried out outside the program. This is notable because theI/Ofunctions would introduceside-effectsto any programming language, but this allowspurely functional programmingto be practical.
The I/O facilities provided by operating systems may berecord-oriented, with files containingrecords, or stream-oriented, with the file containing a stream of bytes.
Channel I/Orequires the use of instructions that are specifically designed to perform I/O operations. The I/O instructions address the channel or the channel and device; the channel asynchronously accesses all other required addressing and control information. This is similar to DMA, but more flexible.
Port-mapped I/Oalso requires the use of special I/O instructions. Typically one or more ports are assigned to the device, each with a special purpose. The port numbers are in a separate address space from that used by normal instructions.
Direct memory access(DMA) is a means for devices to transfer large chunks of data to and from memory independently of the CPU.
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https://en.wikipedia.org/wiki/Input/output
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Configurators, also known as choice boards, design systems, toolkits, or co-design platforms, are responsible for guiding the user[who?]through the configuration[clarification needed]process. Different variations are represented, visualized, assessed and priced which starts a learning-by-doing process for the user. While the term “configurator” or “configuration system” is quoted rather often in literature,[citation needed]it is used for the most part in a technical sense, addressing a software tool. The success of such an interaction system is, however, not only defined by its technological capabilities, but also by its integration in the whole sale environment, its ability to allow for learning by doing, to provide experience and process satisfaction, and its integration into the brand concept. (Franke & Piller (2003))
Configurators can be found in various forms and different industries (Felfernig et al. (2014)). They are employed in B2B (business to business), as well as B2C (business to consumer) markets and are operated either by trained staff or customers themselves. Whereas B2B configurators are primarily used to support sales and lift production efficiency, B2C configurators are often employed as design tools that allow customers to "co-design" their own products. This is reflected in different advantages according to usage:[1]
For B2B:
For B2C:
Configurators enable mass customization, which depends on a deep and efficient integration of customers into value creation. Salvador et al. identified three fundamental capabilities determining the ability of a company to mass-customize its offering, i.e. solution space development, robust process design and choice navigation (Salvador, Martin & Piller (2009)). Configurators serve as an important tool for choice navigation. Configurators have been widely used in e-Commerce. Examples can be found in different industries like accessories, apparel, automobile, food, industrial goods etc. The main challenge of choice navigation lies in the ability to support customers in identifying their own solutions while minimizing complexity and the burden of choice, i.e. improving the experience of customer needs, elicitation and interaction in a configuration process. Many efforts have been put along this direction to enhance the efficiency of configurator design, such as adaptive configurators(Wang & Tseng (2011);Jalali & Leake (2012)). The prediction is integrated into the configurator to improve the quality and speed of configuration process. Configurators may also be used to limit or eliminate mass customization if intended to do so. This is accomplished through limiting of allowable options in data models.
According to (Sabin & Weigel (1998)), configurators can be classified as rule based, model based and case based, depending on the reasoning techniques used.
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https://en.wikipedia.org/wiki/Configurator
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Inlinguistic morphologyand information retrieval,stemmingis the process of reducing inflected (or sometimes derived) words to theirword stem, base orrootform—generally a written word form. The stem need not be identical to themorphological rootof the word; it is usually sufficient that related words map to the same stem, even if this stem is not in itself a valid root.Algorithmsfor stemming have been studied incomputer sciencesince the 1960s. Manysearch enginestreat words with the same stem assynonymsas a kind ofquery expansion, a process called conflation.
Acomputer programor subroutine that stems word may be called astemming program,stemming algorithm, orstemmer.
A stemmer for English operating on the stemcatshould identify suchstringsascats,catlike, andcatty. A stemming algorithm might also reduce the wordsfishing,fished, andfisherto the stemfish. The stem need not be a word, for example the Porter algorithm reducesargue,argued,argues,arguing, andargusto the stemargu.
The first published stemmer was written byJulie Beth Lovinsin 1968.[1]This paper was remarkable for its early date and had great influence on later work in this area.[citation needed]Her paper refers to three earlier major attempts at stemming algorithms, by ProfessorJohn W. TukeyofPrinceton University, the algorithm developed atHarvard UniversitybyMichael Lesk, under the direction of ProfessorGerard Salton, and a third algorithm developed by James L. Dolby of R and D Consultants, Los Altos, California.
A later stemmer was written byMartin Porterand was published in the July 1980 issue of the journalProgram. This stemmer was very widely used and became the de facto standard algorithm used for English stemming. Dr. Porter received theTony Kent Strix awardin 2000 for his work on stemming and information retrieval.
Many implementations of the Porter stemming algorithm were written and freely distributed; however, many of these implementations contained subtle flaws. As a result, these stemmers did not match their potential. To eliminate this source of error, Martin Porter released an officialfree software(mostlyBSD-licensed) implementation[2]of the algorithm around the year 2000. He extended this work over the next few years by buildingSnowball, a framework for writing stemming algorithms, and implemented an improved English stemmer together with stemmers for several other languages.
The Paice-Husk Stemmer was developed byChris D Paiceat Lancaster University in the late 1980s, it is an iterative stemmer and features an externally stored set of stemming rules. The standard set of rules provides a 'strong' stemmer and may specify the removal or replacement of an ending. The replacement technique avoids the need for a separate stage in the process to recode or provide partial matching. Paice also developed a direct measurement for comparing stemmers based on counting the over-stemming and under-stemming errors.
There are several types of stemming algorithms which differ in respect to performance and accuracy and how certain stemming obstacles are overcome.
A simple stemmer looks up the inflected form in alookup table. The advantages of this approach are that it is simple, fast, and easily handles exceptions. The disadvantages are that all inflected forms must be explicitly listed in the table: new or unfamiliar words are not handled, even if they are perfectly regular (e.g. cats ~ cat), and the table may be large. For languages with simple morphology, like English, table sizes are modest, but highly inflected languages like Turkish may have hundreds of potential inflected forms for each root.
A lookup approach may use preliminarypart-of-speech taggingto avoid overstemming.[3]
The lookup table used by a stemmer is generally produced semi-automatically. For example, if the word is "run", then the inverted algorithm might automatically generate the forms "running", "runs", "runned", and "runly". The last two forms are valid constructions, but they are unlikely.[citation needed].
Suffix stripping algorithms do not rely on a lookup table that consists of inflected forms and root form relations. Instead, a typically smaller list of "rules" is stored which provides a path for the algorithm, given an input word form, to find its root form. Some examples of the rules include:
Suffix stripping approaches enjoy the benefit of being much simpler to maintain than brute force algorithms, assuming the maintainer is sufficiently knowledgeable in the challenges of linguistics and morphology and encoding suffix stripping rules. Suffix stripping algorithms are sometimes regarded as crude given the poor performance when dealing with exceptional relations (like 'ran' and 'run'). The solutions produced by suffix stripping algorithms are limited to thoselexical categorieswhich have well known suffixes with few exceptions. This, however, is a problem, as not all parts of speech have such a well formulated set of rules.Lemmatisationattempts to improve upon this challenge.
Prefix stripping may also be implemented. Of course, not all languages use prefixing or suffixing.
Suffix stripping algorithms may differ in results for a variety of reasons. One such reason is whether the algorithm constrains whether the output word must be a real word in the given language. Some approaches do not require the word to actually exist in the language lexicon (the set of all words in the language). Alternatively, some suffix stripping approaches maintain a database (a large list) of all known morphological word roots that exist as real words. These approaches check the list for the existence of the term prior to making a decision. Typically, if the term does not exist, alternate action is taken. This alternate action may involve several other criteria. The non-existence of an output term may serve to cause the algorithm to try alternate suffix stripping rules.
It can be the case that two or more suffix stripping rules apply to the same input term, which creates an ambiguity as to which rule to apply. The algorithm may assign (by human hand or stochastically) a priority to one rule or another. Or the algorithm may reject one rule application because it results in a non-existent term whereas the other overlapping rule does not. For example, given the English termfriendlies, the algorithm may identify theiessuffix and apply the appropriate rule and achieve the result offriendl.Friendlis likely not found in the lexicon, and therefore the rule is rejected.
One improvement upon basic suffix stripping is the use of suffix substitution. Similar to a stripping rule, a substitution rule replaces a suffix with an alternate suffix. For example, there could exist a rule that replacesieswithy. How this affects the algorithm varies on the algorithm's design. To illustrate, the algorithm may identify that both theiessuffix stripping rule as well as the suffix substitution rule apply. Since the stripping rule results in a non-existent term in the lexicon, but the substitution rule does not, the substitution rule is applied instead. In this example,friendliesbecomesfriendlyinstead offriendl'.
Diving further into the details, a common technique is to apply rules in a cyclical fashion (recursively, as computer scientists would say). After applying the suffix substitution rule in this example scenario, a second pass is made to identify matching rules on the termfriendly, where thelystripping rule is likely identified and accepted. In summary,friendliesbecomes (via substitution)friendlywhich becomes (via stripping)friend.
This example also helps illustrate the difference between a rule-based approach and a brute force approach. In a brute force approach, the algorithm would search forfriendliesin the set of hundreds of thousands of inflected word forms and ideally find the corresponding root formfriend. In the rule-based approach, the three rules mentioned above would be applied in succession to converge on the same solution. Chances are that the brute force approach would be slower, as lookup algorithms have a direct access to the solution, while rule-based should try several options, and combinations of them, and then choose which result seems to be the best.
A more complex approach to the problem of determining a stem of a word islemmatisation. This process involves first determining thepart of speechof a word, and applying different normalization rules for each part of speech. The part of speech is first detected prior to attempting to find the root since for some languages, the stemming rules change depending on a word's part of speech.
This approach is highly conditional upon obtaining the correct lexical category (part of speech). While there is overlap between the normalization rules for certain categories, identifying the wrong category or being unable to produce the right category limits the added benefit of this approach over suffix stripping algorithms. The basic idea is that, if the stemmer is able to grasp more information about the word being stemmed, then it can apply more accurate normalization rules (which unlike suffix stripping rules can also modify the stem).
Stochasticalgorithms involve using probability to identify the root form of a word. Stochastic algorithms are trained (they "learn") on a table of root form to inflected form relations to develop a probabilistic model. This model is typically expressed in the form of complex linguistic rules, similar in nature to those in suffix stripping or lemmatisation. Stemming is performed by inputting an inflected form to the trained model and having the model produce the root form according to its internal ruleset, which again is similar to suffix stripping and lemmatisation, except that the decisions involved in applying the most appropriate rule, or whether or not to stem the word and just return the same word, or whether to apply two different rules sequentially, are applied on the grounds that the output word will have the highest probability of being correct (which is to say, the smallest probability of being incorrect, which is how it is typically measured).
Some lemmatisation algorithms are stochastic in that, given a word which may belong to multiple parts of speech, a probability is assigned to each possible part. This may take into account the surrounding words, called the context, or not. Context-free grammars do not take into account any additional information. In either case, after assigning the probabilities to each possible part of speech, the most likely part of speech is chosen, and from there the appropriate normalization rules are applied to the input word to produce the normalized (root) form.
Some stemming techniques use then-gramcontext of a word to choose the correct stem for a word.[4]
Hybrid approaches use two or more of the approaches described above in unison. A simple example is a suffix tree algorithm which first consults a lookup table using brute force. However, instead of trying to store the entire set of relations between words in a given language, the lookup table is kept small and is only used to store a minute amount of "frequent exceptions" like "ran => run". If the word is not in the exception list, apply suffix stripping or lemmatisation and output the result.
Inlinguistics, the termaffixrefers to either aprefixor asuffix. In addition to dealing with suffixes, several approaches also attempt to remove common prefixes. For example, given the wordindefinitely, identify that the leading "in" is a prefix that can be removed. Many of the same approaches mentioned earlier apply, but go by the nameaffix stripping. A study of affix stemming for several European languages can be found here.[5]
Such algorithms use a stem database (for example a set of documents that contain stem words). These stems, as mentioned above, are not necessarily valid words themselves (but rather common sub-strings, as the "brows" in "browse" and in "browsing"). In order to stem a word the algorithm tries to match it with stems from the database, applying various constraints, such as on the relative length of the candidate stem within the word (so that, for example, the short prefix "be", which is the stem of such words as "be", "been" and "being", would not be considered as the stem of the word "beside").[citation needed].
While much of the early academic work in this area was focused on the English language (with significant use of the Porter Stemmer algorithm), many other languages have been investigated.[6][7][8][9][10]
Hebrew and Arabic are still considered difficult research languages for stemming. English stemmers are fairly trivial (with only occasional problems, such as "dries" being the third-person singular present form of the verb "dry", "axes" being the plural of "axe" as well as "axis"); but stemmers become harder to design as the morphology, orthography, and character encoding of the target language becomes more complex. For example, an Italian stemmer is more complex than an English one (because of a greater number of verb inflections), a Russian one is more complex (more noundeclensions), a Hebrew one is even more complex (due tononconcatenative morphology, a writing system without vowels, and the requirement of prefix stripping: Hebrew stems can be two, three or four characters, but not more), and so on.[11]
Multilingual stemming applies morphological rules of two or more languages simultaneously instead of rules for only a single language when interpreting a search query. Commercial systems using multilingual stemming exist.[citation needed]
There are two error measurements in stemming algorithms, overstemming and understemming. Overstemming is an error where two separate inflected words are stemmed to the same root, but should not have been—afalse positive. Understemming is an error where two separate inflected words should be stemmed to the same root, but are not—afalse negative. Stemming algorithms attempt to minimize each type of error, although reducing one type can lead to increasing the other.
For example, the widely used Porter stemmer stems "universal", "university", and "universe" to "univers". This is a case of overstemming: though these three words areetymologicallyrelated, their modern meanings are in widely different domains, so treating them as synonyms in a search engine will likely reduce the relevance of the search results.
An example of understemming in the Porter stemmer is "alumnus" → "alumnu", "alumni" → "alumni", "alumna"/"alumnae" → "alumna". This English word keeps Latin morphology, and so these near-synonyms are not conflated.
Stemming is used as an approximate method for grouping words with a similar basic meaning together. For example, a text mentioning "daffodils" is probably closely related to a text mentioning "daffodil" (without the s). But in some cases, words with the same morphological stem haveidiomaticmeanings which are not closely related: a user searching for "marketing" will not be satisfied by most documents mentioning "markets" but not "marketing".
Stemmers can be used as elements inquery systemssuch asWebsearch engines. The effectiveness of stemming for English query systems were soon found to be rather limited, however, and this has led earlyinformation retrievalresearchers to deem stemming irrelevant in general.[12]An alternative approach, based on searching forn-gramsrather than stems, may be used instead. Also, stemmers may provide greater benefits in other languages than English.[13][14]
Stemming is used to determine domain vocabularies indomain analysis.[15]
Many commercial companies have been using stemming since at least the 1980s and have produced algorithmic and lexical stemmers in many languages.[16][17]
TheSnowballstemmers have been compared with commercial lexical stemmers with varying results.[18][19]
Google Searchadopted word stemming in 2003.[20]Previously a search for "fish" would not have returned "fishing". Other software search algorithms vary in their use of word stemming. Programs that simply search for substrings will obviously find "fish" in "fishing" but when searching for "fishes" will not find occurrences of the word "fish".
Stemming is used as a task in pre-processing texts before performing text mining analyses on it.
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https://en.wikipedia.org/wiki/Stemming
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Normalized compression distance(NCD) is a way of measuring thesimilaritybetween two objects, be it two documents, two letters, two emails, two music scores, two languages, two programs, two pictures, two systems, two genomes, to name a few. Such a measurement should not be application dependent or arbitrary. A reasonable definition for the similarity between two objects is how difficult it is to transform them into each other.
It can be used ininformation retrievalanddata miningforcluster analysis.
We assume that the objects one talks about are finitestrings of 0s and 1s. Thus we meanstring similarity. Every computer file is of this form, that is, if an object is a file in a computer it is of this form. One can define theinformation distancebetween stringsx{\displaystyle x}andy{\displaystyle y}as the length of the shortest programp{\displaystyle p}that computesx{\displaystyle x}fromy{\displaystyle y}and vice versa. This shortest program is in a fixed programming language. For technical reasons one uses the theoretical notion ofTuring machines. Moreover, to express the length ofp{\displaystyle p}one uses the notion ofKolmogorov complexity. Then, it has been shown[1]
up to logarithmic additive terms which can be ignored. This information distance is shown to be ametric(it satisfies the metric inequalities up to a logarithmic additive term), is universal (it minorizes
every computable distance as computed for example from features up to a constant additive term).[1]
The information distance is absolute, but if we want to express similarity, then we are more interested in relative ones. For example, if two strings of length 1,000,000 differ by 1000 bits, then we consider that those strings are relatively more similar than two strings of 1000 bits that differ by 1000 bits. Hence we need to normalize to obtain a similarity metric. This way one obtains the normalized information distance (NID),
whereK(x∣y){\displaystyle K(x\mid y)}isalgorithmic informationofx{\displaystyle x}giveny{\displaystyle y}as input. The NID is called the similarity metric. Since the functionNID(x,y){\displaystyle NID(x,y)}has been shown to satisfy the basic requirements for a metric distance measure.[2][3]However, it is not computable or even semicomputable.[4]
While the NID metric is not computable, it has an abundance of applications. Simply approximatingK{\displaystyle K}by real-world compressors, withZ(x){\displaystyle Z(x)}is the binary length of the filex{\displaystyle x}compressed with compressor Z (for example "gzip", "bzip2", "PPMZ") in order to make NID easy to apply.[2]VitanyiandCilibrasirewrote the NID to obtain the Normalized Compression Distance (NCD)
The NCD is actually a family of distances parametrized with the compressor Z. The better Z is, the closer the NCD approaches the NID, and the better the results are.[3]
The normalized compression distance has been used to fully automatically reconstruct language and phylogenetic trees.[2][3]It can also be used for new applications of generalclusteringandclassificationof natural data in arbitrary domains,[3]for clustering of heterogeneous data,[3]and foranomaly detectionacross domains.[5]The NID and NCD have been applied to numerous subjects, including music classification,[3]to analyze network traffic and cluster computer worms and viruses,[6]authorship attribution,[7]gene expression dynamics,[8]predicting useful versus useless stem cells,[9]critical networks,[10]image registration,[11]question-answer systems.[12]
Researchers from thedataminingcommunity use NCD and variants as "parameter-free, feature-free" data-mining tools.[5]One group have experimentally tested a closely related metric on a large variety of sequence benchmarks. Comparing their compression method with 51 major methods found in 7 major data-mining conferences over the past decade, they established superiority of the compression method for clustering heterogeneous data, and for anomaly detection, and competitiveness in clustering domain data.
NCD has an advantage of beingrobustto noise.[13]However, although NCD appears "parameter-free", practical questions include which compressor to use in computing the NCD and other possible problems.[14]
In order to measure the information of a string relative to another there is the need to rely on relative semi-distances (NRC).[15]These are measures that do not need to respect symmetry and triangle inequality distance properties. Although the NCD and the NRC seem very similar, they address different questions. The NCD measures how similar both strings are, mostly using the information content, while the NRC indicates the fraction of a target string that cannot be constructed using information from another string. For a comparison, with application to the evolution of primate genomes, see.[16]
Objects can be given literally, like the literal four-lettergenome of a mouse, or the literal text ofWar and Peaceby Tolstoy. For simplicity we take it that all meaning of the object is represented by the literal object itself. Objects can also be given by name, like "the four-letter genome of a mouse," or "the text of `War and Peace' by Tolstoy." There are also objects that cannot be given literally, but only by name, and that acquire their meaning from their contexts in background common knowledge in humankind, like "home" or "red."
We are interested insemantic similarity. Using code-word lengths obtained from the page-hit counts returned by Google from the web, we obtain a semantic distance using the NCD formula and viewing Google as a compressor useful for data mining, text comprehension, classification, and translation. The associated NCD, called thenormalized Google distance(NGD) can be rewritten as
wheref(x){\displaystyle f(x)}denotes the number of pages containing the search termx{\displaystyle x}, andf(x,y){\displaystyle f(x,y)}denotes the number of pages containing bothx{\displaystyle x}andy{\displaystyle y},) as returned by Google or any search engine capable of returning an aggregate page count. The numberN{\displaystyle N}can be set to the number of pages indexed although it is more proper to count each page according to the number of search terms or phrases it contains. As rule of the thumb one can multiply the number of pages by, say, a thousand...[17]
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https://en.wikipedia.org/wiki/Normalized_compression_distance
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Account verificationis the process of verifying that a new or existing account is owned and operated by a specified real individual or organization. A number of websites, for examplesocial mediawebsites, offer account verification services. Verified accounts are often visually distinguished bycheck markicons or badges next to the names of individuals or organizations.
Account verification can enhance the quality of online services, mitigatingsockpuppetry,bots,trolling,spam,vandalism,fake news,disinformationandelection interference.
Account verification was introduced byTwitterin June 2009,[1][2][3]initially as a feature for public figures and accounts of interest, individuals in "music, acting, fashion, government, politics, religion, journalism, media, sports, business and other key interest areas".[4]A similar verification system was adopted byGoogle+in 2011,[5]Facebook pagein October 2015 (Available inUnited States,Canada,United Kingdom,AustraliaandNew Zealand)Facebook profileandFacebook pagein 2018 (Available in Worldwide)Instagramin 2014,[6]andPinterestin 2015.[7]On YouTube, users are able to submit a request for a verification badge once they obtain 100,000 or more subscribers.[8]It also has an "official artist" badge for musicians and bands.[9]
In July 2016,Twitterannounced that, beyond public figures, any individual would be able to apply foraccount verification.[10][11]This was temporarily suspended in February 2018, following a backlash over the verification of one of the organisers of the far-rightUnite the Right rallydue to a perception that verification conveys "credibility" or "importance".[12][13]In March 2018, during a live-stream onPeriscope,Jack Dorsey, co-founder and CEO ofTwitter, discussed the idea of allowing any individual to get a verified account.[14]Twitter reopened account verification applications in May 2021 after revamping their account verification criteria.[15]This time offering notability criteria for the account categories of government, companies, brands, and organizations, news organizations and journalists, entertainment, sports and activists, organizers, and other influential individuals.[16]Instagram began allowing users to request verification in August 2018.[17]
In April 2018,Mark Zuckerberg, co-founder and CEO ofFacebook, announced that purchasers of political or issue-based advertisements would be required to verify their identities and locations.[18][19]He also indicated thatFacebookwould require individuals who manage large pages to be verified.[18]In May 2018, Kent Walker, senior vice president ofGoogle, announced that, in the United States, purchasers of political-leaning advertisements would need to verify their identities.[20]
In November 2022,Elon Muskincluded a blue verification check mark with a paid Twitter Blue monthly membership. Prior to Musk'sacquisition of Twitter, Twitter offered this check mark at no charge to confirmed high profile users.[21]On December 19, 2022, Twitter introduced two new check mark colors: gold for accounts from official businesses and organizations, and grey for accounts from governments or multilateral organizations. The type of check mark can be confirmed by visiting the profile page, then clicking or tapping on the check mark.[22]
Identity verification servicesare third-party solutions which can be used to ensure that a person provides information which is associated with the identity of a real person. Such services may verify the authenticity ofidentity documentssuch asdrivers licensesorpassports, called documentary verification, or may verify identity information against authoritative sources such ascredit bureausor government data, called nondocumentary verification.[citation needed]
The uploading of scanned or photographedidentity documentsis a practice in use, for example, atFacebook.[23]According toFacebook, there are two reasons that a person would be asked to send a scan of or photograph of anIDtoFacebook: to show account ownership and to confirm their name.[23]
In January 2018,Facebookpurchased Confirm.io,[24]a startup that was advancing technologies to verify the authenticity ofidentification documentation.
Behavioral verification is the computer-aided and automated detection and analysis of behaviors and patterns of behavior to verify accounts. Behaviors to detect include those ofsockpuppets,bots,cyborgs,trolls,spammers,vandals, and sources and spreaders offake news,disinformationandelection interference. Behavioral verification processes can flag accounts as suspicious, exclude accounts from suspicion, or offercorroborating evidencefor processes of account verification.
Identity verificationis required to establish bank accounts and other financial accounts in many jurisdictions. Verifying identity in the financial sector is often required by regulation such asKnow Your CustomerorCustomer Identification Program. Accordingly, bank accounts can be of use ascorroborating evidencewhen performing account verification.
Bank account information can be provided when creating or verifying an account or when making a purchase.
Postal address information can be provided when creating or verifying an account or when making and subsequently shipping a purchase. A hyperlink or code can be sent to a user by mail, recipients entering it on a website verifying their postal address.
A telephone number can be provided when creating or verifying an account or added to an account to obtain a set of features. During the process of verifying a telephone number, a confirmation code is sent to a phone number specified by a user, for example in anSMS messagesent to a mobile phone. As the user receives the code sent, they can enter it on the website to confirm their receipt.
An email account is often required to create an account. During this process, a confirmation hyperlink is sent in anemail messageto an email address specified by a person. The email recipient is instructed in the email message to navigate to the provided confirmation hyperlink if and only if they are the person creating an account. The act of navigating to the hyperlink confirms receipt of the email by the person.
The added value of an email account for purposes of account verification depends upon the process of account verification performed by the specific email service provider.
Multi-factor account verification is account verification which simultaneously utilizes a number of techniques.
The processes of account verification utilized by multiple service providers cancorroborateone another.OpenID Connectincludes a user information protocol which can be used to link multiple accounts, corroborating user information.[25]
On some services, account verification is synonymous withgood standing.
Twitterreserves the right to remove account verification from users' accounts at any time without notice.[26]Reasons for removal may reflect behaviors on and off Twitter and include: promoting hate and/or violence against, or directly attacking or threatening other people on the basis of race, ethnicity, national origin, sexual orientation, gender, gender identity, religious affiliation, age, disability, or disease; supporting organizations or individuals that promote the above; inciting or engaging in the harassment of others; violence and dangerous behavior;
directly or indirectly threatening or encouraging any form of physical violence against an individual or any group of people, including threatening or promoting terrorism; violent, gruesome, shocking, or disturbing imagery; self-harm, suicide; and engaging in other activity on Twitter that violates the Twitter Rules.[27]
In April 2023, Blue ticks were removed from all Twitter accounts that had not subscribed to Twitter Blue.[28]
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Incomputer science,automatic programming[1]is a type ofcomputer programmingin which some mechanism generates acomputer program, to allow humanprogrammersto write the code at a higher abstraction level.
There has been little agreement on the precise definition of automatic programming, mostly because its meaning has changed over time.David Parnas, tracing the history of "automatic programming" in published research, noted that in the 1940s it described automation of the manual process of punchingpaper tape. Later it referred to translation ofhigh-level programming languageslikeFortranandALGOL. In fact, one of the earliest programs identifiable as acompilerwas calledAutocode.Parnasconcluded that "automatic programming has always been aeuphemismfor programming in a higher-level language than was then available to the programmer."[2]
Program synthesisis one type of automatic programming where a procedure is created from scratch, based on mathematical requirements.
Mildred Koss, an earlyUNIVACprogrammer, explains: "Writing machine code involved several tedious steps—breaking down a process into discrete instructions, assigning specific memory locations to all the commands, and managing the I/O buffers. After following these steps to implement mathematical routines, a sub-routine library, and sorting programs, our task was to look at the larger programming process. We needed to understand how we might reuse tested code and have the machine help in programming. As we programmed, we examined the process and tried to think of ways to abstract these steps to incorporate them into higher-level language. This led to the development of interpreters, assemblers, compilers, and generators—programs designed to operate on or produce other programs, that is,automatic programming."[3]
Generative programmingand the related termmeta-programming[4]are concepts whereby programs can be written "to manufacture software components in an automated way"[5]just as automation has improved "production of traditional commodities such as garments, automobiles, chemicals, and electronics."[6][7]
The goal is to improveprogrammerproductivity.[8]It is often related to code-reuse topics such ascomponent-based software engineering.
Source-code generationis the process of generating source code based on a description of the problem[9]or anontologicalmodel such as a template and is accomplished with aprogramming toolsuch as atemplate processoror anintegrated development environment(IDE). These tools allow the generation ofsource codethrough any of various means.
Modern programming languages are well supported by tools likeJson4Swift(Swift) andJson2Kotlin(Kotlin).
Programs that could generateCOBOLcode include:
These application generators supported COBOL inserts and overrides.
Amacroprocessor, such as theC preprocessor, which replaces patterns in source code according to relatively simple rules, is a simple form of source-code generator.Source-to-sourcecode generation tools also exist.[11][12]
Large language modelssuch asChatGPTare capable of generating a program's source code from a description of the program given in a natural language.[13]
Manyrelational database systemsprovide a function that will export the content of the database asSQLdata definitionqueries, which may then be executed to re-import the tables and their data, or migrate them to another RDBMS.
Alow-code development platform(LCDP) is software that provides an environmentprogrammersuse to createapplication softwarethroughgraphical user interfacesand configuration instead of traditionalcomputer programming.
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Apositional game[1][2]ingame theoryis a kind of acombinatorial gamefor two players. It is described by:
During the game, players alternately claim previously-unclaimed positions, until one of the players wins. If all positions inX{\displaystyle X}are taken while no player wins, the game is considered a draw.
The classic example of a positional game istic-tac-toe. In it,X{\displaystyle X}contains the 9 squares of the game-board,F{\displaystyle {\mathcal {F}}}contains the 8 lines that determine a victory (3 horizontal, 3 vertical and 2 diagonal), and the winning criterion is: the first player who holds an entire winning-set wins. Other examples of positional games areHexand theShannon switching game.
For every positional game there are exactly three options: either the first player has awinning strategy, or the second player has a winning strategy, or both players have strategies to enforce a draw.[2]: 7The main question of interest in the study of these games is which of these three options holds in any particular game.
A positional game is finite, deterministic and hasperfect information; therefore, in theory it is possible to create the fullgame treeand determine which of these three options holds. In practice, however, the game-tree might be enormous. Therefore, positional games are usually analyzed via more sophisticated combinatorial techniques.
Often, the input to a positional game is considered ahypergraph. In this case:
There are many variants of positional games, differing in their rules and their winning criteria.
The following table lists some specific positional games that were widely studied in the literature.
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Incomputer science, theCocke–Younger–Kasami algorithm(alternatively calledCYK, orCKY) is aparsingalgorithmforcontext-free grammarspublished by Itiroo Sakai in 1961.[1][2]The algorithm is named after some of its rediscoverers:John Cocke, Daniel Younger,Tadao Kasami, andJacob T. Schwartz. It employsbottom-up parsinganddynamic programming.
The standard version of CYK operates only on context-free grammars given inChomsky normal form(CNF). However any context-free grammar may be algorithmically transformed into a CNF grammar expressing the same language (Sipser 1997).
The importance of the CYK algorithm stems from its high efficiency in certain situations. UsingbigOnotation, theworst case running timeof CYK isO(n3⋅|G|){\displaystyle {\mathcal {O}}\left(n^{3}\cdot \left|G\right|\right)}, wheren{\displaystyle n}is the length of the parsed string and|G|{\displaystyle \left|G\right|}is the size of the CNF grammarG{\displaystyle G}(Hopcroft & Ullman 1979, p. 140). This makes it one of the most efficient[citation needed]parsing algorithms in terms of worst-caseasymptotic complexity, although other algorithms exist with better average running time in many practical scenarios.
Thedynamic programmingalgorithm requires the context-free grammar to be rendered intoChomsky normal form(CNF), because it tests for possibilities to split the current sequence into two smaller sequences. Any context-free grammar that does not generate the empty string can be represented in CNF using onlyproduction rulesof the formsA→α{\displaystyle A\rightarrow \alpha }andA→BC{\displaystyle A\rightarrow BC}; to allow for the empty string, one can explicitly allowS→ε{\displaystyle S\to \varepsilon }, whereS{\displaystyle S}is the start symbol.[3]
The algorithm inpseudocodeis as follows:
Allows to recover the most probable parse given the probabilities of all productions.
In informal terms, this algorithm considers every possible substring of the input string and setsP[l,s,v]{\displaystyle P[l,s,v]}to be true if the substring of lengthl{\displaystyle l}starting froms{\displaystyle s}can be generated from the nonterminalRv{\displaystyle R_{v}}. Once it has considered substrings of length 1, it goes on to substrings of length 2, and so on. For substrings of length 2 and greater, it considers every possible partition of the substring into two parts, and checks to see if there is some productionA→BC{\displaystyle A\to B\;C}such thatB{\displaystyle B}matches the first part andC{\displaystyle C}matches the second part. If so, it recordsA{\displaystyle A}as matching the whole substring. Once this process is completed, the input string is generated by the grammar if the substring containing the entire input string is matched by the start symbol.
This is an example grammar:
Now the sentenceshe eats a fish with a forkis analyzed using the CYK algorithm. In the following table, inP[i,j,k]{\displaystyle P[i,j,k]},iis the number of the row (starting at the bottom at 1), andjis the number of the column (starting at the left at 1).
For readability, the CYK table forPis represented here as a 2-dimensional matrixMcontaining a set of non-terminal symbols, such thatRkis inM[i,j]{\displaystyle M[i,j]}if, and only if,P[i,j,k]{\displaystyle P[i,j,k]}.
In the above example, since a start symbolSis inM[7,1]{\displaystyle M[7,1]}, the sentence can be generated by the grammar.
The above algorithm is arecognizerthat will only determine if a sentence is in the language. It is simple to extend it into aparserthat also constructs aparse tree, by storing parse tree nodes as elements of the array, instead of the boolean 1. The node is linked to the array elements that were used to produce it, so as to build the tree structure. Only one such node in each array element is needed if only one parse tree is to be produced. However, if all parse trees of an ambiguous sentence are to be kept, it is necessary to store in the array element a list of all the ways the corresponding node can be obtained in the parsing process. This is sometimes done with a second table B[n,n,r] of so-calledbackpointers.
The end result is then a shared-forest of possible parse trees, where common trees parts are factored between the various parses. This shared forest can conveniently be read as anambiguous grammargenerating only the sentence parsed, but with the same ambiguity as the original grammar, and the same parse trees up to a very simple renaming of non-terminals, as shown byLang (1994).
As pointed out byLange & Leiß (2009), the drawback of all known transformations into Chomsky normal form is that they can lead to an undesirable bloat in grammar size. The size of a grammar is the sum of the sizes of its production rules, where the size of a rule is one plus the length of its right-hand side. Usingg{\displaystyle g}to denote the size of the original grammar, the size blow-up in the worst case may range fromg2{\displaystyle g^{2}}to22g{\displaystyle 2^{2g}}, depending on the transformation algorithm used. For the use in teaching, Lange and Leiß propose a slight generalization of the CYK algorithm, "without compromising efficiency of the algorithm, clarity of its presentation, or simplicity of proofs" (Lange & Leiß 2009).
It is also possible to extend the CYK algorithm to parse strings usingweightedandstochastic context-free grammars. Weights (probabilities) are then stored in the table P instead of booleans, so P[i,j,A] will contain the minimum weight (maximum probability) that the substring from i to j can be derived from A. Further extensions of the algorithm allow all parses of a string to be enumerated from lowest to highest weight (highest to lowest probability).
When the probabilistic CYK algorithm is applied to a long string, the splitting probability can become very small due to multiplying many probabilities together. This can be dealt with by summing log-probability instead of multiplying probabilities.
Theworst case running timeof CYK isΘ(n3⋅|G|){\displaystyle \Theta (n^{3}\cdot |G|)}, wherenis the length of the parsed string and |G| is the size of the CNF grammarG. This makes it one of the most efficient algorithms for recognizing general context-free languages in practice.Valiant (1975)gave an extension of the CYK algorithm. His algorithm computes the same parsing table
as the CYK algorithm; yet he showed thatalgorithms for efficient multiplicationofmatrices with 0-1-entriescan be utilized for performing this computation.
Using theCoppersmith–Winograd algorithmfor multiplying these matrices, this gives an asymptotic worst-case running time ofO(n2.38⋅|G|){\displaystyle O(n^{2.38}\cdot |G|)}. However, the constant term hidden by theBig O Notationis so large that the Coppersmith–Winograd algorithm is only worthwhile for matrices that are too large to handle on present-day computers (Knuth 1997), and this approach requires subtraction and so is only suitable for recognition. The dependence on efficient matrix multiplication cannot be avoided altogether:Lee (2002)has proved that any parser for context-free grammars working in timeO(n3−ε⋅|G|){\displaystyle O(n^{3-\varepsilon }\cdot |G|)}can be effectively converted into an algorithm computing the product of(n×n){\displaystyle (n\times n)}-matrices with 0-1-entries in timeO(n3−ε/3){\displaystyle O(n^{3-\varepsilon /3})}, and this was extended by Abboud et al.[4]to apply to a constant-size grammar.
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Inmathematics,trigonometric integralsare afamilyofnonelementary integralsinvolvingtrigonometric functions.
The differentsineintegral definitions areSi(x)=∫0xsinttdt{\displaystyle \operatorname {Si} (x)=\int _{0}^{x}{\frac {\sin t}{t}}\,dt}si(x)=−∫x∞sinttdt.{\displaystyle \operatorname {si} (x)=-\int _{x}^{\infty }{\frac {\sin t}{t}}\,dt~.}
Note that the integrandsin(t)t{\displaystyle {\frac {\sin(t)}{t}}}is thesinc function, and also the zerothspherical Bessel function.
Sincesincis anevenentire function(holomorphicover the entire complex plane),Siis entire, odd, and the integral in its definition can be taken alongany pathconnecting the endpoints.
By definition,Si(x)is theantiderivativeofsinx/xwhose value is zero atx= 0, andsi(x)is the antiderivative whose value is zero atx= ∞. Their difference is given by theDirichlet integral,Si(x)−si(x)=∫0∞sinttdt=π2orSi(x)=π2+si(x).{\displaystyle \operatorname {Si} (x)-\operatorname {si} (x)=\int _{0}^{\infty }{\frac {\sin t}{t}}\,dt={\frac {\pi }{2}}\quad {\text{ or }}\quad \operatorname {Si} (x)={\frac {\pi }{2}}+\operatorname {si} (x)~.}
Insignal processing, the oscillations of the sine integral causeovershootandringing artifactswhen using thesinc filter, andfrequency domainringing if using a truncated sinc filter as alow-pass filter.
Related is theGibbs phenomenon: If the sine integral is considered as theconvolutionof the sinc function with theHeaviside step function, this corresponds to truncating theFourier series, which is the cause of the Gibbs phenomenon.
The differentcosineintegral definitions areCin(x)≡∫0x1−costtdt.{\displaystyle \operatorname {Cin} (x)~\equiv ~\int _{0}^{x}{\frac {\ 1-\cos t\ }{t}}\ \operatorname {d} t~.}
Cinis aneven,entire function. For that reason, some texts defineCinas the primary function, and deriveCiin terms ofCin .
Ci(x)≡−∫x∞costtdt{\displaystyle \operatorname {Ci} (x)~~\equiv ~-\int _{x}^{\infty }{\frac {\ \cos t\ }{t}}\ \operatorname {d} t~}=γ+lnx−∫0x1−costtdt{\displaystyle ~~\qquad ~=~~\gamma ~+~\ln x~-~\int _{0}^{x}{\frac {\ 1-\cos t\ }{t}}\ \operatorname {d} t~}
=γ+lnx−Cinx{\displaystyle ~~\qquad ~=~~\gamma ~+~\ln x~-~\operatorname {Cin} x~}for|Arg(x)|<π,{\displaystyle ~{\Bigl |}\ \operatorname {Arg} (x)\ {\Bigr |}<\pi \ ,}whereγ≈ 0.57721566490 ...is theEuler–Mascheroni constant. Some texts useciinstead ofCi. The restriction onArg(x)is to avoid a discontinuity (shown as the orange vs blue area on the left half of theplot above) that arises because of abranch cutin the standardlogarithm function(ln).
Ci(x)is the antiderivative ofcosx/x(which vanishes asx→∞{\displaystyle \ x\to \infty \ }). The two definitions are related byCi(x)=γ+lnx−Cin(x).{\displaystyle \operatorname {Ci} (x)=\gamma +\ln x-\operatorname {Cin} (x)~.}
Thehyperbolic sineintegral is defined asShi(x)=∫0xsinh(t)tdt.{\displaystyle \operatorname {Shi} (x)=\int _{0}^{x}{\frac {\sinh(t)}{t}}\,dt.}
It is related to the ordinary sine integral bySi(ix)=iShi(x).{\displaystyle \operatorname {Si} (ix)=i\operatorname {Shi} (x).}
Thehyperbolic cosineintegral is
Chi(x)=γ+lnx+∫0xcosht−1tdtfor|Arg(x)|<π,{\displaystyle \operatorname {Chi} (x)=\gamma +\ln x+\int _{0}^{x}{\frac {\cosh t-1}{t}}\,dt\qquad ~{\text{ for }}~\left|\operatorname {Arg} (x)\right|<\pi ~,}whereγ{\displaystyle \gamma }is theEuler–Mascheroni constant.
It has the series expansionChi(x)=γ+ln(x)+x24+x496+x64320+x8322560+x1036288000+O(x12).{\displaystyle \operatorname {Chi} (x)=\gamma +\ln(x)+{\frac {x^{2}}{4}}+{\frac {x^{4}}{96}}+{\frac {x^{6}}{4320}}+{\frac {x^{8}}{322560}}+{\frac {x^{10}}{36288000}}+O(x^{12}).}
Trigonometric integrals can be understood in terms of the so-called "auxiliary functions"f(x)≡∫0∞sin(t)t+xdt=∫0∞e−xtt2+1dt=Ci(x)sin(x)+[π2−Si(x)]cos(x),g(x)≡∫0∞cos(t)t+xdt=∫0∞te−xtt2+1dt=−Ci(x)cos(x)+[π2−Si(x)]sin(x).{\displaystyle {\begin{array}{rcl}f(x)&\equiv &\int _{0}^{\infty }{\frac {\sin(t)}{t+x}}\,dt&=&\int _{0}^{\infty }{\frac {e^{-xt}}{t^{2}+1}}\,dt&=&\operatorname {Ci} (x)\sin(x)+\left[{\frac {\pi }{2}}-\operatorname {Si} (x)\right]\cos(x)~,\\g(x)&\equiv &\int _{0}^{\infty }{\frac {\cos(t)}{t+x}}\,dt&=&\int _{0}^{\infty }{\frac {te^{-xt}}{t^{2}+1}}\,dt&=&-\operatorname {Ci} (x)\cos(x)+\left[{\frac {\pi }{2}}-\operatorname {Si} (x)\right]\sin(x)~.\end{array}}}Using these functions, the trigonometric integrals may be re-expressed as
(cf. Abramowitz & Stegun,p. 232)π2−Si(x)=−si(x)=f(x)cos(x)+g(x)sin(x),andCi(x)=f(x)sin(x)−g(x)cos(x).{\displaystyle {\begin{array}{rcl}{\frac {\pi }{2}}-\operatorname {Si} (x)=-\operatorname {si} (x)&=&f(x)\cos(x)+g(x)\sin(x)~,\qquad {\text{ and }}\\\operatorname {Ci} (x)&=&f(x)\sin(x)-g(x)\cos(x)~.\\\end{array}}}
Thespiralformed by parametric plot ofsi, ciis known as Nielsen's spiral.x(t)=a×ci(t){\displaystyle x(t)=a\times \operatorname {ci} (t)}y(t)=a×si(t){\displaystyle y(t)=a\times \operatorname {si} (t)}
The spiral is closely related to theFresnel integralsand theEuler spiral. Nielsen's spiral has applications in vision processing, road and track construction and other areas.[1]
Various expansions can be used for evaluation of trigonometric integrals, depending on the range of the argument.
Si(x)∼π2−cosxx(1−2!x2+4!x4−6!x6⋯)−sinxx(1x−3!x3+5!x5−7!x7⋯){\displaystyle \operatorname {Si} (x)\sim {\frac {\pi }{2}}-{\frac {\cos x}{x}}\left(1-{\frac {2!}{x^{2}}}+{\frac {4!}{x^{4}}}-{\frac {6!}{x^{6}}}\cdots \right)-{\frac {\sin x}{x}}\left({\frac {1}{x}}-{\frac {3!}{x^{3}}}+{\frac {5!}{x^{5}}}-{\frac {7!}{x^{7}}}\cdots \right)}Ci(x)∼sinxx(1−2!x2+4!x4−6!x6⋯)−cosxx(1x−3!x3+5!x5−7!x7⋯).{\displaystyle \operatorname {Ci} (x)\sim {\frac {\sin x}{x}}\left(1-{\frac {2!}{x^{2}}}+{\frac {4!}{x^{4}}}-{\frac {6!}{x^{6}}}\cdots \right)-{\frac {\cos x}{x}}\left({\frac {1}{x}}-{\frac {3!}{x^{3}}}+{\frac {5!}{x^{5}}}-{\frac {7!}{x^{7}}}\cdots \right)~.}
These series areasymptoticand divergent, although can be used for estimates and even precise evaluation atℜ(x) ≫ 1.
Si(x)=∑n=0∞(−1)nx2n+1(2n+1)(2n+1)!=x−x33!⋅3+x55!⋅5−x77!⋅7±⋯{\displaystyle \operatorname {Si} (x)=\sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n+1}}{(2n+1)(2n+1)!}}=x-{\frac {x^{3}}{3!\cdot 3}}+{\frac {x^{5}}{5!\cdot 5}}-{\frac {x^{7}}{7!\cdot 7}}\pm \cdots }Ci(x)=γ+lnx+∑n=1∞(−1)nx2n2n(2n)!=γ+lnx−x22!⋅2+x44!⋅4∓⋯{\displaystyle \operatorname {Ci} (x)=\gamma +\ln x+\sum _{n=1}^{\infty }{\frac {(-1)^{n}x^{2n}}{2n(2n)!}}=\gamma +\ln x-{\frac {x^{2}}{2!\cdot 2}}+{\frac {x^{4}}{4!\cdot 4}}\mp \cdots }
These series are convergent at any complexx, although for|x| ≫ 1, the series will converge slowly initially, requiring many terms for high precision.
From the Maclaurin series expansion of sine:sinx=x−x33!+x55!−x77!+x99!−x1111!+⋯{\displaystyle \sin \,x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+{\frac {x^{9}}{9!}}-{\frac {x^{11}}{11!}}+\cdots }sinxx=1−x23!+x45!−x67!+x89!−x1011!+⋯{\displaystyle {\frac {\sin \,x}{x}}=1-{\frac {x^{2}}{3!}}+{\frac {x^{4}}{5!}}-{\frac {x^{6}}{7!}}+{\frac {x^{8}}{9!}}-{\frac {x^{10}}{11!}}+\cdots }∴∫sinxxdx=x−x33!⋅3+x55!⋅5−x77!⋅7+x99!⋅9−x1111!⋅11+⋯{\displaystyle \therefore \int {\frac {\sin \,x}{x}}dx=x-{\frac {x^{3}}{3!\cdot 3}}+{\frac {x^{5}}{5!\cdot 5}}-{\frac {x^{7}}{7!\cdot 7}}+{\frac {x^{9}}{9!\cdot 9}}-{\frac {x^{11}}{11!\cdot 11}}+\cdots }
The functionE1(z)=∫1∞exp(−zt)tdtforℜ(z)≥0{\displaystyle \operatorname {E} _{1}(z)=\int _{1}^{\infty }{\frac {\exp(-zt)}{t}}\,dt\qquad ~{\text{ for }}~\Re (z)\geq 0}is called theexponential integral. It is closely related toSiandCi,E1(ix)=i(−π2+Si(x))−Ci(x)=isi(x)−ci(x)forx>0.{\displaystyle \operatorname {E} _{1}(ix)=i\left(-{\frac {\pi }{2}}+\operatorname {Si} (x)\right)-\operatorname {Ci} (x)=i\operatorname {si} (x)-\operatorname {ci} (x)\qquad ~{\text{ for }}~x>0~.}
As each respective function is analytic except for the cut at negative values of the argument, the area of validity of the relation should be extended to (Outside this range, additional terms which are integer factors ofπappear in the expression.)
Cases of imaginary argument of the generalized integro-exponential function are∫1∞cos(ax)lnxxdx=−π224+γ(γ2+lna)+ln2a2+∑n≥1(−a2)n(2n)!(2n)2,{\displaystyle \int _{1}^{\infty }\cos(ax){\frac {\ln x}{x}}\,dx=-{\frac {\pi ^{2}}{24}}+\gamma \left({\frac {\gamma }{2}}+\ln a\right)+{\frac {\ln ^{2}a}{2}}+\sum _{n\geq 1}{\frac {(-a^{2})^{n}}{(2n)!(2n)^{2}}}~,}which is the real part of∫1∞eiaxlnxxdx=−π224+γ(γ2+lna)+ln2a2−π2i(γ+lna)+∑n≥1(ia)nn!n2.{\displaystyle \int _{1}^{\infty }e^{iax}{\frac {\ln x}{x}}\,dx=-{\frac {\pi ^{2}}{24}}+\gamma \left({\frac {\gamma }{2}}+\ln a\right)+{\frac {\ln ^{2}a}{2}}-{\frac {\pi }{2}}i\left(\gamma +\ln a\right)+\sum _{n\geq 1}{\frac {(ia)^{n}}{n!n^{2}}}~.}
Similarly∫1∞eiaxlnxx2dx=1+ia[−π224+γ(γ2+lna−1)+ln2a2−lna+1]+πa2(γ+lna−1)+∑n≥1(ia)n+1(n+1)!n2.{\displaystyle \int _{1}^{\infty }e^{iax}{\frac {\ln x}{x^{2}}}\,dx=1+ia\left[-{\frac {\pi ^{2}}{24}}+\gamma \left({\frac {\gamma }{2}}+\ln a-1\right)+{\frac {\ln ^{2}a}{2}}-\ln a+1\right]+{\frac {\pi a}{2}}{\Bigl (}\gamma +\ln a-1{\Bigr )}+\sum _{n\geq 1}{\frac {(ia)^{n+1}}{(n+1)!n^{2}}}~.}
Padé approximantsof the convergent Taylor series provide an efficient way to evaluate the functions for small arguments. The following formulae, given by Rowe et al. (2015),[2]are accurate to better than10−16for0 ≤x≤ 4,Si(x)≈x⋅(1−4.54393409816329991⋅10−2⋅x2+1.15457225751016682⋅10−3⋅x4−1.41018536821330254⋅10−5⋅x6+9.43280809438713025⋅10−8⋅x8−3.53201978997168357⋅10−10⋅x10+7.08240282274875911⋅10−13⋅x12−6.05338212010422477⋅10−16⋅x141+1.01162145739225565⋅10−2⋅x2+4.99175116169755106⋅10−5⋅x4+1.55654986308745614⋅10−7⋅x6+3.28067571055789734⋅10−10⋅x8+4.5049097575386581⋅10−13⋅x10+3.21107051193712168⋅10−16⋅x12)Ci(x)≈γ+ln(x)+x2⋅(−0.25+7.51851524438898291⋅10−3⋅x2−1.27528342240267686⋅10−4⋅x4+1.05297363846239184⋅10−6⋅x6−4.68889508144848019⋅10−9⋅x8+1.06480802891189243⋅10−11⋅x10−9.93728488857585407⋅10−15⋅x121+1.1592605689110735⋅10−2⋅x2+6.72126800814254432⋅10−5⋅x4+2.55533277086129636⋅10−7⋅x6+6.97071295760958946⋅10−10⋅x8+1.38536352772778619⋅10−12⋅x10+1.89106054713059759⋅10−15⋅x12+1.39759616731376855⋅10−18⋅x14){\displaystyle {\begin{array}{rcl}\operatorname {Si} (x)&\approx &x\cdot \left({\frac {\begin{array}{l}1-4.54393409816329991\cdot 10^{-2}\cdot x^{2}+1.15457225751016682\cdot 10^{-3}\cdot x^{4}-1.41018536821330254\cdot 10^{-5}\cdot x^{6}\\~~~+9.43280809438713025\cdot 10^{-8}\cdot x^{8}-3.53201978997168357\cdot 10^{-10}\cdot x^{10}+7.08240282274875911\cdot 10^{-13}\cdot x^{12}\\~~~-6.05338212010422477\cdot 10^{-16}\cdot x^{14}\end{array}}{\begin{array}{l}1+1.01162145739225565\cdot 10^{-2}\cdot x^{2}+4.99175116169755106\cdot 10^{-5}\cdot x^{4}+1.55654986308745614\cdot 10^{-7}\cdot x^{6}\\~~~+3.28067571055789734\cdot 10^{-10}\cdot x^{8}+4.5049097575386581\cdot 10^{-13}\cdot x^{10}+3.21107051193712168\cdot 10^{-16}\cdot x^{12}\end{array}}}\right)\\&~&\\\operatorname {Ci} (x)&\approx &\gamma +\ln(x)+\\&&x^{2}\cdot \left({\frac {\begin{array}{l}-0.25+7.51851524438898291\cdot 10^{-3}\cdot x^{2}-1.27528342240267686\cdot 10^{-4}\cdot x^{4}+1.05297363846239184\cdot 10^{-6}\cdot x^{6}\\~~~-4.68889508144848019\cdot 10^{-9}\cdot x^{8}+1.06480802891189243\cdot 10^{-11}\cdot x^{10}-9.93728488857585407\cdot 10^{-15}\cdot x^{12}\\\end{array}}{\begin{array}{l}1+1.1592605689110735\cdot 10^{-2}\cdot x^{2}+6.72126800814254432\cdot 10^{-5}\cdot x^{4}+2.55533277086129636\cdot 10^{-7}\cdot x^{6}\\~~~+6.97071295760958946\cdot 10^{-10}\cdot x^{8}+1.38536352772778619\cdot 10^{-12}\cdot x^{10}+1.89106054713059759\cdot 10^{-15}\cdot x^{12}\\~~~+1.39759616731376855\cdot 10^{-18}\cdot x^{14}\\\end{array}}}\right)\end{array}}}
The integrals may be evaluated indirectly viaauxiliary functionsf(x){\displaystyle f(x)}andg(x){\displaystyle g(x)}, which are defined by
Forx≥4{\displaystyle x\geq 4}thePadé rational functionsgiven below approximatef(x){\displaystyle f(x)}andg(x){\displaystyle g(x)}with error less than 10−16:[2]
f(x)≈1x⋅(1+7.44437068161936700618⋅102⋅x−2+1.96396372895146869801⋅105⋅x−4+2.37750310125431834034⋅107⋅x−6+1.43073403821274636888⋅109⋅x−8+4.33736238870432522765⋅1010⋅x−10+6.40533830574022022911⋅1011⋅x−12+4.20968180571076940208⋅1012⋅x−14+1.00795182980368574617⋅1013⋅x−16+4.94816688199951963482⋅1012⋅x−18−4.94701168645415959931⋅1011⋅x−201+7.46437068161927678031⋅102⋅x−2+1.97865247031583951450⋅105⋅x−4+2.41535670165126845144⋅107⋅x−6+1.47478952192985464958⋅109⋅x−8+4.58595115847765779830⋅1010⋅x−10+7.08501308149515401563⋅1011⋅x−12+5.06084464593475076774⋅1012⋅x−14+1.43468549171581016479⋅1013⋅x−16+1.11535493509914254097⋅1013⋅x−18)g(x)≈1x2⋅(1+8.1359520115168615⋅102⋅x−2+2.35239181626478200⋅105⋅x−4+3.12557570795778731⋅107⋅x−6+2.06297595146763354⋅109⋅x−8+6.83052205423625007⋅1010⋅x−10+1.09049528450362786⋅1012⋅x−12+7.57664583257834349⋅1012⋅x−14+1.81004487464664575⋅1013⋅x−16+6.43291613143049485⋅1012⋅x−18−1.36517137670871689⋅1012⋅x−201+8.19595201151451564⋅102⋅x−2+2.40036752835578777⋅105⋅x−4+3.26026661647090822⋅107⋅x−6+2.23355543278099360⋅109⋅x−8+7.87465017341829930⋅1010⋅x−10+1.39866710696414565⋅1012⋅x−12+1.17164723371736605⋅1013⋅x−14+4.01839087307656620⋅1013⋅x−16+3.99653257887490811⋅1013⋅x−18){\displaystyle {\begin{array}{rcl}f(x)&\approx &{\dfrac {1}{x}}\cdot \left({\frac {\begin{array}{l}1+7.44437068161936700618\cdot 10^{2}\cdot x^{-2}+1.96396372895146869801\cdot 10^{5}\cdot x^{-4}+2.37750310125431834034\cdot 10^{7}\cdot x^{-6}\\~~~+1.43073403821274636888\cdot 10^{9}\cdot x^{-8}+4.33736238870432522765\cdot 10^{10}\cdot x^{-10}+6.40533830574022022911\cdot 10^{11}\cdot x^{-12}\\~~~+4.20968180571076940208\cdot 10^{12}\cdot x^{-14}+1.00795182980368574617\cdot 10^{13}\cdot x^{-16}+4.94816688199951963482\cdot 10^{12}\cdot x^{-18}\\~~~-4.94701168645415959931\cdot 10^{11}\cdot x^{-20}\end{array}}{\begin{array}{l}1+7.46437068161927678031\cdot 10^{2}\cdot x^{-2}+1.97865247031583951450\cdot 10^{5}\cdot x^{-4}+2.41535670165126845144\cdot 10^{7}\cdot x^{-6}\\~~~+1.47478952192985464958\cdot 10^{9}\cdot x^{-8}+4.58595115847765779830\cdot 10^{10}\cdot x^{-10}+7.08501308149515401563\cdot 10^{11}\cdot x^{-12}\\~~~+5.06084464593475076774\cdot 10^{12}\cdot x^{-14}+1.43468549171581016479\cdot 10^{13}\cdot x^{-16}+1.11535493509914254097\cdot 10^{13}\cdot x^{-18}\end{array}}}\right)\\&&\\g(x)&\approx &{\dfrac {1}{x^{2}}}\cdot \left({\frac {\begin{array}{l}1+8.1359520115168615\cdot 10^{2}\cdot x^{-2}+2.35239181626478200\cdot 10^{5}\cdot x^{-4}+3.12557570795778731\cdot 10^{7}\cdot x^{-6}\\~~~+2.06297595146763354\cdot 10^{9}\cdot x^{-8}+6.83052205423625007\cdot 10^{10}\cdot x^{-10}+1.09049528450362786\cdot 10^{12}\cdot x^{-12}\\~~~+7.57664583257834349\cdot 10^{12}\cdot x^{-14}+1.81004487464664575\cdot 10^{13}\cdot x^{-16}+6.43291613143049485\cdot 10^{12}\cdot x^{-18}\\~~~-1.36517137670871689\cdot 10^{12}\cdot x^{-20}\end{array}}{\begin{array}{l}1+8.19595201151451564\cdot 10^{2}\cdot x^{-2}+2.40036752835578777\cdot 10^{5}\cdot x^{-4}+3.26026661647090822\cdot 10^{7}\cdot x^{-6}\\~~~+2.23355543278099360\cdot 10^{9}\cdot x^{-8}+7.87465017341829930\cdot 10^{10}\cdot x^{-10}+1.39866710696414565\cdot 10^{12}\cdot x^{-12}\\~~~+1.17164723371736605\cdot 10^{13}\cdot x^{-14}+4.01839087307656620\cdot 10^{13}\cdot x^{-16}+3.99653257887490811\cdot 10^{13}\cdot x^{-18}\end{array}}}\right)\\\end{array}}}
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https://en.wikipedia.org/wiki/Trigonometric_integral
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Halstead complexity measuresaresoftware metricsintroduced byMaurice Howard Halsteadin 1977[1]as part of his treatise on establishing an empirical science of software development.
Halstead made the observation that metrics of the software should reflect the implementation or expression of algorithms in different languages, but be independent of their execution on a specific platform.
These metrics are therefore computed statically from the code.
Halstead's goal was to identify measurable properties of software, and the relations between them.
This is similar to the identification of measurable properties of matter (like the volume, mass, and pressure of a gas) and the relationships between them (analogous to thegas equation).
Thus his metrics are actually not just complexity metrics.
For a given problem, let:
From these numbers, several measures can be calculated:
The difficulty measure is related to the difficulty of the program to write or understand, e.g. when doingcode review.
The effort measure translates into actual coding time using the following relation,
Halstead's delivered bugs (B) is an estimate for the number of errors in the implementation.
Consider the followingCprogram:
The distinct operators (η1{\displaystyle \,\eta _{1}}) are:main,(),{},int,scanf,&,=,+,/,printf,,,;
The distinct operands (η2{\displaystyle \,\eta _{2}}) are:a,b,c,avg,"%d %d %d",3,"avg = %d"
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https://en.wikipedia.org/wiki/Halstead_complexity_measures
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In thedesign of experiments,optimal experimental designs(oroptimum designs[2]) are a class ofexperimental designsthat areoptimalwith respect to somestatisticalcriterion. The creation of this field of statistics has been credited to Danish statisticianKirstine Smith.[3][4]
In thedesign of experimentsforestimatingstatistical models,optimal designsallow parameters to beestimated without biasand withminimum variance. A non-optimal design requires a greater number ofexperimental runstoestimatetheparameterswith the sameprecisionas an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation.
The optimality of a design depends on thestatistical modeland is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding ofstatistical theoryand practical knowledge withdesigning experiments.
Optimal designs offer three advantages over sub-optimalexperimental designs:[5]
Experimental designs are evaluated using statistical criteria.[6]
It is known that theleast squaresestimator minimizes thevarianceofmean-unbiasedestimators(under the conditions of theGauss–Markov theorem). In theestimationtheory forstatistical modelswith onerealparameter, thereciprocalof the variance of an ("efficient") estimator is called the "Fisher information" for that estimator.[7]Because of this reciprocity,minimizingthevariancecorresponds tomaximizingtheinformation.
When thestatistical modelhas severalparameters, however, themeanof the parameter-estimator is avectorand itsvarianceis amatrix. Theinverse matrixof the variance-matrix is called the "information matrix". Because the variance of the estimator of a parameter vector is a matrix, the problem of "minimizing the variance" is complicated. Usingstatistical theory, statisticians compress the information-matrix using real-valuedsummary statistics; being real-valued functions, these "information criteria" can be maximized.[8]The traditional optimality-criteria areinvariantsof theinformationmatrix; algebraically, the traditional optimality-criteria arefunctionalsof theeigenvaluesof the information matrix.
Other optimality-criteria are concerned with the variance ofpredictions:
In many applications, the statistician is most concerned with a"parameter of interest"rather than with"nuisance parameters". More generally, statisticians considerlinear combinationsof parameters, which are estimated via linear combinations of treatment-means in thedesign of experimentsand in theanalysis of variance; such linear combinations are calledcontrasts. Statisticians can use appropriate optimality-criteria for suchparameters of interestand forcontrasts.[12]
Catalogs of optimal designs occur in books and in software libraries.
In addition, majorstatistical systemslikeSASandRhave procedures for optimizing a design according to a user's specification. The experimenter must specify amodelfor the design and an optimality-criterion before the method can compute an optimal design.[13]
Some advanced topics in optimal design require morestatistical theoryand practical knowledge in designing experiments.
Since the optimality criterion of most optimal designs is based on some function of the information matrix, the 'optimality' of a given design ismodeldependent: While an optimal design is best for thatmodel, its performance may deteriorate on othermodels. On othermodels, anoptimaldesign can be either better or worse than a non-optimal design.[14]Therefore, it is important tobenchmarkthe performance of designs under alternativemodels.[15]
The choice of an appropriate optimality criterion requires some thought, and it is useful to benchmark the performance of designs with respect to several optimality criteria. Cornell writes that
since the [traditional optimality] criteria . . . are variance-minimizing criteria, . . . a design that is optimal for a given model using one of the . . . criteria is usually near-optimal for the same model with respect to the other criteria.
Indeed, there are several classes of designs for which all the traditional optimality-criteria agree, according to the theory of "universal optimality" ofKiefer.[17]The experience of practitioners like Cornell and the "universal optimality" theory of Kiefer suggest that robustness with respect to changes in theoptimality-criterionis much greater than is robustness with respect to changes in themodel.
High-quality statistical software provide a combination of libraries of optimal designs or iterative methods for constructing approximately optimal designs, depending on the model specified and the optimality criterion. Users may use a standard optimality-criterion or may program a custom-made criterion.
All of the traditional optimality-criteria areconvex (or concave) functions, and therefore optimal-designs are amenable to the mathematical theory ofconvex analysisand their computation can use specialized methods ofconvex minimization.[18]The practitioner need not selectexactly onetraditional, optimality-criterion, but can specify a custom criterion. In particular, the practitioner can specify a convex criterion using the maxima of convex optimality-criteria andnonnegative combinationsof optimality criteria (since these operations preserveconvex functions). Forconvexoptimality criteria, theKiefer-Wolfowitzequivalence theoremallows the practitioner to verify that a given design is globally optimal.[19]TheKiefer-Wolfowitzequivalence theoremis related with theLegendre-Fenchelconjugacyforconvex functions.[20]
If an optimality-criterion lacksconvexity, then finding aglobal optimumand verifying its optimality often are difficult.
When scientists wish to test several theories, then a statistician can design an experiment that allows optimal tests between specified models. Such "discrimination experiments" are especially important in thebiostatisticssupportingpharmacokineticsandpharmacodynamics, following the work ofCoxand Atkinson.[21]
When practitioners need to consider multiplemodels, they can specify aprobability-measureon the models and then select any design maximizing theexpected valueof such an experiment. Such probability-based optimal-designs are called optimalBayesiandesigns. SuchBayesian designsare used especially forgeneralized linear models(where the response follows anexponential-familydistribution).[22]
The use of aBayesian designdoes not force statisticians to useBayesian methodsto analyze the data, however. Indeed, the "Bayesian" label for probability-based experimental-designs is disliked by some researchers.[23]Alternative terminology for "Bayesian" optimality includes "on-average" optimality or "population" optimality.
Scientific experimentation is an iterative process, and statisticians have developed several approaches to the optimal design of sequential experiments.
Sequential analysiswas pioneered byAbraham Wald.[24]In 1972,Herman Chernoffwrote an overview of optimal sequential designs,[25]whileadaptive designswere surveyed later by S. Zacks.[26]Of course, much work on the optimal design of experiments is related to the theory ofoptimal decisions, especially thestatistical decision theoryofAbraham Wald.[27]
Optimal designs forresponse-surface modelsare discussed in the textbook by Atkinson, Donev and Tobias, and in the survey of Gaffke and Heiligers and in the mathematical text of Pukelsheim. Theblockingof optimal designs is discussed in the textbook of Atkinson, Donev and Tobias and also in the monograph by Goos.
The earliest optimal designs were developed to estimate the parameters of regression models with continuous variables, for example, byJ. D. Gergonnein 1815 (Stigler). In English, two early contributions were made byCharles S. PeirceandKirstine Smith.
Pioneering designs for multivariateresponse-surfaceswere proposed byGeorge E. P. Box. However, Box's designs have few optimality properties. Indeed, theBox–Behnken designrequires excessive experimental runs when the number of variables exceeds three.[28]Box's"central-composite" designsrequire more experimental runs than do the optimal designs of Kôno.[29]
The optimization of sequential experimentation is studied also instochastic programmingand insystemsandcontrol. Popular methods includestochastic approximationand other methods ofstochastic optimization. Much of this research has been associated with the subdiscipline ofsystem identification.[30]In computationaloptimal control, D. Judin & A. Nemirovskii andBoris Polyakhas described methods that are more efficient than the (Armijo-style)step-size rulesintroduced byG. E. P. Boxinresponse-surface methodology.[31]
Adaptive designsare used inclinical trials, and optimaladaptive designsare surveyed in theHandbook of Experimental Designschapter by Shelemyahu Zacks.
There are several methods of finding an optimal design, given ana priorirestriction on the number of experimental runs or replications. Some of these methods are discussed by Atkinson, Donev and Tobias and in the paper by Hardin andSloane. Of course, fixing the number of experimental runsa prioriwould be impractical. Prudent statisticians examine the other optimal designs, whose number of experimental runs differ.
In the mathematical theory on optimal experiments, an optimal design can be aprobability measurethat issupportedon an infinite set of observation-locations. Such optimal probability-measure designs solve a mathematical problem that neglected to specify the cost of observations and experimental runs. Nonetheless, such optimal probability-measure designs can bediscretizedto furnishapproximatelyoptimal designs.[32]
In some cases, a finite set of observation-locations suffices tosupportan optimal design. Such a result was proved by Kôno andKieferin their works onresponse-surface designsfor quadratic models. The Kôno–Kiefer analysis explains why optimal designs for response-surfaces can have discrete supports, which are very similar as do the less efficient designs that have been traditional inresponse surface methodology.[33]
In 1815, an article on optimal designs forpolynomial regressionwas published byJoseph Diaz Gergonne, according toStigler.
Charles S. Peirceproposed an economic theory of scientific experimentation in 1876, which sought to maximize the precision of the estimates. Peirce's optimal allocation immediately improved the accuracy of gravitational experiments and was used for decades by Peirce and his colleagues. In his 1882 published lecture atJohns Hopkins University, Peirce introduced experimental design with these words:
Logic will not undertake to inform you what kind of experiments you ought to make in order best to determine the acceleration of gravity, or the value of the Ohm; but it will tell you how to proceed to form a plan of experimentation.[....] Unfortunately practice generally precedes theory, and it is the usual fate of mankind to get things done in some boggling way first, and find out afterward how they could have been done much more easily and perfectly.[34]
Kirstine Smithproposed optimal designs for polynomial models in 1918. (Kirstine Smith had been a student of the Danish statisticianThorvald N. Thieleand was working withKarl Pearsonin London.)
The textbook by Atkinson, Donev and Tobias has been used for short courses for industrial practitioners as well as university courses.
Optimalblock designsare discussed by Bailey and by Bapat. The first chapter of Bapat's book reviews thelinear algebraused by Bailey (or the advanced books below). Bailey's exercises and discussion ofrandomizationboth emphasize statistical concepts (rather than algebraic computations).
Optimalblock designsare discussed in the advanced monograph by Shah and Sinha and in the survey-articles by Cheng and by Majumdar.
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https://en.wikipedia.org/wiki/Optimal_design
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Ingraph theory, a branch of mathematics, theHajós constructionis anoperation on graphsnamed afterGyörgy Hajós(1961) that may be used to construct anycritical graphor any graph whosechromatic numberis at least some given threshold.
LetGandHbe twoundirected graphs,vwbe an edge ofG, andxybe an edge ofH. Then the Hajós construction forms a new graph that combines the two graphs by identifying verticesvandxinto a single vertex, removing the two edgesvwandxy, and adding a new edgewy.
For example, letGandHeach be acomplete graphK4on four vertices; because of the symmetry of these graphs, the choice of which edge to select from each of them is unimportant. In this case, the result of applying the Hajós construction is theMoser spindle, a seven-vertexunit distance graphthat requires four colors.
As another example, ifGandHarecycle graphsof lengthpandqrespectively, then the result of applying the Hajós construction is itself a cycle graph, of lengthp+q− 1.
A graphGis said to bek-constructible(or Hajós-k-constructible) when it formed in one of the following three ways:[1]
It is straightforward to verify that everyk-constructible graph requires at leastkcolors in anyproper graph coloring. Indeed, this is clear for the complete graphKk, and the effect of identifying two nonadjacent vertices is to force them to have the same color as each other in any coloring, something that does not reduce the number of colors. In the Hajós construction itself, the new edgewyforces at least one of the two verticeswandyto have a different color than the combined vertex forvandx, so any proper coloring of the combined graph leads to a proper coloring of one of the two smaller graphs from which it was formed, which again causes it to requirekcolors.[1]
Hajós proved more strongly that a graph requires at leastkcolors, in anyproper coloring,if and only ifit contains ak-constructible graph as a subgraph. Equivalently, everyk-critical graph(a graph that requireskcolors but for which every proper subgraph requires fewer colors) isk-constructible.[2]Alternatively, every graph that requireskcolors may be formed by combining the Hajós construction, the operation of identifying any two nonadjacent vertices, and the operations of adding a vertex or edge to the given graph, starting from the complete graphKk.[3]
A similar construction may be used forlist coloringin place of coloring.[4]
Fork= 3, everyk-critical graph (that is, every odd cycle) can be generated as ak-constructible graph such that all of the graphs formed in its construction are alsok-critical. Fork= 8, this is not true: a graph found byCatlin (1979)as acounterexampletoHajós's conjecturethatk-chromatic graphs contain a subdivision ofKk, also serves as a counterexample to this problem. Subsequently,k-critical but notk-constructible graphs solely throughk-critical graphs were found for allk≥ 4. Fork= 4, one such example is the graph obtained from thedodecahedrongraph by adding a new edge between each pair ofantipodalvertices[5]
Because merging two non-adjacent vertices reduces the number of vertices in the resulting graph, the number of operations needed to represent a given graphGusing the operations defined by Hajós may exceed the number of vertices inG.[6]
More specifically,Mansfield & Welsh (1982)define theHajós numberh(G)of ak-chromatic graphGto be the minimum number of steps needed to constructGfromKk, where each step forms a new graph by combining two previously formed graphs, merging two nonadjacent vertices of a previously formed graph, or adding a vertex or edge to a previously formed graph. They showed that, for ann-vertex graphGwithmedges,h(G) ≤ 2n2/3 −m+ 1− 1. If every graph has a polynomial Hajós number, this would imply that it is possible to prove non-colorability innondeterministic polynomial time, and therefore imply that NP =co-NP, a conclusion considered unlikely by complexity theorists.[7]However, it is not known how to prove non-polynomial lower bounds on the Hajós number without making some complexity-theoretic assumption, and if such a bound could be proven it would also imply the existence of non-polynomial bounds on certain types ofFrege systeminmathematical logic.[7]
The minimum size of anexpression treedescribing a Hajós construction for a given graphGmay be significantly larger than the Hajós number ofG, because a shortest expression forGmay re-use the same graphs multiple times, an economy not permitted in an expression tree. There exist 3-chromatic graphs for which the smallest such expression tree has exponential size.[8]
Koester (1991)used the Hajós construction to generate aninfinite setof 4-criticalpolyhedral graphs, each having more than twice as many edges as vertices. Similarly,Liu & Zhang (2006)used the construction, starting with theGrötzsch graph, to generate many 4-criticaltriangle-free graphs, which they showed to be difficult to color using traditionalbacktrackingalgorithms.
Inpolyhedral combinatorics,Euler (2003)used the Hajós construction to generatefacetsof thestable setpolytope.
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https://en.wikipedia.org/wiki/Haj%C3%B3s_construction
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Adependent-marking languagehas grammatical markers ofagreementandcase governmentbetween the words ofphrasesthat tend to appear more ondependentsthan onheads. The distinction betweenhead-markingand dependent-marking was first explored byJohanna Nicholsin 1986,[1]and has since become a central criterion in language typology in which languages are classified according to whether they are more head-marking or dependent-marking. Many languages employ both head and dependent-marking, but some employdouble-marking, and yet others employzero-marking. However, it is not clear that the head of a clause has anything to do with the head of a noun phrase, or even what the head of a clause is.
Englishhas few inflectional markers of agreement and so can be construed as zero-marking much of the time. Dependent-marking, however, occurs when a singular or plural noun demands the singular or plural form of the demonstrative determinerthis/theseorthat/thoseand when a verb or preposition demands the subject or object form of a personal pronoun:I/me,he/him,she/her,they/them,who/whom. The following representations ofdependency grammarillustrate some cases:[2]
Plural nouns in English require the plural form of a dependent demonstrative determiner, and prepositions require the object form of a dependent personal pronoun.
Such instances of dependent-marking are a relatively rare occurrence in English, but dependent-marking occurs much more frequently in related languages, such asGerman. There, for instance, dependent-marking is present in most noun phrases. A noun marks its dependent determiner:
The noun marks the dependent determiner in gender (masculine, feminine, or neuter) and number (singular or plural). In other words, the gender and number of the noun determine the form of the determiner that must appear. Nouns in German also mark their dependent adjectives in gender and number, but the markings vary across determiners and adjectives. Also, a head noun in German can mark a dependent noun with the genitive case.
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https://en.wikipedia.org/wiki/Dependent-marking_language
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Similitudeis a concept applicable to the testing ofengineeringmodels. A model is said to havesimilitudewith the real application if the two sharegeometricsimilarity,kinematicsimilarity anddynamicsimilarity.Similarityandsimilitudeare interchangeable in this context.
The termdynamic similitudeis often used as a catch-all because it implies that geometric and kinematic similitude have already been met.
Similitude's main application is inhydraulicandaerospace engineeringto testfluid flowconditions withscaledmodels. It is also the primary theory behind many textbookformulasinfluid mechanics.
The concept of similitude is strongly tied todimensional analysis.
Engineering models are used to study complex fluid dynamics problems where calculations and computer simulations are not reliable. Models are usually smaller than the final design, but not always.Scale modelsallow testing of a design prior to building, and in many cases are a critical step in the development process.
Construction of a scale model, however, must be accompanied by an analysis to determine what conditions it is tested under. While the geometry may be simply scaled, other parameters, such aspressure,temperatureor thevelocityand type offluidmay need to be altered. Similitude is achieved when testing conditions are created such that the test results are applicable to the real design.
The following criteria are required to achieve similitude;
To satisfy the above conditions the application is analyzed;
It is often impossible to achieve strict similitude during a model test. The greater the departure from the application's operating conditions, the more difficult achieving similitude is. In these cases some aspects of similitude may be neglected, focusing on only the most important parameters.
The design of marine vessels remains more of an art than a science in
large part because dynamic similitude is especially difficult to attain
for a vessel that is partially submerged: a ship is affected by wind
forces in the air above it, by hydrodynamic forces within the water
under it, and especially by wave motions at the interface between the
water and the air. The scaling requirements for each of these
phenomena differ, so models cannot replicate what happens to a full
sized vessel nearly so well as can be done for an aircraft or
submarine—each of which operates entirely within one medium.
Similitude is a term used widely in fracture mechanics relating to the strain life approach. Under given loading conditions the fatigue damage in an un-notched specimen is comparable to that of a notched specimen. Similitude suggests that the component fatigue life of the two objects will also be similar.
Consider asubmarinemodeled at 1/40th scale. The application operates in sea water at 0.5 °C, moving at 5 m/s. The model will be tested in fresh water at 20 °C. Find the power required for the submarine to operate at the stated speed.
Afree body diagramis constructed and the relevant relationships of force and velocity are formulated using techniques fromcontinuum mechanics. The variables which describe the system are:
This example has five independent variables and threefundamental units. The fundamental units are:meter,kilogram,second.[1]
Invoking theBuckingham π theoremshows that the system can be described with two dimensionless numbers and one independent variable.[2]
Dimensional analysisis used to rearrange the units to form theReynolds number(Re{\displaystyle R_{e}}) andpressure coefficient(Cp{\displaystyle C_{p}}). These dimensionless numbers account for all the variables listed above exceptF, which will be the test measurement. Since the dimensionless parameters will stay constant for both the test and the real application, they will be used to formulate scaling laws for the test.
Scaling laws:
The pressure (p{\displaystyle p}) is not one of the five variables, but the force (F{\displaystyle F}) is. The pressure difference (Δp{\displaystyle p}) has thus been replaced with (F/L2{\displaystyle F/L^{2}}) in the pressure coefficient. This gives a required test velocity of:
A model test is then conducted at that velocity and the force that is measured in the model (Fmodel{\displaystyle F_{model}}) is then scaled to find the force that can be expected for the real application (Fapplication{\displaystyle F_{application}}):
The powerP{\displaystyle P}in watts required by the submarine is then:
Note that even though the model is scaled smaller, the water velocity needs to be increased for testing. This remarkable result shows how similitude in nature is often counterintuitive.
Similitude has been well documented for a large number of engineering problems and is the basis of many textbook formulas and dimensionless quantities. These formulas and quantities are easy to use without having to repeat the laborious task of dimensional analysis and formula derivation. Simplification of the formulas (by neglecting some aspects of similitude) is common, and needs to be reviewed by the engineer for each application.
Similitude can be used to predict the performance of a new design based on data from an existing, similar design. In this case, the model is the existing design. Another use of similitude and models is in validation ofcomputer simulationswith the ultimate goal of eliminating the need for physical models altogether.
Another application of similitude is to replace the operating fluid with a different test fluid. Wind tunnels, for example, have trouble with air liquefying in certain conditions soheliumis sometimes used. Other applications may operate in dangerous or expensive fluids so the testing is carried out in a more convenient substitute.
Some common applications of similitude and associated dimensionless numbers;
Similitude analysis is a powerful engineering tool to design the scaled-down structures. Although both dimensional analysis and direct use of the governing equations may be used to derive the scaling laws, the latter results in more specific scaling laws.[3]The design of the scaled-down composite structures can be successfully carried out using the complete and partial similarities.[4]In the design of the scaled structures under complete similarity condition, all the derived scaling laws must be satisfied between the model and prototype which yields the perfect similarity between the two scales. However, the design of a scaled-down structure which is perfectly similar to its prototype has the practical limitation, especially for laminated structures. Relaxing some of the scaling laws may eliminate the limitation of the design under complete similarity condition and yields the scaled models that are partially similar to their prototype. However, the design of the scaled structures under the partial similarity condition must follow a deliberate methodology to ensure the accuracy of the scaled structure in predicting the structural response of the prototype.[5]Scaled models can be designed to replicate the dynamic characteristic (e.g. frequencies, mode shapes and damping ratios) of their full-scale counterparts. However, appropriate response scaling laws need to be derived to predict the dynamic response of the full-scale prototype from the experimental data of the scaled model.[6]
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https://en.wikipedia.org/wiki/Similitude
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Incomputer science,graph transformation, orgraph rewriting, concerns the technique of creating a newgraphout of an original graph algorithmically. It has numerous applications, ranging fromsoftware engineering(software constructionand alsosoftware verification) tolayout algorithmsand picture generation.
Graph transformations can be used as a computation abstraction. The basic idea is that if the state of a computation can be represented as a graph, further steps in that computation can then be represented as transformation rules on that graph. Such rules consist of an original graph, which is to be matched to a subgraph in the complete state, and a replacing graph, which will replace the matched subgraph.
Formally, a graphrewritingsystem usually consists of a set of graph rewrite rules of the formL→R{\displaystyle L\rightarrow R}, withL{\displaystyle L}being called pattern graph (or left-hand side) andR{\displaystyle R}being called replacement graph (or right-hand side of the rule). A graph rewrite rule is applied to the host graph by searching for an occurrence of the pattern graph (pattern matching, thus solving thesubgraph isomorphism problem) and by replacing the found occurrence by an instance of the replacement graph. Rewrite rules can be further regulated in the case oflabeled graphs, such as in string-regulated graph grammars.
Sometimesgraph grammaris used as a synonym forgraph rewriting system, especially in the context offormal languages; the different wording is used to emphasize the goal of constructions, like the enumeration of all graphs from some starting graph, i.e. the generation of a graph language – instead of simply transforming a given state (host graph) into a new state.
The algebraic approach to graph rewriting is based uponcategory theory. The algebraic approach is further divided into sub-approaches, the most common of which are thedouble-pushout (DPO) approachand thesingle-pushout (SPO) approach. Other sub-approaches include thesesqui-pushoutand thepullback approach.
From the perspective of the DPO approach a graph rewriting rule is a pair ofmorphismsin the category of graphs andgraph homomorphismsbetween them:r=(L←K→R){\displaystyle r=(L\leftarrow K\rightarrow R)}, also writtenL⊇K⊆R{\displaystyle L\supseteq K\subseteq R}, whereK→L{\displaystyle K\rightarrow L}isinjective. The graph K is calledinvariantor sometimes thegluing graph. Arewritingsteporapplicationof a rule r to ahost graphG is defined by twopushoutdiagrams both originating in the samemorphismk:K→D{\displaystyle k\colon K\rightarrow D}, where D is acontext graph(this is where the namedouble-pushout comes from). Another graph morphismm:L→G{\displaystyle m\colon L\rightarrow G}models an occurrence of L in G and is called amatch. Practical understanding of this is thatL{\displaystyle L}is a subgraph that is matched fromG{\displaystyle G}(seesubgraph isomorphism problem), and after a match is found,L{\displaystyle L}is replaced withR{\displaystyle R}in host graphG{\displaystyle G}whereK{\displaystyle K}serves as an interface, containing the nodes and edges which are preserved when applying the rule. The graphK{\displaystyle K}is needed to attach the pattern being matched to its context: if it is empty, the match can only designate a whole connected component of the graphG{\displaystyle G}.
In contrast a graph rewriting rule of the SPO approach is a single morphism in the category oflabeled multigraphsandpartial mappingsthat preserve the multigraph structure:r:L→R{\displaystyle r\colon L\rightarrow R}. Thus a rewriting step is defined by a singlepushoutdiagram. Practical understanding of this is similar to the DPO approach. The difference is, that there is no interface between the host graph G and the graph G' being the result of the rewriting step.
From the practical perspective, the key distinction between DPO and SPO is how they deal with the deletion of nodes with adjacent edges, in particular, how they avoid that such deletions may leave behind "dangling edges". The DPO approach only deletes a node when the rule specifies the deletion of all adjacent edges as well (thisdangling conditioncan be checked for a given match), whereas the SPO approach simply disposes the adjacent edges, without requiring an explicit specification.
There is also another algebraic-like approach to graph rewriting, based mainly on Boolean algebra and an algebra of matrices, calledmatrix graph grammars.[1]
Yet another approach to graph rewriting, known asdeterminategraph rewriting, came out oflogicanddatabase theory.[2]In this approach, graphs are treated as database instances, and rewriting operations as a mechanism for defining queries and views; therefore, all rewriting is required to yield unique results (up to isomorphism), and this is achieved by applying any rewriting rule concurrently throughout the graph, wherever it applies, in such a way that the result is indeed uniquely defined.
Another approach to graph rewriting isterm graphrewriting, which involves the processing or transformation of term graphs (also known asabstract semantic graphs) by a set of syntactic rewrite rules.
Term graphs are a prominent topic in programming language research since term graph rewriting rules are capable of formally expressing a compiler'soperational semantics. Term graphs are also used as abstract machines capable of modelling chemical and biological computations as well as graphical calculi such as concurrency models. Term graphs can performautomated verificationand logical programming since they are well-suited to representing quantified statements in first order logic. Symbolic programming software is another application for term graphs, which are capable of representing and performing computation with abstract algebraic structures such as groups, fields and rings.
The TERMGRAPH conference[3]focuses entirely on research into term graph rewriting and its applications.
Graph rewriting systems naturally group into classes according to the kind of representation of graphs that are used and how the rewrites are expressed. The term graph grammar, otherwise equivalent to graph rewriting system or graph replacement system, is most often used in classifications. Some common types are:
Graphs are an expressive, visual and mathematically precise formalism for modelling of objects (entities) linked by relations; objects are represented by nodes and relations between them by edges. Nodes and edges are commonly typed and attributed. Computations are described in this model by changes in the relations between the entities or by attribute changes of the graph elements. They are encoded in graph rewrite/graph transformation rules and executed by graph rewrite systems/graph transformation tools.
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https://en.wikipedia.org/wiki/Graph_transformation
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Recurrent neural networks(RNNs) are a class of artificial neural networks designed for processing sequential data, such as text, speech, andtime series,[1]where the order of elements is important. Unlikefeedforward neural networks, which process inputs independently, RNNs utilize recurrent connections, where the output of a neuron at one time step is fed back as input to the network at the next time step. This enables RNNs to capture temporal dependencies and patterns within sequences.
The fundamental building block of RNNs is therecurrent unit, which maintains ahidden state—a form of memory that is updated at each time step based on the current input and the previous hidden state. This feedback mechanism allows the network to learn from past inputs and incorporate that knowledge into its current processing. RNNs have been successfully applied to tasks such as unsegmented, connectedhandwriting recognition,[2]speech recognition,[3][4]natural language processing, andneural machine translation.[5][6]
However, traditional RNNs suffer from thevanishing gradient problem, which limits their ability to learn long-range dependencies. This issue was addressed by the development of thelong short-term memory(LSTM) architecture in 1997, making it the standard RNN variant for handling long-term dependencies. Later,Gated Recurrent Units(GRUs) were introduced as a more computationally efficient alternative.
In recent years,transformers, which rely on self-attention mechanisms instead of recurrence, have become the dominant architecture for many sequence-processing tasks, particularly in natural language processing, due to their superior handling of long-range dependencies and greater parallelizability. Nevertheless, RNNs remain relevant for applications where computational efficiency, real-time processing, or the inherent sequential nature of data is crucial.
One origin of RNN was neuroscience. The word "recurrent" is used to describe loop-like structures in anatomy. In 1901,Cajalobserved "recurrent semicircles" in thecerebellar cortexformed byparallel fiber,Purkinje cells, andgranule cells.[7][8]In 1933,Lorente de Nódiscovered "recurrent, reciprocal connections" byGolgi's method, and proposed that excitatory loops explain certain aspects of thevestibulo-ocular reflex.[9][10]During 1940s, multiple people proposed the existence of feedback in the brain, which was a contrast to the previous understanding of the neural system as a purely feedforward structure.Hebbconsidered "reverberating circuit" as an explanation for short-term memory.[11]The McCulloch and Pitts paper (1943), which proposed theMcCulloch-Pitts neuronmodel, considered networks that contains cycles. The current activity of such networks can be affected by activity indefinitely far in the past.[12]They were both interested in closed loops as possible explanations for e.g.epilepsyandcausalgia.[13][14]Recurrent inhibitionwas proposed in 1946 as a negative feedback mechanism in motor control. Neural feedback loops were a common topic of discussion at theMacy conferences.[15]See[16]for an extensive review of recurrent neural network models in neuroscience.
Frank Rosenblattin 1960 published "close-loop cross-coupled perceptrons", which are 3-layeredperceptronnetworks whose middle layer contains recurrent connections that change by aHebbian learningrule.[18]: 73–75Later, inPrinciples of Neurodynamics(1961), he described "closed-loop cross-coupled" and "back-coupled" perceptron networks, and made theoretical and experimental studies for Hebbian learning in these networks,[17]: Chapter 19, 21and noted that a fully cross-coupled perceptron network is equivalent to an infinitely deep feedforward network.[17]: Section 19.11
Similar networks were published by Kaoru Nakano in 1971,[19][20]Shun'ichi Amariin 1972,[21]andWilliam A. Little[de]in 1974,[22]who was acknowledged by Hopfield in his 1982 paper.
Another origin of RNN wasstatistical mechanics. TheIsing modelwas developed byWilhelm Lenz[23]andErnst Ising[24]in the 1920s[25]as a simple statistical mechanical model of magnets at equilibrium.Glauberin 1963 studied the Ising model evolving in time, as a process towards equilibrium (Glauber dynamics), adding in the component of time.[26]
TheSherrington–Kirkpatrick modelof spin glass, published in 1975,[27]is the Hopfield network with random initialization. Sherrington and Kirkpatrick found that it is highly likely for the energy function of the SK model to have many local minima. In the 1982 paper, Hopfield applied this recently developed theory to study the Hopfield network with binary activation functions.[28]In a 1984 paper he extended this to continuous activation functions.[29]It became a standard model for the study of neural networks through statistical mechanics.[30][31]
Modern RNN networks are mainly based on two architectures: LSTM and BRNN.[32]
At the resurgence of neural networks in the 1980s, recurrent networks were studied again. They were sometimes called "iterated nets".[33]Two early influential works were theJordan network(1986) and theElman network(1990), which applied RNN to studycognitive psychology. In 1993, a neural history compressor system solved a "Very Deep Learning" task that required more than 1000 subsequentlayersin an RNN unfolded in time.[34]
Long short-term memory(LSTM) networks were invented byHochreiterandSchmidhuberin 1995 and set accuracy records in multiple applications domains.[35][36]It became the default choice for RNN architecture.
Bidirectional recurrent neural networks(BRNN) uses two RNN that processes the same input in opposite directions.[37]These two are often combined, giving the bidirectional LSTM architecture.
Around 2006, bidirectional LSTM started to revolutionizespeech recognition, outperforming traditional models in certain speech applications.[38][39]They also improved large-vocabulary speech recognition[3][4]andtext-to-speechsynthesis[40]and was used inGoogle voice search, and dictation onAndroid devices.[41]They broke records for improvedmachine translation,[42]language modeling[43]and Multilingual Language Processing.[44]Also, LSTM combined withconvolutional neural networks(CNNs) improvedautomatic image captioning.[45]
The idea of encoder-decoder sequence transduction had been developed in the early 2010s. The papers most commonly cited as the originators that produced seq2seq are two papers from 2014.[46][47]Aseq2seqarchitecture employs two RNN, typically LSTM, an "encoder" and a "decoder", for sequence transduction, such as machine translation. They became state of the art in machine translation, and was instrumental in the development ofattention mechanismsandtransformers.
An RNN-based model can be factored into two parts: configuration and architecture. Multiple RNN can be combined in a data flow, and the data flow itself is the configuration. Each RNN itself may have any architecture, including LSTM, GRU, etc.
RNNs come in many variants. Abstractly speaking, an RNN is a functionfθ{\displaystyle f_{\theta }}of type(xt,ht)↦(yt,ht+1){\displaystyle (x_{t},h_{t})\mapsto (y_{t},h_{t+1})}, where
In words, it is a neural network that maps an inputxt{\displaystyle x_{t}}into an outputyt{\displaystyle y_{t}}, with the hidden vectorht{\displaystyle h_{t}}playing the role of "memory", a partial record of all previous input-output pairs. At each step, it transforms input to an output, and modifies its "memory" to help it to better perform future processing.
The illustration to the right may be misleading to many because practical neural network topologies are frequently organized in "layers" and the drawing gives that appearance. However, what appears to belayersare, in fact, different steps in time, "unfolded" to produce the appearance oflayers.
Astacked RNN, ordeep RNN, is composed of multiple RNNs stacked one above the other. Abstractly, it is structured as follows
Each layer operates as a stand-alone RNN, and each layer's output sequence is used as the input sequence to the layer above. There is no conceptual limit to the depth of stacked RNN.
Abidirectional RNN(biRNN) is composed of two RNNs, one processing the input sequence in one direction, and another in the opposite direction. Abstractly, it is structured as follows:
The two output sequences are then concatenated to give the total output:((y0,y0′),(y1,y1′),…,(yN,yN′)){\displaystyle ((y_{0},y_{0}'),(y_{1},y_{1}'),\dots ,(y_{N},y_{N}'))}.
Bidirectional RNN allows the model to process a token both in the context of what came before it and what came after it. By stacking multiple bidirectional RNNs together, the model can process a token increasingly contextually. TheELMomodel (2018)[48]is a stacked bidirectionalLSTMwhich takes character-level as inputs and produces word-level embeddings.
Two RNNs can be run front-to-back in anencoder-decoderconfiguration. The encoder RNN processes an input sequence into a sequence of hidden vectors, and the decoder RNN processes the sequence of hidden vectors to an output sequence, with an optionalattention mechanism. This was used to construct state of the artneural machine translatorsduring the 2014–2017 period. This was an instrumental step towards the development oftransformers.[49]
An RNN may process data with more than one dimension. PixelRNN processes two-dimensional data, with many possible directions.[50]For example, the row-by-row direction processes ann×n{\displaystyle n\times n}grid of vectorsxi,j{\displaystyle x_{i,j}}in the following order:x1,1,x1,2,…,x1,n,x2,1,x2,2,…,x2,n,…,xn,n{\displaystyle x_{1,1},x_{1,2},\dots ,x_{1,n},x_{2,1},x_{2,2},\dots ,x_{2,n},\dots ,x_{n,n}}Thediagonal BiLSTMuses two LSTMs to process the same grid. One processes it from the top-left corner to the bottom-right, such that it processesxi,j{\displaystyle x_{i,j}}depending on its hidden state and cell state on the top and the left side:hi−1,j,ci−1,j{\displaystyle h_{i-1,j},c_{i-1,j}}andhi,j−1,ci,j−1{\displaystyle h_{i,j-1},c_{i,j-1}}. The other processes it from the top-right corner to the bottom-left.
Fully recurrent neural networks(FRNN) connect the outputs of all neurons to the inputs of all neurons. In other words, it is afully connected network. This is the most general neural network topology, because all other topologies can be represented by setting some connection weights to zero to simulate the lack of connections between those neurons.
TheHopfield networkis an RNN in which all connections across layers are equally sized. It requiresstationaryinputs and is thus not a general RNN, as it does not process sequences of patterns. However, it guarantees that it will converge. If the connections are trained usingHebbian learning, then the Hopfield network can perform asrobustcontent-addressable memory, resistant to connection alteration.
AnElmannetworkis a three-layer network (arranged horizontally asx,y, andzin the illustration) with the addition of a set of context units (uin the illustration). The middle (hidden) layer is connected to these context units fixed with a weight of one.[51]At each time step, the input is fed forward and alearning ruleis applied. The fixed back-connections save a copy of the previous values of the hidden units in the context units (since they propagate over the connections before the learning rule is applied). Thus the network can maintain a sort of state, allowing it to perform tasks such as sequence-prediction that are beyond the power of a standardmultilayer perceptron.
Jordannetworksare similar to Elman networks. The context units are fed from the output layer instead of the hidden layer. The context units in a Jordan network are also called the state layer. They have a recurrent connection to themselves.[51]
Elman and Jordan networks are also known as "Simple recurrent networks" (SRN).
Variables and functions
Long short-term memory(LSTM) is the most widely used RNN architecture. It was designed to solve thevanishing gradient problem. LSTM is normally augmented by recurrent gates called "forget gates".[54]LSTM prevents backpropagated errors from vanishing or exploding.[55]Instead, errors can flow backward through unlimited numbers of virtual layers unfolded in space. That is, LSTM can learn tasks that require memories of events that happened thousands or even millions of discrete time steps earlier. Problem-specific LSTM-like topologies can be evolved.[56]LSTM works even given long delays between significant events and can handle signals that mix low and high-frequency components.
Many applications use stacks of LSTMs,[57]for which it is called "deep LSTM". LSTM can learn to recognizecontext-sensitive languagesunlike previous models based onhidden Markov models(HMM) and similar concepts.[58]
Gated recurrent unit(GRU), introduced in 2014, was designed as a simplification of LSTM. They are used in the full form and several further simplified variants.[59][60]They have fewer parameters than LSTM, as they lack an output gate.[61]
Their performance on polyphonic music modeling and speech signal modeling was found to be similar to that of long short-term memory.[62]There does not appear to be particular performance difference between LSTM and GRU.[62][63]
Introduced by Bart Kosko,[64]a bidirectional associative memory (BAM) network is a variant of a Hopfield network that stores associative data as a vector. The bidirectionality comes from passing information through a matrix and itstranspose. Typically, bipolar encoding is preferred to binary encoding of the associative pairs. Recently, stochastic BAM models usingMarkovstepping were optimized for increased network stability and relevance to real-world applications.[65]
A BAM network has two layers, either of which can be driven as an input to recall an association and produce an output on the other layer.[66]
Echo state networks(ESN) have a sparsely connected random hidden layer. The weights of output neurons are the only part of the network that can change (be trained). ESNs are good at reproducing certaintime series.[67]A variant forspiking neuronsis known as aliquid state machine.[68]
Arecursive neural network[69]is created by applying the same set of weightsrecursivelyover a differentiable graph-like structure by traversing the structure intopological order. Such networks are typically also trained by the reverse mode ofautomatic differentiation.[70][71]They can processdistributed representationsof structure, such aslogical terms. A special case of recursive neural networks is the RNN whose structure corresponds to a linear chain. Recursive neural networks have been applied tonatural language processing.[72]The Recursive Neural Tensor Network uses atensor-based composition function for all nodes in the tree.[73]
Neural Turing machines(NTMs) are a method of extending recurrent neural networks by coupling them to externalmemoryresources with which they interact. The combined system is analogous to aTuring machineorVon Neumann architecturebut isdifferentiableend-to-end, allowing it to be efficiently trained withgradient descent.[74]
Differentiable neural computers (DNCs) are an extension of Neural Turing machines, allowing for the usage of fuzzy amounts of each memory address and a record of chronology.[75]
Neural network pushdown automata (NNPDA) are similar to NTMs, but tapes are replaced by analog stacks that are differentiable and trained. In this way, they are similar in complexity to recognizers ofcontext free grammars(CFGs).[76]
Recurrent neural networks areTuring completeand can run arbitrary programs to process arbitrary sequences of inputs.[77]
An RNN can be trained into a conditionallygenerative modelof sequences, akaautoregression.
Concretely, let us consider the problem of machine translation, that is, given a sequence(x1,x2,…,xn){\displaystyle (x_{1},x_{2},\dots ,x_{n})}of English words, the model is to produce a sequence(y1,…,ym){\displaystyle (y_{1},\dots ,y_{m})}of French words. It is to be solved by aseq2seqmodel.
Now, during training, the encoder half of the model would first ingest(x1,x2,…,xn){\displaystyle (x_{1},x_{2},\dots ,x_{n})}, then the decoder half would start generating a sequence(y^1,y^2,…,y^l){\displaystyle ({\hat {y}}_{1},{\hat {y}}_{2},\dots ,{\hat {y}}_{l})}. The problem is that if the model makes a mistake early on, say aty^2{\displaystyle {\hat {y}}_{2}}, then subsequent tokens are likely to also be mistakes. This makes it inefficient for the model to obtain a learning signal, since the model would mostly learn to shifty^2{\displaystyle {\hat {y}}_{2}}towardsy2{\displaystyle y_{2}}, but not the others.
Teacher forcingmakes it so that the decoder uses the correct output sequence for generating the next entry in the sequence. So for example, it would see(y1,…,yk){\displaystyle (y_{1},\dots ,y_{k})}in order to generatey^k+1{\displaystyle {\hat {y}}_{k+1}}.
Gradient descent is afirst-orderiterativeoptimizationalgorithmfor finding the minimum of a function. In neural networks, it can be used to minimize the error term by changing each weight in proportion to the derivative of the error with respect to that weight, provided the non-linearactivation functionsaredifferentiable.
The standard method for training RNN by gradient descent is the "backpropagation through time" (BPTT) algorithm, which is a special case of the general algorithm ofbackpropagation. A more computationally expensive online variant is called "Real-Time Recurrent Learning" or RTRL,[78][79]which is an instance ofautomatic differentiationin the forward accumulation mode with stacked tangent vectors. Unlike BPTT, this algorithm is local in time but not local in space.
In this context, local in space means that a unit's weight vector can be updated using only information stored in the connected units and the unit itself such that update complexity of a single unit is linear in the dimensionality of the weight vector. Local in time means that the updates take place continually (on-line) and depend only on the most recent time step rather than on multiple time steps within a given time horizon as in BPTT. Biological neural networks appear to be local with respect to both time and space.[80][81]
For recursively computing the partial derivatives, RTRL has a time-complexity of O(number of hidden x number of weights) per time step for computing theJacobian matrices, while BPTT only takes O(number of weights) per time step, at the cost of storing all forward activations within the given time horizon.[82]An online hybrid between BPTT and RTRL with intermediate complexity exists,[83][84]along with variants for continuous time.[85]
A major problem with gradient descent for standard RNN architectures is thaterror gradients vanishexponentially quickly with the size of the time lag between important events.[55][86]LSTM combined with a BPTT/RTRL hybrid learning method attempts to overcome these problems.[36]This problem is also solved in the independently recurrent neural network (IndRNN)[87]by reducing the context of a neuron to its own past state and the cross-neuron information can then be explored in the following layers. Memories of different ranges including long-term memory can be learned without the gradient vanishing and exploding problem.
The on-line algorithm called causal recursive backpropagation (CRBP), implements and combines BPTT and RTRL paradigms for locally recurrent networks.[88]It works with the most general locally recurrent networks. The CRBP algorithm can minimize the global error term. This fact improves the stability of the algorithm, providing a unifying view of gradient calculation techniques for recurrent networks with local feedback.
One approach to gradient information computation in RNNs with arbitrary architectures is based on signal-flow graphs diagrammatic derivation.[89]It uses the BPTT batch algorithm, based on Lee's theorem for network sensitivity calculations.[90]It was proposed by Wan and Beaufays, while its fast online version was proposed by Campolucci, Uncini and Piazza.[90]
Theconnectionist temporal classification(CTC)[91]is a specialized loss function for training RNNs for sequence modeling problems where the timing is variable.[92]
Training the weights in a neural network can be modeled as a non-linearglobal optimizationproblem. A target function can be formed to evaluate the fitness or error of a particular weight vector as follows: First, the weights in the network are set according to the weight vector. Next, the network is evaluated against the training sequence. Typically, the sum-squared difference between the predictions and the target values specified in the training sequence is used to represent the error of the current weight vector. Arbitrary global optimization techniques may then be used to minimize this target function.
The most common global optimization method for training RNNs isgenetic algorithms, especially in unstructured networks.[93][94][95]
Initially, the genetic algorithm is encoded with the neural network weights in a predefined manner where one gene in thechromosomerepresents one weight link. The whole network is represented as a single chromosome. The fitness function is evaluated as follows:
Many chromosomes make up the population; therefore, many different neural networks are evolved until a stopping criterion is satisfied. A common stopping scheme is:
The fitness function evaluates the stopping criterion as it receives the mean-squared error reciprocal from each network during training. Therefore, the goal of the genetic algorithm is to maximize the fitness function, reducing the mean-squared error.
Other global (and/or evolutionary) optimization techniques may be used to seek a good set of weights, such assimulated annealingorparticle swarm optimization.
The independently recurrent neural network (IndRNN)[87]addresses the gradient vanishing and exploding problems in the traditional fully connected RNN. Each neuron in one layer only receives its own past state as context information (instead of full connectivity to all other neurons in this layer) and thus neurons are independent of each other's history. The gradient backpropagation can be regulated to avoid gradient vanishing and exploding in order to keep long or short-term memory. The cross-neuron information is explored in the next layers. IndRNN can be robustly trained with non-saturated nonlinear functions such as ReLU. Deep networks can be trained using skip connections.
The neural history compressor is an unsupervised stack of RNNs.[96]At the input level, it learns to predict its next input from the previous inputs. Only unpredictable inputs of some RNN in the hierarchy become inputs to the next higher level RNN, which therefore recomputes its internal state only rarely. Each higher level RNN thus studies a compressed representation of the information in the RNN below. This is done such that the input sequence can be precisely reconstructed from the representation at the highest level.
The system effectively minimizes the description length or the negativelogarithmof the probability of the data.[97]Given a lot of learnable predictability in the incoming data sequence, the highest level RNN can use supervised learning to easily classify even deep sequences with long intervals between important events.
It is possible to distill the RNN hierarchy into two RNNs: the "conscious" chunker (higher level) and the "subconscious" automatizer (lower level).[96]Once the chunker has learned to predict and compress inputs that are unpredictable by the automatizer, then the automatizer can be forced in the next learning phase to predict or imitate through additional units the hidden units of the more slowly changing chunker. This makes it easy for the automatizer to learn appropriate, rarely changing memories across long intervals. In turn, this helps the automatizer to make many of its once unpredictable inputs predictable, such that the chunker can focus on the remaining unpredictable events.[96]
Agenerative modelpartially overcame thevanishing gradient problem[55]ofautomatic differentiationorbackpropagationin neural networks in 1992. In 1993, such a system solved a "Very Deep Learning" task that required more than 1000 subsequent layers in an RNN unfolded in time.[34]
Second-order RNNs use higher order weightswijk{\displaystyle w{}_{ijk}}instead of the standardwij{\displaystyle w{}_{ij}}weights, and states can be a product. This allows a direct mapping to afinite-state machineboth in training, stability, and representation.[98][99]Long short-term memory is an example of this but has no such formal mappings or proof of stability.
Hierarchical recurrent neural networks (HRNN) connect their neurons in various ways to decompose hierarchical behavior into useful subprograms.[96][100]Such hierarchical structures of cognition are present in theories of memory presented by philosopherHenri Bergson, whose philosophical views have inspired hierarchical models.[101]
Hierarchical recurrent neural networks are useful inforecasting, helping to predict disaggregated inflation components of theconsumer price index(CPI). The HRNN model leverages information from higher levels in the CPI hierarchy to enhance lower-level predictions. Evaluation of a substantial dataset from the US CPI-U index demonstrates the superior performance of the HRNN model compared to various establishedinflationprediction methods.[102]
Generally, a recurrent multilayer perceptron network (RMLP network) consists of cascaded subnetworks, each containing multiple layers of nodes. Each subnetwork is feed-forward except for the last layer, which can have feedback connections. Each of these subnets is connected only by feed-forward connections.[103]
A multiple timescales recurrent neural network (MTRNN) is a neural-based computational model that can simulate the functional hierarchy of the brain through self-organization depending on the spatial connection between neurons and on distinct types of neuron activities, each with distinct time properties.[104][105]With such varied neuronal activities, continuous sequences of any set of behaviors are segmented into reusable primitives, which in turn are flexibly integrated into diverse sequential behaviors. The biological approval of such a type of hierarchy was discussed in thememory-predictiontheory of brain function byHawkinsin his bookOn Intelligence.[citation needed]Such a hierarchy also agrees with theories of memory posited by philosopherHenri Bergson, which have been incorporated into an MTRNN model.[101][106]
Greg Snider ofHP Labsdescribes a system of cortical computing with memristive nanodevices.[107]Thememristors(memory resistors) are implemented by thin film materials in which the resistance is electrically tuned via the transport of ions or oxygen vacancies within the film.DARPA'sSyNAPSE projecthas funded IBM Research and HP Labs, in collaboration with the Boston University Department of Cognitive and Neural Systems (CNS), to develop neuromorphic architectures that may be based on memristive systems.Memristive networksare a particular type ofphysical neural networkthat have very similar properties to (Little-)Hopfield networks, as they have continuous dynamics, a limited memory capacity and natural relaxation via the minimization of a function which is asymptotic to theIsing model. In this sense, the dynamics of a memristive circuit have the advantage compared to a Resistor-Capacitor network to have a more interesting non-linear behavior. From this point of view, engineering analog memristive networks account for a peculiar type ofneuromorphic engineeringin which the device behavior depends on the circuit wiring or topology.
The evolution of these networks can be studied analytically using variations of theCaravelli–Traversa–Di Ventraequation.[108]
A continuous-time recurrent neural network (CTRNN) uses a system ofordinary differential equationsto model the effects on a neuron of the incoming inputs. They are typically analyzed bydynamical systems theory. Many RNN models in neuroscience are continuous-time.[16]
For a neuroni{\displaystyle i}in the network with activationyi{\displaystyle y_{i}}, the rate of change of activation is given by:
Where:
CTRNNs have been applied toevolutionary roboticswhere they have been used to address vision,[109]co-operation,[110]and minimal cognitive behaviour.[111]
Note that, by theShannon sampling theorem, discrete-time recurrent neural networks can be viewed as continuous-time recurrent neural networks where the differential equations have transformed into equivalentdifference equations.[112]This transformation can be thought of as occurring after the post-synaptic node activation functionsyi(t){\displaystyle y_{i}(t)}have been low-pass filtered but prior to sampling.
They are in factrecursive neural networkswith a particular structure: that of a linear chain. Whereas recursive neural networks operate on any hierarchical structure, combining child representations into parent representations, recurrent neural networks operate on the linear progression of time, combining the previous time step and a hidden representation into the representation for the current time step.
From a time-series perspective, RNNs can appear as nonlinear versions offinite impulse responseandinfinite impulse responsefilters and also as anonlinear autoregressive exogenous model(NARX).[113]RNN has infinite impulse response whereasconvolutional neural networkshavefinite impulseresponse. Both classes of networks exhibit temporaldynamic behavior.[114]A finite impulse recurrent network is adirected acyclic graphthat can be unrolled and replaced with a strictly feedforward neural network, while an infinite impulse recurrent network is adirected cyclic graphthat cannot be unrolled.
The effect of memory-based learning for the recognition of sequences can also be implemented by a more biological-based model which uses the silencing mechanism exhibited in neurons with a relatively high frequency spiking activity.[115]
Additional stored states and the storage under direct control by the network can be added to bothinfinite-impulseandfinite-impulsenetworks. Another network or graph can also replace the storage if that incorporates time delays or has feedback loops. Such controlled states are referred to as gated states or gated memory and are part oflong short-term memorynetworks (LSTMs) andgated recurrent units. This is also called Feedback Neural Network (FNN).
Modern libraries provide runtime-optimized implementations of the above functionality or allow to speed up the slow loop byjust-in-time compilation.
Applications of recurrent neural networks include:
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Incryptography,learning with errors(LWE) is a mathematical problem that is widely used to create secureencryption algorithms.[1]It is based on the idea of representing secret information as a set of equations with errors. In other words, LWE is a way to hide the value of a secret by introducing noise to it.[2]In more technical terms, it refers to thecomputational problemof inferring a linearn{\displaystyle n}-ary functionf{\displaystyle f}over a finiteringfrom given samplesyi=f(xi){\displaystyle y_{i}=f(\mathbf {x} _{i})}some of which may be erroneous. The LWE problem is conjectured to be hard to solve,[1]and thus to be useful in cryptography.
More precisely, the LWE problem is defined as follows. LetZq{\displaystyle \mathbb {Z} _{q}}denote the ring of integersmoduloq{\displaystyle q}and letZqn{\displaystyle \mathbb {Z} _{q}^{n}}denote the set ofn{\displaystyle n}-vectorsoverZq{\displaystyle \mathbb {Z} _{q}}. There exists a certain unknown linear functionf:Zqn→Zq{\displaystyle f:\mathbb {Z} _{q}^{n}\rightarrow \mathbb {Z} _{q}}, and the input to the LWE problem is a sample of pairs(x,y){\displaystyle (\mathbf {x} ,y)}, wherex∈Zqn{\displaystyle \mathbf {x} \in \mathbb {Z} _{q}^{n}}andy∈Zq{\displaystyle y\in \mathbb {Z} _{q}}, so that with high probabilityy=f(x){\displaystyle y=f(\mathbf {x} )}. Furthermore, the deviation from the equality is according to some known noise model. The problem calls for finding the functionf{\displaystyle f}, or some close approximation thereof, with high probability.
The LWE problem was introduced byOded Regevin 2005[3](who won the 2018Gödel Prizefor this work); it is a generalization of theparity learningproblem. Regev showed that the LWE problem is as hard to solve as several worst-caselattice problems. Subsequently, the LWE problem has been used as ahardness assumptionto createpublic-key cryptosystems,[3][4]such as thering learning with errors key exchangeby Peikert.[5]
Denote byT=R/Z{\displaystyle \mathbb {T} =\mathbb {R} /\mathbb {Z} }theadditive group on reals modulo one.
Lets∈Zqn{\displaystyle \mathbf {s} \in \mathbb {Z} _{q}^{n}}be a fixed vector.
Letϕ{\displaystyle \phi }be a fixed probability distribution overT{\displaystyle \mathbb {T} }.
Denote byAs,ϕ{\displaystyle A_{\mathbf {s} ,\phi }}the distribution onZqn×T{\displaystyle \mathbb {Z} _{q}^{n}\times \mathbb {T} }obtained as follows.
Thelearning with errors problemLWEq,ϕ{\displaystyle \mathrm {LWE} _{q,\phi }}is to finds∈Zqn{\displaystyle \mathbf {s} \in \mathbb {Z} _{q}^{n}}, given access to polynomially many samples of choice fromAs,ϕ{\displaystyle A_{\mathbf {s} ,\phi }}.
For everyα>0{\displaystyle \alpha >0}, denote byDα{\displaystyle D_{\alpha }}the one-dimensionalGaussianwith zero mean and varianceα2/(2π){\displaystyle \alpha ^{2}/(2\pi )}, that is, the density function isDα(x)=ρα(x)/α{\displaystyle D_{\alpha }(x)=\rho _{\alpha }(x)/\alpha }whereρα(x)=e−π(|x|/α)2{\displaystyle \rho _{\alpha }(x)=e^{-\pi (|x|/\alpha )^{2}}}, and letΨα{\displaystyle \Psi _{\alpha }}be the distribution onT{\displaystyle \mathbb {T} }obtained by consideringDα{\displaystyle D_{\alpha }}modulo one. The version of LWE considered in most of the results would beLWEq,Ψα{\displaystyle \mathrm {LWE} _{q,\Psi _{\alpha }}}
TheLWEproblem described above is thesearchversion of the problem. In thedecisionversion (DLWE), the goal is to distinguish between noisy inner products and uniformly random samples fromZqn×T{\displaystyle \mathbb {Z} _{q}^{n}\times \mathbb {T} }(practically, some discretized version of it). Regev[3]showed that thedecisionandsearchversions are equivalent whenq{\displaystyle q}is a prime bounded by some polynomial inn{\displaystyle n}.
Intuitively, if we have a procedure for the search problem, the decision version can be solved easily: just feed the input samples for the decision problem to the solver for the search problem. Denote the given samples by{(ai,bi)}⊂Zqn×T{\displaystyle \{(\mathbf {a} _{i},\mathbf {b} _{i})\}\subset \mathbb {Z} _{q}^{n}\times \mathbb {T} }. If the solver returns a candidates{\displaystyle \mathbf {s} }, for alli{\displaystyle i}, calculate{⟨ai,s⟩−bi}{\displaystyle \{\langle \mathbf {a} _{i},\mathbf {s} \rangle -\mathbf {b} _{i}\}}. If the samples are from an LWE distribution, then the results of this calculation will be distributed accordingχ{\displaystyle \chi }, but if the samples are uniformly random, these quantities will be distributed uniformly as well.
For the other direction, given a solver for the decision problem, the search version can be solved as follows: Recovers{\displaystyle \mathbf {s} }one coordinate at a time. To obtain the first coordinate,s1{\displaystyle \mathbf {s} _{1}}, make a guessk∈Zq{\displaystyle k\in \mathbb {Z} _{q}}, and do the following. Choose a numberr∈Zq{\displaystyle r\in \mathbb {Z} _{q}}uniformly at random. Transform the given samples{(ai,bi)}⊂Zqn×T{\displaystyle \{(\mathbf {a} _{i},\mathbf {b} _{i})\}\subset \mathbb {Z} _{q}^{n}\times \mathbb {T} }as follows. Calculate{(ai+(r,0,…,0),bi+(rk)/q)}{\displaystyle \{(\mathbf {a} _{i}+(r,0,\ldots ,0),\mathbf {b} _{i}+(rk)/q)\}}. Send the transformed samples to the decision solver.
If the guessk{\displaystyle k}was correct, the transformation takes the distributionAs,χ{\displaystyle A_{\mathbf {s} ,\chi }}to itself, and otherwise, sinceq{\displaystyle q}is prime, it takes it to the uniform distribution. So, given a polynomial-time solver for the decision problem that errs with very small probability, sinceq{\displaystyle q}is bounded by some polynomial inn{\displaystyle n}, it only takes polynomial time to guess every possible value fork{\displaystyle k}and use the solver to see which one is correct.
After obtainings1{\displaystyle \mathbf {s} _{1}}, we follow an analogous procedure for each other coordinatesj{\displaystyle \mathbf {s} _{j}}. Namely, we transform ourbi{\displaystyle \mathbf {b} _{i}}samples the same way, and transform ourai{\displaystyle \mathbf {a} _{i}}samples by calculatingai+(0,…,r,…,0){\displaystyle \mathbf {a} _{i}+(0,\ldots ,r,\ldots ,0)}, where ther{\displaystyle r}is in thejth{\displaystyle j^{\text{th}}}coordinate.[3]
Peikert[4]showed that this reduction, with a small modification, works for anyq{\displaystyle q}that is a product of distinct, small (polynomial inn{\displaystyle n}) primes. The main idea is ifq=q1q2⋯qt{\displaystyle q=q_{1}q_{2}\cdots q_{t}}, for eachqℓ{\displaystyle q_{\ell }}, guess and check to see ifsj{\displaystyle \mathbf {s} _{j}}is congruent to0modqℓ{\displaystyle 0\mod q_{\ell }}, and then use theChinese remainder theoremto recoversj{\displaystyle \mathbf {s} _{j}}.
Regev[3]showed therandom self-reducibilityof theLWEandDLWEproblems for arbitraryq{\displaystyle q}andχ{\displaystyle \chi }. Given samples{(ai,bi)}{\displaystyle \{(\mathbf {a} _{i},\mathbf {b} _{i})\}}fromAs,χ{\displaystyle A_{\mathbf {s} ,\chi }}, it is easy to see that{(ai,bi+⟨ai,t⟩)/q}{\displaystyle \{(\mathbf {a} _{i},\mathbf {b} _{i}+\langle \mathbf {a} _{i},\mathbf {t} \rangle )/q\}}are samples fromAs+t,χ{\displaystyle A_{\mathbf {s} +\mathbf {t} ,\chi }}.
So, suppose there was some setS⊂Zqn{\displaystyle {\mathcal {S}}\subset \mathbb {Z} _{q}^{n}}such that|S|/|Zqn|=1/poly(n){\displaystyle |{\mathcal {S}}|/|\mathbb {Z} _{q}^{n}|=1/\operatorname {poly} (n)}, and for distributionsAs′,χ{\displaystyle A_{\mathbf {s} ',\chi }}, withs′←S{\displaystyle \mathbf {s} '\leftarrow {\mathcal {S}}},DLWEwas easy.
Then there would be some distinguisherA{\displaystyle {\mathcal {A}}}, who, given samples{(ai,bi)}{\displaystyle \{(\mathbf {a} _{i},\mathbf {b} _{i})\}}, could tell whether they were uniformly random or fromAs′,χ{\displaystyle A_{\mathbf {s} ',\chi }}. If we need to distinguish uniformly random samples fromAs,χ{\displaystyle A_{\mathbf {s} ,\chi }}, wheres{\displaystyle \mathbf {s} }is chosen uniformly at random fromZqn{\displaystyle \mathbb {Z} _{q}^{n}}, we could simply try different valuest{\displaystyle \mathbf {t} }sampled uniformly at random fromZqn{\displaystyle \mathbb {Z} _{q}^{n}}, calculate{(ai,bi+⟨ai,t⟩)/q}{\displaystyle \{(\mathbf {a} _{i},\mathbf {b} _{i}+\langle \mathbf {a} _{i},\mathbf {t} \rangle )/q\}}and feed these samples toA{\displaystyle {\mathcal {A}}}. SinceS{\displaystyle {\mathcal {S}}}comprises a large fraction ofZqn{\displaystyle \mathbb {Z} _{q}^{n}}, with high probability, if we choose a polynomial number of values fort{\displaystyle \mathbf {t} }, we will find one such thats+t∈S{\displaystyle \mathbf {s} +\mathbf {t} \in {\mathcal {S}}}, andA{\displaystyle {\mathcal {A}}}will successfully distinguish the samples.
Thus, no suchS{\displaystyle {\mathcal {S}}}can exist, meaningLWEandDLWEare (up to a polynomial factor) as hard in the average case as they are in the worst case.
For an-dimensional latticeL{\displaystyle L}, letsmoothing parameterηε(L){\displaystyle \eta _{\varepsilon }(L)}denote the smallests{\displaystyle s}such thatρ1/s(L∗∖{0})≤ε{\displaystyle \rho _{1/s}(L^{*}\setminus \{\mathbf {0} \})\leq \varepsilon }whereL∗{\displaystyle L^{*}}is the dual ofL{\displaystyle L}andρα(x)=e−π(|x|/α)2{\displaystyle \rho _{\alpha }(x)=e^{-\pi (|x|/\alpha )^{2}}}is extended to sets by summing over function values at each element in the set. LetDL,r{\displaystyle D_{L,r}}denote the discrete Gaussian distribution onL{\displaystyle L}of widthr{\displaystyle r}for a latticeL{\displaystyle L}and realr>0{\displaystyle r>0}. The probability of eachx∈L{\displaystyle x\in L}is proportional toρr(x){\displaystyle \rho _{r}(x)}.
Thediscrete Gaussian sampling problem(DGS) is defined as follows: An instance ofDGSϕ{\displaystyle DGS_{\phi }}is given by ann{\displaystyle n}-dimensional latticeL{\displaystyle L}and a numberr≥ϕ(L){\displaystyle r\geq \phi (L)}. The goal is to output a sample fromDL,r{\displaystyle D_{L,r}}. Regev shows that there is a reduction fromGapSVP100nγ(n){\displaystyle \operatorname {GapSVP} _{100{\sqrt {n}}\gamma (n)}}toDGSnγ(n)/λ(L∗){\displaystyle DGS_{{\sqrt {n}}\gamma (n)/\lambda (L^{*})}}for any functionγ(n)≥1{\displaystyle \gamma (n)\geq 1}.
Regev then shows that there exists an efficient quantum algorithm forDGS2nηε(L)/α{\displaystyle DGS_{{\sqrt {2n}}\eta _{\varepsilon }(L)/\alpha }}given access to an oracle forLWEq,Ψα{\displaystyle \mathrm {LWE} _{q,\Psi _{\alpha }}}for integerq{\displaystyle q}andα∈(0,1){\displaystyle \alpha \in (0,1)}such thatαq>2n{\displaystyle \alpha q>2{\sqrt {n}}}. This implies the hardness for LWE. Although the proof of this assertion works for anyq{\displaystyle q}, for creating a cryptosystem, the modulusq{\displaystyle q}has to be polynomial inn{\displaystyle n}.
Peikert proves[4]that there is a probabilistic polynomial time reduction from theGapSVPζ,γ{\displaystyle \operatorname {GapSVP} _{\zeta ,\gamma }}problem in the worst case to solvingLWEq,Ψα{\displaystyle \mathrm {LWE} _{q,\Psi _{\alpha }}}usingpoly(n){\displaystyle \operatorname {poly} (n)}samples for parametersα∈(0,1){\displaystyle \alpha \in (0,1)},γ(n)≥n/(αlogn){\displaystyle \gamma (n)\geq n/(\alpha {\sqrt {\log n}})},ζ(n)≥γ(n){\displaystyle \zeta (n)\geq \gamma (n)}andq≥(ζ/n)ωlogn){\displaystyle q\geq (\zeta /{\sqrt {n}})\omega {\sqrt {\log n}})}.
TheLWEproblem serves as a versatile problem used in construction of several[3][4][6][7]cryptosystems. In 2005, Regev[3]showed that the decision version of LWE is hard assuming quantum hardness of thelattice problemsGapSVPγ{\displaystyle \mathrm {GapSVP} _{\gamma }}(forγ{\displaystyle \gamma }as above) andSIVPt{\displaystyle \mathrm {SIVP} _{t}}witht=O(n/α){\displaystyle t=O(n/\alpha )}). In 2009, Peikert[4]proved a similar result assuming only the classical hardness of the related problemGapSVPζ,γ{\displaystyle \mathrm {GapSVP} _{\zeta ,\gamma }}. The disadvantage of Peikert's result is that it bases itself on a non-standard version of an easier (when compared to SIVP) problem GapSVP.
Regev[3]proposed apublic-key cryptosystembased on the hardness of theLWEproblem. The cryptosystem as well as the proof of security and correctness are completely classical. The system is characterized bym,q{\displaystyle m,q}and a probability distributionχ{\displaystyle \chi }onT{\displaystyle \mathbb {T} }. The setting of the parameters used in proofs of correctness and security is
The cryptosystem is then defined by:
The proof of correctness follows from choice of parameters and some probability analysis. The proof of security is by reduction to the decision version ofLWE: an algorithm for distinguishing between encryptions (with above parameters) of0{\displaystyle 0}and1{\displaystyle 1}can be used to distinguish betweenAs,χ{\displaystyle A_{s,\chi }}and the uniform distribution overZqn×T{\displaystyle \mathbb {Z} _{q}^{n}\times \mathbb {T} }
Peikert[4]proposed a system that is secure even against anychosen-ciphertext attack.
The idea of using LWE and Ring LWE for key exchange was proposed and filed at the University of Cincinnati in 2011 by Jintai Ding. The idea comes from the associativity of matrix multiplications, and the errors are used to provide the security. The paper[8]appeared in 2012 after a provisional patent application was filed in 2012.
The security of the protocol is proven based on the hardness of solving the LWE problem. In 2014, Peikert presented a key-transport scheme[9]following the same basic idea of Ding's, where the new idea of sending an additional 1-bit signal for rounding in Ding's construction is also used. The "new hope" implementation[10]selected for Google's post-quantum experiment,[11]uses Peikert's scheme with variation in the error distribution.
A RLWE version of the classicFeige–Fiat–Shamir Identification protocolwas created and converted to adigital signaturein 2011 by Lyubashevsky. The details of this signature were extended in 2012 by Gunesyu, Lyubashevsky, and Popplemann in 2012 and published in their paper "Practical Lattice Based Cryptography – A Signature Scheme for Embedded Systems." These papers laid the groundwork for a variety of recent signature algorithms some based directly on the ring learning with errors problem and some which are not tied to the same hard RLWE problems.
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Aradiotelephone(orradiophone), abbreviatedRT,[1]is aradio communicationsystem for conducting aconversation;radiotelephonymeanstelephonyby radio. It is in contrast toradiotelegraphy, which is radio transmission oftelegrams(messages), ortelevision, transmission ofmoving picturesand sound. The term is related toradio broadcasting, which transmit audio one way to listeners. Radiotelephony refers specifically totwo-way radiosystems for bidirectional person-to-person voice communication between separated users, such asCB radioormarine radio. In spite of the name, radiotelephony systems are not necessarily connected to or have anything to do with thetelephone network, and in some radio services, includingGMRS,[2]interconnection is prohibited.
The wordphonehas a long precedent beginning with early US wired voice systems. The term meansvoiceas opposed to telegraph orMorse code. This would include systems fitting into the category of two-way radio or one-way voice broadcasts such as coastal maritime weather. The term is still popular in theamateur radiocommunity and in USFederal Communications Commissionregulations.
A standardlandlinetelephone allows both users to talk and listen simultaneously; effectively there are two opencommunication channelsbetween the two end-to-end users of the system. In a radiotelephone system, this form of working, known asfull-duplex, requires a radio system to simultaneously transmit and receive on two separate frequencies, which both wastesbandwidthand presents some technical challenges. It is, however, the most comfortable method of voice communication for users, and it is currently used in cell phones and was used in the formerIMTS.
The most common method of working for radiotelephones ishalf-duplex, operation, which allows one person to talk and the other to listen alternately. If a single frequency is used, both parties take turns to transmit on it, known as simplex. Dual-frequency working or duplex splits the communication into two separate frequencies, but only one is used to transmit at a time with the other frequency dedicated to receiving.
The user presses a special switch on the transmitter when they wish to talk—this is called the "press-to-talk" switch or PTT. It is usually fitted on the side of the microphone or other obvious position. Users may use aprocedural code-wordsuch as "over" to signal that they have finished transmitting.[3]
Radiotelephones may operate at anyfrequencywhere they are licensed to do so, though typically they are used in the various bands between 60 and 900MHz(25and 960 MHz in the United States). They may use simplemodulationschemes such asAMorFM, or more complex techniques such as digital coding,spread spectrum, and so on. Licensing terms for a given band will usually specify the type of modulation to be used. For example,airbandradiotelephones used for air to ground communication between pilots and controllers operates in theVHFband from 118.0 to 136.975 MHz, using amplitude modulation.
Radiotelephonereceiversare usually designed to a very high standard, and are usually of thedouble-conversion superhetdesign. Likewise, transmitters are carefully designed to avoid unwanted interference and feature power outputs from a few tens of milliwatts to perhaps 50wattsfor a mobile unit, up to a couple of hundred watts for abase station. Multiple channels are often provided using afrequency synthesizer.
Receivers usually feature asquelchcircuitto cut off theaudiooutput from the receiver when there is notransmissionto listen to. This is in contrast tobroadcastreceivers, which often dispense with this.
Often, on a small network system, there are many mobile units and one main base station. This would be typical for police or taxi services for example. To help direct messages to the correct recipients and avoid irrelevant traffic on the network being a distraction to other units, a variety of means have been devised to create addressing systems.
The crudest and oldest of these is calledCTCSS, or Continuous Tone-Controlled Squelch System. This consists of superimposing a precise very low frequency tone on the audio signal. Only the receiver tuned to this specific tone turns the signal into audio: this receiver shuts off the audio when the tone is not present or is a different frequency. By assigning a unique frequency to each mobile, private channels can be imposed on a public network. However this is only a convenience feature—it does not guarantee privacy.
A more commonly used system is called selective calling orSelcall. This also uses audio tones, but these are not restricted to sub-audio tones and are sent as a short burst in sequence. The receiver will be programmed to respond only to a unique set of tones in a precise sequence, and only then will it open the audio circuits for open-channel conversation with the base station. This system is much more versatile than CTCSS, as relatively few tones yield a far greater number of "addresses". In addition, special features (such as broadcast modes and emergency overrides) can be designed in, using special addresses set aside for the purpose. A mobile unit can also broadcast a Selcall sequence with its unique address to the base, so the user can know before the call is picked up which unit is calling. In practice many selcall systems also have automatictranspondingbuilt in, which allows the base station to "interrogate" a mobile even if the operator is not present. Such transponding systems usually have a status code that the user can set to indicate what they are doing. Features like this, while very simple, are one reason why they are very popular with organisations that need to manage a large number of remote mobile units. Selcall is widely used, though is becoming superseded by much more sophisticated digital systems.
Mobile radio telephonesystems, such asMobile Telephone ServiceandImproved Mobile Telephone Service, allowed a mobile unit to have a telephone number allowing access from the general telephone network, although some systems required mobile operators to set up calls to mobile stations. Mobile radio telephone systems before the introduction ofcellular telephoneservices suffered from few usable channels, heavy congestion, and very high operating costs.
TheMarine Radiotelephone ServiceorHF ship-to-shoreoperates onshortwaveradio frequencies, usingsingle-sideband modulation. The usual method is that a ship calls a shore station, and the shore station's marine operator connects the caller to thepublic switched telephone network. This service is retained for safety reasons, but in practice has been made obsolete by satellite telephones (particularly INMARSAT) andVoIPtelephone and email viasatellite internet.
Short wave radio is used because it bounces between theionosphereand the ground, giving a modest 1,000 watt transmitter (the standard power) a worldwide range.[4]
Most shore stations monitor several frequencies. The frequencies with the longest range are usually near 20MHz, but the ionosphere weather (propagation) can dramatically change which frequencies work best.
Single-sideband (SSB) is used because the short wave bands are crowded with many users, and SSB permits a single voice channel to use a narrower range of radio frequencies (bandwidth) when compared to earlier AM systems.[5]SSB uses about 3.5kHz, whileAM radiouses about 8 kHz, andnarrowband(voice or communication-quality)FMuses 9 kHz.
Marine radiotelephone first became common in the 1930s, and was used extensively for communications to ships and aircraft over water.[6]In that time, most long-range aircraft had long-wire antennas that would be let out during a call, and reeled-in afterward. Marine radiotelephony originally used AM mode in the 2-3 MHz region before the transition to SSB and the adoption of various higher frequency bands in addition to the 2 MHz frequencies.
One of the most important uses of marine radiotelephony has been to change ships' itineraries, and to perform other business at sea.
In the United States, since the Communications Act of 1934 theFederal Communications Commission(FCC) has issued various commercial "radiotelephone operator" licenses and permits to qualified applicants. These allow them to install, service, and maintain voice-only radio transmitter systems for use on ships and aircraft.[7](Until deregulation in the 1990s they were also required for commercial domestic radio and television broadcast systems. Because of treaty obligations they are still required for engineers of internationalshortwavebroadcast stations.) The certificate currently issued is thegeneral radiotelephone operator license.
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The termsGoogle bombingandGoogle washingrefer to the practice of causing awebsiteto rank highly inweb search engineresults for irrelevant, unrelated or off-topic search terms. In contrast,search engine optimization(SEO) is the practice of improving thesearch enginelistings of web pages forrelevantsearch terms.
Google-bombing is done for either business, political, or comedic purposes (or some combination thereof).[1]Google'ssearch-rank algorithmranks pages higher for a particular search phrase if enough other pages linked to it use similaranchor text. By January 2007, however, Google had tweaked its search algorithm to counter popular Google bombs such as "miserable failure" leading toGeorge W. BushandMichael Moore; now, search results list pages about the Google bomb itself.[2]On 21 June 2015, the first result in a Google search for "miserable failure" was this article.[3]Used both as averband anoun, "Google bombing" was introduced to theNew Oxford American Dictionaryin May 2005.[4]
Google bombing is related tospamdexing, the practice of deliberately modifyingHTMLto increase the chance of a website being placed close to the beginning of search engine results, or to influence the category to which the page is assigned in a misleading or dishonest manner.[5]
The termGooglewashingwas coined byAndrew Orlowskiin 2003 in order to describe the use ofmedia manipulationto change the perception of a term, or push out competition fromsearch engine results pages(SERPs).[6][7]
Google bombs date back as far as 1999, when a search for "moreevilthanSatanhimself" resulted in theMicrosofthomepage as the top result.[8][9]
In September 2000 the first Google bomb with a verifiable creator was created byHugedisk Men's Magazine, a now-defunct online humor magazine, when it linked the text "dumb motherfucker" to a site sellingGeorge W. Bush-related merchandise.[10]Hugedisk had also unsuccessfully attempted to Google bomb an equally derogatory term to bring up anAl Gore-related site. After a fair amount of publicity the George W. Bush-related merchandise site retained lawyers and sent acease-and-desistletter toHugedisk, thereby ending the Google bomb.[11]
Adam Mathes is credited with coining the term "Google bombing" when he mentioned it in an April 6, 2001, article in the online magazineuber.nu. In the article Mathes details his connection of the search term "talentless hack" to the website of his friend, Andy Pressman, by recruiting fellow webloggers to link to his friend's page with the desired term.[12]Some experts forecast that the practice of Google Bombing is over, as changes to Google's algorithm over the years have minimised the effect of the technique.
The Google Bomb has been used fortactical mediaas a way of performing a "hit-and-run" media attack on popular topics. Such attacks include Anthony Cox's attack in 2003. He created a parody of the "404 – page not found" browser error message in response to the war in Iraq. The page looked like the error page but was titled "These Weapons of Mass Destruction cannot be displayed". This website could be found as one of the top hits on Google after the start of the war in Iraq.[13]Also, in an attempt to detract attention from the far-right groupEnglish Defence League(EDL), a parody group has been made known as "English Disco Lovers", with the expressed purpose of Google bombing the acronym.[14]
The Google bomb is often misunderstood by those in the media and publishing industry who do not retain technical knowledge of Google's ranking factors. For example, talk radio hostAlex Joneshas often conducted what he calls "Google bombs" by dispatching instructions to his radio/Internet listeners.[15][16]In this context, the term is used to describe a rapid and massive influx of keyword searches for a particular phrase. The keyword surge gives the impression that the related content has suddenly become popular. The strategy behind this type of Google bombing is to attract attention from the larger mainstream media and influence them to publish content related to the keyword.[citation needed]
By studying what types of ranking manipulations a search engine is using, a company can provoke a search engine intoloweringthe ranking of a competitor's website. This practice, known asGoogle bowlingornegative SEO, is often done by purchasing Google bombing services (or otherSEOtechniques) not for one's own website, but rather for that of a competitor. The attacker provokes the search company into punishing the "offending" competitor by displaying their page further down in the search results.[17][18]For victims of Google bowling, it may be difficult to appeal the ranking decrease because Google avoids explaining penalties, preferring not to "educate" real offenders. If the situation is clear-cut, however, Google could lift the penalty after submitting a request for reconsideration. Furthermore, after theGoogle Penguinupdate, Google search rankings now take Google bowling into account and very rarely will a website be penalized due to low-quality "farm" backlinks.[citation needed]
Other search engines use similar techniques to rank results and are also affected by Google bombs. A search for "miserable failure" or "failure" on September 29, 2006, brought up the official George W. Bush biography number one onGoogle,Yahoo!, andMSNand number two on Ask.com. On June 2, 2005, Tooter reported that George Bush was ranked first for the keyword "miserable", "failure", and "miserable failure" in both Google and Yahoo!; Google has since addressed this and disarmed the George Bush Google bomb and many others.[citation needed]
TheBBC, reporting on Google bombs in 2002, used the headline "Google Hit By Link Bombers",[19]acknowledging to some degree the idea of "link bombing". In 2004,Search Engine Watchsuggested that the term be "link bombing" because of its application beyond Google, and continues to use thattermas it is considered more accurate.[20]
We don't condone the practice of googlebombing, or any other action that seeks to affect the integrity of our search results, but we're also reluctant to alter our results by hand in order to prevent such items from showing up. Pranks like this may be distracting to some, but they don't affect the overall quality of our search service, whose objectivity, as always, remains the core of our mission.[21]
By January 2007, Google changed its indexing structure[2]so that Google bombs such as "miserable failure" would "typically return commentary, discussions, and articles" about the tactic itself.[2]Google announced the changes on its official blog. In response to criticism for allowing the Google bombs,Matt Cutts, head of Google's Webspam team, said that Google bombs had not "been a very high priority for us".[2][22]
Over time, we’ve seen more people assume that they are Google's opinion, or that Google has hand-coded the results for these Google-bombed queries. That's not true, and it seemed like it was worth trying to correct that misperception.[23]
In May 2004, the websites Dark Blue and SearchGuild teamed up to create what they termed the "SEO Challenge" to Google bomb the phrase "nigritude ultramarine".[24]
The contest sparked controversy around the Internet, as some groups worried thatsearch engine optimization(SEO) companies would abuse the techniques used in the competition to alter queries more relevant to the average user. This fear was offset by the belief thatGooglewould alter their algorithm based on the methods used by the Google bombers.
In September 2004, anotherSEO contestwas created. This time, the objective was to get the top result for the phrase "seraphim proudleduck". A large sum of money was offered to the winner, but the competition turned out to be a hoax.[citation needed]
In March 2005's issue of.netmagazine, a contest was created among five professional web developers to make their site the number-one site for the made-up phrase "crystalline incandescence".
Some of the most famous Google bombs are also expressions of political opinions (e.g. "liar" leading toTony Blairor "miserable failure" leading to the White House's biography of George W. Bush):
Some website operators have adapted Google bombing techniques to do "spamdexing". This includes, among other techniques, posting of links to a site in anInternet forumalong with phrases the promoter hopes to associate with the site (seespam in blogs). Unlike conventional message board spam, the object is not to attract readers to the site directly, but to increase the site's ranking under those search terms. Promoters using this technique frequently target forums with low reader traffic, in hopes that it will fly under the moderators' radar.Wikisin particular are often the target of this kind of page rank vandalism, as all of the pages are freely editable. This practice was also called "money bombing" byJohn Hilercirca 2004.[65][66]
Another technique is for the owner of an Internetdomain nameto set up the domain'sDNSentry so that allsubdomainsare directed to the same server. The operator then sets up the server so that page requests generate a page full of desired Google search terms, each linking to a subdomain of the same site, with the same title as the subdomain in the requestedURL. Frequently the subdomain matches the linked phrase, with spaces replaced byunderscoresorhyphens. Since Google treats subdomains as distinct sites, the effect of many subdomains linking to each other is a boost to thePageRankof those subdomains and of any other site they link to.
On February 2, 2007, many users noticed changes in the Google algorithm. These changes largely affected (among other things) Google bombs: as of February 15, 2007, only roughly 10% of the Google bombs still worked. This change was largely due to Google refactoring its valuation of PageRank.[citation needed][67][68]
Quixtar, amulti-level marketingcompany now known asAmway North America, has been accused by its critics of using its large network of websites to move sites critical of Quixtar lower in search engine rankings. A Quixtar/Amway independent business owner (IBO) reports that a Quixtar leader advocated the practice in a meeting of Quixtar IBOs. Quixtar/Amway denied wrongdoing and states that its practices are in accordance with search engine rules.[69]
On December 26, 2011, a bomb was started againstGoDaddyto remove them from the #1 place on Google for "domain registration" in retaliation for its support forSOPA.[70]This was then disseminated throughHacker News.[71]
In Australia, one of the first examples of Google bombs was when the keyword "old rice and monkey nuts" was used to generate traffic forHerald SuncolumnistAndrew Bolt's website. The keyword phrase references the alleged $4 billion in loan deals brokered byTirath Khemlanito Australia in 1974.[72]
In May 2019,David BenioffandD. B. Weisswere targets of multiple Google bombs caused byRedditusers' dissatisfaction with the eighth season of their showGame of Thrones. Targeted phrases included "bad writers" and "Dumb and Dumber".[73]
In Indonesia, PresidentJoko Widodowas target of Googlebombing on Google Picture Search when typing "Monyet Pakai Jas Hujan" (Monkey Wearing Raincoat) the results were President Joko Widodo wearing greenraincoatwhen on an official visit.[74]
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Themobile identification number(MIN) ormobile subscription identification number(MSIN) refers to the 10-digitunique number that awireless carrieruses to identify amobile phone, which is the last part of theinternational mobile subscriber identity(IMSI). The MIN is a number that uniquely identifies a mobile phone working under TIA standards for cellular andPCStechnologies (e.g. EIA/TIA–553 analog, IS–136 TDMA, IS–95 or IS-2000 CDMA). MIN usage became prevalent for mobile number portability to switch providers. It can also be called theMSID(Mobile Station ID) orIMSI_S(Short IMSI).
The mobile identification number (MIN) is a number that is derived from the 10-digit directorytelephone numberassigned to a mobile station. The rules for deriving the MIN from the 10-digit telephone number are given in theIS-95standard. MIN1 is the first or least significant 24 binary digits of the MIN. MIN2 is the second part of the MIN containing the 10 most significant binary digits. MIN1, and theESN, along with other digital input, are used during the authentication process. The MIN is used to identify a mobile station.
In the case ofanalog cellular, the MIN is used to route the call. In most second generation systems, temporary numbers are assigned to the handset when routing calls as a security precaution.
This article related totelecommunicationsis astub. You can help Wikipedia byexpanding it.
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Anoutput deviceis any piece ofcomputer hardwarethat converts information or data into a human-perceptible form or, historically, into a physical machine-readable form for use with other non-computerized equipment. It can be text, graphics, tactile, audio, or video. Examples includemonitors,printersandsound cards.
In an industrial setting, output devices also include "printers" for paper tape and punched cards, especially where the tape or cards are subsequently used to control industrial equipment, such as an industrial loom with electrical robotics which is not fully computerized
Adisplay deviceis the most common form of output device which presents output visually on computer screen. The output appears temporarily on the screen and can easily be altered or erased.
With all-in-one PCs, notebook computers, hand held PCs and other devices; the term display screen is used for the display device. The display devices are also used in home entertainment systems, mobile systems, cameras and video game systems.
Display devices form images by illuminating a desired configuration of . Raster display devices are organized in the form of a 2-dimensional matrix with rows and columns. This is done many times within a second, typically 60, 75, 120 or 144 Hz on consumer devices.
The interface between a computer'sCPUand the display is aGraphics Processing Unit(GPU). This processor is used to form images on aframebuffer. When the image is to be sent to the display, the GPU sends its image through avideo display controllerto generate avideo signal, which is then sent to adisplay interfacesuch asHDMI,VGA, orDVI
GPUs can be divided intodiscreteandintegratedunits, the former being an external unit and the latter of which is included within a CPU die.[1]Discrete graphics cards are almost always connected to the host through thePCI Expressbus, while older graphics cards may have usedAGPorPCI. Some mobile computers support an external graphics card throughThunderbolt(via PCIe).
A monitor is a standalone display commonly used with adesktop computer, or in conjunction to alaptopas an external display. The monitor is connected to the host through the use of a display cable, such asHDMI,DisplayPort,VGA, and more.
Older monitors useCRTtechnology, while modern monitors are typicallyflat panel displaysusing a plethora of technologies such asTFT-LCD,LED,OLED, and more.
Almost all mobile devices incorporate an internal display. These internal displays are connected to the computer through an internal display interface such asLVDSoreDP. The chief advantage of these displays is their portability.
Prior to the development of modern pixel-oriented displays,computer terminalswere used, composed of a character-oriented display device known as aVDUand acomputer keyboard.[2]
These terminals were often monochromatic, and could only display text. Rudimentary graphics could be displayed through the use ofASCII artalong withbox-drawing characters.Teleprinterswere the precursors to these devices.
A projector is a display that projects the computer image onto a surface through the use of a high power lamp. These displays are seen in use to show slideshow presentations or in movie screenings.[3]
Display technologies can be classified based on working principle, lighting (or lack thereof), pixel layout, and more.
A monochrome display is a type of CRT common in the early days ofcomputing, from the 1960s through the 1980s, before color monitors became popular.[4]
They are still widely used in applications such as computerized cash register systems. Green screen was the common name for a monochrome monitor using a green "P1" phosphor screen.
Color monitors, sometimes calledRGBmonitors, accept three separate signals (red, green, and blue), unlike a monochromatic display which accepts one. Color monitors implement the RGB color model by using three different phosphors that appear red, green, and blue when activated. By placing the phosphors directly next to each other, and activating them with different intensities, color monitors can create an unlimited number of colors. In practice, however, the real number of colors that any monitor can display is controlled by thevideo adapter.[5]
Aspeakeris an output device that produces sound through an oscillatingtransducercalled a driver. The equivalent input device is amicrophone.
Speakers are plugged into a computer'ssound cardvia a myriad of interfaces, such as aphone connectorfor analog audio, orSPDIFfor digital audio. While speakers can be connected through cables,wireless speakersare connected to the host device through radio technology such asBluetooth.
Speakers are most often used in pairs, which allows the speaker system to producepositional audio. When more than one pair is used, it is referred to assurround sound.
Certain models of computers includes a built-in speaker, which may sacrifice audio quality in favor of size. For example, the built-in speaker of a smartphone allows the users to listen to media without attaching an external speaker.
The interface between an auditory output device and a computer is thesound card. Sound cards may beincludedon a computer'smotherboard, installed as anexpansion card, or as adesktop unit.[6][7]
The sound card may offer either an analog ordigitaloutput. In the latter case, output is often transmitted usingSPDIFas either an electrical signal or anopticalinterface known asTOSLINK. Digital outputs are then decoded by anAV receiver.
In the case of wireless audio, the computer merely transmits aradio signal, and responsibility of decoding and output is shifted to the speaker.
While speakers can be used for any purpose, there arecomputer speakerswhich are built for computer use. These speakers are designed to sit on a desk, and as such, cannot be as large as conventional speakers.[8]
Computer speakers may be powered viaUSB, and are most often connected through a 3.5mm phone connector.
ThePC speakeris a simple loudspeaker built intoIBM PCcompatible computers. Unlike a speaker used with a sound card, the PC speaker is only meant to producesquare wavesto produce sounds such asbeeping.
Modern computers utilize apiezoelectric buzzeror a small speaker as the PC speaker.
PC speakers are used duringPower-on self-testto identify errors during the computer's boot process, without needing a video output device to be present and functional.
AStudio monitoris a speaker used in astudioenvironment. These speakers optimize for accuracy.[9]A monitor produces a flat (linear) frequency response which does not emphasize or de-emphasize of particular frequencies.
Headphones,earphones, andearpiecesare a kind of speaker which is supported either on the user's head, or the user's ear.
Unlike a speaker, headphones are not meant to be audible to people nearby, which suits them for use in thepublic,officeor other quiet environments.
Noise-cancelling headphonesare built withambient noise reductioncapabilities which may employactive noise cancelling.
Loudspeakers are composed of several components within anenclosure, such as severaldrivers,active amplifiers,crossovers, and other electronics. Multiple drivers are used to reproduce the full frequencyrange of human hearing, withtweetersproducing high pitches andwoofersproducing low pitches.Full-range speakersuse only one driver to produce as much of a frequency response as possible.[10]
WhileHi-Fispeakers attempt to produce high quality sound, computer speakers may compromise on these aspects due to their limited size and to be inexpensive, and the latter often uses full-range speakers as a result.[8]
Arefreshable braille displayoutputs braille characters through the use of pins raised out of holes on its surface. It is ordinarily used byvisually-impairedindividuals as an alternative to ascreen reader.[11]
Haptic technologyinvolves the use of vibration and other motion to induce a sense of touch.[12]Haptic technology was introduced in the late 1990s for use ingame controllers, to provide tactile feedback while a user is playing a video game. Haptic feedback has seen further uses in the automotive field,aircraft simulationsystems, andbrain-computer interfaces.[13][14]
In mobile devices,Appleadded haptic technology in various devices, marketed as 3D Touch andForce Touch. In this form, several devices could sense the amount of force exerted on its touchscreen, whileMacBookscould sense two levels of force on itstouchpad, which will produce a haptic sensation.[15]
Aprinteris a device that outputs data to be put on a physical item, usually a piece ofpaper. Printers operate by transferring ink onto this medium in the form of the image received from the host.
Early printers could only print text, but later developments allowed printing of graphics. Modern printers can receive data in multiple forms likevector graphics, as animage, a program written in apage description language, or a string of characters.
Multiple types of printers exist:
Aplotteris a type of printer used to printvector graphics. Instead of drawing pixels onto the printing medium, the plotter draws lines, which may be done with awriting implementsuch as a pencil or pen.[16]
Ateleprinterorteletypewriter(TTY) is a type of printer that is meant for sending and receiving messages. Before displays were used to display data visually, early computers would only have a teleprinter for use to access thesystem console. As the operator would enter commands into its keyboard, the teleprinter would output the results onto a piece of paper. The teleprinter would ultimately be succeeded by acomputer terminal, which had a display instead of a printer.
A computer can still function without an output device, as is commonly done withservers, where the primary interaction is typically over a data network. A number of protocols exist over serial ports or LAN cables to determine operational status, and to gain control over low-level configuration from a remote location without having a local display device. If the server is configured with a video output, it is often possible to connect a temporary display device for maintenance or administration purposes while the server continues to operate normally; sometimes several servers are multiplexed to a single display device though aKVM switchor equivalent.
Some methods to use remote systems are:
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Terminology extraction(also known astermextraction,glossaryextraction, termrecognition, or terminologymining) is a subtask ofinformation extraction. The goal of terminology extraction is to automatically extract relevant terms from a givencorpus.[1]
In thesemantic webera, a growing number of communities and networked enterprises started to access and interoperate through theinternet. Modeling these communities and their information needs is important for severalweb applications, like topic-drivenweb crawlers,[2]web services,[3]recommender systems,[4]etc. The development of terminology extraction is also essential to thelanguage industry.
One of the first steps to model aknowledge domainis to collect a vocabulary of domain-relevant terms, constituting the linguistic surface manifestation of domainconcepts. Several methods to automatically extract technical terms from domain-specific document warehouses have been described in the literature.[5][6][7][8][9][10][11][12][13][14][15][16][17]
Typically, approaches to automatic term extraction make use of linguistic processors (part of speech tagging,phrase chunking) to extract terminological candidates, i.e. syntactically plausible terminologicalnoun phrases. Noun phrases include compounds (e.g. "credit card"), adjective noun phrases (e.g. "local tourist information office"), and prepositional noun phrases (e.g. "board of directors"). In English, the first two (compounds and adjective noun phrases) are the most frequent.[18]Terminological entries are then filtered from the candidate list using statistical andmachine learningmethods. Once filtered, because of their low ambiguity and high specificity, these terms are particularly useful for conceptualizing a knowledge domain or for supporting the creation of adomain ontologyor a terminology base. Furthermore, terminology extraction is a very useful starting point forsemantic similarity,knowledge management,human translationandmachine translation, etc.
The methods for terminology extraction can be applied toparallel corpora. Combined with e.g.co-occurrencestatistics, candidates for term translations can be obtained.[19]Bilingual terminology can be extracted also from comparable corpora[20](corpora containing texts within the same text type, domain but not translations of documents between each other).
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Incontractlaw, anon-compete clause(oftenNCC),restrictive covenant, orcovenant not to compete(CNC), is a clause under which one party (usually an employee) agrees not to enter into or start a similar profession or trade in competition against another party (usually the employer). In thelabor market, these agreements prevent workers from freely moving across employers, and weaken the bargaining leverage of workers.[1]
Non-compete agreements are rooted in the medieval system ofapprenticeshipwhereby an older master craftsman took on a younger apprentice, trained the apprentice, and in some cases entered into an agreement whereby the apprentice could not compete with the master after the apprenticeship.[2]Modern uses of non-compete agreements are generally premised on preventing high-skilled workers from transferringtrade secretsor a customer list from one firm to a competing firm, thus giving the competing firm a competitive advantage.[1][2]However, many non-compete clauses apply to low-wage workers or individuals who do not possess transferable trade secrets.[2]
The extent to which non-compete clauses are legally allowed and enforced varies under different jurisdictions. Some localities and states ban non-compete clauses or highly restrict their applicability. In jurisdictions where non-compete agreements are legal, courts tend to evaluate whether a non-compete agreement covers a worker's move to a relevant industry and reasonable geographic area, as well as whether the former is still bound by the agreement over a reasonable time period. An employer bringing a lawsuit may also be asked to identify a protectable business interest that was harmed by the employee's move to a different firm.[2]
Research shows that non-compete agreements make labor markets less competitive, reduce wages and reduce labor mobility.[3][1]While non-compete agreements may incentivize company investment into their workers and research, they may also reduce innovation and productivity by employees who may be forced to leave a sector when they leave a firm.[4][5]The labor movementtends to advocate for restrictions on non-compete agreements while support for non-compete agreements is common among some employers and business associations.
As far back asDyer's Casein 1414, Englishcommon lawchose not to enforce non-compete agreements because of their nature asrestraints on trade.[6]That ban remained unchanged until 1621, when a restriction that was limited to a specific geographic location was found to be an enforceable exception to the previously absolute rule. Almost a hundred years later, the exception became the rule with the 1711 watershed case ofMitchel v Reynolds[7]whichestablished the modern frameworkfor the analysis of the enforceability of non-compete agreements.[8]
Traditionally, non-competes were used to prevent high-skilled workers from transferringtrade secretsor a customer list from one firm to a competing firm.[1][2]However, such clauses can frequently be found in the contracts of low-wage workers and other workers who are unlikely to be in a position to share trade secrets.[2]
When courts consider the enforceability of non-compete agreements, they usually ask the employer to identify a protectable business interest that was harmed by the employee's move to a different firm. Courts consider whether the non-compete covers a relevant industry (does the worker do work for a firm in the same industry?), reasonable geographic area, and reasonable time period.[2]
University of Chicago Law School Professor Eric A. Posner has argued that since non-competes have an adverse impact on competition, they should be covered under a strong anti-trust regime, and the "law should treat noncompetes as presumptively illegal, allowing employers to rebut the presumption if they can prove that the noncompetes they use will benefit rather than harm their workers."[2]
In April, 2024, theFederal Trade Commission(FTC) banned all non compete agreements in the United States.[9]Within a few days, business groups including the U.S. Chamber of Commerce sued to block the new rule.[10]
Studies show that non-compete agreements make labor markets less competitive, reduce wages and reduce labor mobility.[3][1]Existing evidence suggests that the wage suppressing effects of non-competes are disproportionately concentrated on lower-income workers.[1]Non-compete agreements can incentivize firms to increase investment into worker training and research, as those workers are less likely to leave the firm.[1]Non-competes may reduce overall hiring costs and employee turnover for companies, which may result in savings that could in theory be passed on to customers in the form of lower prices and to investors as higher returns.[2]
Non-competes are more common for technical, high-wage workers and more likely to be enforced for those workers. However, even when non-compete agreements are unlikely to be enforced (such as for individual low-wage workers or in states that do not enforce these agreements), the agreements may still have an intimidating impact on those workers.[3][11]
A 2021 study of theU.S. health caresector from 1996–2007 found that noncompete agreements in this sector led to higher prices for physicians, smaller medical practices and greater medical firmconcentration.[12]
A 2021 study found that noncompete agreements for low-wage workers have been shown to lower wages; a study determined that the 2008 Oregon ban on noncompete agreements for workers paid by the hour "increased hourly wages by 2%–3% on average."[13]The study also showed that the Oregon ban on noncompete agreements for low-wage workers "improved averageoccupational statusin Oregon,raised job-to-job mobility, and increased the proportion of salaried workers without affecting hours worked."[13]
Studies have found that non-compete agreements can prompt technical workers to involuntarily leave their technical field to avoid a potential lawsuit from their former employer.[4][5]For this reason, non-compete agreements have been linked to less innovation and lower productivity as inventors switch fields in order to avoid violating non-competes.[5]
InBelgium, CNCs are restricted to new employments within Belgium and for no more than one year. The employer must pay financial compensation for the duration of the CNC, amounting at least half of the gross salary for the corresponding period.[14]
Canadiancourts will enforce non-competition andnon-solicitation agreements; however, the agreement must be limited in time frame, business scope, and geographic scope to what is reasonably required to protect the company's proprietary rights, such as confidential marketing information or client relations[15]and the scope of the agreement must be unambiguously defined. The 2009Supreme Court of CanadacaseShafron v. KRG Insurance Brokers (Western) Inc. 2009 SCC 6held a non-compete agreement to be invalid due to the term "Metropolitan City of Vancouver" not being legally defined.[16]
In 2021, employees in Ontario may no longer enter into non-compete agreements. There are exceptions for when a business is sold, and for chief officers (such asCEOs,CFOs, etc.).[17]
InFrance, CNCs must be limited in time to a maximum of two years and to a region where the employee's new work can reasonably be seen as competitive. The region can be a city or the whole country, depending on the circumstances. The employer must pay financial compensation, typically 30 percent of the previous salary.[18]A CNC may not unreasonably limit the possibilities of the employee to find new employment.
InGermany, CNCs are allowed for a term up to two years. The employer must provide financial compensation for the duration of the CNC amounting to at least half the gross salary.[19]Unreasonable clauses – for example, excluding similar jobs throughout the whole of Germany – can be invalidated.
Section 27 of theIndian Contract Acthas a general bar on any agreement that puts a restriction on trade.[20]The Supreme Court of India has clarified that some non-compete clauses—specifically, those backed by a clear objective that is considered to be in advantage of trade and commerce—are not barred by Section 27 of the Contract Act, and therefore valid in India.[21]
Non-compete agreements are prevalent in Italy.[22]InItaly, CNCs are regulated by articles 2125, 2596, and 1751 bis of the civil code.
In theNetherlands, non-compete clauses (non-concurrentiebedingorconcurrentiebeding) are allowed regarding issues such as moving to a new employer and approaching customers of the old company. Unreasonable clauses can be invalidated in court.[23]
According to Section 27 of the Contract Act, 1872, any agreement that restrains a person from exercising a lawful profession, trade or business is void.[24]However, courts of Pakistan have made decisions in the past in favour of such restrictive clauses given that the restrictions are "reasonable".[25]The definition of "reasonable" depends on the time-period, geographical location and the designation of employee. In the case ofExide Pakistan Limited vs. Abdul Wadood, 2008 CLD 1258 (Karachi), the High Court of Sindh stated that reasonableness of the clause will vary from case to case and depends mainly on duration and extent of geographical territory[26]
InPortugal, CNCs are regulated by article 136 of the labor code and restricted to two years extendible to three years in cases of access to particularly sensitive information. The employer must pay financial compensation for the duration of the CNC, but the law does not specify anything regarding the amount of the compensation.[27]
InRomania, CNCs are regulated by articles 21–24 of the labor code and restricted to two years. The employer must pay financial compensation for the duration of the CNC, amounting to at least 50 percent of the last 6 months salary.
InSpain, CNCs are regulated by article 21 of the labor law. CNCs are allowed up to two years for technical professions and six months for other professions, given that adequate compensation is given.
In theUnited Kingdom, CNCs are often calledrestraint of tradeor restrictive covenant clauses, and may be used only if the employer can prove a legitimate business interest to protect in entering the clause into the contract. Mere competition will not amount to a legitimate business interest.[28]The UK's regulator, theCompetition and Markets Authority, advises that non-compete clauses are a form of employer collusion and are a form of a business cartel.[29]
Restrictions are normally limited in duration, geographical area (an "area covenant"),[30]and content.[31]
In theCrown dependencies, many financial and other institutions require employees to sign 10-year or longer CNCs which could be seen to apply even if they leave the country or enter an unrelated field of work.[citation needed]
In May 2023, the UK Government announced plans to limit non-compete clauses to a maximum of three months.[32]
The majority of American states recognize and enforce various forms of non-compete agreements. A few states, such as California,North Dakota, andOklahoma, totally ban noncompete agreements for employees, or prohibit all noncompete agreements except in limited circumstances.[33]
Data from 2018 indicates that non-compete clauses cover 18 percent of Americanlabor force participants.[34]A 2023 petition to the FTC to ban non-compete agreements estimated that about 30 million workers (about 20% of all U.S. workers) were subject to a noncompete clause.[35]While higher-wage workers are comparatively more likely to be covered by non-compete clauses, non-competes covered 14 percent of workers without college degrees in 2018.[36]By some estimates, nearly half of all technical workers are covered by non-compete agreements.[4]
In March 2019, Democratic officials, labor unions, and workers' advocacy groups urged the U.S. FTC to ban non-compete clauses. A petition to the FTC, seeking a ban on noncompete clauses, was submitted by theAFL-CIO,SEIU, andPublic Citizen.[35]In July 2021, President Joe Biden signedExecutive Order 14036, directing the FTC (whose chair,Lina Khan, he had recently appointed), as well as other federal agencies, to "curtail the unfair use of non-compete clauses and other clauses or agreements that may unfairly limit worker mobility". On January 5, 2023, the FTC proposed a rule banning non-compete agreements.[37]
TheU.S. Chamber of Commercehas lobbied against bans on non-compete agreements; in 2023, it threatened to sue the FTC if it bans non-compete agreements.[38]The Chamber argued that "noncompete agreements are an important tool in fostering innovation and preserving competition".[38]
On April 23, 2024, theFederal Trade Commission(FTC) issued a ban on nearly all non-compete agreements.[39][40]The rule was published on theFederal Registeron May 7 and was to go into effect on September 4, 2024.[41]
The FTC found as shown the use of non-compete clauses by employers has negatively affected competition in labor markets, resulting in reduced wages for workers across the labor force—including workers not bound by non-compete clauses[42]and that by suppressing labor mobility, non-compete clauses have negatively affected competition in product and service markets in several ways.[43]The commission noted that the existing legal frameworks governing non-compete clauses—formed decades ago, without the benefit of this evidence—allow serious anticompetitive harm to labor, product, and service markets to go unchecked.[43]The Commission noted "that instead of using noncompetes to lock in workers, employers that wish to retain employees can compete on the merits for the worker's labor services by improving wages and working conditions."[44]In 2024, approximately one in five American workers, or about 30 million people, are subject to noncompetes.[44]
On August 20, 2024, JudgeAda Brownof theDistrict Court for the Northern District of Texasissued an injunction blocking the rule, ruling that the FTC "lacks statutory authority to promulgate the Non-Compete Rule, and that the Rule is arbitrary and capricious."[45][46]
While CNCs are one of the most common types of restrictive covenants, there are many others. Each serves a specific purpose and provides specific rights and remedies. The most common types of restrictive covenants are as follows:
The enforceability of these agreements depends on the law of the particular state. As a general rule, however, with the exception of invention assignment agreements, they are subject to the same analysis as other CNCs.[47]
No-poaching agreementsbetween employers are typically considered illegalanti-competitivecollusion. (See for exampleHigh-Tech Employee Antitrust Litigationconcerning Silicon Valley employers in the 2000s.)
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Pruningis adata compressiontechnique inmachine learningandsearch algorithmsthat reduces the size ofdecision treesby removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the finalclassifier, and hence improves predictive accuracy by the reduction ofoverfitting.
One of the questions that arises in a decision tree algorithm is the optimal size of the final tree. A tree that is too large risksoverfittingthe training data and poorly generalizing to new samples. A small tree might not capture important structural information about the sample space. However, it is hard to tell when a tree algorithm should stop because it is impossible to tell if the addition of a single extra node will dramatically decrease error. This problem is known as thehorizon effect. A common strategy is to grow the tree until each node contains a small number of instances then use pruning to remove nodes that do not provide additional information.[1]
Pruning should reduce the size of a learning tree without reducing predictive accuracy as measured by across-validationset. There are many techniques for tree pruning that differ in the measurement that is used to optimize performance.
Pruning processes can be divided into two types (pre- and post-pruning).
Pre-pruningprocedures prevent a complete induction of the training set by replacing a stop () criterion in the induction algorithm (e.g. max. Tree depth or information gain (Attr)> minGain). Pre-pruning methods are considered to be more efficient because they do not induce an entire set, but rather trees remain small from the start. Prepruning methods share a common problem, the horizon effect. This is to be understood as the undesired premature termination of the induction by the stop () criterion.
Post-pruning(or just pruning) is the most common way of simplifying trees. Here, nodes and subtrees are replaced with leaves to reduce complexity. Pruning can not only significantly reduce the size but also improve the classification accuracy of unseen objects. It may be the case that the accuracy of the assignment on the train set deteriorates, but the accuracy of the classification properties of the tree increases overall.
The procedures are differentiated on the basis of their approach in the tree (top-down or bottom-up).
These procedures start at the last node in the tree (the lowest point). Following recursively upwards, they determine the relevance of each individual node. If the relevance for the classification is not given, the node is dropped or replaced by a leaf. The advantage is that no relevant sub-trees can be lost with this method.
These methods include Reduced Error Pruning (REP), Minimum Cost Complexity Pruning (MCCP), or Minimum Error Pruning (MEP).
In contrast to the bottom-up method, this method starts at the root of the tree. Following the structure below, a relevance check is carried out which decides whether a node is relevant for the classification of all n items or not. By pruning the tree at an inner node, it can happen that an entire sub-tree (regardless of its relevance) is dropped. One of these representatives is pessimistic error pruning (PEP), which brings quite good results with unseen items.
One of the simplest forms of pruning is reduced error pruning. Starting at the leaves, each node is replaced with its most popular class. If the prediction accuracy is not affected then the change is kept. While somewhat naive, reduced error pruning has the advantage ofsimplicity and speed.
Cost complexity pruning generates a series of treesT0…Tm{\displaystyle T_{0}\dots T_{m}}whereT0{\displaystyle T_{0}}is the initial tree andTm{\displaystyle T_{m}}is the root alone. At stepi{\displaystyle i}, the tree is created by removing a subtree from treei−1{\displaystyle i-1}and replacing it with a leaf node with value chosen as in the tree building algorithm. The subtree that is removed is chosen as follows:
The functionprune(T,t){\displaystyle \operatorname {prune} (T,t)}defines the tree obtained by pruning the subtreest{\displaystyle t}from the treeT{\displaystyle T}. Once the series of trees has been created, the best tree is chosen by generalized accuracy as measured by a training set or cross-validation.
Pruning could be applied in acompression schemeof a learning algorithm to remove the redundant details without compromising the model's performances. In neural networks, pruning removes entire neurons or layers of neurons.
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XOR gate(sometimesEOR, orEXORand pronounced asExclusive OR) is a digitallogic gatethat gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements anexclusive or(↮{\displaystyle \nleftrightarrow }) frommathematical logic; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "must have one or the other but not both".
An XOR gate may serve as a "programmable inverter" in which one input determines whether to invert the other input, or to simply pass it along with no change. Hence it functions as ainverter(a NOT gate) which may be activated or deactivated by a switch.[1][2]
XOR can also be viewed as additionmodulo2. As a result, XOR gates are used to implement binary addition in computers. Ahalf adderconsists of an XOR gate and anAND gate. The gate is also used insubtractorsandcomparators.[3]
Thealgebraic expressionsA⋅B¯+A¯⋅B{\displaystyle A\cdot {\overline {B}}+{\overline {A}}\cdot B}or(A+B)⋅(A¯+B¯){\displaystyle (A+B)\cdot ({\overline {A}}+{\overline {B}})}or(A+B)⋅(A⋅B)¯{\displaystyle (A+B)\cdot {\overline {(A\cdot B)}}}orA⊕B{\displaystyle A\oplus B}all represent the XOR gate with inputsAandB. The behavior of XOR is summarized in thetruth tableshown on the right.
There are three schematic symbols for XOR gates: the traditional ANSI and DIN symbols and theIECsymbol. In some cases, the DIN symbol is used with ⊕ instead of ≢. For more information seeLogic Gate Symbols.
The "=1" on the IEC symbol indicates that the output is activated by only one active input.
Thelogic symbols⊕,Jpq, and ⊻ can be used to denote an XOR operation in algebraic expressions.
C-like languagesuse thecaretsymbol^to denote bitwise XOR. (Note that the caret does not denotelogical conjunction(AND) in these languages, despite the similarity of symbol.)
The XOR gate is most commonly implemented usingMOSFETscircuits. Some of those implementations include:
XOR gates can be implemented using AND-OR-Invert (AOI) or OR-AND-Invert (OAI) logic.[4]
The metal–oxide–semiconductor (CMOS) implementations of the XOR gate corresponding to the AOI logic above
are shown below.
On the left, thenMOSandpMOStransistors are arranged so that the input pairsA⋅B¯{\displaystyle A\cdot {\overline {B}}}andA¯⋅B{\displaystyle {\overline {A}}\cdot B}activate the 2 pMOS transistors of the top left or the 2 pMOS transistors of the top right respectively, connecting Vdd to the output for a logic high. The remaining input pairsA⋅B{\displaystyle A\cdot B}andA¯⋅B¯{\displaystyle {\overline {A}}\cdot {\overline {B}}}activate each one of the two nMOS paths in the bottom to Vss for a logic low.[5]
If inverted inputs (for example from aflip-flop) are available, this gate can be used directly. Otherwise, two additional inverters with two transistors each are needed to generateA¯{\displaystyle {\overline {A}}}andB¯{\displaystyle {\overline {B}}}, bringing the total number of transistors to twelve.
The AOI implementation without inverted input has been used, for example, in theIntel 386CPU.[6]
The XOR gate can also be implemented through the use oftransmission gateswithpass transistor logic.
This implementation uses two Transmission gates and two inverters not shown in the diagram to generateA¯{\displaystyle {\overline {A}}}andB¯{\displaystyle {\overline {B}}}for a total of eight transistors, four less than in the previous design.
The XOR function is implemented by passing through to the output the inverted value of A when B is high and passing the value of A when B is at a logic low. so when both inputs are low the transmission gate at the bottom is off and the one at the top is on and lets A through which is low so the output is low. When both are high only the one at the bottom is active and lets the inverted value of A through and since A is high the output will again be low. Similarly if B stays high but A is low the output would beA¯{\displaystyle {\overline {A}}}which is high as expected and if B is low but A is high the value of A passes through and the output is high completing the truth table for the XOR gate.[7]
The trade-off with the previous implementation is that since transmission gates are not ideal switches, there is resistance associated with them, so depending on the signal strength of the input, cascading them may degrade the output levels.[8]
The previous transmission gate implementation can be further optimized from eight to six transistors by implementing the functionality of the inverter that generatesA¯{\displaystyle {\overline {A}}}and the bottom pass-gate with just two transistors arranged like an inverter but with the source of the pMOS connected toB{\displaystyle B}instead ofVddand the source of the nMOS connected toB¯{\displaystyle {\overline {B}}}instead of GND.[8]
The two leftmost transistors mentioned above, perform an optimized conditional inversion of A when B is at a logic high using pass transistor logic to reduce the transistor count and when B is at a logic low, their output is at a high impedance state. The two in the middle are atransmission gatethat drives the output to the value of A when B is at a logic low and the two rightmost transistors form an inverter needed to generateB¯{\displaystyle {\overline {B}}}used by the transmission gate and the pass transistor logic circuit.[9]
As with the previous implementation, the direct connection of the inputs to the outputs through the pass gate transistors or through the two leftmost transistors, should be taken into account, especially when cascading them.</ref>
Replacing the second NOR with a normalOR Gatewill create anXNOR Gate.[8]
If a specific type of gate is not available, a circuit that implements the same function can be constructed from other available gates. A circuit implementing an XOR function can be trivially constructed from anXNOR gatefollowed by aNOT gate. If we consider the expression(A⋅B¯)+(A¯⋅B){\displaystyle (A\cdot {\overline {B}})+({\overline {A}}\cdot B)}, we can construct an XOR gate circuit directly using AND, OR andNOT gates. However, this approach requires five gates of three different kinds.
As alternative, if different gates are available we can applyBoolean algebrato transform(A⋅B¯)+(A¯⋅B)≡(A+B)⋅(A¯+B¯){\displaystyle (A\cdot {\overline {B}})+({\overline {A}}\cdot B)\equiv (A+B)\cdot ({\overline {A}}+{\overline {B}})}as stated above, and applyde Morgan's lawto the last term to get(A+B)⋅(A⋅B)¯{\displaystyle (A+B)\cdot {\overline {(A\cdot B)}}}which can be implemented using only four gates as shown on the right. intuitively, XOR is equivalent to OR except for when both A and B are high. So the AND of the OR with then NAND that gives a low only when both A and B are high is equivalent to the XOR.
An XOR gate circuit can be made from fourNAND gates. In fact, both NAND andNOR gatesare so-called "universal gates" and any logical function can be constructed from eitherNAND logicorNOR logicalone. If the fourNAND gatesare replaced byNOR gates, this results in anXNOR gate, which can be converted to an XOR gate by inverting the output or one of the inputs (e.g. with a fifthNOR gate).
An alternative arrangement is of fiveNOR gatesin a topology that emphasizes the construction of the function from(A+B)⋅(A¯+B¯){\displaystyle (A+B)\cdot ({\overline {A}}+{\overline {B}})}, noting fromde Morgan's Lawthat aNOR gateis an inverted-inputAND gate. Another alternative arrangement is of fiveNAND gatesin a topology that emphasizes the construction of the function from(A⋅B¯)+(A¯⋅B){\displaystyle (A\cdot {\overline {B}})+({\overline {A}}\cdot B)}, noting fromde Morgan's Lawthat aNAND gateis an inverted-inputOR gate.
For the NAND constructions, the upper arrangement requires fewer gates. For the NOR constructions, the lower arrangement offers the advantage of a shorter propagation delay (the time delay between an input changing and the output changing).
XOR chips are readily available. The most common standard chip codes are:
Literal interpretation of the name "exclusive or", or observation of the IEC rectangular symbol, raises the question of correct behaviour with additional inputs.[12]If a logic gate were to accept three or more inputs and produce a true output if exactly one of those inputs were true, then it would in effect be aone-hotdetector (and indeed this is the case for only two inputs). However, it is rarely implemented this way in practice.
It is most common to regard subsequent inputs as being applied through a cascade of binary exclusive-or operations: the first two signals are fed into an XOR gate, then the output of that gate is fed into a second XOR gate together with the third signal, and so on for any remaining signals. The result is a circuit that outputs a 1 when the number of 1s at its inputs is odd, and a 0 when the number of incoming 1s is even. This makes it practically useful as aparity generatoror a modulo-2adder.
For example, the74LVC1G386microchip is advertised as a three-input logic gate, and implements a parity generator.[13]
XOR gates and AND gates are the two most-used structures inVLSIapplications.[14]
The XOR logic gate can be used as a one-bitadderthat adds any two bits together to output one bit. For example, if we add1plus1inbinary, we expect a two-bit answer,10(i.e.2in decimal). Since the trailingsumbit in this output is achieved with XOR, the precedingcarrybit is calculated with anAND gate. This is the main principle inHalf Adders. A slightly largerFull Addercircuit may be chained together in order to add longer binary numbers.
In certain situations, the inputs to an OR gate (for example, in a full-adder) or to an XOR gate can never be both 1's. As this is the only combination for which the OR and XOR gate outputs differ, anOR gatemay be replaced by an XOR gate (or vice versa) without altering the resulting logic. This is convenient if the circuit is being implemented using simple integrated circuit chips which contain only one gate type per chip.
Pseudo-random number (PRN) generators, specificallylinear-feedback shift registers(LFSR), are defined in terms of the exclusive-or operation. Hence, a suitable setup of XOR gates can model a linear-feedback shift register, in order to generate random numbers.
XOR gates may be used in simplestphase detectors.[15]: 425
An XOR gate may be used to easily change between buffering or inverting a signal. For example, XOR gates can be added to the output of aseven-segment displaydecoder circuitto allow a user to choose between active-low or active-high output.
XOR gates produce a0when both inputs match. When searching for a specific bit pattern or PRN sequence in a very long data sequence, a series of XOR gates can be used to compare a string of bits from the data sequence against the target sequence in parallel. The number of0outputs can then be counted to determine how well the data sequence matches the target sequence. Correlators are used in many communications devices such asCDMAreceivers and decoders for error correction and channel codes. In a CDMA receiver, correlators are used to extract the polarity of a specific PRN sequence out of a combined collection of PRN sequences.
A correlator looking for11010in the data sequence1110100101would compare the incoming data bits against the target sequence at every possible offset while counting the number of matches (zeros):
In this example, the best match occurs when the target sequence is offset by 1 bit and all five bits match. When offset by 5 bits, the sequence exactly matches its inverse. By looking at the difference between the number of ones and zeros that come out of the bank of XOR gates, it is easy to see where the sequence occurs and whether or not it is inverted. Longer sequences are easier to detect than short sequences.
f(a,b)=a+b−2ab{\displaystyle f(a,b)=a+b-2ab}is an analytical representation of XOR gate:
f(a,b)=|a−b|{\displaystyle f(a,b)=|a-b|}is an alternative analytical representation.
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Inprintingandpublishing,proofsare the preliminary versions of publications meant for review by authors, editors, and proofreaders, often with extra-wide margins.Galley proofsmay be uncut andunbound, or in some caseselectronically transmitted. They are created forproofreadingandcopyeditingpurposes, but may also be used for promotional and review purposes.[1][2][3]
Proof, in thetypographicalsense, is a term that dates to around 1600.[4]The primary goal of proofing is to create a tool for verification that the job is accurate separate from the pages produced on the press. All needed or suggested changes are physically marked on paper proofs or electronically marked on electronic proofs by the author, editor, and proofreaders. Thecompositor, typesetter, or printer receives the edited copies, corrects and re-arranges the type or the pagination, and arranges for the press workers to print the final or published copies.
Galley proofsorgalleysare so named because in the days of hand-setletterpress printingin the 1650s, the printer would set the page into "galleys", metal trays into which type was laid and tightened into place.[5]A small proof press would then be used to print a limited number of copies forproofreading.[5]Galley proofs are thus, historically speaking, galleys printed on a proof press.
From the printer's point of view, the galley proof, as it originated during the era of hand-set physical type, had two primary purposes, those being to check that the compositor had set the copy accurately (because sometimes individual pieces of type did get put in the wrong case after use) and that the type was free of defects (because type metal is comparatively soft, so type can get damaged).
Once a defect-free galley proof was produced, the publishing house requested a number of galley proofs to be run off for distribution to editors and authors for a final reading and corrections to the text before the type was fixed in the case for printing.
An uncorrected proof is a proof version (on paper or in digital form) which is yet to receive final author and publisher approval. The term may also appear on the covers of advance reading copies; see below.
These days, because much typesetting and pre-press work is conducted digitally and transmitted electronically, the term uncorrected proof is more common than the older term galley proof, which refers exclusively to a paper proofing system. However, if a paper print-out of an uncorrected proof is made on a desk-top printer or copy machine and used as a paper proof for authorial or editorial mark-up, it approximates a galley proof, and it may be referred to as a galley.
Preliminary electronic proof versions are also sometimes calleddigital proofs,PDF proofs, andpre-fascicleproofs, the last because they are viewed as single pages, not as they will look when gathered into fascicles orsignaturesfor the press.[6]
Proofs created by the printer for approval by the publisher before going to press are calledfinal proofs. At this stage in production, all mistakes are supposed to have been corrected and the pages are set up in imposition for folding and cutting on the press. To correct a mistake at this stage entails an extra cost per page, so authors are discouraged from making many changes to final proofs, while last-minute corrections by the in-house publishing staff may be accepted.
In the final proof stage, page layouts are examined closely. Additionally, because final page proofs contain the finalpagination, if an index was not compiled at an earlier stage in production, this pagination facilitates compiling a book'sindexand correcting its table of contents.
Historically, some publishers have used paper galley proofs asadvance copies or advance reading copies(ARCs) or as pre-publication publicity proofs. These are provided to reviewers, magazines, and libraries in advance of final publication. These galleys are not sent out for correction, but to ensure timely reviews of newly published works. The list of recipients designated by the publisher limits the number of copies to only what is required, making advance copies a form ofprint-on-demand(POD) publication.
Pre-publication publicity proofs are normally gathered and bound in paper, but in the case of books with four-color printed illustrations, publicity proofs may be lacking illustrations or have them in black and white only.[citation needed]They may be marked or stamped on the cover "uncorrected proof", but the recipient is not expected to proofread them, merely to overlook any minor errors of typesetting.
Galley proofs in electronic form are rarely used as advance reading copies due to the possibility of a recipient editing the proof and issuing it as their own. However, trusted colleagues are occasionally offered electronic advance reading copies, especially if the publisher wishes to quickly typeset a page or two of "advance praise" notices within the book itself.
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Cryptography, orcryptology(fromAncient Greek:κρυπτός,romanized:kryptós"hidden, secret"; andγράφεινgraphein, "to write", or-λογία-logia, "study", respectively[1]), is the practice and study of techniques forsecure communicationin the presence ofadversarialbehavior.[2]More generally, cryptography is about constructing and analyzingprotocolsthat prevent third parties or the public from reading private messages.[3]Modern cryptography exists at the intersection of the disciplines of mathematics,computer science,information security,electrical engineering,digital signal processing, physics, and others.[4]Core concepts related toinformation security(data confidentiality,data integrity,authentication, andnon-repudiation) are also central to cryptography.[5]Practical applications of cryptography includeelectronic commerce,chip-based payment cards,digital currencies,computer passwords, andmilitary communications.
Cryptography prior to the modern age was effectively synonymous withencryption, converting readable information (plaintext) to unintelligiblenonsensetext (ciphertext), which can only be read by reversing the process (decryption). The sender of an encrypted (coded) message shares the decryption (decoding) technique only with the intended recipients to preclude access from adversaries. The cryptography literatureoften uses the names"Alice" (or "A") for the sender, "Bob" (or "B") for the intended recipient, and "Eve" (or "E") for theeavesdroppingadversary.[6]Since the development ofrotor cipher machinesinWorld War Iand the advent of computers inWorld War II, cryptography methods have become increasingly complex and their applications more varied.
Modern cryptography is heavily based onmathematical theoryand computer science practice; cryptographicalgorithmsare designed aroundcomputational hardness assumptions, making such algorithms hard to break in actual practice by any adversary. While it is theoretically possible to break into a well-designed system, it is infeasible in actual practice to do so. Such schemes, if well designed, are therefore termed "computationally secure". Theoretical advances (e.g., improvements ininteger factorizationalgorithms) and faster computing technology require these designs to be continually reevaluated and, if necessary, adapted.Information-theoretically secureschemes that provably cannot be broken even with unlimited computing power, such as theone-time pad, are much more difficult to use in practice than the best theoretically breakable but computationally secure schemes.
The growth of cryptographic technology has raiseda number of legal issuesin theInformation Age. Cryptography's potential for use as a tool for espionage andseditionhas led many governments to classify it as a weapon and to limit or even prohibit its use and export.[7]In some jurisdictions where the use of cryptography is legal, laws permit investigators tocompel the disclosureofencryption keysfor documents relevant to an investigation.[8][9]Cryptography also plays a major role indigital rights managementandcopyright infringementdisputes with regard todigital media.[10]
The first use of the term "cryptograph" (as opposed to "cryptogram") dates back to the 19th century—originating from "The Gold-Bug", a story byEdgar Allan Poe.[11][12]
Until modern times, cryptography referred almost exclusively to "encryption", which is the process of converting ordinary information (calledplaintext) into an unintelligible form (calledciphertext).[13]Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. Acipher(or cypher) is a pair of algorithms that carry out the encryption and the reversing decryption. The detailed operation of a cipher is controlled both by the algorithm and, in each instance, by a "key". The key is a secret (ideally known only to the communicants), usually a string of characters (ideally short so it can be remembered by the user), which is needed to decrypt the ciphertext. In formal mathematical terms, a "cryptosystem" is the ordered list of elements of finite possible plaintexts, finite possible cyphertexts, finite possible keys, and the encryption and decryption algorithms that correspond to each key. Keys are important both formally and in actual practice, as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore useless (or even counter-productive) for most purposes. Historically, ciphers were often used directly for encryption or decryption without additional procedures such asauthenticationor integrity checks.
There are two main types of cryptosystems:symmetricandasymmetric. In symmetric systems, the only ones known until the 1970s, the same secret key encrypts and decrypts a message. Data manipulation in symmetric systems is significantly faster than in asymmetric systems. Asymmetric systems use a "public key" to encrypt a message and a related "private key" to decrypt it. The advantage of asymmetric systems is that the public key can be freely published, allowing parties to establish secure communication without having a shared secret key. In practice, asymmetric systems are used to first exchange a secret key, and then secure communication proceeds via a more efficient symmetric system using that key.[14]Examples of asymmetric systems includeDiffie–Hellman key exchange, RSA (Rivest–Shamir–Adleman), ECC (Elliptic Curve Cryptography), andPost-quantum cryptography. Secure symmetric algorithms include the commonly used AES (Advanced Encryption Standard) which replaced the older DES (Data Encryption Standard).[15]Insecure symmetric algorithms include children's language tangling schemes such asPig Latinor othercant, and all historical cryptographic schemes, however seriously intended, prior to the invention of theone-time padearly in the 20th century.
Incolloquialuse, the term "code" is often used to mean any method of encryption or concealment of meaning. However, in cryptography, code has a more specific meaning: the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with acode word(for example, "wallaby" replaces "attack at dawn"). A cypher, in contrast, is a scheme for changing or substituting an element below such a level (a letter, a syllable, or a pair of letters, etc.) to produce a cyphertext.
Cryptanalysisis the term used for the study of methods for obtaining the meaning of encrypted information without access to the key normally required to do so; i.e., it is the study of how to "crack" encryption algorithms or their implementations.
Some use the terms "cryptography" and "cryptology" interchangeably in English,[16]while others (including US military practice generally) use "cryptography" to refer specifically to the use and practice of cryptographic techniques and "cryptology" to refer to the combined study of cryptography and cryptanalysis.[17][18]English is more flexible than several other languages in which "cryptology" (done by cryptologists) is always used in the second sense above.RFC2828advises thatsteganographyis sometimes included in cryptology.[19]
The study of characteristics of languages that have some application in cryptography or cryptology (e.g. frequency data, letter combinations, universal patterns, etc.) is calledcryptolinguistics. Cryptolingusitics is especially used in military intelligence applications for deciphering foreign communications.[20][21]
Before the modern era, cryptography focused on message confidentiality (i.e., encryption)—conversion ofmessagesfrom a comprehensible form into an incomprehensible one and back again at the other end, rendering it unreadable by interceptors oreavesdropperswithout secret knowledge (namely the key needed for decryption of that message). Encryption attempted to ensuresecrecyin communications, such as those ofspies, military leaders, and diplomats. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication,digital signatures,interactive proofsandsecure computation, among others.
The main classical cipher types aretransposition ciphers, which rearrange the order of letters in a message (e.g., 'hello world' becomes 'ehlol owrdl' in a trivially simple rearrangement scheme), andsubstitution ciphers, which systematically replace letters or groups of letters with other letters or groups of letters (e.g., 'fly at once' becomes 'gmz bu podf' by replacing each letter with the one following it in theLatin alphabet).[22]Simple versions of either have never offered much confidentiality from enterprising opponents. An early substitution cipher was theCaesar cipher, in which each letter in the plaintext was replaced by a letter three positions further down the alphabet.[23]Suetoniusreports thatJulius Caesarused it with a shift of three to communicate with his generals.Atbashis an example of an early Hebrew cipher. The earliest known use of cryptography is some carved ciphertext on stone inEgypt(c.1900 BCE), but this may have been done for the amusement of literate observers rather than as a way of concealing information.
TheGreeks of Classical timesare said to have known of ciphers (e.g., thescytaletransposition cipher claimed to have been used by theSpartanmilitary).[24]Steganography(i.e., hiding even the existence of a message so as to keep it confidential) was also first developed in ancient times. An early example, fromHerodotus, was a message tattooed on a slave's shaved head and concealed under the regrown hair.[13]Other steganography methods involve 'hiding in plain sight,' such as using amusic cipherto disguise an encrypted message within a regular piece of sheet music. More modern examples of steganography include the use ofinvisible ink,microdots, anddigital watermarksto conceal information.
In India, the 2000-year-oldKama SutraofVātsyāyanaspeaks of two different kinds of ciphers called Kautiliyam and Mulavediya. In the Kautiliyam, the cipher letter substitutions are based on phonetic relations, such as vowels becoming consonants. In the Mulavediya, the cipher alphabet consists of pairing letters and using the reciprocal ones.[13]
InSassanid Persia, there were two secret scripts, according to the Muslim authorIbn al-Nadim: thešāh-dabīrīya(literally "King's script") which was used for official correspondence, and therāz-saharīyawhich was used to communicate secret messages with other countries.[25]
David Kahnnotes inThe Codebreakersthat modern cryptology originated among theArabs, the first people to systematically document cryptanalytic methods.[26]Al-Khalil(717–786) wrote theBook of Cryptographic Messages, which contains the first use ofpermutations and combinationsto list all possible Arabic words with and without vowels.[27]
Ciphertexts produced by aclassical cipher(and some modern ciphers) will reveal statistical information about the plaintext, and that information can often be used to break the cipher. After the discovery offrequency analysis, nearly all such ciphers could be broken by an informed attacker.[28]Such classical ciphers still enjoy popularity today, though mostly aspuzzles(seecryptogram). TheArab mathematicianandpolymathAl-Kindi wrote a book on cryptography entitledRisalah fi Istikhraj al-Mu'amma(Manuscript for the Deciphering Cryptographic Messages), which described the first known use of frequency analysis cryptanalysis techniques.[29][30]
Language letter frequencies may offer little help for some extended historical encryption techniques such ashomophonic cipherthat tend to flatten the frequency distribution. For those ciphers, language letter group (or n-gram) frequencies may provide an attack.
Essentially all ciphers remained vulnerable to cryptanalysis using the frequency analysis technique until the development of thepolyalphabetic cipher, most clearly byLeon Battista Albertiaround the year 1467, though there is some indication that it was already known to Al-Kindi.[30]Alberti's innovation was to use different ciphers (i.e., substitution alphabets) for various parts of a message (perhaps for each successive plaintext letter at the limit). He also invented what was probably the first automaticcipher device, a wheel that implemented a partial realization of his invention. In theVigenère cipher, apolyalphabetic cipher, encryption uses akey word, which controls letter substitution depending on which letter of the key word is used. In the mid-19th centuryCharles Babbageshowed that the Vigenère cipher was vulnerable toKasiski examination, but this was first published about ten years later byFriedrich Kasiski.[31]
Although frequency analysis can be a powerful and general technique against many ciphers, encryption has still often been effective in practice, as many a would-be cryptanalyst was unaware of the technique. Breaking a message without using frequency analysis essentially required knowledge of the cipher used and perhaps of the key involved, thus making espionage, bribery, burglary, defection, etc., more attractive approaches to the cryptanalytically uninformed. It was finally explicitly recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible nor practical safeguard of message security; in fact, it was further realized that any adequate cryptographic scheme (including ciphers) should remain secure even if the adversary fully understands the cipher algorithm itself. Security of the key used should alone be sufficient for a good cipher to maintain confidentiality under an attack. This fundamental principle was first explicitly stated in 1883 byAuguste Kerckhoffsand is generally calledKerckhoffs's Principle; alternatively and more bluntly, it was restated byClaude Shannon, the inventor ofinformation theoryand the fundamentals of theoretical cryptography, asShannon's Maxim—'the enemy knows the system'.
Different physical devices and aids have been used to assist with ciphers. One of the earliest may have been the scytale of ancient Greece, a rod supposedly used by the Spartans as an aid for a transposition cipher. In medieval times, other aids were invented such as thecipher grille, which was also used for a kind of steganography. With the invention of polyalphabetic ciphers came more sophisticated aids such as Alberti's owncipher disk,Johannes Trithemius'tabula rectascheme, andThomas Jefferson'swheel cypher(not publicly known, and reinvented independently byBazeriesaround 1900). Many mechanical encryption/decryption devices were invented early in the 20th century, and several patented, among themrotor machines—famously including theEnigma machineused by the German government and military from the late 1920s and duringWorld War II.[32]The ciphers implemented by better quality examples of these machine designs brought about a substantial increase in cryptanalytic difficulty after WWI.[33]
Cryptanalysis of the new mechanical ciphering devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts atBletchley Parkduring WWII spurred the development of more efficient means for carrying out repetitive tasks, suchas military code breaking (decryption). This culminated in the development of theColossus, the world's first fully electronic, digital,programmablecomputer, which assisted in the decryption of ciphers generated by the German Army'sLorenz SZ40/42machine.
Extensive open academic research into cryptography is relatively recent, beginning in the mid-1970s. In the early 1970sIBMpersonnel designed the Data Encryption Standard (DES) algorithm that became the first federal government cryptography standard in the United States.[34]In 1976Whitfield DiffieandMartin Hellmanpublished the Diffie–Hellman key exchange algorithm.[35]In 1977 theRSA algorithmwas published inMartin Gardner'sScientific Americancolumn.[36]Since then, cryptography has become a widely used tool in communications,computer networks, andcomputer securitygenerally.
Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems areintractable, such as theinteger factorizationor thediscrete logarithmproblems, so there are deep connections withabstract mathematics. There are very few cryptosystems that are proven to be unconditionally secure. Theone-time padis one, and was proven to be so by Claude Shannon. There are a few important algorithms that have been proven secure under certain assumptions. For example, the infeasibility of factoring extremely large integers is the basis for believing that RSA is secure, and some other systems, but even so, proof of unbreakability is unavailable since the underlying mathematical problem remains open. In practice, these are widely used, and are believed unbreakable in practice by most competent observers. There are systems similar to RSA, such as one byMichael O. Rabinthat are provably secure provided factoringn = pqis impossible; it is quite unusable in practice. Thediscrete logarithm problemis the basis for believing some other cryptosystems are secure, and again, there are related, less practical systems that are provably secure relative to the solvability or insolvability discrete log problem.[37]
As well as being aware of cryptographic history,cryptographic algorithmand system designers must also sensibly consider probable future developments while working on their designs. For instance, continuous improvements in computer processing power have increased the scope ofbrute-force attacks, so when specifyingkey lengths, the required key lengths are similarly advancing.[38]The potential impact ofquantum computingare already being considered by some cryptographic system designers developing post-quantum cryptography.[when?]The announced imminence of small implementations of these machines may be making the need for preemptive caution rather more than merely speculative.[5]
Claude Shannon's two papers, his1948 paperoninformation theory, and especially his1949 paperon cryptography, laid the foundations of modern cryptography and provided a mathematical basis for future cryptography.[39][40]His 1949 paper has been noted as having provided a "solid theoretical basis for cryptography and for cryptanalysis",[41]and as having turned cryptography from an "art to a science".[42]As a result of his contributions and work, he has been described as the "founding father of modern cryptography".[43]
Prior to the early 20th century, cryptography was mainly concerned withlinguisticandlexicographicpatterns. Since then cryptography has broadened in scope, and now makes extensive use of mathematical subdisciplines, including information theory,computational complexity, statistics,combinatorics,abstract algebra,number theory, andfinite mathematics.[44]Cryptography is also a branch of engineering, but an unusual one since it deals with active, intelligent, and malevolent opposition; other kinds of engineering (e.g., civil or chemical engineering) need deal only with neutral natural forces. There is also active research examining the relationship between cryptographic problems andquantum physics.
Just as the development of digital computers and electronics helped in cryptanalysis, it made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data representable in any binary format, unlike classical ciphers which only encrypted written language texts; this was new and significant. Computer use has thus supplanted linguistic cryptography, both for cipher design and cryptanalysis. Many computer ciphers can be characterized by their operation onbinarybitsequences (sometimes in groups or blocks), unlike classical and mechanical schemes, which generally manipulate traditional characters (i.e., letters and digits) directly. However, computers have also assisted cryptanalysis, which has compensated to some extent for increased cipher complexity. Nonetheless, good modern ciphers have stayed ahead of cryptanalysis; it is typically the case that use of a quality cipher is very efficient (i.e., fast and requiring few resources, such as memory or CPU capability), while breaking it requires an effort many orders of magnitude larger, and vastly larger than that required for any classical cipher, making cryptanalysis so inefficient and impractical as to be effectively impossible.
Symmetric-key cryptography refers to encryption methods in which both the sender and receiver share the same key (or, less commonly, in which their keys are different, but related in an easily computable way). This was the only kind of encryption publicly known until June 1976.[35]
Symmetric key ciphers are implemented as eitherblock ciphersorstream ciphers. A block cipher enciphers input in blocks of plaintext as opposed to individual characters, the input form used by a stream cipher.
TheData Encryption Standard(DES) and theAdvanced Encryption Standard(AES) are block cipher designs that have been designatedcryptography standardsby the US government (though DES's designation was finally withdrawn after the AES was adopted).[45]Despite its deprecation as an official standard, DES (especially its still-approved and much more securetriple-DESvariant) remains quite popular; it is used across a wide range of applications, from ATM encryption[46]toe-mail privacy[47]andsecure remote access.[48]Many other block ciphers have been designed and released, with considerable variation in quality. Many, even some designed by capable practitioners, have been thoroughly broken, such asFEAL.[5][49]
Stream ciphers, in contrast to the 'block' type, create an arbitrarily long stream of key material, which is combined with the plaintext bit-by-bit or character-by-character, somewhat like theone-time pad. In a stream cipher, the output stream is created based on a hidden internal state that changes as the cipher operates. That internal state is initially set up using the secret key material.RC4is a widely used stream cipher.[5]Block ciphers can be used as stream ciphers by generating blocks of a keystream (in place of aPseudorandom number generator) and applying anXORoperation to each bit of the plaintext with each bit of the keystream.[50]
Message authentication codes(MACs) are much likecryptographic hash functions, except that a secret key can be used to authenticate the hash value upon receipt;[5][51]this additional complication blocks an attack scheme against baredigest algorithms, and so has been thought worth the effort. Cryptographic hash functions are a third type of cryptographic algorithm. They take a message of any length as input, and output a short, fixed-lengthhash, which can be used in (for example) a digital signature. For good hash functions, an attacker cannot find two messages that produce the same hash.MD4is a long-used hash function that is now broken;MD5, a strengthened variant of MD4, is also widely used but broken in practice. The USNational Security Agencydeveloped the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew;SHA-1is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; theSHA-2family improves on SHA-1, but is vulnerable to clashes as of 2011; and the US standards authority thought it "prudent" from a security perspective to develop a new standard to "significantly improve the robustness ofNIST's overall hash algorithm toolkit."[52]Thus, ahash function design competitionwas meant to select a new U.S. national standard, to be calledSHA-3, by 2012. The competition ended on October 2, 2012, when the NIST announced thatKeccakwould be the new SHA-3 hash algorithm.[53]Unlike block and stream ciphers that are invertible, cryptographic hash functions produce a hashed output that cannot be used to retrieve the original input data. Cryptographic hash functions are used to verify the authenticity of data retrieved from an untrusted source or to add a layer of security.
Symmetric-key cryptosystems use the same key for encryption and decryption of a message, although a message or group of messages can have a different key than others. A significant disadvantage of symmetric ciphers is thekey managementnecessary to use them securely. Each distinct pair of communicating parties must, ideally, share a different key, and perhaps for each ciphertext exchanged as well. The number of keys required increases as thesquareof the number of network members, which very quickly requires complex key management schemes to keep them all consistent and secret.
In a groundbreaking 1976 paper, Whitfield Diffie and Martin Hellman proposed the notion ofpublic-key(also, more generally, calledasymmetric key) cryptography in which two different but mathematically related keys are used—apublickey and aprivatekey.[54]A public key system is so constructed that calculation of one key (the 'private key') is computationally infeasible from the other (the 'public key'), even though they are necessarily related. Instead, both keys are generated secretly, as an interrelated pair.[55]The historianDavid Kahndescribed public-key cryptography as "the most revolutionary new concept in the field since polyalphabetic substitution emerged in the Renaissance".[56]
In public-key cryptosystems, the public key may be freely distributed, while its paired private key must remain secret. In a public-key encryption system, thepublic keyis used for encryption, while theprivateorsecret keyis used for decryption. While Diffie and Hellman could not find such a system, they showed that public-key cryptography was indeed possible by presenting theDiffie–Hellman key exchangeprotocol, a solution that is now widely used in secure communications to allow two parties to secretly agree on ashared encryption key.[35]TheX.509standard defines the most commonly used format forpublic key certificates.[57]
Diffie and Hellman's publication sparked widespread academic efforts in finding a practical public-key encryption system. This race was finally won in 1978 byRonald Rivest,Adi Shamir, andLen Adleman, whose solution has since become known as theRSA algorithm.[58]
TheDiffie–HellmanandRSA algorithms, in addition to being the first publicly known examples of high-quality public-key algorithms, have been among the most widely used. Otherasymmetric-key algorithmsinclude theCramer–Shoup cryptosystem,ElGamal encryption, and variouselliptic curve techniques.
A document published in 1997 by the Government Communications Headquarters (GCHQ), a British intelligence organization, revealed that cryptographers at GCHQ had anticipated several academic developments.[59]Reportedly, around 1970,James H. Ellishad conceived the principles of asymmetric key cryptography. In 1973,Clifford Cocksinvented a solution that was very similar in design rationale to RSA.[59][60]In 1974,Malcolm J. Williamsonis claimed to have developed the Diffie–Hellman key exchange.[61]
Public-key cryptography is also used for implementingdigital signatureschemes. A digital signature is reminiscent of an ordinary signature; they both have the characteristic of being easy for a user to produce, but difficult for anyone else toforge. Digital signatures can also be permanently tied to the content of the message being signed; they cannot then be 'moved' from one document to another, for any attempt will be detectable. In digital signature schemes, there are two algorithms: one forsigning, in which a secret key is used to process the message (or a hash of the message, or both), and one forverification, in which the matching public key is used with the message to check the validity of the signature. RSA andDSAare two of the most popular digital signature schemes. Digital signatures are central to the operation ofpublic key infrastructuresand many network security schemes (e.g.,SSL/TLS, manyVPNs, etc.).[49]
Public-key algorithms are most often based on thecomputational complexityof "hard" problems, often fromnumber theory. For example, the hardness of RSA is related to theinteger factorizationproblem, while Diffie–Hellman and DSA are related to thediscrete logarithmproblem. The security ofelliptic curve cryptographyis based on number theoretic problems involvingelliptic curves. Because of the difficulty of the underlying problems, most public-key algorithms involve operations such asmodularmultiplication and exponentiation, which are much more computationally expensive than the techniques used in most block ciphers, especially with typical key sizes. As a result, public-key cryptosystems are commonlyhybrid cryptosystems, in which a fast high-quality symmetric-key encryption algorithm is used for the message itself, while the relevant symmetric key is sent with the message, but encrypted using a public-key algorithm. Similarly, hybrid signature schemes are often used, in which a cryptographic hash function is computed, and only the resulting hash is digitally signed.[5]
Cryptographic hash functions are functions that take a variable-length input and return a fixed-length output, which can be used in, for example, a digital signature. For a hash function to be secure, it must be difficult to compute two inputs that hash to the same value (collision resistance) and to compute an input that hashes to a given output (preimage resistance).MD4is a long-used hash function that is now broken;MD5, a strengthened variant of MD4, is also widely used but broken in practice. The USNational Security Agencydeveloped the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew;SHA-1is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; theSHA-2family improves on SHA-1, but is vulnerable to clashes as of 2011; and the US standards authority thought it "prudent" from a security perspective to develop a new standard to "significantly improve the robustness ofNIST's overall hash algorithm toolkit."[52]Thus, ahash function design competitionwas meant to select a new U.S. national standard, to be calledSHA-3, by 2012. The competition ended on October 2, 2012, when the NIST announced thatKeccakwould be the new SHA-3 hash algorithm.[53]Unlike block and stream ciphers that are invertible, cryptographic hash functions produce a hashed output that cannot be used to retrieve the original input data. Cryptographic hash functions are used to verify the authenticity of data retrieved from an untrusted source or to add a layer of security.
The goal of cryptanalysis is to find some weakness or insecurity in a cryptographic scheme, thus permitting its subversion or evasion.
It is a common misconception that every encryption method can be broken. In connection with his WWII work atBell Labs,Claude Shannonproved that theone-time padcipher is unbreakable, provided the key material is trulyrandom, never reused, kept secret from all possible attackers, and of equal or greater length than the message.[62]Mostciphers, apart from the one-time pad, can be broken with enough computational effort bybrute force attack, but the amount of effort needed may beexponentiallydependent on the key size, as compared to the effort needed to make use of the cipher. In such cases, effective security could be achieved if it is proven that the effort required (i.e., "work factor", in Shannon's terms) is beyond the ability of any adversary. This means it must be shown that no efficient method (as opposed to the time-consuming brute force method) can be found to break the cipher. Since no such proof has been found to date, the one-time-pad remains the only theoretically unbreakable cipher. Although well-implemented one-time-pad encryption cannot be broken, traffic analysis is still possible.
There are a wide variety of cryptanalytic attacks, and they can be classified in any of several ways. A common distinction turns on what Eve (an attacker) knows and what capabilities are available. In aciphertext-only attack, Eve has access only to the ciphertext (good modern cryptosystems are usually effectively immune to ciphertext-only attacks). In aknown-plaintext attack, Eve has access to a ciphertext and its corresponding plaintext (or to many such pairs). In achosen-plaintext attack, Eve may choose a plaintext and learn its corresponding ciphertext (perhaps many times); an example isgardening, used by the British during WWII. In achosen-ciphertext attack, Eve may be able tochooseciphertexts and learn their corresponding plaintexts.[5]Finally in aman-in-the-middleattack Eve gets in between Alice (the sender) and Bob (the recipient), accesses and modifies the traffic and then forward it to the recipient.[63]Also important, often overwhelmingly so, are mistakes (generally in the design or use of one of theprotocolsinvolved).
Cryptanalysis of symmetric-key ciphers typically involves looking for attacks against the block ciphers or stream ciphers that are more efficient than any attack that could be against a perfect cipher. For example, a simple brute force attack against DES requires one known plaintext and 255decryptions, trying approximately half of the possible keys, to reach a point at which chances are better than even that the key sought will have been found. But this may not be enough assurance; alinear cryptanalysisattack against DES requires 243known plaintexts (with their corresponding ciphertexts) and approximately 243DES operations.[64]This is a considerable improvement over brute force attacks.
Public-key algorithms are based on the computational difficulty of various problems. The most famous of these are the difficulty ofinteger factorizationofsemiprimesand the difficulty of calculatingdiscrete logarithms, both of which are not yet proven to be solvable inpolynomial time(P) using only a classicalTuring-completecomputer. Much public-key cryptanalysis concerns designing algorithms inPthat can solve these problems, or using other technologies, such asquantum computers. For instance, the best-known algorithms for solving theelliptic curve-basedversion of discrete logarithm are much more time-consuming than the best-known algorithms for factoring, at least for problems of more or less equivalent size. Thus, to achieve an equivalent strength of encryption, techniques that depend upon the difficulty of factoring large composite numbers, such as the RSA cryptosystem, require larger keys than elliptic curve techniques. For this reason, public-key cryptosystems based on elliptic curves have become popular since their invention in the mid-1990s.
While pure cryptanalysis uses weaknesses in the algorithms themselves, other attacks on cryptosystems are based on actual use of the algorithms in real devices, and are calledside-channel attacks. If a cryptanalyst has access to, for example, the amount of time the device took to encrypt a number of plaintexts or report an error in a password or PIN character, they may be able to use atiming attackto break a cipher that is otherwise resistant to analysis. An attacker might also study the pattern and length of messages to derive valuable information; this is known astraffic analysis[65]and can be quite useful to an alert adversary. Poor administration of a cryptosystem, such as permitting too short keys, will make any system vulnerable, regardless of other virtues.Social engineeringand other attacks against humans (e.g., bribery,extortion,blackmail, espionage,rubber-hose cryptanalysisor torture) are usually employed due to being more cost-effective and feasible to perform in a reasonable amount of time compared to pure cryptanalysis by a high margin.
Much of the theoretical work in cryptography concernscryptographicprimitives—algorithms with basic cryptographic properties—and their relationship to other cryptographic problems. More complicated cryptographic tools are then built from these basic primitives. These primitives provide fundamental properties, which are used to develop more complex tools calledcryptosystemsorcryptographic protocols, which guarantee one or more high-level security properties. Note, however, that the distinction between cryptographicprimitivesand cryptosystems, is quite arbitrary; for example, the RSA algorithm is sometimes considered a cryptosystem, and sometimes a primitive. Typical examples of cryptographic primitives includepseudorandom functions,one-way functions, etc.
One or more cryptographic primitives are often used to develop a more complex algorithm, called a cryptographic system, orcryptosystem. Cryptosystems (e.g.,El-Gamal encryption) are designed to provide particular functionality (e.g., public key encryption) while guaranteeing certain security properties (e.g.,chosen-plaintext attack (CPA)security in therandom oracle model). Cryptosystems use the properties of the underlying cryptographic primitives to support the system's security properties. As the distinction between primitives and cryptosystems is somewhat arbitrary, a sophisticated cryptosystem can be derived from a combination of several more primitive cryptosystems. In many cases, the cryptosystem's structure involves back and forth communication among two or more parties in space (e.g., between the sender of a secure message and its receiver) or across time (e.g., cryptographically protectedbackupdata). Such cryptosystems are sometimes calledcryptographic protocols.
Some widely known cryptosystems include RSA,Schnorr signature,ElGamal encryption, andPretty Good Privacy(PGP). More complex cryptosystems includeelectronic cash[66]systems,signcryptionsystems, etc. Some more 'theoretical'[clarification needed]cryptosystems includeinteractive proof systems,[67](likezero-knowledge proofs)[68]and systems forsecret sharing.[69][70]
Lightweight cryptography (LWC) concerns cryptographic algorithms developed for a strictly constrained environment. The growth ofInternet of Things (IoT)has spiked research into the development of lightweight algorithms that are better suited for the environment. An IoT environment requires strict constraints on power consumption, processing power, and security.[71]Algorithms such as PRESENT,AES, andSPECKare examples of the many LWC algorithms that have been developed to achieve the standard set by theNational Institute of Standards and Technology.[72]
Cryptography is widely used on the internet to help protect user-data and prevent eavesdropping. To ensure secrecy during transmission, many systems use private key cryptography to protect transmitted information. With public-key systems, one can maintain secrecy without a master key or a large number of keys.[73]But, some algorithms likeBitLockerandVeraCryptare generally not private-public key cryptography. For example, Veracrypt uses a password hash to generate the single private key. However, it can be configured to run in public-private key systems. TheC++opensource encryption libraryOpenSSLprovidesfree and opensourceencryption software and tools. The most commonly used encryption cipher suit isAES,[74]as it has hardware acceleration for allx86based processors that hasAES-NI. A close contender isChaCha20-Poly1305, which is astream cipher, however it is commonly used for mobile devices as they areARMbased which does not feature AES-NI instruction set extension.
Cryptography can be used to secure communications by encrypting them. Websites use encryption viaHTTPS.[75]"End-to-end" encryption, where only sender and receiver can read messages, is implemented for email inPretty Good Privacyand for secure messaging in general inWhatsApp,SignalandTelegram.[75]
Operating systems use encryption to keep passwords secret, conceal parts of the system, and ensure that software updates are truly from the system maker.[75]Instead of storing plaintext passwords, computer systems store hashes thereof; then, when a user logs in, the system passes the given password through a cryptographic hash function and compares it to the hashed value on file. In this manner, neither the system nor an attacker has at any point access to the password in plaintext.[75]
Encryption is sometimes used to encrypt one's entire drive. For example,University College Londonhas implementedBitLocker(a program by Microsoft) to render drive data opaque without users logging in.[75]
Cryptographic techniques enablecryptocurrencytechnologies, such asdistributed ledger technologies(e.g.,blockchains), which financecryptoeconomicsapplications such asdecentralized finance (DeFi). Key cryptographic techniques that enable cryptocurrencies and cryptoeconomics include, but are not limited to:cryptographic keys, cryptographic hash function,asymmetric (public key) encryption,Multi-Factor Authentication (MFA),End-to-End Encryption (E2EE), andZero Knowledge Proofs (ZKP).
Cryptography has long been of interest to intelligence gathering andlaw enforcement agencies.[9]Secret communications may be criminal or eventreasonous.[citation needed]Because of its facilitation ofprivacy, and the diminution of privacy attendant on its prohibition, cryptography is also of considerable interest to civil rights supporters. Accordingly, there has been a history of controversial legal issues surrounding cryptography, especially since the advent of inexpensive computers has made widespread access to high-quality cryptography possible.
In some countries, even the domestic use of cryptography is, or has been, restricted. Until 1999, France significantly restricted the use of cryptography domestically, though it has since relaxed many of these rules. InChinaandIran, a license is still required to use cryptography.[7]Many countries have tight restrictions on the use of cryptography. Among the more restrictive are laws inBelarus,Kazakhstan,Mongolia,Pakistan, Singapore,Tunisia, andVietnam.[76]
In the United States, cryptography is legal for domestic use, but there has been much conflict over legal issues related to cryptography.[9]One particularly important issue has been theexport of cryptographyand cryptographic software and hardware. Probably because of the importance of cryptanalysis inWorld War IIand an expectation that cryptography would continue to be important for national security, many Western governments have, at some point, strictly regulated export of cryptography. After World War II, it was illegal in the US to sell or distribute encryption technology overseas; in fact, encryption was designated as auxiliary military equipment and put on theUnited States Munitions List.[77]Until the development of the personal computer, asymmetric key algorithms (i.e., public key techniques), and the Internet, this was not especially problematic. However, as the Internet grew and computers became more widely available, high-quality encryption techniques became well known around the globe.
In the 1990s, there were several challenges to US export regulation of cryptography. After thesource codeforPhilip Zimmermann'sPretty Good Privacy(PGP) encryption program found its way onto the Internet in June 1991, a complaint byRSA Security(then called RSA Data Security, Inc.) resulted in a lengthy criminal investigation of Zimmermann by the US Customs Service and theFBI, though no charges were ever filed.[78][79]Daniel J. Bernstein, then a graduate student atUC Berkeley, brought a lawsuit against the US government challenging some aspects of the restrictions based onfree speechgrounds. The 1995 caseBernstein v. United Statesultimately resulted in a 1999 decision that printed source code for cryptographic algorithms and systems was protected asfree speechby the United States Constitution.[80]
In 1996, thirty-nine countries signed theWassenaar Arrangement, an arms control treaty that deals with the export of arms and "dual-use" technologies such as cryptography. The treaty stipulated that the use of cryptography with short key-lengths (56-bit for symmetric encryption, 512-bit for RSA) would no longer be export-controlled.[81]Cryptography exports from the US became less strictly regulated as a consequence of a major relaxation in 2000;[82]there are no longer very many restrictions on key sizes in US-exportedmass-market software. Since this relaxation in US export restrictions, and because most personal computers connected to the Internet include US-sourcedweb browserssuch asFirefoxorInternet Explorer, almost every Internet user worldwide has potential access to quality cryptography via their browsers (e.g., viaTransport Layer Security). TheMozilla ThunderbirdandMicrosoft OutlookE-mail clientprograms similarly can transmit and receive emails via TLS, and can send and receive email encrypted withS/MIME. Many Internet users do not realize that their basic application software contains such extensivecryptosystems. These browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally do not find it practical to do much to control distribution or use of cryptography of this quality, so even when such laws are in force, actual enforcement is often effectively impossible.[citation needed]
Another contentious issue connected to cryptography in the United States is the influence of theNational Security Agencyon cipher development and policy.[9]The NSA was involved with the design ofDESduring its development atIBMand its consideration by theNational Bureau of Standardsas a possible Federal Standard for cryptography.[83]DES was designed to be resistant todifferential cryptanalysis,[84]a powerful and general cryptanalytic technique known to the NSA and IBM, that became publicly known only when it was rediscovered in the late 1980s.[85]According toSteven Levy, IBM discovered differential cryptanalysis,[79]but kept the technique secret at the NSA's request. The technique became publicly known only when Biham and Shamir re-discovered and announced it some years later. The entire affair illustrates the difficulty of determining what resources and knowledge an attacker might actually have.
Another instance of the NSA's involvement was the 1993Clipper chipaffair, an encryption microchip intended to be part of theCapstonecryptography-control initiative. Clipper was widely criticized by cryptographers for two reasons. The cipher algorithm (calledSkipjack) was then classified (declassified in 1998, long after the Clipper initiative lapsed). The classified cipher caused concerns that the NSA had deliberately made the cipher weak to assist its intelligence efforts. The whole initiative was also criticized based on its violation ofKerckhoffs's Principle, as the scheme included a specialescrow keyheld by the government for use by law enforcement (i.e.wiretapping).[79]
Cryptography is central to digital rights management (DRM), a group of techniques for technologically controlling use ofcopyrightedmaterial, being widely implemented and deployed at the behest of some copyright holders. In 1998, U.S. PresidentBill Clintonsigned theDigital Millennium Copyright Act(DMCA), which criminalized all production, dissemination, and use of certain cryptanalytic techniques and technology (now known or later discovered); specifically, those that could be used to circumvent DRM technological schemes.[86]This had a noticeable impact on the cryptography research community since an argument can be made that any cryptanalytic research violated the DMCA. Similar statutes have since been enacted in several countries and regions, including the implementation in theEU Copyright Directive. Similar restrictions are called for by treaties signed byWorld Intellectual Property Organizationmember-states.
TheUnited States Department of JusticeandFBIhave not enforced the DMCA as rigorously as had been feared by some, but the law, nonetheless, remains a controversial one.Niels Ferguson, a well-respected cryptography researcher, has publicly stated that he will not release some of his research into anIntelsecurity design for fear of prosecution under the DMCA.[87]CryptologistBruce Schneierhas argued that the DMCA encouragesvendor lock-in, while inhibiting actual measures toward cyber-security.[88]BothAlan Cox(longtimeLinux kerneldeveloper) andEdward Felten(and some of his students at Princeton) have encountered problems related to the Act.Dmitry Sklyarovwas arrested during a visit to the US from Russia, and jailed for five months pending trial for alleged violations of the DMCA arising from work he had done in Russia, where the work was legal. In 2007, the cryptographic keys responsible forBlu-rayandHD DVDcontent scrambling werediscovered and released onto the Internet. In both cases, theMotion Picture Association of Americasent out numerous DMCA takedown notices, and there was a massive Internet backlash[10]triggered by the perceived impact of such notices onfair useandfree speech.
In the United Kingdom, theRegulation of Investigatory Powers Actgives UK police the powers to force suspects to decrypt files or hand over passwords that protect encryption keys. Failure to comply is an offense in its own right, punishable on conviction by a two-year jail sentence or up to five years in cases involving national security.[8]Successful prosecutions have occurred under the Act; the first, in 2009,[89]resulted in a term of 13 months' imprisonment.[90]Similar forced disclosure laws in Australia, Finland, France, and India compel individual suspects under investigation to hand over encryption keys or passwords during a criminal investigation.
In the United States, the federal criminal case ofUnited States v. Fricosuaddressed whether a search warrant can compel a person to reveal anencryptionpassphraseor password.[91]TheElectronic Frontier Foundation(EFF) argued that this is a violation of the protection from self-incrimination given by theFifth Amendment.[92]In 2012, the court ruled that under theAll Writs Act, the defendant was required to produce an unencrypted hard drive for the court.[93]
In many jurisdictions, the legal status of forced disclosure remains unclear.
The 2016FBI–Apple encryption disputeconcerns the ability of courts in the United States to compel manufacturers' assistance in unlocking cell phones whose contents are cryptographically protected.
As a potential counter-measure to forced disclosure some cryptographic software supportsplausible deniability, where the encrypted data is indistinguishable from unused random data (for example such as that of adrive which has been securely wiped).
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https://en.wikipedia.org/wiki/Cryptography#Kerckhoffs%27_principle
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Ingraph theory, aflow network(also known as atransportation network) is adirected graphwhere each edge has acapacityand each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often inoperations research, a directed graph is called anetwork, the vertices are callednodesand the edges are calledarcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is asource, which has only outgoing flow, orsink, which has only incoming flow. A flow network can be used to model traffic in a computer network, circulation with demands, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes. As such, efficient algorithms for solving network flows can also be applied to solve problems that can be reduced to a flow network, including survey design, airline scheduling,image segmentation, and thematching problem.
Anetworkis a directed graphG= (V,E)with a non-negativecapacityfunctioncfor each edge, and without multiple arcs (i.e. edges with the same source and target nodes).Without loss of generality, we may assume that if(u,v) ∈E, then(v,u)is also a member ofE. Additionally, if(v,u) ∉Ethen we may add(v,u)toEand then set thec(v,u) = 0.
If two nodes inGare distinguished – one as the sourcesand the other as the sinkt– then(G,c,s,t)is called aflow network.[1]
Flow functions model the net flow of units between pairs of nodes, and are useful when asking questions such aswhat is the maximum number of units that can be transferred from the source node s to the sink node t?The amount of flow between two nodes is used to represent the net amount of units being transferred from one node to the other.
Theexcessfunctionxf:V→ ℝrepresents the net flow entering a given nodeu(i.e. the sum of the flows enteringu) and is defined byxf(u)=∑w∈Vf(w,u)−∑w∈Vf(u,w).{\displaystyle x_{f}(u)=\sum _{w\in V}f(w,u)-\sum _{w\in V}f(u,w).}A nodeuis said to beactiveifxf(u) > 0(i.e. the nodeuconsumes flow),deficientifxf(u) < 0(i.e. the nodeuproduces flow), orconservingifxf(u) = 0. In flow networks, the sourcesis deficient, and the sinktis active.
Pseudo-flows, feasible flows, and pre-flows are all examples of flow functions.
Thevalue|f|of a feasible flowffor a network, is the net flow into the sinktof the flow network, that is:|f| =xf(t). Note, the flow value in a network is also equal to the total outgoing flow of sources, that is:|f| = −xf(s). Also, if we defineAas a set of nodes inGsuch thats∈Aandt∉A, the flow value is equal to the total net flow going out of A (i.e.|f| =fout(A) −fin(A)).[2]The flow value in a network is the total amount of flow fromstot.
Flow decomposition[3]is a process of breaking down a given flow into a collection of path flows and cycle flows. Every flow through a network can be decomposed into one or more paths and corresponding quantities, such that each edge in the flow equals the sum of all quantities of paths that pass through it. Flow decomposition is a powerful tool in optimization problems to maximize or minimize specific flow parameters.
We do not use multiple arcs within a network because we can combine those arcs into a single arc. To combine two arcs into a single arc, we add their capacities and their flow values, and assign those to the new arc:
Along with the other constraints, the skew symmetry constraint must be remembered during this step to maintain the direction of the original pseudo-flow arc. Adding flow to an arc is the same as adding an arc with the capacity of zero.[citation needed]
Theresidual capacityof an arcewith respect to a pseudo-flowfis denotedcf, and it is the difference between the arc's capacity and its flow. That is,cf(e) =c(e) −f(e). From this we can construct aresidual network, denotedGf(V,Ef), with a capacity functioncfwhich models the amount ofavailablecapacity on the set of arcs inG= (V,E). More specifically, capacity functioncfof each arc(u,v)in the residual network represents the amount of flow which can be transferred fromutovgiven the current state of the flow within the network.
This concept is used inFord–Fulkerson algorithmwhich computes themaximum flowin a flow network.
Note that there can be an unsaturated path (a path with available capacity) fromutovin the residual network, even though there is no such path fromutovin the original network.[citation needed]Since flows in opposite directions cancel out,decreasingthe flow fromvtouis the same asincreasingthe flow fromutov.
Anaugmenting pathis a path(u1,u2, ...,uk)in the residual network, whereu1=s,uk=t, andfor allui,ui+ 1(cf(ui,ui+ 1) > 0) (1 ≤ i < k). More simply, an augmenting path is an available flow path from the source to the sink. A network is atmaximum flowif and only if there is no augmenting path in the residual networkGf.
Thebottleneckis the minimum residual capacity of all the edges in a given augmenting path.[2]See example explained in the "Example" section of this article. The flow network is at maximum flow if and only if it has a bottleneck with a value equal to zero. If any augmenting path exists, its bottleneck weight will be greater than 0. In other words, if there is a bottleneck value greater than 0, then there is an augmenting path from the source to the sink. However, we know that if there is any augmenting path, then the network is not at maximum flow, which in turn means that, if there is a bottleneck value greater than 0, then the network is not at maximum flow.
The term "augmenting the flow" for an augmenting path means updating the flowfof each arc in this augmenting path to equal the capacitycof the bottleneck. Augmenting the flow corresponds to pushing additional flow along the augmenting path until there is no remaining available residual capacity in the bottleneck.
Sometimes, when modeling a network with more than one source, asupersourceis introduced to the graph.[4]This consists of a vertex connected to each of the sources with edges of infinite capacity, so as to act as a global source. A similar construct for sinks is called asupersink.[5]
In Figure 1 you see a flow network with source labeleds, sinkt, and four additional nodes. The flow and capacity is denotedf/c{\displaystyle f/c}. Notice how the network upholds the capacity constraint and flow conservation constraint. The total amount of flow fromstotis 5, which can be easily seen from the fact that the total outgoing flow fromsis 5, which is also the incoming flow tot. By the skew symmetry constraint, fromctoais -2 because the flow fromatocis 2.
In Figure 2 you see the residual network for the same given flow. Notice how there is positive residual capacity on some edges where the original capacity is zero in Figure 1, for example for the edge(d,c){\displaystyle (d,c)}. This network is not atmaximum flow. There is available capacity along the paths(s,a,c,t){\displaystyle (s,a,c,t)},(s,a,b,d,t){\displaystyle (s,a,b,d,t)}and(s,a,b,d,c,t){\displaystyle (s,a,b,d,c,t)}, which are then the augmenting paths.
The bottleneck of the(s,a,c,t){\displaystyle (s,a,c,t)}path is equal tomin(c(s,a)−f(s,a),c(a,c)−f(a,c),c(c,t)−f(c,t)){\displaystyle \min(c(s,a)-f(s,a),c(a,c)-f(a,c),c(c,t)-f(c,t))}=min(cf(s,a),cf(a,c),cf(c,t)){\displaystyle =\min(c_{f}(s,a),c_{f}(a,c),c_{f}(c,t))}=min(5−3,3−2,2−1){\displaystyle =\min(5-3,3-2,2-1)}=min(2,1,1)=1{\displaystyle =\min(2,1,1)=1}.
Picture a series of water pipes, fitting into a network. Each pipe is of a certain diameter, so it can only maintain a flow of a certain amount of water. Anywhere that pipes meet, the total amount of water coming into that junction must be equal to the amount going out, otherwise we would quickly run out of water, or we would have a buildup of water. We have a water inlet, which is the source, and an outlet, the sink. A flow would then be one possible way for water to get from source to sink so that the total amount of water coming out of the outlet is consistent. Intuitively, the total flow of a network is the rate at which water comes out of the outlet.
Flows can pertain to people or material over transportation networks, or to electricity overelectrical distributionsystems. For any such physical network, the flow coming into any intermediate node needs to equal the flow going out of that node. This conservation constraint is equivalent toKirchhoff's current law.
Flow networks also find applications inecology: flow networks arise naturally when considering the flow of nutrients and energy between different organisms in afood web. The mathematical problems associated with such networks are quite different from those that arise in networks of fluid or traffic flow. The field of ecosystem network analysis, developed byRobert Ulanowiczand others, involves using concepts frominformation theoryandthermodynamicsto study the evolution of these networks over time.
The simplest and most common problem using flow networks is to find what is called themaximum flow, which provides the largest possible total flow from the source to the sink in a given graph. There are many other problems which can be solved using max flow algorithms, if they are appropriately modeled as flow networks, such asbipartite matching, theassignment problemand thetransportation problem. Maximum flow problems can be solved inpolynomial timewith various algorithms (see table). Themax-flow min-cut theoremstates that finding a maximal network flow is equivalent to finding acutof minimum capacity that separates the source and the sink, where a cut is the division of vertices such that the source is in one division and the sink is in another.
Richard Peng, Maximilian Probst Gutenberg,
Sushant Sachdeva
In amulti-commodity flow problem, you have multiple sources and sinks, and various "commodities" which are to flow from a given source to a given sink. This could be for example various goods that are produced at various factories, and are to be delivered to various given customers through thesametransportation network.
In aminimum cost flow problem, each edgeu,v{\displaystyle u,v}has a given costk(u,v){\displaystyle k(u,v)}, and the cost of sending the flowf(u,v){\displaystyle f(u,v)}across the edge isf(u,v)⋅k(u,v){\displaystyle f(u,v)\cdot k(u,v)}. The objective is to send a given amount of flow from the source to the sink, at the lowest possible price.
In acirculation problem, you have a lower boundℓ(u,v){\displaystyle \ell (u,v)}on the edges, in addition to the upper boundc(u,v){\displaystyle c(u,v)}. Each edge also has a cost. Often, flow conservation holds forallnodes in a circulation problem, and there is a connection from the sink back to the source. In this way, you can dictate the total flow withℓ(t,s){\displaystyle \ell (t,s)}andc(t,s){\displaystyle c(t,s)}. The flowcirculatesthrough the network, hence the name of the problem.
In anetwork with gainsorgeneralized networkeach edge has again, a real number (not zero) such that, if the edge has gaing, and an amountxflows into the edge at its tail, then an amountgxflows out at the head.
In asource localization problem, an algorithm tries to identify the most likely source node of information diffusion through a partially observed network. This can be done in linear time for trees and cubic time for arbitrary networks and has applications ranging from tracking mobile phone users to identifying the originating source of disease outbreaks.[8]
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https://en.wikipedia.org/wiki/Random_networks
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TheData Analysis and Real World Interrogation Network(DARWIN EU) is aEuropean Union(EU) initiative coordinated by theEuropean Medicines Agency(EMA) to generate and utilizereal world evidence(RWE) to support the evaluation and supervision of medicines across the EU. The project aims to enhance decision-making in regulatory processes by drawing on anonymized data from routine healthcare settings.[1][2][3]
DARWIN EU was officially launched in 2022 as part of the EMA's broader strategy to harness big data for public health benefits. The network facilitates access to real-world data from a wide array of sources, including electronic health records, disease registries, hospital databases, and biobanks. These data are standardized using the OMOP (Observational Medical Outcomes Partnership) common data model to ensure interoperability and comparability across datasets.[4][5][6]
The key goals of DARWIN EU include:
DARWIN EU is managed by a coordination center based atErasmus University Medical CenterinRotterdam,Netherlands. The center is responsible for expanding the network of data partners, managing study requests, and ensuring the scientific quality of outputs.[1]
As of early 2024, DARWIN EU had completed 14 studies and had 11 more underway. The EMA plans to scale up DARWIN EU's capacity to deliver over 140 studies annually by 2025.[1][4]
As part of the DARWIN EU project scientists at Honeywell'sBrnobranch have developed an AI-powered monitoring system designed to detect early signs of pilot fatigue, inattention, or health issues. Using a camera equipped with artificial intelligence, the system continuously observes the pilot's condition and responds with alerts or wake-up calls if necessary. Even though designed for aviation safety, these technologies could be used in the future to contribute valuable physiological data to the DARWIN EU network—supporting proactive health interventions and contributing to the long-term goals of the European Health Data Space.[7][8]
DARWIN EU plays a crucial role in the EU's regulatory ecosystem by integrating real-world data into evidence-based healthcare policymaking. It is instrumental in advancing personalized medicine, pharmacovigilance, and pandemic preparedness through timely, data-driven insights.[1]
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https://en.wikipedia.org/wiki/DARWIN_EU
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Property Specification Language(PSL) is atemporal logicextendinglinear temporal logicwith a range of operators for both ease of expression and enhancement of expressive power. PSL makes an extensive use ofregular expressionsand syntactic sugaring. It is widely used in the hardware design and verification industry, whereformal verificationtools (such asmodel checking) and/orlogic simulationtools are used to prove or refute that a given PSL formula holds on a given design.
PSL was initially developed byAccellerafor specifyingpropertiesorassertionsabout hardware designs. Since September 2004 thestandardizationon the language has been done inIEEE1850 working group. In September 2005, the IEEE 1850 Standard for Property Specification Language (PSL) was announced.
PSL can express that if some scenario happens now, then another scenario should happen some time later. For instance, the property "arequestshould always eventually begranted" can be expressed by the PSL formula:
The property "everyrequestthat is immediately followed by anacksignal, should be followed by a completedata transfer, where a complete data transfer is a sequence starting with signalstart, ending with signalendin whichbusyholds at the meantime" can be expressed by the PSL formula:
A trace satisfying this formula is given in the figure on the right.
PSL's temporal operators can be roughly classified intoLTL-styleoperators andregular-expression-styleoperators. Many PSL operators come in two versions, a strong version, indicated by an exclamation mark suffix (!), and a weak version. Thestrong versionmakes eventuality requirements (i.e. require that something will hold in the future), while theweak versiondoes not. Anunderscore suffix(_) is used to differentiateinclusivevs.non-inclusiverequirements. The_aand_esuffixes are used to denoteuniversal(all) vs.existential(exists) requirements. Exact time windows are denoted by[n]and flexible by[m..n].
The most commonly used PSL operator is the "suffix-implication" operator (also known as the "triggers" operator), which is denoted by|=>. Its left operand is a PSL regular expression and its right operand is any PSL formula (be it in LTL style or regular expression style). The semantics ofr |=> pis that on every time point i such that the sequence of time points up to i constitute a match to the regular expression r, the path from i+1 should satisfy the property p. This is exemplified in the figures on the right.
The regular expressions of PSL have the common operators for concatenation (;), Kleene-closure (*), and union (|), as well as operator for fusion (:), intersection (&&) and a weaker version (&), and many variations for consecutive counting[*n]and in-consecutive counting e.g.[=n]and[->n].
The trigger operator comes in several variations, shown in the table below.
Heresandtare PSL-regular expressions, andpis a PSL formula.
Operators for concatenation, fusion, union, intersection and their variations are shown in the table below.
Heresandtare PSL regular expressions.
Operators for consecutive repetitions are shown in the table below.
Heresis a PSL regular expression.
Operators for non-consecutive repetitions are shown in the table below.
Herebis any PSL Boolean expression.
Below is a sample of some LTL-style operators of PSL.
Herepandqare any PSL formulas.
Sometimes it is desirable to change the definition of thenext time-point, for instance in multiply-clocked designs, or when a higher level of abstraction is desired. Thesampling operator(also known as theclock operator), denoted@, is used for this purpose. The formulap @ cwherepis a PSL formula andca PSL Boolean expressions holds on a given path ifpon that path projected on the cycles in whichcholds, as exemplified in the figures to the right.
The first property states that "everyrequestthat is immediately followed by anacksignal, should be followed by a completedata transfer, where a complete data transfer is a sequence starting with signalstart, ending with signalendin whichdatashould hold at least 8 times:
But sometimes it is desired to consider only the cases where the above signals occur on a cycle whereclkis high.
This is depicted in the second figure in which although the formula
usesdata[*3]and[*n]is consecutive repetition, the matching trace has 3 non-consecutive time points wheredataholds, but when considering only the time points whereclkholds, the time points wheredatahold become consecutive.
The semantics of formulas with nested @ is a little subtle. The interested reader is referred to [2].
PSL has several operators to deal with truncated paths (finite paths that may correspond to a prefix of the computation). Truncated paths occur in bounded-model checking, due to resets and in many other scenarios. The abort operators, specify how eventualities should be dealt with when a path has been truncated. They rely on the truncated semantics proposed in [1].
Herepis any PSL formula andbis any PSL Boolean expression.
PSL subsumes the temporal logicLTLand extends its expressive power to that of theomega-regular languages. The augmentation in expressive power, compared to that of LTL, which has the expressive power of the star-free ω-regular expressions, can be attributed to thesuffix implication, also known as thetriggersoperator, denoted "|->". The formular |-> fwhereris a regular expression andfis a temporal logic formula holds on a computationwif any prefix ofwmatchingrhas a continuation satisfyingf. Other non-LTL operators of PSL are the@operator, for specifying multiply-clocked designs, theabortoperators, for dealing with hardware resets, andlocal variablesfor succinctness.
PSL is defined in 4 layers: theBoolean layer, thetemporal layer, themodeling layerand theverification layer.
Property Specification Language can be used with multiple electronic system design languages (HDLs) such as:
When PSL is used in conjunction with one of the above HDLs, its Boolean layer uses the operators of the respective HDL.
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https://en.wikipedia.org/wiki/Property_Specification_Language
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Abarrel processoris aCPUthat switches betweenthreadsof execution on everycycle. ThisCPU designtechnique is also known as "interleaved" or "fine-grained"temporal multithreading. Unlikesimultaneous multithreadingin modernsuperscalararchitectures, it generally does not allow execution of multiple instructions in one cycle.
Likepreemptive multitasking, each thread of execution is assigned its ownprogram counterand otherhardware registers(each thread'sarchitectural state). A barrel processor can guarantee that each thread will execute one instruction everyncycles, unlike apreemptive multitaskingmachine, that typically runs one thread of execution for tens of millions of cycles, while all other threads wait their turn.
A technique calledC-slowingcan automatically generate a corresponding barrel processor design from a single-tasking processor design. Ann-way barrel processor generated this way acts much likenseparatemultiprocessingcopies of the original single-tasking processor, each one running at roughly 1/nthe original speed.[citation needed]
One of the earliest examples of a barrel processor was the I/O processing system in theCDC 6000 seriessupercomputers. These executed oneinstruction(or a portion of an instruction) from each of 10 different virtual processors (called peripheral processors or PPs) before returning to the first processor.[1]FromCDC 6000 serieswe read that "The peripheral processors are collectively implemented as a barrel processor. Each executes routines independently of the others. They are a loose predecessor of bus mastering ordirect memory access."
One motivation for barrel processors was to reduce hardware costs. In the case of the CDC 6x00 PPUs, the digital logic of the processor was much faster than the core memory, so rather than having ten separate processors, there are ten separate core memory units for the PPUs, but they all share the single set of processor logic.
Another example is theHoneywell 800, which had 8 groups of registers, allowing up to 8 concurrent programs. After each instruction, the processor would (in most cases) switch to the next active program in sequence.[2]
Barrel processors have also been used as large-scale central processors. TheTeraMTA(1988) was a large-scale barrel processor design with 128 threads per core.[3][4]The MTA architecture has seen continued development in successive products, such as theCray Urika-GD, originally introduced in 2012 (as the YarcData uRiKA) and targeted at data-mining applications.[5]
Barrel processors are also found in embedded systems, where they are particularly useful for their deterministicreal-timethread performance.
An early example is the “Dual CPU” version of thefour-bitCOP400that was introduced byNational Semiconductorin 1981. This single-chipmicrocontrollercontains two ostensibly independent CPUs that share instructions, memory, and most IO devices. In reality, the dual CPUs are a single two-thread barrel processor. It works by duplicating certain sections of the processor—those that store thearchitectural state—but not duplicating the main execution resources such asALU, buses, and memory. Separate architectural states are established with duplicated A (accumulators), B (pointer registers), C (carry flags), N (stack pointers), and PC (program counters).[6]
Another example is theXMOSXCore XS1(2007), a four-stage barrel processor with eight threads per core. (Newer processors fromXMOSalso have the same type of architecture.) The XS1 is found in Ethernet, USB, audio, and control devices, and other applications where I/O performance is critical. When the XS1 is programmed in the 'XC' language, software controlleddirect memory accessmay be implemented.
Barrel processors have also been used in specialized devices such as the eight-threadUbicomIP3023 network I/O processor (2004).
Some 8-bitmicrocontrollersbyPadauk Technologyfeature barrel processors with up to 8 threads per core.
A single-tasking processor spends a lot of time idle, not doing anything useful whenever acache missorpipeline stalloccurs. Advantages to employing barrel processors over single-tasking processors include:
There are a few disadvantages to barrel processors.
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https://en.wikipedia.org/wiki/Barrel_processor
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Inmathematics, thetensor-hom adjunctionis that thetensor product−⊗X{\displaystyle -\otimes X}andhom-functorHom(X,−){\displaystyle \operatorname {Hom} (X,-)}form anadjoint pair:
This is made more precise below. The order of terms in the phrase "tensor-hom adjunction" reflects their relationship: tensor is the left adjoint, while hom is the right adjoint.
SayRandSare (possibly noncommutative)rings, and consider the rightmodulecategories (an analogous statement holds for left modules):
Fix an(R,S){\displaystyle (R,S)}-bimoduleX{\displaystyle X}and define functorsF:D→C{\displaystyle F\colon {\mathcal {D}}\rightarrow {\mathcal {C}}}andG:C→D{\displaystyle G\colon {\mathcal {C}}\rightarrow {\mathcal {D}}}as follows:
ThenF{\displaystyle F}is leftadjointtoG{\displaystyle G}. This means there is anatural isomorphism
This is actually an isomorphism ofabelian groups. More precisely, ifY{\displaystyle Y}is an(A,R){\displaystyle (A,R)}-bimodule andZ{\displaystyle Z}is a(B,S){\displaystyle (B,S)}-bimodule, then this is an isomorphism of(B,A){\displaystyle (B,A)}-bimodules. This is one of the motivating examples of the structure in a closedbicategory.[1]
Like all adjunctions, the tensor-hom adjunction can be described by its counit and unitnatural transformations. Using the notation from the previous section, the counit
hascomponents
given by evaluation: For
Thecomponentsof the unit
are defined as follows: Fory{\displaystyle y}inY{\displaystyle Y},
is a rightS{\displaystyle S}-module homomorphism given by
Thecounit and unit equations[broken anchor]can now be explicitly verified. ForY{\displaystyle Y}inD{\displaystyle {\mathcal {D}}},
is given onsimple tensorsofY⊗X{\displaystyle Y\otimes X}by
Likewise,
Forϕ{\displaystyle \phi }inHomS(X,Z){\displaystyle \operatorname {Hom} _{S}(X,Z)},
is a rightS{\displaystyle S}-module homomorphism defined by
and therefore
TheHom functorhom(X,−){\displaystyle \hom(X,-)}commutes with arbitrary limits, while the tensor product−⊗X{\displaystyle -\otimes X}functor commutes with arbitrary colimits that exist in their domain category. However, in general,hom(X,−){\displaystyle \hom(X,-)}fails to commute with colimits, and−⊗X{\displaystyle -\otimes X}fails to commute with limits; this failure occurs even among finite limits or colimits. This failure to preserve shortexact sequencesmotivates the definition of theExt functorand theTor functor.
We can illustrate thetensor-hom adjunctionin thecategoryoffunctionsof finitesets. Given a setN{\displaystyle N}, itsHom functortakes any setA{\displaystyle A}to the set of functions fromN{\displaystyle N}toA{\displaystyle A}. Theisomorphism classof this set of functions is thenatural numberAN{\displaystyle A^{N}}. Similarly, the tensor product−⊗N{\displaystyle -\otimes N}takes a setA{\displaystyle A}to itscartesian productwithN{\displaystyle N}. Its isomorphism class is thus the natural numberAN{\displaystyle AN}.
This allows us to interpret the isomorphism ofhom-sets
thatuniversally characterizesthe tensor-hom adjunction, as thecategorificationof the remarkably basiclaw of exponents
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https://en.wikipedia.org/wiki/Tensor-hom_adjunction
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Psychologyis the scientific study ofmindandbehavior.[1][2]Its subject matter includes the behavior of humans and nonhumans, bothconsciousandunconsciousphenomena, and mental processes such asthoughts,feelings, andmotives. Psychology is an academic discipline of immense scope, crossing the boundaries between thenaturalandsocial sciences. Biological psychologists seek an understanding of theemergentproperties of brains, linking the discipline toneuroscience. As social scientists, psychologists aim to understand the behavior of individuals and groups.[3][4]
A professional practitioner or researcher involved in the discipline is called apsychologist. Some psychologists can also be classified asbehavioralorcognitive scientists. Some psychologists attempt to understand the role of mental functions in individual andsocial behavior. Others explore thephysiologicalandneurobiologicalprocesses that underlie cognitive functions and behaviors.
Psychologists are involved in research onperception,cognition,attention,emotion,intelligence,subjective experiences,motivation,brain functioning, andpersonality. Psychologists' interests extend tointerpersonal relationships,psychological resilience,family resilience, and other areas withinsocial psychology. They also consider the unconscious mind.[5]Research psychologists employempirical methodsto infercausalandcorrelationalrelationships between psychosocialvariables. Some, but not all,clinicalandcounselingpsychologists rely onsymbolic interpretation.
While psychological knowledge is often applied to the assessment and treatment of mental health problems, it is also directed towards understanding and solving problems in several spheres of human activity. By many accounts, psychology ultimately aims to benefit society.[6][7][8]Many psychologists are involved in some kind of therapeutic role, practicingpsychotherapyin clinical, counseling, orschoolsettings. Other psychologists conduct scientific research on a wide range of topics related to mental processes and behavior. Typically the latter group of psychologists work in academic settings (e.g., universities, medical schools, or hospitals). Another group of psychologists is employed inindustrial and organizationalsettings.[9]Yet others are involved in work onhuman development, aging,sports, health,forensic science,education, and themedia.
The wordpsychologyderives from the Greek wordpsyche, for spirit orsoul. The latter part of the wordpsychologyderives from -λογία-logia, which means "study" or "research".[10]The word psychology was first used in the Renaissance.[11]In itsLatinformpsychiologia, it was first employed by theCroatianhumanistandLatinistMarko Marulićin his bookPsichiologia de ratione animae humanae(Psychology, on the Nature of the Human Soul) in the decade 1510–1520[11][12]The earliest known reference to the wordpsychologyin English was bySteven Blankaartin 1694 inThe Physical Dictionary. The dictionary refers to "Anatomy, which treats the Body, and Psychology, which treats of the Soul."[13]
Ψ(psi), the firstletterof the Greek wordpsychefrom which the term psychology is derived, is commonly associated with the field of psychology.
In 1890,William Jamesdefinedpsychologyas "the science of mental life, both of its phenomena and their conditions."[14]This definition enjoyed widespread currency for decades. However, this meaning was contested, notably byJohn B. Watson, who in 1913 asserted themethodological behavioristview of psychology as a purely objective experimental branch ofnatural science, the theoretical goal of which "is the prediction and control of behavior."[15]Since James defined "psychology", the term more strongly implicates scientific experimentation.[16][15]Folk psychologyis the understanding of the mental states and behaviors of people held byordinary people, as contrasted with psychology professionals' understanding.[17]
The ancient civilizations of Egypt, Greece, China, India, and Persia all engaged in the philosophical study of psychology. In Ancient Egypt theEbers Papyrusmentioneddepressionand thought disorders.[18]Historians note that Greek philosophers, includingThales,Plato, andAristotle(especially in hisDe Animatreatise),[19]addressed the workings of the mind.[20]As early as the 4th century BC, the Greek physicianHippocratestheorized thatmental disordershad physical rather than supernatural causes.[21]In 387 BCE, Plato suggested that the brain is where mental processes take place, and in 335 BCE Aristotle suggested that it was the heart.[22]
In China, the foundations of psychological thought emerged from the philosophical works of ancient thinkers likeLaoziandConfucius, as well as the teachings ofBuddhism.[23]This body of knowledge drew insights from introspection, observation, and techniques for focused thinking and behavior. It viewed the universe as comprising physical and mental realms, along with the interplay between the two.[24]Chinese philosophy also emphasized purifying the mind in order to increase virtue and power. An ancient text known asThe Yellow Emperor's Classic of Internal Medicineidentifies the brain as the nexus of wisdom and sensation, includes theories of personality based onyin–yangbalance, and analyzes mental disorder in terms of physiological and social disequilibria. Chinese scholarship that focused on the brain advanced during theQing dynastywith the work of Western-educated Fang Yizhi (1611–1671),Liu Zhi(1660–1730), and Wang Qingren (1768–1831). Wang Qingren emphasized the importance of the brain as the center of the nervous system, linked mental disorder with brain diseases, investigated the causes of dreams andinsomnia, and advanced a theory ofhemispheric lateralizationin brain function.[25]
Influenced byHinduism,Indian philosophyexplored distinctions in types of awareness. A central idea of theUpanishadsand otherVedictexts that formed the foundations of Hinduism was the distinction between a person's transient mundane self and theireternal, unchanging soul. Divergent Hindu doctrines andBuddhismhave challenged this hierarchy of selves, but have all emphasized the importance of reaching higher awareness.Yogaencompasses a range of techniques used in pursuit of this goal.Theosophy, a religion established byRussian-AmericanphilosopherHelena Blavatsky, drew inspiration from these doctrines during her time inBritish India.[26][27]
Psychology was of interest toEnlightenment thinkersin Europe. In Germany,Gottfried Wilhelm Leibniz(1646–1716) applied his principles of calculus to the mind, arguing that mental activity took place on an indivisible continuum. He suggested that the difference between conscious and unconscious awareness is only a matter of degree.Christian Wolffidentified psychology as its own science, writingPsychologia Empiricain 1732 andPsychologia Rationalisin 1734.Immanuel Kantadvanced the idea ofanthropologyas a discipline, with psychology an important subdivision. Kant, however, explicitly rejected the idea of anexperimental psychology, writing that "the empirical doctrine of the soul can also never approach chemistry even as a systematic art of analysis or experimental doctrine, for in it the manifold of inner observation can be separated only by mere division in thought, and cannot then be held separate and recombined at will (but still less does another thinking subject suffer himself to be experimented upon to suit our purpose), and even observation by itself already changes and displaces the state of the observed object."
In 1783, Ferdinand Ueberwasser (1752–1812) designated himselfProfessor of Empirical Psychology and Logicand gave lectures on scientific psychology, though these developments were soon overshadowed by theNapoleonic Wars.[28]At the end of the Napoleonic era, Prussian authorities discontinued the Old University of Münster.[28]Having consulted philosophersHegelandHerbart, however, in 1825the Prussian stateestablished psychology as a mandatory discipline in its rapidly expanding and highly influentialeducational system. However, this discipline did not yet embrace experimentation.[29]In England, early psychology involvedphrenologyand the response to social problems including alcoholism, violence, and the country's crowded "lunatic" asylums.[30]
PhilosopherJohn Stuart Millbelieved that the human mind was open to scientific investigation, even if the science is in some ways inexact.[31]Mill proposed a "mentalchemistry" in which elementary thoughts could combine into ideas of greater complexity.[31]Gustav Fechnerbegan conductingpsychophysicsresearch inLeipzigin the 1830s. He articulated the principle that human perception of a stimulus varieslogarithmicallyaccording to its intensity.[32]: 61The principle became known as theWeber–Fechner law. Fechner's 1860Elements of Psychophysicschallenged Kant's negative view with regard to conducting quantitative research on the mind.[33][29]Fechner's achievement was to show that "mental processes could not only be given numerical magnitudes, but also that these could be measured by experimental methods."[29]In Heidelberg,Hermann von Helmholtzconducted parallel research on sensory perception, and trained physiologistWilhelm Wundt. Wundt, in turn, came to Leipzig University, where he established the psychological laboratory that brought experimental psychology to the world. Wundt focused on breaking down mental processes into the most basic components, motivated in part by an analogy to recent advances in chemistry, and its successful investigation of the elements and structure of materials.[34]Paul FlechsigandEmil Kraepelinsoon created another influential laboratory at Leipzig, a psychology-related lab, that focused more on experimental psychiatry.[29]
James McKeen Cattell, a professor of psychology at theUniversity of PennsylvaniaandColumbia Universityand the co-founder ofPsychological Review, was the first professor of psychology in theUnited States.[35]
The German psychologistHermann Ebbinghaus, a researcher at theUniversity of Berlin, was a 19th-century contributor to the field. He pioneered the experimental study of memory and developed quantitative models of learning and forgetting.[36]In the early 20th century,Wolfgang Kohler,Max Wertheimer, andKurt Koffkaco-founded the school ofGestalt psychologyofFritz Perls. The approach of Gestalt psychology is based upon the idea that individuals experience things as unified wholes. Rather thanreducingthoughts and behavior into smaller component elements, as in structuralism, the Gestaltists maintain that whole of experience is important, "and is something else than the sum of its parts, because summing is a meaningless procedure, whereas the whole-part relationship is meaningful."[37]
Psychologists in Germany, Denmark, Austria, England, and the United States soon followed Wundt in setting up laboratories.[38]G. Stanley Hall, an American who studied with Wundt, founded a psychology lab that became internationally influential. The lab was located atJohns Hopkins University. Hall, in turn, trainedYujiro Motora, who brought experimental psychology, emphasizing psychophysics, to theImperial University of Tokyo.[39]Wundt's assistant,Hugo Münsterberg, taught psychology at Harvard to students such asNarendra Nath Sen Gupta—who, in 1905, founded a psychology department and laboratory at theUniversity of Calcutta.[26]Wundt's studentsWalter Dill Scott,Lightner Witmer, andJames McKeen Cattellworked on developing tests of mental ability. Cattell, who also studied witheugenicistFrancis Galton, went on to found thePsychological Corporation. Witmer focused on the mental testing of children; Scott, on employee selection.[32]: 60
Another student of Wundt, the EnglishmanEdward Titchener, created the psychology program atCornell Universityand advanced "structuralist" psychology. The idea behind structuralism was to analyze and classify different aspects of the mind, primarily through the method ofintrospection.[40]William James,John Dewey, andHarvey Carradvanced the idea offunctionalism, an expansive approach to psychology that underlined the Darwinian idea of a behavior's usefulness to the individual. In 1890, James wrote an influential book,The Principles of Psychology, which expanded on the structuralism. He memorably described "stream of consciousness." James's ideas interested many American students in the emerging discipline.[40][14][32]: 178–82Dewey integrated psychology with societal concerns, most notably by promotingprogressive education, inculcating moral values in children, and assimilating immigrants.[32]: 196–200
A different strain of experimentalism, with a greater connection to physiology, emerged in South America, under the leadership of Horacio G. Piñero at theUniversity of Buenos Aires.[41]In Russia, too, researchers placed greater emphasis on the biological basis for psychology, beginning withIvan Sechenov's 1873 essay, "Who Is to Develop Psychology and How?" Sechenov advanced the idea of brainreflexesand aggressively promoted adeterministicview of human behavior.[42]The Russian-SovietphysiologistIvan Pavlovdiscovered in dogs a learning process that was later termed "classical conditioning" and applied the process to human beings.[43]
One of the earliest psychology societies wasLa Société de Psychologie Physiologiquein France, which lasted from 1885 to 1893. The first meeting of the International Congress of Psychology sponsored by theInternational Union of Psychological Sciencetook place in Paris, in August 1889, amidstthe World's Faircelebrating the centennial of the French Revolution. William James was one of three Americans among the 400 attendees. TheAmerican Psychological Association(APA) was founded soon after, in 1892. The International Congress continued to be held at different locations in Europe and with wide international participation. The Sixth Congress, held in Geneva in 1909, included presentations in Russian, Chinese, and Japanese, as well asEsperanto. After a hiatus for World War I, the Seventh Congress met in Oxford, with substantially greater participation from the war-victorious Anglo-Americans. In 1929, the Congress took place at Yale University in New Haven, Connecticut, attended by hundreds of members of the APA.[38]Tokyo Imperial University led the way in bringing new psychology to the East. New ideas about psychology diffused from Japan into China.[25][39]
American psychology gained status upon the U.S.'s entry into World War I. A standing committee headed byRobert Yerkesadministered mental tests ("Army Alpha" and "Army Beta") to almost 1.8 million soldiers.[44]Subsequently, theRockefeller family, via theSocial Science Research Council, began to provide funding for behavioral research.[45][46]Rockefeller charities funded the National Committee on Mental Hygiene, which disseminated the concept of mental illness and lobbied for applying ideas from psychology to child rearing.[44][47]Through the Bureau of Social Hygiene and later funding ofAlfred Kinsey, Rockefeller foundations helped establish research on sexuality in the U.S.[48]Under the influence of the Carnegie-fundedEugenics Record Office, the Draper-fundedPioneer Fund, and other institutions, theeugenics movementalso influenced American psychology. In the 1910s and 1920s, eugenics became a standard topic in psychology classes.[49]In contrast to the US, in the UK psychology was met with antagonism by the scientific and medical establishments, and up until 1939, there were only six psychology chairs in universities in England.[50]
During World War II and the Cold War, the U.S. military and intelligence agencies established themselves as leading funders of psychology by way of the armed forces and in the newOffice of Strategic Servicesintelligence agency. University of Michigan psychologist Dorwin Cartwright reported that university researchers began large-scale propaganda research in 1939–1941. He observed that "the last few months of the war saw a social psychologist become chiefly responsible for determining the week-by-week-propaganda policy for the United States Government." Cartwright also wrote that psychologists had significant roles in managing the domestic economy.[51]The Army rolled out its newGeneral Classification Testto assess the ability of millions of soldiers. The Army also engaged in large-scale psychological research oftroop morale and mental health.[52]In the 1950s, theRockefeller FoundationandFord Foundationcollaborated with theCentral Intelligence Agency(CIA) to fund research onpsychological warfare.[53]In 1965, public controversy called attention to the Army'sProject Camelot, the "Manhattan Project" ofsocial science, an effort which enlisted psychologists and anthropologists to analyze the plans and policies of foreign countries for strategic purposes.[54][55]
In Germany after World War I, psychology held institutional power through the military, which was subsequently expanded along with the rest of the military duringNazi Germany.[29]Under the direction ofHermann Göring's cousinMatthias Göring, theBerlin Psychoanalytic Institutewas renamed the Göring Institute.Freudian psychoanalystswere expelled and persecuted under the anti-Jewish policies of theNazi Party, and all psychologists had to distance themselves fromFreudandAdler, founders ofpsychoanalysiswho were also Jewish.[56]The Göring Institute was well-financed throughout the war with a mandate to create a "New German Psychotherapy." This psychotherapy aimed to align suitable Germans with the overall goals of the Reich. As described by one physician, "Despite the importance of analysis, spiritual guidance and the active cooperation of the patient represent the best way to overcome individual mental problems and to subordinate them to the requirements of theVolkand theGemeinschaft." Psychologists were to provideSeelenführung[lit., soul guidance], the leadership of the mind, to integrate people into the new vision of a German community.[57]Harald Schultz-Henckemelded psychology with the Nazi theory of biology and racial origins, criticizing psychoanalysis as a study of the weak and deformed.[58]Johannes Heinrich Schultz, a German psychologist recognized for developing the technique ofautogenic training, prominently advocated sterilization and euthanasia of men considered genetically undesirable, and devised techniques for facilitating this process.[59]
After the war, new institutions were created although some psychologists, because of their Nazi affiliation, were discredited.Alexander Mitscherlichfounded a prominent applied psychoanalysis journal calledPsyche. With funding from the Rockefeller Foundation, Mitscherlich established the first clinical psychosomatic medicine division at Heidelberg University. In 1970, psychology was integrated into the required studies of medical students.[60]
After theRussian Revolution, theBolshevikspromoted psychology as a way to engineer the "New Man" of socialism. Consequently, university psychology departments trained large numbers of students in psychology. At the completion of training, positions were made available for those students at schools, workplaces, cultural institutions, and in the military. The Russian state emphasizedpedologyand the study of child development.Lev Vygotskybecame prominent in the field of child development.[42]The Bolsheviks also promotedfree loveand embraced the doctrine of psychoanalysis as an antidote to sexual repression.[61]:84–6[62]Although pedology and intelligence testing fell out of favor in 1936, psychology maintained its privileged position as an instrument of the Soviet Union.[42]Stalinist purgestook a heavy toll and instilled a climate of fear in the profession, as elsewhere in Soviet society.[61]:22Following World War II, Jewish psychologists past and present, includingLev Vygotsky,A.R. Luria, and Aron Zalkind, were denounced; Ivan Pavlov (posthumously) and Stalin himself were celebrated as heroes of Soviet psychology.[61]: 25–6, 48–9Soviet academics experienced a degree of liberalization during theKhrushchev Thaw. The topics of cybernetics, linguistics, and genetics became acceptable again. The new field ofengineering psychologyemerged. The field involved the study of the mental aspects of complex jobs (such as pilot and cosmonaut). Interdisciplinary studies became popular and scholars such asGeorgy Shchedrovitskydeveloped systems theory approaches to human behavior.[61]:27–33
Twentieth-century Chinese psychology originally modeled itself on U.S. psychology, with translations from American authors like William James, the establishment of university psychology departments and journals, and the establishment of groups including the Chinese Association of Psychological Testing (1930) and theChinese Psychological Society(1937). Chinese psychologists were encouraged to focus on education and language learning. Chinese psychologists were drawn to the idea that education would enable modernization. John Dewey, who lectured to Chinese audiences between 1919 and 1921, had a significant influence on psychology in China. ChancellorT'sai Yuan-p'eiintroduced him atPeking Universityas a greater thinker than Confucius.Kuo Zing-yangwho received a PhD at the University of California, Berkeley, became President ofZhejiang Universityand popularizedbehaviorism.[63]: 5–9After theChinese Communist Partygained control of the country, the Stalinist Soviet Union became the major influence, withMarxism–Leninismthe leading social doctrine and Pavlovian conditioning the approved means of behavior change. Chinese psychologists elaborated on Lenin's model of a "reflective" consciousness, envisioning an "active consciousness" (pinyin:tzu-chueh neng-tung-li) able to transcend material conditions through hard work and ideological struggle. They developed a concept of "recognition" (pinyin:jen-shih) which referred to the interface between individual perceptions and the socially accepted worldview; failure to correspond with party doctrine was "incorrect recognition."[63]:9–17Psychology education was centralized under theChinese Academy of Sciences, supervised by theState Council. In 1951, the academy created a Psychology Research Office, which in 1956 became the Institute of Psychology. Because most leading psychologists were educated in the United States, the first concern of the academy was the re-education of these psychologists in the Soviet doctrines. Child psychology and pedagogy for the purpose of a nationally cohesive education remained a central goal of the discipline.[63]: 18–24
Women in the early 1900s started to make key findings within the world of psychology. In 1923,Anna Freud,[64]the daughter ofSigmund Freud, built on her father's work using differentdefense mechanisms(denial, repression, and suppression) topsychoanalyzechildren. She believed that once a child reached thelatency period,child analysiscould be used as a mode oftherapy. She stated it is important focus on the child's environment, support their development, and preventneurosis. She believed a child should be recognized as their own person with their own right and have each session catered to the child's specific needs. She encouraged drawing, moving freely, and expressing themselves in any way. This helped build a strong therapeutic alliance with child patients, which allows psychologists to observe their normal behavior. She continued her research on the impact of children after family separation, children with socio-economically disadvantaged backgrounds, and all stages of child development from infancy to adolescence.[65]
Functional periodicity, the belief women are mentally and physically impaired duringmenstruation, impactedwomen's rightsbecause employers were less likely to hire them due to the belief they would be incapable of working for 1 week a month.Leta Stetter Hollingworthwanted to prove this hypothesis andEdward L. Thorndike'stheory, that women have lesser psychological and physical traits than men and were simply mediocre, incorrect.Hollingworthworked to prove differences were not from male genetic superiority, but from culture. She also included the concept of women's impairment duringmenstruationin her research. She recorded both women and men performances on tasks (cognitive, perceptual, and motor) for three months. No evidence was found of decreased performance due to a woman'smenstrualcycle.[66]She also challenged the belief intelligence is inherited and women here are intellectually inferior to men. She stated that women do not reach positions of power due to thesocietal normsand roles they are assigned. As she states in her article, "Variability as related to sex differences in achievement: A Critique",[67]the largest problem women have is the social order that was built due to the assumption women have less interests and abilities than men. To further prove her point, she completed another experiment with infants who have not been influenced by the environment of social norms, like the adult male getting more opportunities than women. She found no difference between infants besides size. After this research proved the original hypothesis wrong,Hollingworthwas able to show there is no difference between the physiological and psychological traits of men and women, and women are not impaired duringmenstruation.[68]
The first half of the 1900s was filled with new theories and it was a turning point for women's recognition within the field of psychology. In addition to the contributions made byLeta Stetter HollingworthandAnna Freud,Mary Whiton Calkinsinvented the paired associates technique of studying memory and developedself-psychology.[69]Karen Horneydeveloped the concept of "womb envy" and neurotic needs.[70]PsychoanalystMelanie Kleinimpacteddevelopmental psychologywith her research ofplay therapy.[71]These great discoveries and contributions were made during struggles ofsexism,discrimination, and little recognition for their work.
Women in the second half of the 20th century continued to do research that had large-scale impacts on the field of psychology.Mary Ainsworth's work centered aroundattachment theory. Building off fellow psychologistJohn Bowlby, Ainsworth spent years doingfieldworkto understand the development of mother-infant relationships. In doing this field research, Ainsworth developed the Strange Situation Procedure, a laboratory procedure meant to study attachment style by separating and uniting a child with their mother several different times under different circumstances. These field studies are also where she developed herattachment theoryand the order ofattachment styles, which was a landmark fordevelopmental psychology.[72][73]Because of her work, Ainsworth became one of the most cited psychologists of all time.[74]Mamie Phipps Clarkwas another woman in psychology that changed the field with her research. She was one of the first African-Americans to receive a doctoral degree in psychology fromColumbia University, along with her husband,Kenneth Clark. Her master's thesis, "The Development of Consciousness in Negro Pre-School Children," argued that black children'sself-esteemwas negatively impacted byracial discrimination. She and her husband conduced research building off her thesis throughout the 1940s. These tests, called thedoll tests, asked young children to choose between identical dolls whose only difference was race, and they found that the majority of the children preferred the white dolls and attributed positive traits to them. Repeated over and over again, these tests helped to determine the negative effects ofracial discriminationandsegregationon black children'sself-imageand development. In 1954, this research would help decide the landmarkBrown v. Board of Educationdecision, leading to the end of legal segregation across the nation. Clark went on to be an influential figure in psychology, her work continuing to focus on minority youth.[75]
As the field of psychology developed throughout the latter half of the 20th century, women in the field advocated for their voices to be heard and their perspectives to be valued.Second-wave feminismdid not miss psychology. An outspoken feminist in psychology wasNaomi Weisstein, who was an accomplished researcher in psychology andneuroscience, and is perhaps best known for her paper, "Kirche, Kuche, Kinder as Scientific Law: Psychology Constructs the Female." Psychology Constructs the Female criticized the field of psychology for centering men and using biology too much to explain gender differences without taking into account social factors.[76]Her work set the stage for further research to be done insocial psychology, especially ingender construction.[77]Other women in the field also continued advocating for women in psychology, creating theAssociation for Women in Psychologyto criticize how the field treated women.E. Kitsch Child,Phyllis Chesler, andDorothy Riddlewere some of the founding members of the organization in 1969.[78][79]
The latter half of the 20th century further diversified the field of psychology, with women of color reaching new milestones. In 1962,Martha Bernalbecame the first Latina woman to get a Ph.D. in psychology. In 1969,Marigold Linton, the first Native American woman to get a Ph.D. in psychology, founded theNational Indian Education Association. She was also a founding member of theSociety for Advancement of Chicanos and Native Americans in Science. In 1971, The Network of Indian Psychologists was established byCarolyn Attneave. Harriet McAdoo was appointed to the White House Conference on Families in 1979.[80]
In the 21st century, women have gained greater prominence in psychology, contributing significantly to a wide range of subfields. Many have taken on leadership roles, directed influential research labs, and guided the next generation of psychologists. However, gender disparities remain, especially when it comes to equal pay and representation in senior academic positions.[81]The number of women pursuing education and training in psychological science has reached a record high. In the United States, estimates suggest that women make up about 78% of undergraduate students and 71% of graduate students in psychology.[81]
In 1920,Édouard ClaparèdeandPierre Bovetcreated a new applied psychology organization called the International Congress of Psychotechnics Applied to Vocational Guidance, later called the International Congress of Psychotechnics and then theInternational Association of Applied Psychology.[38]The IAAP is considered the oldest international psychology association.[82]Today, at least 65 international groups deal with specialized aspects of psychology.[82]In response to male predominance in the field, female psychologists in the U.S. formed the National Council of Women Psychologists in 1941. This organization became the International Council of Women Psychologists after World War II and the International Council of Psychologists in 1959. Several associations including theAssociation of Black Psychologistsand the Asian American Psychological Association have arisen to promote the inclusion of non-European racial groups in the profession.[82]
TheInternational Union of Psychological Science(IUPsyS) is the world federation of national psychological societies. The IUPsyS was founded in 1951 under the auspices of theUnited Nations Educational, Cultural and Scientific Organization (UNESCO).[38][83]Psychology departments have since proliferated around the world, based primarily on the Euro-American model.[26][83]Since 1966, the Union has published theInternational Journal of Psychology.[38]IAAP and IUPsyS agreed in 1976 each to hold a congress every four years, on a staggered basis.[82]
IUPsyS recognizes 66 national psychology associations and at least 15 others exist.[82]The American Psychological Association is the oldest and largest.[82]Its membership has increased from 5,000 in 1945 to 100,000 in the present day.[40]The APA includes54 divisions, which since 1960 have steadily proliferated to include more specialties. Some of these divisions, such as theSociety for the Psychological Study of Social Issuesand theAmerican Psychology–Law Society, began as autonomous groups.[82]
TheInteramerican Psychological Society, founded in 1951, aspires to promote psychology across the Western Hemisphere. It holds the Interamerican Congress of Psychology and had 1,000 members in year 2000. The European Federation of Professional Psychology Associations, founded in 1981, represents 30 national associations with a total of 100,000 individual members. At least 30 other international organizations represent psychologists in different regions.[82]
In some places, governments legally regulate who can provide psychological services or represent themselves as a "psychologist."[84]The APA defines a psychologist as someone with a doctoral degree in psychology.[85]
Early practitioners of experimental psychology distinguished themselves fromparapsychology, which in the late nineteenth century enjoyed popularity (including the interest of scholars such as William James). Some people considered parapsychology to be part of "psychology". Parapsychology,hypnotism, andpsychismwere major topics at the early International Congresses. But students of these fields were eventually ostracized, and more or less banished from the Congress in 1900–1905.[38]Parapsychology persisted for a time at Imperial University in Japan, with publications such asClairvoyance and Thoughtographyby Tomokichi Fukurai, but it was mostly shunned by 1913.[39]
As a discipline, psychology has long sought to fend off accusations that it is a"soft" science. Philosopher of scienceThomas Kuhn's 1962 critique implied psychology overall was in a pre-paradigm state, lacking agreement on the type of overarching theory found in mature hard sciences such as chemistry and physics.[86]Because some areas of psychology rely on research methods such asself-reportsin surveys and questionnaires, critics asserted that psychology is not anobjectivescience. Skeptics have suggested that personality, thinking, and emotion cannot be directly measured and are often inferred from subjective self-reports, which may be problematic. Experimental psychologists have devised a variety of ways to indirectly measure these elusive phenomenological entities.[87][88][89]
Divisions still exist within the field, with some psychologists more oriented towards the unique experiences of individual humans, which cannot be understood only as data points within a larger population. Critics inside and outside the field have argued that mainstream psychology has become increasingly dominated by a "cult of empiricism", which limits the scope of research because investigators restrict themselves to methods derived from the physical sciences.[90]:36–7Feminist critiques have argued that claims to scientific objectivity obscure the values and agenda of (historically) mostly male researchers.[44]Jean Grimshaw, for example, argues that mainstream psychological research has advanced apatriarchalagenda through its efforts to control behavior.[90]:120
Psychologists generally consider biology the substrate of thought and feeling, and therefore an important area of study. Behaviorial neuroscience, also known as biological psychology, involves the application of biological principles to the study of physiological and genetic mechanisms underlying behavior in humans and other animals. The allied field ofcomparative psychologyis the scientific study of the behavior and mental processes of non-human animals.[92]A leading question in behavioral neuroscience has been whether and how mental functions arelocalized in the brain. FromPhineas GagetoH.M.andClive Wearing, individual people with mental deficits traceable to physical brain damage have inspired new discoveries in this area.[93]Modern behavioral neuroscience could be said to originate in the 1870s, when in FrancePaul Brocatraced production of speech to the left frontal gyrus, thereby also demonstrating hemispheric lateralization of brain function. Soon after,Carl Wernickeidentified a related area necessary for the understanding of speech.[94]: 20–2
The contemporary field ofbehavioral neurosciencefocuses on the physical basis of behavior. Behaviorial neuroscientists use animal models, often relying on rats, to study the neural, genetic, and cellular mechanisms that underlie behaviors involved in learning, memory, and fear responses.[95]Cognitive neuroscientists, by using neural imaging tools, investigate the neural correlates of psychological processes in humans.Neuropsychologistsconduct psychological assessments to determine how an individual's behavior and cognition are related to the brain. Thebiopsychosocial modelis a cross-disciplinary, holistic model that concerns the ways in which interrelationships of biological, psychological, and socio-environmental factors affect health and behavior.[96]
Evolutionary psychologyapproaches thought and behavior from a modernevolutionaryperspective. This perspective suggests that psychological adaptations evolved to solve recurrent problems in human ancestral environments. Evolutionary psychologists attempt to find out how human psychological traits are evolved adaptations, the results ofnatural selectionorsexual selectionover the course of human evolution.[97]
The history of the biological foundations of psychology includes evidence of racism. The idea of white supremacy and indeed the modern concept of race itself arose during the process of world conquest by Europeans.[98]Carl von Linnaeus's four-fold classification of humans classifies Europeans as intelligent and severe, Americans as contented and free, Asians as ritualistic, and Africans as lazy and capricious. Race was also used to justify the construction of socially specific mental disorders such asdrapetomaniaanddysaesthesia aethiopica—the behavior of uncooperative African slaves.[99]After the creation of experimental psychology, "ethnical psychology" emerged as a subdiscipline, based on the assumption that studying primitive races would provide an important link between animal behavior and the psychology of more evolved humans.[100]
A tenet of behavioral research is that a large part of both human and lower-animal behavior is learned. A principle associated with behavioral research is that the mechanisms involved in learning apply to humans and non-human animals. Behavioral researchers have developed a treatment known asbehavior modification, which is used to help individuals replace undesirable behaviors with desirable ones.
Early behavioral researchers studied stimulus–response pairings, now known asclassical conditioning. They demonstrated that when a biologically potent stimulus (e.g., food that elicits salivation) is paired with a previously neutral stimulus (e.g., a bell) over several learning trials, the neutral stimulus by itself can come to elicit the response the biologically potent stimulus elicits.Ivan Pavlov—known best for inducing dogs to salivate in the presence of a stimulus previously linked with food—became a leading figure in the Soviet Union and inspired followers to use his methods on humans.[42]In the United States,Edward Lee Thorndikeinitiated "connectionist" studies by trapping animals in "puzzle boxes" and rewarding them for escaping. Thorndike wrote in 1911, "There can be no moral warrant for studying man's nature unless the study will enable us to control his acts."[32]: 212–5From 1910 to 1913 the American Psychological Association went through a sea change of opinion, away frommentalismand towards "behavioralism." In 1913, John B. Watson coined the term behaviorism for this school of thought.[32]: 218–27Watson's famousLittle Albert experimentin 1920 was at first thought to demonstrate that repeated use of upsetting loud noises could instillphobias(aversions to other stimuli) in an infant human,[15][101]although such a conclusion was likely an exaggeration.[102]Karl Lashley, a close collaborator with Watson, examined biological manifestations of learning in the brain.[93]
Clark L. Hull,Edwin Guthrie, and others did much to help behaviorism become a widely used paradigm.[40]A new method of "instrumental" or "operant" conditioning added the concepts ofreinforcementandpunishmentto the model of behavior change.Radical behavioristsavoided discussing the inner workings of the mind, especially the unconscious mind, which they considered impossible to assess scientifically.[103]Operant conditioning was first described by Miller and Kanorski and popularized in the U.S. byB.F. Skinner, who emerged as a leading intellectual of the behaviorist movement.[104][105]
Noam Chomskypublished an influential critique of radical behaviorism on the grounds that behaviorist principles could not adequately explain the complex mental process oflanguage acquisitionand language use.[106][107]The review, which was scathing, did much to reduce the status of behaviorism within psychology.[32]: 282–5Martin Seligmanand his colleagues discovered that they could condition in dogs a state of "learned helplessness", which was not predicted by the behaviorist approach to psychology.[108][109]Edward C. Tolmanadvanced a hybrid "cognitive behavioral" model, most notably with his 1948 publication discussing thecognitive mapsused by rats to guess at the location of food at the end of a maze.[110]Skinner's behaviorism did not die, in part because it generated successful practical applications.[107]
TheAssociation for Behavior Analysis Internationalwas founded in 1974 and by 2003 had members from 42 countries. The field has gained a foothold in Latin America and Japan.[111]Applied behavior analysisis the term used for the application of the principles of operant conditioning to change socially significant behavior (it supersedes the term, "behavior modification").[112]
GreenRedBluePurpleBluePurple
BluePurpleRedGreenPurpleGreen
The Stroop effect is the fact that naming the color of the first set of words is easier and quicker than the second.
Cognitive psychology involves the study ofmental processes, includingperception,attention, language comprehension and production,memory, and problem solving.[113]Researchers in the field of cognitive psychology are sometimes calledcognitivists. They rely on aninformation processingmodel of mental functioning. Cognitivist research is informed byfunctionalismand experimental psychology.
Starting in the 1950s, the experimental techniques developed by Wundt, James, Ebbinghaus, and others re-emerged as experimental psychology became increasingly cognitivist and, eventually, constituted a part of the wider, interdisciplinarycognitive science.[114][115]Some called this development thecognitive revolutionbecause it rejected the anti-mentalist dogma of behaviorism as well as the strictures of psychoanalysis.[115]
Albert Bandurahelped along the transition in psychology from behaviorism to cognitive psychology. Bandura and othersocial learning theoristsadvanced the idea of vicarious learning. In other words, they advanced the view that a child can learn by observing the immediate social environment and not necessarily from having been reinforced for enacting a behavior, although they did not rule out the influence of reinforcement on learning a behavior.[116]
Technological advances also renewed interest in mental states and mental representations. English neuroscientistCharles Sherringtonand Canadian psychologistDonald O. Hebbused experimental methods to link psychological phenomena to the structure and function of the brain. The rise of computer science,cybernetics, andartificial intelligenceunderlined the value of comparing information processing in humans and machines.
A popular and representative topic in this area iscognitive bias, or irrational thought. Psychologists (and economists) have classified and described asizeable catalog of biaseswhich recur frequently in human thought. Theavailability heuristic, for example, is the tendency to overestimate the importance of something which happens to come readily to mind.[117]
Elements of behaviorism and cognitive psychology were synthesized to formcognitive behavioral therapy, a form of psychotherapy modified from techniques developed by American psychologistAlbert Ellisand American psychiatristAaron T. Beck.
On a broader level, cognitive science is an interdisciplinary enterprise involving cognitive psychologists, cognitive neuroscientists, linguists, and researchers in artificial intelligence, human–computer interaction, andcomputational neuroscience. The discipline of cognitive science covers cognitive psychology as well as philosophy of mind, computer science, and neuroscience.[118]Computer simulations are sometimes used to model phenomena of interest.
Social psychology is concerned with howbehaviors,thoughts,feelings, and the social environment influence human interactions.[119]Social psychologists study such topics as the influence of others on an individual's behavior (e.g.conformity,persuasion) and the formation of beliefs,attitudes, andstereotypesabout other people.Social cognitionfuses elements of social and cognitive psychology for the purpose of understanding how people process, remember, or distort social information. The study ofgroup dynamicsinvolves research on the nature of leadership, organizational communication, and related phenomena. In recent years, social psychologists have become interested inimplicitmeasures,mediationalmodels, and the interaction of person and social factors in accounting for behavior. Some concepts thatsociologistshave applied to the study of psychiatric disorders, concepts such as the social role, sick role, social class, life events, culture, migration, andtotal institution, have influenced social psychologists.[120]
Psychoanalysis is a collection of theories and therapeutic techniques intended to analyze the unconscious mind and its impact on everyday life. These theories and techniques inform treatments for mental disorders.[121][122][123]Psychoanalysis originated in the 1890s, most prominently with the work ofSigmund Freud. Freud's psychoanalytic theory was largely based on interpretive methods,introspection, and clinical observation. It became very well known, largely because it tackled subjects such assexuality,repression, and the unconscious.[61]: 84–6Freud pioneered the methods offree associationanddream interpretation.[124][125]
Psychoanalytic theory is not monolithic. Other well-known psychoanalytic thinkers who diverged from Freud includeAlfred Adler,Carl Jung,Erik Erikson,Melanie Klein,D.W. Winnicott,Karen Horney,Erich Fromm,John Bowlby, Freud's daughterAnna Freud, andHarry Stack Sullivan. These individuals ensured that psychoanalysis would evolve into diverse schools of thought. Among these schools areego psychology,object relations, andinterpersonal,Lacanian, andrelational psychoanalysis.
Psychologists such asHans Eysenckand philosophers includingKarl Poppersharply criticized psychoanalysis. Popper argued that psychoanalysis was notfalsifiable(no claim it made could be proven wrong) and therefore inherently not a scientific discipline,[126]whereas Eysenck advanced the view that psychoanalytic tenets had been contradicted by experimental data. By the end of the 20th century, psychology departments inAmerican universitiesmostly had marginalized Freudian theory, dismissing it as a "desiccated and dead" historical artifact.[127]Researchers such asAntónio Damásio,Oliver Sacks, andJoseph LeDoux; and individuals in the emerging field ofneuro-psychoanalysishave defended some of Freud's ideas on scientific grounds.[128]
Humanistic psychology, which has been influenced by existentialism and phenomenology,[130]stressesfree willandself-actualization.[131]It emerged in the 1950s as a movement within academic psychology, in reaction to both behaviorism and psychoanalysis.[132]The humanistic approach seeks to view the whole person, not just fragmented parts of the personality or isolated cognitions.[133]Humanistic psychology also focuses on personal growth,self-identity, death, aloneness, and freedom. It emphasizes subjective meaning, the rejection of determinism, and concern for positive growth rather than pathology. Some founders of the humanistic school of thought were American psychologistsAbraham Maslow, who formulated ahierarchy of human needs, andCarl Rogers, who created and developedclient-centered therapy.[134]
Later,positive psychologyopened up humanistic themes to scientific study. Positive psychology is the study of factors which contribute to human happiness and well-being, focusing more on people who are currently healthy. In 2010,Clinical Psychological Reviewpublished a special issue devoted to positive psychological interventions, such asgratitude journalingand the physical expression of gratitude. It is, however, far from clear that positive psychology is effective in making people happier.[135][136]Positive psychological interventions have been limited in scope, but their effects are thought to be somewhat better thanplaceboeffects.
TheAmerican Association for Humanistic Psychology, formed in 1963, declared:
Humanistic psychology is primarily an orientation toward the whole of psychology rather than a distinct area or school. It stands for respect for the worth of persons, respect for differences of approach, open-mindedness as to acceptable methods, and interest in exploration of new aspects of human behavior. As a "third force" in contemporary psychology, it is concerned with topics having little place in existing theories and systems: e.g., love, creativity, self, growth, organism, basic need-gratification, self-actualization, higher values, being, becoming, spontaneity, play, humor, affection, naturalness, warmth, ego-transcendence, objectivity, autonomy, responsibility, meaning, fair-play, transcendental experience, peak experience, courage, and related concepts.[137]
Existential psychology emphasizes the need to understand a client's total orientation towards the world. Existential psychology is opposed to reductionism, behaviorism, and other methods that objectify the individual.[131]In the 1950s and 1960s, influenced by philosophersSøren KierkegaardandMartin Heidegger, psychoanalytically trained American psychologistRollo Mayhelped to develop existential psychology.Existential psychotherapy, which follows from existential psychology, is a therapeutic approach that is based on the idea that a person's inner conflict arises from that individual's confrontation with the givens of existence. Swiss psychoanalystLudwig Binswangerand American psychologistGeorge Kellymay also be said to belong to the existential school.[138]Existential psychologists tend to differ from more "humanistic" psychologists in the former's relatively neutral view of human nature and relatively positive assessment of anxiety.[139]Existential psychologists emphasized the humanistic themes of death, free will, and meaning, suggesting that meaning can be shaped by myths and narratives; meaning can be deepened by the acceptance of free will, which is requisite to living anauthenticlife, albeit often with anxiety with regard to death.[140]
Austrian existential psychiatrist andHolocaustsurvivorViktor Frankldrew evidence of meaning's therapeutic power from reflections upon his owninternment.[141]He created a variation of existential psychotherapy calledlogotherapy, a type ofexistentialistanalysis that focuses on awill to meaning(in one's life), as opposed to Adler'sNietzscheandoctrine ofwill to poweror Freud'swill to pleasure.[142]
Personality psychology is concerned with enduring patterns of behavior, thought, and emotion. Theories of personality vary across different psychological schools of thought. Each theory carries different assumptions about such features as the role of the unconscious and the importance of childhood experience. According to Freud, personality is based on the dynamic interactions of theid, ego, and super-ego.[143]By contrast,trait theoristshave developed taxonomies of personality constructs in describing personality in terms of key traits. Trait theorists have often employed statistical data-reduction methods, such asfactor analysis. Although the number of proposed traits has varied widely,Hans Eysenck's early biologically based model suggests at least three major trait constructs are necessary to describe human personality,extraversion–introversion,neuroticism-stability, andpsychoticism-normality.Raymond Cattellempirically derived a theory of16 personality factorsat the primary-factor level and up to eight broader second-stratum factors.[144][145][146][147]Since the 1980s, theBig Five(openness to experience,conscientiousness,extraversion,agreeableness, andneuroticism) emerged as an important trait theory of personality.[148]Dimensional models of personality disordersare receiving increasing support, and a version of dimensional assessment, namely theAlternative DSM-5 Model for Personality Disorders, has been included in theDSM-5. However, despite a plethora of research into the various versions of the "Big Five" personality dimensions, it appears necessary to move on from static conceptualizations of personality structure to a more dynamic orientation, acknowledging that personality constructs are subject to learning and change over the lifespan.[149][150]
An early example of personality assessment was theWoodworth Personal Data Sheet, constructed during World War I. The popular, although psychometrically inadequate,Myers–Briggs Type Indicator[151]was developed to assess individuals' "personality types" according to thepersonality theories of Carl Jung. TheMinnesota Multiphasic Personality Inventory(MMPI), despite its name, is more a dimensional measure of psychopathology than a personality measure.[152]California Psychological Inventorycontains 20 personality scales (e.g., independence, tolerance).[153]TheInternational Personality Item Pool, which is in the public domain, has become a source of scales that can be used personality assessment.[154]
Study of the unconscious mind, a part of the psyche outside the individual's awareness but that is believed to influence conscious thought and behavior, was a hallmark of early psychology. In one of the first psychology experiments conducted in the United States,C.S. PeirceandJoseph Jastrowfound in 1884 that research subjects could choose the minutely heavier of two weights even if consciously uncertain of the difference.[155]Freud popularized the concept of the unconscious mind, particularly when he referred to an uncensored intrusion of unconscious thought into one's speech (aFreudian slip) or to his effortsto interpret dreams.[156]His 1901 bookThe Psychopathology of Everyday Lifecatalogs hundreds of everyday events that Freud explains in terms of unconscious influence.Pierre Janetadvanced the idea of a subconscious mind, which could contain autonomous mental elements unavailable to the direct scrutiny of the subject.[157]
The concept of unconscious processes has remained important in psychology. Cognitive psychologists have used a "filter" model of attention. According to the model, much information processing takes place below the threshold of consciousness, and only certain stimuli, limited by their nature and number, make their way through the filter. Much research has shown that subconsciousprimingof certain ideas can covertly influence thoughts and behavior.[157]Because of the unreliability of self-reporting, a major hurdle in this type of research involves demonstrating that a subject's conscious mind has not perceived a target stimulus. For this reason, some psychologists prefer to distinguish betweenimplicitandexplicitmemory. In another approach, one can also describe asubliminal stimulusas meeting anobjectivebut not asubjectivethreshold.[158]
Theautomaticitymodel ofJohn Barghand others involves the ideas of automaticity and unconscious processing in our understanding ofsocial behavior,[159][160]although there has been dispute with regard to replication.[161][162]Some experimental data suggest that thebrain begins to consider taking actionsbefore the mind becomes aware of them.[163]The influence of unconscious forces on people's choices bears on the philosophical question of free will. John Bargh,Daniel Wegner, andEllen Langerdescribe free will as an illusion.[159][160][164]
Some psychologists study motivation or the subject of why people or lower animals initiate a behavior at a particular time. It also involves the study of why humans and lower animals continue or terminate a behavior. Psychologists such as William James initially used the termmotivationto refer to intention, in a sense similar to the concept ofwillin European philosophy. With the steady rise of Darwinian and Freudian thinking, instinct also came to be seen as a primary source of motivation.[165]According todrive theory, the forces of instinct combine into a single source of energy which exerts a constant influence. Psychoanalysis, like biology, regarded these forces as demands originating in the nervous system. Psychoanalysts believed that these forces, especially the sexual instincts, could become entangled and transmuted within the psyche. Classical psychoanalysis conceives of a struggle between the pleasure principle and thereality principle, roughly corresponding to id and ego. Later, inBeyond the Pleasure Principle, Freud introduced the concept of thedeath drive, a compulsion towards aggression, destruction, andpsychic repetition of traumatic events.[166]Meanwhile, behaviorist researchers used simple dichotomous models (pleasure/pain, reward/punishment) and well-established principles such as the idea that a thirsty creature will take pleasure in drinking.[165][167]Clark Hullformalized the latter idea with hisdrive reductionmodel.[168]
Hunger, thirst, fear, sexual desire, and thermoregulation constitute fundamental motivations in animals.[167]Humans seem to exhibit a more complex set of motivations—though theoretically these could be explained as resulting from desires for belonging, positive self-image, self-consistency, truth, love, and control.[169][170]
Motivation can be modulated or manipulated in many different ways. Researchers have found thateating, for example, depends not only on the organism's fundamental need forhomeostasis—an important factor causing the experience of hunger—but also on circadian rhythms, food availability, food palatability, and cost.[167]Abstract motivations are also malleable, as evidenced by such phenomena asgoal contagion: the adoption of goals, sometimes unconsciously, based on inferences about the goals of others.[171]Vohs andBaumeistersuggest that contrary to the need-desire-fulfillment cycle of animal instincts, human motivations sometimes obey a "getting begets wanting" rule: the more you get a reward such as self-esteem, love, drugs, or money, the more you want it. They suggest that this principle can even apply to food, drink, sex, and sleep.[172]
Developmental psychology is the scientific study of how and why the thought processes, emotions, and behaviors of humans change over the course of their lives.[173]Some credit Charles Darwin with conducting the first systematic study within the rubric of developmental psychology, having published in 1877 a short paper detailing the development of innate forms of communication based on his observations of his infant son.[174]The main origins of the discipline, however, are found in the work ofJean Piaget. Like Piaget, developmental psychologists originally focused primarily on the development of cognition from infancy to adolescence. Later, developmental psychology extended itself to the study cognition over the life span. In addition to studying cognition, developmental psychologists have also come to focus on affective, behavioral, moral, social, and neural development.
Developmental psychologists who study children use a number of research methods. For example, they make observations of children in natural settings such as preschools[175]and engage them in experimental tasks.[176]Such tasks often resemble specially designed games and activities that are both enjoyable for the child and scientifically useful. Developmental researchers have even devised clever methods to study the mental processes of infants.[177]In addition to studying children, developmental psychologists also study aging and processes throughout the life span, including old age.[178]These psychologists draw on the full range of psychological theories to inform their research.[173]
All researched psychological traits are influenced by bothgenesandenvironment, to varying degrees.[179][180]These two sources of influence are often confounded in observational research of individuals and families. An example of this confounding can be shown in the transmission ofdepressionfrom a depressed mother to her offspring. A theory based on environmental transmission would hold that an offspring, by virtue of their having a problematic rearing environment managed by a depressed mother, is at risk for developing depression. On the other hand, a hereditarian theory would hold that depression risk in an offspring is influenced to some extent by genes passed to the child from the mother. Genes and environment in these simple transmission models are completely confounded. A depressed mother may both carry genes that contribute to depression in her offspring and also create a rearing environment that increases the risk of depression in her child.[181]
Behavioral genetics researchers have employed methodologies that help to disentangle this confound and understand the nature and origins of individual differences in behavior.[97]Traditionally the research has involvedtwin studiesandadoption studies, two designs where genetic and environmental influences can be partially un-confounded. More recently, gene-focused research has contributed to understanding genetic contributions to the development of psychological traits.
The availability ofmicroarraymolecular geneticorgenome sequencingtechnologies allows researchers to measure participant DNA variation directly, and test whether individual genetic variants within genes are associated with psychological traits andpsychopathologythrough methods includinggenome-wide association studies. One goal of such research is similar to that inpositional cloningand its success inHuntington's: once a causal gene is discovered biological research can be conducted to understand how that gene influences the phenotype. One major result of genetic association studies is the general finding that psychological traits and psychopathology, as well as complex medical diseases, are highlypolygenic,[182][183][184][185][186]where a large number (on the order of hundreds to thousands) of genetic variants, each of small effect, contribute to individual differences in the behavioral trait or propensity to the disorder. Active research continues to work toward understanding the genetic and environmental bases of behavior and their interaction.
Psychology encompasses many subfields and includes different approaches to the study of mental processes and behavior.
Psychological testing has ancient origins, dating as far back as 2200 BC, in theexaminations for the Chinese civil service. Written exams began during theHan dynasty(202 BC – AD 220). By 1370, the Chinese system required a stratified series of tests, involving essay writing and knowledge of diverse topics. The system was ended in 1906.[187]: 41–2In Europe, mental assessment took a different approach, with theories ofphysiognomy—judgment of character based on the face—described by Aristotle in 4th century BC Greece. Physiognomy remained current through the Enlightenment, and added the doctrine of phrenology: a study of mind and intelligence based on simple assessment of neuroanatomy.[187]: 42–3
When experimental psychology came to Britain, Francis Galton was a leading practitioner. By virtue of his procedures for measuring reaction time and sensation, he is considered an inventor of modern mental testing (also known aspsychometrics).[187]: 44–5James McKeen Cattell, a student of Wundt and Galton, brought the idea of psychological testing to the United States, and in fact coined the term "mental test".[187]: 45–6In 1901, Cattell's studentClark Wisslerpublished discouraging results, suggesting that mental testing of Columbia and Barnard students failed to predict academic performance.[187]: 45–6In response to 1904 orders from theMinister of Public Instruction, One example of an observational study was run by Arthur Bandura. This observational study focused on children who were exposed to an adult exhibiting aggressive behaviors and their reaction to toys versus other children who were not exposed to these stimuli. The result shows that children who had seen the adult acting aggressively towards a toy, in turn, were aggressive towards their own toy when put in a situation that frustrated them.[188]psychologistsAlfred BinetandThéodore Simondeveloped and elaborated a new test of intelligence in 1905–1911. They used a range of questions diverse in their nature and difficulty. Binet and Simon introduced the concept ofmental ageand referred to the lowest scorers on their test asidiots.Henry H. Goddardput the Binet-Simon scale to work and introduced classifications of mental level such asimbecileandfeebleminded. In 1916, (after Binet's death), Stanford professorLewis M. Termanmodified the Binet-Simon scale (renamed theStanford–Binet scale) and introduced theintelligence quotientas a score report.[187]: 50–56Based on his test findings, and reflecting the racism common to that era, Terman concluded that intellectual disability "represents the level of intelligence which is very, very common among Spanish-Indians and Mexican families of the Southwest and also among negroes. Their dullness seems to be racial."[189]
Following the Army Alpha and Army Beta tests, which was developed by psychologistRobert Yerkesin 1917 and then used in World War 1 by industrial and organizational psychologists for large-scale employee testing and selection of military personnel.[190]Mental testing also became popular in the U.S., where it was applied to schoolchildren. The federally created National Intelligence Test was administered to 7 million children in the 1920s. In 1926, theCollege Entrance Examination Boardcreated theScholastic Aptitude Testto standardize college admissions.[187]: 61The results of intelligence tests were used to argue for segregated schools and economic functions, including the preferential training of Black Americans for manual labor. These practices were criticized by Black intellectuals such aHorace Mann BondandAllison Davis.[189]Eugenicists used mental testing to justify and organize compulsory sterilization of individuals classified as mentally retarded (now referred to asintellectual disability).[49]In the United States, tens of thousands of men and women were sterilized. Setting a precedent that has never been overturned, the U.S. Supreme Court affirmed the constitutionality of this practice in the 1927 caseBuck v. Bell.[191]
Today mental testing is a routine phenomenon for people of all ages in Western societies.[187]:2Modern testing aspires to criteria including standardization of procedure,consistency of results, output of an interpretable score, statistical norms describing population outcomes, and, ideally,effective predictionof behavior and life outcomes outside of testing situations.[187]: 4–6Psychological testing is regularly used in forensic contexts to aid legal judgments and decisions.[192]Developments in psychometrics include work on test and scalereliabilityandvalidity.[193]Developments initem-response theory,[194]structural equation modeling,[195]and bifactor analysis[196]have helped in strengthening test and scale construction.
The provision of psychological health services is generally called clinical psychology in the U.S. Sometimes, however, members of the school psychology and counseling psychology professions engage in practices that resemble that of clinical psychologists. Clinical psychologists typically include people who have graduated from doctoral programs in clinical psychology. In Canada, some of the members of the abovementioned groups usually fall within the larger category ofprofessional psychology. In Canada and the U.S., practitioners get bachelor's degrees and doctorates; doctoral students in clinical psychology usually spend one year in a predoctoral internship and one year in postdoctoral internship. In Mexico and most other Latin American and European countries, psychologists do not get bachelor's and doctoral degrees; instead, they take a three-year professional course following high school.[85]Clinical psychology is at present the largest specialization within psychology.[197]It includes the study and application of psychology for the purpose of understanding, preventing, and relieving psychological distress, dysfunction, and/ormental illness. Clinical psychologists also try to promote subjective well-being and personal growth. Central to the practice of clinical psychology are psychological assessment and psychotherapy although clinical psychologists may also engage in research, teaching, consultation, forensic testimony, and program development and administration.[198]
Credit for the first psychology clinic in the United States typically goes toLightner Witmer, who established his practice in Philadelphia in 1896. Another modern psychotherapist wasMorton Prince, an early advocate for the establishment of psychology as a clinical and academic discipline.[197]In the first part of the twentieth century, most mental health care in the United States was performed by psychiatrists, who are medical doctors. Psychology entered the field with its refinements of mental testing, which promised to improve the diagnosis of mental problems. For their part, some psychiatrists became interested in usingpsychoanalysisand other forms ofpsychodynamic psychotherapyto understand and treat the mentally ill.[44][199]
Psychotherapy as conducted by psychiatrists blurred the distinction between psychiatry and psychology, and this trend continued with the rise ofcommunity mental health facilities. Some in the clinical psychology community adoptedbehavioral therapy, a thoroughly non-psychodynamic model that used behaviorist learning theory to change the actions of patients. A key aspect of behavior therapy is empirical evaluation of the treatment's effectiveness. In the 1970s,cognitive-behavior therapyemerged with the work ofAlbert EllisandAaron Beck. Although there are similarities between behavior therapy and cognitive-behavior therapy, cognitive-behavior therapy required the application of cognitive constructs. Since the 1970s, the popularity of cognitive-behavior therapy among clinical psychologists increased. A key practice in behavioralandcognitive-behavioral therapy is exposing patients to things they fear, based on the premise that their responses (fear, panic, anxiety) can be deconditioned.[200]
Mental health care today involves psychologists and social workers in increasing numbers. In 1977, National Institute of Mental Health directorBertram Browndescribed this shift as a source of "intense competition and role confusion."[44]Graduate programs issuing doctorates in clinical psychology emerged in the 1950s and underwent rapid increase through the 1980s. The PhD degree is intended to train practitioners who could also conduct scientific research. The PsyD degree is more exclusively designed to train practitioners.[85]
Some clinical psychologists focus on the clinical management of patients with brain injury. This subspecialty is known asclinical neuropsychology. In many countries, clinical psychology is a regulated mental health profession. The emerging field ofdisaster psychology(seecrisis intervention) involves professionals who respond to large-scale traumatic events.[201]
The work performed by clinical psychologists tends to be influenced by various therapeutic approaches, all of which involve a formal relationship between professional and client (usually an individual, couple, family, or small group). Typically, these approaches encourage new ways of thinking, feeling, or behaving. Four major theoretical perspectives are psychodynamic, cognitive behavioral, existential–humanistic, and systems or family therapy. There has been a growing movement to integrate the various therapeutic approaches, especially with an increased understanding of issues regarding culture, gender, spirituality, and sexual orientation. With the advent of more robust research findings regarding psychotherapy, there is evidence that most of the major therapies have equal effectiveness, with the key common element being a strongtherapeutic alliance.[202][203]Because of this, more training programs and psychologists are now adopting aneclectic therapeutic orientation.[204][205][206][207][208]
Diagnosis in clinical psychology usually follows theDiagnostic and Statistical Manual of Mental Disorders(DSM).[209]The study of mental illnesses is calledabnormal psychology.
Educational psychology is the study of how humans learn in educational settings, the effectiveness of educational interventions, the psychology of teaching, and the social psychology of schools as organizations. Educational psychologists can be found in preschools, schools of all levels including post secondary institutions, community organizations and learning centers, Government or private research firms, and independent or private consultant.[210]The work of developmental psychologists such as Lev Vygotsky,Jean Piaget, andJerome Brunerhas been influential in creating teaching methods and educational practices. Educational psychology is often included in teacher education programs in places such as North America, Australia, and New Zealand.
School psychology combines principles from educational psychology and clinical psychology to understand and treat students with learning disabilities; to foster the intellectual growth ofgiftedstudents; to facilitateprosocial behaviorsin adolescents; and otherwise to promote safe, supportive, and effective learning environments. School psychologists are trained in educational and behavioral assessment, intervention, prevention, and consultation, and many have extensive training in research.[211]
Industrial and organizational (I/O) psychology involves research and practices that apply psychological theories and principles to organizations and individuals' work-lives.[212]In the field's beginnings, industrialists brought the nascent field of psychology to bear on the study ofscientific managementtechniques for improving workplace efficiency. The field was at first calledeconomic psychologyorbusiness psychology; later,industrial psychology,employment psychology, orpsychotechnology.[213]An influential early study examined workers at Western Electric's Hawthorne plant in Cicero, Illinois from 1924 to 1932. Western Electric experimented on factory workers to assess their responses to changes in illumination, breaks, food, and wages. The researchers came to focus on workers' responses to observation itself, and the termHawthorne effectis now used to describe the fact that people's behavior can change when they think they are being observed.[214]Although the Hawthorne research can be found in psychology textbooks, the research and its findings were weak at best.[215][216]
The name industrial and organizational psychology emerged in the 1960s. In 1973, it became enshrined in the name of theSociety for Industrial and Organizational Psychology, Division 14 of the American Psychological Association.[213]One goal of the discipline is to optimize human potential in the workplace. Personnel psychology is a subfield of I/O psychology. Personnel psychologists apply the methods and principles of psychology in selecting and evaluating workers. Another subfield,organizational psychology, examines the effects of work environments and management styles on worker motivation, job satisfaction, and productivity.[217]Most I/O psychologists work outside of academia, for private and public organizations and as consultants.[213]A psychology consultant working in business today might expect to provide executives with information and ideas about their industry, their target markets, and the organization of their company.[218][219]
Organizational behavior (OB) is an allied field involved in the study of human behavior within organizations.[220]One way to differentiate I/O psychology from OB is that I/O psychologists train in university psychology departments and OB specialists, in business schools.
One role forpsychologists in the militaryhas been to evaluate and counsel soldiers and other personnel. In the U.S., this function began during World War I, when Robert Yerkes established the School of Military Psychology atFort Oglethorpein Georgia. The school provided psychological training for military staff.[44][221]Today, U.S. Army psychologists perform psychological screening, clinical psychotherapy,suicide prevention, and treatment for post-traumatic stress, as well as provide prevention-related services, for example, smoking cessation.[222]The United States Army's Mental Health Advisory Teams implement psychological interventions to help combat troops experiencing mental problems.[223][224]
Psychologists may also work on a diverse set of campaigns known broadly as psychological warfare. Psychological warfare chiefly involves the use of propaganda to influence enemy soldiers and civilians. This so-called black propaganda is designed to seem as if it originates from a source other than the Army.[225]TheCIA'sMKULTRAprogram involved more individualized efforts atmind control, involving techniques such as hypnosis, torture, and covert involuntary administration ofLSD.[226]The U.S. military used the namePsychological Operations(PSYOP) until 2010, when these activities were reclassified as Military Information Support Operations (MISO), part ofInformation Operations(IO).[227]Psychologists have sometimes been involved in assisting the interrogation and torture of suspects, staining the records of the psychologists involved.[228]
An example of the contribution of psychologists to social change involves the research ofKennethandMamie Phipps Clark. These two African American psychologists studied segregation's adverse psychological impact on Black children. Their research findings played a role in the desegregation caseBrown v. Board of Education(1954).[229]
The impact of psychology on social change includes the discipline's broad influence on teaching and learning. Research has shown that compared to the "whole word" or "whole language" approach, the phonics approach to reading instruction is more efficacious.[230]
Medical facilities increasingly employ psychologists to perform various roles. One aspect of health psychology is thepsychoeducationof patients: instructing them in how to follow a medical regimen. Health psychologists can also educate doctors and conduct research on patient compliance.[231][232]Psychologists in the field of public health use a wide variety of interventions to influence human behavior. These range from public relations campaigns and outreach to governmental laws and policies. Psychologists study the composite influence of all these different tools in an effort to influence whole populations of people.[233]
Psychologists work with organizations to apply findings from psychological research to improve the health and well-being of employees. Some work as external consultants hired by organizations to solve specific problems, whereas others are full-time employees of the organization. Applications include conducting surveys to identify issues and designing interventions to make work healthier. Some of the specific health areas include:
Interventions that improve climates are a way to address accidents and violence. Interventions that reduce stress at work or provide employees with tools to better manage it can help in areas where stress is an important component.
Industrial psychology became interested in worker fatigue during World War I, when government ministers in Britain were concerned about the impact of fatigue on workers in munitions factories but not other types of factories.[241][242]In the U. K. some interest in workerwell-beingemerged with the efforts ofCharles Samuel Myersand his National Institute of Industrial Psychology (NIIP) during the inter-War years.[243]In the U. S. during the mid-twentieth century industrial psychologistArthur Kornhauserpioneered the study of occupational mental health, linking industrial working conditions to mental health as well as the spillover of an unsatisfying job into a worker's personal life.[244][245]Zickar accumulated evidence to show that "no other industrial psychologist of his era was as devoted to advocating management and labor practices that would improve the lives of working people."[244]
As interest in the worker health expanded toward the end of the twentieth century, the field ofoccupational health psychology(OHP) emerged. OHP is a branch of psychology that is interdisciplinary.[52][246]OHP is concerned with the health and safety of workers.[52][246]OHP addresses topic areas such as the impact of occupational stressors on physical and mental health, mistreatment of workers (e.g., bullying and violence), work-family balance, the impact ofinvoluntary unemploymenton physical and mental health, the influence of psychosocial factors on safety and accidents, and interventions designed to improve/protect worker health.[52][247]OHP grew out ofhealth psychology,industrial and organizational psychology, andoccupational medicine.[248]OHP has also been informed by disciplines outside psychology, includingindustrial engineering, sociology, and economics.[249][250]
Quantitative psychological researchlends itself to the statistical testing of hypotheses. Although the field makes abundant use ofrandomized and controlled experimentsin laboratory settings, such research can only assess a limited range of short-term phenomena. Some psychologists rely on less rigorously controlled, but moreecologically valid,field experimentsas well. Other research psychologists rely on statistical methods to glean knowledge from population data.[251]The statistical methods research psychologists employ include thePearson product–moment correlation coefficient, theanalysis of variance,multiple linear regression,logistic regression,structural equation modeling, andhierarchical linear modeling. Themeasurementandoperationalizationof importantconstructsis an essential part of these research designs.
Although this type of psychological research is much less abundant than quantitative research, some psychologists conductqualitative research. This type of research can involve interviews, questionnaires, and first-hand observation.[252]While hypothesis testing is rare, virtually impossible, in qualitative research, qualitative studies can be helpful in theory and hypothesis generation, interpreting seemingly contradictory quantitative findings, and understanding why some interventions fail and others succeed.[253]
Atrue experimentwith random assignment of research participants (sometimes called subjects) to rival conditions allows researchers to make strong inferences about causal relationships. When there are large numbers of research participants, the random assignment (also called random allocation) of those participants to rival conditions ensures that the individuals in those conditions will, on average, be similar on most characteristics, including characteristics that went unmeasured. In an experiment, the researcher alters one or more variables of influence, calledindependent variables, and measures resulting changes in the factors of interest, calleddependent variables. Prototypical experimental research is conducted in a laboratory with a carefully controlled environment.
Aquasi-experimentis a situation in which different conditions are being studied, but random assignment to the different conditions is not possible. Investigators must work with preexisting groups of people. Researchers can use common sense to consider how much the nonrandom assignment threatens the study'svalidity.[256]For example, in research on the best way to affect reading achievement in the first three grades of school, school administrators may not permit educational psychologists to randomly assign children to phonics and whole language classrooms, in which case the psychologists must work with preexisting classroom assignments. Psychologists will compare the achievement of children attending phonics and whole language classes and, perhaps, statistically adjust for any initial differences in reading level.
Experimental researchers typically use astatistical hypothesis testingmodel which involves making predictions before conducting the experiment, then assessing how well the data collected are consistent with the predictions. These predictions are likely to originate from one or more abstract scientifichypothesesabout how the phenomenon under study actually works.[257]
Surveysare used in psychology for the purpose of measuringattitudesandtraits, monitoring changes inmood, and checking the validity of experimental manipulations (checking research participants' perception of the condition they were assigned to). Psychologists have commonly used paper-and-pencil surveys. However, surveys are also conducted over the phone or through e-mail. Web-based surveys are increasingly used to conveniently reach many subjects.
Observational studiesare commonly conducted in psychology. Incross-sectionalobservational studies, psychologists collect data at a single point in time. The goal of many cross-sectional studies is the assess the extent factors are correlated with each other. By contrast, inlongitudinal studiespsychologists collect data on the same sample at two or more points in time. Sometimes the purpose of longitudinal research is to study trends across time such as the stability of traits or age-related changes in behavior. Because some studies involve endpoints that psychologists cannot ethically study from an experimental standpoint, such as identifying the causes of depression, they conduct longitudinal studies a large group of depression-free people, periodically assessing what is happening in the individuals' lives. In this way psychologists have an opportunity to test causal hypotheses regarding conditions that commonly arise in people's lives that put them at risk for depression. Problems that affect longitudinal studies includeselective attrition, the type of problem in which bias is introduced when a certain type of research participant disproportionately leaves a study.
One example of an observational study was run by Arthur Bandura. This observational study focused on children who were exposed to an adult exhibiting aggressive behaviors and their reaction to toys versus other children who were not exposed to these stimuli. The result shows that children who had seen the adult acting aggressively towards a toy, in turn, were aggressive towards their own toy when put in a situation that frustrated them.[188]
Exploratory data analysisincludes a variety of practices that researchers use to reduce a great many variables to a small number overarching factors. InPeirce's three modes of inference, exploratory data analysis corresponds toabduction.[258]Meta-analysisis the technique research psychologists use to integrate results from many studies of the same variables and arriving at a grand average of the findings.[259]
A classic and popular tool used to relate mental and neural activity is theelectroencephalogram(EEG), a technique using amplified electrodes on a person's scalp to measure voltage changes in different parts of the brain.Hans Berger, the first researcher to use EEG on an unopened skull, quickly found that brains exhibit signature "brain waves": electric oscillations which correspond to different states of consciousness. Researchers subsequently refined statistical methods for synthesizing the electrode data, and identified unique brain wave patterns such as thedelta waveobserved during non-REM sleep.[260]
Newerfunctional neuroimagingtechniques includefunctional magnetic resonance imagingandpositron emission tomography, both of which track the flow of blood through the brain. These technologies provide more localized information about activity in the brain and create representations of the brain with widespread appeal. They also provide insight which avoids the classic problems of subjective self-reporting. It remains challenging to draw hard conclusions about where in the brain specific thoughts originate—or even how usefully such localization corresponds with reality. However, neuroimaging has delivered unmistakable results showing the existence of correlations between mind and brain. Some of these draw on a systemicneural networkmodel rather than a localized function model.[261][262][263]
Interventions such astranscranial magnetic stimulationand drugs also provide information about brain–mind interactions.Psychopharmacologyis the study of drug-induced mental effects.
Computational modeling is a tool used inmathematical psychologyand cognitive psychology to simulate behavior.[264]This method has several advantages. Since modern computers process information quickly, simulations can be run in a short time, allowing for high statistical power. Modeling also allows psychologists to visualize hypotheses about the functional organization of mental events that could not be directly observed in a human. Computational neuroscience uses mathematical models to simulate the brain. Another method is symbolic modeling, which represents many mental objects using variables and rules. Other types of modeling includedynamic systemsandstochasticmodeling.
Animal experiments aid in investigating many aspects of human psychology, including perception, emotion, learning, memory, and thought, to name a few. In the 1890s, Russian physiologist Ivan Pavlov famously used dogs to demonstrate classical conditioning. Non-human primates, cats, dogs, pigeons, and rats and other rodents are often used in psychological experiments. Ideally, controlled experiments introduce only one independent variable at a time, in order to ascertain its unique effects upon dependent variables. These conditions are approximated best in laboratory settings. In contrast, human environments and genetic backgrounds vary so widely, and depend upon so many factors, that it is difficult to control importantvariablesfor human subjects. There are pitfalls, however, in generalizing findings from animal studies to humans through animal models.[265]
Comparative psychology is the scientific study of the behavior and mental processes of non-human animals, especially as these relate to the phylogenetic history, adaptive significance, and development of behavior. Research in this area explores the behavior of many species, from insects to primates. It is closely related to other disciplines that study animal behavior such asethology.[266]Research in comparative psychology sometimes appears to shed light on human behavior, but some attempts to connect the two have been quite controversial, for example theSociobiologyofE.O. Wilson.[267]Animal models are often used to study neural processes related to human behavior, e.g. in cognitive neuroscience.
Qualitative research is often designed to answer questions about the thoughts, feelings, and behaviors of individuals. Qualitative research involving first-hand observation can help describe events as they occur, with the goal of capturing the richness of everyday behavior and with the hope of discovering and understanding phenomena that might have been missed if only more cursory examinations are made.
Qualitative psychological researchmethods include interviews, first-hand observation, and participant observation. Creswell (2003) identified five main possibilities for qualitative research, including narrative, phenomenology,ethnography,case study, andgrounded theory. Qualitative researchers[269]sometimes aim to enrich our understanding of symbols, subjective experiences, or social structures. Sometimeshermeneuticand critical aims can give rise to quantitative research, as inErich Fromm's application of psychological and sociological theories, in his bookEscape from Freedom, to understanding why many ordinary Germans supported Hitler.[270]
Just asJane Goodallstudied chimpanzee social and family life by careful observation of chimpanzee behavior in the field, psychologists conductnaturalistic observationof ongoing human social, professional, and family life. Sometimes the participants are aware they are being observed, and other times the participants do not know they are being observed. Strict ethical guidelines must be followed when covert observation is being carried out.
Program evaluationinvolves the systematic collection, analysis, and application of information to answer questions about projects, policies and programs, particularly about their effectiveness.[271][272]In both the public and private sectors, stakeholders often want to know the extent which the programs they are funding, implementing, voting for, receiving, or objecting to are producing the intended effects. While program evaluation first focuses on effectiveness, important considerations often include how much the program costs per participant, how the program could be improved, whether the program is worthwhile, whether there are better alternatives, if there are unintended outcomes, and whether the program goals are appropriate and useful.[273]
Metascience involves the application of scientific methodology to study science itself. The field ofmetasciencehas revealed problems in psychological research. Some psychological research has suffered frombias,[274]problematicreproducibility,[275]andmisuse of statistics.[276]These findings have led to calls for reform from within and from outside the scientific community.[277]
In 1959, statistician Theodore Sterling examined the results of psychological studies and discovered that 97% of them supported their initial hypotheses, implying possiblepublication bias.[278][279][280]Similarly, Fanelli (2010)[281]found that 91.5% of psychiatry/psychology studies confirmed the effects they were looking for, and concluded that the odds of this happening (a positive result) was around five times higher than in fields such asspace scienceorgeosciences. Fanelli argued that this is because researchers in "softer" sciences have fewer constraints to their conscious and unconscious biases.
Areplication crisisin psychology has emerged. Many notable findings in the field have not been replicated. Some researchers were even accused of publishing fraudulent results.[282][283][284]Systematic efforts, including efforts by theReproducibility Projectof theCenter for Open Science, to assess the extent of the problem found that as many as two-thirds of highly publicized findings in psychology failed to be replicated.[285]Reproducibility has generally been stronger in cognitive psychology (in studies and journals) than social psychology[285]and subfields ofdifferential psychology.[286][287]Other subfields of psychology have also been implicated in the replication crisis, including clinical psychology,[288][289][290]developmental psychology,[291][292][293]and a field closely related to psychology,educational research.[294][295][296][297][298]
Focus on the replication crisis has led to other renewed efforts in the discipline to re-test important findings.[299][300]In response to concerns about publication bias anddata dredging(conducting a large number of statistical tests on a great many variables but restricting reporting to the results that were statistically significant), 295 psychology and medical journals have adoptedresult-blind peer reviewwhere studies are accepted not on the basis of their findings and after the studies are completed, but before the studies are conducted and upon the basis of the methodological rigor of their experimental designs and the theoretical justifications for their proposed statistical analysis before data collection or analysis is conducted.[301][302]In addition, large-scale collaborations among researchers working in multiple labs in different countries have taken place. The collaborators regularly make their data openly available for different researchers to assess.[303]Allen and Mehler[304]estimated that 61 per cent of result-blind studies have yieldednull results, in contrast to an estimated 5 to 20 per cent in traditional research.
Some critics viewstatistical hypothesis testingas misplaced. Psychologist and statisticianJacob Cohenwrote in 1994 that psychologists routinely confuse statistical significance with practical importance, enthusiastically reporting great certainty in unimportant facts.[305]Some psychologists have responded with an increased use ofeffect sizestatistics, rather than sole reliance onp-values.[306]
In 2008, Arnett pointed out that most articles in American Psychological Association journals were about U.S. populations when U.S. citizens are only 5% of the world's population. He complained that psychologists had no basis for assuming psychological processes to be universal and generalizing research findings to the rest of the global population.[307]In 2010, Henrich, Heine, and Norenzayan reported a bias in conducting psychology studies with participants from "WEIRD" ("Western, Educated, Industrialized, Rich, and Democratic") societies.[308][309]Henrich et al. found that "96% of psychological samples come from countries with only 12% of the world's population" (p. 63). The article gave examples of results that differ significantly between people from WEIRD and tribal cultures, including theMüller-Lyer illusion. Arnett (2008),Altmaierand Hall (2008) and Morgan-Consoli et al. (2018) view the Western bias in research and theory as a serious problem considering psychologists are increasingly applying psychological principles developed in WEIRD regions in their research, clinical work, and consultation with populations around the world.[307][310][311]In 2018, Rad, Martingano, and Ginges showed that nearly a decade after Henrich et al.'s paper, over 80% of the samples used in studies published in the journalPsychological Scienceemployed WEIRD samples. Moreover, their analysis showed that several studies did not fully disclose the origin of their samples; the authors offered a set of recommendations to editors and reviewers to reduce WEIRD bias.[312]
Similar to theWEIRDbias, starting in 2020, researchers of non-human behavior have started to emphasize the need to document the possibility of the STRANGE (Social background, Trappability and self-selection, Rearing history, Acclimation and habituation, Natural changes in responsiveness, Genetic makeup, and Experience) bias in study conclusions.[313]
Some observers perceive a gap between scientific theory and its application—in particular, the application of unsupported or unsound clinical practices.[314]Critics say there has been an increase in the number of mental health training programs that do not instill scientific competence.[315]Practices such as "facilitated communicationfor infantile autism"; memory-recovery techniques includingbody work; and other therapies, such asrebirthingandreparenting, may be dubious or even dangerous, despite their popularity.[316]These practices, however, are outside the mainstream practices taught in clinical psychology doctoral programs.
Ethical standards in the discipline have changed over time. Some famous past studies are today considered unethical and in violation ofestablished codes(e.g., the Canadian Code of Conduct for Research Involving Humans, and theBelmont Report). The American Psychological Association has advanced a set of ethical principles and acodeof conduct for the profession.[317]
The most important contemporary standards include informed and voluntary consent. After World War II, theNuremberg Codewas established because of Nazi abuses of experimental subjects. Later, most countries (and scientific journals) adopted theDeclaration of Helsinki. In the U.S., theNational Institutes of Healthestablished theInstitutional Review Boardin 1966, and in 1974 adopted theNational Research Act(HR 7724). All of these measures encouraged researchers to obtain informed consent from human participants in experimental studies. A number of influential but ethically dubious studies led to the establishment of this rule; such studies included theMIT-Harvard Fernald School radioisotope studies, theThalidomide tragedy, theWillowbrook hepatitis study,Stanley Milgram's studies of obedience to authority, and theStanford Prison Experiment.
Theethics code of the American Psychological Associationoriginated in 1951 as "Ethical Standards of Psychologists." This code has guided the formation of licensing laws in most American states. It has changed multiple times over the decades since its adoption, and contains both aspirational principles and binding ethical standards.
The APA's Ethical Principles of Psychologists and Code of Conduct consists of five General Principles, which are meant to guide psychologists to higher ethical practice where a particular standard does not apply. Those principles are:
A. Beneficence and Nonmaleficence- meaning the psychologists must work to benefit those they work with and "do no harm." This includes awareness of indirect benefits and harms their work might have on others due to personal, social, political, or other factors.
B. Fidelity and Responsibility- an awareness of public trust in the profession and adherence to ethical standards and clarification of roles to preserve that trust. This includes managing conflicts of interest, as well as committing some portion of a psychologist's professional time to low-cost or pro bono work.
C. Integrity- upholding honesty and accuracy in all psychological practices, including avoiding misrepresentations and fraud. In situations where psychologists would use deception (i.e., certain research), psychologists must consider the necessity, benefits, and harms, and mitigate any harms where possible.
D. Justice -an understanding that psychology must be for everyone's benefit, and that psychologists take special care to avoid unjust practices as a result of biases or limitations of expertise.
E. Respect for People's Rights and Dignity- the preservation of people's rights when working with psychologists, including confidentially, privacy, and autonomy. Psychologists should consider a multitude of factors, including a need for special safeguards for protected populations (e.g., minors, incarcerated individuals) and awareness of differences based on numerous factors, including culture, race, age, gender, and socioeconomic status.
In 1989, the APA revised its policies on advertising and referral fees to negotiate the end of an investigation by the Federal Trade Commission. The 1992 incarnation was the first to distinguish between "aspirational" ethical standards and "enforceable" ones. The APA code was further revised in 2010 to prevent the use of the code to justify violating human rights, which was in response to the participation of APA members in interrogations under the administration of United States President George W. Bush.[318]Members of the public have a five-year window to file ethics complaints about APA members with the APA ethics committee; members of the APA have a three-year window.[319]
The Canadian Psychological Association used the APA code until 1986, when it developed its own code drawing from four similar principles: 1) Respect for the Dignity of Persons and Peoples, 2) Responsible Caring, 3) Integrity in Relationships, 4) Responsibility to Society.[320][321]The European Federation of Psychologist's Associations, have adopted a model code using the principles of the Canadian Code, while also drawing from the APA code.[322][323]
Universities have ethics committees dedicated to protecting the rights (e.g., voluntary nature of participation in the research, privacy) and well-being (e.g., minimizing distress) of research participants. University ethics committees evaluate proposed research to ensure that researchers protect the rights and well-being of participants; an investigator's research project cannot be conducted unless approved by such an ethics committee.[324]
The field of psychology also identifies certain categories of people that require additional or special protection due to particular vulnerabilities, unequal power dynamics, or diminished capacity for informed consent. This list often includes, but is not limited to, children, incarcerated individuals, pregnant women, human fetuses and neonates, institutionalized persons, those with physical or mental disabilities, and the educationally or economically disadvantaged.[325]
Some of the ethical issues considered most important are the requirement to practice only within the area of competence, to maintain confidentiality with the patients, and to avoid sexual relations with them. Another important principle isinformed consent, the idea that a patient or research subject must understand and freely choose a procedure they are undergoing.[319]Some of the most common complaints against clinical psychologists include sexual misconduct[319]and breaches in confidentiality or privacy.[326]
Psychology ethics apply to all types of human contact in a psychologist's professional capacity, including therapy, assessment, teaching, training, work with research subjects, testimony in courts and before government bodies, consulting, and statements to the public or media pertaining to matters of psychology.[317]
Research on other animals is governed by university ethics committees. Research on nonhuman animals cannot proceed without permission of the ethics committee, of the researcher's home institution. Ethical guidelines state that using non-human animals for scientific purposes is only acceptable when the harm (physical or psychological) done to animals is outweighed by the benefits of the research.[327]Psychologists can use certain research techniques on animals that could not be used on humans.
Comparative psychologistHarry Harlowdrew moral condemnation forisolation experimentson rhesus macaque monkeys at theUniversity of Wisconsin–Madisonin the 1970s.[328]The aim of the research was to produce an animal model ofclinical depression. Harlow also devised what he called a "rape rack", to which the female isolates were tied in normal monkey mating posture.[329]In 1974, American literary criticWayne C. Boothwrote that, "Harry Harlow and his colleagues go on torturing their nonhuman primates decade after decade, invariably proving what we all knew in advance—that social creatures can be destroyed by destroying their social ties." He writes that Harlow made no mention of the criticism of the morality of his work.[330]
Animal research is influential in psychology, while still being debated among academics. The testing of animals for research has led to medical breakthroughs in human medicine. Many psychologists argue animal experimentation is essential for human advancement, but must be regulated by the government to ensure ethicality.
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Inprobability theory, thelaw of the iterated logarithmdescribes the magnitude of the fluctuations of arandom walk. The original statement of the law of the iterated logarithm is due toA. Ya. Khinchin(1924).[1]Another statement was given byA. N. Kolmogorovin 1929.[2]
Let {Yn} be independent, identically distributedrandom variableswith zero means and unit variances. LetSn=Y1+ ... +Yn. Then
where "log" is thenatural logarithm, "lim sup" denotes thelimit superior, and "a.s." stands for "almost surely".[3][4]
Another statement given byA. N. Kolmogorovin 1929[2]is as follows.
Let{Yn}{\displaystyle \{Y_{n}\}}be independentrandom variableswith zero means and finite variances. LetSn=Y1+⋯+Yn{\displaystyle S_{n}=Y_{1}+\dots +Y_{n}}andBn=Var(Y1)+⋯+Var(Yn){\displaystyle B_{n}=\operatorname {Var} (Y_{1})+\dots +\operatorname {Var} (Y_{n})}. IfBn→∞{\displaystyle B_{n}\to \infty }and there exists a sequence of positive constants{Mn}{\displaystyle \{M_{n}\}}such that|Yn|≤Mn{\displaystyle |Y_{n}|\leq M_{n}}a.s. and
then we have
Note that, the first statement covers the case of the standard normal distribution, but the second does not.
The law of iterated logarithms operates "in between" thelaw of large numbersand thecentral limit theorem. There are two versions of the law of large numbers —the weakandthe strong— and they both state that the sumsSn, scaled byn−1, converge to zero, respectivelyin probabilityandalmost surely:
On the other hand, the central limit theorem states that the sumsSnscaled by the factorn−1/2converge in distribution to a standard normal distribution. ByKolmogorov's zero–one law, for any fixedM, the probability that the eventlim supnSnn≥M{\displaystyle \limsup _{n}{\frac {S_{n}}{\sqrt {n}}}\geq M}occurs is 0 or 1.
Then
so
An identical argument shows that
This implies that these quantities cannot converge almost surely. In fact, they cannot even converge in probability, which follows from the equality
and the fact that the random variables
are independent and both converge in distribution toN(0,1).{\displaystyle {\mathcal {N}}(0,1).}
Thelaw of the iterated logarithmprovides the scaling factor where the two limits become different:
Thus, although the absolute value of the quantitySn/2nloglogn{\displaystyle S_{n}/{\sqrt {2n\log \log n}}}is less than any predefinedε> 0 with probability approaching one, it will nevertheless almost surely be greater thanεinfinitely often; in fact, the quantity will be visiting the neighborhoods of any point in the interval (-1,1) almost surely.
The law of the iterated logarithm (LIL) for a sum of independent and identically distributed (i.i.d.) random variables with zero mean and bounded increment dates back toKhinchinandKolmogorovin the 1920s.
Since then, there has been a tremendous amount of work on the LIL for various kinds of
dependent structures and for stochastic processes. The following is a small sample of notable developments.
Hartman–Wintner(1940) generalized LIL to random walks with increments with zero mean and finite variance. De Acosta (1983) gave a simple proof of the Hartman–Wintner version of the LIL.[5]
Chung(1948) proved another version of the law of the iterated logarithm for the absolute value of a brownian motion.[6]
Strassen(1964) studied the LIL from the point of view of invariance principles.[7]
Stout (1970) generalized the LIL to stationary ergodic martingales.[8]
Wittmann (1985) generalized Hartman–Wintner version of LIL to random walks satisfying milder conditions.[9]
Vovk (1987) derived a version of LIL valid for a single chaotic sequence (Kolmogorov random sequence).[10]This is notable, as it is outside the realm of classical probability theory.
Yongge Wang(1996) showed that the law of the iterated logarithm holds for polynomial time pseudorandom sequences also.[11][12]The Java-based softwaretesting tooltests whether a pseudorandom generator outputs sequences that satisfy the LIL.
Balsubramani (2014) proved a non-asymptotic LIL that holds over finite-timemartingalesample paths.[13]This subsumes the martingale LIL as it provides matching finite-sample concentration and anti-concentration bounds, and enables sequential testing[14]and other applications.[15]
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Incomputer science,shared memoryismemorythat may be simultaneously accessed by multiple programs with an intent to provide communication among them or avoid redundant copies. Shared memory is an efficient means of passing data between programs. Depending on context, programs may run on a single processor or on multiple separate processors.
Using memory for communication inside a single program, e.g. among its multiplethreads, is also referred to as shared memory.
In computer hardware,shared memoryrefers to a (typically large) block ofrandom access memory(RAM) that can be accessed by several differentcentral processing units(CPUs) in amultiprocessor computer system.
Shared memory systems may use:[1]
A shared memory system is relatively easy to program since all processors share a single view of data and the communication between processors can be as fast as memory accesses to the same location. The issue with shared memory systems is that many CPUs need fast access to memory and will likelycache memory, which has two complications:
Technologies likecrossbar switches,Omega networks,HyperTransportorfront-side buscan be used to dampen the bottleneck-effects.
In case of aHeterogeneous System Architecture(processor architecture that integrates different types of processors, such asCPUsandGPUs, with shared memory), thememory management unit(MMU) of the CPU and theinput–output memory management unit(IOMMU) of the GPU have to share certain characteristics, like a common address space.
The alternatives to shared memory aredistributed memoryanddistributed shared memory, each having a similar set of issues.
In computer software,shared memoryis either
Since both processes can access the shared memory area like regular working memory, this is a very fast way of communication (as opposed to other mechanisms of IPC such asnamed pipes,Unix domain socketsorCORBA). On the other hand, it is less scalable, as for example the communicating processes must be running on the same machine (of other IPC methods, only Internet domain sockets—not Unix domain sockets—can use acomputer network), and care must be taken to avoid issues if processes sharing memory are running on separate CPUs and the underlying architecture is notcache coherent.
IPC by shared memory is used for example to transfer images between the application and theX serveron Unix systems, or inside the IStream object returned by CoMarshalInterThreadInterfaceInStream in the COM libraries underWindows.
Dynamic librariesare generally held in memory once and mapped to multiple processes, and only pages that had to be customized for the individual process (because a symbol resolved differently there) are duplicated, usually with a mechanism known ascopy-on-writethat transparently copies the page when a write is attempted, and then lets the write succeed on the private copy.
Compared to multiple address space operating systems,
memory sharing -- especially of sharing procedures or pointer-based structures --
is simpler insingle address space operating systems.[2]
POSIXprovides a standardized API for using shared memory,POSIX Shared Memory. This uses the functionshm_openfrom sys/mman.h.[3]POSIX interprocess communication (part of the POSIX:XSI Extension) includes the shared-memory functionsshmat,shmctl,shmdtandshmget.[4][5]Unix System V provides an API for shared memory as well. This uses shmget from sys/shm.h. BSD systems provide "anonymous mapped memory" which can be used by several processes.
The shared memory created byshm_openis persistent. It stays in the system until explicitly removed by a process. This has a drawback in that if the process crashes and fails to clean up shared memory it will stay until system shutdown; that limitation is not present in an Android-specific implementation dubbedashmem.[6]
POSIX also provides themmapAPI for mapping files into memory; a mapping can be shared, allowing the file's contents to be used as shared memory.
Linux distributions based on the 2.6 kernel and later offer /dev/shm as shared memory in the form of aRAM disk, more specifically as a world-writable directory (a directory in which every user of the system can create files) that is stored in memory. Both theRedHatandDebianbased distributions include it by default. Support for this type of RAM disk is completely optional within the kernelconfiguration file.[7]
On Windows, one can useCreateFileMappingandMapViewOfFilefunctions to map a region of a file into memory in multiple processes.[8]
Some C++ libraries provide a portable and object-oriented access to shared memory functionality. For example,Boostcontains the Boost.Interprocess C++ Library[9]andQtprovides the QSharedMemory class.[10]
For programming languages with POSIX bindings (say, C/C++), shared memory regions can be created and accessed by calling the functions provided by the operating system. Other programming languages may have their own ways of using these operating facilities for similar effect. For example,PHPprovides anAPIto create shared memory, similar toPOSIXfunctions.[11]
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Theangular displacement(symbol θ, ϑ, or φ) – also calledangle of rotation,rotational displacement, orrotary displacement– of aphysical bodyis theangle(inunitsofradians,degrees,turns, etc.) through which the bodyrotates(revolves or spins) around a centre oraxis of rotation. Angular displacement may be signed, indicating the sense of rotation (e.g.,clockwise); it may also be greater (inabsolute value) than a fullturn.
When a body rotates about its axis, the motion cannot simply be analyzed as a particle, as incircular motionit undergoes a changing velocity and acceleration at any time. When dealing with the rotation of a body, it becomes simpler to consider the body itself rigid. A body is generally considered rigid when the separations between all the particles remains constant throughout the body's motion, so for example parts of its mass are not flying off. In a realistic sense, all things can be deformable, however this impact is minimal and negligible.
In the example illustrated to the right (or above in some mobile versions), a particle or body P is at a fixed distancerfrom the origin,O, rotating counterclockwise. It becomes important to then represent the position of particle P in terms of its polar coordinates (r,θ). In this particular example, the value ofθis changing, while the value of the radius remains the same. (In rectangular coordinates (x,y) bothxandyvary with time.) As the particle moves along the circle, it travels anarc lengths, which becomes related to the angular position through the relationship:
Angular displacement may be expressed inradiansor degrees. Using radians provides a very simple relationship between distance traveled around the circle (circular arclength) and the distancerfrom the centre (radius):
For example, if a body rotates 360° around a circle of radiusr, the angular displacement is given by the distance traveled around the circumference - which is 2πr- divided by the radius:θ=2πrr{\displaystyle \theta ={\frac {2\pi r}{r}}}which easily simplifies to:θ=2π{\displaystyle \theta =2\pi }. Therefore, 1revolutionis2π{\displaystyle 2\pi }radians.
The above definition is part of theInternational System of Quantities(ISQ), formalized in the international standardISO 80000-3(Space and time),[1]and adopted in theInternational System of Units(SI).[2][3]
Angular displacement may be signed, indicating the sense of rotation (e.g.,clockwise);[1]it may also be greater (inabsolute value) than a fullturn.
In the ISQ/SI, angular displacement is used to define thenumber of revolutions,N=θ/(2π rad), a ratio-typequantity of dimension one.
In three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which always exists by virtue of theEuler's rotation theorem; the magnitude specifies the rotation inradiansabout that axis (using theright-hand ruleto determine direction). This entity is called anaxis-angle.
Despite having direction and magnitude, angular displacement is not avectorbecause it does not obey thecommutative lawfor addition.[4]Nevertheless, when dealing with infinitesimal rotations, second order infinitesimals can be discarded and in this case commutativity appears.
Several ways to describe rotations exist, likerotation matricesorEuler angles. Seecharts on SO(3)for others.
Given that any frame in the space can be described by a rotation matrix, the displacement among them can also be described by a rotation matrix. BeingA0{\displaystyle A_{0}}andAf{\displaystyle A_{f}}two matrices, the angular displacement matrix between them can be obtained asΔA=AfA0−1{\displaystyle \Delta A=A_{f}A_{0}^{-1}}. When this product is performed having a very small difference between both frames we will obtain a matrix close to the identity.
In the limit, we will have an infinitesimal rotation matrix.
Aninfinitesimal rotation matrixor differential rotation matrix is amatrixrepresenting aninfinitelysmallrotation.
While arotation matrixis anorthogonal matrixRT=R−1{\displaystyle R^{\mathsf {T}}=R^{-1}}representing an element ofSO(n){\displaystyle SO(n)}(thespecial orthogonal group), thedifferentialof a rotation is askew-symmetric matrixAT=−A{\displaystyle A^{\mathsf {T}}=-A}in thetangent spaceso(n){\displaystyle {\mathfrak {so}}(n)}(thespecial orthogonal Lie algebra), which is not itself a rotation matrix.
An infinitesimal rotation matrix has the form
whereI{\displaystyle I}is the identity matrix,dθ{\displaystyle d\theta }is vanishingly small, andA∈so(n).{\displaystyle A\in {\mathfrak {so}}(n).}
For example, ifA=Lx,{\displaystyle A=L_{x},}representing an infinitesimal three-dimensional rotation about thex-axis, a basis element ofso(3),{\displaystyle {\mathfrak {so}}(3),}then
and
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Inmathematics, specificallyprojective geometry, aconfigurationin the plane consists of a finite set ofpoints, and a finitearrangement of lines, such that each point isincidentto the same number of lines and each line is incident to the same number of points.[1]
Although certain specific configurations had been studied earlier (for instance byThomas Kirkmanin 1849), the formal study of configurations was first introduced byTheodor Reyein 1876, in the second edition of his bookGeometrie der Lage, in the context of a discussion ofDesargues' theorem.Ernst Steinitzwrote his dissertation on the subject in 1894, and they were popularized byHilbertandCohn-Vossen's 1932 bookAnschauliche Geometrie, reprinted in English asHilbert & Cohn-Vossen (1952).
Configurations may be studied either as concrete sets of points and lines in a specific geometry, such as theEuclideanorprojective planes(these are said to berealizablein that geometry), or as a type of abstractincidence geometry. In the latter case they are closely related toregularhypergraphsandbiregularbipartite graphs, but with some additional restrictions: every two points of the incidence structure can be associated with at most one line, and every two lines can be associated with at most one point. That is, thegirthof the corresponding bipartite graph (theLevi graphof the configuration) must be at least six.
A configuration in the plane is denoted by (pγℓπ), wherepis the number of points,ℓthe number of lines,γthe number of lines per point, andπthe number of points per line. These numbers necessarily satisfy the equation
as this product is the number of point-line incidences (flags).
Configurations having the same symbol, say (pγℓπ), need not beisomorphicasincidence structures. For instance, there exist three different (9393) configurations: thePappus configurationand two less notable configurations.
In some configurations,p=ℓand consequently,γ=π. These are calledsymmetricorbalancedconfigurations[2]and the notation is often condensed to avoid repetition. For example, (9393) abbreviates to (93).
Notable projective configurations include the following:
Theprojective dualof a configuration (pγℓπ) is a (ℓπpγ) configuration in which the roles of "point" and "line" are exchanged. Types of configurations therefore come in dual pairs, except when taking the dual results in an isomorphic configuration. These exceptions are calledself-dualconfigurations and in such casesp=ℓ.[5]
The number of nonisomorphic configurations of type (n3), starting atn= 7, is given by the sequence
These numbers count configurations as abstract incidence structures, regardless of realizability.[6]AsGropp (1997)discusses, nine of the ten (103) configurations, and all of the (113) and (123) configurations, are realizable in the Euclidean plane, but for eachn≥ 16there is at least one nonrealizable (n3) configuration. Gropp also points out a long-lasting error in this sequence: an 1895 paper attempted to list all (123) configurations, and found 228 of them, but the 229th configuration, the Gropp configuration, was not discovered until 1988.
There are several techniques for constructing configurations, generally starting from known configurations. Some of the simplest of these techniques construct symmetric (pγ) configurations.
Some self dual configurations (pk) are cyclic configurations and can be constructed by one "generator line", like {0,1,3}, with vertices indexed from zero, and where indices in following lines are cycled forward modulop. This is guaranteed to produce a symmetric configuration when valid. An invalid generator line produces disconnected configurations, or it may break the axiom requiring at most one line between any two points.[7]
Everypolygonas configuration (p2) is trivially a cyclic configuration with generator line {0,1}. A triangle (32) has lines {{0,1},{1,2},{2,0}}.
The Fano plane, (73), the smallest self-dual order 3 symmetric configuration, can be defined by generator line {0,1,3} as lines {{0,1,3}, {1,2,4}, {2,3,5}, {3,4,6}, {4,5,0}, {5,6,1}, {6,0,2}}. They also can be represented in configuration table:
The smallest self-dual order 5 symmetric configuration is (215) is a cyclic configuration and can be generated by the line {0,3,4,9,11}.[8]
Anyfinite projective planeof ordern, PG(2,n), is an [(n2+n+1)n+1] configuration. Since projective planes are known to exist for all ordersnwhich are powers of primes, these constructions provide infinite families of symmetric configurations.
Automorphismsfor PG(2,n), withn=qm(qprime) are (m!)(n3-1)(n3-n)(n3-n2)/(n-1).[9]
Not all symmetric configurations are realizable. Specificallynmust be a power prime. For instance, PG(2,6) or (437) configuration does not exist.[10]However,Gropp (1990)has provided a construction which shows that fork≥ 3, a (pk) configuration exists for allp≥ 2ℓk+ 1, whereℓkis the length of an optimalGolomb rulerof orderk.
The concept of a configuration may be generalized to higher dimensions,[11]for instance to points and lines or planes inspace. In such cases, the restrictions that no two points belong to more than one line may be relaxed, because it is possible for two points to belong to more than one plane.
Notable three-dimensional configurations are theMöbius configuration, consisting of two mutually inscribed tetrahedra,Reye's configuration, consisting of twelve points and twelve planes, with six points per plane and six planes per point, theGray configurationconsisting of a 3×3×3 grid of 27 points and the 27 orthogonal lines through them, and theSchläfli double six, a configuration with 30 points, 12 lines, two lines per point, and five points per line.
Configuration in the projective plane that is realized by points andpseudolinesis called
topological configuration.[2]For instance, it is known that there exists no point-line (194) configurations, however, there exists a topological configuration with these parameters.
Another generalization of the concept of a configuration concerns configurations of points and circles, a notable example being the (8364)Miquel configuration.[2]
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Inmereology, an area ofmetaphysics, the termgunkapplies to any whole whose parts all have further proper parts. That is, a gunky object is not made of indivisibleatomsorsimples. Because parthood istransitive, any part of gunk is itself gunk. The term was first used byDavid Lewisin his workParts of Classes(1991),[1]in which he conceived of the possibility of "atomless gunk",[2]which was shortened to "gunk" by later writers. Dean W. Zimmerman defends the possibility of atomless gunk.[3]
If point-sized objects are always simple, then a gunky object does not have any point-sized parts, and may be best described by an approach such asWhitehead's point-free geometry. By usual accounts of gunk, such asAlfred Tarski's in 1929,[4]three-dimensional gunky objects also do not have other degenerate parts shaped like one-dimensional curves or two-dimensional surfaces.
Gunk is an important test case for accounts of the composition of material objects: for instance,Ted Siderhas challengedPeter van Inwagen's account of composition because it is inconsistent with the possibility of gunk. Sider's argument also applies to a simpler view than van Inwagen's: mereologicalnihilism, the view that only material simples exist. If nihilism isnecessarily true, then gunk is impossible. But, as Sider argues, because gunk is both conceivable and possible, nihilism is false, or at best a contingent truth.[5]
Gunk has also played an important role in the history oftopology[6]in recent debates concerning change, contact, and the structure of physicalspace. The composition of space and the composition of material objects are related byreceptacles—regions of space that could harbour a material object. (The term receptacles was coined byRichard Cartwright.)[7]It seems reasonable to assume that if space is gunky, a receptacle is gunky and then a material object is possibly gunky.
Arguably, discussions of material gunk run all the way back to at leastAristotleand possibly as far back asAnaxagoras, and include such thinkers asWilliam of Ockham,René Descartes, and Alfred Tarski.[5][8]However, the first contemporary mentionings of gunk is found in the writings ofA. N. WhiteheadandBertrand Russell, and later in the writings of David Lewis.[8]Elements of gunk thought are present inZeno's famous paradoxes of plurality. Zeno argued that if there were such things as discrete instants of time, then objects can never move through time. Aristotle's solution toZeno's paradoxesinvolves the idea that time is not made out of durationless instants, but ever smaller temporal intervals. Every interval of time can be divided into smaller and smaller intervals, without ever terminating in some privileged set of durationless instants.[9]In other words, motion is possible because time is gunky. Despite having been a relatively common position inmetaphysics, afterCantor's discovery of the distinction between denumerable and non-denumerable infinitecardinalities, and mathematical work byAdolf Grünbaum, gunk theory was no longer seen as a necessary alternative to a topology of space made out of points.[8]Recent mathematical work in the topology of spacetime by scholars such as Peter Roeper and Frank Arntzenius have reopened the question of whether a gunky spacetime is a feasible framework for doingphysics.[9][10]
Possibly the most influential formulation of a theory of gunky spacetime comes from A. N. Whitehead in his seminal workProcess and Reality.[11]Whitehead argues that there are no point regions of space and that every region of space has some three-dimensional extension. Under a Whiteheadian conception of spacetime, points, lines, planes, and other less-than-three-dimensional objects are constructed out of a method of "extensive abstraction", in which points, lines, and planes are identified with infinitely converging abstract sets of nested extended regions.[11]
Ted Siderhas argued that even the possibility of gunk undermines another position, that ofmereological nihilism.[5]Sider's argument is as follows:
This argument only depends on whether or not gunk is even possible, not whether or not the actual world is a gunky one. Sider defends premise #1 by appealing to the fact that since nihilism is a metaphysical thesis, it must be true or false of necessity.[5]In defense of premise #2, Sider argues that since a gunk world is conceivable; that is, we can imagine a gunky world without any internal contradiction, the gunk must be possible. Premise #3 follows from an understanding of necessity and possibility that stems from an understanding of possible world semantics. Simply put, a proposition P is necessarily false if and only if it is false in all possible worlds, and if a proposition P is possible, it is true in at least one possible world. Thus, if a proposition is possible, then it is not necessarily false, as it is not false in all possible worlds. The conclusion, #4, follows deductively from the other premises.
Sider's argument is valid, so most strategies to resist the argument have focused on denying one or more of his premises. Strategies that deny #1 have been called the "contingency defense". Deniers of #1 say that the facts that determine the composition of objects are not necessary facts, but can differ in different possible worlds. As such, nihilism is a contingent matter of fact, and the possibility of gunk does not undermine the possibility of nihilism. This is the strategy endorsed by Cameron[12]and Miller.[13]
Alternatively, one could deny #2 and say that gunk is metaphysically impossible. Most strategies that take this route deny #2 in virtue of denying another relatively common intuition: that conceivability entails metaphysical possibility. Although this metaphysical principle dates back to at least the works of Descartes, recent work by philosophers such as Marcus[14]and Roca-Royes[15]has shed some doubt on the reliability of conceivability as a guide to metaphysical possibility. Furthermore, Sider's own arguments in defense of #1 seem to undermine the argument: gunk is also a metaphysical thesis, thus, it seems that (like #1) it would also have to be either necessarily true or necessarily false. The argument would only work if gunk were necessarily true, but this would amount to question-begging.
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Quantum machine learningis the integration ofquantum algorithmswithinmachine learningprograms.[1][2][3][4][5][6][7][8]
The most common use of the term refers to machine learning algorithms for the analysis of classical data executed on aquantum computer, i.e. quantum-enhanced machine learning.[9][10][11]While machine learning algorithms are used to compute immense quantities of data, quantum machine learning utilizesqubitsand quantum operations or specialized quantum systems to improve computational speed and data storage done by algorithms in a program.[12]This includes hybrid methods that involve both classical and quantum processing, where computationally difficult subroutines are outsourced to a quantum device.[13][14][15]These routines can be more complex in nature and executed faster on a quantum computer.[7]Furthermore, quantum algorithms can be used to analyzequantum statesinstead of classical data.[16][17]
Beyond quantum computing, the term "quantum machine learning" is also associated with classical machine learning methods applied to data generated from quantum experiments (i.e.machine learning of quantum systems), such as learning thephase transitionsof a quantum system[18][19]or creating new quantum experiments.[20][21][22]
Quantum machine learning also extends to a branch of research that explores methodological and structural similarities between certain physical systems and learning systems, in particular neural networks. For example, some mathematical and numerical techniques from quantum physics are applicable to classical deep learning and vice versa.[23][24][25]
Furthermore, researchers investigate more abstract notions of learning theory with respect to quantum information, sometimes referred to as "quantum learning theory".[26][27]
Quantum-enhanced machine learning refers toquantum algorithmsthat solve tasks in machine learning, thereby improving and often expediting classical machine learning techniques. Such algorithms typically require one to encode the given classical data set into a quantum computer to make it accessible for quantum information processing. Subsequently, quantum information processing routines are applied and the result of the quantum computation is read out by measuring the quantum system. For example, the outcome of the measurement of a qubit reveals the result of a binary classification task. While many proposals of quantum machine learning algorithms are still purely theoretical and require a full-scale universalquantum computerto be tested, others have been implemented on small-scale or special purpose quantum devices.
Associative (or content-addressable memories) are able to recognize stored content on the basis of a similarity measure, rather than fixed addresses, like in random access memories. As such they must be able to retrieve both incomplete and corrupted patterns, the essential machine learning task of pattern recognition.
Typical classical associative memories store p patterns in theO(n2){\displaystyle O(n^{2})}interactions (synapses) of a real, symmetric energy matrix over a network of n artificial neurons. The encoding is such that the desired patterns are local minima of the energy functional and retrieval is done by minimizing the total energy, starting from an initial configuration.
Unfortunately, classical associative memories are severely limited by the phenomenon ofcross-talk. When too many patterns are stored, spurious memories appear which quickly proliferate, so that the energy landscape becomes disordered and no retrieval is anymore possible. The number of storable patterns is typically limited by a linear function of the number of neurons,p≤O(n){\displaystyle p\leq O(n)}.
Quantum associative memories[2][3][4](in their simplest realization) store patterns in a unitary matrix U acting on theHilbert spaceof n qubits. Retrieval is realized by theunitary evolutionof a fixed initial state to aquantum superpositionof the desired patterns with probability distribution peaked on the most similar pattern to an input. By its very quantum nature, the retrieval process is thus probabilistic. Because quantum associative memories are free from cross-talk, however, spurious memories are never generated. Correspondingly, they have a superior capacity than classical ones. The number of parameters in the unitary matrix U isO(pn){\displaystyle O(pn)}. One can thus have efficient, spurious-memory-free quantum associative memories for any polynomial number of patterns.
A number of quantum algorithms for machine learning are based on the idea of amplitude encoding, that is, to associate theamplitudesof a quantum state with the inputs and outputs of computations.[30][31][32]Since a state ofn{\displaystyle n}qubits is described by2n{\displaystyle 2^{n}}complex amplitudes, this information encoding can allow for an exponentially compact representation. Intuitively, this corresponds to associating a discrete probability distribution over binary random variables with a classical vector. The goal of algorithms based on amplitude encoding is to formulate quantum algorithms whoseresourcesgrow polynomially in the number of qubitsn{\displaystyle n}, which amounts to a logarithmictime complexityin the number of amplitudes and thereby the dimension of the input.
Many quantum machine learning algorithms in this category are based on variations of thequantum algorithm for linear systems of equations[33](colloquially called HHL, after the paper's authors) which, under specific conditions, performs a matrix inversion using an amount of physical resources growing only logarithmically in the dimensions of the matrix. One of these conditions is that aHamiltonianwhich entry wise corresponds to the matrix can be simulated efficiently, which is known to be possible if the matrix is sparse[34]or low rank.[35]For reference, any known classical algorithm formatrix inversionrequires a number of operations that growsmore than quadratically in the dimension of the matrix(e.g.O(n2.373){\displaystyle O{\mathord {\left(n^{2.373}\right)}}}), but they are not restricted to sparse matrices.
Quantum matrix inversion can be applied to machine learning methods in which the training reduces to solving alinear system of equations, for example in least-squares linear regression,[31][32]the least-squares version ofsupport vector machines,[30]and Gaussian processes.[36]
A crucial bottleneck of methods that simulate linear algebra computations with the amplitudes of quantum states is state preparation, which often requires one to initialise a quantum system in a state whose amplitudes reflect the features of the entire dataset. Although efficient methods for state preparation are known for specific cases,[37][38]this step easily hides the complexity of the task.[39][40]
VQAs are one of the most studied classes of quantum algorithms, as modern research demonstrates their applicability to the vast majority of known major applications of the quantum computer, and they appear to be a leading hope for gaining quantum supremacy.[41]VQAs are a mixed quantum-classical approach where the quantum processor prepares quantum states and measurement is made and the optimization is done by a classical computer. VQAs are considered best for NISQ as VQAs are noise tolerant compared to other algorithms and give quantum superiority with only a few hundred qubits. Researchers have studied circuit-based algorithms to solve optimization problems and find the ground state energy of complex systems, which were difficult to solve or required a large time to perform the computation using a classical computer.[42][43]
Variational Quantum Circuits also known as Parametrized Quantum Circuits (PQCs) are based on Variational Quantum Algorithms (VQAs). VQCs consist of three parts: preparation of initial states, quantum circuit, and measurement. Researchers are extensively studying VQCs, as it uses the power of quantum computation to learn in a short time and also use fewer parameters than its classical counterparts. It is theoretically and numerically proven that we can approximate non-linear functions, like those used in neural networks, on quantum circuits. Due to VQCs superiority, neural network has been replaced by VQCs in Reinforcement Learning tasks and Generative Algorithms. The intrinsic nature of quantum devices towards decoherence, random gate error and measurement errors caused to have high potential to limit the training of the variation circuits. Training the VQCs on the classical devices before employing them on quantum devices helps to overcome the problem of decoherence noise that came through the number of repetitions for training.[44][45][46]
Pattern reorganization is one of the important tasks of machine learning,binary classificationis one of the tools or algorithms to find patterns. Binary classification is used insupervised learningand inunsupervised learning. In quantum machine learning, classical bits are converted to qubits and they are mapped to Hilbert space; complex value data are used in a quantum binary classifier to use the advantage of Hilbert space.[47][48]By exploiting the quantum mechanic properties such as superposition, entanglement, interference the quantum binary classifier produces the accurate result in short period of time.[49]
Another approach to improving classical machine learning with quantum information processing usesamplitude amplificationmethods based onGrover's searchalgorithm, which has been shown to solve unstructured search problems with a quadratic speedup compared to classical algorithms. These quantum routines can be employed for learning algorithms that translate into an unstructured search task, as can be done, for instance, in the case of thek-medians[50]and thek-nearest neighbors algorithms.[9]Other applications include quadratic speedups in the training ofperceptron[51]and the computation ofattention.[52]
An example of amplitude amplification being used in a machine learning algorithm is Grover's search algorithm minimization. In which a subroutine uses Grover's search algorithm to find an element less than some previously defined element. This can be done with an oracle that determines whether or not a state with a corresponding element is less than the predefined one. Grover's algorithm can then find an element such that our condition is met. The minimization is initialized by some random element in our data set, and iteratively does this subroutine to find the minimum element in the data set. This minimization is notably used in quantum k-medians, and it has a speed up of at leastO(nk){\displaystyle {\mathcal {O}}\left({\sqrt {\frac {n}{k}}}\right)}compared to classical versions of k-medians, wheren{\displaystyle n}is the number of data points andk{\displaystyle k}is the number of clusters.[50]
Amplitude amplification is often combined withquantum walksto achieve the same quadratic speedup. Quantum walks have been proposed to enhance Google's PageRank algorithm[53]as well as the performance of reinforcement learning agents in the projective simulation framework.[54]
Reinforcement learningis a branch of machine learning distinct from supervised and unsupervised learning, which also admits quantum enhancements.[55][54][56]In quantum-enhanced reinforcement learning, a quantum agent interacts with a classical or quantum environment and occasionally receives rewards for its actions, which allows the agent to adapt its behavior—in other words, to learn what to do in order to gain more rewards. In some situations, either because of the quantum processing capability of the agent,[54]or due to the possibility to probe the environment insuperpositions,[29]a quantum speedup may be achieved. Implementations of these kinds of protocols have been proposed for systems oftrapped ions[57]andsuperconducting circuits.[58]A quantum speedup of the agent's internal decision-making time[54]has been experimentally demonstrated in trapped ions,[59]while a quantum speedup of the learning time in a fully coherent (`quantum') interaction between agent and environment has been experimentally realized in a photonic setup.[60]
Quantum annealingis an optimization technique used to determine the local minima and maxima of a function over a given set of candidate functions. This is a method of discretizing a function with many local minima or maxima in order to determine the observables of the function. The process can be distinguished fromSimulated annealingby theQuantum tunnelingprocess, by which particles tunnel through kinetic or potential barriers from a high state to a low state. Quantum annealing starts from a superposition of all possible states of a system, weighted equally. Then the time-dependentSchrödinger equationguides the time evolution of the system, serving to affect the amplitude of each state as time increases. Eventually, the ground state can be reached to yield the instantaneous Hamiltonian of the system.
As the depth of the quantum circuit advances onNISQdevices, the noise level rises, posing a significant challenge to accurately computing costs and gradients on training models. The noise tolerance will be improved by using the quantumperceptronand the quantum algorithm on the currently accessible quantum hardware.[citation needed]
A regular connection of similar components known asneuronsforms the basis of even the most complex brain networks. Typically, a neuron has two operations: the inner product and anactivation function. As opposed to the activation function, which is typicallynonlinear, the inner product is a linear process. With quantum computing, linear processes may be easily accomplished additionally, due to the simplicity of implementation, the threshold function is preferred by the majority of quantum neurons for activation functions.[citation needed]
Sampling from high-dimensional probability distributions is at the core of a wide spectrum of computational techniques with important applications across science, engineering, and society. Examples includedeep learning,probabilistic programming, and other machine learning and artificial intelligence applications.
A computationally hard problem, which is key for some relevant machine learning tasks, is the estimation of averages over probabilistic models defined in terms of aBoltzmann distribution. Sampling from generic probabilistic models is hard: algorithms relying heavily on sampling are expected to remain intractable no matter how large and powerful classical computing resources become. Even though quantum annealers, like those produced by D-Wave Systems, were designed for challenging combinatorial optimization problems, it has been recently recognized as a potential candidate to speed up computations that rely on sampling by exploiting quantum effects.[61]
Some research groups have recently explored the use of quantum annealing hardware for trainingBoltzmann machinesanddeep neural networks.[62][63][64]The standard approach to training Boltzmann machines relies on the computation of certain averages that can be estimated by standardsamplingtechniques, such asMarkov chain Monte Carloalgorithms. Another possibility is to rely on a physical process, like quantum annealing, that naturally generates samples from a Boltzmann distribution. The objective is to find the optimal control parameters that best represent the empirical distribution of a given dataset.
The D-Wave 2X system hosted at NASA Ames Research Center has been recently used for the learning of a special class of restricted Boltzmann machines that can serve as a building block for deep learning architectures.[63]Complementary work that appeared roughly simultaneously showed that quantum annealing can be used for supervised learning in classification tasks.[62]The same device was later used to train a fully connected Boltzmann machine to generate, reconstruct, and classify down-scaled, low-resolution handwritten digits, among other synthetic datasets.[65]In both cases, the models trained by quantum annealing had a similar or better performance in terms of quality. The ultimate question that drives this endeavour is whether there is quantum speedup in sampling applications. Experience with the use of quantum annealers for combinatorial optimization suggests the answer is not straightforward. Reverse annealing has been used as well to solve a fully connected quantum restricted Boltzmann machine.[66]
Inspired by the success of Boltzmann machines based on classical Boltzmann distribution, a new machine learning approach based on quantum Boltzmann distribution of a transverse-field Ising Hamiltonian was recently proposed.[67]Due to the non-commutative nature of quantum mechanics, the training process of the quantum Boltzmann machine can become nontrivial. This problem was, to some extent, circumvented by introducing bounds on the quantum probabilities, allowing the authors to train the model efficiently by sampling. It is possible that a specific type of quantum Boltzmann machine has been trained in the D-Wave 2X by using a learning rule analogous to that of classical Boltzmann machines.[65][64][68]
Quantum annealing is not the only technology for sampling. In a prepare-and-measure scenario, a universal quantum computer prepares a thermal state, which is then sampled by measurements. This can reduce the time required to train a deep restricted Boltzmann machine, and provide a richer and more comprehensive framework for deep learning than classical computing.[69]The same quantum methods also permit efficient training of full Boltzmann machines and multi-layer, fully connected models and do not have well-known classical counterparts. Relying on an efficient thermal state preparation protocol starting from an arbitrary state, quantum-enhancedMarkov logic networksexploit the symmetries and the locality structure of theprobabilistic graphical modelgenerated by afirst-order logictemplate.[70][19]This provides an exponential reduction in computational complexity in probabilistic inference, and, while the protocol relies on a universal quantum computer, under mild assumptions it can be embedded on contemporary quantum annealing hardware.
Quantum analogues or generalizations of classical neural nets are often referred to asquantum neural networks. The term is claimed by a wide range of approaches, including the implementation and extension of neural networks using photons, layered variational circuits or quantum Ising-type models. Quantum neural networks are often defined as an expansion on Deutsch's model of a quantum computational network.[71]Within this model, nonlinear and irreversible gates, dissimilar to the Hamiltonian operator, are deployed to speculate the given data set.[71]Such gates make certain phases unable to be observed and generate specific oscillations.[71]Quantum neural networks apply the principals quantum information and quantum computation to classical neurocomputing.[72]Current research shows that QNN can exponentially increase the amount of computing power and the degrees of freedom for a computer, which is limited for a classical computer to its size.[72]A quantum neural network has computational capabilities to decrease the number of steps, qubits used, and computation time.[71]The wave function to quantum mechanics is the neuron for Neural networks. To test quantum applications in a neural network, quantum dot molecules are deposited on a substrate of GaAs or similar to record how they communicate with one another. Each quantum dot can be referred as an island of electric activity, and when such dots are close enough (approximately 10 - 20 nm)[73]electrons can tunnel underneath the islands. An even distribution across the substrate in sets of two create dipoles and ultimately two spin states, up or down. These states are commonly known as qubits with corresponding states of|0⟩{\displaystyle |0\rangle }and|1⟩{\displaystyle |1\rangle }in Dirac notation.[73]
A novel design for multi-dimensional vectors that uses circuits as convolution filters[74]is QCNN. It was inspired by the advantages of CNNs[75][76]and the power of QML. It is made using a combination of a variational quantum circuit(VQC)[77]and adeep neural network[78](DNN), fully utilizing the power of extremely parallel processing on a superposition of a quantum state with a finite number of qubits. The main strategy is to carry out an iterative optimization process in theNISQ[79]devices, without the negative impact of noise, which is possibly incorporated into the circuit parameter, and without the need for quantum error correction.[80]
The quantum circuit must effectively handle spatial information in order for QCNN to function as CNN. The convolution filter is the most basic technique for making use of spatial information. One or more quantum convolutional filters make up a quantum convolutional neural network (QCNN), and each of these filters transforms input data using a quantum circuit that can be created in an organized or randomized way. Three parts that make up the quantum convolutional filter are: the encoder, the parameterized quantum circuit (PQC),[81]and the measurement. The quantum convolutional filter can be seen as an extension of the filter in the traditional CNN because it was designed with trainable parameters.
Quantum neural networks take advantage of the hierarchical structures,[82]and for each subsequent layer, the number of qubits from the preceding layer is decreased by a factor of two. For n input qubits, these structure have O(log(n)) layers, allowing for shallow circuit depth. Additionally, they are able to avoid "barren plateau," one of the most significant issues with PQC-based algorithms, ensuring trainability.[83]Despite the fact that the QCNN model does not include the corresponding quantum operation, the fundamental idea of thepooling layeris also offered to assure validity. In QCNN architecture, the pooling layer is typically placed between succeeding convolutional layers. Its function is to shrink the representation's spatial size while preserving crucial features, which allows it to reduce the number of parameters, streamline network computing, and manage over-fitting. Such process can be accomplished applyingfull Tomographyon the state to reduce it all the way down to one qubit and then processed it in subway. The most frequently used unit type in thepooling layeris max pooling, although there are other types as well. Similar toconventional feed-forwardneural networks, the last module is a fully connected layer with full connections to all activations in the preceding layer. Translational invariance, which requires identical blocks of parameterized quantum gates within a layer, is a distinctive feature of the QCNN architecture.[84]
Dissipative QNNs (DQNNs) are constructed from layers of qubits coupled by perceptron called building blocks, which have an arbitrary unitary design. Each node in the network layer of a DQNN is given a distinct collection of qubits, and each qubit is also given a unique quantum perceptron unitary to characterize it.[85][86]The input states information are transported through the network in a feed-forward fashion, layer-to-layer transition mapping on the qubits of the two adjacent layers, as the name implies. Dissipative term also refers to the fact that the output layer is formed by the ancillary qubits while the input layers are dropped while tracing out the final layer.[87]When performing a broad supervised learning task, DQNN are used to learn a unitary matrix connecting the input and output quantum states. The training data for this task consists of the quantum state and the corresponding classical labels.
Inspired by the extremely successful classicalGenerative adversarial network(GAN),[88]dissipative quantum generative adversarial network (DQGAN) is introduced forunsupervised learningof the unlabeled training data . The generator and the discriminator are the two DQNNs that make up a single DQGAN.[86]The generator's goal is to create false training states that the discriminator cannot differentiate from the genuine ones, while the discriminator's objective is to separate the real training states from the fake states created by the generator. The relevant features of the training set are learned by the generator by alternate and adversarial training of the networks that aid in the production of sets that extend the training set. DQGAN has a fully quantum architecture and is trained in quantum data.
Entangled Hidden Markov Models
AnEntangled Hidden Markov Model(EHMM) is a quantum extension of the classical Hidden Markov Model (HMM), introduced by Abdessatar Souissi and El Gheteb Souedidi.[89]EHMMs establish a bridge between classical probability and quantum entanglement, providing a more profound understanding of quantum systems using observational data.
Let \( d_H, d_O \) be two positive integers representing the dimensions of the hidden and observable states, respectively. Define:
- \( \mathcal{M}_{d_H} \) as the \( C^* \)-algebra of \( d_H \times d_H \) matrices.
- \( \mathcal{M}_{d_O} \) as the \( C^* \)-algebra of \( d_O \times d_O \) matrices.
- The identity element in \( \mathcal{M}_{d_H} \) is denoted by \( \mathbb{I}_{d_H} \).
- The Schur (Hadamard) product for two matrices \( A, B \in \mathcal{M}_{d_H} \) is defined as:
Define the hidden and observable sample algebras:
\[ \mathcal{A}_H = \bigotimes_{\mathbb{N}} \mathcal{M}_{d_H}, \quad \mathcal{A}_O = \bigotimes_{\mathbb{N}} \mathcal{M}_{d_O}, \]
with the full sample algebra:
\[ \mathcal{A}_{H,O} = \bigotimes_{\mathbb{N}} (\mathcal{M}_{d_H} \otimes \mathcal{M}_{d_O}). \]
Hidden Quantum Markov Models(HQMMs) are a quantum-enhanced version of classicalHidden Markov Models(HMMs), which are typically used to model sequential data in various fields likeroboticsandnatural language processing.[90]Unlike other quantum-enhanced machine learning algorithms, HQMMs can be viewed as models inspired by quantum mechanics that can be run on classical computers as well.[91]Where classical HMMs use probability vectors to represent hidden 'belief' states, HQMMs use the quantum analogue:density matrices.
Recent work has extended HQMMs through the introduction of **Entangled Hidden Markov Models (EHMMs)**, which incorporate quantum entanglement into their structure.[92]The EHMM framework builds upon classical HQMMs by defining entangled transition expectations, which allow for enhanced modeling of quantum systems.[93]Additionally, EHMMs have been linked to Matrix Product States (MPS) and provide a new perspective on probabilistic graphical models in quantum settings.
Since classical HMMs are a particular kind ofBayes net, HQMMs and EHMMs provide insights into quantum-analogousBayesian inference, offering new pathways for modeling quantum probability and non-classical correlations in quantum information processing. Furthermore, empirical studies suggest that EHMMs improve the ability to model sequential data when compared to their classical counterparts, though further research is required to fully understand these benefits.
A linear map \( \mathcal{E}_H : \mathcal{M}_{d_H} \otimes \mathcal{M}_{d_H} \to \mathcal{M}_{d_H} \) is called a **transition expectation** if it is completely positive and identity-preserving \cite{SSB23}. Similarly, a linear map \( \mathcal{E}_{H,O} : \mathcal{M}_{d_H} \otimes \mathcal{M}_{d_O} \to \mathcal{M}_{d_H} \) is called an **emission operator** if it is completely positive and identity-preserving.
In the most general case of quantum machine learning, both the learning device and the system under study, as well as their interaction, are fully quantum. This section gives a few examples of results on this topic.
One class of problem that can benefit from the fully quantum approach is that of 'learning' unknown quantum states, processes or measurements, in the sense that one can subsequently reproduce them on another quantum system. For example, one may wish to learn a measurement that discriminates between two coherent states, given not a classical description of the states to be discriminated, but instead a set of example quantum systems prepared in these states. The naive approach would be to first extract a classical description of the states and then implement an ideal discriminating measurement based on this information. This would only require classical learning. However, one can show that a fully quantum approach is strictly superior in this case.[94](This also relates to work on quantum pattern matching.[95]) The problem of learning unitary transformations can be approached in a similar way.[96]
Going beyond the specific problem of learning states and transformations, the task ofclusteringalso admits a fully quantum version, wherein both the oracle which returns the distance between data-points and the information processing device which runs the algorithm are quantum.[97]Finally, a general framework spanning supervised, unsupervised and reinforcement learning in the fully quantum setting was introduced in,[29]where it was also shown that the possibility of probing the environment in superpositions permits a quantum speedup in reinforcement learning. Such a speedup in the reinforcement-learning paradigm has been experimentally demonstrated in a photonic setup.[60]
The need for models that can be understood by humans emerges in quantum machine learning in analogy to classical machine learning and drives the research field of explainable quantum machine learning (or XQML[98]in analogy toXAI/XML). These efforts are often also referred to as Interpretable Machine Learning (IML, and by extension IQML).[99]XQML/IQML can be considered as an alternative research direction instead of finding a quantum advantage.[100]For example, XQML has been used in the context of mobile malware detection and classification.[101]QuantumShapley valueshave also been proposed to interpret gates within a circuit based on a game-theoretic approach.[98]For this purpose, gates instead of features act as players in a coalitional game with a value function that depends on measurements of the quantum circuit of interest. Additionally, a quantum version of the classical technique known as LIME (Linear Interpretable Model-Agnostic Explanations)[102]has also been proposed, known as Q-LIME.[103]
The term "quantum machine learning" sometimes refers to classical machine learning performed on data from quantum systems. A basic example of this isquantum state tomography, where a quantum state is learned from measurement. Other applications include learning Hamiltonians[104]and automatically generating quantum experiments.[20]
Quantum learning theory pursues a mathematical analysis of the quantum generalizations of classical learning models and of the possible speed-ups or other improvements that they may provide. The framework is very similar to that of classicalcomputational learning theory, but the learner in this case is a quantum information processing device, while the data may be either classical or quantum. Quantum learning theory should be contrasted with the quantum-enhanced machine learning discussed above, where the goal was to consider specific problems and to use quantum protocols to improve the time complexity of classical algorithms for these problems. Although quantum learning theory is still under development, partial results in this direction have been obtained.[105]
The starting point in learning theory is typically a concept class, a set of possible concepts. Usually a concept is a function on some domain, such as{0,1}n{\displaystyle \{0,1\}^{n}}. For example, the concept class could be the set ofdisjunctive normal form(DNF) formulas on n bits or the set of Boolean circuits of some constant depth. The goal for the learner is to learn (exactly or approximately) an unknown target concept from this concept class. The learner may be actively interacting with the target concept, or passively receiving samples from it.
In active learning, a learner can make membership queries to the target concept c, asking for its value c(x) on inputs x chosen by the learner. The learner then has to reconstruct the exact target concept, with high probability. In the model of quantum exact learning, the learner can make membership queries in quantum superposition. If the complexity of the learner is measured by the number of membership queries it makes, then quantum exact learners can be polynomially more efficient than classical learners for some concept classes, but not more.[106]If complexity is measured by the amount of time the learner uses, then there are concept classes that can be learned efficiently by quantum learners but not by classical learners (under plausible complexity-theoretic assumptions).[106]
A natural model of passive learning is Valiant'sprobably approximately correct (PAC) learning. Here the learner receives random examples (x,c(x)), where x is distributed according to some unknown distribution D. The learner's goal is to output a hypothesis function h such that h(x)=c(x) with high probability when x is drawn according to D. The learner has to be able to produce such an 'approximately correct' h for every D and every target concept c in its concept class. We can consider replacing the random examples by potentially more powerful quantum examples∑xD(x)|x,c(x)⟩{\displaystyle \sum _{x}{\sqrt {D(x)}}|x,c(x)\rangle }. In the PAC model (and the related agnostic model), this doesn't significantly reduce the number of examples needed: for every concept class, classical and quantum sample complexity are the same up to constant factors.[107]However, for learning under some fixed distribution D, quantum examples can be very helpful, for example for learning DNF under the uniform distribution.[108]When considering time complexity, there exist concept classes that can be PAC-learned efficiently by quantum learners, even from classical examples, but not by classical learners (again, under plausible complexity-theoretic assumptions).[106]
This passive learning type is also the most common scheme in supervised learning: a learning algorithm typically takes the training examples fixed, without the ability to query the label of unlabelled examples. Outputting a hypothesis h is a step of induction. Classically, an inductive model splits into a training and an application phase: the model parameters are estimated in the training phase, and the learned model is applied an arbitrary many times in the application phase. In the asymptotic limit of the number of applications, this splitting of phases is also present with quantum resources.[109]
The earliest experiments were conducted using the adiabaticD-Wavequantum computer, for instance, to detect cars in digital images using regularized boosting with a nonconvex objective function in a demonstration in 2009.[110]Many experiments followed on the same architecture, and leading tech companies have shown interest in the potential of quantum machine learning for future technological implementations. In 2013, Google Research,NASA, and theUniversities Space Research Associationlaunched theQuantum Artificial Intelligence Labwhich explores the use of the adiabatic D-Wave quantum computer.[111][112]A more recent example trained a probabilistic generative models with arbitrary pairwise connectivity, showing that their model is capable of generating handwritten digits as well as reconstructing noisy images of bars and stripes and handwritten digits.[65]
Using a different annealing technology based onnuclear magnetic resonance(NMR), a quantumHopfield networkwas implemented in 2009 that mapped the input data and memorized data to Hamiltonians, allowing the use of adiabatic quantum computation.[113]NMR technology also enables universal quantum computing,[citation needed]and it was used for the first experimental implementation of a quantum support vector machine to distinguish hand written number ‘6’ and ‘9’ on a liquid-state quantum computer in 2015.[114]The training data involved the pre-processing of the image which maps them to normalized 2-dimensional vectors to represent the images as the states of a qubit. The two entries of the vector are the vertical and horizontal ratio of the pixel intensity of the image. Once the vectors are defined on thefeature space, the quantum support vector machine was implemented to classify the unknown input vector. The readout avoids costlyquantum tomographyby reading out the final state in terms of direction (up/down) of the NMR signal.
Photonic implementations are attracting more attention,[115]not the least because they do not require extensive cooling. Simultaneous spoken digit and speaker recognition and chaotic time-series prediction were demonstrated at data rates beyond 1 gigabyte per second in 2013.[116]Using non-linear photonics to implement an all-optical linear classifier, a perceptron model was capable of learning the classification boundary iteratively from training data through a feedback rule.[117]A core building block in many learning algorithms is to calculate the distance between two vectors: this was first experimentally demonstrated for up to eight dimensions using entangled qubits in a photonic quantum computer in 2015.[118]
Recently, based on a neuromimetic approach, a novel ingredient has been added to the field of quantum machine learning, in the form of a so-called quantum memristor, a quantized model of the standard classicalmemristor.[119]This device can be constructed by means of a tunable resistor, weak measurements on the system, and a classical feed-forward mechanism. An implementation of a quantum memristor in superconducting circuits has been proposed,[120]and an experiment with quantum dots performed.[121]A quantum memristor would implement nonlinear interactions in the quantum dynamics which would aid the search for a fully functional quantum neural network.
Since 2016, IBM has launched an online cloud-based platform for quantum software developers, called theIBM Q Experience. This platform consists of several fully operational quantum processors accessible via the IBM Web API. In doing so, the company is encouraging software developers to pursue new algorithms through a development environment with quantum capabilities. New architectures are being explored on an experimental basis, up to 32 qubits, using both trapped-ion and superconductive quantum computing methods.
In October 2019, it was noted that the introduction of Quantum Random Number Generators (QRNGs) to machine learning models including Neural Networks and Convolutional Neural Networks for random initial weight distribution and Random Forests for splitting processes had a profound effect on their ability when compared to the classical method of Pseudorandom Number Generators (PRNGs).[122]However, in a more recent publication from 2021, these claims could not be reproduced for Neural Network weight initialization and no significant advantage of using QRNGs over PRNGs was found.[123]The work also demonstrated that the generation of fair random numbers with a gate quantum computer is a non-trivial task on NISQ devices, and QRNGs are therefore typically much more difficult to use in practice than PRNGs.
A paper published in December 2018 reported on an experiment using a trapped-ion system demonstrating a quantum speedup of the deliberation time of reinforcement learning agents employing internal quantum hardware.[59]
In March 2021, a team of researchers from Austria, The Netherlands, the US and Germany reported the experimental demonstration of a quantum speedup of the learning time of reinforcement learning agents interacting fully quantumly with the environment.[124][60]The relevant degrees of freedom of both agent and environment were realized on a compact and fully tunable integrated nanophotonic processor.
Whilemachine learningitself is now not only a research field but an economically significant and fast growing industry andquantum computingis a well established field of both theoretical and experimental research, quantum machine learning remains a purely theoretical field of studies. Attempts to experimentally demonstrate concepts of quantum machine learning remain insufficient.[citation needed]Further, another obstacle exists at the prediction stage because the outputs of quantum learning models are inherently random.[125]This creates an often considerable overhead, as many executions of a quantum learning model have to be aggregated to obtain an actual prediction.
Many of the leading scientists that extensively publish in the field of quantum machine learning warn about the extensive hype around the topic and are very restrained if asked about its practical uses in the foreseeable future. Sophia Chen[126]collected some of the statements made by well known scientists in the field:
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TheLeiden algorithmis a community detection algorithm developed by Traaget al[1]atLeiden University. It was developed as a modification of theLouvain method. Like the Louvain method, the Leiden algorithm attempts to optimizemodularityin extracting communities from networks; however, it addresses key issues present in the Louvain method, namely poorly connected communities and theresolution limit of modularity.
Broadly, the Leiden algorithm uses the same two primary phases as the Louvain algorithm: a local node moving step (though, the method by which nodes are considered in Leiden is more efficient[1]) and a graph aggregation step. However, to address the issues with poorly-connected communities and the merging of smaller communities into larger communities (the resolution limit of modularity), the Leiden algorithm employs an intermediate refinement phase in which communities may be split to guarantee that all communities are well-connected.
Consider, for example, the following graph:
Three communities are present in this graph (each color represents a community). Additionally, the center "bridge" node (represented with an extra circle) is a member of the community represented by blue nodes. Now consider the result of a node-moving step which merges the communities denoted by red and green nodes into a single community (as the two communities are highly connected):
Notably, the center "bridge" node is now a member of the larger red community after node moving occurs (due to the greedy nature of the local node moving algorithm). In the Louvain method, such a merging would be followed immediately by the graph aggregation phase. However, this causes a disconnection between two different sections of the community represented by blue nodes. In the Leiden algorithm, the graph is instead refined:
The Leiden algorithm's refinement step ensures that the center "bridge" node is kept in the blue community to ensure that it remains intact and connected, despite the potential improvement in modularity from adding the center "bridge" node to the red community.
Before defining theLeiden algorithm, it will be helpful to define some of the components of a graph.
A graph is composed ofvertices (nodes)andedges. Each edge is connected to two vertices, and each vertex may be connected to zero or more edges. Edges are typically represented by straight lines, while nodes are represented by circles or points. In set notation, letV{\displaystyle V}be the set of vertices, andE{\displaystyle E}be the set of edges:
V:={v1,v2,…,vn}E:={eij,eik,…,ekl}{\displaystyle {\begin{aligned}V&:=\{v_{1},v_{2},\dots ,v_{n}\}\\E&:=\{e_{ij},e_{ik},\dots ,e_{kl}\}\end{aligned}}}
whereeij{\displaystyle e_{ij}}is the directed edge from vertexvi{\displaystyle v_{i}}to vertexvj{\displaystyle v_{j}}. We can also write this as an ordered pair:
eij:=(vi,vj){\displaystyle {\begin{aligned}e_{ij}&:=(v_{i},v_{j})\end{aligned}}}
A community is a unique set of nodes:
Ci⊆VCi⋂Cj=∅∀i≠j{\displaystyle {\begin{aligned}C_{i}&\subseteq V\\C_{i}&\bigcap C_{j}=\emptyset ~\forall ~i\neq j\end{aligned}}}
and the union of all communities must be the total set of vertices:
V=⋃i=1Ci{\displaystyle {\begin{aligned}V&=\bigcup _{i=1}C_{i}\end{aligned}}}
A partition is the set of all communities:
P={C1,C2,…,Cn}{\displaystyle {\begin{aligned}{\mathcal {P}}&=\{C_{1},C_{2},\dots ,C_{n}\}\end{aligned}}}
How communities are partitioned is an integral part on the Leiden algorithm. How partitions are decided can depend on how their quality is measured. Additionally, many of these metrics contain parameters of their own that can change the outcome of their communities.
Modularityis a highly used quality metric for assessing how well a set of communities partition a graph. The equation for this metric is defined for an adjacency matrix, A, as:[2]
Q=12m∑ij(Aij−kikj2m)δ(ci,cj){\displaystyle Q={\frac {1}{2m}}\sum _{ij}(A_{ij}-{\frac {k_{i}k_{j}}{2m}})\delta (c_{i},c_{j})}
where:
δ(ci,cj)={1ifciandcjare the same community0otherwise{\displaystyle {\begin{aligned}\delta (c_{i},c_{j})&={\begin{cases}1&{\text{if }}c_{i}{\text{ and }}c_{j}{\text{ are the same community}}\\0&{\text{otherwise}}\end{cases}}\end{aligned}}}
One of the most well used metrics for the Leiden algorithm is the Reichardt Bornholdt Potts Model (RB).[3]This model is used by default in most mainstream Leiden algorithm libraries under the nameRBConfigurationVertexPartition.[4][5]This model introduces a resolution parameterγ{\displaystyle \gamma }and is highly similar to the equation for modularity. This model is defined by the following quality function for an adjacency matrix, A, as:[4]
Q=∑ij(Aij−γkikj2m)δ(ci,cj){\displaystyle Q=\sum _{ij}(A_{ij}-\gamma {\frac {k_{i}k_{j}}{2m}})\delta (c_{i},c_{j})}
where:
Another metric similar to RB, is the Constant Potts Model (CPM). This metric also relies on a resolution parameterγ{\displaystyle \gamma }[6]The quality function is defined as:
H=−∑ij(Aijwij−γ)δ(ci,cj){\displaystyle H=-\sum _{ij}(A_{ij}w_{ij}-\gamma )\delta (c_{i},c_{j})}
Typically Potts models such as RB or CPM include a resolution parameter in their calculation.[3][6]Potts models are introduced as a response to the resolution limit problem that is present in modularity maximization based community detection. The resolution limit problem is that, for some graphs, maximizing modularity may cause substructures of a graph to merge and become a single community and thus smaller structures are lost.[7]These resolution parameters allow modularity adjacent methods to be modified to suit the requirements of the user applying the Leiden algorithm to account for small substructures at a certain granularity.
The figure on the right illustrates why resolution can be a helpful parameter when using modularity based quality metrics. In the first graph, modularity only captures the large scale structures of the graph; however, in the second example, a more granular quality metric could potentially detect all substructures in a graph.
The Leiden algorithm starts with a graph of disorganized nodes(a)and sorts it by partitioning them to maximizemodularity(the difference in quality between the generated partition and a hypothetical randomized partition of communities). The method it uses is similar to the Louvain algorithm, except that after moving each node it also considers that node's neighbors that are not already in the community it was placed in. This process results in our first partition(b), also referred to asP{\displaystyle {\mathcal {P}}}. Then the algorithm refines this partition by first placing each node into its own individual community and then moving them from one community to another to maximize modularity. It does this iteratively until each node has been visited and moved, and each community has been refined - this creates partition(c), which is the initial partition ofPrefined{\displaystyle {\mathcal {P}}_{\text{refined}}}. Then an aggregate network(d)is created by turning each community into a node.Prefined{\displaystyle {\mathcal {P}}_{\text{refined}}}is used as the basis for the aggregate network whileP{\displaystyle {\mathcal {P}}}is used to create its initial partition. Because we use the original partitionP{\displaystyle {\mathcal {P}}}in this step, we must retain it so that it can be used in future iterations. These steps together form the first iteration of the algorithm.
In subsequent iterations, the nodes of the aggregate network (which each represent a community) are once again placed into their own individual communities and then sorted according to modularity to form a newPrefined{\displaystyle {\mathcal {P}}_{\text{refined}}}, forming(e)in the above graphic. In the case depicted by the graph, the nodes were already sorted optimally, so no change took place, resulting in partition(f). Then the nodes of partition(f)would once again be aggregated using the same method as before, with the original partitionP{\displaystyle {\mathcal {P}}}still being retained. This portion of the algorithm repeats until each aggregate node is in its own individual network; this means that no further improvements can be made.
The Leiden algorithm consists of three main steps: local moving of nodes, refinement of the partition, and aggregation of the network based on the refined partition. All of the functions in the following steps are called using our main function Leiden, depicted below: The Fast Louvain method is borrowed by the authors of Leiden from "A Simple Acceleration Method for the Louvain Algorithm".[8]
Step 1: Local Moving of Nodes
First, we move the nodes fromP{\displaystyle {\mathcal {P}}}into neighboring communities to maximizemodularity(the difference in quality between the generated partition and a hypothetical randomized partition of communities). In the above image, our initial collection of unsorted nodes is represented by the graph on the left, with each node's unique color representing that they do not belong to a community yet. The graph on the right is a representation of this step's result, the sorted graphP{\displaystyle {\mathcal {P}}}; note how the nodes have all been moved into one of three communities, as represented by the nodes' colors (red, blue, and green).
Step 2: Refinement of the Partition
Next, each node in the network is assigned to its own individual community and then moved them from one community to another to maximize modularity. This occurs iteratively until each node has been visited and moved, and is very similar to the creation ofP{\displaystyle {\mathcal {P}}}except that each community is refined after a node is moved. The result is our initial partition forPrefined{\displaystyle {\mathcal {P}}_{\text{refined}}}, as shown on the right. Note that we're also keeping track of the communities fromP{\displaystyle {\mathcal {P}}}, which are represented by the colored backgrounds behind the nodes.
Step 3: Aggregation of the Network
We then convert each community inPrefined{\displaystyle {\mathcal {P}}_{\text{refined}}}into a single node. Note how, as is depicted in the above image, the communities ofP{\displaystyle {\mathcal {P}}}are used to sort these aggregate nodes after their creation.
We repeat these steps until each community contains only one node, with each of these nodes representing an aggregate of nodes from the original network that are strongly connected with each other.
The Leiden algorithm does a great job of creating a quality partition which places nodes into distinct communities. However, Leiden creates a hard partition, meaning nodes can belong to only one community. In many networks such as social networks, nodes may belong to multiple communities and in this case other methods may be preferred.
Leiden is more efficient than Louvain, but in the case of massive graphs may result in extended processing times. Recent advancements have boosted the speed using a "parallel multicore implementation of the Leiden algorithm".[9]
The Leiden algorithm does much to overcome the resolution limit problem. However, there is still the possibility that small substructures can be missed in certain cases. The selection of the gamma parameter is crucial to ensure that these structures are not missed, as it can vary significantly from one graph to the next.
[3]
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Brainais avirtual assistant[1][2]and speech-to-text dictation[3]application forMicrosoft Windowsdeveloped by Brainasoft.[4]Braina usesnatural language interface,[5]speech synthesis, andspeech recognitiontechnology[6]to interact with its users and allows them to use natural language sentences to perform various tasks on a computer. The name Braina is a short form of "Brain Artificial".[7][8]
Braina is marketed as aMicrosoft Copilotalternative.[9]It provides a voice interface for several locally run[10]and cloudlarge language models, including the latest LLMs from providers such as OpenAI, Anthropic, Google, Grok, Meta, Mistral, etc., while improving data privacy.[7]Braina also allows responses from its in-house large language models like Braina Swift and Braina Pinnacle.[11]It has an "Artificial Brain"[7]feature that provides persistent memory support for supported LLMs.[12]
Braina provides is able to carry out various tasks on a computer, including automation.[13][14]Braina can take commands inputted through typing or through dictation[3][15][13][16]to store reminders, find information online, perform mathematical operations, open files,generate images from text, transcribe speech, and control open windows or programs.[17][18][4][19]Braina adapts to user behavior over time with a goal of better anticipating needs.[13]
Braina Pro can type spoken words into an active window at the location of a user's cursor.[15][13][16]Itsspeech recognitiontechnology supports more than 100 languages and dialects[2][7][20][13]and is able to isolate the recognition of a user's voice from disturbing environmental factors such as background noise,[21]other human voices, or external devices. Braina can also be taught to dictate uncommon legal, medical, and scientific terms.[13][22]Users can also teach Braina uncommon names and vocabulary.[16]Users can edit or correct dictated text without using a keyboard or mouse by giving built-in voice commands.[13]
Braina can read aloud selected texts, such as e-books.[4][13]
Braina can automate computer tasks.[14]It lets users create custom voice commands to perform tasks such as opening files, programs, websites, or emails, as well as executing keyboard or mouse macros.[4][23][24][13][25]
Braina can transcribe media file formats such asWAV,MP3, andMP4into text.[26]
Braina can store and recall notes and reminders. These can include scheduled or unscheduled commands, checklist items, alarms, chat conversations, memos, website snippets, bookmarks, contacts.[13][4][27]
Brainasoft states that Braina can generate images from text usingtext-to-image modelsincludingStable DiffusionandDALL-E.[28]
In addition to the desktop version for Windows operating systems,[28]Braina is also available for the iOS and Android operating systems.[29][3][30]
The mobile version of Braina has a feature allowing remote management of a Windows PC connected viaWi-Fi.[31]
Braina is distributed in multiple modes. These include Braina Lite, a freeware version with limitations,[3]and premium versions Braina Pro,[13]Pro Plus, and Pro Ultra.[32]
Some additional features in the Pro version include dictation, custom vocabulary,[21]video transcription, automation,[3]custom voice commands, and persistent LLM memory.
TechRadarhas consistently listed Braina as one of the best dictation and virtual assistant apps between 2015 and 2024.[4][33][34][35]
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Inmathematics, in particularfunctional analysis, thesingular valuesof acompact operatorT:X→Y{\displaystyle T:X\rightarrow Y}acting betweenHilbert spacesX{\displaystyle X}andY{\displaystyle Y}, are the square roots of the (necessarily non-negative)eigenvaluesof the self-adjoint operatorT∗T{\displaystyle T^{*}T}(whereT∗{\displaystyle T^{*}}denotes theadjointofT{\displaystyle T}).
The singular values are non-negativereal numbers, usually listed in decreasing order (σ1(T),σ2(T), …). The largest singular valueσ1(T) is equal to theoperator normofT(seeMin-max theorem).
IfTacts on Euclidean spaceRn{\displaystyle \mathbb {R} ^{n}}, there is a simple geometric interpretation for the singular values: Consider the image byT{\displaystyle T}of theunit sphere; this is anellipsoid, and the lengths of its semi-axes are the singular values ofT{\displaystyle T}(the figure provides an example inR2{\displaystyle \mathbb {R} ^{2}}).
The singular values are the absolute values of theeigenvaluesof anormal matrixA, because thespectral theoremcan be applied to obtain unitary diagonalization ofA{\displaystyle A}asA=UΛU∗{\displaystyle A=U\Lambda U^{*}}. Therefore,A∗A=UΛ∗ΛU∗=U|Λ|U∗{\textstyle {\sqrt {A^{*}A}}={\sqrt {U\Lambda ^{*}\Lambda U^{*}}}=U\left|\Lambda \right|U^{*}}.
Mostnormson Hilbert space operators studied are defined using singular values. For example, theKy Fan-k-norm is the sum of firstksingular values, the trace norm is the sum of all singular values, and theSchatten normis thepth root of the sum of thepth powers of the singular values. Note that each norm is defined only on a special class of operators, hence singular values can be useful in classifying different operators.
In the finite-dimensional case, amatrixcan always be decomposed in the formUΣV∗{\displaystyle \mathbf {U\Sigma V^{*}} }, whereU{\displaystyle \mathbf {U} }andV∗{\displaystyle \mathbf {V^{*}} }areunitary matricesandΣ{\displaystyle \mathbf {\Sigma } }is arectangular diagonal matrixwith the singular values lying on the diagonal. This is thesingular value decomposition.
ForA∈Cm×n{\displaystyle A\in \mathbb {C} ^{m\times n}}, andi=1,2,…,min{m,n}{\displaystyle i=1,2,\ldots ,\min\{m,n\}}.
Min-max theorem for singular values. HereU:dim(U)=i{\displaystyle U:\dim(U)=i}is a subspace ofCn{\displaystyle \mathbb {C} ^{n}}of dimensioni{\displaystyle i}.
Matrix transpose and conjugate do not alter singular values.
For any unitaryU∈Cm×m,V∈Cn×n.{\displaystyle U\in \mathbb {C} ^{m\times m},V\in \mathbb {C} ^{n\times n}.}
Relation to eigenvalues:
Relation totrace:
IfA∗A{\displaystyle A^{*}A}is full rank, the product of singular values isdetA∗A{\displaystyle \det {\sqrt {A^{*}A}}}.
IfAA∗{\displaystyle AA^{*}}is full rank, the product of singular values isdetAA∗{\displaystyle \det {\sqrt {AA^{*}}}}.
IfA{\displaystyle A}is square and full rank, the product of singular values is|detA|{\displaystyle |\det A|}.
IfA{\displaystyle A}isnormal, thenσ(A)=|λ(A)|{\displaystyle \sigma (A)=|\lambda (A)|}, that is, its singular values are the absolute values of its eigenvalues.
For a generic rectangular matrixA{\displaystyle A}, letA~=[0AA∗0]{\textstyle {\tilde {A}}={\begin{bmatrix}0&A\\A^{*}&0\end{bmatrix}}}be its augmented matrix. It has eigenvalues±σ(A){\textstyle \pm \sigma (A)}(whereσ(A){\textstyle \sigma (A)}are the singular values ofA{\textstyle A}) and the remaining eigenvalues are zero. LetA=UΣV∗{\textstyle A=U\Sigma V^{*}}be the singular value decomposition, then the eigenvectors ofA~{\textstyle {\tilde {A}}}are[ui±vi]{\textstyle {\begin{bmatrix}\mathbf {u} _{i}\\\pm \mathbf {v} _{i}\end{bmatrix}}}for±σi{\displaystyle \pm \sigma _{i}}[1]: 52
The smallest singular value of a matrixAisσn(A). It has the following properties for a non-singular matrix A:
Intuitively, ifσn(A) is small, then the rows of A are "almost" linearly dependent. If it isσn(A) = 0, then the rows of A are linearly dependent and A is not invertible.
See also.[3]
ForA∈Cm×n.{\displaystyle A\in \mathbb {C} ^{m\times n}.}
ForA,B∈Cm×n{\displaystyle A,B\in \mathbb {C} ^{m\times n}}
ForA,B∈Cn×n{\displaystyle A,B\in \mathbb {C} ^{n\times n}}
ForA,B∈Cm×n{\displaystyle A,B\in \mathbb {C} ^{m\times n}}[4]2σi(AB∗)≤σi(A∗A+B∗B),i=1,2,…,n.{\displaystyle 2\sigma _{i}(AB^{*})\leq \sigma _{i}\left(A^{*}A+B^{*}B\right),\quad i=1,2,\ldots ,n.}
ForA∈Cn×n{\displaystyle A\in \mathbb {C} ^{n\times n}}.
This concept was introduced byErhard Schmidtin 1907. Schmidt called singular values "eigenvalues" at that time. The name "singular value" was first quoted by Smithies in 1937. In 1957, Allahverdiev proved the following characterization of thenth singular number:[6]
This formulation made it possible to extend the notion of singular values to operators inBanach space.
Note that there is a more general concept ofs-numbers, which also includes Gelfand and Kolmogorov width.
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This article presents atimelineof events in the history of 16-bitx86DOS-familydisk operating systemsfrom 1980 to present.Non-x86 operating systems named "DOS"are not part of the scope of this timeline.
Also presented is a timeline of events in the history of the 8-bit8080-based and 16-bit x86-basedCP/Moperating systems from 1974 to 2014, as well as the hardware and software developments from 1973 to 1995 which formed the foundation for the initial version and subsequent enhanced versions of these operating systems.
DOS releases have been in the forms of:
IBM combined SYSINIT with its customized ROM-BIOS interface code to create the BIOS extensionsfileIBMBIO.COM, the DOS-BIOS which deals withinput/outputhandling, ordevicehandling, and added a few external commands of their own:COMP,DISKCOMP,DISKCOPY, andMODE(configureprinter) to finish their product. The 160 KB DOS diskette also included 23 sample BASICprogramsdemonstrating the abilities of the PC, including the gameDONKEY.BAS. The twosystem files, IBMBIO.COM and IBMDOS.COM, arehidden. The first sector of DOS-formatted diskettes is theboot record. Two copies of the File Allocation Table occupy the two sectors which follow the boot record. Sectors four through seven hold theroot directory. The remaining 313 sectors (160,256 bytes) store the data contents of files. Disk space is allocated inclusters, which are one-sector in length. Because an 8-bit FAT can't support over 300 clusters, Paterson implemented a new 12-bit FAT, which would be calledFAT12.[D]DOS 1.0 diskettes have up to 64 32-byte directory entries, holding the 8-bytefilename, 3-bytefilename extension, 1-bytefile attribute(with a hidden bit, system bit and six undefined bits), 12 bytes reserved for future use, 2-byte last modified date, 2-byte starting cluster number and 4-bytefile size. The two standard formats for program files areCOMandEXE; aProgram Segment Prefixis built when they are loaded into memory. The third kind of command processing file is thebatch file.AUTOEXEC.BATis checked for, and executed by COMMAND.COM at start-up.[83]Special batch file commands arePAUSEandREM. I/O is madedevice independentby treatingperipheralsas if they were files. Whenever thereserved filenamesCON:(console),PRN:(printer), orAUX:(auxiliaryserial port) appear in theFile Control Blockof a file named in a command, all operations are directed to the device.[24]Thevideo controller, floppy disk controller, further memory, serial andparallel portsare added via up to five 8-bitISAexpansion cards. Delivery of the computer is scheduled for October.[86]
In addition to Microsoft's new commands in MS-DOS 2.0 (above), IBM adds more includingFDISK, the fixed disk[F]setup program, used to write themaster boot recordwhich supports up to fourpartitionson hard drives. Only one DOS partition is allowed, the others are intended for other operating systems such as CP/M-86, UCSD p-System and Xenix. The fixed disk has 10,618,880 bytes[G]of raw space.
The DOS partition on the fixed disk continues to use the FAT12 format, but with adaptations to support the much larger size of the fixed disk partition compared to floppy disks. Space in the user data area of the disk is allocated in clusters which are fixed at 8 sectors each. With DOS the only partition, the combined overhead is 50 sectors[H]leaving 10,592,256 bytes[I]for user data.[83]ABIOS parameter block(BPB) is added to volume boot records.
PC DOS does not include the FC command, which is similar to COMP. DOS 2 is about 12 KB larger than DOS 1.1 – despite its complex new features, it's only 24 KB of code.[24][134][135][136]Under pressure from IBM to leave sufficient memory available for applications on smaller PC systems, the developers had reduced the system size from triple that of DOS 1.1.[21]Peter Norton found many problems with the release.Interrupts25h and 26h, which read or write complete sectors, redefined their rules for absolute sector addressing, "sabotaging" programs using these services.[83][137]The XT motherboard uses 64-kilobit DIP chips, supporting up to 256 KB on board. With 384 KB on expansion cards, users could officially reach the 640 KB barrier ofconventional memory.[138]The power supply capacity was doubled to about 130 watts, to accommodate the hard drive.[139]
The other EMS 4.0 partners are evaluating the XMS spec, but stopped short of endorsing it.[212][360]
Excluding maintenance releases, this is the last version of Windows that could run on 8088 and 8086-based XT-class PCs (in real mode).
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Software verificationis a discipline ofsoftware engineering,programming languages, andtheory of computationwhose goal is to assure that software satisfies the expected requirements.
A broad definition of verification makes it related tosoftware testing. In that case, there are two fundamental approaches to verification:
Under theACM Computing Classification System, software verification topics appear under "Software and its engineering", within "Software creation", whereasProgram verificationalso appears underTheory of computationunder Semantics and reasoning, Program reasoning.
Dynamic verification is performed during the execution of software, and dynamically checks its behavior; it is commonly known as theTestphase.
Verification is a Review Process.
Depending on the scope of tests, we can categorize them in three families:
The aim of software dynamic verification is to find the errors introduced by an activity (for example, having a medical software to analyze bio-chemical data); or by the repetitive performance of one or more activities (such as a stress test for a web server, i.e. check if the current product of the activity is as correct as it was at the beginning of the activity).
Static verification is the process of checking that software meets requirements by inspecting the code before it runs. For example:
Verification by Analysis - The analysis verification method applies to verification by investigation, mathematical calculations, logical evaluation, and calculations using classical textbook methods or accepted general use computer methods. Analysis includes sampling and correlating measured data and observed test results with calculated expected values to establish conformance with requirements.
When it is defined more strictly, verification is equivalent only to static testing and it is intended to be applied to artifacts. And, validation (of the whole software product) would be equivalent to dynamic testing and intended to be applied to the running software product (not its artifacts, except requirements). Notice that requirements validation can be performed statically and dynamically (Seeartifact validation).
Software verification is often confused with software validation. The difference betweenverificationandvalidation:
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https://en.wikipedia.org/wiki/Software_verification
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The termscheduling analysisinreal-time computingincludes the analysis and testing of theschedulersystem and thealgorithmsused in real-time applications. Incomputer science, real-time scheduling analysis is the evaluation, testing and verification of thescheduling systemand thealgorithmsused in real-time operations. For critical operations, a real-time system must be tested and verified for performance.
A real-time scheduling system is composed of the scheduler, clock and the processing hardware elements. In a real-time system, a process or task has schedulability; tasks are accepted by a real-time system and completed as specified by the task deadline depending on the characteristic of the scheduling algorithm.[1]Modeling and evaluation of a real-time scheduling system concern is on the analysis of the algorithm capability to meet a process deadline. A deadline is defined as the time required for a task to be processed.
For example, in a real-time scheduling algorithm a deadline could be set to five nano-seconds. In a critical operation the task must be processed in the time specified by the deadline (i.e. five nano-seconds). A task in a real-time system must be completed "neither too early nor too late;..".[2]A system is said to be unschedulable when tasks can not meet the specified deadlines.[3]A task can be classified as either a periodic or aperiodic process.[4]
The criteria of a real-time can be classified ashard,firmorsoft. The scheduler set the algorithms for executing tasks according to a specified order.[4]There are multiple mathematical models to represent a scheduling System, most implementations of real-time scheduling algorithm are modeled for the implementation of uniprocessors or multiprocessors configurations. The more challenging scheduling algorithm is found in multiprocessors, it is not always feasible to implement a uniprocessor scheduling algorithm in a multiprocessor.[4]The algorithms used in scheduling analysis "can be classified aspre-emptiveornon-pre-emptive".[1]
A scheduling algorithm defines how tasks are processed by the scheduling system. In general terms, in the algorithm for a real-time scheduling system, each task is assigned a description, deadline and an identifier (indicating priority). The selected scheduling algorithm determines how priorities are assigned to a particular task. A real-time scheduling algorithm can be classified as static or dynamic. For a static scheduler, task priorities are determined before the system runs. A dynamic scheduler determines task priorities as it runs.[4]Tasks are accepted by the hardware elements in a real-time scheduling system from the computing environment and processed in real-time. An output signal indicates the processing status.[5]A task deadline indicates the time set to complete for each task.
It is not always possible to meet the required deadline; hence further verification of the scheduling algorithm must be conducted. Two different models can be implemented using a dynamic scheduling algorithm; a task deadline can be assigned according to the task priority (earliest deadline) or a completion time for each task is assigned by subtracting the processing time from the deadline (least laxity).[4]Deadlines and the required task execution time must be understood in advance to ensure the effective use of the processing elements execution times.
The performance verification and execution of a real-time scheduling algorithm is performed by the analysis of the algorithm execution times. Verification for the performance of a real-time scheduler will require testing the scheduling algorithm under different test scenarios including theworst-case execution time. These testing scenarios include worst case and unfavorable cases to assess the algorithm performance. The time calculations required for the analysis of scheduling systems require evaluating the algorithm at the code level.[4]
Different methods can be applied to testing a scheduling System in a real-time system. Some methods include: input/output verifications and code analysis. One method is by testing each input condition and performing observations of the outputs. Depending on the number of inputs this approach could result in a lot of effort. Another faster and more economical method is a risk based approach where representative critical inputs are selected for testing. This method is more economical but could result in less than optimal conclusions over the validity of the system if the incorrect approach is used. Retesting requirements after changes to the scheduling System are considered in a case by case basis.
Testing and verification of real-time systems should not be limited to input/output and codes verifications but are performed also in running applications using intrusive or non-intrusive methods.
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TheData Protection Directive,officially Directive 95/46/EC, enacted in October 1995, was aEuropean Union directivewhich regulated the processing ofpersonal datawithin theEuropean Union(EU) and the free movement of such data. The Data Protection Directive was an important component of EUprivacyandhuman rights law.
The principles set out in the Data Protection Directive were aimed at the protection offundamental rightsand freedoms in the processing of personal data.[1]TheGeneral Data Protection Regulation, adopted in April 2016, superseded the Data Protection Directive and became enforceable on 25 May 2018.[2]
The right toprivacyis a highly developed area of law in Europe. All the member states of theCouncil of Europe(CoE) are also signatories of theEuropean Convention on Human Rights(ECHR).[3]Article 8 of the ECHR provides a right to respect for one's "private and family life, his home and his correspondence", subject to certain restrictions. TheEuropean Court of Human Rightshas given this article a very broad interpretation in its jurisprudence.
In 1973, American scholarWillis WarepublishedRecords, Computers, and the Rights of Citizens, a report that was to be influential on the directions these laws would take.[4][5]
In 1980, in an effort to create a comprehensive data protection system throughout Europe, theOrganisation for Economic Co-operation and Development(OECD) issued its "Recommendations of the Council Concerning Guidelines Governing the Protection of Privacy and Trans-Border Flows of Personal Data".[6]The seven principles governing theOECD's recommendations for protection of personal data were:
TheOECDGuidelines, however, were non-binding, anddata privacylaws still varied widely across Europe. The United States, meanwhile, while endorsing theOECD's recommendations, did nothing to implement them within the United States.[7]However, the first six principles were incorporated into the EU Directive.[7]
In 1981, the Members States of theCouncil of Europeadopted theConvention for the Protection of Individuals with regard to Automatic Processing of Personal Data(Convention 108) to implement Article 8 of the ECHR. Convention 108 obliges the signatories to enact legislation concerning the automatic processing of personal data, and was modernised and reinforced in 2018 to become "Convention 108+".[8]
In 1989 with German reunification, the data the East German secret police (Stasi) collected became well known, increasing the demand for privacy in Germany. At the time West Germany already had privacy laws since 1977 (Bundesdatenschutzgesetz). TheEuropean Commissionrealized that diverging data protection legislation amongst EU member states impeded the free flow of data within the EU and accordingly proposed the Data Protection Directive.[citation needed]
The directive regulates the processing of personal data regardless of whether such processing is automated or not.
Personal dataare defined as "any information relating to an identified or identifiablenatural person('data subject'); an identifiable person is one who can be identified, directly or indirectly, in particular by reference to an identification number or to one or more factors specific to his physical, physiological, mental, economic, cultural or social identity" (art. 2 a).
This definition is meant to be very broad. Data are "personal data" when someone is able to link the information to a person, even if the person holding the data cannot make this link. Some examples of "personal data" are: address,credit card number, bank statements, criminal record, etc.
The notionprocessingmeans "any operation or set of operations which is performed upon personal data, whether or not by automatic means, such as collection, recording, organization, storage, adaptation or alteration, retrieval, consultation, use, disclosure by transmission, dissemination or otherwise making available, alignment or combination, blocking, erasure or destruction" (art. 2 b).
The responsibility for compliance rests on the shoulders of the "controller", meaning thenaturalorartificial person, public authority, agency or any other body which alone or jointly with others determines the purposes and means of the processing of personal data (art. 2 d).
The data protection rules are applicable not only when the controller is established within the EU, but whenever the controller uses equipment situated within the EU in order to process data. (art. 4) Controllers from outside the EU, processing data in the EU, will have to follow data protection regulation. In principle, any online business trading with EU residents would process some personal data and would be using equipment in the EU to process the data (i.e. the customer's computer). As a consequence, the website operator would have to comply with the European data protection rules. The directive was written before the breakthrough of the Internet, and to date there is littlejurisprudenceon this subject.
Personal data should not be processed at all, except when certain conditions are met. These conditions fall into three categories: transparency, legitimate purpose, and proportionality.
The data subject has the right to be informed when his personal data is being processed. The controller must provide his name and address, the purpose of processing, the recipients of the data and all other information required to ensure the processing is fair. (art. 10 and 11)
Data may be processed only if at least one of the following is true (art. 7):
Personal data can only be processed for specified explicit and legitimate purposes and may not be processed further in a way incompatible with those purposes. (art. 6 b) The personal data must have protection from misuse and respect for the "certain rights of the data owners which are guaranteed by EU law".[9]
Personal data may be processed only insofar as it is adequate, relevant and not excessive in relation to the purposes for which they are collected and/or further processed.
The data must be accurate and, where necessary, kept up to date; every reasonable step must be taken to ensure that data which are inaccurate or incomplete, having regard to the purposes for which they were collected or for which they are further processed, are erased or rectified;
The data shouldn't be kept in a form which permits identification of data subjects for longer than is necessary for the purposes for which the data were collected or for which they are further processed. Member States shall lay down appropriate safeguards for personal data stored for longer periods for historical, statistical or scientific use. (art. 6).
When sensitive personal data (can be: religious beliefs, political opinions, health, sexual orientation, race, membership of past organisations) are being processed, extra restrictions apply. (art. 8).
The data subject may object at any time to the processing of personal data for the purpose of direct marketing. (art. 14)
An algorithmic-based decision which produces legal effects or significantly affects the data subject may not be based solely on automated processing of data. (art. 15) A form of appeal should be provided when automatic decision making processes are used.
Each member state must set up a supervisory authority, an independent body that will monitor the data protection level in that member state, give advice to the government about administrative measures and regulations, and start legal proceedings when data protection regulation has been violated. (art. 28) Individuals may lodge complaints about violations to the supervisory authority or in a court of law.
The controller must notify the supervisory authority before he starts to process data. The notification contains at least the following information (art. 19):
This information is kept in a public register.
Third countriesis the term used in legislation to designate countries outside theEuropean Union.
Personal data may only be transferred to a third country if that country provides an adequate level of protection of the data. Some exceptions to this rule are provided, for instance when the controller himself can guarantee that the recipient will comply with the data protection rules.
The Directive's Article 29 created the "Working party on the Protection of Individuals with regard to the Processing of Personal Data", commonly known as the "Article 29 Working Party". The Working Party gives advice about the level of protection in the European Union and third countries.
The Working Party negotiated with United States representatives about the protection of personal data, theSafe Harbour Principleswere the result. According to critics the Safe Harbour Principles do not provide for an adequate level of protection, because they contain fewer obligations for the controller and allow the contractual waiver of certain rights.
In October 2015 the European Court of Justice ruled that the Safe Harbour regime was invalid as a result of an action brought by an Austrian privacy campaigner in relation to the export of subscribers' data by Facebook's European business to Facebook in the United States.[10]The US and European Authorities worked on a replacement for Safe Harbour and an agreement was reached in February 2016, leading to the European Commission adopting theEU–US Privacy Shieldframework on 12 July 2016. This was likewise found invalid in 2020 and replaced with theEU–US Data Privacy Frameworkin 2023.
In July 2007, a new, controversial,[11]passenger name record(PNR) agreement between the US and the EU was undersigned.[12]
In February 2008,Jonathan Faull, the head of the EU's Commission of Home Affairs, complained about the United States bilateral policy concerning PNR.[13][14][not specific enough to verify]The US had signed in February 2008 a memorandum of understanding[15](MOU) with theCzech Republicin exchange of a visa waiver scheme, without first consulting Brussels.[11]The tensions between Washington and Brussels are mainly caused by the lower level ofdata protectionin the US, especially since foreigners do not benefit from the USPrivacy Act of 1974. Other countries approached for bilateral Memoranda of Understanding included the United Kingdom,Estonia, (Germany) andGreece.[16][not specific enough to verify]
EU directives are addressed to the member states, and are not legally binding for individuals in principle. The member states must transpose the directive into internal law.
Directive 95/46/EC on the protection of personal data had to be transposed by the end of 1998. All member states had enacted their own data protection legislation.
On 25 January 2012, theEuropean Commission(EC) announced it would be unifying data protection law across a unified European Union via legislation called the "General Data Protection Regulation." The EC's objectives with this legislation included:[17]
The original proposal also dictated that the legislation would in theory "apply for all non-EU companies without any establishment in the EU, provided that the processing of data is directed at EU residents," one of the biggest changes with the new legislation.[17]This change carried on through to the legislation's final approval on 14 April 2016, affecting entities around the world. "The Regulation applies to processing outside the EU that relates to the offering of goods or services to data subjects (individuals) in the EU or the monitoring of their behavior," according to W. Scott Blackmer of the InfoLawGroup, though he added "[i]t is questionable whether European supervisory authorities or consumers would actually try to sue US-based operators over violations of the Regulation."[2]Additional changes include stricter conditions for consent, broader definition of sensitive data, new provisions on protecting children's privacy, and the inclusion of "rights to be forgotten."[2]
The EC then set a compliance date of 25 May 2018, giving businesses around the world a chance to prepare for compliance, review data protection language in contracts, consider transition to international standards, updateprivacy policies, and review marketing plans.
As of 2003[update], the United States has no single data protection law comparable to the EU's Data Protection Directive.[18]
United States privacy legislation tends to be adopted on anad hocbasis, with legislation arising when certain sectors and circumstances require (e.g., theVideo Privacy Protection Actof 1988, theCable Television Protection and Competition Actof 1992,[19]theFair Credit Reporting Act, and the 1996Health Insurance Portability and Accountability Act, HIPAA (US)). Therefore, while certain sectors may already satisfy parts of the EU Directive most do not.[20]The United States prefers what it calls a 'sectoral' approach[21]to data protection legislation, which relies on a combination of legislation, regulation, and self-regulation, rather than governmental regulation alone.[22][23]Former US PresidentBill Clintonand former Vice-PresidentAl Goreexplicitly recommended in their "Framework for Global Electronic Commerce" that the private sector should lead, and companies should implement self-regulation in reaction to issues brought on by Internet technology.[24]
The reasoning behind this approach has as much to do with Americanlaissez-faire economicsas with different social perspectives.[25]TheFirst Amendmentof theUnited States Constitutionguarantees the right to free speech.[26]While free speech is an explicit right guaranteed by the United States Constitution, privacy is an implicit right guaranteed by the Constitution as interpreted by theUnited States Supreme Court,[27]although it is often an explicit right in many state constitutions.[28]
Europe's extensive privacy regulation is justified with reference to experiences underWorld War II-era fascist governments and post-WarCommunistregimes, where there was widespread unchecked use of personal information.[29][30][31]World War II and the post-War period was a time in Europe when disclosure of race or ethnicity led to secret denunciations and seizures that sent friends and neighbours to work camps and concentration camps.[7]In the age of computers, Europeans' guardedness of secret government files has translated into a distrust of corporate databases, and governments in Europe took decided steps to protect personal information from abuses in the years following World War II.[32](Germany) and France, in particular, set forth comprehensive data protection laws.[33]
Critics of Europe's data policies, however, have said that they have impeded Europe's ability to monetize the data of users on the internet and are the primary reason why there are noBig Techcompanies in Europe, with most of them instead being in the United States.[34]Furthermore, withAlibabaandTencentjoining the ranks of the world's 10 most valuable tech companies in recent years,[35]even China is moving ahead of Europe in the performance of its digital economy,[36]which was valued at $5.09 trillion in 2019 (35.8 trillion yuan).[37]
Meanwhile, Europe's preoccupation with the US is likely misplaced in the first place, as China and Russia are increasingly identified by European policymakers as "hybrid threat" aggressors, using a combination ofpropagandaon social media and hacking to intentionally undermine the functioning of European institutions.[38]
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Test-driven development(TDD) is a way of writingcodethat involves writing anautomatedunit-leveltest casethat fails, then writing just enough code to make the test pass, thenrefactoringboth the test code and the production code, then repeating with another new test case.
Alternative approaches to writing automated tests is to write all of the production code before starting on the test code or to write all of the test code before starting on the production code. With TDD, both are written together, therefore shortening debugging time necessities.[1]
TDD is related to the test-first programming concepts ofextreme programming, begun in 1999,[2]but more recently has created more general interest in its own right.[3]
Programmers also apply the concept to improving anddebugginglegacy codedeveloped with older techniques.[4]
Software engineerKent Beck, who is credited with having developed or "rediscovered"[5]the technique, stated in 2003 that TDD encourages simple designs and inspires confidence.[6]
The original description of TDD was in an ancient book about programming. It said you take the input tape, manually type in the output tape you expect, then program until the actual output tape matches the expected output. After I'd written the first xUnit framework inSmalltalkI remembered reading this and tried it out. That was the origin of TDD for me. When describing TDD to older programmers, I often hear, "Of course. How else could you program?" Therefore I refer to my role as "rediscovering" TDD.
The TDD steps vary somewhat by author in count and description, but are generally as follows. These are based on the bookTest-Driven Development by Example,[6]and Kent Beck's Canon TDD article.[8]
Each tests should be small and commits made often. If new code fails some tests, the programmer canundoor revert rather thandebugexcessively.
When usingexternal libraries, it is important not to write tests that are so small as to effectively test merely the library itself,[3]unless there is some reason to believe that the library is buggy or not feature-rich enough to serve all the needs of the software under development.
TDD has been adopted outside of software development, in both product and service teams, astest-driven work.[9]For testing to be successful, it needs to be practiced at the micro and macro levels. Every method in a class, every input data value, log message, and error code, amongst other data points, need to be tested.[10]Similar to TDD, non-software teams developquality control(QC) checks (usually manual tests rather than automated tests) for each aspect of the work prior to commencing. These QC checks are then used to inform the design and validate the associated outcomes. The six steps of the TDD sequence are applied with minor semantic changes:
There are various aspects to using test-driven development, for example the principles of "keep it simple, stupid" (KISS) and "You aren't gonna need it" (YAGNI). By focusing on writing only the code necessary to pass tests, designs can often be cleaner and clearer than is achieved by other methods.[6]InTest-Driven Development by Example, Kent Beck also suggests the principle "Fake it till you make it".
To achieve some advanced design concept such as adesign pattern, tests are written that generate that design. The code may remain simpler than the target pattern, but still pass all required tests. This can be unsettling at first but it allows the developer to focus only on what is important.
Writing the tests first: The tests should be written before the functionality that is to be tested. This has been claimed to have many benefits. It helps ensure that the application is written for testability, as the developers must consider how to test the application from the outset rather than adding it later. It also ensures that tests for every feature gets written. Additionally, writing the tests first leads to a deeper and earlier understanding of the product requirements, ensures the effectiveness of the test code, and maintains a continual focus onsoftware quality.[11]When writing feature-first code, there is a tendency by developers and organizations to push the developer on to the next feature, even neglecting testing entirely. The first TDD test might not even compile at first, because the classes and methods it requires may not yet exist. Nevertheless, that first test functions as the beginning of an executable specification.[12]
Each test case fails initially: This ensures that the test really works and can catch an error. Once this is shown, the underlying functionality can be implemented. This has led to the "test-driven development mantra", which is "red/green/refactor", where red meansfailand green meanspass. Test-driven development constantly repeats the steps of adding test cases that fail, passing them, and refactoring. Receiving the expected test results at each stage reinforces the developer's mental model of the code, boosts confidence and increases productivity.
Test code needs access to the code it is testing, but testing should not compromise normal design goals such asinformation hiding, encapsulation and theseparation of concerns. Therefore, unit test code is usually located in the same project ormoduleas the code being tested.
Inobject oriented designthis still does not provide access to private data and methods. Therefore, extra work may be necessary for unit tests. InJavaand other languages, a developer can usereflectionto access private fields and methods.[13]Alternatively, aninner classcan be used to hold the unit tests so they have visibility of the enclosing class's members and attributes. In the.NET Frameworkand some other programming languages,partial classesmay be used to expose private methods and data for the tests to access.
It is important that such testing hacks do not remain in the production code. InCand other languages,compiler directivessuch as#if DEBUG ... #endifcan be placed around such additional classes and indeed all other test-related code to prevent them being compiled into the released code. This means the released code is not exactly the same as what was unit tested. The regular running of fewer but more comprehensive, end-to-end, integration tests on the final release build can ensure (among other things) that no production code exists that subtly relies on aspects of the test harness.
There is some debate among practitioners of TDD, documented in their blogs and other writings, as to whether it is wise to test private methods and data anyway. Some argue that private members are a mere implementation detail that may change, and should be allowed to do so without breaking numbers of tests. Thus it should be sufficient to test any class through its public interface or through its subclass interface, which some languages call the "protected" interface.[14]Others say that crucial aspects of functionality may be implemented in private methods and testing them directly offers advantage of smaller and more direct unit tests.[15][16]
Unit tests are so named because they each testone unitof code. A complex module may have a thousand unit tests and a simple module may have only ten. The unit tests used for TDD should never cross process boundaries in a program, let alone network connections. Doing so introduces delays that make tests run slowly and discourage developers from running the whole suite. Introducing dependencies on external modules or data also turnsunit testsintointegration tests. If one module misbehaves in a chain of interrelated modules, it is not so immediately clear where to look for the cause of the failure.
When code under development relies on a database, a web service, or any other external process or service, enforcing a unit-testable separation is also an opportunity and a driving force to design more modular, more testable and more reusable code.[17]Two steps are necessary:
Fake and mock object methods that return data, ostensibly from a data store or user, can help the test process by always returning the same, realistic data that tests can rely upon. They can also be set into predefined fault modes so that error-handling routines can be developed and reliably tested. In a fault mode, a method may return an invalid, incomplete ornullresponse, or may throw anexception. Fake services other than data stores may also be useful in TDD: A fake encryption service may not, in fact, encrypt the data passed; a fake random number service may always return 1. Fake or mock implementations are examples ofdependency injection.
A test double is a test-specific capability that substitutes for a system capability, typically a class or function, that the UUT depends on. There are two times at which test doubles can be introduced into a system: link and execution. Link time substitution is when the test double is compiled into the load module, which is executed to validate testing. This approach is typically used when running in an environment other than the target environment that requires doubles for the hardware level code for compilation. The alternative to linker substitution is run-time substitution in which the real functionality is replaced during the execution of a test case. This substitution is typically done through the reassignment of known function pointers or object replacement.
Test doubles are of a number of different types and varying complexities:
A corollary of such dependency injection is that the actual database or other external-access code is never tested by the TDD process itself. To avoid errors that may arise from this, other tests are needed that instantiate the test-driven code with the "real" implementations of the interfaces discussed above. These areintegration testsand are quite separate from the TDD unit tests. There are fewer of them, and they must be run less often than the unit tests. They can nonetheless be implemented using the same testing framework.
Integration tests that alter anypersistent storeor database should always be designed carefully with consideration of the initial and final state of the files or database, even if any test fails. This is often achieved using some combination of the following techniques:
For TDD, a unit is most commonly defined as a class, or a group of related functions often called a module. Keeping units relatively small is claimed to provide critical benefits, including:
Advanced practices of test-driven development can lead toacceptance test–driven development(ATDD) andspecification by examplewhere the criteria specified by the customer are automated into acceptance tests, which then drive the traditional unit test-driven development (UTDD) process.[18]This process ensures the customer has an automated mechanism to decide whether the software meets their requirements. With ATDD, the development team now has a specific target to satisfy – the acceptance tests – which keeps them continuously focused on what the customer really wants from each user story.
Effective layout of a test case ensures all required actions are completed, improves the readability of the test case, and smooths the flow of execution. Consistent structure helps in building a self-documenting test case. A commonly applied structure for test cases has (1) setup, (2) execution, (3) validation, and (4) cleanup.
Some best practices that an individual could follow would be to separate common set-up and tear-down logic into test support services utilized by the appropriate test cases, to keep eachtest oraclefocused on only the results necessary to validate its test, and to design time-related tests to allow tolerance for execution in non-real time operating systems. The common practice of allowing a 5-10 percent margin for late execution reduces the potential number of false negatives in test execution. It is also suggested to treat test code with the same respect as production code. Test code must work correctly for both positive and negative cases, last a long time, and be readable and maintainable. Teams can get together and review tests and test practices to share effective techniques and catch bad habits.[19]
Test-driven development is related to, but different fromacceptance test–driven development(ATDD).[20]TDD is primarily a developer's tool to help create well-written unit of code (function, class, or module) that correctly performs a set of operations. ATDD is a communication tool between the customer, developer, and tester to ensure that the requirements are well-defined. TDD requires test automation. ATDD does not, although automation helps with regression testing. Tests used in TDD can often be derived from ATDD tests, since the code units implement some portion of a requirement. ATDD tests should be readable by the customer. TDD tests do not need to be.
BDD (behavior-driven development) combines practices from TDD and from ATDD.[21]It includes the practice of writing tests first, but focuses on tests which describe behavior, rather than tests which test a unit of implementation. Tools such asJBehave,Cucumber,MspecandSpecflowprovide syntaxes which allow product owners, developers and test engineers to define together the behaviors which can then be translated into automated tests.
There are many testing frameworks and tools that are useful in TDD.
Developers may use computer-assistedtesting frameworks, commonly collectively namedxUnit(which are derived from SUnit, created in 1998), to create and automatically run the test cases. xUnit frameworks provide assertion-style test validation capabilities and result reporting. These capabilities are critical for automation as they move the burden of execution validation from an independent post-processing activity to one that is included in the test execution. The execution framework provided by these test frameworks allows for the automatic execution of all system test cases or various subsets along with other features.[22]
Testing frameworks may accept unit test output in the language-agnosticTest Anything Protocolcreated in 1987.
Exercising TDD on large, challenging systems requires a modular architecture, well-defined components with published interfaces, and disciplined system layering with maximization of platform independence. These proven practices yield increased testability and facilitate the application of build and test automation.[11]
Complex systems require an architecture that meets a range of requirements. A key subset of these requirements includes support for the complete and effective testing of the system. Effective modular design yields components that share traits essential for effective TDD.
A key technique for building effective modular architecture is Scenario Modeling where a set of sequence charts is constructed, each one focusing on a single system-level execution scenario. The Scenario Model provides an excellent vehicle for creating the strategy of interactions between components in response to a specific stimulus. Each of these Scenario Models serves as a rich set of requirements for the services or functions that a component must provide, and it also dictates the order in which these components and services interact together. Scenario modeling can greatly facilitate the construction of TDD tests for a complex system.[11]
In a larger system, the impact of poor component quality is magnified by the complexity of interactions. This magnification makes the benefits of TDD accrue even faster in the context of larger projects. However, the complexity of the total population of tests can become a problem in itself, eroding potential gains. It sounds simple, but a key initial step is to recognize that test code is also important software and should be produced and maintained with the same rigor as the production code.
Creating and managing thearchitectureof test software within a complex system is just as important as the core product architecture. Test drivers interact with the UUT,test doublesand the unit test framework.[11]
Test Driven Development (TDD) is a software development approach where tests are written before the actual code. It offers several advantages:
However, TDD is not without its drawbacks:
A 2005 study found that using TDD meant writing more tests and, in turn, programmers who wrote more tests tended to be more productive.[25]Hypotheses relating to code quality and a more direct correlation between TDD and productivity were inconclusive.[26]
Programmers using pure TDD on new ("greenfield") projects reported they only rarely felt the need to invoke adebugger. Used in conjunction with aversion control system, when tests fail unexpectedly, reverting the code to the last version that passed all tests may often be more productive than debugging.[27]
Test-driven development offers more than just simple validation of correctness, but can also drive the design of a program.[28]By focusing on the test cases first, one must imagine how the functionality is used by clients (in the first case, the test cases). So, the programmer is concerned with the interface before the implementation. This benefit is complementary todesign by contractas it approaches code through test cases rather than through mathematical assertions or preconceptions.
Test-driven development offers the ability to take small steps when required. It allows a programmer to focus on the task at hand as the first goal is to make the test pass. Exceptional cases and error handling are not considered initially, and tests to create these extraneous circumstances are implemented separately. Test-driven development ensures in this way that all written code is covered by at least one test. This gives the programming team, and subsequent users, a greater level of confidence in the code.
While it is true that more code is required with TDD than without TDD because of the unit test code, the total code implementation time could be shorter based on a model by Müller and Padberg.[29]Large numbers of tests help to limit the number of defects in the code. The early and frequent nature of the testing helps to catch defects early in the development cycle, preventing them from becoming endemic and expensive problems. Eliminating defects early in the process usually avoids lengthy and tedious debugging later in the project.
TDD can lead to more modularized, flexible, and extensible code. This effect often comes about because the methodology requires that the developers think of the software in terms of small units that can be written and tested independently and integrated together later. This leads to smaller, more focused classes, loosercoupling, and cleaner interfaces. The use of themock objectdesign pattern also contributes to the overall modularization of the code because this pattern requires that the code be written so that modules can be switched easily between mock versions for unit testing and "real" versions for deployment.
Because no more code is written than necessary to pass a failing test case, automated tests tend to cover every code path. For example, for a TDD developer to add anelsebranch to an existingifstatement, the developer would first have to write a failing test case that motivates the branch. As a result, the automated tests resulting from TDD tend to be very thorough: they detect any unexpected changes in the code's behaviour. This detects problems that can arise where a change later in the development cycle unexpectedly alters other functionality.
Madeyski[30]provided empirical evidence (via a series of laboratory experiments with over 200 developers) regarding the superiority of the TDD practice over the traditional Test-Last approach or testing for correctness approach, with respect to the lower coupling between objects (CBO). The mean effect size represents a medium (but close to large) effect on the basis of meta-analysis of the performed experiments which is a substantial finding. It suggests a better modularization (i.e., a more modular design), easier reuse and testing of the developed software products due to the TDD programming practice.[30]Madeyski also measured the effect of the TDD practice on unit tests using branch coverage (BC) and mutation score indicator (MSI),[31][32][33]which are indicators of the thoroughness and the fault detection effectiveness of unit tests, respectively. The effect size of TDD on branch coverage was medium in size and therefore is considered substantive effect.[30]These findings have been subsequently confirmed by further, smaller experimental evaluations of TDD.[34][35][36][37]
Test-driven development does not perform sufficient testing in situations where full functional tests are required to determine success or failure, due to extensive use of unit tests.[38]Examples of these areuser interfaces, programs that work withdatabases, and some that depend on specificnetworkconfigurations. TDD encourages developers to put the minimum amount of code into such modules and to maximize the logic that is in testable library code, using fakes andmocksto represent the outside world.[39]
Management support is essential. Without the entire organization believing that test-driven development is going to improve the product, management may feel that time spent writing tests is wasted.[40]
Unit tests created in a test-driven development environment are typically created by the developer who is writing the code being tested. Therefore, the tests may share blind spots with the code: if, for example, a developer does not realize that certain input parameters must be checked, most likely neither the test nor the code will verify those parameters. Another example: if the developer misinterprets the requirements for the module they are developing, the code and the unit tests they write will both be wrong in the same way. Therefore, the tests will pass, giving a false sense of correctness.
A high number of passing unit tests may bring a false sense of security, resulting in fewer additionalsoftware testingactivities, such asintegration testingandcompliance testing.
Tests become part of the maintenance overhead of a project. Badly written tests, for example ones that include hard-coded error strings, are themselves prone to failure, and they are expensive to maintain. This is especially the case withfragile tests.[41]There is a risk that tests that regularly generate false failures will be ignored, so that when a real failure occurs, it may not be detected. It is possible to write tests for low and easy maintenance, for example by the reuse of error strings, and this should be a goal during thecode refactoringphase described above.
Writing and maintaining an excessive number of tests costs time. Also, more-flexible modules (with limited tests) might accept new requirements without the need for changing the tests. For those reasons, testing for only extreme conditions, or a small sample of data, can be easier to adjust than a set of highly detailed tests.
The level of coverage and testing detail achieved during repeated TDD cycles cannot easily be re-created at a later date. Therefore, these original, or early, tests become increasingly precious as time goes by. The tactic is to fix it early. Also, if a poor architecture, a poor design, or a poor testing strategy leads to a late change that makes dozens of existing tests fail, then it is important that they are individually fixed. Merely deleting, disabling or rashly altering them can lead to undetectable holes in the test coverage.
First TDD Conference was held during July 2021.[42]Conferences were recorded onYouTube[43]
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Insociolinguistics,hypercorrectionis thenonstandarduse of languagethat results from the overapplication of a perceived rule oflanguage-usage prescription. A speaker or writer who produces a hypercorrection generally believes through a misunderstanding of such rules that the form or phrase they use is more "correct",standard, or otherwise preferable, often combined with a desire to appear formal or educated.[1][2]
Linguistic hypercorrection occurs when a real or imagined grammatical rule is applied in an inappropriate context, so that an attempt to be "correct" leads to an incorrect result. It does not occur when a speaker follows "a natural speech instinct", according toOtto Jespersenand Robert J. Menner.[3]
Hypercorrection can be found among speakers of lessprestigiouslanguage varietieswho attempt to produce forms associated with high-prestige varieties, even in situations where speakers of those varieties would not. Some commentators call such productionhyperurbanism.[4]
Hypercorrection can occur in many languages and wherever multiple languages or language varieties are in contact.
Studies insociolinguisticsandapplied linguisticshave noted the overapplication of rules ofphonology,syntax, ormorphology, resulting either from different rules in varieties of the same language orsecond-language learning. An example of a common hypercorrection based on application of the rules of a second (i.e., new, foreign) language is the use ofoctopifor theplural ofoctopusin English; this is based on the faulty assumption thatoctopusis asecond declensionword ofLatin originwhen in fact it isthird declensionand comes fromGreek.[5][better source needed]
Sociolinguists often note hypercorrection in terms of pronunciation (phonology). For example,William Labovnoted that all of the English speakers he studied inNew York Cityin the 1960s tended to pronounce words such ashardasrhotic(pronouncing the "R" as/hɑːrd/rather than/hɑːd/) more often when speaking carefully. Furthermore,middle classspeakers had more rhotic pronunciation thanworking classspeakers did.
However, lower-middle class speakers had more rhotic pronunciation than upper-middle class speakers. Labov suggested that these lower-middle class speakers were attempting to emulate the pronunciation of upper-middle class speakers, but were actually over-producing the very noticeable R-sound.[6]
A common source of hypercorrection in English speakers' use of the language's morphology and syntax happens in the use of pronouns (see§ Personal pronouns).[4]
Hypercorrection can also occur when learners of a new-to-them (second, foreign) language try to avoid applying grammatical rules from theirnative languageto the new language (a situation known aslanguage transfer). The effect can occur, for example, when a student of a new language has learned that certain sounds of their original language must usually be replaced by another in the studied language, but has not learned whennotto replace them.[7]
In addition, the special case of a pseudo-hypercorrection has been identified where standard usage is at issue, butaccidentally, i.e., where a speaker luckily produces acorrectresult.[8]
English has no authoritative body orlanguage academycodifyingnorms forstandard usage, unlike some otherlanguages. Nonetheless, within groups of users of English, certain usages are considered unduly elaborate adherences to formal rules. Such speech or writing is sometimes calledhyperurbanism, defined byKingsley Amisas an "indulged desire to be posher than posh".[citation needed]
In 2004, Jack Lynch,assistant professorof English atRutgers University, said onVoice of Americathat the correction of the subject-positioned "you and me" to "you and I" leads people to "internalize the rule that 'you and I' is somehow more proper, and they end up using it in places where they should not – such as 'he gave it to you and I' when it should be 'he gave it to you and me.'"[9]
However, the linguistsRodney HuddlestonandGeoffrey K. Pullumwrite thatutterancessuch as "They invited Sandy and I" are "heard constantly in the conversation of people whose status as speakers of Standard English is clear" and that "[t]hose who condemn it simply assume that the case of a pronoun in a coordination must be the same as when it stands alone. Actual usage is in conflict with this assumption."[10]
Some British accents, such asCockney, drop the initialhfrom words; e.g.,havebecomes'ave. A hypercorrection associated with this isH-adding, adding an initialhto a word which would not normally have one. An example of this can be found in the speech of the characterParkerin themarionetteTV seriesThunderbirds, e.g., "We'll 'ave the haristocrats 'ere soon" (from the episode "Vault of Death"). Parker's speech was based on a real person the creators encountered at a restaurant inCookham.[11]
The same, for the same reason, is often heard when a person of Italian origins speaks English: "I'mhangryhat Francesco", "I'd like toheat something". This should not be expected to be consistent with the h-dropping common in the Italian accent, so the same person may say "an edge-og" instead of "a hedgehog" or just say it correctly.[12]
Hyperforeignism arises from speakers misidentifying the distribution of a pattern found in loanwords and extending it to other environments. The result of this process does not reflect the rules of either language.[13]For example,habanerois sometimes pronounced as though it were spelled "habañero", in imitation of other Spanish words likejalapeñoandpiñata.[14]Machismois sometimes pronounced "makizmo", apparently as if it were Italian, rather than the phonetic English pronunciation which resembles the original Spanish word,/mɑːˈtʃiz.mo/. Similarly, the z inchorizois sometimes pronounced as /ts/ (as if it were Italian), whereas the original Spanish pronunciation has/θ/or/s/.
Some English-Spanishcognatesprimarily differ by beginning withsinstead ofes, such as the English wordspectacularand the Spanish wordespectacular. A native Spanish speaker may conscientiously hypercorrect for the wordescapeby writing or sayingscape, or for the wordestablishby writing or sayingstablish, which isarchaic, or an informal pronunciation in some dialects.[15]
As thelocative caseis rarely found invernacularusage in the southern and eastern dialects of Serbia, and theaccusativeis used instead, speakers tend to overcorrect when trying to deploy thestandard varietyof the language in more formal occasions, thus using the locative even when the accusative should be used (typically, when indicating direction rather than location): "Izlazim na kolovozu" instead of "izlazim na kolovoz".[18]
Ghil'ad Zuckermannargues that the following hypercorrect pronunciations inIsraeli Hebreware "snobbatives" (fromsnob+-ative, modelled uponcomparatives and superlatives):[19]
The last two hypercorrection examples derive from a confusion related to theQamatz GadolHebrew vowel, which in the acceptedSephardi Hebrewpronunciation is rendered as/aː/but which is pronounced/ɔ/inAshkenazi Hebrew, and in Hebrew words that also occur inYiddish. However, theQamatz Qaṭanvowel, which is visually indistinguishable from the Qamatz Gadol vowel, is rendered as/o/in both pronunciations. This leads to hypercorrections in both directions.
Other hypercorrections occur when speakers of Israeli Hebrew (which is based on Sephardic) attempt to pronounce Ashkenazi Hebrew, for example for religious purposes. The month ofShevat(שבט) is mistakenly pronouncedShvas, as if it were spelled *שְׁבַת. In an attempt to imitatePolishandLithuaniandialects,qamatz(bothgadolandqatan), which would normally be pronounced[ɔ], is hypercorrected to the pronunciation ofholam,[ɔj], renderingגדול ('large') asgoydlandברוך ('blessed') asboyrukh.
In some Spanish dialects, the final intervocalic/d/([ð]) is dropped, such as inpescado(fish), which would typically be pronounced[pesˈkaðo]but can be manifested as[pesˈkao]dialectically. Speakers sensitive to this variation may insert a/d/intervocalically into a word without such a consonant, such as in the case ofbacalao(cod), correctly pronounced[bakaˈlao]but occasionally hypercorrected to[bakaˈlaðo].[20]
Outside Spain and inAndalusia, the phonemes/θ/and/s/have merged, mostly into the realization[s]butceceo, i.e. the pronunciation of both as[s̟], is found in some areas as well, primarily parts of Andalusia. Speakers of varieties that have[s]in all cases will frequently produce[θ]even in places wherepeninsular Spanishhas[s]when trying to imitate a peninsular accent. AsSpanish orthographydistinguishes the two phonemes in all varieties, but the pronunciation is not differentiated in Latin American varieties, some speakers also get mixed up with the spelling.
Many Spanish dialects tend toaspiratesyllable-final/s/, and some even elide it often. Since this phenomenon is somewhat stigmatized, some speakers in theCaribbeanand especially theDominican Republicmay attempt to correct for it by pronouncing an/s/where it does not belong. For example,catorce años'14 years' may be pronounced ascatorces año.[21]
TheEast Franconian dialectsare notable forlenitionof stops /p/ /t/ /k/ to [b], [d], [g]. Thus, a common hypercorrection is thefortitionof properly lenis stops, sometimes including aspiration as evidenced by the speech ofGünther Beckstein.
Thedigraph⟨ig⟩ in word-final position is pronounced[ɪç]per theBühnendeutschstandard, but this pronunciation is frequently perceived as nonstandard and instead realized as[ɪɡ̊]or[ɪk](final obstruent devoicing) even by speakers fromdialect areasthat pronounce the digraph[ɪç]or[ɪʃ].
Palatinate German languagespeakers are among those who pronounce both the digraph⟨ch⟩and the trigraph⟨sch⟩as[ʃ]. A common hypercorrection is to produce[ç]even where standard German has[ʃ]such as inHelmut Kohl's hypercorrect rendering of "Geschichte", the German word for "history" with aGerman pronunciation:[ç]both for the ⟨sch⟩ (standard German[ʃ]) and the⟨ch⟩.
Proper names and German loanwords into other languages that have beenreborrowed, particularly when they have gone through or are perceived to have gone through the English language are often pronounced "hyperforeign". Examples include "Hamburger" or the names ofGerman-Americansand the companies named after them, even if they were or are first generation immigrants.
Some German speakers pronounce themetal umlautas if it were a "normal" German umlaut. For example, whenMötley Crüevisited Germany, singer Vince Neil said the band could not figure out why "the crowds were chanting, 'Mutley Cruh! Mutley Cruh!'"[22]
In Swedish, the wordattis sometimes pronounced/ɔ/when used as an infinitive marker (its conjunction homograph is never pronounced that way, however). The conjunctionochis also sometimes pronounced the same way. Both pronunciations can informally be speltå. ("Jag älskar å fiska å jag tycker också om å baka.") When spelt more formally, the infinitive marker/ˈɔ/is sometimes misspeltoch. (*"Få mig och hitta tillbaka.")
The third person plural pronoun, pronounceddomin many dialects, is formally speltdein the subjective case anddemin the objective case. Informally it can be spelleddom("Dom tycker om mig."), yetdomis only acceptable in spoken language.[23]When spelt more formally, they are often confused with each other. ("De tycker om mig." as a correct form, compared to *"Dem tycker om mig." as an incorrect form in this case). As an object form, usingdemin a sentence would be correct in the sentence "Jag ger dem en present." ("I give them a gift.")
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TheLinux kernelprovides multiple interfaces touser-space and kernel-modecode. The interfaces can be classified as eitherapplication programming interface(API) orapplication binary interface(ABI), and they can be classified as either kernel–user space or kernel-internal.
The Linux API includes the kernel–user space API, which allows code in user space to access system resources and services of the Linux kernel.[3]It is composed of the system call interface of the Linux kernel and the subroutines in theC standard library. The focus of the development of the Linux API has been to provide theusable featuresof the specifications defined inPOSIXin a way which is reasonably compatible, robust and performant, and to provide additional useful features not defined in POSIX, just as the kernel–user space APIs of other systems implementing the POSIX API also provide additional features not defined in POSIX.
The Linux API, by choice, has been kept stable over the decades through a policy of not introducing breaking changes; this stability guarantees the portability ofsource code.[4]At the same time, Linux kernel developers have historically been conservative and meticulous about introducing new system calls.[citation needed]
Much availablefree and open-source softwareis written for the POSIX API. Since so much more development flows into the Linux kernel as compared to the other POSIX-compliant combinations of kernel and C standard library,[citation needed]the Linux kernel and its API have been augmented with additional features. Programming for the full Linux API, rather than just the POSIX API, may provide advantages in cases where those additional features are useful. Well-known current examples areudev,systemdandWeston.[5]People such asLennart Poetteringopenly advocate to prefer the Linux API over the POSIX API, where this offers advantages.[6]
AtFOSDEM2016,Michael Kerriskexplained some of the perceived issues with the Linux kernel's user-space API, describing that it contains multiple design errors by being non-extensible, unmaintainable, overly complex, of limited purpose, in violation of standards, and inconsistent. Most of those mistakes cannot be fixed because doing so would break the ABI that the kernel presents to the user space.[7]
Thesystem call interfaceof a kernel is the set of all implemented and availablesystem callsin a kernel. In the Linux kernel, various subsystems, such as theDirect Rendering Manager(DRM), define their own system calls, all of which are part of the system call interface.
Various issues with the organization of the Linux kernel system calls are being publicly discussed. Issues have been pointed out by Andy Lutomirski,Michael Kerriskand others.[8][9][10][11]
AC standard libraryfor Linux includes wrappers around the system calls of the Linux kernel; the combination of the Linux kernel system call interface and a C standard library is what builds the Linux API. Some popular implementations of the C standard library are
Although the landscape is shifting, amongst these options, glibc remains the most popular implementation, to the point of many treating it as the default and the term equivalent to libc.
As in otherUnix-likesystems, additional capabilities of the Linux kernel exist that are not part of POSIX:
DRMhas been paramount for the development and implementations of well-defined and performantfree and open-source graphics device driverswithout which no rendering acceleration would be available at all, only the 2D drivers would be available in theX.Org Server. DRM was developed for Linux, and since has been ported to other operating systems as well.[14]
The Linux ABI is a kernel–user space ABI. As ABI is amachine codeinterface, the Linux ABI is bound to theinstruction set. Defining a useful ABI and keeping it stable is less the responsibility of the Linux kernel developers or of the developers of the GNU C Library, and more the task forLinux distributionsandindependent software vendors(ISVs) who wish to sell and provide support for their proprietary software as binaries only for such a single Linux ABI, as opposed to supporting multiple Linux ABIs.
An ABI has to be defined for every instruction set, such asx86,x86-64,MIPS,ARMv7-A(32-Bit),ARMv8-A(64-Bit), etc. with theendianness, if both are supported.
It should be able to compile the software with different compilers against the definitions specified in the ABI and achieve full binary compatibility. Compilers that arefree and open-source softwareare e.g.GNU Compiler Collection,LLVM/Clang.
Many kernel-internal APIs exist, allowing kernel subsystems to interface with one another. These are being kept fairly stable, but there is no guarantee for stability. A kernel-internal API can be changed when such a need is indicated by new research or insights; all necessary modifications and testing have to be done by the author.
The Linux kernel is a monolithic kernel, hence device drivers are kernel components. To ease the burden of companies maintaining their (proprietary) device drivers outside of the main kernel tree, stable APIs for the device drivers have been repeatedly requested. The Linux kernel developers have repeatedly denied guaranteeing stable in-kernel APIs for device drivers. Guaranteeing such would have faltered the development of the Linux kernel in the past and would still in the future and, due to the nature of free and open-source software, are not necessary. Ergo, by choice, the Linux kernel has nostablein-kernel API.[15]
Since there are no stable in-kernel APIs, there cannot be stable in-kernel ABIs.[16]
For many use cases, the Linux API is considered too low-level, so APIs of higher abstraction must be used. Higher-level APIs must be implemeted on top of lower-level APIs. Examples:
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Inmodular arithmetic,Thue's lemmaroughly states that every modular integer may be represented by a "modular fraction" such that the numerator and the denominator haveabsolute valuesnot greater than thesquare rootof the modulus.
More precisely, for every pair ofintegers(a,m)withm> 1, given two positive integersXandYsuch thatX≤m<XY, there are two integersxandysuch that
and
Usually, one takesXandYequal to the smallest integer greater than the square root ofm, but the general form is sometimes useful, and makes the uniqueness theorem (below) easier to state.[1]
The first known proof is attributed toAxel Thue(1902)[2]who used apigeonholeargument.[3]It can be used to proveFermat's theorem on sums of two squaresby takingmto be aprimepthat iscongruentto 1 modulo 4 and takingato satisfya2+ 1 ≡ 0 modp. (Such an "a" is guaranteed for "p" byWilson's theorem.[4])
In general, the solution whose existence is asserted by Thue's lemma is not unique. For example, whena= 1there are usually several solutions(x,y) = (1, 1), (2, 2), (3, 3), ..., provided thatXandYare not too small. Therefore, one may only hope for uniqueness for therational numberx/y, to whichais congruent modulomifyandmarecoprime. Nevertheless, this rational number need not be unique; for example, ifm= 5,a= 2andX=Y= 3, one has the two solutions
However, forXandYsmall enough, if a solution exists, it is unique. More precisely, with above notation, if
and
with
and
then
This result is the basis forrational reconstruction, which allows using modular arithmetic for computing rational numbers for which one knows bounds for numerators and denominators.[5]
The proof is rather easy: by multiplying each congruence by the otheryiand subtracting, one gets
The hypotheses imply that each term has an absolute value lower thanXY<m/2, and thus that the absolute value of their difference is lower thanm. This implies thaty2x1−y1x2=0{\displaystyle y_{2}x_{1}-y_{1}x_{2}=0}, hence the result.
The original proof of Thue's lemma is not efficient, in the sense that it does not provide any fast method for computing the solution.
Theextended Euclidean algorithm, allows us to provide a proof that leads to an efficient algorithm that has the samecomputational complexityof theEuclidean algorithm.[6]
More precisely, given the two integersmandaappearing in Thue's lemma, the extended Euclidean algorithm computes three sequences of integers(ti),(xi)and(yi)such that
where thexiare non-negative and strictly decreasing. The desired solution is, up to the sign, the first pair(xi,yi)such thatxi<X.
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Inpredictive analytics,data science,machine learningand related fields,concept driftordriftis an evolution of data that invalidates thedata model. It happens when the statistical properties of the target variable, which the model is trying to predict, change over time in unforeseen ways. This causes problems because the predictions become less accurate as time passes.Drift detectionanddrift adaptationare of paramount importance in the fields that involve dynamically changing data and data models.
In machine learning andpredictive analyticsthis drift phenomenon is called concept drift. In machine learning, a common element of a data model are the statistical properties, such asprobability distributionof the actual data. If they deviate from the statistical properties of thetraining data set, then the learned predictions may become invalid, if the drift is not addressed.[1][2][3][4]
Another important area issoftware engineering, where three types of data drift affectingdata fidelitymay be recognized. Changes in the software environment ("infrastructure drift") may invalidate software infrastructure configuration. "Structural drift" happens when the dataschemachanges, which may invalidate databases. "Semantic drift" is changes in the meaning of data while the structure does not change. In many cases this may happen in complicated applications when many independent developers introduce changes without proper awareness of the effects of their changes in other areas of the software system.[5][6]
For many application systems, the nature of data on which they operate are subject to changes for various reasons, e.g., due to changes in business model, system updates, or switching the platform on which the system operates.[6]
In the case ofcloud computing, infrastructure drift that may affect the applications running on cloud may be caused by the updates of cloud software.[5]
There are several types of detrimental effects of data drift on data fidelity. Data corrosion is passing the drifted data into the system undetected. Data loss happens when valid data are ignored due to non-conformance with the applied schema. Squandering is the phenomenon when new data fields are introduced upstream the data processing pipeline, but somewhere downstream there data fields are absent.[6]
"Data drift" may refer to the phenomenon when database records fail to match the real-world data due to the changes in the latter over time. This is a common problem with databases involving people, such as customers, employees, citizens, residents, etc. Human data drift may be caused by unrecorded changes in personal data, such as place of residence or name, as well as due to errors during data input.[7]
"Data drift" may also refer to inconsistency of data elements between several replicas of a database. The reasons can be difficult to identify. A simple drift detection is to runchecksumregularly. However the remedy may be not so easy.[8]
The behavior of the customers in anonline shopmay change over time. For example, if weekly merchandise sales are to be predicted, and apredictive modelhas been developed that works satisfactorily. The model may use inputs such as the amount of money spent onadvertising,promotionsbeing run, and other metrics that may affect sales. The model is likely to become less and less accurate over time – this is concept drift. In the merchandise sales application, one reason for concept drift may be seasonality, which means that shopping behavior changes seasonally. Perhaps there will be higher sales in the winter holiday season than during the summer, for example. Concept drift generally occurs when the covariates that comprise the data set begin to explain the variation of your target set less accurately — there may be someconfoundingvariables that have emerged, and that one simply cannot account for, which renders the model accuracy to progressively decrease with time. Generally, it is advised to perform health checks as part of the post-production analysis and to re-train the model with new assumptions upon signs of concept drift.
To prevent deterioration inpredictionaccuracy because of concept drift,reactiveandtrackingsolutions can be adopted. Reactive solutions retrain the model in reaction to a triggering mechanism, such as a change-detection test,[9][10]to explicitly detect concept drift as a change in the statistics of the data-generating process. When concept drift is detected, the current model is no longer up-to-date and must be replaced by a new one to restore prediction accuracy.[11][12]A shortcoming of reactive approaches is that performance may decay until the change is detected. Tracking solutions seek to track the changes in the concept by continually updating the model. Methods for achieving this includeonline machine learning, frequent retraining on the most recently observed samples,[13]and maintaining an ensemble of classifiers where one new classifier is trained on the most recent batch of examples and replaces the oldest classifier in the ensemble.[14]
Contextual information, when available, can be used to better explain the causes of the concept drift: for instance, in the sales prediction application, concept drift might be compensated by adding information about the season to the model. By providing information about the time of the year, the rate of deterioration of your model is likely to decrease, but concept drift is unlikely to be eliminated altogether. This is because actual shopping behavior does not follow any static,finite model. New factors may arise at any time that influence shopping behavior, the influence of the known factors or their interactions may change.
Concept drift cannot be avoided for complex phenomena that are not governed by fixedlaws of nature. All processes that arise from human activity, such associoeconomicprocesses, andbiological processesare likely to experience concept drift. Therefore, periodic retraining, also known as refreshing, of any model is necessary.
Many papers have been published describing algorithms for concept drift detection. Only reviews, surveys and overviews are here:
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Hyperrealityis a concept inpost-structuralismthat refers to the process of the evolution of notions of reality, leading to a cultural state of confusion betweensignsand symbols invented to stand in for reality, and direct perceptions ofconsensus reality.[1]Hyperreality is seen as a condition in which, because of the compression of perceptions of reality in culture and media, what is generally regarded as real and what is understood as fiction are seamlessly blended together in experiences so that there is no longer any clear distinction between where one ends and the other begins.[2]
The term was proposed by French philosopherJean Baudrillard, whosepostmodernwork contributed to a scholarly tradition in the field of communication studies that speaks directly to larger social concerns. Postmodernism was established through the social turmoil of the 1960s, spurred by social movements that questioned preexisting conventions and social institutions. Through the postmodern lens, reality is viewed as a fragmented, complimentary and polysemic system with components that are produced by social and cultural activity.Social realitiesthat constitute consensus reality are constantly produced and reproduced, changing through the extended use of signs and symbols which hence contribute to the creation of a greater hyperreality.
The postmodern semiotic concept of hyperreality was contentiously coined by Baudrillard inSimulacra and Simulation(1981).[3]Baudrillard defined "hyperreality" as "the generation by models of a real without origin or reality";[4]and his earlier bookSymbolic Exchange and Death. Hyperreality is a representation, a sign, without an original referent. According to Baudrillard, the commodities in this theoretical state do not haveuse-valueas defined byKarl Marxbut can be understood assignsas defined byFerdinand de Saussure.[5]He believes hyperreality goes further than confusing or blending the 'real' with the symbol which represents it; it involves creating a symbol or set of signifiers which represent something that does not actually exist, like Santa Claus. Baudrillard borrows, fromJorge Luis Borges' "On Exactitude in Science" (already borrowed fromLewis Carroll), the example of a society whosecartographerscreate a map so detailed that it covers the very things it wasdesigned to represent. When the empire declines, the map fades into the landscape.[6]He says that, in such a case, neither the representation nor the real remains, just the hyperreal.
Baudrillard's idea of hyperreality was heavily influenced byphenomenology,semiotics, and the philosophy ofMarshall McLuhan. Baudrillard, however, challenges McLuhan's famous statement that "the medium is the message," by suggesting that information devours its own content. He also suggested that there is a difference between the media and reality and what they represent.[6]Hyperreality is the inability of consciousness to distinguish reality from a simulation of reality, especially in technologically advanced societies.[7]However, Baudrillard's hyperreality theory goes a step further than McLuhan's medium theory: "There is not only an implosion of the message in the medium, there is, in the same movement, the implosion of the medium itself in the real, the implosion of the medium and of the real in a sort of hyperreal nebula, in which even the definition and distinct action of the medium can no longer be determined".[8]
Italian authorUmberto Ecoexplores the notion of hyperreality further by suggesting that the action of hyperreality is to desire reality and in the attempt to achieve that desire, to fabricate a false reality that is to be consumed as real.[9]Linked to contemporarywestern culture, Umberto Eco andpost-structuralistswould argue that in current cultures, fundamental ideals are built on desire and particularsign-systems. Temenuga Trifonova fromUniversity of California, San Diegonotes,
[...]it is important to consider Baudrillard's texts as articulating anontologyrather than anepistemology.[10]
Hyperreality is significant as aparadigmto explain current cultural conditions.Consumerism, because of its reliance on sign exchange value (e.g. brand X shows that one is fashionable, car Y indicates one's wealth), could be seen as a contributing factor in the creation of hyperreality or the hyperreal condition. Hyperreality tricks consciousness into detaching from any real emotional engagement, instead opting for artificial simulation, and endless reproductions of fundamentally empty appearance. Essentially (although Baudrillard himself may balk at the use of this word), fulfillment orhappinessis found through simulation and imitation of a transientsimulacrumof reality, rather than any interaction with any "real"reality.[11]
While hyperreality is not a new concept, its effects are more relevant in modern society, incorporating technological advancements like artificial intelligence, virtual reality andneurotechnology(simulated reality). This is attributed to the way it effectively captured the postmodern condition, particularly how people in the postmodern world seek stimulation by creating unreal worlds of spectacle and seduction and nothing more.[12]There are dangers to the use of hyperreality within our culture; individuals may observe and accept hyperreal images as role models when the images don't necessarily represent real physical people. This can result in a desire to strive for an unobtainable ideal, or it may lead to a lack of unimpaired role models.Daniel J. Boorstincautions against confusing celebrity worship with hero worship, "we come dangerously close to depriving ourselves of all real models. We lose sight of the men and women who do not simply seem great because they are famous but who are famous because they are great".[13]He bemoans the loss of old heroes likeMoses,Julius CaesarandAbraham Lincoln, who did not havepublic relations(PR) agencies to construct hyperreal images of themselves.[14]The dangers of hyperreality are also facilitated by information technologies, which provide tools to dominant powers that seek to encourage it to drive consumption and materialism.[15]The danger in the pursuit of stimulation and seduction emerge not in the lack of meaning but, as Baudrillard maintained, "we are gorged with meaning and it is killing us."[16]
Hyperreality, some sources point out, may provide insights into the postmodern movement by analyzing how simulations disrupt thebinary oppositionbetween reality andillusionbut it does not address or resolve the contradictions inherent in this tension.[17]
The concepts most fundamental to hyperreality are those of simulation and the simulacrum, first conceptualized byJean Baudrillardin his bookSimulacra and Simulation. The two terms are separate entities with relational origin connections to Baudrillard's theory of hyperreality.
Simulationis characterized by a blending of 'reality' and representation, where there is no clear indication of where the former stops and the latter begins. Simulation is no longer that of a territory, a referential being, or a substance; "It is the generation by models of a real without origin or reality: a hyperreal."[18]Baudrillard suggests that simulation no longer takes place in a physical realm; it takes place within a space not categorized by physical limits i.e., within ourselves, technological simulations, etc.
Thesimulacrumis "an image without resemblance"; asGilles Deleuzesummarized, it is the forsaking of "moral existence in order to enter into aesthetic existence".[19]However, Baudrillard argues that a simulacrum is not a copy of the real, but becomes—through sociocultural compression—truth in its own right.
There are four steps of hyperreal reproduction:
The concept of "hyperstition" as expounded upon by the English collectiveCybernetic Culture Research Unitgeneralizes the notion of hyperreality to encompass the concept of "fictional entities that make themselves real." In Nick Land's own words:[21]
Hyperstition is a positivefeedback circuitincluding culture as a component. It can be defined as the experimental (techno-)science ofself-fulfilling prophecies. Superstitions are merely false beliefs, but hyperstitions – by their very existence as ideas –function causally to bring about their own reality.
The concept of hyperstition is also related to the concept of "theory-fiction", in which philosophy,critical theoryandpostmodern literaturespeculate on actual reality and engage with concepts for potentialities and virtualities. An oft-cited example of such a concept iscyberspace—originating inWilliam Gibson's 1984 novelNeuromancer—which is a concept for the convergence between virtualities and actualities.[22]By the mid-1990s, the realization of this concept had begun to emerge on a mass scale in the form of the internet.
The truth was already being called into question with the rise of media andtechnology, but with the presence of hyperreality being used most and embraced as a new technology, there are a couple of issues or consequences of hyperreality. It's difficult enough to hear something on the news and choose not to believe it, but it's quite another to see an image of an event or anything and use your empirical sense to determine whether the news is true or false, which is one of the consequences of hyperrealism.[23]The first is the possibility of various simulations being used to influence the audience, resulting in an inability to differentiate fiction from reality, which affects the overall truth value of a subject at hand. Another implication or disadvantage is the possibility of being manipulated by what we see.
The audience can interpret different messages depending on the ideology of the entity behind an image. As a result, power equates to control over the media and the people.[24]Celebrities, for example, have their photographs taken and altered so that the public can see the final result. The public then perceives celebrities based on what they have seen rather than how they truly are. It can progress to the point where celebrities appear completely different. As a result of celebrities' body modifications and editing, there has been an increase in surgeries and a decrease in self-esteem during adolescence.[25]Because the truth is threatened, a similar outcome for hyperreality is possible.
There is a strong link between media and the impact that the presence of hyperreality has on its viewers. This has shown to blur the lines between artificial realities and reality, influencing the day to day experiences of those exposed to it.[26]As hyperreality captures the inability to distinguish reality from a simulation of reality, common media outlets such as news, social media platforms, radio and television contribute to this misconception of true reality.[27]Descriptions of the impact of hyperreality can be found in popular media. They present themselves as becoming blended with reality, which influences the experience of life and truth for its viewers.
Baudrillard, likeRoland Barthesbefore him, explained that these impacts have a direct effect on younger generations who idolize the heroes, characters orinfluencersfound on these platforms. As media is a social institution that shapes and develops its members within society, the exposure to hyperreality found within these platforms presents an everlasting effect.[28]Baudrillard concludes that exposure to hyperreality over time will lead, from the conservative perspective of the institutions themselves, to confusion and chaos, in turn leading to the destruction of identity, originality and character while ironically still being the mainstay of the institutions.
The hyperreality environment on the internet has shifted dramatically over the course of theCOVID-19 pandemic, so much so that it has an influence on theItalian Stock Exchangein 2021.[29]
TheHollywood signin Los Angeles, California, itself produces similar notions, but is more asymbolof a facet of hyperreality—the creation of a city with its main target being media production.[30]
BothUmberto EcoandJean Baudrillardrefer toDisneylandas an example of hyperreality. Eco believes that Disneyland with its settings such asMain Streetand full sized houses has been created to look "absolutely realistic", taking visitors' imagination to a "fantastic past".[31]This false reality creates an illusion and makes it more desirable for people to buy this reality. Disneyland works in a system that enables visitors to feel that technology and the created atmosphere "can give us more reality than nature can".[32]The "fake nature" of Disneyland satisfies our imagination and daydream fantasies in real life. The idea is that nothing in this world is real. Nothing is original, but all are endless copies of reality. Since we do not imagine the reality of simulations, both imagined and real are equally hyperreal, for example, the numerous simulated rides, including thesubmarine rideand theMississippi boat tour.[8]When entering Disneyland, consumers form into lines to gain access to each attraction. Then they are ordered by people with special uniforms to follow the rules, such as where to stand or where to sit. If the consumers follow each rule correctly, they can enjoy "the real thing" and see things that are not available to them outside of Disneyland's doors.[33]
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Condorcet methods
Positional voting
Cardinal voting
Quota-remainder methods
Approval-based committees
Fractional social choice
Semi-proportional representation
By ballot type
Pathological response
Strategic voting
Paradoxes ofmajority rule
Positive results
Proxy votingis a form ofvotingwhereby a member of a decision-making body may delegate their voting power to a representative, to enable a vote in absence. The representative may be another member of the same body, or external. A person so designated is called a "proxy" and the person designating them is called a "principal".[1]: 3Proxy appointments can be used to form avoting blocthat can exercise greater influence indeliberationsornegotiations. Proxy voting is a particularly important practice with respect to corporations; in the United States, investment advisers often vote proxies on behalf of their client accounts.[2]
A related topic isliquid democracy, a family of electoral systems where votes are transferable and grouped by voters, candidates or combination of both to create proportional representation, and delegated democracy.
Another related topic is the so-called Proxy Plan, orinteractive representationelectoral systemwhereby elected representatives would wield as many votes as they received in the previous election. Oregon held a referendum on adopting such anelectoral systemin 1912.[3]
The United States parliamentary manualRiddick's Rules of Procedurenotes that, under proxy voting, voting for officers should be done by ballot, due to the difficulties involved in authentication if a member simply calls out, "I cast 17 votes for Mr. X."[4]
Proxy voting is also an important feature incorporate governancein the United States through theproxy statement. Companies use proxy solicitation agencies to secure proxy votes.
The rules of some assemblies presently forbid proxy voting. There is a plan to forbid proxy voting in the United States House of Representatives. A recent vote showed 53 Democrats and 26 Republicans voted by proxy.[5]Forbidding proxy voting can result, however, in the absence of a quorum and the need to compel attendance by a sufficient number of missing members to get a quorum. Seecall of the house.
It is possible for automatic proxy voting to be used in legislatures, by way ofdirect representation(this idea is essentially a form ofweighted voting). For example, it has been proposed that instead of electing members from single-member districts (that may have beengerrymandered), members be elected at large, but when seated each member cast the number of votes he or she received in the last election. Thus, if, for example, a state were allocated 32 members in the U.S. House of Representatives, the 32 candidates who received the most votes in the at-large election would be seated, but each would cast a different number of votes on the floor and in committee. This proposal would allow for representation of minority views in legislative deliberations, as it does in deliberations at shareholder meetings of corporations. Such a concept was proposed in a submission to the 2007 Ontario Citizens' Assembly process.[6]
Another example isEvaluative Proportional Representation (EPR). It elects all the members of a legislative body. Each citizen grades the fitness for office of as many of the candidates as they wish as either Excellent (ideal), Very Good, Good, Acceptable, Poor, or Reject. Multiple candidates may be given the same grade by a voter. Each citizen elects their representative at-large for a city council. For a large and diverse state legislature, each citizen chooses to vote through any of the districts or official electoral associations in the country. Each grades any number of candidates in the whole country. Each elected representative has a different voting power (a different number of weighted votes) in the legislative body. This number is equal to the total number of highest available grades counted for them from all the voters – no citizen's vote is "wasted".[7]Each voter is represented equally.
Two real-life examples of weighted voting include theCouncil of Ministers of the European Unionand theUS Electoral College.[8]
TheParliament of New Zealandallows proxy voting. Sections 155-156 of the Standing Orders of theNew Zealand House of Representativesspecify the procedures for doing so. A member can designate another member or a party to cast his or her vote. However, a party may not exercise proxies for more than 25% of its members (rounded upwards).[9]TheNew Zealand Listenernotes a controversial occurrence of proxy voting. TheLabour Partywas allowed to cast votes on behalf ofTaito Phillip Field, who was frequently absent. Theoretically, this was to be allowed only if a legislator was absent on parliamentary business, public business or pressing private business, such as illness or bereavement.[10]
Until theRepublicanreforms of 1995 banished the practice, proxy voting was also used inU.S. House of Representativescommittees. Often members would delegate their vote to the ranking member of their party in the committee. Republicans opposed proxy voting on the grounds that it allowed an indolent Democratic majority to move legislation through committee with antimajoritarian procedures. According to this criticism, on days when Democratic committee members were absent, the Democratic leader in the committee would successfully oppose the sitting Republican majority by wielding the proxies of absent Democrats.[11]Democratic House SpeakerNancy Pelositemporary reinstated proxy voting in 2020 for members who were unable to be physically present in the chamber due to the ongoingCOVID-19 pandemic.[12]
During the COVID-19 pandemic emergency, proxy voting was temporarily introduced in theUK House of Commons. Deputy Chief WhipStuart Andrewheld a large number of proxy votes for other Conservative MPs, and at one stage in 2021 personally controlled a majority of votes in the whole house.[13]He did not always cast these proxy votes the same way, instead following the instructions of individual MPs.[14]
Thomas E. Mann and Norman J. Ornstein write, "In a large and fragmented institution in which every member has five or six places to be at any given moment, proxy voting is a necessary evil".[15]
Proxy voting is sometimes described as "the frequency with which spouses, union workers, and friends of friends are in effect sent off to the polls with an assignment to complete." The potential for proxy voting exists in roughly one voter out of five, and it is about twice as high at the middle levels of the sophistication continuum. According to W. Russell Neuman, the net effect of the cues provided by friends and associates is not likely to be as significant as those of the political parties.[16]
The possibility of expanded use of proxy voting has been the subject of much speculation. Terry F. Buss et al. write thatinternet votingwould result in de facto approval of proxy voting, since passwords could be shared with others: "Obviously, cost-benefit calculations around the act of voting could also change substantially as organizations attempt to identify and provide inducements to control proxy votes without violating vote-buying prohibitions in the law."[17]
One of the criticisms of proxy voting is that it carries a risk of fraud or intimidation.[18]Another criticism is that it violates the concept of a secret ballot, in that paperwork may be filed, for instance, designating a party worker as one's proxy.[19]
It has been proposed that proxy voting be combined withinitiative and referendumto form a hybrid ofdirect democracyandrepresentative democracy.[20][21][unreliable source?]James C. Miller III,Ronald Reagan's budget director, suggested scrapping representative democracy and instead implementing a "program for direct and proxy voting in the legislative process."[22]It has been suggested by Joseph Francis Zimmerman that proxy voting be allowed inNew England town meetings.[23]
Proxy voting can eliminate some of the problems associated with thepublic choicedilemma ofbundling.
According to Arch Puddington et al., in Albanian Muslim areas, many women have been effectively disenfranchised through proxy voting by male relatives.[24]
In Algeria, restrictions on proxy voting were institutedc.1991in order to undermine theIslamic Salvation Front.[25]
In Canada, the province of Nova Scotia allows citizens to vote by proxy if they expect to be absent. The territories of Yukon, Northwest Territories, and Nunavut also allow for proxy voting.[26]Canadian prisoners of war in enemy camps were allowed to vote through proxy voting.[27]David Stewart and Keith Archer opine that proxy voting can result in leadership selection processes to become leader-dominated.[28]Proxy voting had only been available to military personnel since World War II, but was extended in 1970 and 1977 to include voters in special circumstances such as northern camp operators, fishermen, and prospectors. TheAlberta Liberal Partyran into some difficulties, in that an unknown number of proxy ballots that were counted may have been invalid.[29]Those who, through proxy voting or assistance of invalids, become knowledgeable of the principal's choice are bound to secrecy.[30]
SomeChinese provincesallow village residents to designate someone to vote on their behalf. Lily L. Tsai notes that "In practice, one family member often casts votes for everyone in the family even if they are present for the election."[31]In 1997, aCarter Centerdelegation recommended abolishing the proxy voting that allowed one person to vote for three; theInternational Republican Institutehad made a similar recommendation.[32]Proxy voting also became an issue in relation to many of theWenzhoupeople doing business outside.[clarification needed]Most election disputes revolved around proxy votes, including the issues of who could represent them to vote and what kinds of evidence were acceptable for proxy voting. Intense competition made the proxy voting process more and more formal and transparent. Some villages required anotaryto validate faxed proxy votes; some villages asked forfaxedsignatures; more often villages publicized those proxy votes so that villagers could directly monitor them.Taicanggovernment reported a 99.4% voter turnout in its 1997 election, but a study showed that after removing proxy votes, only 48% of the eligible voters in the sample reported that they actually went to the central polling station to vote.[33]
In France, voters are allowed to temporarily give thepower of attorneyto another registered voter (online or by paper form) for purpose of voting in an election, provided that the voter making the request visits the national police station or gendarmerie with proof of identity. Applying voters then receive an e-mail receipt to indicate the validation or invalidation of their request.[34]This method is allowed instead orearlyormail voting.
Proxy voting was intensely used in both rounds of the2024 snap legislative election, when many voters were travelling or scheduled to travel on holiday when the election was called. The election resulted in historically-high turnout for a legislative election.
According to Mim Kelber, "in Central Africa, all it takes for a man to cast a proxy vote for his wife is to produce an unwitnessed letter mentioning the name of the person to whom the voting power is delegated." The Gabon respondent to anInter-Parliamentary Unionletter commented, "It has been observed that this possibility was exploited to a far greater extent by men than by women, for reasons not always noble."[35]
Proxy voting played an important role inGuyanapolitics in the 1960s. Prior to and during the 1961 elections, proxies had been severely restricted. Some restrictions were lifted, and there was a rise in proxy votes cast from 300 in 1961 to 6,635 in 1964. After that election, theCommonwealth Team of Observersvoiced concern about proxy votes being liable to fraud. The proxy voting rules were relaxed further, and in 1969, official figures recorded 19,287 votes cast by proxy, about 7% of the total votes cast (an increase from 2.5% in 1964 to 1968).[36]Amidst allegations of fraud, more restrictions were placed on proxy voting in 1973; in that year, about 10,000 votes were cast by proxy.[37]
In 2003, India'sPeople's Representative Actwas amended to allow armed forces personnel to appoint a proxy to vote on their behalf.[38]
In Iraq, the Electoral Laws of 1924 and 1946 ruled out the possibility of proxy voting, except for illiterates, who could appoint someone to write for them.[39]
Some instances of proxy voting (usually by family members) in the Russian parliamentary elections of 1995 were noted by observers from theOrganization for Security and Cooperation in Europe.[40]
The provision for proxy voting in the UK dates back toJames I. Long beforewomen's suffrage, women sometimes voted as proxies for absent male family heads.
Under British electoral law, ballot papers could not be sent overseas.[19]British emigrants had no right to vote until the mid-1980s. They can now vote by proxy in general elections if they have been on a British electoral register at some point in the past 15 years.[41]They can also vote by post.[42]
In the United Kingdom, electors may appoint a proxy. An elector can only act as a proxy for two people to whom they are not directly related. However, they can be a proxy for any number of electors if they are directly related to those electors. The voter can change his mind and vote in the election personally as long as his proxy has not already voted on his behalf or applied tovote by mail.[43]
Voters must provide a reason for using a proxy, such as being away on vacation. A narrower subset of reasons is permissible if the proxy is to be for more than one election. Except in cases of blindness, the validity of all proxies must be certified by someone such as an employer or doctor.[44]
In 2004, twoLiberal Democratcouncillors were found guilty of submitting 55 fraudulent proxy votes and sentenced to 18 months imprisonment.[45]
TheElectoral Reform Societyhas proposed the abolition of proxy voting in the UK except in special circumstances such as when the voter is abroad.[46]
In 1635–36, Massachusetts granted to the frontier towns "liberty to stay soe many of their freemen at home for the safety of their towne as they judge needful, and that the said freemen that are appoyncted by the towne to stay at home shall have liberty for this court to send their voices by proxy." According to Charles Seymour and Donald Paige Frary, had not proxy voting been implemented, the inhabitants of the frontier towns would have lost their franchises, and the government would have represented only the freemen in the vicinity of Boston. The roads were poor; the drawing of all a village's men at once would have exposed it to Indian attacks; and at election time, the emigrants' labor was needed to get the spring planting into the ground. As late as 1680, and probably even after the charter was revoked in 1684, the Freeman might give his vote for Magistrates in person or proxy at the Court of Elections.[47]
Proxy voting was also adopted in colonies adjacent to Massachusetts.[48]Indeed, traces of the practice of proxy voting remained in Connecticut's election laws until the final supersedure of her charter in 1819.[49]
In Maryland, theprimary assembliesallowed proxy voting. After the assembly of 1638, protests were sent to the proprietor in England. It was said that the Governor and his friends were able to exercise too much influence through the proxies they had obtained.
Proxy voting was also used in South Carolina; the proprietors in September 1683 complained to the governor about this system. Proxy voting was used inLong Island, New York as well, at that time. Phraseology was sometimes designed to hide the fact that a proxy system was in use and that the majority of voters did not actually attend the elections. In Rhode Island, the system described as a "proxy" system, from 1664 onward, was actually simply the sending of written ballots from voters who did not attend the election, rather than a true proxy system, as in the assembly of 1647.[50]
In Alabama, the Perry County Civic League's members' assisting illiterate voters by marking a ballot on their behalf was deemed "proxy voting" and "voting more than once" and thus held to be illegal.[51]
During theAmerican Civil War, some northern soldiers used proxy voting.[52]AfterIra Eastman's near-victory in New Hampshire, Republicans supported a bill to allow soldiers to vote by proxy, but it was ruled unconstitutional by the state supreme court.[53]
In theProgressive Era, proxy voting was used in Republican Party state conventions in New Hampshire. TheBoston and Maine Railroad, the Republican Party's ally, maintained control over the Party by means of these conventions. "At the 1906 state convention, for instance, party delegates were quite willing to trade, sell, or exchange their voting power in return for various forms of remuneration from the party machine. Public outcry led to the end of such 'proxy' voting".[54]
Proxy voting was used in some American U.S. presidential nominating caucuses. In one case,Eugene McCarthysupporters were in the majority of those present but were outvoted when the presiding party official cast 492 proxy votes – three times the number present – for his own slate of delegates.[55]After the nomination ofHubert Humphrey, theNew Politicsmovement charged that Humphrey and party bosses had circumvented the will of Democratic Party members by manipulating the rules to Humphrey's advantage. In response, the Commission on Party Structure and Delegate Selection, also known as theMcGovern–Fraser Commission, was created to rework the rules in time for the1972 Democratic National Convention. State parties were required to ban proxy voting in order to have their delegates seated at the national convention.[54]It was said that these rules had been used in "highly selective" ways.[56]
Several attempts have been made to place proxy voting-related initiatives on the California ballot, but all have failed.[57]
Proxy is defined by supreme courts as "anauthorityor power todoa certain thing."[58]A person can confer on his proxy any power which he himself possesses. He may also give him secret instructions as to voting upon particular questions.[59]But a proxy is ineffectual when it is contrary to law or public policy.[60]Where the proxy is duly appointed and he acts within the scope of the proxy, the person authorizing the proxy is bound by his appointee's acts, including his errors or mistakes.[61]When the appointer sends his appointee to a meeting, the proxy may do anything at that meeting necessary to a full and complete exercise of the appointer's right to vote at such meeting. This includes the right to vote to take the vote by ballot, or to adjourn (and, hence, he may also vote on other ordinary parliamentary motions, such as to refer, postpone, reconsider, etc., when necessary or when deemed appropriate and advantageous to the overall object or purpose of the proxy).[62]
A proxy can vote only in the principal's absence, not when the principal is present and voting.[63]Where the authority conferred upon a proxy is limited to a designated or special purpose, a vote for another and different purpose is ineffective.[64]A proxy in the usual, ordinary form confers authority to act only at the meeting then in contemplation, and in any adjourned-meetings of the same; hence, it may not be voted at another or different meeting held under anew call.[65]A proxy's unauthorized acts may beratifiedby his appointer, and such ratification is equivalent to previous authority.[66]According to the weight of authority, a proxy only to vote stock may be revoked at any time, notwithstanding any agreement that it shall be irrevocable.[67]The sale in the meantime by a stockholder of his shares in a corporation or company automatically revokes any proxies made or given to vote in respect of such shares.[68]And a proxy is also revoked where the party giving it attends the election in person, or gives subsequent proxy.[69]Hence, a proxy cannot vote when the owner of the stock arrives late or is present and votes.[70]
In Vietnam, proxy voting was used to increase turnout. Presently, proxy voting is illegal, but it has nonetheless been occurring since before 1989. It is estimated to contribute about 20% to voter turnout, and has been described as "a convenient way to fulfil one's duty, avoid possible risks, and avoid having to participate directly in the act of voting". It is essentially a compromise between the party-state, which wants to have high turnouts as proof of public support, and voters who do not want to go to the polling stations. In the Soviet Union, proxy voting was also illegal but done in order to increase turnout figures.[71]
Proxy voting is automatically prohibited in organizations that have adoptedRobert's Rules of Order Newly Revised(RONR) orThe Standard Code of Parliamentary Procedure(TSC) as their parliamentary authority, unless it is provided for in its bylaws or charter or required by the laws of its state of incorporation.[72][73]Robert's Rules says, "If the law under which an organization is incorporated allows proxy voting to be prohibited by a provision of the bylaws, the adoption of this book as parliamentary authority by prescription in the bylaws should be treated as sufficient provision to accomplish that result".[74]Demetersays the same thing, but also states that "if these laws donotprohibit voting by proxy, the body can pass a law permitting proxy voting for any purpose desired."[75]RONR opines, "Ordinarily it should neither be allowed nor required, because proxy voting is incompatible with the essential characteristics of a deliberative assembly in which membership is individual, personal, and nontransferable. In a stock corporation, on the other hand, where the ownership is transferable, the voice and vote of the member also is transferable, by use of a proxy."[76]While Riddick opines that "proxy voting properly belongs in incorporate organizations that deal with stocks or real estate, and in certain political organizations," it also states, "If a state empowers an incorporated organization to use proxy voting, that right cannot be denied in the bylaws." Riddick further opines, "Proxy voting is not recommended for ordinary use. It can discourage attendance, and transfers an inalienable right to another without positive assurance that the vote has not been manipulated."[4]
Parliamentary Lawexpounds on this point:[77]
It is used only in stock corporations where the control is in the majority of the stock, not in the majority of the stockholders. If one person gets control of fifty-one per cent of the stock he can control the corporation, electing such directors as he pleases in defiance of the hundreds or thousands of holders of the remaining stock. The laws for stock corporations are nearly always made on the theory that the object of the organization is to make money by carrying on a certain business, using capital supplied by a large number of persons whose control of the business should be in proportion to the capital they have put into the concern. The people who have furnished the majority of the capital should control the organization, and yet they may live in different parts of the country, or be traveling at the time of the annual meeting. By the system of proxy voting they can control the election of directors without attending the meetings.
Nonetheless, it is common practice in conventions for a delegate to have an alternate, who is basically the same as a proxy.Demeter's Manualnotes that the alternate has all the privileges of voting, debate and participation in the proceedings to which the delegate is entitled.[75]Moreover, "if voting has for years ... been conducted ... by proxy ... such voting by long and continuous custom has the force of law, and the proceedings are valid."[78]
Thomas E. Arend notes that U.S. laws allow proxy votes to be conducted electronically in certain situations: "The use of electronic media may be permissible for proxy voting, but such voting is generally limited to members. Given the fiduciary duties that are personal to each director, and the need for directors to deliberate to ensure properly considered decisions, proxy voting by directors is usually prohibited by statute. In contrast, a number of state nonprofit corporate statutes allow for member proxy voting and may further allow members to use electronic media to grant a proxy right to another party for member voting purposes."[79]Sturgis agrees, "Directors or board members cannot vote by proxy in their meetings, since this would mean the delegation of a discretionary legislative duty which they cannot delegate."[73]
Proxy voting, even if allowed, may be limited to infrequent use if the rules governing a body specify minimum attendance requirements. For instance, bylaws may prescribe that a member can be dropped for missing three consecutive meetings.[80]
The Journal of Mental Science noted the arguments raised against adopting proxy voting for the Association. These included that possibility that it would diminish attendance at meetings. The rejoinder was that people did not go there to vote; they attending the meetings for the sake of the meeting, the discussion, and the good fellowship.[81]
In 2005, theLibertarian Party of Colorado, following intense debate, enacted rules allowing proxy voting.[82]A motion to limit proxies to 5 per person was defeated.[83]Some people favored requiring members attending the convention to bring a certain number of proxies, in order to encourage them to politick.[84]In 2006, the party repealed those bylaw provisions due to concerns that a small group of individuals could use it to take control of the organization.[85]
Under thecommon law, shareholders had no right to cast votes by proxy in corporate meetings without special authorization. InWalker v. Johnson,[86]theCourt of Appeals for the District of Columbiaexplained that the reason was that early corporations were of a municipal, religious or charitable nature, in which the shareholder had no pecuniary interest. The normal mode of conferring corporate rights was by an issue of a charter from the crown, essentially establishing the corporation as a part of the government. Given the personal trust placed in these voters by the king, it was inappropriate for them to delegate to others. In the Pennsylvania case ofCommonwealth ex rel. Verree v. Bringhurst,[87]the court held that members of a corporation had no right to vote by proxy at a corporate election unless such right was expressly conferred by the charter or by a bylaw. The attorneys for the plaintiff argued that the common law rules had no application to trading or moneyed corporations where the relation was not personal. The court found, "The fact that it is a business corporation in no wise dispenses with the obligation of all members to assemble together, unless otherwise provided, for the exercise of a right to participate in the election of their officers." At least as early as the 18th century, however, clauses permitting voting by proxy were being inserted in corporate charters in England.[88]
Proxy voting is commonly used in corporations for voting by members or shareholders, because it allows members who have confidence in the judgment of other members to vote for them and allows the assembly to have a quorum of votes when it is difficult for all members to attend, or there are too many members for all of them to conveniently meet and deliberate.Proxy firmscommonly advise institutional shareholders on how they should vote. Proxy solicitation firms assist in helping corral votes for a certain resolution.[89]
Domini notes that in the corporate world, "Proxy ballots typically contain proposals from company management on issues of corporate governance, including capital structure, auditing, board composition, and executive compensation."[90]
Proxies are essentially the corporate law equivalent ofabsentee balloting.[91]: 10–11Shareholders send in a card (called a proxy card) on which they mark their vote. The card authorizes a proxy agent to vote the shareholder's stock as directed on the card.[91]: 10–11The proxy card may specify how shares are to be voted or may simply give the proxy agent discretion to decide how the shares are to be voted.[91]: 10–11The Securities Exchange Act of 1934 transferred this responsibility from the FTC to the SEC. The Securities Exchange Act of 1934 also gave the SEC the power to regulate the solicitation of proxies, though some of the rules the SEC has since proposed (like the universal proxy) have been controversial.[1]: 4UnderSecurities Exchange CommissionRule 14a-3, the incumbent board of directors' first step in soliciting proxies must be the distribution to shareholders of the firm's annual report. An insurgent may independently prepare proxy cards and proxy statements, which are sent to the shareholders.[92]In 2009, the SEC proposed a new rule allowing shareholders meeting certain criteria to add nominees to the proxy statement; though this rule has been the subject of intense debate.[93]: 1
Associations ofinstitutional investorssometimes attempt to effect social change. For instance, several hundred faith-based institutional investors, such as denominations, pensions, etc. belong to the Interfaith Center on Corporate Responsibility. These organizations commonly exercise influence throughshareholder resolutions, which may spur management to action and lead to the resolutions' withdrawal before an actual vote on the resolution is taken.[94]
Fiduciaries for ERISA and other pension plans are generally expected to vote proxies on behalf of these plans in a manner than maximizes the economic value for plan participants. In these regards, for ERISA plans, fiduciaries and advisers are very limited in the extent to which they can take social or other goals into account.[95]
In the absence of his principal from the annual meeting of a business corporation, the proxy has the right to vote in all instances, but he has not the right to debate or otherwise participate in the proceedings unless he is a stockholder in that same corporation.[75]
TheSecurities and Exchange Commission(SEC) has ruled that an investment adviser who exercises voting authority over his clients' proxies has a fiduciary responsibility to adopt policies and procedures reasonably designed to ensure that the adviser votes proxies in the best interests of clients, to disclose to clients information about those policies and procedures, to disclose to clients how they may obtain information on how the adviser has voted their proxies, and to keep certain records related to proxy voting.[96]This ruling has been criticized on many grounds, including the contention that it places unnecessary burdens on investment advisers and would not have prevented the majoraccounting scandalsof the early 2000s.[97]Mutual funds must report their proxy votes periodically on Form N-PX.[98]
It is possible forovervotesandundervotesto occur in corporate proxy situations.[99]
Even in corporate settings, proxy voting's use is generally limited to voting at the annual meeting for directors, for the ratification of acts of the directors, for enlargement or diminution of capital, and for other vital changes in the policy of the organization. These proposed changes are summarized in the circular sent to shareholders prior to the annual meeting. The stock-transfer book is closed at least ten days before the annual meeting to enable the secretary to prepare a list of stockholders and the number of shares held by each. Stock is voted as shown by the stock book when posted. All proxies are checked against this list.[77]
It is possible to designate two or more persons to act as proxy by using language appointing, for instance, "A, B, C, D, and E, F, or any of them, attorneys and agents for me, irrevocable, with full power by the affirmative vote of a majority of said attorneys and agents to appoint a substitute or substitutes for and in the name and stead of me."[77]
Proxy voting is said to have some anti-deliberative consequences, in that proxy holders often lack discretion about how to cast votes due to the instructions given by their principal. Thus, they cannot alter their decision based on the deliberative process of testing the strength of arguments and counter-arguments.[100]
In Germany, corporate proxy voting is done through banks.[101]Proxy voting by banks has been a key feature of the connection of banks to corporate ownership in Germany since the industrialization period.[102]
Indelegated voting, the proxy istransitiveand the transfer recursive. Put simply, the vote may be further delegated to the proxy's proxy, and so on. This is also called transitive proxy or delegate cascade.[103]An early proposal of delegate voting was that ofLewis Carrollin 1884.[104][105]
Delegate voting is used by the Swedish local political partyDemoex. Demoex won its first seat in the city council of Vallentuna,Sweden, in 2002. The first years of activity in the party have been evaluated byMitthögskolan Universityin a paper by Karin Ottesen in 2003.[106]In Demoex, a voter can also vote directly, even if he has delegated his vote to a proxy; the direct vote overrules the proxy vote. It is also possible to change the proxy at any time.
In 2005, in a pilot study in Pakistan,Structural Deep Democracy, SD2[107][108]was used for leadership selection in a sustainable agriculture group called Contact Youth. SD2 usesPageRankfor the processing of the transitive proxy votes, with the additional constraints of mandating at least two initial proxies per voter, and all voters are proxy candidates. More complex variants can be built on top of SD2, such as adding specialist proxies and direct votes for specific issues, but SD2 as the underlying umbrella system, mandates that generalist proxies should always be used.
Delegated voting is also used in the World Parliament Experiment, and in implementations ofliquid democracy.
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Cyborg anthropologyis a discipline that studies the interaction between humanity and technology from ananthropologicalperspective. The discipline offers novel insights on new technological advances and their effect on culture and society.
Donna Haraway’s 1984"A Cyborg Manifesto"was the first widely-read academic text to explore the philosophical and sociological ramifications of the cyborg.[1]A sub-focus group within theAmerican Anthropological Association's annual meeting in 1992 presented a paper entitled "Cyborg Anthropology", which cites Haraway's "Manifesto". The group described cyborg anthropology as the study of how humans define humanness in relationship to machines, as well as the study of science and technology as activities that can shape and be shaped by culture. This includes studying the ways that all people, including those who are not scientific experts, talk about and conceptualize technology.[2]The sub-group was closely related toSTSand theSociety for the Social Studies of Science.[3]More recently,Amber Casehas been responsible for explicating the concept of Cyborg Anthropology to the general public.[4]She believes that a key aspect of cyborg anthropology is the study of networks of information among humans and technology.[5]
Many academics have helped develop cyborg anthropology, and many more who haven't heard the term still are today conducting research that may be considered cyborg anthropology, particularly research regarding technologically advanced prosthetics and how they can influence an individual's life. A 2014 summary of holistic American anthropology intersections with cyborg concepts (whether explicit or not) by Joshua Wells explained how the information-rich and culture-laden ways in which humans imagine, construct, and use tools may extend the cyborg concept through the human evolutionary lineage.[6]Amber Case generally tells people that the actual number of self-described cyborg anthropologists is "about seven".[7]The Cyborg Anthropology Wiki, overseen by Case, aims to make the discipline as accessible as possible, even to people who do not have a background in anthropology.
Cyborg anthropology uses traditional methods of anthropological research like ethnography and participant observation, accompanied by statistics, historical research, and interviews. By nature it is a multidisciplinary study; cyborg anthropology can include aspects ofscience and technology Studies,cybernetics,feminist theory, and more. It primarily focuses on how people use discourse about science and technology in order to make these meaningful in their lives.[8]
The wordcyborgwas originally coined in a 1960 paper aboutspace exploration, the term is short for cybernetic organism.[9]A cyborg is traditionally defined as a system with both organic and inorganic parts. In the narrowest sense of the word, cyborgs are people with machinated body parts. These cyborg parts may be restorative technologies that help a body function where the organic system has failed, likepacemakers,insulin pumps, andbioniclimbs, or enhanced technologies that improve the human body beyond its natural state.[10]In the broadest sense, all human interactions with technology could qualify as a cyborg. Most cyborg anthropologists lean towards the latter view of the cyborg; some, like Amber Case, even claim that humans are already cyborgs because people's daily life and sense of self is so intertwined with technology.[5]Haraway's "Cyborg Manifesto" suggests that technology like virtual avatars, artificial insemination, sexual reassignment surgery, and artificial intelligence might make dichotomies of sex and gender irrelevant, even nonexistent. She goes on to say that other human distinctions (like life and death, human and machine, virtual and real) may similarly disappear in the wake of the cyborg.[1]
Digital anthropologyis concerned with how digital advances are changing how people live their lives, as well as consequent changes to how anthropologists do ethnography and to a lesser extent how digital technology can be used to represent and undertake research.[11]Cyborg anthropology also looks at disciplines likegeneticsand nanotechnology, which are not strictly digital. Cybernetics/informatics covers the range of cyborg advances better than the label digital.
Questions ofsubjectivity, agency, actors, and structures have always been of interest insocialandcultural anthropology. In cyborg anthropology the question of what type of cybernetic system constitutes an actor/subject becomes all the more important. Is it the actual technology that acts on humanity (the Internet), the general techno-culture (Silicon Valley), government sanctions (net neutrality), specific innovative humans (Steve Jobs), or some type of combination of these elements? Some academics believe that only humans have agency and technology is an object humans act upon, while others argue that humans have no agency and culture is entirely shaped by material and technological conditions.Actor-network theory(ANT), proposed byBruno Latour, is a theory that helps scholars understand how these elements work together to shape techno-cultural phenomena. Latour suggests that actors and the subjects they act on are parts of larger networks of mutual interaction and feedback loops. Humans and technology both have the agency to shape one another.[12]ANT best describes the way cyborg anthropology approaches the relationship between humans and technology.[13]Similarly, Wells explain how new forms of networked political expression such as thePirate Partymovement andfree and open-source softwarephilosophies are generated from human reliance on information technologies in all walks of life.[6]
Researchers like Kathleen Richardson have conducted ethnographic research on the humans who build and interact with artificial intelligence.[14]Recently, Stuart Geiger, a PhD student atUniversity of California, Berkeleysuggested that robots may be capable of creating a culture of their own, which researchers could study with ethnographic methods. Anthropologists react to Geiger with skepticism because, according to Geiger, they believe that culture is specific to living creatures and ethnography limited to human subjects.[15]
The most basic definition of anthropology is the study of humans.[16]However, cyborgs, by definition, describe something that is not entirely an organic human. Moreover, limiting a discipline to the study of humans may be difficult the more that technology allows humans to transcend the normal conditions of organic life. The prospect of aposthumancondition calls into question the nature and necessity of a field focused on studying humans.
Sociologistof technologyZeynep Tufekciargues that any symbolic expression of ourselves, even the most ancient cave painting, can be considered "posthuman" because it exists outside of our physical bodies. To her, this means that the human and the "posthuman" have always existed alongside one another, and anthropology has always concerned itself with the posthuman as well as the human.[17]Neil L. Whitehead and Michael Welsch point out that the concern that posthumanism will decenter the human in anthropology ignores the discipline's long history of engaging with the unhuman (like spirits and demons that humans believe in) and the culturally "subhuman" (like marginalized groups within a society).[17]Contrarily, Wells, taking a deep-time perspective, points out the ways that tool-centric and technologically communicated values and ethics typify the human condition, and that cross-cultural and ethnological trends in conceptions of lifeways, power dynamics, and definitions of humanity often incorporate information-rich technological symbology.[6]
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In mathematics and computer science, thepinwheel schedulingproblem is a problem inreal-time schedulingwith repeating tasks of unit length and hard constraints on the time between repetitions.
When a pinwheel scheduling problem has a solution, it has one in which the schedule repeats periodically. This repeating pattern resembles the repeating pattern of set and unset pins on the gears of apinwheel cipher machine, justifying the name.[1]If the fraction of time that is required by each task totals less than 5/6 of the total time, a solution always exists, but some pinwheel scheduling problems whose tasks use a total of slightly more than 5/6 of the total time do not have solutions.
Certain formulations of the pinwheel scheduling problem areNP-hard.
The input to pinwheel scheduling consists of a list of tasks, each of which is assumed to take unit time per instantiation. Each task has an associated positive integer value, its maximum repeat time (the maximum time from the start of one instantiation of the task to the next). Only one task can be performed at any given time.[1]
The desired output is an infinite sequence specifying which task to perform in each unit of time. Each input task should appear infinitely often in the sequence, with the largest gap between two consecutive instantiations of a task at most equal to the repeat time of the task.[1]
For example, the infinitely repeating sequence ABACABACABAC... would be a valid pinwheel schedule for three tasks A, B, and C with repeat times that are at least 2, 4, and 4 respectively.
If the task to be scheduled are numbered from1{\displaystyle 1}ton{\displaystyle n}, letti{\displaystyle t_{i}}denote the repeat time for taski{\displaystyle i}. In any valid schedule, taski{\displaystyle i}must use a1/ti{\displaystyle 1/t_{i}}fraction of the total time, the amount that would be used in a schedule that repeats that task at exactly its specified repeat time. Thedensityof a pinwheel scheduling problem is defined as the sum of these fractions,∑1/ti{\displaystyle \textstyle \sum 1/t_{i}}. For a solution to exist, the times devoted to each task cannot sum to more than the total available time, so it is necessary for the density to be atmost1{\displaystyle 1}.[2]
This condition on density is also sufficient for a schedule to exist in the special case that all repeat times are multiples of each other. For instance, this would be true when all repeat times arepowers of two. In this case one can solve the problem using a disjointcovering system.[1]Having density at most1{\displaystyle 1}is also sufficient when there are exactly two distinct repeat times.[2]However, having density at most 1 is not sufficient in some other cases. In particular, there is no schedule for three items with repeat timest1=2{\displaystyle t_{1}=2},t2=3{\displaystyle t_{2}=3}, andt3{\displaystyle t_{3}}, no matter how larget3{\displaystyle t_{3}}may be, even though the density of this system is only5/6+1/t3{\displaystyle 5/6+1/t_{3}}.[3]
In 1993, it was conjectured that, when the density of a pinwheel scheduling is at most5/6{\displaystyle 5/6}, a solution exists.[3]This was proven in 2024.[4]
When a solution exists, it can be assumed to be periodic, with a period at most equal to the product of the repeat times. However, it is not always possible to find a repeating schedule of sub-exponential length.[2]
With a compact input representation that specifies, for each distinct repeat time, the number of objects that have that repeat time, pinwheel scheduling isNP-hard.[2]
Despite the NP-hardness of the pinwheel scheduling problem for general inputs, some types of inputs can be scheduled efficiently. An example of this occurs for inputs where (when listed in sorted order) each repeat time evenly divides the next one, and the density is at most one. In this case, the problem can be solved by agreedy algorithmthat schedules the tasks in sorted order, scheduling each task to repeat at exactly its repeat time. At each step in this algorithm, the time slots that have already been assigned form a repeating sequence, with period equal to the repeat time of the most recently-scheduled task. This pattern allows each successive task to be scheduled greedily, maintaining the same invariant.[1]
The same idea can be used for arbitrary instances with density at most 1/2,
by rounding down each repeat time to apower of twothat is less than or equal to it. This rounding process at most doubles the density, keeping it at most one. After rounding, all densities are multiples of each other, allowing the greedy algorithm to work. The resulting schedule repeats each task at its rounded repeat time; because these rounded times do not exceed the input times, the schedule is valid.[1]Instead of rounding to powers of two, a greater density threshold can be achieved by rounding to other sequences of multiples, such as the numbers of the formx⋅2i{\displaystyle x\cdot 2^{i}}for a careful choice of the coefficientx{\displaystyle x},[3]or by rounding to two differentgeometric seriesand generalizing the idea that tasks with two distinct repeat times can be scheduled up to density one.[3][5]
The original work on pinwheel scheduling proposed it for an application in which a single base station must communicate with multiplesatellitesorremote sensors, one at a time, with distinct communications requirements. In this application, each satellite becomes a task in a pinwheel scheduling problem, with a repeat time chosen to give it adequate bandwidth. The resulting schedule is used to assign time slots for each satellite to communicate with the base station.[1]
Other applications of pinwheel scheduling include scheduling maintenance sessions for a collection of objects (such as oil changes for automobiles), the arrangement of repeated symbols on the print chains ofline printers,[3]computer processing of multimedia data,[6]and contention resolution in real-time wireless computer networks.[7]
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Oracle Solarisis aproprietaryUnixoperating systemoffered byOracleforSPARCandx86-64basedworkstationsandservers. Originally developed bySun Microsystemsas Solaris, it superseded the company's earlierSunOSin 1993 and became known for itsscalability, especially on SPARC systems, and for originating many innovative features such asDTrace,ZFSand Time Slider.[3][4]After theSun acquisition by Oraclein 2010, it was renamed Oracle Solaris.[5]
Solaris was registered as compliant with theSingle UNIX Specificationuntil April 29, 2019.[6][7][8]Historically, Solaris was developed asproprietary software. In June 2005, Sun Microsystems released most of thecodebaseunder theCDDLlicense, and founded theOpenSolarisopen-sourceproject.[9]Sun aimed to build a developer and user community with OpenSolaris; after the Oracle acquisition in 2010, the OpenSolaris distribution was discontinued[10][11]and later Oracle discontinued providing public updates to the source code of the Solaris kernel, effectively turning Solaris version 11 back into aclosed sourceproprietary operating system.[12]Following that, OpenSolaris was forked asIllumosand is alive through severalIllumos distributions. In September 2017, Oracle laid off most of the Solaris teams.[13]
In 1987,AT&T Corporationand Sun announced that they were collaborating on a project to merge the most popular Unix variants on the market at that time:Berkeley Software Distribution,UNIX System V, andXenix. This became UnixSystem V Release 4(SVR4).[14]
On September 4, 1991, Sun announced that it would replace its existing BSD-derived Unix,SunOS 4, with one based on SVR4. This was identified internally asSunOS 5, but a new marketing name was introduced at the same time:Solaris 2.[15]The justification for this new overbrand was that it encompassed not only SunOS, but also theOpenWindowsgraphical user interfaceandOpen Network Computing(ONC) functionality.
Although SunOS 4.1.xmicro releases wereretroactively namedSolaris 1by Sun, the Solaris name is used almost exclusively to refer only to the releases based on SVR4-derived SunOS 5.0 and later.[16]
For releases based on SunOS 5, the SunOS minor version is included in the Solaris release number. For example, Solaris 2.4 incorporates SunOS 5.4. After Solaris 2.6, the2.was dropped from the release name, so Solaris 7 incorporates SunOS 5.7, and the latest release SunOS 5.11 forms the core of Solaris 11.4.
Although SunSoft stated in its initial Solaris 2 press release their intent to eventually support both SPARC and x86 systems, the first two Solaris 2 releases, 2.0 and 2.1, were SPARC-only. An x86 version of Solaris 2.1 was released in June 1993, about 6 months after the SPARC version, as adesktopand uniprocessor workgroup server operating system. It included theWabiemulator to support Windows applications.[17]At the time, Sun also offered theInteractive Unixsystem that it had acquired fromInteractive Systems Corporation.[18]In 1994, Sun released Solaris 2.4, supporting both SPARC and x86 systems from a unified source code base.
In 2011, the Solaris 11 kernelsource codeleaked.[19][20]
On September 2, 2017,Simon Phipps, a former Sun Microsystems employee not hired by Oracle in the acquisition, reported onTwitterthat Oracle had laid off the Solaris core development staff, which many interpreted as sign that Oracle no longer intended to support future development of the platform.[21]While Oracle did have a large layoff of Solaris development engineering staff, development continued and Solaris 11.4 was released in 2018.[22][23]
Solaris uses a commoncode basefor the platforms it supports: 64-bitSPARCandx86-64.[24]
Solaris has a reputation for being well-suited tosymmetric multiprocessing, supporting a large number ofCPUs.[25]It has historically been tightly integrated with Sun's SPARC hardware (including support for64-bitSPARCapplications since Solaris 7), with which it is marketed as a combined package. This has led to more reliable systems, but at a cost premium compared tocommodity PC hardware. However, it has supported x86 systems since Solaris 2.1 and 64-bit x86 applications since Solaris 10, allowing Sun to capitalize on the availability of commodity 64-bit CPUs based on thex86-64architecture. Sun heavily marketed Solaris for use with both its own x86-64-basedSun Java Workstationand the x86-64 models of theSun Ultra seriesworkstations, andserversbased onAMDOpteronandIntelXeonprocessors, as well as x86 systems manufactured by companies such asDell,[26]Hewlett-Packard, andIBM. As of 2009[update], the following vendors support Solaris for their x86 server systems:
Solaris 2.5.1 included support for thePowerPCplatform (PowerPC Reference Platform), but the port was canceled before the Solaris 2.6 release.[31]In January 2006, a community of developers at Blastwave began work on a PowerPC port which they namedPolaris.[32]In October 2006, anOpenSolariscommunity project based on the Blastwave efforts and Sun Labs'Project Pulsar,[33]which re-integrated the relevant parts from Solaris 2.5.1 into OpenSolaris,[31]announced its first official source code release.[34]
A port of Solaris to the IntelItaniumarchitecture was announced in 1997 but never brought to market.[35]
On November 28, 2007,IBM, Sun, and Sine Nomine Associates demonstrated a preview ofOpenSolaris for System zrunning on anIBM System zmainframeunderz/VM,[36]calledSirius(in analogy to the Polaris project, and also due to the primary developer's Australian nationality:HMSSiriusof 1786 was a ship of theFirst FleettoAustralia). On October 17, 2008, a prototype release of Sirius was made available[37]and on November 19 the same year, IBM authorized the use of Sirius on System zIntegrated Facility for Linux(IFL) processors.[38]
Solaris also supports theLinuxplatformapplication binary interface(ABI), allowing Solaris to run native Linuxbinarieson x86 systems. This feature is calledSolaris Containers for Linux Applications(SCLA), based on thebranded zonesfunctionality introduced in Solaris 10 8/07.[39]
Solaris can be installed from various pre-packaged software groups, ranging from a minimalisticReduced Network Supportto a completeEntire PlusOEM. Installation of Solaris is not necessary for an individual to use the system. The DVD ISO image can be used to load Solaris, running in-memory, rather than initiating the installation.
Additional software, like Apache, MySQL, etc. can be installed as well in a packaged form fromsunfreeware[40]andOpenCSW.[41]Solaris can be installed from physical media or a network for use on a desktop or server, or be used without installing on a desktop or server.[clarification needed][citation needed]
There are several types of updates within each major release, including the Software Packages, and the Oracle Solaris Image.
Additional minor updates called Support Repository Updates (SRUs) and Critical Patch Update Packages (CPUs), require a support credential, thus are not freely available to the public.[42]
Early releases of Solaris usedOpenWindowsas the standard desktop environment. In Solaris 2.0 to 2.2, OpenWindows supported bothNeWSandXapplications, and providedbackward compatibilityforSunViewapplications from Sun's older desktop environment. NeWS allowed applications to be built in anobject-orientedway usingPostScript, a common printing language released in 1982. TheX Window Systemoriginated fromMIT'sProject Athenain 1984 and allowed for the display of an application to be disconnected from the machine where the application was running, separated by a network connection. Sun's original bundled SunView application suite was ported to X.
Sun later dropped support for legacy SunView applications and NeWS with OpenWindows 3.3, which shipped with Solaris 2.3, and switched toX11R5withDisplay Postscriptsupport. The graphical look and feel remained based uponOPEN LOOK. OpenWindows 3.6.2 was the last release under Solaris 8. The OPEN LOOK Window Manager (olwm) with other OPEN LOOK specific applications were dropped in Solaris 9, but support libraries were still bundled, providing long term binary backwards compatibility with existing applications. The OPEN LOOK Virtual Window Manager (olvwm) can still be downloaded for Solaris from sunfreeware and works on releases as recent as Solaris 10.
Sun and other Unix vendors created an industry alliance to standardize Unix desktops. As a member of theCommon Open Software Environment(COSE) initiative, Sun helped co-develop theCommon Desktop Environment(CDE). This was an initiative to create a standard Unix desktop environment. Each vendor contributed different components:Hewlett-Packardcontributed thewindow manager,IBMprovided thefile manager, and Sun provided thee-mailand calendar facilities as well as drag-and-drop support (ToolTalk). This new desktop environment was based upon theMotiflook and feel and the old OPEN LOOK desktop environment was considered legacy. CDE unified Unix desktops across multipleopen systemvendors. CDE was available as an unbundled add-on for Solaris 2.4 and 2.5, and was included in Solaris 2.6 through 10.
In 2001, Sun issued a preview release of the open-source desktop environmentGNOME1.4, based on theGTK+toolkit, for Solaris 8.[43]Solaris 9 8/03 introduced GNOME 2.0 as an alternative to CDE. Solaris 10 includes Sun'sJava Desktop System(JDS), which is based on GNOME and comes with a large set of applications, includingStarOffice, Sun'soffice suite. Sun describes JDS as a "major component" of Solaris 10.[44]The Java Desktop System is not included in Solaris 11 which instead ships with a stock version of GNOME.[45]Likewise, CDE applications are no longer included in Solaris 11, but many libraries remain for binary backwards compatibility.
The open source desktop environmentsKDEandXfce, along with numerous otherwindow managers, also compile and run on recent versions of Solaris.
Sun was investing in a new desktop environment calledProject Looking Glasssince 2003. The project has been inactive since late 2006.[46]
For versions up to 2005 (Solaris 9), Solaris was licensed under a license that permitted a customer to buy licenses in bulk, and install the software on any machine up to a maximum number. The key license grant was:
License to Use. Customer is granted a non-exclusive and non-transferable license ("License") for the use of the accompanying binary software in machine-readable form, together with accompanying documentation ("Software"), by the number of users and the class of computer hardware for which the corresponding fee has been paid.
In addition, the license provided a "License to Develop" granting rights to create derivative works, restricted copying to only a single archival copy, disclaimer of warranties, and the like. The license varied only little through 2004.
From 2005 to 2010, Sun began to release the source code for development builds of Solaris under theCommon Development and Distribution License(CDDL) via theOpenSolarisproject. This code was based on the work being done for the post-Solaris 10 release (code-named "Nevada"; eventually released as Oracle Solaris 11). As the project progressed, it grew to encompass most of the necessary code to compile an entire release, with a few exceptions.[47]
When Sun was acquired byOraclein 2010, the OpenSolaris project was discontinued after the board became unhappy with Oracle's stance on the project.[48]In March 2010, the previously freely available Solaris 10 was placed under a restrictive license that limited the use, modification and redistribution of the operating system.[49]The license allowed the user to download the operating system free of charge, through theOracle Technology Network, and use it for a 90-day trial period. After that trial period had expired the user would then have to purchase a support contract from Oracle to continue using the operating system.
With the release of Solaris 11 in 2011, the license terms changed again. The new license allows Solaris 10 and Solaris 11 to be downloaded free of charge from the Oracle Technology Network and used without a support contract indefinitely; however, the license only expressly permits the user to use Solaris as a development platform and expressly forbids commercial and "production" use.[50]Educational use is permitted in some circumstances. From the OTN license:
If You are an educational institution vested with the power to confer official high school, associate, bachelor, master and/or doctorate degrees, or local equivalent, ("Degree(s)"), You may also use the Programs as part of Your educational curriculum for students enrolled in Your Degree program(s) solely as required for the conferral of such Degree (collectively "Educational Use").
When Solaris is used without a support contract it can be upgraded to each new "point release"; however, a support contract is required for access to patches and updates that are released monthly.[51]
Notable features of Solaris includeDTrace,Doors,Service Management Facility,Solaris Containers,Solaris Multiplexed I/O,Solaris Volume Manager,ZFS, andSolaris Trusted Extensions.
Updates to Solaris versions are periodically issued. In the past, these were named after the month and year of their release, such as "Solaris 10 1/13"; as of Solaris 11, sequential update numbers are appended to the release name with a period, such as "Oracle Solaris 11.4".
In ascending order, the following versions of Solaris have been released:
[90][91][92]
A more comprehensive summary of some Solaris versions is also available.[93]Solaris releases are also described in the Solaris 2 FAQ.[94]
The underlying Solaris codebase has been under continuous development since work began in the late 1980s on what was eventually released as Solaris 2.0. Each version such as Solaris 10 is based on a snapshot of this development codebase, taken near the time of its release, which is then maintained as a derived project. Updates to that project are built and delivered several times a year until the next official release comes out.
The Solaris version under development by Sun since the release of Solaris 10 in 2005, wascodenamedNevada, and is derived from what is now theOpenSolariscodebase.
In 2003, an addition to the Solaris development process was initiated. Under the program nameSoftware Express for Solaris(or justSolaris Express), a binary release based on the current development basis was made available for download on a monthly basis, allowing anyone to try out new features and test the quality and stability of the OS as it progressed to the release of the next official Solaris version.[95]A later change to this program introduced a quarterly release model with support available, renamedSolaris Express Developer Edition(SXDE).
In 2007, Sun announcedProject Indianawith several goals, including providing an open source binary distribution of the OpenSolaris project, replacing SXDE.[96]The first release of this distribution wasOpenSolaris 2008.05.
TheSolaris Express Community Edition(SXCE)was intended specifically for OpenSolaris developers.[97]It was updated every two weeks until it was discontinued in January 2010, with a recommendation that users migrate to the OpenSolaris distribution.[98]Although the download license seen when downloading the image files indicates its use is limited to personal, educational and evaluation purposes, the license acceptance form displayed when the user actually installs from these images lists additional uses including commercial and production environments.
SXCE releases terminated with build 130 and OpenSolaris releases terminated with build 134 a few weeks later. The next release of OpenSolaris based on build 134 was due in March 2010, but it was never fully released, though the packages were made available on the package repository. Instead, Oracle renamed the binary distribution Solaris 11 Express, changed the license terms and released build 151a as 2010.11 in November 2010.
All in all, Sun has stayed the course with Solaris 9. While its more user-friendly management is welcome, that probably won't be enough to win over converts. What may is the platform's reliability, flexibility, and power.
Be that as it may, since the Solaris 10 download is free, it behooves any IT manager to load it on an extra server and at least give it a try.
Solaris 10 provides a flexible background for securely dividing system resources, providing performance guarantees and tracking usage for these containers. Creating basic containers and populating them with user applications and resources is simple. But some cases may require quite a bit of fine-tuning.
I think that Sun has put some really nice touches on Solaris 10 that make it a better operating system for both administrators and users. The security enhancements are a long time coming, but are worth the wait. Is Solaris 10 perfect, in a word no it is not. But for most uses, including a desktop OS I think Solaris 10 is a huge improvement over previous releases.
We've had fun with Solaris 10. It's got virtues that we definitely admire. What it needs to compete with Linux will be easier to bring about than what it's already got. It could become a Linux killer, or at least a serious competitor on Linux's turf. The only question is whether Sun has the will to see it through.
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Dijkstra's algorithm(/ˈdaɪkstrəz/DYKE-strəz) is analgorithmfor finding theshortest pathsbetweennodesin a weightedgraph, which may represent, for example, aroad network. It was conceived bycomputer scientistEdsger W. Dijkstrain 1956 and published three years later.[4][5][6]
Dijkstra's algorithm finds the shortest path from a given source node to every other node.[7]: 196–206It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of edges represent the distances between pairs of cities connected by a direct road, then Dijkstra's algorithm can be used to find the shortest route between one city and all other cities. A common application of shortest path algorithms is networkrouting protocols, most notablyIS-IS(Intermediate System to Intermediate System) andOSPF(Open Shortest Path First). It is also employed as asubroutinein algorithms such asJohnson's algorithm.
The algorithm uses amin-priority queuedata structure for selecting the shortest paths known so far. Before more advanced priority queue structures were discovered, Dijkstra's original algorithm ran inΘ(|V|2){\displaystyle \Theta (|V|^{2})}time, where|V|{\displaystyle |V|}is the number of nodes.[8][9]Fredman & Tarjan 1984proposed aFibonacci heappriority queue to optimize the running time complexity toΘ(|E|+|V|log|V|){\displaystyle \Theta (|E|+|V|\log |V|)}. This isasymptoticallythe fastest known single-sourceshortest-path algorithmfor arbitrarydirected graphswith unbounded non-negative weights. However, specialized cases (such as bounded/integer weights, directed acyclic graphs etc.) can beimproved further. If preprocessing is allowed, algorithms such ascontraction hierarchiescan be up to seven orders of magnitude faster.
Dijkstra's algorithm is commonly used on graphs where the edge weights are positive integers or real numbers. It can be generalized to any graph where the edge weights arepartially ordered, provided the subsequent labels (a subsequent label is produced when traversing an edge) aremonotonicallynon-decreasing.[10][11]
In many fields, particularlyartificial intelligence, Dijkstra's algorithm or a variant offers auniform cost searchand is formulated as an instance of the more general idea ofbest-first search.[12]
What is the shortest way to travel fromRotterdamtoGroningen, in general: from given city to given city.It is the algorithm for the shortest path, which I designed in about twenty minutes. One morning I was shopping inAmsterdamwith my young fiancée, and tired, we sat down on the café terrace to drink a cup of coffee and I was just thinking about whether I could do this, and I then designed the algorithm for the shortest path. As I said, it was a twenty-minute invention. In fact, it was published in '59, three years later. The publication is still readable, it is, in fact, quite nice. One of the reasons that it is so nice was that I designed it without pencil and paper. I learned later that one of the advantages of designing without pencil and paper is that you are almost forced to avoid all avoidable complexities. Eventually, that algorithm became to my great amazement, one of the cornerstones of my fame.
Dijkstra thought about the shortest path problem while working as a programmer at theMathematical Center in Amsterdamin 1956. He wanted to demonstrate the capabilities of the new ARMAC computer.[13]His objective was to choose a problem and a computer solution that non-computing people could understand. He designed the shortest path algorithm and later implemented it for ARMAC for a slightly simplified transportation map of 64 cities in the Netherlands (he limited it to 64, so that 6 bits would be sufficient to encode the city number).[5]A year later, he came across another problem advanced by hardware engineers working on the institute's next computer: minimize the amount of wire needed to connect the pins on the machine's back panel. As a solution, he re-discoveredPrim's minimal spanning tree algorithm(known earlier toJarník, and also rediscovered byPrim).[14][15]Dijkstra published the algorithm in 1959, two years after Prim and 29 years after Jarník.[16][17]
The algorithm requires a starting node, and computes the shortest distance from that starting node to each other node. Dijkstra's algorithm starts with infinite distances and tries to improve them step by step:
The shortest path between twointersectionson a city map can be found by this algorithm using pencil and paper. Every intersection is listed on a separate line: one is the starting point and is labeled (given a distance of) 0. Every other intersection is initially labeled with a distance of infinity. This is done to note that no path to these intersections has yet been established. At each iteration one intersection becomes the current intersection. For the first iteration, this is the starting point.
From the current intersection, the distance to everyneighbor(directly-connected) intersection is assessed by summing the label (value) of the current intersection and the distance to the neighbor and thenrelabelingthe neighbor with the lesser of that sum and the neighbor's existing label. I.e., the neighbor is relabeled if the path to it through the current intersection is shorter than previously assessed paths. If so, mark the road to the neighbor with an arrow pointing to it, and erase any other arrow that points to it. After the distances to each of the current intersection's neighbors have been assessed, the current intersection is marked as visited. The unvisited intersection with the smallest label becomes the current intersection and the process repeats until all nodes with labels less than the destination's label have been visited.
Once no unvisited nodes remain with a label smaller than the destination's label, the remaining arrows show the shortest path.
In the followingpseudocode,distis an array that contains the current distances from thesourceto other vertices, i.e.dist[u]is the current distance from the source to the vertexu. Theprevarray contains pointers to previous-hop nodes on the shortest path from source to the given vertex (equivalently, it is thenext-hopon the pathfromthe given vertextothe source). The codeu ← vertex inQwith min dist[u], searches for the vertexuin the vertex setQthat has the leastdist[u]value.Graph.Edges(u,v)returns the length of the edge joining (i.e. the distance between) the two neighbor-nodesuandv. The variablealton line 14 is the length of the path from thesourcenode to the neighbor nodevif it were to go throughu. If this path is shorter than the current shortest path recorded forv, then the distance ofvis updated toalt.[7]
To find the shortest path between verticessourceandtarget, the search terminates after line 10 ifu=target. The shortest path fromsourcetotargetcan be obtained by reverse iteration:
Now sequenceSis the list of vertices constituting one of the shortest paths fromsourcetotarget, or the empty sequence if no path exists.
A more general problem is to find all the shortest paths betweensourceandtarget(there might be several of the same length). Then instead of storing only a single node in each entry ofprev[]all nodes satisfying the relaxation condition can be stored. For example, if bothrandsourceconnect totargetand they lie on different shortest paths throughtarget(because the edge cost is the same in both cases), then bothrandsourceare added toprev[target]. When the algorithm completes,prev[]data structure describes a graph that is a subset of the original graph with some edges removed. Its key property is that if the algorithm was run with some starting node, then every path from that node to any other node in the new graph is the shortest path between those nodes graph, and all paths of that length from the original graph are present in the new graph. Then to actually find all these shortest paths between two given nodes, a path finding algorithm on the new graph, such asdepth-first searchwould work.
A min-priority queue is an abstract data type that provides 3 basic operations:add_with_priority(),decrease_priority()andextract_min(). As mentioned earlier, using such a data structure can lead to faster computing times than using a basic queue. Notably,Fibonacci heap[19]orBrodal queueoffer optimal implementations for those 3 operations. As the algorithm is slightly different in appearance, it is mentioned here, in pseudocode as well:
Instead of filling the priority queue with all nodes in the initialization phase, it is possible to initialize it to contain onlysource; then, inside theifalt< dist[v]block, thedecrease_priority()becomes anadd_with_priority()operation.[7]: 198
Yet another alternative is to add nodes unconditionally to the priority queue and to instead check after extraction (u←Q.extract_min()) that it isn't revisiting, or that no shorter connection was found yet in theif alt < dist[v]block. This can be done by additionally extracting the associated prioritypfrom the queue and only processing furtherifp== dist[u]inside thewhileQis not emptyloop.[20]
These alternatives can use entirely array-based priority queues without decrease-key functionality, which have been found to achieve even faster computing times in practice. However, the difference in performance was found to be narrower for denser graphs.[21]
To prove thecorrectnessof Dijkstra's algorithm,mathematical inductioncan be used on the number of visited nodes.[22]
Invariant hypothesis: For each visited nodev,dist[v]is the shortest distance fromsourcetov, and for each unvisited nodeu,dist[u]is the shortest distance fromsourcetouwhen traveling via visited nodes only, or infinity if no such path exists. (Note: we do not assumedist[u]is the actual shortest distance for unvisited nodes, whiledist[v]is the actual shortest distance)
The base case is when there is just one visited node,source. Its distance is defined to be zero, which is the shortest distance, since negative weights are not allowed. Hence, the hypothesis holds.
Assuming that the hypothesis holds fork{\displaystyle k}visited nodes, to show it holds fork+1{\displaystyle k+1}nodes, letube the next visited node, i.e. the node with minimumdist[u]. The claim is thatdist[u]is the shortest distance fromsourcetou.
The proof is by contradiction. If a shorter path were available, then this shorter path either contains another unvisited node or not.
For all other visited nodesv, thedist[v]is already known to be the shortest distance fromsourcealready, because of the inductive hypothesis, and these values are unchanged.
After processingu, it is still true that for each unvisited nodew,dist[w]is the shortest distance fromsourcetowusing visited nodes only. Any shorter path that did not useu, would already have been found, and if a shorter path useduit would have been updated when processingu.
After all nodes are visited, the shortest path fromsourceto any nodevconsists only of visited nodes. Therefore,dist[v]is the shortest distance.
Bounds of the running time of Dijkstra's algorithm on a graph with edgesEand verticesVcan be expressed as a function of the number of edges, denoted|E|{\displaystyle |E|}, and the number of vertices, denoted|V|{\displaystyle |V|}, usingbig-O notation. The complexity bound depends mainly on the data structure used to represent the setQ. In the following, upper bounds can be simplified because|E|{\displaystyle |E|}isO(|V|2){\displaystyle O(|V|^{2})}for any simple graph, but that simplification disregards the fact that in some problems, other upper bounds on|E|{\displaystyle |E|}may hold.
For any data structure for the vertex setQ, the running time i s:[2]
whereTdk{\displaystyle T_{\mathrm {dk} }}andTem{\displaystyle T_{\mathrm {em} }}are the complexities of thedecrease-keyandextract-minimumoperations inQ, respectively.
The simplest version of Dijkstra's algorithm stores the vertex setQas a linked list or array, and edges as anadjacency listormatrix. In this case, extract-minimum is simply a linear search through all vertices inQ, so the running time isΘ(|E|+|V|2)=Θ(|V|2){\displaystyle \Theta (|E|+|V|^{2})=\Theta (|V|^{2})}.
Forsparse graphs, that is, graphs with far fewer than|V|2{\displaystyle |V|^{2}}edges, Dijkstra's algorithm can be implemented more efficiently by storing the graph in the form of adjacency lists and using aself-balancing binary search tree,binary heap,pairing heap,Fibonacci heapor a priority heap as apriority queueto implement extracting minimum efficiently. To perform decrease-key steps in a binary heap efficiently, it is necessary to use an auxiliary data structure that maps each vertex to its position in the heap, and to update this structure as the priority queueQchanges. With a self-balancing binary search tree or binary heap, the algorithm requires
time in the worst case; for connected graphs this time bound can be simplified toΘ(|E|log|V|){\displaystyle \Theta (|E|\log |V|)}. TheFibonacci heapimproves this to
When using binary heaps, theaverage casetime complexity is lower than the worst-case: assuming edge costs are drawn independently from a commonprobability distribution, the expected number ofdecrease-keyoperations is bounded byΘ(|V|log(|E|/|V|)){\displaystyle \Theta (|V|\log(|E|/|V|))}, giving a total running time of[7]: 199–200
In common presentations of Dijkstra's algorithm, initially all nodes are entered into the priority queue. This is, however, not necessary: the algorithm can start with a priority queue that contains only one item, and insert new items as they are discovered (instead of doing a decrease-key, check whether the key is in the queue; if it is, decrease its key, otherwise insert it).[7]: 198This variant has the same worst-case bounds as the common variant, but maintains a smaller priority queue in practice, speeding up queue operations.[12]
Moreover, not inserting all nodes in a graph makes it possible to extend the algorithm to find the shortest path from a single source to the closest of a set of target nodes on infinite graphs or those too large to represent in memory. The resulting algorithm is calleduniform-cost search(UCS) in the artificial intelligence literature[12][23][24]and can be expressed in pseudocode as
Its complexity can be expressed in an alternative way for very large graphs: whenC*is the length of the shortest path from the start node to any node satisfying the "goal" predicate, each edge has cost at leastε, and the number of neighbors per node is bounded byb, then the algorithm's worst-case time and space complexity are both inO(b1+⌊C*⁄ε⌋).[23]
Further optimizations for the single-target case includebidirectionalvariants, goal-directed variants such as theA* algorithm(see§ Related problems and algorithms), graph pruning to determine which nodes are likely to form the middle segment of shortest paths (reach-based routing), and hierarchical decompositions of the input graph that reduces–trouting to connectingsandtto their respective "transit nodes" followed by shortest-path computation between these transit nodes using a "highway".[25]Combinations of such techniques may be needed for optimal practical performance on specific problems.[26]
As well as simply computing distances and paths, Dijkstra's algorithm can be used to sort vertices by their distances from a given starting vertex.
In 2023, Haeupler, Rozhoň, Tětek, Hladík, andTarjan(one of the inventors of the 1984 heap), proved that, for this sorting problem on a positively-weighted directed graph, a version of Dijkstra's algorithm with a special heap data structure has a runtime and number of comparisons that is within a constant factor of optimal amongcomparison-basedalgorithms for the same sorting problem on the same graph and starting vertex but with variable edge weights. To achieve this, they use a comparison-based heap whose cost of returning/removing the minimum element from the heap is logarithmic in the number of elements inserted after it rather than in the number of elements in the heap.[27][28]
When arc weights are small integers (bounded by a parameterC{\displaystyle C}), specialized queues can be used for increased speed. The first algorithm of this type was Dial's algorithm[29]for graphs with positive integer edge weights, which uses abucket queueto obtain a running timeO(|E|+|V|C){\displaystyle O(|E|+|V|C)}. The use of aVan Emde Boas treeas the priority queue brings the complexity toO(|E|+|V|logC/loglog|V|C){\displaystyle O(|E|+|V|\log C/\log \log |V|C)}.[30]Another interesting variant based on a combination of a newradix heapand the well-known Fibonacci heap runs in timeO(|E|+|V|logC){\displaystyle O(|E|+|V|{\sqrt {\log C}})}.[30]Finally, the best algorithms in this special case run inO(|E|loglog|V|){\displaystyle O(|E|\log \log |V|)}[31]time andO(|E|+|V|min{(log|V|)1/3+ε,(logC)1/4+ε}){\displaystyle O(|E|+|V|\min\{(\log |V|)^{1/3+\varepsilon },(\log C)^{1/4+\varepsilon }\})}time.[32]
Dijkstra's original algorithm can be extended with modifications. For example, sometimes it is desirable to present solutions which are less than mathematically optimal. To obtain a ranked list of less-than-optimal solutions, the optimal solution is first calculated. A single edge appearing in the optimal solution is removed from the graph, and the optimum solution to this new graph is calculated. Each edge of the original solution is suppressed in turn and a new shortest-path calculated. The secondary solutions are then ranked and presented after the first optimal solution.
Dijkstra's algorithm is usually the working principle behindlink-state routing protocols.OSPFandIS-ISare the most common.
Unlike Dijkstra's algorithm, theBellman–Ford algorithmcan be used on graphs with negative edge weights, as long as the graph contains nonegative cyclereachable from the source vertexs. The presence of such cycles means that no shortest path can be found, since the label becomes lower each time the cycle is traversed. (This statement assumes that a "path" is allowed to repeat vertices. Ingraph theorythat is normally not allowed. Intheoretical computer scienceit often is allowed.) It is possible to adapt Dijkstra's algorithm to handle negative weights by combining it with the Bellman-Ford algorithm (to remove negative edges and detect negative cycles):Johnson's algorithm.
TheA* algorithmis a generalization of Dijkstra's algorithm that reduces the size of the subgraph that must be explored, if additional information is available that provides a lower bound on the distance to the target.
The process that underlies Dijkstra's algorithm is similar to thegreedyprocess used inPrim's algorithm. Prim's purpose is to find aminimum spanning treethat connects all nodes in the graph; Dijkstra is concerned with only two nodes. Prim's does not evaluate the total weight of the path from the starting node, only the individual edges.
Breadth-first searchcan be viewed as a special-case of Dijkstra's algorithm on unweighted graphs, where the priority queue degenerates into aFIFOqueue.
Thefast marching methodcan be viewed as a continuous version of Dijkstra's algorithm which computes the geodesic distance on a triangle mesh.
From adynamic programmingpoint of view, Dijkstra's algorithm is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by theReachingmethod.[33][34][35]
In fact, Dijkstra's explanation of the logic behind the algorithm:[36]
Problem 2.Find the path of minimum total length between two given nodesPandQ.
We use the fact that, ifRis a node on the minimal path fromPtoQ, knowledge of the latter implies the knowledge of the minimal path fromPtoR.
is a paraphrasing ofBellman'sPrinciple of Optimalityin the context of the shortest path problem.
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Inmathematicsandgroup theory, the termmultiplicative grouprefers to one of the following concepts:
Thegroup scheme ofn-throots of unityis by definition the kernel of then-power map on the multiplicative group GL(1), considered as agroup scheme. That is, for any integern> 1 we can consider the morphism on the multiplicative group that takesn-th powers, and take an appropriatefiber product of schemes, with the morphismethat serves as the identity.
The resulting group scheme is written μn(orμμn{\displaystyle \mu \!\!\mu _{n}}[2]). It gives rise to areduced scheme, when we take it over a fieldK,if and only ifthecharacteristicofKdoes not dividen. This makes it a source of some key examples of non-reduced schemes (schemes withnilpotent elementsin theirstructure sheaves); for example μpover afinite fieldwithpelements for anyprime numberp.
This phenomenon is not easily expressed in the classical language of algebraic geometry. For example, it turns out to be of major importance in expressing theduality theory of abelian varietiesin characteristicp(theory ofPierre Cartier). TheGalois cohomologyof this group scheme is a way of expressingKummer theory.
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Pitch circularityis a fixed series oftonesthat are perceived to ascend or descend endlessly inpitch. It's an example of anauditory illusion.
Pitch is often defined as extending along a one-dimensionalcontinuumfrom high to low, as can be experienced by sweeping one’s hand up or down a piano keyboard. This continuum is known as pitch height. However pitch also varies in a circular fashion, known aspitch class: as one plays up a keyboard in semitone steps, C, C♯, D, D♯, E, F, F♯, G, G♯, A, A♯and B sound in succession, followed by C again, but oneoctavehigher. Because the octave is the most consonant interval after theunison, tones that stand in octave relation, and are so of the same pitch class, have a certain perceptual equivalence—all Cs sound more alike to other Cs than to any other pitch class, as do all D♯s, and so on; this creates the auditory equivalent of aBarber's pole, where all tones of the same pitch class are located on the same side of the pole, but at different heights.
Researchers have demonstrated that by creating banks of tones whose note names are clearly defined perceptually but whose perceived heights are ambiguous, one can create scales that appear to ascend or descend endlessly in pitch.Roger Shepardachieved this ambiguity of height by creating banks of complex tones, with each tone composed only of components that stood in octave relationship. In other words, the components of the complex tone C consisted only of Cs, but in different octaves, and the components of the complex tone F♯consisted only of F♯s, but in different octaves.[2]When such complex tones are played in semitone steps the listener perceives a scale that appears to ascend endlessly in pitch.Jean-Claude Rissetachieved the same effect using gliding tones instead, so that a single tone appeared to glide up or down endlessly in pitch.[3]Circularity effects based on this principle have been produced in orchestral music and electronic music, by having multiple instruments playing simultaneously in different octaves.
Normann et al.[4]showed that pitch circularity can be created using a bank of single tones; here the relative amplitudes of the odd and even harmonics of each tone are manipulated so as to create ambiguities of height.
A different algorithm that creates ambiguities of pitch height by manipulating the relative amplitudes of the odd and even harmonics, was developed byDiana Deutschand colleagues.[5]Using this algorithm, gliding tones that appear to ascend or descend endlessly are also produced. This development has led to the intriguing possibility that, using this new algorithm, one might transform banks of natural instrument samples so as to produce tones that sound like those of natural instruments but still have the property of circularity. This development opens up new avenues for music composition and performance.[6]
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Cantor's diagonal argument(among various similar names[note 1]) is amathematical proofthat there areinfinite setswhich cannot be put intoone-to-one correspondencewith the infinite set ofnatural numbers– informally, that there aresetswhich in some sense contain more elements than there are positive integers. Such sets are now calleduncountable sets, and the size of infinite sets is treated by the theory ofcardinal numbers, which Cantor began.
Georg Cantorpublished this proof in 1891,[1][2]: 20–[3]but it was nothis first proofof the uncountability of thereal numbers, which appeared in 1874.[4][5]However, it demonstrates a general technique that has since been used in a wide range of proofs,[6]including the first ofGödel's incompleteness theorems[2]and Turing's answer to theEntscheidungsproblem. Diagonalization arguments are often also the source of contradictions likeRussell's paradox[7][8]andRichard's paradox.[2]: 27
Cantor considered the setTof all infinitesequencesofbinary digits(i.e. each digit is zero or one).[note 2]He begins with aconstructive proofof the followinglemma:
The proof starts with an enumeration of elements fromT, for example
Next, a sequencesis constructed by choosing the 1st digit ascomplementaryto the 1st digit ofs1(swapping0s for1s and vice versa), the 2nd digit as complementary to the 2nd digit ofs2, the 3rd digit as complementary to the 3rd digit ofs3, and generally for everyn, then-th digit as complementary to then-th digit ofsn. For the example above, this yields
By construction,sis a member ofTthat differs from eachsn, since theirn-th digits differ (highlighted in the example).
Hence,scannot occur in the enumeration.
Based on this lemma, Cantor then uses aproof by contradictionto show that:
The proof starts by assuming thatTiscountable.
Then all its elements can be written in an enumerations1,s2, ... ,sn, ... .
Applying the previous lemma to this enumeration produces a sequencesthat is a member ofT, but is not in the enumeration. However, ifTis enumerated, then every member ofT, including thiss, is in the enumeration. This contradiction implies that the original assumption is false. Therefore,Tis uncountable.[1]
The uncountability of thereal numberswas already established byCantor's first uncountability proof, but it also follows from the above result. To prove this, aninjectionwill be constructed from the setTof infinite binary strings to the setRof real numbers. SinceTis uncountable, theimageof this function, which is a subset ofR, is uncountable. Therefore,Ris uncountable. Also, by using a method of construction devised by Cantor, abijectionwill be constructed betweenTandR. Therefore,TandRhave the same cardinality, which is called the "cardinality of the continuum" and is usually denoted byc{\displaystyle {\mathfrak {c}}}or2ℵ0{\displaystyle 2^{\aleph _{0}}}.
An injection fromTtoRis given by mapping binary strings inTtodecimal fractions, such as mappingt= 0111... to the decimal 0.0111.... This function, defined byf(t) = 0.t, is an injection because it maps different strings to different numbers.[note 4]
Constructing a bijection betweenTandRis slightly more complicated.
Instead of mapping 0111... to the decimal 0.0111..., it can be mapped to thebase-bnumber: 0.0111...b. This leads to the family of functions:fb(t) = 0.tb. The functionsfb(t)are injections, except forf2(t). This function will be modified to produce a bijection betweenTandR.
This construction uses a method devised by Cantor that was published in 1878. He used it to construct a bijection between theclosed interval[0, 1] and theirrationalsin theopen interval(0, 1). He first removed acountably infinitesubset from each of these sets so that there is a bijection between the remaining uncountable sets. Since there is a bijection between the countably infinite subsets that have been removed, combining the two bijections produces a bijection between the original sets.[9]
Cantor's method can be used to modify the functionf2(t) = 0.t2to produce a bijection fromTto (0, 1). Because some numbers have two binary expansions,f2(t)is not eveninjective. For example,f2(1000...) =0.1000...2= 1/2 andf2(0111...) =0.0111...2=1/4 + 1/8 + 1/16 + ...=1/2, so both 1000... and 0111... map to the same number, 1/2.
To modifyf2(t), observe that it is a bijection except for a countably infinite subset of (0, 1) and a countably infinite subset ofT. It is not a bijection for the numbers in (0, 1) that have twobinary expansions. These are calleddyadicnumbers and have the formm/2nwheremis an odd integer andnis a natural number. Put these numbers in the sequence:r= (1/2, 1/4, 3/4, 1/8, 3/8, 5/8, 7/8, ...). Also,f2(t)is not a bijection to (0, 1) for the strings inTappearing after thebinary pointin the binary expansions of 0, 1, and the numbers in sequencer. Put these eventually-constant strings in the sequence:s= (000...,111..., 1000..., 0111..., 01000..., 00111..., 11000..., 10111..., ...). Define the bijectiong(t) fromTto (0, 1): Iftis thenthstring in sequences, letg(t) be thenthnumber in sequencer; otherwise,g(t) = 0.t2.
To construct a bijection fromTtoR, start with thetangent functiontan(x), which is a bijection from (−π/2, π/2) toR(see the figure shown on the right). Next observe that thelinear functionh(x) =πx– π/2is a bijection from (0, 1) to (−π/2, π/2) (see the figure shown on the left). Thecomposite functiontan(h(x)) =tan(πx– π/2)is a bijection from (0, 1) toR. Composing this function withg(t) produces the function tan(h(g(t))) =tan(πg(t) – π/2), which is a bijection fromTtoR.
A generalized form of the diagonal argument was used by Cantor to proveCantor's theorem: for everysetS, thepower setofS—that is, the set of allsubsetsofS(here written asP(S))—cannot be inbijectionwithSitself. This proof proceeds as follows:
Letfbe anyfunctionfromStoP(S). It suffices to prove thatfcannot besurjective. This means that some memberTofP(S), i.e. some subset ofS, is not in theimageoff. As a candidate consider the set
For everysinS, eithersis inTor not. Ifsis inT, then by definition ofT,sis not inf(s), soTis not equal tof(s). On the other hand, ifsis not inT, then by definition ofT,sis inf(s), so againTis not equal tof(s); see picture.
For a more complete account of this proof, seeCantor's theorem.
With equality defined as the existence of a bijection between their underlying sets, Cantor also defines binary predicate of cardinalities|S|{\displaystyle |S|}and|T|{\displaystyle |T|}in terms of theexistence of injectionsbetweenS{\displaystyle S}andT{\displaystyle T}. It has the properties of apreorderand is here written "≤{\displaystyle \leq }". One can embed the naturals into the binary sequences, thus proving variousinjection existencestatements explicitly, so that in this sense|N|≤|2N|{\displaystyle |{\mathbb {N} }|\leq |2^{\mathbb {N} }|}, where2N{\displaystyle 2^{\mathbb {N} }}denotes the function spaceN→{0,1}{\displaystyle {\mathbb {N} }\to \{0,1\}}. But following from the argument in the previous sections, there isno surjectionand so also no bijection, i.e. the set is uncountable. For this one may write|N|<|2N|{\displaystyle |{\mathbb {N} }|<|2^{\mathbb {N} }|}, where "<{\displaystyle <}" is understood to mean the existence of an injection together with the proven absence of a bijection (as opposed to alternatives such as the negation of Cantor's preorder, or a definition in terms ofassignedordinals). Also|S|<|P(S)|{\displaystyle |S|<|{\mathcal {P}}(S)|}in this sense, as has been shown, and at the same time it is the case that¬(|P(S)|≤|S|){\displaystyle \neg (|{\mathcal {P}}(S)|\leq |S|)}, for all setsS{\displaystyle S}.
Assuming thelaw of excluded middle,characteristic functionssurject onto powersets, and then|2S|=|P(S)|{\displaystyle |2^{S}|=|{\mathcal {P}}(S)|}. So the uncountable2N{\displaystyle 2^{\mathbb {N} }}is also not enumerable and it can also be mapped ontoN{\displaystyle {\mathbb {N} }}. Classically, theSchröder–Bernstein theoremis valid and says that any two sets which are in the injective image of one another are in bijection as well. Here, every unbounded subset ofN{\displaystyle {\mathbb {N} }}is then in bijection withN{\displaystyle {\mathbb {N} }}itself, and everysubcountableset (a property in terms of surjections) is then already countable, i.e. in the surjective image ofN{\displaystyle {\mathbb {N} }}. In this context the possibilities are then exhausted, making "≤{\displaystyle \leq }" anon-strict partial order, or even atotal orderwhen assumingchoice. The diagonal argument thus establishes that, although both sets under consideration are infinite, there are actuallymoreinfinite sequences of ones and zeros than there are natural numbers.
Cantor's result then also implies that the notion of theset of all setsis inconsistent: IfS{\displaystyle S}were the set of all sets, thenP(S){\displaystyle {\mathcal {P}}(S)}would at the same time be bigger thanS{\displaystyle S}and a subset ofS{\displaystyle S}.
Also inconstructive mathematics, there is no surjection from the full domainN{\displaystyle {\mathbb {N} }}onto the space of functionsNN{\displaystyle {\mathbb {N} }^{\mathbb {N} }}or onto the collection of subsetsP(N){\displaystyle {\mathcal {P}}({\mathbb {N} })}, which is to say these two collections are uncountable. Again using "<{\displaystyle <}" for proven injection existence in conjunction with bijection absence, one hasN<2N{\displaystyle {\mathbb {N} }<2^{\mathbb {N} }}andS<P(S){\displaystyle S<{\mathcal {P}}(S)}. Further,¬(P(S)≤S){\displaystyle \neg ({\mathcal {P}}(S)\leq S)}, as previously noted. Likewise,2N≤NN{\displaystyle 2^{\mathbb {N} }\leq {\mathbb {N} }^{\mathbb {N} }},2S≤P(S){\displaystyle 2^{S}\leq {\mathcal {P}}(S)}and of courseS≤S{\displaystyle S\leq S}, also inconstructive set theory.
It is however harder or impossible to order ordinals and also cardinals, constructively. For example, the Schröder–Bernstein theorem requires the law of excluded middle.[10]In fact, the standard ordering on the reals, extending the ordering of the rational numbers, is not necessarily decidable either. Neither are most properties of interesting classes of functions decidable, byRice's theorem, i.e. the set of counting numbers for the subcountable sets may not berecursiveand can thus fail to be countable. The elaborate collection of subsets of a set is constructively not exchangeable with the collection of its characteristic functions. In an otherwise constructive context (in which the law of excluded middle is not taken as axiom), it is consistent to adopt non-classical axioms that contradict consequences of the law of excluded middle. Uncountable sets such as2N{\displaystyle 2^{\mathbb {N} }}orNN{\displaystyle {\mathbb {N} }^{\mathbb {N} }}may be asserted to besubcountable.[11][12]This is a notion of size that is redundant in the classical context, but otherwise need not imply countability. The existence of injections from the uncountable2N{\displaystyle 2^{\mathbb {N} }}orNN{\displaystyle {\mathbb {N} }^{\mathbb {N} }}intoN{\displaystyle {\mathbb {N} }}is here possible as well.[13]So the cardinal relation fails to beantisymmetric. Consequently, also in the presence of function space sets that are even classically uncountable,intuitionistsdo not accept this relation to constitute a hierarchy of transfinite sizes.[14]When theaxiom of powersetis not adopted, in a constructive framework even the subcountability of all sets is then consistent. That all said, in common set theories, the non-existence of a set of all sets also already follows fromPredicative Separation.
In a set theory, theories of mathematics aremodeled. Weaker logical axioms mean fewer constraints and so allow for a richer class of models. A set may be identified as amodel of the field of real numberswhen it fulfills someaxioms of real numbersor aconstructive rephrasingthereof. Various models have been studied, such as theCauchy realsor theDedekind reals, among others. The former relate to quotients of sequences while the later are well-behaved cuts taken from a powerset, if they exist. In the presence of excluded middle, those are all isomorphic and uncountable. Otherwise,variantsof the Dedekind reals can be countable[15]or inject into the naturals, but not jointly. When assumingcountable choice, constructive Cauchy reals even without an explicitmodulus of convergenceare thenCauchy-complete[16]and Dedekind reals simplify so as to become isomorphic to them. Indeed, here choice also aids diagonal constructions and when assuming it, Cauchy-complete models of the reals are uncountable.
Russell's paradoxhas shown that set theory that includes anunrestricted comprehensionscheme is contradictory. Note that there is a similarity between the construction ofTand the set in Russell's paradox. Therefore, depending on how we modify the axiom scheme of comprehension in order to avoid Russell's paradox, arguments such as the non-existence of a set of all sets may or may not remain valid.
Analogues of the diagonal argument are widely used in mathematics to prove the existence or nonexistence of certain objects. For example, the conventional proof of the unsolvability of thehalting problemis essentially a diagonal argument. Also, diagonalization was originally used to show the existence of arbitrarily hardcomplexity classesand played a key role in early attempts to proveP does not equal NP.
The above proof fails forW. V. Quine's "New Foundations" set theory (NF). In NF, thenaive axiom scheme of comprehensionis modified to avoid the paradoxes by introducing a kind of "local"type theory. In this axiom scheme,
isnota set — i.e., does not satisfy the axiom scheme. On the other hand, we might try to create a modified diagonal argument by noticing that
isa set in NF. In which case, ifP1(S) is the set of one-element subsets ofSandfis a proposed bijection fromP1(S) toP(S), one is able to useproof by contradictionto prove that |P1(S)| < |P(S)|.
The proof follows by the fact that iffwere indeed a mapontoP(S), then we could findrinS, such thatf({r}) coincides with the modified diagonal set, above. We would conclude that ifris not inf({r}), thenris inf({r}) and vice versa.
It isnotpossible to putP1(S) in a one-to-one relation withS, as the two have different types, and so any function so defined would violate the typing rules for the comprehension scheme.
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https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument
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Translation studiesis an academicinterdisciplinedealing with the systematic study of the theory, description and application oftranslation,interpreting, andlocalization. As an interdiscipline, translation studies borrows much from the various fields of study that support translation. These includecomparative literature,computer science,history,linguistics,philology,philosophy,semiotics, andterminology.
The term “translation studies” was coined by the Amsterdam-based American scholarJames S. Holmesin his 1972 paper “The name and nature of translation studies”, which is considered a foundational statement for the discipline. Writers in English occasionally use the term "translatology" (and less commonly "traductology") to refer to translation studies, and the corresponding French term for the discipline is usuallytraductologie(as in theSociété Française de Traductologie). In the United States, there is a preference for the term "translation and interpreting studies" (as in the American Translation and Interpreting Studies Association), although European tradition includes interpreting within translation studies (as in theEuropean Society for Translation Studies).
Historically, translation studies has long been "prescriptive" (telling translators how to translate), to the point that discussions of translation that were not prescriptive were generally not considered to be about translation at all. When historians of translation studies trace early Western thought about translation, for example, they most often set the beginning at the renowned oratorCicero's remarks on how he used translation from Greek to Latin to improve his oratorical abilities—an early description of whatJeromeended up callingsense-for-sense translation. The descriptive history of interpreters in Egypt provided byHerodotusseveral centuries earlier is typically not thought of as translation studies—presumably because it does not tell translators how to translate. InChina, the discussion onhow to translateoriginated with the translation ofBuddhist sutrasduring theHan dynasty.
In 1958, at the Fourth Congress of Slavists in Moscow, the debate between linguistic and literary approaches to translation reached a point where it was proposed that the best thing might be to have a separate science that was able to study all forms of translation, without being wholly within linguistics or wholly within literary studies.[1]Within comparative literature, translation workshops were promoted in the 1960s in some American universities like theUniversity of IowaandPrinceton.[2]
During the 1950s and 1960s, systematic linguistic-oriented studies of translation began to appear. In 1958, the French linguistsJean-Paul Vinayand Jean Darbelnet carried out a contrastive comparison of French and English.[3]In 1964,Eugene NidapublishedToward a Science of Translating, a manual forBible translationinfluenced to some extent byHarris'stransformational grammar.[4]In 1965,J. C. Catfordtheorized translation from a linguistic perspective.[5]In the 1960s and early 1970s, the Czech scholarJiří Levýand the Slovak scholarsAnton Popovičand František Miko worked on the stylistics of literary translation.[6]
These initial steps toward research on literary translation were collected in James S. Holmes' paper at the Third International Congress of Applied Linguistics held inCopenhagenin 1972. In that paper, "The name and nature of translation studies", Holmes asked for the consolidation of a separate discipline and proposed a classification of the field. A visual "map" of Holmes' proposal was later presented byGideon Touryin his 1995Descriptive Translation Studies and beyond.[7]
Before the 1990s, translation scholars tended to form particular schools of thought, particularly within the prescriptive, descriptive and Skopos paradigms. Since the "cultural turn" in the 1990s, the discipline has tended to divide into separate fields of inquiry, where research projects run parallel to each other, borrowing methodologies from each other and from other academic disciplines.
The main schools of thought on the level of research have tended to cluster around key theoretical concepts, most of which have become objects of debate.
Through to the 1950s and 1960s, discussions in translation studies tended to concern how best to attain "equivalence". The term "equivalence" had two distinct meanings, corresponding to different schools of thought. In the Russian tradition, "equivalence" was usually a one-to-one correspondence between linguistic forms, or a pair of authorized technical terms or phrases, such that "equivalence" was opposed to a range of "substitutions". However, in the French tradition of Vinay and Darbelnet, drawing onBally, "equivalence" was the attainment of equal functional value, generally requiringchangesin form.Catford's notion of equivalence in 1965 was as in the French tradition. In the course of the 1970s, Russian theorists adopted the wider sense of "equivalence" as somethingresultingfromlinguistic transformations.
At about the same time, theInterpretive Theory of Translation[8]introduced the notion of deverbalized sense into translation studies, drawing a distinction between word correspondences and sense equivalences, and showing the difference between dictionary definitions of words and phrases (word correspondences) and the sense of texts or fragments thereof in a given context (sense equivalences).
The discussions of equivalence accompanied typologies of translation solutions (also called "procedures", "techniques" or "strategies"), as in Fedorov (1953) and Vinay and Darbelnet (1958). In 1958, Loh Dianyang'sTranslation: Its Principles and Techniques(英汉翻译理论与技巧) drew on Fedorov and English linguistics to present a typology of translation solutions between Chinese and English.
In these traditions, discussions of the ways to attain equivalence have mostly been prescriptive and have been related to translator training.
Descriptive translation studies aims at building an empirical descriptive discipline, to fill one section of the Holmes map. The idea that scientific methodology could be applicable to cultural products had been developed by the Russian Formalists in the early years of the 20th century, and had been recovered by various researchers incomparative literature. It was now applied to literary translation. Part of this application was thetheory of polysystems(Even-Zohar 1990[9]) in which translated literature is seen as a sub-system of the receiving or target literary system. Gideon Toury bases his theory on the need to consider translations as "facts of the target culture" for the purposes of research. The concepts of "manipulation"[10]and "patronage"[11]have also been developed in relation to literary translations.
Another discovery in translation theory can be dated from 1984 in Europe and the publication of two books in German:Foundation for a General Theory of TranslationbyKatharina Reiss(also written Reiß) andHans Vermeer,[12]andTranslatorial Action(Translatorisches Handeln) by Justa Holz-Mänttäri.[13]From these two came what is known asSkopos theory, which gives priority to the purpose to be fulfilled by the translation instead of prioritizing equivalence.
The cultural turn meant still another step forward in the development of the discipline. It was sketched bySusan BassnettandAndré LefevereinTranslation - History - Culture, and quickly represented by the exchanges between translation studies and other area studies and concepts:gender studies, cannibalism, post-colonialism[14]or cultural studies, among others.
The concept of "cultural translation" largely ensues fromHomi Bhabha's reading ofSalman RushdieinThe Location of Culture.[15]Cultural translation is a concept used incultural studiesto denote the process of transformation, linguistic or otherwise, in a givenculture.[16]The concept uses linguistic translation as a tool or metaphor in analyzing the nature of transformation and interchange in cultures.
Translation history concerns the history of translators as a professional and social group, as well as the history of translations as indicators of the way cultures develop, interact and may die. Some principles for translation history have been proposed by Lieven D'hulst[17]andPym.[18]Major projects in translation history have included theOxford History of Literary Translation in English[19]andHistoire des traductions en langue française.[20]
Historical anthologies of translation theories have been compiled byRobinson(2002)[21]for Western theories up to Nietzsche; by D'hulst (1990)[22]for French theories, 1748–1847; by Santoyo (1987)[23]for the Spanish tradition; byEdward Balcerzan(1977)[24]for the Polish experience, 1440–1974; and byCheung(2006)[25]for Chinese.
The sociology of translation includes the study of who translators are, what their forms of work are (workplace studies) and what data on translations can say about the movements of ideas between languages.
Post-colonial studies look at translations between a metropolis and former colonies, or within complex former colonies.[26]They radically question the assumption that translation occurs between cultures and languages that are radically separated.
Gender studies look at the sexuality of translators,[27]at the gendered nature of the texts they translate,[28]at the possibly gendered translation processes employed, and at the gendered metaphors used to describe translation. Pioneering studies are by Luise von Flotow,Sherry Simonand Keith Harvey.[29]The effacement or inability to efface threatening forms of same-sex sexuality is a topic taken up, when for instance ancient writers are translated by Renaissance thinkers in a Christian context.[30]
In the field of ethics, much-discussed publications have been the essays ofAntoine BermanandLawrence Venutithat differ in some aspects but agree on the idea of emphasizing the differences between source and target language and culture when translating. Both are interested in how the "cultural other [...] can best preserve [...] that otherness".[31]In more recent studies, scholars have appliedEmmanuel Levinas' philosophical work on ethics and subjectivity on this issue.[32]As his publications have been interpreted in different ways, various conclusions on his concept of ethical responsibility have been drawn from this. Some have come to the assumption that the idea of translation itself could be ethically doubtful, while others receive it as a call for considering the relationship betweenauthoror text andtranslatoras more interpersonal, thus making it an equal and reciprocal process.
Parallel to these studies, the general recognition of the translator's responsibility has increased. More and more translators and interpreters are being seen as active participants in geopolitical conflicts, which raises the question of how to act ethically independent from their own identity or judgement. This leads to the conclusion that translating and interpreting cannot be considered solely as a process oflanguage transfer, but also as socially and politically directed activities.[33]
There is general agreement on the need for an ethicalcode of practiceproviding some guiding principles to reduce uncertainties and improve professionalism, as having been stated in other disciplines (for examplemilitary medical ethicsorlegal ethics). However, as there is still no clear understanding of the concept ofethicsin this field, opinions about the particular appearance of such a code vary considerably.
Audiovisual translationstudies (AVT) is concerned with translation that takes place in audio and/or visual settings, such as the cinema, television, video games and also some live events such as opera performances.[34]The common denominator for studies in this field is that translation is carried out on multiplesemioticsystems, as the translated texts (so-called polysemiotic texts)[35]have messages that are conveyed through more than one semiotic channel, i.e. not just through the written or spoken word, but also via sound and/or images.[36]The main translation modes under study aresubtitling,film dubbingandvoice-over, but alsosurtitlingfor the opera and theatre.[37]
Media accessibility studies is often considered a part of this field as well,[38]withaudio description for the blind and partially sightedandsubtitles for the deaf or hard-of-hearingbeing the main objects of study. The various conditions and constraints imposed by the different media forms and translation modes, which influence how translation is carried out, are often at the heart of most studies of the product or process of AVT. Many researchers in the field of AVT Studies are organized in the European Association for Studies in Screen Translation, as are many practitioners in the field.
Non-professional translation refers to the translation activities performed by translators who are not working professionally, usually in ways made possible by the Internet.[39]These practices have mushroomed with the recentdemocratization of technologyand the popularization of the Internet. Volunteer translation initiatives have emerged all around the world, and deal with the translations of various types of written and multimedia products.
Normally, it is not required for volunteers to have been trained in translation, but trained translators could also participate, such as the case of Translators without Borders.[40]
Depending on the feature that each scholar considers the most important, different terms have been used to label "non-professional translation". O'Hagan has used "user-generated translation",[41]"fan translation"[42]and "community translation".[39]Fernández-Costales and Jiménez-Crespo prefer "collaborative translation",[43]while Pérez-González labels it "amateur subtitling".[44]Pym proposes that the fundamental difference between this type of translation and professional translation relies on monetary reward, and he suggests it should be called "volunteer translation".[45]
Some of the most popular fan-controlled non-professional translation practices arefansubbing,fandubbing,ROM hackingorfan translation of video games, andscanlation. These practices are mostly supported by a strong and consolidated fan base, although larger non-professional translation projects normally applycrowdsourcingmodels and are controlled by companies or organizations. Since 2008,Facebookhas used crowdsourcing to have its website translated by its users andTED conferencehas set up the open translation project TED Translators[46]in which volunteers use the Amara[47]platform to create subtitles online for TED talks.
Studies oflocalizationconcern the way the contemporary language industries translate and adapt ("localize") technical texts across languages, tailoring them for a specific "locale" (a target location defined by language variety and various cultural parameters). Localization usually concerns software, product documentation, websites andvideo games, where the technological component is key.[citation needed]
A key concept in localization isinternationalization, in which the start product is stripped of its culture-specific features in such a way that it can be simultaneously localized into several languages.
The field refers to the set of pedagogical approaches used by academic educators to teach translation, train translators, and endeavor to develop the translation discipline thoroughly. Moreover, translation learners face many difficulties in trying to come up with the right equivalence of a particular source text. For these reasons, translation education is an important field of study that encompasses a number of questions to be answered in research.
The discipline of interpreting studies is often referred to as the sister of translation studies. This is due to the similarities between the two disciplines, consisting in the transfer of ideas from one language into another. Indeed, interpreting as an activity was long seen as a specialized form of translation, before scientifically founded interpreting studies emancipated gradually from translation studies in the second half of the 20th century. While they were strongly oriented towards the theoretic framework of translation studies,[48]interpreting studies have always been concentrating on the practical and pedagogical aspect of the activity.[49]This led to the steady emancipation of the discipline and the consecutive development of a separate theoretical framework based—as are translation studies—on interdisciplinary premises. Interpreting studies have developed several approaches and undergone various paradigm shifts,[50]leading to the most recent surge of sociological studies of interpreters and their work(ing conditions).
Metaphoricalusage can challenge translators striving to balance the idiomatic with a natural style; and translation can unmask hidden metaphors.[a]The study of translation "can reveal new insights into the relationship between images and culture".[51]
The study of translating for younger audiences constitutes a relatively young research field that has developed profoundly in the four decades, ever sinceGöte Klingberg, Swedish researcher and pedagogue, organized an International Research in Children’s Literature (IRSCL) conference in Södertälje in Sweden 1976 on the translation of children’s literature. Since then, the field has attempted to build its own research area and to gain independence and recognition from other fields. Indeed, children’s literature had itself suffered from low prestige globally and its combination with translation studies had made it considered a minor research interest in disciplines of greater standing at the time, such as comparative literature, linguistics and even translation studies.[citation needed]
However, due to the recent economic success of children’s and young adult literature, the establishment of international literary prizes like theAstrid Lindgren Memorial Award (ALMA), and the existence of a large number of institutions such as IRSCL (International Research Society for Children’s Literature), in addition to IBBY (International Board on Books for Young People), established scientific research/journals (The Lion and the Unicorn: A Critical Journal of Children’s Literature, Hopkins Press orBarnboken, The Swedish Institute for Children’s Books), as well as courses in children’s literature at the university level, children’s literature has gained enough prestige since the beginning of the century to be considered its own discipline.[citation needed]
Translation studies is also a relatively new and established scientific discipline, having been grouped together with linguistics or the study of literature after World War II. Despite the seminal work of Zohar Shavit (1986), who studied children’s literature through the lens of polysystem theory, children’s literature only began to get traction in translation studies around the turn of the century. According to Borodo, “it was not before 2000 that the term 'children’s literature translation studies' (CLTS) seems to have first appeared in [an] article by Fernández López" (cited in Borodo 2017:36).[citation needed]At the beginning of the 2000s, the field grew fast, but still, few researchers identified with this field, as the discipline was not distinct (See Borodo’s Children’s Literature Translation Studies survey from 2007 in Borodo 2017:40).[citation needed]At this point things picked up with the publication of some fundamental books for the discipline such as Riita Oittinen’sTranslating for Children(2000) and Gillian Lathey’sThe Translation of Children’s Literature. A Reader(2006). Then, the discipline finally got its own entries in, e.g.,The Routledge Encyclopedia of Translation Studies(2009) by Lathey,The Routledge Handbook of Translation Studies(2010) by Alvstad, then (2013) by O’Sullivan, and much later inThe Routledge Handbook of Literary Translation(2018) by Alvstad – showing a recognition of the intersection between those two disciplines.[citation needed]
Some international conferences on translation and children’s literature were organized: in 2004 in Brussels there was “Children’s Literature in Translation: Challenges and Strategies”; in 2005 in London, “No Child is an Island: The Case of Children’s Books in Translation” (IBBY- International Board on Books for Young People); in 2012 in London “Crossing Boundaries: Translations and Migrations’ (IBBY) and in Brussels and Antwerp in 2017 by the Center of Reception Studies (CERES): “Translation Studies and Children’s Literature” (KU Leuven/Antwerp University), which resulted in a notable publicationChildren’s Literature in Translation, Texts and Contexts(2020) by Jan van Coillie and Jack McMartin. This publication won the IRSCL Edited Book Award 2021, providing official recognition of CLTS.[citation needed]
The pandemic put a stop to international events meeting face-to-face, but to compensate for the need of scholars to meet and interact, Pilar Alderete Diez from the University of Galway (IR) with the support of Owen Harrington from Heriot-Watt University (UK) created the Children in Translation Network (CITN) in 2021 and a webinar series on translation studies and children’s literature. The success was immediate, providing evidence of the interest in the discipline, and gathering more than 150 participants from 21 different countries.[citation needed]
The most recent international conference in CLTS was organized 2024 The Institute of Interpreting and Translation Studies (TÖI) of Stockholm University in Sweden under the banner of “New Voices in Children’s Literature in Translation: Culture, Power and Transnationalism”.[citation needed]The conference was held 22-23 August 2024 in Stockholm in Sweden, and around 120 persons attended from around 40 different countries with more than 80 presentations in two days.[citation needed]
As attested by the number of scientific articles/books in this specific area (e.g., 17,400[citation needed]results on Google Scholar for the period 2017-2023;[citation needed]3,338 results on EBSCO host for the same period[citation needed]), the creation of courses at the university level devoted solely to translation and children’s literature, the number of theses and dissertations being defended in this area, recent international conferences and networks like CITN identifying the growing interest for this discipline.[citation needed]
Translation studies has developed alongside the growth in translation schools and courses at the university level. In 1995, a study of 60 countries revealed there were 250 bodies at university level offering courses in translation or interpreting.[52]In 2013, the same database listed 501 translator-training institutions.[53]Accordingly, there has been a growth in conferences on translation, translation journals and translation-related publications. The visibility acquired by translation has also led to the development of national and international associations of translation studies. Ten of these associations formed the International Network of Translation and Interpreting Studies Associations in September 2016.
The growing variety of paradigms is mentioned as one of the possible sources of conflict in the discipline. As early as 1999, the conceptual gap between non-essentialist and empirical approaches came up for debate at the Vic Forum on Training Translators and Interpreters: New Directions for the Millennium. The discussants, Rosemary Arrojo andAndrew Chesterman, explicitly sought common shared ground for both approaches.[54]
Interdisciplinarity has made the creation of new paradigms possible, as most of the developed theories grew from contact with other disciplines like linguistics, comparative literature, cultural studies, philosophy, sociology or historiography. At the same time, it might have provoked the fragmentation of translation studies as a discipline on its own right.[55]
A second source of conflict rises from the breach between theory and practice. As the prescriptivism of the earlier studies gives room to descriptivism and theorization, professionals see less applicability of the studies. At the same time, university research assessment places little if any importance on translation practice.[56]
Translation studies has shown a tendency to broaden its fields of inquiry, and this trend may be expected to continue. This particularly concerns extensions into adaptation studies, intralingual translation, translation between semiotic systems (image to text to music, for example), and translation as the form of all interpretation and thus of all understanding, as suggested in Roman Jakobson's work,On Linguistic Aspects of Translation.[citation needed]
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Partial-matchingis a technique that can be used with aMITM attack. Partial-matching is where the intermediate values of the MITM attack,i{\displaystyle i}andj{\displaystyle j}, computed from the plaintext and ciphertext, are matched on only a few select bits, instead of on the complete state.
A limitation with MITM attacks is the amount of intermediate values that needs to be stored. In order to compare the intermediate valuesi{\displaystyle i}andj{\displaystyle j}, alli{\displaystyle i}'s need to be computed and stored first, before each computedj{\displaystyle j}can be compared against them.
If the two subciphers identified by the MITM attack both has a sufficiently large subkey, then an unfeasible amount of intermediate values need to be stored.
While there are techniques such as cycle detection algorithms[1]that allows one to perform a MITM attack without storing either all values ofi{\displaystyle i}orj{\displaystyle j}, these techniques requires that the subciphers of the MITM attack are symmetric.
Thus it is a solution that allows one to perform a MITM attack in a situation, where the subkeys are of a cardinality just large enough to make the amount of temporary values that need to be stored infeasible.
While this allows one to store more temporary values, its use is still limited, as it only allows one to perform a MITM attack on a subcipher with a few more bits. As an example: If only 1/8 of the intermediate value is stored, then the subkey needs only be 3 bits larger, before the same amount of memory is required anyway, since2−3=1/8{\displaystyle 2^{-3}=1/8}
A in most cases far more useful feature provided by partial-matching in MITM attacks, is the ability to compare intermediate values computed at different rounds in the attacked cipher. If the diffusion in each round of the cipher is low enough, it might be possible over a span of rounds to find bits in the intermediate states that has not changed with a probability of 1. These bits in the intermediate states can still be compared.
The disadvantage for both of these uses, is that there will be more false positives for key candidates, which needs to be tested.
As a rule, the chance for a false positive is given by the probability2−|i|{\displaystyle 2^{-|i|}}, where|i|{\displaystyle |i|}is the amount of matched bits.
For a step-by-step example of the complete attack on KTANTAN,[2]see the example on the3-subset MITMpage. This example only deals with the part that needs partial-matching.What is useful to know is that KTANTAN is a 254-round blockcipher, where each round uses 2 bits from the 80-bit key.
In the 3-subset attack on the KTANTAN family of ciphers, it was necessary to utilize partial-matching in order to stage the attack. Partial-matching was needed, because the intermediate values of the plain- and ciphertext in the MITM attack, were computed at the end of round 111 and at the start of round 131, respectively. Since they had a span of 20 rounds between them, they could not be compared directly.
The authors of the attack, however, identified some useful characteristics of KTANTAN that held with a probability of 1. Due to the low diffusion per round in KTANTAN (the security is in the number of rounds), they found out by computing forwards from round 111 and backwards from round 131 that at round 127, 8 bits from both intermediate states would remain unchanged. (It was 8 bits at round 127 for KTANTAN32. It was 10 bits at round 123 and 47 bits at round 131 for KTANTAN48 and KTANTAN64, respectively). by only comparing the 8 bits of each intermediate value, the authors was able to orchestrate a MITM attack on the cipher, despite there being 20 rounds between the two subciphers.
Using partial-matching increased the amount of false positives, but nothing that noticeably increased the complexity of the attack.
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MobileStar Networkwas awireless Internet service providerwhich first gained notability in deploying Wi-Fi Internet access points inStarbuckscoffee shops,American AirlinesAdmiral Club locations across theUnited Statesand at Hilton Hotels. Founded by Mark Goode and Greg Jackson in 1998, MobileStar was the first wireless ISP to place a WiFi hotspot in an airport, a hotel, or a coffee shop. MobileStar's core value proposition was to provide wireless broadband connectivity for the business traveler in all the places s/he was likely to "sleep, eat, move, or meet." MobileStar's founder, Mark Goode, was the first to coin the now industry standard expression "hotspot," as a reference to a location equipped with an 802.11 wireless access point.
MobileStar's financing was initially provided by Greg Jackson. A predecessor entity, PLANCOM (Public Local Area Network Communications), was disbanded and the intellectual property moved into MobileStar Network. During the Series A financing round, funds were obtained from high-net-worth investors, corporate investors including Proxim and Comdisco, and institutional investors from New York. The Series B investors, who invested $38 million, included theMayfield Fund[1]and Blueprint Ventures.
MobileStar's initial deployments used a frequency hopping product supplied by Proxim. As reported in the EE Times, "In a move that represents the first use of unlicensed wireless LAN technology in the industrial scientific and medical (ISM) bands to develop a nationwide Internet-access network, Proxim Inc. has teamed up with Dallas-based MobileStar Network Inc. to link its 2.4-GHz unlicensed RangeLAN2 wireless LAN to a national network of Internet access points." However, after the IEEE 802.11b standard was adopted, MobileStar converted its network infrastructure to the 802.11b industry standard. The initial infrastructure was manufactured and financed by Cisco.
MobileStar's founders faced many challenges in developing the company: evolving technology standards, fluid business models, no industry standard billing system, and questions about the competitive value of a site license agreement instead of licensed spectrum. Over time each of these issues were addressed and the agreement with Starbucks in late 2000 signaled a maturing of the marketplace.[2]American Airlines also entered into an agreement with MobileStar[3]as did Hilton Hotels[4]As more laptop vendors included integrated 802.11 wireless connectivity within their laptops, users came to expect broadband connectivity in their residences, workplaces, and in public locations such as airports, coffee shops, and hotels. License-free broadband connectivity exploded with the advent of the iPhone in 2007, further validating the premise that license-free spectrum could open up a large domain of connectivity at a cost far less than licensed spectrum. The rise of voice over IP (VOIP) communications operating on the 2.4 MHz spectrum via the 802.11 standard was another indicator of the power of ubiquitous, low to no cost wireless broadband communications.
MobileStar Network's demise in 2001 was the result of at least two important factors: the collapse in the private equity markets in mid-2001 and the events of September 11. While MobileStar's investors provided a bridge loan during the mid-2001 time frame, the terrorist attacks in New York and Washington brought a steep decline in business travel, MobileStar Network's initial core market. MobileStar's investors could not continue to finance the business and new investors were skittish about investing in a company focused on serving a market that had recently and rapidly collapsed.
MobileStar Network ceased operation in October 2001, but its bankrupt assets and contracts were bought byVoicestream Wirelessand by February 2002, was operating asT-MobileBroadband. T-Mobile Broadband was the first part of VoiceStream to rebrand to the T-Mobile name. It was officially launched as T-Mobile HotSpot in August 2002.[5]Many of the original MobileStar Network employees still work for T-Mobile Hotspot and have been responsible for its expansion.
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Semiotics(/ˌsɛmiˈɒtɪks/SEM-ee-OT-iks) is the systematic study ofsign processesand the communication ofmeaning. In semiotics, asignis defined as anything that communicates intentional and unintentional meaning or feelings to the sign's interpreter.
Semiosis is any activity, conduct, or process that involves signs. Signs often are communicated by verbal language, but also by gestures, or by other forms of language, e.g. artistic ones (music, painting, sculpture, etc.). Contemporary semiotics is a branch of science that generally studies meaning-making (whether communicated or not) and various types of knowledge.[1]
Unlikelinguistics, semiotics also studies non-linguisticsign systems. Semiotics includes the study of indication, designation, likeness,analogy,allegory,metonymy,metaphor,symbolism, signification, and communication.
Semiotics is frequently seen as having importantanthropologicalandsociologicaldimensions. Some semioticians regard every cultural phenomenon as being able to be studied as communication.[2]Semioticians also focus on thelogicaldimensions of semiotics, examiningbiologicalquestions such as how organisms make predictions about, and adapt to, their semioticnichein the world.
Fundamental semiotic theories take signs or sign systems as their object of study. Applied semiotics analyzes cultures and cultural artifacts according to the ways they construct meaning through their being signs. The communication of information in living organisms is covered inbiosemioticsincludingzoosemioticsandphytosemiotics.
The importance of signs and signification has been recognized throughout much of the history ofphilosophyandpsychology. The term derives fromAncient Greekσημειωτικός(sēmeiōtikós)'observant of signs'[3](fromσημεῖον(sēmeîon)'a sign, mark, token').[4]For the Greeks, 'signs' (σημεῖονsēmeîon) occurred in the world of nature and 'symbols' (σύμβολονsýmbolon) in the world of culture. As such,PlatoandAristotleexplored the relationship between signs and the world.[5]
It would not be untilAugustine of Hippo[6]that the nature of the sign would be considered within a conventional system. Augustine introduced a thematic proposal for uniting the two under the notion of 'sign' (signum) as transcending thenature–culture divideand identifying symbols as no more than a species (or sub-species) ofsignum.[7]A monograph study on this question was done by Manetti (1987).[8][a]These theories have had a lasting effect inWestern philosophy, especially throughscholasticphilosophy.[citation needed]
The general study of signs that began in Latin with Augustine culminated with the 1632Tractatus de SignisofJohn Poinsotand then began anew in late modernity with the attempt in 1867 byCharles Sanders Peirceto draw up a "new list ofcategories". More recentlyUmberto Eco, in hisSemiotics and the Philosophy of Language, has argued that semiotic theories are implicit in the work of most, perhaps all, major thinkers.[citation needed]
John Locke(1690), himself a man ofmedicine, was familiar with this "semeiotics" as naming a specialized branch within medical science. In his personal library were two editions of Scapula's 1579 abridgement ofHenricus Stephanus'Thesaurus Graecae Linguae, which listedσημειωτικήas the name for'diagnostics',[9]the branch of medicine concerned with interpreting symptoms of disease ("symptomatology"). Physician and scholarHenry Stubbe(1670) had transliterated this term of specialized science into English precisely as "semeiotics", marking the first use of the term in English:[10]
"...nor is there any thing to be relied upon in Physick, but an exact knowledge of medicinal phisiology (founded on observation, not principles), semeiotics, method of curing, and tried (not excogitated, not commanding) medicines...."
Locke would use the termsem(e)iotikeinAn Essay Concerning Human Understanding(book IV, chap. 21),[11][b]in which he explains how science may be divided into three parts:[12]: 174
All that can fall within the compass of human understanding, being either, first, the nature of things, as they are in themselves, their relations, and their manner of operation: or, secondly, that which man himself ought to do, as a rational and voluntary agent, for the attainment of any end, especially happiness: or, thirdly, the ways and means whereby the knowledge of both the one and the other of these is attained and communicated; I think science may be divided properly into these three sorts.
Locke then elaborates on the nature of this third category, naming itΣημειωτική(Semeiotike), and explaining it as "the doctrine of signs" in the following terms:[12]: 175
Thirdly, the third branch [of sciences] may be termedσημειωτικὴ, or the doctrine of signs, the most usual whereof being words, it is aptly enough termed alsoΛογικὴ, logic; the business whereof is to consider the nature of signs the mind makes use of for the understanding of things, or conveying its knowledge to others.
Juri Lotmanintroduced Eastern Europe to semiotics and adopted Locke's coinage (Σημειωτική) as the name to subtitle his founding at theUniversity of Tartuin Estonia in 1964 of the first semiotics journal,Sign Systems Studies.
Ferdinand de Saussurefounded his semiotics, which he calledsemiology, in the social sciences:[13]
It is...possible to conceive of a science which studies the role of signs as part of social life. It would form part of social psychology, and hence of general psychology. We shall call it semiology (from the Greeksemeîon, 'sign'). It would investigate the nature of signs and the laws governing them. Since it does not yet exist, one cannot say for certain that it will exist. But it has a right to exist, a place ready for it in advance. Linguistics is only one branch of this general science. The laws which semiology will discover will be laws applicable in linguistics, and linguistics will thus be assigned to a clearly defined place in the field of human knowledge.
Thomas Sebeok[c]would assimilatesemiologytosemioticsas a part to a whole, and was involved in choosing the nameSemioticafor the first international journal devoted to the study of signs. Saussurean semiotics have exercised a great deal of influence on the schools of structuralism and post-structuralism.Jacques Derrida, for example, takes as his object the Saussurean relationship of signifier and signified, asserting that signifier and signified are not fixed, coining the expressiondifférance, relating to the endless deferral of meaning, and to the absence of a "transcendent signified".
In the nineteenth century,Charles Sanders Peircedefined what he termed "semiotic" (which he would sometimes spell as "semeiotic") as the "quasi-necessary, or formal doctrine of signs," which abstracts "what must be the characters of all signs used by...an intelligence capable of learning by experience,"[14]and which is philosophical logic pursued in terms of signs and sign processes.[15][16]
Peirce's perspective is considered as philosophical logic studied in terms of signs that are not always linguistic or artificial, and sign processes, modes of inference, and the inquiry process in general. The Peircean semiotic addresses not only the external communication mechanism, as per Saussure, but the internal representation machine, investigating sign processes, and modes of inference, as well as the whole inquiry process in general.[citation needed]
Peircean semiotic is triadic, including sign, object, interpretant, as opposed to the dyadicSaussuriantradition (signifier, signified). Peircean semiotics further subdivides each of the three triadic elements into three sub-types, positing the existence of signs that are symbols; semblances ("icons"); and "indices," i.e., signs that are such through a factual connection to their objects.[17]
Peircean scholar and editor Max H. Fisch (1978)[d]would claim that "semeiotic" was Peirce's own preferred rendering of Locke's σημιωτική.[18]Charles W. Morrisfollowed Peirce in using the term "semiotic" and in extending the discipline beyond human communication to animal learning and use of signals.
While the Saussurean semiotic is dyadic (sign/syntax, signal/semantics), the Peircean semiotic is triadic (sign, object, interpretant), being conceived as philosophical logic studied in terms of signs that are not always linguistic or artificial.
Peirce would aim to base his new list directly upon experience precisely as constituted by action of signs, in contrast with the list of Aristotle's categories which aimed to articulate within experience the dimension of being that is independent of experience and knowable as such, through human understanding.[citation needed]
The estimative powers of animals interpret the environment as sensed to form a "meaningful world" of objects, but the objects of this world (orUmwelt, inJakob von Uexküll's term)[19]consist exclusively of objects related to the animal as desirable (+), undesirable (–), or "safe to ignore" (0).
In contrast to this, human understanding adds to the animalUmwelta relation of self-identity within objects which transforms objects experienced into 'things' as well as +, –, 0 objects.[20][e]Thus, the generically animal objective world asUmwelt, becomes a species-specifically human objective world orLebenswelt('life-world'), wherein linguistic communication, rooted in the biologically underdeterminedInnenwelt('inner-world') of humans, makes possible the further dimension of cultural organization within the otherwise merely social organization of non-human animals whose powers of observation may deal only with directly sensible instances of objectivity.[citation needed]
This further point, that human culture depends upon language understood first of all not as communication, but as the biologically underdetermined aspect or feature of the human animal'sInnenwelt, was originally clearly identified byThomas A. Sebeok.[21][22]Sebeok also played the central role in bringing Peirce's work to the center of the semiotic stage in the twentieth century,[f]first with his expansion of the human use of signs (anthroposemiosis) to include also the generically animal sign-usage (zoösemiosis),[g]then with his further expansion of semiosis to include the vegetative world (phytosemiosis). Such would initially be based on the work ofMartin Krampen,[23]but takes advantage of Peirce's point that an interpretant, as the third item within a sign relation, "need not be mental".[24][25][26]
Peirce distinguished between the interpretant and the interpreter. The interpretant is the internal, mental representation that mediates between the object and its sign. The interpreter is the human who is creating the interpretant.[27]Peirce's "interpretant" notion opened the way to understanding an action of signs beyond the realm of animal life (study of phytosemiosis + zoösemiosis + anthroposemiosis =biosemiotics), which was his first advance beyond Latin Age semiotics.[h]
Other early theorists in the field of semiotics includeCharles W. Morris.[28]Writing in 1951,Jozef Maria Bochenskisurveyed the field in this way: "Closely related to mathematical logic is the so-called semiotics (Charles Morris) which is now commonly employed by mathematical logicians. Semiotics is the theory of symbols and falls in three parts;
Max Blackargued that the work ofBertrand Russellwas seminal in the field.[30]
Semioticians classify signs or sign systems in relation to the way they aretransmitted. This process of carrying meaning depends on the use ofcodesthat may be the individual sounds or letters that humans use to form words, the body movements they make to show attitude or emotion, or even something as general as the clothes they wear. Tocoina word to refer to athing, thecommunitymust agree on a simple meaning (adenotativemeaning) within their language, but that word can transmit that meaning only within the language'sgrammatical structuresandcodes. Codes also represent thevaluesof theculture, and are able to add new shades ofconnotationto every aspect of life.[citation needed]
To explain the relationship between semiotics andcommunication studies,communicationis defined as the process of transferring data and-or meaning from a source to a receiver. Hence, communication theorists construct models based on codes, media, andcontextsto explain thebiology,psychology, andmechanicsinvolved. Both disciplines recognize that the technical process cannot be separated from the fact that the receiver mustdecodethe data, i.e., be able to distinguish the data assalient, and make meaning out of it. This implies that there is a necessary overlap between semiotics and communication. Indeed, many of the concepts are shared, although in each field the emphasis is different. InMessages and Meanings: An Introduction to Semiotics,Marcel Danesi(1994) suggested that semioticians' priorities were to studysignificationfirst, and communication second. A more extreme view is offered byJean-Jacques Nattiezwho, as amusicologist, considered the theoretical study of communication irrelevant to his application of semiotics.[31]: 16
Semiotics differs fromlinguisticsin that it generalizes the definition of a sign to encompass signs in any medium or sensory modality. Thus it broadens the range of sign systems and sign relations, and extends the definition of language in what amounts to its widest analogical or metaphorical sense. The branch of semiotics that deals with such formal relations between signs or expressions in abstraction from their signification and their interpreters,[32]or—more generally—with formal properties of symbol systems[33](specifically, with reference to linguistic signs,syntax)[34]is referred to assyntactics.
Peirce's definition of the termsemioticas the study of necessary features of signs also has the effect of distinguishing the discipline from linguistics as the study of contingent features that the world's languages happen to have acquired in the course of their evolutions. From a subjective standpoint, perhaps more difficult is the distinction between semiotics and thephilosophy of language. In a sense, the difference lies between separate traditions rather than subjects. Different authors have called themselves "philosopher of language" or "semiotician." This difference doesnotmatch the separation betweenanalyticandcontinental philosophy. On a closer look, there may be found some differences regarding subjects. Philosophy of language pays more attention tonatural languagesor to languages in general, while semiotics is deeply concerned with non-linguistic signification. Philosophy of language also bears connections to linguistics, while semiotics might appear closer to some of thehumanities(includingliterary theory) and tocultural anthropology.
Semiosis orsemeiosisis the process that forms meaning from any organism's apprehension of the world through signs. Scholars who have talked about semiosis in their subtheories of semiotics includeC. S. Peirce,John Deely, andUmberto Eco. Cognitive semiotics is combining methods and theories developed in the disciplines of semiotics and the humanities, with providing new information into human signification and its manifestation in cultural practices. The research on cognitive semiotics brings together semiotics from linguistics, cognitive science, and related disciplines on a common meta-theoretical platform of concepts, methods, and shared data.
Cognitive semioticsmay also be seen as the study ofmeaning-makingby employing and integrating methods and theories developed in the cognitive sciences. This involves conceptual and textual analysis as well as experimental investigations. Cognitive semiotics initially was developed at the Center for Semiotics atAarhus University(Denmark), with an important connection with the Center of Functionally Integrated Neuroscience (CFIN) at Aarhus Hospital. Amongst the prominent cognitive semioticians arePer Aage Brandt, Svend Østergaard, Peer Bundgård,Frederik Stjernfelt, Mikkel Wallentin, Kristian Tylén, Riccardo Fusaroli, and Jordan Zlatev. Zlatev later in co-operation with Göran Sonesson established CCS (Center for Cognitive Semiotics) atLund University, Sweden.
Finite semiotics, developed by Cameron Shackell (2018, 2019),[35][36][37][38]aims to unify existing theories of semiotics for application to the post-Baudrillardianworld of ubiquitous technology. Its central move is to place the finiteness of thought at the root of semiotics and the sign as a secondary but fundamental analytical construct. The theory contends that the levels of reproduction that technology is bringing to human environments demands this reprioritisation if semiotics is to remain relevant in the face of effectively infinite signs. The shift in emphasis allows practical definitions of many core constructs in semiotics which Shackell has applied to areas such ashuman computer interaction,[39]creativitytheory,[40]and acomputational semioticsmethod for generatingsemiotic squaresfrom digital texts.[41]
Pictorial semiotics[42]is intimately connected to art history and theory. It goes beyond them both in at least one fundamental way, however. Whileart historyhas limited its visual analysis to a small number of pictures that qualify as "works of art", pictorial semiotics focuses on the properties of pictures in a general sense, and on how the artistic conventions of images can be interpreted through pictorial codes. Pictorial codes are the way in which viewers of pictorial representations seem automatically to decipher the artistic conventions of images by being unconsciously familiar with them.[43]
According to Göran Sonesson, a Swedish semiotician, pictures can be analyzed by three models: the narrative model, which concentrates on the relationship between pictures and time in a chronological manner as in a comic strip; the rhetoric model, which compares pictures with different devices as in a metaphor; and the Laokoon model, which considers the limits and constraints of pictorial expressions by comparing textual mediums that utilize time with visual mediums that utilize space.[44]
The break from traditional art history and theory—as well as from other major streams of semiotic analysis—leaves open a wide variety of possibilities for pictorial semiotics. Some influences have been drawn from phenomenological analysis, cognitive psychology, structuralist, and cognitivist linguistics, and visual anthropology and sociology.
Studies have shown that semiotics may be used to make or break abrand.Culture codesstrongly influence whether a population likes or dislikes a brand's marketing, especially internationally. If the company is unaware of a culture's codes, it runs the risk of failing in its marketing.Globalizationhas caused the development of a global consumer culture where products have similar associations, whether positive or negative, across numerous markets.[45]
Mistranslations may lead to instances of "Engrish" or "Chinglish" terms for unintentionally humorous cross-cultural slogans intended to be understood in English. Whentranslating surveys, the same symbol may mean different things in the source and target language thus leading to potential errors. For example, the symbol of "x" is used to mark a response in English language surveys but "x" usually means'no'in the Chinese convention.[46]This may be caused by a sign that, in Peirce's terms, mistakenly indexes or symbolizes something in one culture, that it does not in another.[47]In other words, it creates a connotation that is culturally-bound, and that violates some culture code. Theorists who have studied humor (such asSchopenhauer) suggest that contradiction or incongruity creates absurdity and therefore, humor.[48]Violating a culture code creates this construct of ridiculousness for the culture that owns the code. Intentional humor also may fail cross-culturally because jokes are not on code for the receiving culture.[49]
A good example of branding according to cultural code isDisney's internationaltheme parkbusiness. Disney fits well withJapan's cultural code because the Japanese value "cuteness", politeness, and gift-giving as part of their culture code;Tokyo Disneylandsells the most souvenirs of any Disney theme park. In contrast,Disneyland Parisfailed when it launched asEuro Disneybecause the company did not research the codes underlying European culture. Its storybook retelling of European folktales was taken aselitistand insulting, and the strict appearance standards that it had for employees resulted in discrimination lawsuits in France. Disney souvenirs were perceived as cheap trinkets. The park was a financial failure because its code violated the expectations of European culture in ways that were offensive.[50]
However, some researchers have suggested that it is possible to successfully pass a sign perceived as a cultural icon, such as thelogosforCoca-ColaorMcDonald's, from one culture to another. This may be accomplished if the sign is migrated from a more economically developed to a less developed culture.[50]The intentional association of a product with another culture has been called "foreign consumer culture positioning" (FCCP). Products also may be marketed using global trends or culture codes, for example, saving time in a busy world; but even these may be fine-tuned for specific cultures.[45]
Research also found that, as airline industry brandings grow and become more international their logos become more symbolic and less iconic. The iconicity andsymbolismof a sign depends on the cultural convention and are, on that ground, in relation with each other. If the cultural convention has greater influence on the sign, the signs get more symbolic value.[51]
The flexibility of human semiotics is well demonstrated in dreams.Sigmund Freud[52]spelled out how meaning in dreams rests on a blend of images,affects, sounds, words, and kinesthetic sensations. In his chapter on "The Means of Representation," he showed how the most abstract sorts of meaning and logical relations can be represented by spatial relations. Two images in sequence may indicate "if this, then that" or "despite this, that." Freud thought the dream started with "dream thoughts" which were like logical, verbal sentences. He believed that the dream thought was in the nature of a taboo wish that would awaken the dreamer. In order to safeguard sleep, the midbrain converts and disguises the verbal dream thought into an imagistic form, through processes he called the "dream-work."
Kofi Agawu[53]quotes the distinction made by Roman Jakobson[54]between "introversive semiosis, a language which signifies itself," and extoversive semiosis, the referential component of the semiosis. Jakobson writes that introversive semiosis "is indissolubly linked with the esthetic function of sign systems and dominates not only music but also glossolalic poetry and nonrepresentational painting and sculpture",[55]but Agawu uses the distinction mainly in music, proposing Schenkerian analysis as a path to introversive semiosis and topic theory as an example of extroversive semiosis. Jean-Jacques Nattiez makes the same distinction: "Roman Jakobson sees in music a semiotic system in which the 'introversive semiosis' – that is, the reference of each sonic element to the other elements to come — predominates over the 'extroversive semiosis' – or the referential link with the exterior world."[56]
Semiotics can be directly linked to the ideals of musical topic theory, which traces patterns in musical figures throughout their prevalent context in order to assign some aspect of narrative, affect, or aesthetics to the gesture. Danuta Mirka'sThe Oxford Handbook of Topic Theorypresents a holistic recognition and overview regarding the subject, offering insight into the development of the theory.[57]In recognizing the indicative and symbolic elements of a musical line, gesture, or occurrence, one can gain a greater understanding of aspects regarding compositional intent and identity.
Philosopher Charles Pierce discusses the relationship of icons and indexes in relation to signification and semiotics. In doing so, he draws on the elements of various ideas, acts, or styles that can be translated into a different field. Whereas indexes consist of a contextual representation of a symbol, icons directly correlate with the object or gesture that is being referenced.
In his 1980 bookClassic Music: Expression, Form, and Style,Leonard Ratner amends the conversation surrounding musical tropes—or "topics"—in order to create a collection of musical figures that have historically been indicative of a given style.[58]Robert Hatten continues this conversation inBeethoven, Markedness, Correlation, and Interpretation(1994), in which he states that "richly coded style types which carry certain features linked to affect, class, and social occasion such as church styles, learned styles, and dance styles. In complex forms these topics mingle, providing a basis for musical allusion."[59]
Subfields that have sprouted out of semiotics include, but are not limited to, the following:
Thomas Carlyle(1795–1881) ascribed great importance to symbols in a religious context, noting that all worship "must proceed by Symbols"; he propounded this theory in such works as "Characteristics" (1831),[67]Sartor Resartus(1833–4),[68]andOn Heroes(1841),[69]which have been retroactively recognized as containing semiotic theories.
Charles Sanders Peirce(1839–1914), anoted logicianwho founded philosophicalpragmatism, definedsemiosisas an irreducibly triadic process wherein something, as an object, logically determines or influences something as a sign to determine or influence something as an interpretation orinterpretant, itself a sign, thus leading to further interpretants.[70]Semiosis is logically structured to perpetuate itself. The object may be quality, fact, rule, or even fictional (Hamlet), and may be "immediate" to the sign, the object as represented in the sign, or "dynamic", the object as it really is, on which the immediate object is founded. The interpretant may be "immediate" to the sign, all that the sign immediately expresses, such as a word's usual meaning; or "dynamic", such as a state of agitation; or "final" or "normal", the ultimate ramifications of the sign about its object, to which inquiry taken far enough would be destined and with which any interpretant, at most, may coincide.[71]Hissemiotic[72]covered not only artificial, linguistic, and symbolic signs, but also semblances such as kindred sensible qualities, and indices such as reactions. He came c. 1903[73]toclassify any signby three interdependent trichotomies, intersecting to form ten (rather than 27) classes of sign.[74]Signs also enter into various kinds of meaningful combinations; Peirce covered both semantic and syntactical issues in his speculative grammar. He regarded formal semiotic as logicper seand part of philosophy; as also encompassing study of arguments (hypothetical,deductive, andinductive) and inquiry's methods including pragmatism; and as allied to, but distinct from logic's pure mathematics. In addition to pragmatism, Peirce provided a definition of "sign" as arepresentamen, in order to bring out the fact that a sign is something that "represents" something else in order to suggest it (that is, "re-present" it) in some way:[75][H]
A sign, or representamen, is something which stands to somebody for something in some respect or capacity. It addresses somebody, that is, creates in the mind of that person an equivalent sign. That sign which it creates I call the interpretant of the first sign. The sign stands for something, its object not in all respects, but in reference to a sort of idea.
Ferdinand de Saussure(1857–1913), the "father" of modernlinguistics, proposed a dualistic notion of signs, relating thesignifieras the form of the word or phrase uttered, to thesignifiedas the mental concept. According to Saussure, the sign is completelyarbitrary—i.e., there is no necessary connection between the sign and its meaning. This sets him apart from previous philosophers, such asPlatoor thescholastics, who thought that there must be some connection between a signifier and the object it signifies. In hisCourse in General Linguistics, Saussure credits the American linguistWilliam Dwight Whitney(1827–1894) with insisting on the arbitrary nature of the sign. Saussure's insistence on the arbitrariness of the sign also has influenced later philosophers and theorists such asJacques Derrida,Roland Barthes, andJean Baudrillard. Ferdinand de Saussure coined the termsémiologiewhile teaching his landmark "Course on General Linguistics" at theUniversity of Genevafrom 1906 to 1911. Saussure posited that no word is inherently meaningful. Rather a word is only a "signifier." i.e., the representation of something, and it must be combined in the brain with the "signified", or the thing itself, in order to form a meaning-imbued "sign." Saussure believed that dismantling signs was a real science, for in doing so we come to an empirical understanding of how humans synthesize physical stimuli into words and other abstract concepts.
Jakob von Uexküll(1864–1944) studied thesign processesin animals. He used the German wordUmwelt,'environment', to describe the individual's subjective world, and he invented the concept of functional circle (funktionskreis) as a general model of sign processes. In hisTheory of Meaning(Bedeutungslehre, 1940), he described the semiotic approach tobiology, thus establishing the field that now is calledbiosemiotics.
Valentin Voloshinov(1895–1936) was aSoviet-Russian linguist, whose work has been influential in the field ofliterary theoryandMarxisttheory of ideology. Written in the late 1920s in the USSR, Voloshinov'sMarxism and the Philosophy of Language(Russian:Marksizm i Filosofiya Yazyka) developed a counter-Saussurean linguistics, which situated language use in social process rather than in an entirely decontextualized Saussureanlangue.[citation needed]
Louis Hjelmslev(1899–1965) developed a formalist approach to Saussure's structuralist theories. His best known work isProlegomena to a Theory of Language, which was expanded inRésumé of the Theory of Language, a formal development ofglossematics, his scientific calculus of language.[citation needed]
Charles W. Morris(1901–1979): Unlike his mentorGeorge Herbert Mead, Morris was a behaviorist and sympathetic to theVienna Circlepositivismof his colleague,Rudolf Carnap. Morris was accused byJohn Deweyof misreading Peirce.[76]
In his 1938Foundations of the Theory of Signs, he defined semiotics as grouped into three branches:
Thure von Uexküll(1908–2004), the "father" of modernpsychosomatic medicine, developed a diagnostic method based on semiotic and biosemiotic analyses.
Roland Barthes(1915–1980) was a French literary theorist and semiotician. He often would critique pieces of cultural material to expose how bourgeois society used them to impose its values upon others. For instance, the portrayal of wine drinking in French society as a robust and healthy habit would be a bourgeois ideal perception contradicted by certain realities (i.e. that wine can be unhealthy and inebriating). He found semiotics useful in conducting these critiques. Barthes explained that these bourgeois cultural myths were second-order signs, or connotations. A picture of a full, dark bottle is a sign, a signifier relating to a signified: a fermented, alcoholic beverage—wine. However, the bourgeois take this signified and apply their own emphasis to it, making "wine" a new signifier, this time relating to a new signified: the idea of healthy, robust, relaxing wine. Motivations for such manipulations vary from a desire to sell products to a simple desire to maintain the status quo. These insights brought Barthes very much in line with similar Marxist theory.
Algirdas Julien Greimas(1917–1992) developed a structural version of semiotics named, "generative semiotics", trying to shift the focus of discipline from signs to systems of signification. His theories develop the ideas of Saussure, Hjelmslev,Claude Lévi-Strauss, andMaurice Merleau-Ponty.
Thomas A. Sebeok(1920–2001), a student of Charles W. Morris, was a prolific and wide-ranging American semiotician. Although he insisted that animals are not capable of language, he expanded the purview of semiotics to include non-human signaling and communication systems, thus raising some of the issues addressed byphilosophy of mindand coining the termzoosemiotics. Sebeok insisted that all communication was made possible by the relationship between an organism and the environment in which it lives. He also posed the equation betweensemiosis(the activity of interpreting signs) andlife—a view that theCopenhagen-Tartu biosemiotic schoolhas further developed.
Juri Lotman(1922–1993) was the founding member of theTartu(or Tartu-Moscow)Semiotic School. He developed a semiotic approach to the study of culture—semiotics of culture—and established a communication model for the study of text semiotics. He also introduced the concept of thesemiosphere. Among his Moscow colleagues wereVladimir Toporov,Vyacheslav IvanovandBoris Uspensky.
Christian Metz(1931–1993) pioneered the application of Saussurean semiotics tofilm theory, applyingsyntagmatic analysisto scenes of films and groundingfilm semioticsin greater context.
Eliseo Verón(1935–2014) developed his "Social Discourse Theory" inspired in the Peircian conception of "Semiosis."
Groupe μ(founded 1967) developed a structural version ofrhetorics, and thevisual semiotics.
Umberto Eco(1932–2016) was an Italian novelist, semiotician and academic. He made a wider audience aware of semiotics by various publications, most notablyA Theory of Semioticsand his novel,The Name of the Rose, which includes (second to its plot) applied semiotic operations. His most important contributions to the field bear on interpretation, encyclopedia, and model reader. He also criticized in several works (A theory of semiotics,La struttura assente,Le signe,La production de signes) the "iconism" or "iconic signs" (taken from Peirce's most famous triadic relation, based on indexes, icons, and symbols), to which he proposed four modes of sign production: recognition, ostension, replica, and invention.
Julia Kristeva(born 1941), a student ofLucien GoldmannandRoland Barthes, Bulgarian-French semiotician,literary critic,psychoanalyst,feminist, andnovelist. She uses psychoanalytical concepts together with the semiotics, distinguishing the two components in the signification, the symbolic and the semiotic.Kristeva also studies therepresentation of women and women's bodies in popular culture, such as horror filmsand has had a remarkable influence on feminism and feminist literary studies.
Michael Silverstein(1945–2020), a theoretician of semiotics and linguistic anthropology. Over the course of his career he created an original synthesis of research on the semiotics of communication, the sociology of interaction, Russian formalist literary theory, linguistic pragmatics, sociolinguistics, early anthropological linguistics and structuralist grammatical theory, together with his own theoretical contributions, yielding a comprehensive account of the semiotics of human communication and its relation to culture. His main influence wasCharles Sanders Peirce,Ferdinand de Saussure, andRoman Jakobson.
Some applications of semiotics include:[citation needed]
In some countries, the role of semiotics is limited toliterary criticismand an appreciation of audio and visual media. This narrow focus may inhibit a more general study of the social and political forces shaping how different media are used and their dynamic status within modern culture. Issues of technologicaldeterminismin the choice of media and the design of communication strategies assume new importance in this age of mass media.[citation needed]
A world organization of semioticians, theInternational Association for Semiotic Studies, and its journalSemiotica, was established in 1969. The larger research centers together with teaching program include the semiotics departments at theUniversity of Tartu,University of Limoges,Aarhus University, andBologna University.[citation needed]
Publication of research is both in dedicated journals such asSign Systems Studies, established byJuri Lotmanand published byTartu University Press;Semiotica, founded byThomas A. Sebeokand published byMouton de Gruyter;Zeitschrift für Semiotik;European Journal of Semiotics;Versus(founded and directed byUmberto Eco),The American Journal of Semiotics, et al.; and as articles accepted in periodicals of other disciplines, especially journals oriented toward philosophy and cultural criticism, communication theory, etc.[citation needed]
The major semiotic book seriesSemiotics, Communication, Cognition, published byDe Gruyter Mouton(series editors Paul Cobley andKalevi Kull) replaces the former "Approaches to Semiotics" (series editorThomas A. Sebeok, 127 volumes) and "Approaches to Applied Semiotics" (7 volumes). Since 1980 theSemiotic Society of Americahas produced an annual conference series:Semiotics: The Proceedings of the Semiotic Society of America.[citation needed]
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Theabsolute differenceof tworeal numbersx{\displaystyle x}andy{\displaystyle y}is given by|x−y|{\displaystyle |x-y|}, theabsolute valueof theirdifference. It describes the distance on thereal linebetween the points corresponding tox{\displaystyle x}andy{\displaystyle y}, and is a special case of theLpdistancefor all1≤p≤∞{\displaystyle 1\leq p\leq \infty }. Its applications in statistics include theabsolute deviationfrom acentral tendency.
Absolute difference has the following properties:
Because it is non-negative, nonzero for distinct arguments, symmetric, and obeys the triangle inequality, the real numbers form ametric spacewith the absolute difference as its distance, the familiar measure of distance along a line.[4]It has been called "the most natural metric space",[5]and "the most important concrete metric space".[2]This distance generalizes in many different ways to higher dimensions, as a special case of theLpdistancesfor all1≤p≤∞{\displaystyle 1\leq p\leq \infty }, including thep=1{\displaystyle p=1}andp=2{\displaystyle p=2}cases (taxicab geometryandEuclidean distance, respectively). It is also the one-dimensional special case ofhyperbolic distance.
Instead of|x−y|{\displaystyle |x-y|}, the absolute difference may also be expressed asmax(x,y)−min(x,y).{\displaystyle \max(x,y)-\min(x,y).}Generalizing this to more than two values, in any subsetS{\displaystyle S}of the real numbers which has aninfimumand asupremum, the absolute difference between any two numbers inS{\displaystyle S}is less or equal then the absolute difference of the infimum and supremumofS{\displaystyle S}.
The absolute difference takes non-negative integers to non-negative integers. As a binary operation that is commutative but not associative, with an identity element on the non-negative numbers, the absolute difference gives the non-negative numbers (whether real or integer) the algebraic structure of acommutative magmawith identity.[1]
The absolute difference is used to define therelative difference, the absolute difference between a given value and a reference value divided by the reference value itself.[6]
In the theory ofgraceful labelingsingraph theory, vertices are labeled bynatural numbersand edges are labeled by the absolute difference of the numbers at their two vertices. A labeling of this type is graceful when the edge labels are distinct and consecutive from 1 to the number of edges.[7]
As well as being a special case of the Lpdistances, absolute difference can be used to defineChebyshev distance(L∞), in which the distance between points is the maximum or supremum of the absolute differences of their coordinates.[8]
In statistics, theabsolute deviationof a sampled number from acentral tendencyis its absolute difference from the center, theaverage absolute deviationis the average of the absolute deviations of a collection of samples, andleast absolute deviationsis a method forrobust statisticsbased on minimizing the average absolute deviation.
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Proactive cyber defensemeans acting in anticipation to oppose an attack through cyber and cognitive domains.[1]Proactive cyber defense can be understood as options between offensive and defensive measures. It includes interdicting, disrupting or deterring an attack or a threat's preparation to attack, either pre-emptively or in self-defence.
Proactive cyber defense differs from active defence, in that the former is pre-emptive (does not waiting for an attack to occur). Furthermore, active cyber defense differs from offensive cyber operations (OCO) in that the latter requires legislative exceptions to undertake. Hence, offensive cyber capabilities may be developed in collaboration with industry and facilitated by private sector; these operations are often led by nation-states.
Common methods of proactive cyber defense include cyber deception, attribution, threat hunting and adversarial pursuit. The mission of the pre-emptive and proactive operations is to conduct aggressive interception and disruption activities against an adversary using:psychological operations, managed information dissemination, precision targeting, information warfare operations, computer network exploitation, and other active threat reduction measures.
The proactive defense strategy is meant to improve information collection by stimulating reactions of the threat agents and to provide strike options as well as to enhance operational preparation of the real or virtual battlespace. Proactive cyber defence can be a measure for detecting and obtaining information before a cyber attack, or it can also be impending cyber operation and be determining the origin of an operation that involves launching a pre-emptive, preventive, or cyber counter-operation.
The offensive capacity includes the manipulation and/or disruption of networks and systems with the purpose of limiting or eliminating the adversary's operational capability. This capability can be required to guarantee one's freedom of action in the cyber domain.Cyber-attackscan be launched to repel an attack (active defence) or to support the operational action.
Strategically, cyber defence refers to operations that are conducted in the cyber domain in support of mission objectives. The main difference betweencyber securityand cyber defence is that cyber defence requires a shift fromnetwork assurance(security) tomission assurance. Cyber defence focuses on sensing, detecting, orienting, and engaging adversaries in order to assure mission success and to outmanoeuver the adversary. This shift from security to defence requires a strong emphasis on intelligence, and reconnaissance, and the integration of staff activities to include intelligence, operations, communications, and planning.
Defensive cyber operations refer to activities on or through the global information infrastructure to help protect an institutions' electronic information and information infrastructures as a matter of mission assurance. Defensive cyber does not normally involve direct engagement with the adversary.
Active cyber operations refers to activities on the global information infrastructure to degrade, disrupt, influence, respond, and interfere with the capabilities, intentions, and activities of a foreign individual, state, organization, and terrorist groups. Active cyber defence decisively engages the adversary and includes adversarial pursuit activities.
In the fifth century, B.C.,Sun Tzuadvocated foreknowledge (predictive analysis) as part of a winning strategy. He warned that planners must have a precise understanding of the active threat and not "remain ignorant of the enemy's condition". The thread of proactive defense is spun throughout his teachings. PsychiatristViktor Franklwas likely the first to use the term proactive in his 1946 bookMan's Search for Meaningto distinguish the act of taking responsibility for one's own circumstances rather than attributing one's condition to external factors.
Later in 1982, theUnited States Department of Defense(DoD) used "proactive" as a contrary concept to "reactive" inassessing risk. In the framework of risk management "proactive" meant taking initiative by acting rather than reacting to threat events. Conversely "reactive" measures respond to a stimulus or past events rather than predicting the event.Military scienceconsiders defence as the science-art of thwarting an attack. Furthermore, doctrine poses that if a party attacks an enemy who is about to attack this could be called active-defence. Defence is also aeuphemismfor war but does not carry the negative connotation of an offensive war. Usage in this way has broadened the concept of proactive defence to include most military issues including offensive, which is implicitly referred to as active-defence. Politically, the concept of national self-defence to counter a war of aggression refers to a defensive war involving pre-emptive offensive strikes and is one possible criterion in the 'Just War Theory'. Proactive defence has moved beyond theory, and it has been put into practice in theatres of operation. In 1989Stephen Covey's study transformed the meaning of proactive as "to act before a situation becomes a source of confrontation or crisis".[2]Since then, "proactive" has been placed in opposition to the words "reactive" or "passive".
Cyber is derived from "cybernetics", a word originally coined by a group of scientists led byNorbert Wienerand made popular by Wiener's book of 1948,Cybernetics or Control and Communication in the Animal and the Machine.[3]Cyberspace typically refers to the vast and growing logical domain composed of public and private networks; it means independently managed networks linked together the Internet. The definition of Cyberspace has been extended to include all network-space which at some point, through some path, may have eventual access to the public internet. Under this definition, cyberspace becomes virtually every networked device in the world, which is not devoid of a network interface entirely. With the rapid evolution of information warfare operations doctrine in the 1990s, we have begun to see the use of proactive and preemptive cyber defence concepts used by policymakers and scholars.
The National Strategy to Secure Cyberspace,a book written by George W. Bush, was published in February 2003 outlining the initial framework for both organizing and prioritizing efforts to secure the cyberspace. It highlighted the necessity for public-private partnerships. In this book, proactive threads include the call to deter malicious activity and prevent cyber attacks against America's critical infrastructures.
The notion of "proactive defence" has a rich history. The hype of "proactive cyber defence" reached its zenith around 1994, under the auspices of Information Warfare. Much of the current doctrine related to proactive cyber defence was fully developed by 1995. Now most of the discussions around proactive defence in the literature are much less "proactive" than the earlier discussions in 1994. Present-day proactive cyber defence strategy was conceived within the context of the rich discussion that preceded it, existing doctrine and real proactive cyber defence programs that have evolved globally over the past decade.
As one of the founding members of Canada's interdepartmental committee on Information Warfare, Dr. Robert Garigue and Dave McMahon pointed out that "strategic listening, core intelligence, and proactive defence provide time and precision. Conversely, reacting in surprise is ineffective, costly and leaves few options. Strategic deterrence needs a credible offensive, proactive defence and information peacekeeping capability in which to project power and influence globally through Cyberspace in the defence of the nation. Similarly, deterrence and diplomacy are required in the right dosage to dissuade purposeful interference with the national critical cyber infrastructures in influence in the democratic process by foreign states.[4]
Intelligence agencies, such as the National Security Agency, were criticized for buying up and stockpilingzero-day vulnerabilitiesand keeping them secret and developing mainlyoffensive capabilitiesinstead of defensive measures and, thereby, helping patch vulnerabilities.[5][6][7][8]This criticism was widely reiterated and recognized after the May 2017WannaCry ransomware attack.[9][10][11][12][13][14]
The notion of a proactive pre-emptive operations group (P2OG) emerged from a report of theDefense Science Board's(DSB) 2002 briefing. The briefing was reported by Dan Dupont inInside the Pentagonon September 26, 2002, and was also discussed by William M. Arkin in theLos Angeles Timeson October 27, 2002.[15]TheLos Angeles Timeshas subsequently quotedU.S. Secretary of DefenseDonald Rumsfeldrevealing the creation of the "Proactive, Pre-emptive Operations Group". The mission was to conduct Aggressive, Proactive, Pre-emptive Operations to interdiction and disruption the threat using: psychological operations, managed information dissemination, precision targeting, and information warfare operations.[16]Today, the proactive defence strategy means improving information collection by stimulating reactions of the threat agents, provide strike options to enhance operational preparation of the real as well as virtual battle space. The P2OG has been recommended to be constituted of one hundred highly specialized people with unique technical and intelligence skills. The group would be overseen by the White House's deputy national security adviser and would carry out missions coordinated by the secretary of defence. Proactive measures, according to DoD are those actions taken directly against the preventive stage of an attack by the enemy.
The discipline of world politics and the notions of pre-emptive cyber defence topics are the two important concepts that need to be examined because we are living in a dynamic international system in which actors (countries) update their threat perceptions according to the developments in the technological realm.[17]Given this logic employed frequently by the policymakers, countries prefer using pre-emptive measures before being targeted. This topic is extensively studied by the political scientists focusing on the power transition theory (PTT), where Organski and Kugler first discussed that powerful countries start the attack before the balance of power changes in favor of the relatively weaker but the rising state.[18]Although the PTT has relevance to explain the use of pre-emptive cyber defence policies, this theory can still be difficult to apply when it comes to cyber defence entirely because it is not easy to understand the relative power differentials of the international actors in terms of their cyber capabilities. On the other hand, we can still use the PTT to explain the security perceptions of the United States and China, as a rising country, in terms of their use of pre-emptive cyber defence policies. Many scholars have already begun to examine the likelihood of cyber war between these countries and examined the relevance of the PTT and other similar international relations theories.[19][20][21]
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Incomputing, ashared resource, ornetwork share, is acomputer resourcemade available from onehostto other hosts on acomputer network.[1][2]It is a device or piece of information on a computer that can be remotely accessed from another computer transparently as if it were a resource in the local machine. Network sharing is made possible byinter-process communicationover the network.[2][3]
Some examples of shareable resources arecomputer programs,data,storage devices, andprinters. E.g.shared file access(also known asdisk sharingandfolder sharing), shared printer access, shared scanner access, etc. The shared resource is called ashared disk,shared folderorshared document
The termfile sharingtraditionally means shared file access, especially in the context of operating systems andLANandIntranetservices, for example in Microsoft Windows documentation.[4]Though, asBitTorrentand similar applications became available in the early 2000s, the termfile sharingincreasingly has become associated withpeer-to-peer file sharingover the Internet.
Shared file and printer access require anoperating systemon the client that supports access to resources on a server, an operating system on the server that supports access to its resources from a client, and anapplication layer(in the four or five layerTCP/IP reference model) file sharingprotocolandtransport layerprotocol to provide that shared access. Modern operating systems forpersonal computersincludedistributed file systemsthat support file sharing, while hand-held computing devices sometimes require additional software for shared file access.
The most common such file systems and protocols are:
The "primary operating system" is the operating system on which the file sharing protocol in question is most commonly used.
OnMicrosoft Windows, a network share is provided by the Windows network component "File and Printer Sharing for Microsoft Networks", using Microsoft's SMB (Server Message Block) protocol. Other operating systems might also implement that protocol; for example,Sambais an SMB server running onUnix-likeoperating systems and some other non-MS-DOS/non-Windows operating systems such asOpenVMS. Samba can be used to create network shares which can be accessed, using SMB, from computers runningMicrosoft Windows. An alternative approach is ashared disk file system, where each computer has access to the "native" filesystem on a shared disk drive.
Shared resource access can also be implemented withWeb-based Distributed Authoring and Versioning(WebDAV).
The share can be accessed by client computers through some naming convention, such asUNC(Universal Naming Convention) used onDOSandWindowsPC computers. This implies that a network share can be addressed according to the following:
whereServerComputerNameis theWINSname,DNSname orIP addressof the server computer, andShareNamemay be a folder or file name, or itspath. The shared folder can also be given a ShareName that is different from the folder local name at the server side. For example,\\ServerComputerName\c$usually denotes a drive with drive letterC:on a Windows machine.
A shared drive or folder is oftenmappedat the client PC computer, meaning that it is assigned adrive letteron the local PC computer. For example, the drive letterH:is typically used for the user home directory on a central file server.
A network share can become a security liability when access to the shared files is gained (often by devious means) by those who should not have access to them. Manycomputer wormshave spread through network shares. Network shares would consume extensive communication capacity in non-broadband network access. Because of that, shared printer and file access is normally prohibited infirewallsfrom computers outside thelocal area networkor enterpriseIntranet. However, by means ofvirtual private networks(VPN), shared resources can securely be made available for certified users outside the local network.
A network share is typically made accessible to other users by marking anyfolderor file as shared, or by changing thefile system permissionsor access rights in the properties of the folder. For example, a file or folder may be accessible only to one user (the owner), to system administrators, to a certain group of users to public, i.e. to all logged in users. The exact procedure varies by platform.
In operating system editions for homes and small offices, there may be a specialpre-shared folderthat is accessible to all users with a user account and password on the local computer. Network access to the pre-shared folder can be turned on. In the English version of theWindows XP Home Editionoperating system, the preshared folder is namedShared documents, typically with thepathC:\Documents and Settings\All users\Shared documents. InWindows VistaandWindows 7, the pre-shared folder is namedPublic documents, typically with the pathC:\Users\Public\Public documents.[6]
In home and small office networks, adecentralizedapproach is often used, where every user may make their local folders and printers available to others. This approach is sometimes denoted aWorkgrouporpeer-to-peernetwork topology, since the same computer may be used as client as well as server.
In large enterprise networks, a centralizedfile serverorprint server, sometimes denotedclient–server paradigm, is typically used. A client process on the local user computer takes the initiative to start the communication, while a server process on thefile serverorprint serverremote computer passively waits for requests to start a communication session
In very large networks, aStorage Area Network(SAN) approach may be used.
Online storageon a server outside the local network is currently an option, especially for homes and small office networks.
Shared file access should not be confused with file transfer using thefile transfer protocol(FTP), or theBluetoothIRDAOBject EXchange(OBEX) protocol. Shared access involves automatic synchronization of folder information whenever a folder is changed on the server, and may provide server side file searching, while file transfer is a more rudimentary service.[7]
Shared file access is normally considered as a local area network (LAN) service, while FTP is an Internet service.
Shared file access is transparent to the user, as if it was a resource in the local file system, and supports a multi-user environment. This includesconcurrency controlorlockingof a remote file while a user is editing it, andfile system permissions.
Shared file access involves but should not be confused withfile synchronizationand other information synchronization. Internet-based information synchronization may, for example, use theSyncMLlanguage. Shared file access is based on server-side pushing of folder information, and is normally used over an "always on"Internet socket. File synchronization allows the user to be offline from time to time and is normally based on an agent software that polls synchronized machines at reconnect, and sometimes repeatedly with a certain time interval, to discover differences. Modern operating systems often include a localcacheof remote files, allowingoffline accessand synchronization when reconnected.
The first international heterogenous network for resource sharing was the 1973 interconnection of theARPANETwith earlyBritish academic networksthrough the computer science department atUniversity College London(UCL).[8][9][10]
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Alingua franca(/ˌlɪŋɡwəˈfræŋkə/;lit.'Frankish tongue'; for plurals see§ Usage notes), also known as abridge language,common language,trade language,auxiliary language,link languageorlanguage of wider communication(LWC), is alanguagesystematically used to make communication possible between groups of people who do not share anative languageor dialect, particularly when it is a third language that is distinct from both of the speakers' native languages.[1]
Linguae francae have developed around the world throughout human history, sometimes for commercial reasons (so-called "trade languages" facilitated trade), but also for cultural, religious, diplomatic and administrative convenience, and as a means of exchanging information between scientists and other scholars of different nationalities.[2][3]The term is taken from the medievalMediterranean Lingua Franca, aRomance-basedpidgin languageused especially by traders in theMediterranean Basinfrom the 11th to the 19th centuries.[4]Aworld language—a language spoken internationally and by many people—is a language that may function as a global lingua franca.[5]
Any language regularly used for communication between people who do not share a native language is a lingua franca.[6]Lingua franca is a functional term, independent of any linguistic history or language structure.[7]
Pidginsare therefore lingua francas;creolesand arguablymixed languagesmay similarly be used for communication between language groups. But lingua franca is equally applicable to a non-creole language native to one nation (often a colonial power) learned as asecond languageand used for communication between diverse language communities in a colony or former colony.[8]
Lingua francas are often pre-existing languages with native speakers, but they can also be pidgins or creoles developed for that specific region or context. Pidgins are rapidly developed and simplified combinations of two or more established languages, while creoles are generally viewed as pidgins that have evolved into fully complex languages in the course of adaptation by subsequent generations.[9]Pre-existing lingua francas such as French are used to facilitate intercommunication in large-scale trade or political matters, while pidgins and creoles often arise out of colonial situations and a specific need for communication between colonists and indigenous peoples.[10]Pre-existing lingua francas are generally widespread, highly developed languages with many native speakers.[11]Conversely, pidgins are very simplified means of communication, containing loose structuring, few grammatical rules, and possessing few or no native speakers.Creolelanguages are more developed than their ancestral pidgins, utilizing more complex structure, grammar, and vocabulary, as well as having substantial communities of native speakers.[12]
Whereas avernacularlanguage is the native language of a specific geographical community,[13]a lingua franca is used beyond the boundaries of its original community, for trade, religious, political, or academic reasons.[14]For example,Englishis avernacularin theUnited Kingdombut it is used as alingua francain thePhilippines, alongsideFilipino. Likewise,Arabic,French,Standard Chinese,RussianandSpanishserve similar purposes as industrial and educational lingua francas across regional and national boundaries.
Even though they are used as bridge languages,international auxiliary languagessuch asEsperantohave not had a great degree of adoption, so they are not described as lingua francas.[15]
The termlingua francaderives fromMediterranean Lingua Franca(also known asSabir), the pidgin language that people around theLevantand the eastern Mediterranean Sea used as the main language of commerce and diplomacy from the lateMiddle Agesto the 18th century, most notably during theRenaissance era.[16][8]During that period, a simplified version of mainlyItalianin the eastern Mediterranean andSpanishin the western Mediterranean that incorporated manyloanwordsfromGreek,Slavic languages,Arabic, andTurkishcame to be widely used as the "lingua franca" of the region, although some scholars claim that the Mediterranean Lingua Franca was just poorly used Italian.[14]
In Lingua Franca (the specific language),linguais from the Italian for 'a language'.Francais related to GreekΦρᾰ́γκοι(Phránkoi) and Arabicإِفْرَنْجِي(ʾifranjiyy) as well as the equivalent Italian—in all three cases, the literal sense is 'Frankish', leading to the direct translation: 'language of theFranks'. During the lateByzantine Empire,Frankswas a term that applied to all Western Europeans.[17][18][19][20]
Through changes of the term in literature,lingua francahas come to be interpreted as a general term for pidgins, creoles, and some or all forms of vehicular languages. This transition in meaning has been attributed to the idea that pidgin languages only became widely known from the 16th century on due to European colonization of continents such as The Americas, Africa, and Asia. During this time, the need for a term to address these pidgin languages arose, hence the shift in the meaning of Lingua Franca from a single proper noun to a common noun encompassing a large class of pidgin languages.[21]
As recently as the late 20th century, some restricted the use of the generic term to mean only mixed languages that are used as vehicular languages, its original meaning.[22]
Douglas Harper'sOnline Etymology Dictionarystates that the termLingua Franca(as the name of the particular language) was first recorded in English during the 1670s,[23]although an even earlier example of the use of it in English is attested from 1632, where it is also referred to as "Bastard Spanish".[24]
The term is well established in its naturalization to English and so major dictionaries do not italicize it as a "foreign" term.[25][26][27]
Its plurals in English arelingua francasandlinguae francae,[26][27]with the former being first-listed[26][27]or only-listed[25]in major dictionaries.
The use of lingua francas has existed since antiquity.
Akkadianremained the common language of a large part of Western Asia from several earlier empires, until it was supplanted in this role byAramaic.[28][29]
Sanskrithistorically served as a lingua franca throughout the majority of South Asia.[30][31][32]The Sanskrit language's historic presence is attested across a wide geography beyond South Asia. Inscriptions and literary evidence suggest that Sanskrit was already being adopted in Southeast Asia and Central Asia in the 1st millennium CE, through monks, religious pilgrims and merchants.[33][34][35]
Until the early 20th century,Literary Chineseserved as both the written lingua franca and the diplomatic language in East Asia, including China,Korea,Japan,Ryūkyū, andVietnam.[36]In the early 20th century,vernacular written Chinesereplaced Classical Chinese within China as both the written and spoken lingua franca for speakers of different Chinese dialects, and because of the declining power and cultural influence of China in East Asia, English has since replaced Classical Chinese as the lingua franca in East Asia.
Koine Greekwas the lingua franca of the Hellenistic culture. Koine Greek[37][38][39](ModernGreek:Ελληνιστική Κοινή,romanized:Ellinistikí Kiní,lit.'Common Greek';Greek:[elinistiˈciciˈni]), also known as Alexandrian dialect, common Attic, Hellenistic, or Biblical Greek, was thecommon supra-regional formof Greek spoken and written during theHellenistic period, theRoman Empireand the earlyByzantine Empire. It evolved from the spread of Greek following the conquests ofAlexander the Greatin the fourth century BC, and served as the lingua franca of much of the Mediterranean region and the Middle East during the following centuries.[40]
Latin, through the power of theRoman Republic, became the dominant language inItalyand subsequently throughout the realms of the Roman Empire. Even after theFall of the Western Roman Empire, Latin was the common language of communication, science, and academia in Europe until well into the 18th century, when other regional vernaculars (including its own descendants, the Romance languages) supplanted it in common academic and political usage, and it eventually became adead languagein the modern linguistic definition.
Old Tamilwas once the lingua franca for most of ancientTamilakamandSri Lanka.John Guystates that Tamil was also the lingua franca for early maritime traders from India.[41]The language and its dialects were used widely in the state of Kerala as the major language of administration, literature and common usage until the 12th century CE.[42]
Classical Māoriis the retrospective name for the language (formed out of many dialects, albeit all mutually intelligible)[43]of both the North Island and the South Island for the 800 years before theEuropean settlement of New Zealand.[44][45][46][47][48]Māorishared a common language that was used for trade, inter-iwidialogue onmarae, and education throughwānanga.[49][50]After the signing of theTreaty of Waitangi, Māori language was the lingua franca of theColony of New Zealanduntil English superseded it in the 1870s.[43][51]The description of Māori language as New Zealand's 19th-century lingua franca has been widely accepted.[52][53][54][55]The language was initially vital for all European andChinese migrantsin New Zealand to learn,[56][57][58]as Māori formed a majority of the population, owned nearly all the country's land and dominated the economy until the 1860s.[56][59]Discriminatory laws such as theNative Schools Act 1867contributed to the demise of Māori language as a lingua franca.[43]
Sogdianwas used to facilitate trade between those who spoke different languages along theSilk Road, which is why native speakers of Sogdian were employed as translators inTang China.[60]The Sogdians also ended up circulating spiritual beliefs and texts, including those ofBuddhismandChristianity, thanks to their ability to communicate to many people in the region through their native language.[61]
Old Church Slavonic, anEastern South Slaviclanguage, is the first Slavicliterary language. Between 9th and 11th century, it was the lingua franca of a great part of the predominantlySlavicstates and populations inSoutheastandEastern Europe, inliturgyand church organization, culture, literature, education and diplomacy, as anOfficial languageandNational languagein the case ofBulgaria. It was the first national and also international Slavic literary language (autonymсловѣ́ньскъ ѩꙁꙑ́къ,slověnĭskŭ językŭ).[62][63]The Glagolitic alphabet was originally used at both schools, though theCyrillic scriptwas developed early on at thePreslav Literary School, where it superseded Glagolitic as the official script inBulgariain 893. Old Church Slavonic spread to other South-Eastern, Central, and Eastern European Slavic territories, most notablyCroatia,Serbia,Bohemia,Lesser Poland, and principalities of theKievan Rus'while retaining characteristicallySouth Slaviclinguistic features. It spread also to not completely Slavic territories between theCarpathian Mountains, theDanubeand theBlack Sea, corresponding toWallachiaandMoldavia. Nowadays, the Cyrillicwriting systemis used for various languages across Eurasia, and as the national script in various Slavic,Turkic,Mongolic,Uralic,CaucasianandIranic-speaking countries inSoutheastern Europe, Eastern Europe, theCaucasus, Central, North, and East Asia.
TheMediterranean Lingua Francawas largely based on Italian andProvençal. This language was spoken from the 11th to 19th centuries around the Mediterranean basin, particularly in the European commercial empires of Italian cities (Genoa, Venice,Florence, Milan,Pisa,Siena) and in trading ports located throughout the eastern Mediterranean rim.[64]
During theRenaissance, standard Italian was spoken as a language of culture in the main royal courts of Europe, and among intellectuals. This lasted from the 14th century to the end of the 16th, when French replaced Italian as the usual lingua franca in northern Europe.[citation needed]Italian musical terms, in particular dynamic and tempo notations, have continued in use to the present day.[65][66]
Classical Quechuais either of two historical forms ofQuechua, the exact relationship and degree of closeness between which is controversial, and which have sometimes been identified with each other.[67]These are:
Ajem-Turkicfunctioned as lingua franca in the Caucasus region and in southeasternDagestan, and was widely spoken at the court and in the army ofSafavid Iran.[76]
English is sometimes described as the foremost global lingua franca, being used as a working language by individuals of diverse linguistic and cultural backgrounds in a variety of fields and international organizations to communicate with one another.[77]English is themost spoken languagein the world, primarily due to the historical global influence of theBritish Empireas well as theUnited States.[78]It is aco-official language of the United Nationsand many other international and regional organizations and has also become thede factolanguage ofdiplomacy,science,international trade,tourism,aviation,entertainmentand theInternet.[79]
When theUnited Kingdombecame a colonial power, English served as the lingua franca of the colonies of theBritish Empire. In the post-colonial period, most of the newly independent nations which had manyindigenous languagesopted to continue using English as one of their official languages such asGhanaandSouth Africa.[77]In other former colonies with several official languages such asSingaporeandFiji, English is the primary medium of education and serves as the lingua franca among citizens.[80][81][82]
Even in countries not associated with theEnglish-speaking world, English has emerged as a lingua franca in certain situations where its use is perceived to be more efficient to communicate, especially among groups consisting of native speakers of many languages. InQatar, the medical community is primarily made up of workers from countries without English as a native language. In medical practices and hospitals, nurses typically communicate with other professionals in English as a lingua franca.[83]This occurrence has led to interest in researching the consequences of the medical community communicating in a lingua franca.[83]English is also sometimes used inSwitzerlandbetween people who do not share one of Switzerland'sfour official languages, or with foreigners who are not fluent in the local language.[84]In theEuropean Union, the use of English as a lingua franca has led researchers to investigate whether aEuro Englishdialect has emerged.[85]In the fields of technology and science, English emerged as a lingua franca in the 20th century.[86]English has also significantlyinfluencedmany other languages.[87]
The Spanish language spread mainly throughout theNew World, becoming a lingua franca in the territories and colonies of theSpanish Empire, which also included parts of Africa, Asia, and Oceania. After the breakup of much of the empire in the Americas, its function as a lingua franca was solidified by the governments of the newly independent nations of what is nowHispanic America.[88]While its usage in Spain's Asia-Pacific colonies has largely died out except in thePhilippines, where it is still spoken by a small minority, Spanish became the lingua franca of what is nowEquatorial Guinea, being the main language of government and education and is spoken by the vast majority of the population.[89]
Due to large numbers of immigrants from Latin America in the second half of the 20th century and resulting influence, Spanish has also emerged somewhat as a lingua franca in parts of theSouthwestern United Statesand southernFlorida, especially in communities where native Spanish speakers form the majority of the population.[90][91]
At present it is the second most used language in international trade, and the third most used in politics, diplomacy and culture after English and French.[92]
It is also one of the most taught foreign languages throughout the world[93]and is also one of thesix official languages of the United Nations.
French is sometimes regarded as the first global lingua franca, having supplantedLatinas the prestige language of politics, trade, education, diplomacy, and military inearly modernEurope and later spreading around the world with the establishment of theFrench colonial empire.[94]WithFranceemerging as the leading political, economic, and cultural power of Europe in the 16th century, the language was adopted by royal courts throughout the continent, including the United Kingdom, Sweden, and Russia, and as the language of communication between European academics, merchants, and diplomats.[95]With the expansion of Western colonial empires, French became the main language of diplomacy and international relations up untilWorld War IIwhen it was replaced by English due the rise of theUnited Statesas the leadingsuperpower. Stanley Meisler of theLos Angeles Timessaid that the fact that theTreaty of Versailleswas written in English as well as French was the "first diplomatic blow" against the language.[96]Nevertheless, it remains the second most used language in international affairs and is one of thesix official languages of the United Nations.[97][98][99]
As a legacy of French andBelgiancolonial rule, most former colonies of these countries maintain French as an official language or lingua franca due to the many indigenous languages spoken in their territory. Notably, in most FrancophoneWestandCentral Africancountries, French has transitioned from being only a lingua franca to the native language among some communities, mostly in urban areas or among the elite class.[100]In other regions such as the French-speaking countries of theMaghreb(Algeria,Tunisia,Morocco, andMauritania) and parts of theFrench Caribbean, French is the lingua franca in professional sectors and education, even though it is not the native language of the majority.[101][102][103]
French continues to be used as a lingua franca in certain cultural fields such ascuisine,fashion, andsport.[104][94]
As a consequence ofBrexit, French has been increasingly used as a lingua franca in theEuropean Unionand its institutions either alongside or, at times, in place of English.[105][106]
Germanis used as a lingua franca in Switzerland to some extent; however, English is generally preferred to avoid favoring it over the three other official languages.Middle Low Germanused to be the Lingua franca during the lateHohenstaufentill the mid-15th century periods, in theNorth Seaand theBaltic Seawhen extensive trading was done by theHanseatic Leaguealong the Baltic and North Seas. German remains a widely studied language in Central Europe and the Balkans, especially informer Yugoslavia. It is recognized as an official language in countries outside of Europe, specificallyNamibia. German is also one of theworking languagesof the EU along English and French, but it is used less in that role than the other two.
Today,Standard Mandarin Chineseis the lingua franca ofChinaandTaiwan, which are home to many mutually unintelligiblevarieties of Chineseand, in the case of Taiwan, indigenousFormosan languages. Among manyChinese diasporacommunities,Cantoneseis often used as the lingua franca instead, particularly in Southeast Asia, due to a longer history of immigration and trade networks with southern China, although Mandarin has also been adopted in some circles since the 2000s.[107]
Arabicwas used as a lingua franca across the Islamic empires, whose sizes necessitated a common language, and spread across the Arab and Muslim worlds.[108]InDjiboutiand parts ofEritrea, both of which are countries where multiple official languages are spoken, Arabic has emerged as a lingua franca in part thanks to the population of the region being predominantly Muslim and Arabic playing a crucial role in Islam. In addition, after having fled from Eritrea due toongoing warfareand gone to some of the nearby Arab countries, Eritrean emigrants are contributing to Arabic becoming a lingua franca in the region by coming back to their homelands having picked up the Arabic language.[109]
Russian is in use and widely understood inCentral Asiaand theCaucasus, areas formerly part of the Russian Empire and Soviet Union. Its use remains prevalent in manypost-Soviet states. Russian has some presence as a minority language in theBaltic statesand some other states in Eastern Europe, as well as in pre-openingChina.[citation needed]It remains the official language of theCommonwealth of Independent States. Russian is also one of the six official languages of the United Nations.[110]Since thecollapse of the Soviet Union, its use has declined in post-Soviet states. Parts of the Russian speaking minorities outside Russia have either emigrated to Russia or assimilated into their countries of residence by learning the local language, which they now prefer to use in daily communication.
For contrast, inCentral Europeancountries that after the Second World War were included in the Soviet Union's sphere of influence, the Russian language was used only asEastern Bloc's language of internal political communication. There are no Russian minorities in these countries, in schools the primary foreign language is English and nowadays the Russian language practically does not exist.
Portugueseserved as lingua franca in the Portuguese Empire, Africa, South America and Asia in the 15th and 16th centuries. When the Portuguese started exploring the seas of Africa, America, Asia and Oceania, they tried to communicate with the natives by mixing a Portuguese-influenced version of lingua franca with the local languages. When Dutch, English or French ships came to compete with the Portuguese, the crews tried to learn this "broken Portuguese". Through a process of change the lingua franca and Portuguese lexicon was replaced with the languages of the people in contact. Portuguese remains an important lingua franca in thePortuguese-speaking African countries,East Timor, and to a certain extent inMacauwhere it is recognized as an official language alongside Chinese though in practice not commonly spoken. Portuguese and Spanish have a certain degree ofmutual intelligibilityandmixed languagessuch asPortuñolare used[citation needed]to facilitate communication in areas like the border area between Brazil and Uruguay.
TheHindustani language, withHindiandUrduas dual standard varieties, serves as the lingua franca ofPakistanandNorthern India.[111][self-published source?][112][page needed]Many Hindi-speaking North Indian states have adopted thethree-language formulain which students are taught: "(a) Hindi (with Sanskrit as part of the composite course); (b) Any other modern Indian language including Urdu and (c) English or any other modern European language." The order in non-Hindi speaking states is: "(a) the major language of the state or region; (b) Hindi; (c) Any other modern Indian language including Urdu but excluding (a) and (b) above; and (d) English or any other modern European language."[113]Hindi has also emerged as a lingua franca inArunachal Pradesh, a linguistically diverse state in Northeast India.[114][115]It is estimated that nine-tenths of the state's population knows Hindi.[116]
Urdu is the lingua franca of Pakistan and had gained significant influence amongst its people, administration and education. While it shares official status with English, Urdu is the preferred and dominant language used for inter-communication between different ethnic groups of Pakistan.[117]
Malayis understood across a cultural region in Southeast Asia called the "Malay world" includingBrunei, Indonesia, Malaysia, Singapore, southernThailand, and certain parts of the Philippines. It ispluricentric, with several nations codifying a local vernacular variety into several national literary standards:[118]AlthoughJavanesehas more native speakers, Indonesia uses a standardized form ofRiauMalay as the basis for the national language "Indonesian." Bahasa Indonesia is the sole official language even though it is the mother tongue ofonly 7%of Indonesians.[119]
Swahilideveloped as a lingua franca between severalBantu-speaking tribal groups on the east coast of Africa with heavy influence from Arabic.[120]The earliest examples of writing in Swahili are from 1711.[121]In the early 19th century the use of Swahili as a lingua franca moved inland with the Arabic ivory and slave traders. It was eventually adopted by Europeans as well during periods of colonization in the area. German colonizers used it as the language of administration inGerman East Africa, later becomingTanganyika, which influenced the choice to use it as a national language in what is now independentTanzania.[120]Swahili is currently one of the national languages and it is taught in schools and universities in several East African countries, thus prompting it to be regarded as a modern-day lingua franca by many people in the region. SeveralPan-Africanwriters and politicians have unsuccessfully called for Swahili to become the lingua franca of Africa as a means of unifying the African continent and overcoming the legacy of colonialism.[122]
Persian, anIranian language, is the official language ofIran,Afghanistan(Dari) andTajikistan(Tajik). It acts as a lingua franca in both Iran and Afghanistan between the various ethnic groups in those countries. The Persian language in South Asia, before theBritish colonized the Indian subcontinent, was the region's lingua franca and a widely used official language in north India and Pakistan.
Hausais the language of communication between speakers of different languages in NorthernNigeriaand other West African countries,[123]including the northern region of Ghana.[124]
Amharicis the lingua franca and most widely spoken language in Ethiopia, and is known by most people who speak another Ethiopian language.[125][126]
Creoles, such asNigerian Pidginin Nigeria, are used as lingua francas across the world. This is especially true in Africa, theCaribbean,Melanesia, Southeast Asia and in parts of Australia byIndigenous Australians.
The majority of pre-colonial North American nations communicated internationally usingHand Talk.[127][128]Also called Prairie Sign Language, Plains Indian Sign Language, or First Nations Sign Language, this language functioned predominantly—and still continues to function[129]—as a second language within most of the (now historical) countries of the Great Plains, fromNewe Segobiain the West toAnishinaabewakiin the East, down into what are now the northern states of Mexico and up intoCreeCountry stopping beforeDenendeh.[130][131]The relationship remains unknown between Hand Talk and other manual Indigenous languages likeKeresan Sign LanguageandPlateau Sign Language, the latter of which is now extinct (though Ktunaxa Sign Language is still used).[132]Although unrelated, perhapsInuit Sign Languageplayed and continues to play a similar role acrossInuit Nunangatand the variousInuitdialects. The original Hand Talk is found acrossIndian Countryin pockets, but it has also been employed to create new or revive old languages, such as withOneida Sign Language.[133]
International Sign, though a pidgin language, is present at most significant international gatherings, from which interpretations of nationalsign languagesare given, such as inLSF,ASL,BSL,Libras, orAuslan. International Sign, or IS and formerly Gestuno, interpreters can be found at manyEuropean Unionparliamentary or committee sittings,[134]during certain United Nations affairs,[135]conducting international sporting events like theDeaflympics, in allWorld Federation of the Deaffunctions, and across similar settings. The language has few set internal grammatical rules, instead co-opting national vocabularies of the speaker and audience, and modifying the words to bridge linguistic gaps, with heavy use of gestures andclassifiers.[136]
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Thehistory of technologyis the history of the invention of tools and techniques by humans. Technology includes methods ranging from simplestone toolsto the complexgenetic engineeringand information technology that has emerged since the 1980s. The termtechnologycomes from the Greek wordtechne, meaning art and craft, and the wordlogos, meaning word and speech. It was first used to describeapplied arts, but it is now used to describe advancements and changes that affect the environment around us.[1]
New knowledge has enabled people to create new tools, and conversely, many scientific endeavors are made possible by newtechnologies, for examplescientific instrumentswhich allow us to study nature in more detail than our natural senses.
Since much of technology isapplied science, technical history is connected to thehistory of science. Since technology uses resources, technical history is tightly connected toeconomic history. From those resources, technology produces other resources, includingtechnological artifactsused in everyday life.Technological changeaffects, and is affected by, a society's cultural traditions. It is a force for economic growth and a means to develop and project economic, political, military power and wealth.
Manysociologistsandanthropologistshave createdsocial theoriesdealing withsocialandcultural evolution. Some, likeLewis H. Morgan,Leslie White, andGerhard Lenskihave declared technological progress to be the primary factor driving the development of human civilization. Morgan's concept of three major stages of social evolution (savagery,barbarism, andcivilization) can be divided by technological milestones, such as fire. White argued the measure by which to judge the evolution of culture is energy.[2]
For White, "the primary function of culture" is to "harness and control energy." White differentiates between five stages ofhuman development: In the first, people use the energy of their own muscles. In the second, they use the energy ofdomesticated animals. In the third, they use the energy of plants (agricultural revolution). In the fourth, they learn to use the energy ofnatural resources: coal, oil, gas. In the fifth, they harnessnuclear energy. White introduced the formula P=E/T, where P is the development index, E is a measure of energy consumed, and T is the measure of the efficiency of technical factors using the energy. In his own words, "culture evolves as the amount of energy harnessed per capita per year is increased, or as the efficiency of the instrumental means of putting the energy to work is increased".Nikolai Kardashevextrapolated his theory, creating theKardashev scale, which categorizes the energy use of advanced civilizations.
Lenski's approach focuses on information. The more information and knowledge (especially allowing the shaping ofnatural environment) a given society has, the more advanced it is. He identifies four stages of human development, based on advances in thehistory of communication. In the first stage, information is passed bygenes. In the second, when humans gainsentience, they can learn and pass information through experience. In the third, the humans start using signs and developlogic. In the fourth, they can create symbols, develop language and writing. Advancements incommunications technologytranslate into advancements in theeconomic systemandpolitical system,distribution of wealth,social inequalityand other spheres of social life. He also differentiates societies based on their level of technology, communication, and economy:
In economics, productivity is a measure of technological progress. Productivity increases when fewer inputs (classically labor and capital but some measures include energy and materials) are used in the production of a unit of output. Another indicator of technological progress is the development of new products and services, which is necessary to offset unemployment that would otherwise result as labor inputs are reduced. In developed countries productivity growth has been slowing since the late 1970s; however, productivity growth was higher in some economic sectors, such as manufacturing.[3]For example, employment in manufacturing in the United States declined from over 30% in the 1940s to just over 10% 70 years later. Similar changes occurred in other developed countries. This stage is referred to aspost-industrial.
In the late 1970s sociologists and anthropologists likeAlvin Toffler(author ofFuture Shock),Daniel BellandJohn Naisbitthave approached the theories ofpost-industrial societies, arguing that the current era ofindustrial societyis coming to an end, andservicesand information are becoming more important than industry and goods. Some extreme visions of the post-industrial society, especially infiction, are strikingly similar to the visions of near and post-singularitysocieties.[4]
The following is a summary of the history of technology by time period and geography:
During most of thePaleolithic– the bulk of the Stone Age – all humans had a lifestyle which involved limited tools and few permanent settlements. The first major technologies were tied to survival, hunting, and food preparation. Stone tools and weapons,fire, andclothingwere technological developments of major importance during this period.
Human ancestors have been using stone and other tools since long before the emergence ofHomo sapiensapproximately 300,000 years ago.[5]The earliest direct evidence of tool usage was found inEthiopiawithin theGreat Rift Valley, dating back to 2.5 million years ago.[6]The earliest methods ofstone toolmaking, known as theOldowan"industry", date back to at least 2.3 million years ago.[7]This era of stone tool use is called thePaleolithic, or "Old stone age", and spans all of human history up to the development of agriculture approximately 12,000 years ago.
To make a stone tool, a "core" of hard stone with specific flaking properties (such asflint) was struck with ahammerstone. This flaking produced sharp edges which could be used as tools, primarily in the form ofchoppersorscrapers.[8]These tools greatly aided the early humans in theirhunter-gathererlifestyle to perform a variety of tasks including butchering carcasses (and breaking bones to get at themarrow); chopping wood; cracking open nuts; skinning an animal for its hide, and even forming other tools out of softer materials such as bone and wood.[9]
The earliest stone tools were irrelevant, being little more than a fractured rock. In theAcheulianera, beginning approximately 1.65 million years ago, methods of working these stones into specific shapes, such ashand axesemerged. This early Stone Age is described as theLower Paleolithic.
TheMiddle Paleolithic, approximately 300,000 years ago, saw the introduction of theprepared-core technique, where multiple blades could be rapidly formed from a single core stone.[8]TheUpper Paleolithic, beginning approximately 40,000 years ago, saw the introduction ofpressure flaking, where a wood, bone, or antlerpunchcould be used to shape a stone very finely.[10]
The end of the last Ice Age about 10,000 years ago is taken as the end point of theUpper Paleolithicand the beginning of theEpipaleolithic/Mesolithic. The Mesolithic technology included the use ofmicrolithsas composite stone tools, along with wood, bone, and antler tools.
The later Stone Age, during which the rudiments of agricultural technology were developed, is called theNeolithicperiod. During this period, polished stone tools were made from a variety of hard rocks such asflint,jade,jadeite, andgreenstone, largely by working exposures as quarries, but later the valuable rocks were pursued by tunneling underground, the first steps in mining technology. The polished axes were used for forest clearance and the establishment of crop farming and were so effective as to remain in use when bronze and iron appeared. These stone axes were used alongside a continued use of stone tools such as a range ofprojectiles, knives, andscrapers, as well as tools, made from organic materials such as wood, bone, and antler.[11]
Stone Age cultures developedmusicand engaged in organizedwarfare. Stone Age humans developed ocean-worthyoutrigger canoetechnology, leading tomigrationacross theMalay Archipelago, across the Indian Ocean toMadagascarand also across the Pacific Ocean, which required knowledge of the ocean currents, weather patterns, sailing, andcelestial navigation.
Although Paleolithic cultures left no written records, the shift from nomadic life to settlement and agriculture can be inferred from a range of archaeological evidence. Such evidence includes ancient tools,[12]cave paintings, and otherprehistoric art, such as theVenus of Willendorf. Human remains also provide direct evidence, both through the examination of bones, and the study ofmummies. Scientists and historians have been able to form significant inferences about the lifestyle and culture of various prehistoric peoples, and especially their technology.
Metallic copper occurs on the surface of weathered copper ore deposits and copper was used before coppersmeltingwas known. Copper smelting is believed to have originated when the technology of potterykilnsallowed sufficiently high temperatures.[13]The concentration of various elements such as arsenic increase with depth in copper ore deposits and smelting of these ores yieldsarsenical bronze, which can be sufficientlywork hardenedto be suitable for making tools.[13]
Bronzeis an alloy of copper with tin; the latter being found in relatively few deposits globally caused a long time to elapse before true tin bronze became widespread. (See:Tin sources and trade in ancient times) Bronze was a major advancement over stone as a material for making tools, both because of its mechanical properties like strength and ductility and because it could be cast in molds to make intricately shaped objects. Bronze significantly advanced shipbuilding technology with better tools and bronze nails. Bronze nails replaced the old method of attaching boards of the hull with cord woven through drilled holes.[14]Better ships enabled long-distance trade and the advance of civilization.
This technological trend apparently began in theFertile Crescentand spread outward over time.[citation needed]These developments were not, and still are not, universal. Thethree-age systemdoes not accurately describe the technology history of groups outside ofEurasia, and does not apply at all in the case of some isolated populations, such as theSpinifex People, theSentinelese, and various Amazonian tribes, which still make use of Stone Age technology, and have not developed agricultural or metal technology. These villages preserve traditional customs in the face of global modernity, exhibiting a remarkable resistance to the rapid advancement of technology.
Before iron smelting was developed the only iron was obtained from meteorites and is usually identified by having nickel content.Meteoric ironwas rare and valuable, but was sometimes used to make tools and other implements, such as fish hooks.
TheIron Ageinvolved the adoption ofiron smeltingtechnology. It generally replaced bronze and made it possible to produce tools which were stronger, lighter and cheaper to make than bronze equivalents. The raw materials to make iron, such as ore and limestone, are far more abundant than copper and especially tin ores. Consequently, iron was produced in many areas.
It was not possible to mass manufacture steel or pure iron because of the high temperatures required. Furnaces could reach melting temperature but the crucibles and molds needed for melting and casting had not been developed. Steel could be produced byforgingbloomery iron to reduce the carbon content in a somewhat controllable way, but steel produced by this method was not homogeneous.
In many Eurasian cultures, the Iron Age was the last major step before the development of written language, though again this was not universally the case.
In Europe, largehill fortswere built either as a refuge in time of war or sometimes as permanent settlements. In some cases, existing forts from the Bronze Age were expanded and enlarged. The pace of land clearance using the more effective iron axes increased, providing more farmland to support the growing population.
Mesopotamia(modern Iraq) and its peoples (Sumerians,Akkadians,AssyriansandBabylonians) lived in cities from c. 4000 BC,[15]and developed a sophisticated architecture in mud-brick and stone,[16]including the use of thetrue arch. The walls of Babylon were so massive they were quoted as aWonder of the World. They developed extensive water systems; canals for transport and irrigation in the alluvial south, and catchment systems stretching for tens of kilometers in the hilly north. Their palaces had sophisticated drainage systems.[17]
Writing was invented in Mesopotamia, using thecuneiformscript. Many records on clay tablets and stone inscriptions have survived. These civilizations were early adopters of bronze technologies which they used for tools, weapons and monumental statuary. By 1200 BC they could cast objects 5 m long in a single piece.
Several of the six classicsimple machineswere invented in Mesopotamia.[18]Mesopotamians have been credited with the invention of the wheel. Thewheel and axlemechanism first appeared with thepotter's wheel, invented inMesopotamia(modern Iraq) during the 5th millennium BC.[19]This led to the invention of thewheeled vehiclein Mesopotamia during the early 4th millennium BC. Depictions of wheeledwagonsfound onclay tabletpictographsat theEanna districtofUrukare dated between 3700 and 3500 BC.[20]Theleverwas used in theshadoofwater-lifting device, the firstcranemachine, which appeared in Mesopotamia circa 3000 BC,[21]and then inancient Egyptian technologycirca 2000 BC.[22]The earliest evidence ofpulleysdate back to Mesopotamia in the early 2nd millennium BC.[23]
Thescrew, the last of the simple machines to be invented,[24]first appeared in Mesopotamia during theNeo-Assyrianperiod (911–609) BC.[23]The Assyrian KingSennacherib(704–681 BC) claims to have invented automatic sluices and to have been the first to use waterscrew pumps, of up to 30 tons weight, which were cast using two-part clay molds rather than by the 'lost wax' process.[17]The Jerwan Aqueduct (c. 688 BC) is made with stone arches and lined with waterproof concrete.[25]
TheBabylonian astronomical diariesspanned 800 years. They enabled meticulous astronomers to plot the motions of the planets and to predict eclipses.[26]
The earliest evidence ofwater wheelsandwatermillsdate back to theancient Near Eastin the 4th century BC,[27]specifically in thePersian Empirebefore 350 BC, in the regions of Mesopotamia (Iraq) andPersia(Iran).[28]This pioneering use ofwater powerconstituted the first human-devised motive force not to rely on muscle power (besides thesail).
TheEgyptians, known for building pyramids centuries before the creation of modern tools, invented and used many simple machines, such as therampto aid construction processes. Historians and archaeologists have found evidence that thepyramidswere built using three of what is called theSix Simple Machines, from which all machines are based. These machines are theinclined plane, thewedge, and thelever, which allowed the ancient Egyptians to move millions of limestone blocks which weighed approximately 3.5 tons (7,000 lbs.) each into place to create structures like theGreat Pyramid of Giza, which is 481 feet (147 meters) high.[29]
They also made writing medium similar to paper frompapyrus, which Joshua Mark states is the foundation for modern paper. Papyrus is a plant (cyperus papyrus) which grew in plentiful amounts in the Egyptian Delta and throughout the Nile River Valley during ancient times. The papyrus was harvested by field workers and brought to processing centers where it was cut into thin strips. The strips were then laid-out side by side and covered in plant resin. The second layer of strips was laid on perpendicularly, then both pressed together until the sheet was dry. The sheets were then joined to form a roll and later used for writing.[30]
Egyptian society made several significant advances during dynastic periods in many areas of technology. According to Hossam Elanzeery, they were the first civilization to use timekeeping devices such as sundials, shadow clocks, and obelisks and successfully leveraged their knowledge of astronomy to create a calendar model that society still uses today. They developed shipbuilding technology that saw them progress from papyrus reed vessels to cedar wood ships while also pioneering the use of rope trusses and stem-mounted rudders. The Egyptians also used their knowledge of anatomy to lay the foundation for many modern medical techniques and practiced the earliest known version of neuroscience. Elanzeery also states that they used and furthered mathematical science, as evidenced in the building of the pyramids.[31]
Ancient Egyptians also invented and pioneered many food technologies that have become the basis of modern food technology processes. Based on paintings and reliefs found in tombs, as well as archaeological artifacts, scholars like Paul T Nicholson believe that the Ancient Egyptians established systematic farming practices, engaged in cereal processing, brewed beer and baked bread, processed meat, practiced viticulture and created the basis for modern wine production, and created condiments to complement, preserve and mask the flavors of their food.[32]
TheIndus Valley Civilization, situated in a resource-rich area (in modernPakistanand northwestern India), is notable for its early application of city planning,sanitation technologies, and plumbing.[33]Indus Valley construction and architecture, called 'Vaastu Shastra', suggests a thorough understanding of materials engineering, hydrology, and sanitation.
The Chinese made many first-known discoveries and developments. Majortechnological contributions from Chinainclude the earliest known form of thebinary codeand epigenetic sequencing,[34][35]earlyseismological detectors,matches, paper,Helicopter rotor,Raised-relief map, the double-action piston pump,cast iron, water powered blast furnacebellows, the ironplough, the multi-tubeseed drill, the wheelbarrow, the parachute, thecompass, therudder, thecrossbow, theSouth Pointing Chariotand gunpowder. China also developed deep well drilling, which they used to extract brine for making salt. Some of these wells, which were as deep as 900 meters, produced natural gas which was used for evaporating brine.[36]
Other Chinese discoveries and inventions from the medieval period includeblock printing,movable type printing, phosphorescent paint, endless powerchain driveand the clock escapement mechanism. The solid-fuelrocketwas invented in China about 1150, nearly 200 years after the invention ofgunpowder(which acted as the rocket's fuel). Decades before the West's age of exploration, the Chinese emperors of theMing Dynastyalso sentlarge fleetson maritime voyages, some reaching Africa.
TheHellenistic periodofMediterranean historybegan in the 4th century BC withAlexander's conquests, which led to the emergence of aHellenistic civilizationrepresenting a synthesis ofGreekandNear-Easterncultures in theEastern Mediterraneanregion, including theBalkans,LevantandEgypt.[37]WithPtolemaic Egyptas its intellectual center and Greek as the lingua franca, the Hellenistic civilization includedGreek,Egyptian, Jewish,PersianandPhoenicianscholars and engineers who wrote in Greek.[38]
Hellenistic engineers of the Eastern Mediterranean were responsible for a number ofinventions and improvementsto existing technology. TheHellenistic periodsaw a sharp increase in technological advancement, fostered by a climate of openness to new ideas, the blossoming of a mechanistic philosophy, and the establishment of theLibrary of AlexandriainPtolemaic Egyptand its close association with the adjacentmuseion. In contrast to the typically anonymous inventors of earlier ages, ingenious minds such asArchimedes,Philo of Byzantium,Heron,Ctesibius, andArchytasremain known by name to posterity.
Ancient agriculture, as in any period prior to the modern age the primary mode of production and subsistence, and its irrigation methods, were considerably advanced by the invention and widespread application of a number of previously unknown water-lifting devices, such as the verticalwater-wheel, the compartmented wheel, the waterturbine,Archimedes' screw, the bucket-chain and pot-garland, theforce pump, thesuction pump, the double-actionpiston pumpand quite possibly thechain pump.[39]
In music, thewater organ, invented by Ctesibius and subsequently improved, constituted the earliest instance of a keyboard instrument. In time-keeping, the introduction of the inflowclepsydraand its mechanization by the dial and pointer, the application of afeedback systemand theescapementmechanism far superseded the earlier outflow clepsydra.
Innovations in mechanical technology included the newly devised right-angledgear, which would become particularly important to the operation of mechanical devices. Hellenistic engineers also devisedautomatasuch as suspended ink pots, automaticwashstands, and doors, primarily as toys, which however featured new useful mechanisms such as thecamandgimbals.
TheAntikythera mechanism, a kind ofanalogous computerworking with adifferential gear, and theastrolabeboth show great refinement in astronomical science.
In other fields, ancient Greek innovations include thecatapultand thegastraphetescrossbow in warfare, hollow bronze-casting in metallurgy, thedioptrafor surveying, in infrastructure thelighthouse,central heating, atunnel excavated from both ends by scientific calculations, and theship trackway. In transport, great progress resulted from the invention of thewinchand theodometer.
Further newly created techniques and items werespiral staircases, thechain drive,sliding calipersand showers.
TheRoman Empireexpanded fromItaliaacross the entireMediterranean regionbetween the 1st century BC and 1st century AD. Its most advanced and economically productive provinces outside of Italia were theEastern Romanprovinces in theBalkans,Asia Minor,Egypt, and theLevant, withRoman Egyptin particular being the wealthiest Roman province outside of Italia.[40][41]
The Roman Empire developed an intensive and sophisticated agriculture, expanded upon existing iron working technology, createdlawsproviding for individual ownership, advanced stone masonry technology, advancedroad-building(exceeded only in the 19th century), military engineering, civil engineering, spinning and weaving and several different machines like theGallic reaperthat helped to increase productivity in many sectors of the Roman economy.Roman engineerswere the first to build monumental arches,amphitheatres,aqueducts,public baths,true arch bridges,harbours, reservoirs and dams, vaults and domes on a very large scale across their Empire. Notable Roman inventions include thebook (Codex),glass blowingand concrete. Because Rome was located on a volcanic peninsula, with sand which contained suitable crystalline grains, the concrete which the Romans formulated was especially durable. Some of their buildings have lasted 2000 years, to the present day.
In Roman Egypt, the inventorHero of Alexandriawas the first to experiment with awind-poweredmechanical device (seeHeron's windwheel) and even created the earlieststeam-powereddevice (theaeolipile), opening up new possibilities in harnessing natural forces. He also devised avending machine. However, his inventions were primarily toys, rather than practical machines.
The engineering skills of theIncaandMayawere great, even by today's standards. An example of this exceptional engineering is the use of pieces weighing upwards of one ton in their stonework placed together so that not even a blade can fit into the cracks. Inca villages used irrigation canals anddrainagesystems, making agriculture very efficient. While some claim that the Incas were the first inventors ofhydroponics, their agricultural technology was still soil based, if advanced.
Though theMaya civilizationdid not incorporate metallurgy or wheel technology in their architectural constructions, they developed complex writing and astronomical systems, and created beautiful sculptural works in stone and flint. Like the Inca, the Maya also had command of fairly advanced agricultural and construction technology. The Maya are also responsible for creating the first pressurized water system in Mesoamerica, located in the Maya site ofPalenque.[42]
The main contribution of theAztecrule was a system of communications between the conquered cities and the ubiquity of the ingenious agricultural technology ofchinampas. InMesoamerica, without draft animals for transport (nor, as a result, wheeled vehicles), the roads were designed for travel on foot, just as in the Inca and Mayan civilizations. The Aztec, subsequently to the Maya, inherited many of the technologies and intellectual advancements of their predecessors: theOlmec(seeNative American inventions and innovations).
One of the most significant developments of the medieval were economies in which water and wind power were more significant than animal and human muscle power.[43]: 38Most water and wind power was used for milling grain. Water power was also used for blowing air inblast furnace, pulping rags for paper making and for felting wool. TheDomesday Bookrecorded 5,624 water mills in Great Britain in 1086, being about one per thirty families.[43]
The Muslimcaliphatesunited in trade large areas that had previously traded little, including the Middle East, North Africa, Central Asia, theIberian Peninsula, and parts of theIndian subcontinent. The science and technology of previous empires in the region, including the Mesopotamian, Egyptian, Persian, Hellenistic and Roman empires, were inherited by theMuslim world, where Arabic replaced Syriac, Persian and Greek as the lingua franca of the region. Significant advances were made in the region during theIslamic Golden Age(8th–16th centuries).
TheArab Agricultural Revolutionoccurred during this period. It was a transformation in agriculture from the8th to the 13th century in the Islamic regionof theOld World. The economy established byAraband otherMuslim tradersacross the Old World enabled the diffusion of many crops and farming techniques throughout the Islamic world, as well as the adaptation of crops and techniques from and to regions outside it.[44]Advances were made inanimal husbandry,irrigation, and farming, with the help of new technology such as thewindmill. These changes made agriculture much more productive, supporting population growth, urbanisation, and increased stratification of society.
Muslim engineers in the Islamic world made wide use ofhydropower, along with early uses oftidal power,wind power,[45]fossil fuelssuch as petroleum, and large factory complexes (tirazin Arabic).[46]A variety of industrial mills were employed in the Islamic world, includingfullingmills,gristmills,hullers,sawmills,ship mills,stamp mills,steel mills, andtide mills. By the 11th century, every province throughout the Islamic world had these industrial mills in operation.[47]Muslim engineers also employedwater turbinesandgearsin mills and water-raising machines, and pioneered the use ofdamsas a source of water power, used to provide additional power towatermillsand water-raising machines.[48]Many of these technologies were transferred to medieval Europe.[49]
Wind-poweredmachines used to grind grain and pump water, the windmill andwind pump, first appeared in what are nowIran,Afghanistanand Pakistan by the 9th century.[50][51][52][53]They were used to grind grains and draw up water, and used in the gristmilling and sugarcane industries.[54]Sugar millsfirst appeared in themedieval Islamic world.[55]They were first driven by watermills, and then windmills from the 9th and 10th centuries in what are todayAfghanistan, Pakistan andIran.[56]Crops such asalmondsandcitrusfruit were brought to Europe throughAl-Andalus, and sugar cultivation was gradually adopted across Europe. Arab merchants dominated trade in the Indian Ocean until the arrival of the Portuguese in the 16th century.
The Muslim world adoptedpapermakingfrom China.[47]The earliestpaper millsappeared inAbbasid-eraBaghdadduring 794–795.[57]The knowledge ofgunpowderwas also transmitted from China via predominantly Islamic countries,[58]where formulas for purepotassium nitratewere developed.[59][60]
Thespinning wheelwas invented in theIslamic worldby the early 11th century.[61]It was later widely adopted in Europe, where it was adapted into thespinning jenny, a key device during theIndustrial Revolution.[62]Thecrankshaftwas invented byAl-Jazariin 1206,[63][64]and is central to modern machinery such as thesteam engine,internal combustion engineandautomatic controls.[65][66]Thecamshaftwas also first described by Al-Jazari in 1206.[67]
Earlyprogrammable machineswere also invented in the Muslim world. The firstmusic sequencer, a programmablemusical instrument, was an automated flute player invented by theBanu Musabrothers, described in theirBook of Ingenious Devices, in the 9th century.[68][69]In 1206, Al-Jazari invented programmableautomata/robots. He described fourautomatonmusicians, including two drummers operated by a programmabledrum machine, where the drummer could be made to play different rhythms and different drum patterns.[70]Thecastle clock, ahydropoweredmechanicalastronomical clockinvented by Al-Jazari, was an earlyprogrammableanalog computer.[71][72][73]
In theOttoman Empire, a practical impulsesteam turbinewas invented in 1551 byTaqi ad-Din Muhammad ibn Ma'rufinOttoman Egypt. He described a method for rotating aspitby means of a jet of steam playing on rotary vanes around the periphery of a wheel. Known as asteam jack, a similar device for rotating a spit was also later described byJohn Wilkinsin 1648.[74][75]
While medieval technology has been long depicted as a step backward in the evolution of Western technology, a generation of medievalists (like the American historian of scienceLynn White) stressed from the 1940s onwards the innovative character of many medieval techniques. Genuine medieval contributions include for examplemechanical clocks,spectaclesand verticalwindmills. Medieval ingenuity was also displayed in the invention of seemingly inconspicuous items like thewatermarkor thefunctional button. In navigation, the foundation to the subsequentAge of Discoverywas laid by the introduction of pintle-and-gudgeonrudders,lateen sails, thedry compass, the horseshoe and theastrolabe.
Significant advances were also made in military technology with the development ofplate armour, steelcrossbowsandcannon. The Middle Ages are perhaps best known for their architectural heritage: While the invention of therib vaultandpointed archgave rise to the high risingGothic style, the ubiquitous medieval fortifications gave the era the almost proverbial title of the 'age of castles'.
Papermaking, a 2nd-century Chinese technology, was carried to the Middle East when a group of Chinese papermakers were captured in the 8th century.[76]Papermaking technology was spread to Europe by theUmayyad conquest of Hispania.[77]A paper mill was established in Sicily in the 12th century. In Europe the fiber to make pulp for making paper was obtained from linen and cotton rags.Lynn Townsend White Jr.credited the spinning wheel with increasing the supply of rags, which led to cheap paper, which was a factor in the development of printing.[78]
Before the development of modern engineering, mathematics was used by artisans and craftsmen, such asmillwrights, clock makers, instrument makers and surveyors. Aside from these professions, universities were not believed to have had much practical significance to technology.[79]: 32
A standard reference for the state of mechanical arts during the Renaissance is given in the mining engineering treatiseDe re metallica(1556), which also contains sections on geology, mining and chemistry.De re metallicawas the standard chemistry reference for the next 180 years.[79]Among the water powered mechanical devices in use wereore stamping mills, forge hammers, blast bellows, and suction pumps.
Due to the casting of cannon, theblast furnacecame into widespread use in France in the mid 15th century. The blast furnace had been used in China since the 4th century BC.[13][80]
The invention of the movable cast metal typeprinting press, whose pressing mechanism was adapted from an olive screw press, (c. 1441) lead to a tremendous increase in the number of books and the number of titles published. Movable ceramic type had been used in China for a few centuries and woodblock printing dated back even further.[81]
The era is marked by such profound technical advancements likelinear perceptivity,double shell domesorBastion fortresses. Note books of the Renaissance artist-engineers such asTaccolaandLeonardo da Vincigive a deep insight into the mechanical technology then known and applied. Architects and engineers were inspired by the structures ofAncient Rome, and men likeBrunelleschicreated the large dome ofFlorence Cathedralas a result. He was awarded one of the first patents ever issued to protect an ingeniouscranehe designed to raise the large masonry stones to the top of the structure. Military technology developed rapidly with the widespread use of thecross-bowand ever more powerfulartillery, as the city-states of Italy were usually in conflict with one another. Powerful families like theMediciwere strong patrons of the arts and sciences.Renaissance sciencespawned theScientific Revolution; science and technology began a cycle of mutual advancement.
An improved sailing ship, the nau orcarrack, enabled theAge of Explorationwith theEuropean colonization of the Americas, epitomized byFrancis Bacon'sNew Atlantis. Pioneers likeVasco da Gama,Cabral,MagellanandChristopher Columbusexplored the world in search of new trade routes for their goods and contacts with Africa, India and China to shorten the journey compared with traditional routes overland. They produced new maps and charts which enabled following mariners to explore further with greater confidence. Navigation was generally difficult, however, owing to theproblem of longitudeand the absence of accuratechronometers. European powers rediscovered the idea of thecivil code, lost since the time of the Ancient Greeks.
Thestocking frame, which was invented in 1598, increased a knitter's number of knots per minute from 100 to 1000.[82]
Mines were becoming increasingly deep and were expensive to drain with horse powered bucket and chain pumps and wooden piston pumps. Some mines used as many as 500 horses. Horse-powered pumps were replaced by theSavery steam pump(1698) and theNewcomen steam engine(1712).[83]
The revolution was driven by cheap energy in the form of coal, produced in ever-increasing amounts from the abundant resources ofBritain. The BritishIndustrial Revolutionis characterized by developments in the areas of textile machinery, mining,metallurgy, transport and the invention ofmachine tools.
Before invention of machinery to spin yarn and weave cloth, spinning was done using the spinning wheel and weaving was done on a hand-and-foot-operated loom. It took from three to five spinners to supply one weaver.[84][85]The invention of theflying shuttlein 1733 doubled the output of a weaver, creating a shortage of spinners. Thespinning framefor wool was invented in 1738. Thespinning jenny, invented in 1764, was a machine that used multiple spinning wheels; however, it produced low quality thread. Thewater framepatented by Richard Arkwright in 1767, produced a better quality thread than the spinning jenny. Thespinning mule, patented in 1779 bySamuel Crompton, produced a high quality thread.[84][85]Thepower loomwas invented by Edmund Cartwright in 1787.[84]
In the mid-1750s, thesteam enginewas applied to the water power-constrained iron, copper and lead industries for powering blast bellows. These industries were located near the mines, some of which were using steam engines for mine pumping. Steam engines were too powerful for leather bellows, so cast iron blowing cylinders were developed in 1768. Steam powered blast furnaces achieved higher temperatures, allowing the use of more lime in iron blast furnace feed. (Lime rich slag was not free-flowing at the previously used temperatures.) With a sufficient lime ratio, sulfur from coal or coke fuel reacts with the slag so that the sulfur does not contaminate the iron. Coal and coke were cheaper and more abundant fuel. As a result, iron production rose significantly during the last decades of the 18th century.[13]Coal converted tocokefueled higher temperatureblast furnacesand produced cast iron in much larger amounts than before, allowing the creation of a range of structures such asThe Iron Bridge. Cheap coal meant that industry was no longer constrained by water resources driving the mills, although it continued as a valuable source of power.
The steam engine helped drain the mines, so more coal reserves could be accessed, and the output of coal increased. The development of the high-pressure steam engine made locomotives possible, and a transport revolution followed.[86]The steam engine which had existed since the early 18th century, was practically applied to bothsteamboatand railway transportation. TheLiverpool and Manchester Railway, the first purpose-built railway line, opened in 1830, theRocket locomotiveofRobert Stephensonbeing one of its first workinglocomotivesused.
Manufacture of ships' pulleyblocksby all-metal machines at thePortsmouth Block Millsin 1803 instigated the age of sustainedmass production.Machine toolsused by engineers to manufacture parts began in the first decade of the century, notably byRichard RobertsandJoseph Whitworth. The development ofinterchangeable partsthrough what is now called theAmerican system of manufacturingbegan in the firearms industry at the U.S. Federal arsenals in the early 19th century, and became widely used by the end of the century.
Until theEnlightenment era, little progress was made inwater supply and sanitationand the engineering skills of the Romans were largely neglected throughout Europe. The first documented use ofsand filtersto purify the water supply dates to 1804, when the owner of a bleachery inPaisley, Scotland, John Gibb, installed an experimental filter, selling his unwanted surplus to the public. The first treated public water supply in the world was installed by engineerJames Simpsonfor theChelsea Waterworks Companyin London in 1829.[87]The first screw-downwater tapwas patented in 1845 by Guest and Chrimes, a brass foundry inRotherham.[88]The practice of water treatment soon became mainstream, and the virtues of the system were made starkly apparent after the investigations of the physicianJohn Snowduring the1854 Broad Street cholera outbreakdemonstrated the role of the water supply in spreading the cholera epidemic.[89]
The 19th century saw astonishing developments in transportation, construction, manufacturing and communication technologies originating in Europe. After a recession at the end of the 1830s and a general slowdown in major inventions, theSecond Industrial Revolutionwas a period of rapid innovation and industrialization that began in the 1860s or around 1870 and lasted untilWorld War I. It included rapid development of chemical, electrical, petroleum, and steel technologies connected with highly structured technology research.
Telegraphydeveloped into a practical technology in the 19th century to help run the railways safely.[90]Along with the development of telegraphy was the patenting of the first telephone. March 1876 marks the date that Alexander Graham Bell officially patented his version of an "electric telegraph". Although Bell is noted with the creation of the telephone, it is still debated about who actually developed the first working model.[91]
Building on improvements in vacuum pumps and materials research,incandescent light bulbsbecame practical for general use in the late 1870s. Edison Electric Illuminating Company, a company founded by Thomas Edison with financial backing fromSpencer Trask, built and managed the first electricity network. Electrification was rated the most important technical development of the 20th century as the foundational infrastructure for modern civilization.[92]This invention had a profound effect on the workplace because factories could now have second and third shift workers.[93]
Shoe production was mechanized during the mid 19th century.[94]Mass production ofsewing machinesandagricultural machinerysuch as reapers occurred in the mid to late 19th century.[95]Bicycles were mass-produced beginning in the 1880s.[95]
Steam-powered factories became widespread, although the conversion from water power to steam occurred in England earlier than in the U.S.[96]Ironclad warshipswere found in battle starting in the 1860s, and played a role in the opening of Japan and China to trade with the West.
Between 1825 and 1840, the technology ofphotographywas introduced. For much of the rest of the century, many engineers and inventors tried to combine it and the much older technique ofprojectionto create a complete illusion or a complete documentation of reality. Colour photography was usually included in these ambitions and the introduction of thephonographin 1877 seemed to promise the addition ofsynchronized sound recordings. Between 1887 and 1894, the first successful shortcinematographicpresentations were established.
Mass productionbroughtautomobilesand other high-tech goods to masses of consumers.Military researchand development sped advances including electroniccomputingandjet engines. Radio andtelephonygreatly improved and spread to larger populations of users, though near-universal access would not be possible untilmobile phonesbecame affordable todeveloping worldresidents in the late 2000s and early 2010s.
Energy and engine technology improvements includednuclear power, developed after theManhattan projectwhich heralded the newAtomic Age.Rocketdevelopment led to long range missiles and the firstspace agethat lasted from the 1950s with the launch of Sputnik to the mid-1980s.
Electrificationspread rapidly in the 20th century. At the beginning of the century electric power was for the most part only available to wealthy people in a few major cities. By 2019, an estimated 87 percent of the world's population had access to electricity.[98]
Birth controlalso became widespread during the 20th century.Electron microscopeswere very powerful by the late 1970s and genetic theory and knowledge were expanding, leading to developments ingenetic engineering.
The first "test tube baby"Louise Brownwas born in 1978, which led to the first successfulgestational surrogacypregnancy in 1985 and the first pregnancy byICSIin 1991, which is the implanting of a single sperm into an egg.Preimplantation genetic diagnosiswas first performed in late 1989 and led to successful births in July 1990. These procedures have become relatively common.
Computers were connected by means of local area,telecomandfiber optic networks, powered by theoptical amplifierthat ushered in theInformation Age.[99][100]Thisoptical networkingtechnology exploded the capacity of the Internet beginning in 1996 with the launch of the first high-capacitywave division multiplexing(WDM) system byCiena Corp.[101]WDM, as the common basis for telecom backbone networks,[102]increased transmission capacity by orders of magnitude, thus enabling the mass commercialization and popularization of the Internet and its widespread impact on culture, economics, business, and society.
The commercial availability of the first portable cell phone in 1981 and the first pocket-sized phone in 1985,[103]both developed by Comvik in Sweden, coupled with the first transmission of data over a cellular network byVodafone(formerlyRacal-Millicom) in 1992 were the breakthroughs that led directly to the form and function of smartphones today. By 2014, there were more cell phones in use than people on Earth[104]and The Supreme Court of the United States of America has ruled that a mobile phone was a private part of a person.[105]Providing consumers wireless access to each other and to the Internet, the mobile phone stimulated one of the most important technology revolutions in human history.[106]
The Human Genome Project sequenced and identified all three billion chemical units in human DNA with a goal of finding the genetic roots of disease and developing treatments. The project became feasible due to two technical advances made during the late 1970s: gene mapping by restriction fragment length polymorphism (RFLP) markers and DNA sequencing. Sequencing was invented by Frederick Sanger and, separately, by Dr. Walter Gilbert. Gilbert also conceived of the Human Genome Project on May 27, 1985, and first publicly advocated it in August 1985 at the first International Conference on Genes and Computers in August 1985.[107]The U.S. Federal Government sponsored Human Genome Project began October 1, 1990, and was declared complete in 2003.[107]
The massive data analysis resources necessary for running transatlantic research programs such as theHuman Genome Projectand theLarge Electron–Positron Colliderled to a necessity for distributed communications, causing Internet protocols to be more widely adopted by researchers and also creating a justification forTim Berners-Leeto create theWorld Wide Web.
Vaccinationspread rapidly to the developing world from the 1980s onward due to many successful humanitarian initiatives, greatly reducing childhood mortality in many poor countries with limited medical resources.
The USNational Academy of Engineering, by expert vote, established the following ranking of the most important technological developments of the 20th century:[108]
In the early 21st century, research is ongoing intoquantum computers,gene therapy(introduced 1990),3D printing(introduced 1981),nanotechnology(introduced 1985),bioengineering/biotechnology,nuclear technology,advanced materials(e.g., graphene), thescramjetanddrones(along withrailgunsand high-energy laser beams for military uses),superconductivity, thememristor, and green technologies such asalternative fuels(e.g.,fuel cells, self-driving electric andplug-in hybridcars),augmented realitydevices andwearable electronics,artificial intelligence, and more efficient and powerfulLEDs,solar cells,integrated circuits,wireless powerdevices, engines, andbatteries.
Large Hadron Collider, the largest single machine ever built, was constructed between 1998 and 2008. The understanding ofparticle physicsis expected to expand with better instruments including largerparticle acceleratorssuch as the LHC[109]and betterneutrino detectors.Dark matteris sought via underground detectors and observatories likeLIGOhave started to detectgravitational waves.
Genetic engineering technology continues to improve, and the importance ofepigeneticson development and inheritance has also become increasingly recognized.[110]
Newspaceflighttechnology andspacecraftare also being developed, like the Boeing'sOrionand SpaceX'sDragon 2. New, more capablespace telescopes, such as theJames Webb Space Telescopewhich was launched to orbit in December, 2021, and theColossus Telescope, have been designed. TheInternational Space Stationwas completed in the 2000s, andNASAandESAplan ahuman mission to Marsin the 2030s. TheVariable Specific Impulse Magnetoplasma Rocket(VASIMR) is an electro-magnetic thruster for spacecraft propulsion and is expected to be tested in 2015.[needs update]
TheBreakthrough Initiativesproject plans to sendthe first ever spacecraft to visit another star, which will consist of numerous super-light chips driven byElectric propulsionin the 2030s, and receive images of theProxima Centaurisystem, along with, possibly, thepotentially habitable planetProxima Centauri b, by midcentury.[111]
2004 saw thefirst crewed commercial spaceflightwhenMike Melvillcrossed theboundary of spaceon June 21, 2004.
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https://en.wikipedia.org/wiki/History_of_technology
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The following is alist of UK government data losses. It lists reported instances of the loss of personal data by UK central and local government, agencies, non-departmental public bodies, etc., whether directly or indirectly because of the actions of private-sector contractors. Such losses tend to receive widespread media coverage in the UK.
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https://en.wikipedia.org/wiki/List_of_UK_government_data_losses
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Algorithm selection(sometimes also calledper-instance algorithm selectionoroffline algorithm selection) is a meta-algorithmic techniqueto choose an algorithm from a portfolio on an instance-by-instance basis. It is motivated by the observation that on many practical problems, different algorithms have different performance characteristics. That is, while one algorithm performs well in some scenarios, it performs poorly in others and vice versa for another algorithm. If we can identify when to use which algorithm, we can optimize for each scenario and improve overall performance. This is what algorithm selection aims to do. The only prerequisite for applying algorithm selection techniques is that there exists (or that there can be constructed) a set of complementary algorithms.
Given a portfolioP{\displaystyle {\mathcal {P}}}of algorithmsA∈P{\displaystyle {\mathcal {A}}\in {\mathcal {P}}}, a set of instancesi∈I{\displaystyle i\in {\mathcal {I}}}and a cost metricm:P×I→R{\displaystyle m:{\mathcal {P}}\times {\mathcal {I}}\to \mathbb {R} }, the algorithm selection problem consists of finding a mappings:I→P{\displaystyle s:{\mathcal {I}}\to {\mathcal {P}}}from instancesI{\displaystyle {\mathcal {I}}}to algorithmsP{\displaystyle {\mathcal {P}}}such that the cost∑i∈Im(s(i),i){\displaystyle \sum _{i\in {\mathcal {I}}}m(s(i),i)}across all instances is optimized.[1][2]
A well-known application of algorithm selection is theBoolean satisfiability problem. Here, the portfolio of algorithms is a set of (complementary)SAT solvers, the instances are Boolean formulas, the cost metric is for example average runtime or number of unsolved instances. So, the goal is to select a well-performing SAT solver for each individual instance. In the same way, algorithm selection can be applied to many otherNP{\displaystyle {\mathcal {NP}}}-hard problems (such asmixed integer programming,CSP,AI planning,TSP,MAXSAT,QBFandanswer set programming). Competition-winning systems in SAT are SATzilla,[3]3S[4]and CSHC[5]
Inmachine learning, algorithm selection is better known asmeta-learning. The portfolio of algorithms consists of machine learning algorithms (e.g., Random Forest, SVM, DNN), the instances are data sets and the cost metric is for example the error rate. So, the goal is to predict which machine learning algorithm will have a small error on each data set.
The algorithm selection problem is mainly solved with machine learning techniques. By representing the problem instances by numerical featuresf{\displaystyle f}, algorithm selection can be seen as amulti-class classificationproblem by learning a mappingfi↦A{\displaystyle f_{i}\mapsto {\mathcal {A}}}for a given instancei{\displaystyle i}.
Instance features are numerical representations of instances. For example, we can count the number of variables, clauses, average clause length for Boolean formulas,[6]or number of samples, features, class balance for ML data sets to get an impression about their characteristics.
We distinguish between two kinds of features:
Depending on the used performance metricm{\displaystyle m}, feature computation can be associated with costs.
For example, if we use running time as performance metric, we include the time to compute our instance features into the performance of an algorithm selection system.
SAT solving is a concrete example, where such feature costs cannot be neglected, since instance features forCNFformulas can be either very cheap (e.g., to get the number of variables can be done in constant time for CNFs in the DIMACs format) or very expensive (e.g., graph features which can cost tens or hundreds of seconds).
It is important to take the overhead of feature computation into account in practice in such scenarios; otherwise a misleading impression of the performance of the algorithm selection approach is created. For example, if the decision which algorithm to choose can be made with perfect accuracy, but the features are the running time of the portfolio algorithms, there is no benefit to the portfolio approach. This would not be obvious if feature costs were omitted.
One of the first successful algorithm selection approaches predicted the performance of each algorithmm^A:I→R{\displaystyle {\hat {m}}_{\mathcal {A}}:{\mathcal {I}}\to \mathbb {R} }and selected the algorithm with the best predicted performanceargminA∈Pm^A(i){\displaystyle arg\min _{{\mathcal {A}}\in {\mathcal {P}}}{\hat {m}}_{\mathcal {A}}(i)}for an instancei{\displaystyle i}.[3]
A common assumption is that the given set of instancesI{\displaystyle {\mathcal {I}}}can be clustered into homogeneous subsets
and for each of these subsets, there is one well-performing algorithm for all instances in there.
So, the training consists of identifying the homogeneous clusters via an unsupervised clustering approach and associating an algorithm with each cluster.
A new instance is assigned to a cluster and the associated algorithm selected.[7]
A more modern approach is cost-sensitivehierarchical clustering[5]using supervised learning to identify the homogeneous instance subsets.
A common approach for multi-class classification is to learn pairwise models between every pair of classes (here algorithms)
and choose the class that was predicted most often by the pairwise models.
We can weight the instances of the pairwise prediction problem by the performance difference between the two algorithms.
This is motivated by the fact that we care most about getting predictions with large differences correct, but the penalty for an incorrect prediction is small if there is almost no performance difference.
Therefore, each instancei{\displaystyle i}for training a classification modelA1{\displaystyle {\mathcal {A}}_{1}}vsA2{\displaystyle {\mathcal {A}}_{2}}is associated with a cost|m(A1,i)−m(A2,i)|{\displaystyle |m({\mathcal {A}}_{1},i)-m({\mathcal {A}}_{2},i)|}.[8]
The algorithm selection problem can be effectively applied under the following assumptions:
Algorithm selection is not limited to single domains but can be applied to any kind of algorithm if the above requirements are satisfied.
Application domains include:
For an extensive list of literature about algorithm selection, we refer to a literature overview.
Online algorithm selection refers to switching between different algorithms during the solving process. This is useful as ahyper-heuristic. In contrast, offline algorithm selection selects an algorithm for a given instance only once and before the solving process.
An extension of algorithm selection is the per-instance algorithm scheduling problem, in which we do not select only one solver, but we select a time budget for each algorithm on a per-instance base. This approach improves the performance of selection systems in particular if the instance features are not very informative and a wrong selection of a single solver is likely.[11]
Given the increasing importance of parallel computation,
an extension of algorithm selection for parallel computation is parallel portfolio selection,
in which we select a subset of the algorithms to simultaneously run in a parallel portfolio.[12]
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https://en.wikipedia.org/wiki/Algorithm_selection
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Athlonis a family of CPUs designed byAMD, targeted mostly at the desktop market. The name "Athlon" has been largely unused as just "Athlon" since 2001 when AMD started naming its processorsAthlon XP, but in 2008 began referring to single core 64-bit processors from theAMD Athlon X2andAMD Phenomproduct lines. Later the name began being used for someAPUs.
APU features table
A0750APT3B
A0900DMT3B
A0950APT3B
A0950DMT3B
A1000DMT3B
A1000DMT3C
A1100AMT3B
A1300APS3B
Cores/threads
(GHz)
(GHz)
Mem.
(W)
(MB)
10/1
Cores/threads
Mem.
(W)
(MB)
Memorysupport
(W)
(GHz)
(MHz)
(MB)
Cores/threads
Cores/threads
Cores/threads
Graphics (Vega)
Common features:
Note 1:Athlons use adouble data rate(DDR)front-side bus, (EV-6) meaning that the actual data transfer rate of the bus is twice its physical clock rate. The FSB's true data rate, 200 or 266 MT/s, is used in the tables, and the physical clock rates are 100 and 133 MHz, respectively. The multipliers in the tables above apply to the physical clock rate, not the data transfer rate.
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https://en.wikipedia.org/wiki/List_of_AMD_Athlon_processors
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Acellular networkormobile networkis atelecommunications networkwhere the link to and from end nodes iswirelessand the network is distributed over land areas calledcells, each served by at least one fixed-locationtransceiver(such as abase station). These base stations provide the cell with the network coverage which can be used for transmission of voice, data, and other types of content viaradio waves. Each cell's coverage area is determined by factors such as the power of the transceiver, the terrain, and the frequency band being used. A cell typically uses a different set of frequencies from neighboring cells, to avoid interference and provide guaranteed service quality within each cell.[1][2]
When joined together, these cells provide radio coverage over a wide geographic area. This enables numerousdevices, includingmobile phones,tablets,laptopsequipped withmobile broadband modems, andwearable devicessuch assmartwatches, to communicate with each other and with fixed transceivers and telephones anywhere in the network, via base stations, even if some of the devices are moving through more than one cell during transmission. The design of cellular networks allows for seamlesshandover, enabling uninterrupted communication when a device moves from one cell to another.
Modern cellular networks utilize advanced technologies such asMultiple Input Multiple Output(MIMO),beamforming, and small cells to enhance network capacity and efficiency.
Cellular networks offer a number of desirable features:[2]
Major telecommunications providers have deployed voice and data cellular networks over most of the inhabited land area ofEarth. This allows mobile phones and other devices to be connected to thepublic switched telephone networkand publicInternet access. In addition to traditional voice and data services, cellular networks now supportInternet of Things(IoT) applications, connecting devices such assmart meters, vehicles, and industrial sensors.
The evolution of cellular networks from1Gto5Ghas progressively introduced faster speeds, lower latency, and support for a larger number of devices, enabling advanced applications in fields such as healthcare, transportation, andsmart cities.
Private cellular networks can be used for research[3]or for large organizations and fleets, such as dispatch for local public safety agencies or a taxicab company, as well as for local wireless communications in enterprise and industrial settings such as factories, warehouses, mines, power plants, substations, oil and gas facilities and ports.[4]
In acellular radiosystem, a land area to be supplied with radio service is divided into cells in a pattern dependent on terrain and reception characteristics. These cell patterns roughly take the form of regular shapes, such as hexagons, squares, or circles although hexagonal cells are conventional. Each of these cells is assigned with multiple frequencies (f1–f6) which have correspondingradio base stations. The group of frequencies can be reused in other cells, provided that the same frequencies are not reused in adjacent cells, which would causeco-channel interference.
The increasedcapacityin a cellular network, compared with a network with a single transmitter, comes from the mobile communication switching system developed byAmos Joelof Bell Labs[5]that permitted multiple callers in a given area to use the same frequency by switching calls to the nearest available cellular tower having that frequency available. This strategy is viable because a given radio frequency can be reused in a different area for an unrelated transmission. In contrast, a single transmitter can only handle one transmission for a given frequency. Inevitably, there is some level ofinterferencefrom the signal from the other cells which use the same frequency. Consequently, there must be at least one cell gap between cells which reuse the same frequency in a standardfrequency-division multiple access(FDMA) system.
Consider the case of a taxi company, where each radio has a manually operated channel selector knob to tune to different frequencies. As drivers move around, they change from channel to channel. The drivers are aware of whichfrequencyapproximately covers some area. When they do not receive a signal from the transmitter, they try other channels until finding one that works. The taxi drivers only speak one at a time when invited by the base station operator. This is a form oftime-division multiple access(TDMA).
The idea to establish a standard cellular phone network was first proposed on December 11, 1947. This proposal was put forward byDouglas H. Ring, aBell Labsengineer, in an internal memo suggesting the development of a cellular telephone system byAT&T.[6][7]
The first commercial cellular network, the1Ggeneration, was launched in Japan byNippon Telegraph and Telephone(NTT) in 1979, initially in the metropolitan area ofTokyo. However, NTT did not initially commercialize the system; the early launch was motivated by an effort to understand a practical cellular system rather than by an interest to profit from it.[8][9]In 1981, theNordic Mobile Telephonesystem was created as the first network to cover an entire country. The network was released in 1981 in Sweden and Norway, then in early 1982 in Finland and Denmark.Televerket, a state-owned corporation responsible for telecommunications in Sweden, launched the system.[8][10][11]
In September 1981,Jan Stenbeck, a financier and businessman, launchedComvik, a new Swedish telecommunications company. Comvik was the first European telecommunications firm to challenge the state's telephone monopoly on the industry.[12][13][14]According to some sources, Comvik was the first to launch a commercial automatic cellular system before Televerket launched its own in October 1981. However, at the time of the new network’s release, theSwedish Post and Telecom Authoritythreatened to shut down the system after claiming that the company had used an unlicensed automatic gear that could interfere with its own networks.[14][15]In December 1981, Sweden awarded Comvik with a license to operate its own automatic cellular network in the spirit of market competition.[14][15][16]
TheBell Systemhad developed cellular technology since 1947, and had cellular networks in operation inChicago, Illinois,[17]andDallas, Texas, prior to 1979; however, regulatory battles delayed AT&T's deployment of cellular service to 1983,[18]when itsRegional Holding CompanyIllinois Bellfirst provided cellular service.[19]
First-generation cellular network technology continued to expand its reach to the rest of the world. In 1990,Millicom Inc., a telecommunications service provider, strategically partnered with Comvik’s international cellular operations to become Millicom International Cellular SA.[20]The company went on to establish a 1G systems foothold in Ghana, Africa under the brand name Mobitel.[21]In 2006, the company’s Ghana operations were renamed to Tigo.[22]
Thewireless revolutionbegan in the early 1990s,[23][24][25]leading to the transition from analog todigital networks.[26]The MOSFET invented atBell Labsbetween 1955 and 1960,[27][28][29][30][31]was adapted for cellular networks by the early 1990s, with the wide adoption ofpower MOSFET,LDMOS(RF amplifier), andRF CMOS(RF circuit) devices leading to the development and proliferation of digital wireless mobile networks.[26][32][33]
The first commercial digital cellular network, the2Ggeneration, was launched in 1991. This sparked competition in the sector as the new operators challenged the incumbent 1G analog network operators.
To distinguish signals from several different transmitters, a number ofchannel access methodshave been developed, includingfrequency-division multiple access(FDMA, used by analog andD-AMPS[citation needed]systems),time-division multiple access(TDMA, used byGSM) andcode-division multiple access(CDMA, first used forPCS, and the basis of3G).[2]
With FDMA, the transmitting and receiving frequencies used by different users in each cell are different from each other. Each cellular call was assigned a pair of frequencies (one for base to mobile, the other for mobile to base) to providefull-duplexoperation. The originalAMPSsystems had 666 channel pairs, 333 each for theCLEC"A" system andILEC"B" system. The number of channels was expanded to 416 pairs per carrier, but ultimately the number of RF channels limits the number of calls that a cell site could handle. FDMA is a familiar technology to telephone companies, which usedfrequency-division multiplexingto add channels to their point-to-point wireline plants beforetime-division multiplexingrendered FDM obsolete.
With TDMA, the transmitting and receiving time slots used by different users in each cell are different from each other. TDMA typically usesdigitalsignaling tostore and forwardbursts of voice data that are fit into time slices for transmission, and expanded at the receiving end to produce a somewhat normal-sounding voice at the receiver. TDMA must introducelatency(time delay) into the audio signal. As long as the latency time is short enough that the delayed audio is not heard as an echo, it is not problematic. TDMA is a familiar technology for telephone companies, which usedtime-division multiplexingto add channels to their point-to-point wireline plants beforepacket switchingrendered FDM obsolete.
The principle of CDMA is based onspread spectrumtechnology developed for military use duringWorld War IIand improved during theCold Warintodirect-sequence spread spectrumthat was used for early CDMA cellular systems andWi-Fi. DSSS allows multiple simultaneous phone conversations to take place on a single wideband RF channel, without needing to channelize them in time or frequency. Although more sophisticated than older multiple access schemes (and unfamiliar to legacy telephone companies because it was not developed byBell Labs), CDMA has scaled well to become the basis for 3G cellular radio systems.
Other available methods of multiplexing such asMIMO, a more sophisticated version ofantenna diversity, combined with activebeamformingprovides much greaterspatial multiplexingability compared to original AMPS cells, that typically only addressed one to three unique spaces. Massive MIMO deployment allows much greater channel reuse, thus increasing the number of subscribers per cell site, greater data throughput per user, or some combination thereof.Quadrature Amplitude Modulation(QAM) modems offer an increasing number of bits per symbol, allowing more users per megahertz of bandwidth (and decibels of SNR), greater data throughput per user, or some combination thereof.
The key characteristic of a cellular network is the ability to reuse frequencies to increase both coverage and capacity. As described above, adjacent cells must use different frequencies, however, there is no problem with two cells sufficiently far apart operating on the same frequency, provided the masts and cellular network users' equipment do not transmit with too much power.[2]
The elements that determine frequency reuse are the reuse distance and the reuse factor. The reuse distance,Dis calculated as
whereRis the cell radius andNis the number of cells per cluster. Cells may vary in radius from 1 to 30 kilometres (0.62 to 18.64 mi). The boundaries of the cells can also overlap between adjacent cells and large cells can be divided into smaller cells.[34]
The frequency reuse factor is the rate at which the same frequency can be used in the network. It is1/K(orKaccording to some books) whereKis the number of cells which cannot use the same frequencies for transmission. Common values for the frequency reuse factor are 1/3, 1/4, 1/7, 1/9 and 1/12 (or 3, 4, 7, 9 and 12, depending on notation).[35]
In case ofNsector antennas on the same base station site, each with different direction, the base station site can serve N different sectors.Nis typically 3. Areuse patternofN/Kdenotes a further division in frequency amongNsector antennas per site. Some current and historical reuse patterns are 3/7 (North American AMPS), 6/4 (Motorola NAMPS), and 3/4 (GSM).
If the total availablebandwidthisB, each cell can only use a number of frequency channels corresponding to a bandwidth ofB/K, and each sector can use a bandwidth ofB/NK.
Code-division multiple access-based systems use a wider frequency band to achieve the same rate of transmission as FDMA, but this is compensated for by the ability to use a frequency reuse factor of 1, for example using a reuse pattern of 1/1. In other words, adjacent base station sites use the same frequencies, and the different base stations and users are separated by codes rather than frequencies. WhileNis shown as 1 in this example, that does not mean the CDMA cell has only one sector, but rather that the entire cell bandwidth is also available to each sector individually.
Recently alsoorthogonal frequency-division multiple accessbased systems such asLTEare being deployed with a frequency reuse of 1. Since such systems do not spread the signal across the frequency band,
inter-cell radio resource management is important to coordinate resource allocation between different cell sites and to limit the inter-cell interference. There are various means ofinter-cell interference coordination(ICIC) already defined in the standard.[36]Coordinated scheduling, multi-site MIMO or multi-site beamforming are other examples for inter-cell radio resource management that might be standardized in the future.
Cell towers frequently use adirectional signalto improve reception in higher-traffic areas. In theUnited States, theFederal Communications Commission(FCC) limits omnidirectional cell tower signals to 100 watts of power. If the tower has directional antennas, the FCC allows the cell operator to emit up to 500 watts ofeffective radiated power(ERP).[37]
Although the original cell towers created an even, omnidirectional signal, were at the centers of the cells and were omnidirectional, a cellular map can be redrawn with the cellular telephone towers located at the corners of the hexagons where three cells converge.[38]Each tower has three sets of directional antennas aimed in three different directions with 120 degrees for each cell (totaling 360 degrees) and receiving/transmitting into three different cells at different frequencies. This provides a minimum of three channels, and three towers for each cell and greatly increases the chances of receiving a usable signal from at least one direction.
The numbers in the illustration are channel numbers, which repeat every 3 cells. Large cells can be subdivided into smaller cells for high volume areas.[39]
Cell phone companies also use this directional signal to improve reception along highways and inside buildings like stadiums and arenas.[37]
Practically every cellular system has some kind of broadcast mechanism. This can be used directly for distributing information to multiple mobiles. Commonly, for example inmobile telephonysystems, the most important use of broadcast information is to set up channels for one-to-one communication between the mobile transceiver and the base station. This is calledpaging. The three different paging procedures generally adopted are sequential, parallel and selective paging.
The details of the process of paging vary somewhat from network to network, but normally we know a limited number of cells where the phone is located (this group of cells is called a Location Area in theGSMorUMTSsystem, or Routing Area if a data packet session is involved; inLTE, cells are grouped into Tracking Areas). Paging takes place by sending the broadcast message to all of those cells. Paging messages can be used for information transfer. This happens inpagers, inCDMAsystems for sendingSMSmessages, and in theUMTSsystem where it allows for low downlink latency in packet-based connections.
In LTE/4G, the Paging procedure is initiated by the MME when data packets need to be delivered to the UE.
Paging types supported by the MME are:
In a primitive taxi system, when the taxi moved away from a first tower and closer to a second tower, the taxi driver manually switched from one frequency to another as needed. If communication was interrupted due to a loss of a signal, the taxi driver asked the base station operator to repeat the message on a different frequency.
In a cellular system, as the distributed mobile transceivers move from cell to cell during an ongoing continuous communication, switching from one cell frequency to a different cell frequency is done electronically without interruption and without a base station operator or manual switching. This is called thehandoveror handoff. Typically, a new channel is automatically selected for the mobile unit on the new base station which will serve it. The mobile unit then automatically switches from the current channel to the new channel and communication continues.
The exact details of the mobile system's move from one base station to the other vary considerably from system to system (see the example below for how a mobile phone network manages handover).
The most common example of a cellular network is a mobile phone (cell phone) network. Amobile phoneis a portable telephone which receives or makes calls through acell site(base station) or transmitting tower.Radio wavesare used to transfer signals to and from the cell phone.
Modern mobile phone networks use cells because radio frequencies are a limited, shared resource. Cell-sites and handsets change frequency under computer control and use low power transmitters so that the usually limited number of radio frequencies can be simultaneously used by many callers with less interference.
A cellular network is used by themobile phone operatorto achieve both coverage and capacity for their subscribers. Large geographic areas are split into smaller cells to avoid line-of-sight signal loss and to support a large number of active phones in that area. All of the cell sites are connected totelephone exchanges(or switches), which in turn connect to thepublic telephone network.
In cities, each cell site may have a range of up to approximately1⁄2mile (0.80 km), while in rural areas, the range could be as much as 5 miles (8.0 km). It is possible that in clear open areas, a user may receive signals from a cell site 25 miles (40 km) away. In rural areas with low-band coverage and tall towers, basic voice and messaging service may reach 50 miles (80 km), with limitations on bandwidth and number of simultaneous calls.[citation needed]
Since almost all mobile phones usecellular technology, includingGSM,CDMA, andAMPS(analog), the term "cell phone" is in some regions, notably the US, used interchangeably with "mobile phone". However,satellite phonesare mobile phones that do not communicate directly with a ground-based cellular tower but may do so indirectly by way of a satellite.
There are a number of different digital cellular technologies, including:Global System for Mobile Communications(GSM),General Packet Radio Service(GPRS),cdmaOne,CDMA2000,Evolution-Data Optimized(EV-DO),Enhanced Data Rates for GSM Evolution(EDGE),Universal Mobile Telecommunications System(UMTS),Digital Enhanced Cordless Telecommunications(DECT),Digital AMPS(IS-136/TDMA), andIntegrated Digital Enhanced Network(iDEN). The transition from existing analog to the digital standard followed a very different path in Europe and theUS.[40]As a consequence, multiple digital standards surfaced in the US, whileEuropeand many countries converged towards theGSMstandard.
A simple view of the cellular mobile-radio network consists of the following:
This network is the foundation of theGSMsystem network. There are many functions that are performed by this network in order to make sure customers get the desired service including mobility management, registration, call set-up, andhandover.
Any phone connects to the network via an RBS (Radio Base Station) at a corner of the corresponding cell which in turn connects to theMobile switching center(MSC). The MSC provides a connection to thepublic switched telephone network(PSTN). The link from a phone to the RBS is called anuplinkwhile the other way is termeddownlink.
Radio channels effectively use the transmission medium through the use of the following multiplexing and access schemes:frequency-division multiple access(FDMA),time-division multiple access(TDMA),code-division multiple access(CDMA), andspace-division multiple access(SDMA).
Small cells, which have a smaller coverage area than base stations, are categorised as follows:
As the phone user moves from one cell area to another cell while a call is in progress, the mobile station will search for a new channel to attach to in order not to drop the call. Once a new channel is found, the network will command the mobile unit to switch to the new channel and at the same time switch the call onto the new channel.
WithCDMA, multiple CDMA handsets share a specific radio channel. The signals are separated by using apseudonoisecode (PN code) that is specific to each phone. As the user moves from one cell to another, the handset sets up radio links with multiple cell sites (or sectors of the same site) simultaneously. This is known as "soft handoff" because, unlike with traditionalcellular technology, there is no one defined point where the phone switches to the new cell.
InIS-95inter-frequency handovers and older analog systems such asNMTit will typically be impossible to test the target channel directly while communicating. In this case, other techniques have to be used such as pilot beacons in IS-95. This means that there is almost always a brief break in the communication while searching for the new channel followed by the risk of an unexpected return to the old channel.
If there is no ongoing communication or the communication can be interrupted, it is possible for the mobile unit to spontaneously move from one cell to another and then notify the base station with the strongest signal.
The effect of frequency on cell coverage means that different frequencies serve better for different uses. Low frequencies, such as 450 MHz NMT, serve very well for countryside coverage.GSM900 (900 MHz) is suitable for light urban coverage.GSM1800 (1.8 GHz) starts to be limited by structural walls.UMTS, at 2.1 GHz is quite similar in coverage toGSM1800.
Higher frequencies are a disadvantage when it comes to coverage, but it is a decided advantage when it comes to capacity. Picocells, covering e.g. one floor of a building, become possible, and the same frequency can be used for cells which are practically neighbors.
Cell service area may also vary due to interference from transmitting systems, both within and around that cell. This is true especially in CDMA based systems. The receiver requires a certainsignal-to-noise ratio, and the transmitter should not send with too high transmission power in view to not cause interference with other transmitters. As the receiver moves away from the transmitter, the power received decreases, so thepower controlalgorithm of the transmitter increases the power it transmits to restore the level of received power. As the interference (noise) rises above the received power from the transmitter, and the power of the transmitter cannot be increased anymore, the signal becomes corrupted and eventually unusable. InCDMA-based systems, the effect of interference from other mobile transmitters in the same cell on coverage area is very marked and has a special name,cell breathing.
One can see examples of cell coverage by studying some of the coverage maps provided by real operators on their web sites or by looking at independently crowdsourced maps such asOpensignalorCellMapper. In certain cases they may mark the site of the transmitter; in others, it can be calculated by working out the point of strongest coverage.
Acellular repeateris used to extend cell coverage into larger areas. They range from wideband repeaters for consumer use in homes and offices to smart or digital repeaters for industrial needs.
The following table shows the dependency of the coverage area of one cell on the frequency of aCDMA2000network:[41]
Lists and technical information:
Starting with EVDO the following techniques can also be used to improve performance:
Equipment:
Other:
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In apositional numeral system, theradix(pl.:radices) orbaseis the number of uniquedigits, including the digit zero, used to represent numbers. For example, for thedecimal system(the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9.
In any standard positional numeral system, a number is conventionally written as(x)ywithxas thestringof digits andyas its base. For base ten, the subscript is usually assumed and omitted (together with the enclosingparentheses), as it is the most common way to expressvalue. For example,(100)10is equivalent to 100(the decimal system is implied in the latter) and represents the number one hundred, while (100)2(in thebinary systemwith base 2) represents the number four.[1]
Radixis a Latin word for "root".Rootcan be considered a synonym forbase,in the arithmetical sense.
Generally, in a system with radixb(b> 1), a string of digitsd1...dndenotes the numberd1bn−1+d2bn−2+ ... +dnb0, where0 ≤di<b.[1]In contrast to decimal, or radix 10, which has a ones' place, tens' place, hundreds' place, and so on, radixbwould have a ones' place, then ab1s' place, ab2s' place, etc.[2]
For example, ifb= 12, a string of digits such as 59A (where the letter "A" represents the value of ten) would represent the value5×122+9×121+10×120= 838 in base 10.
Commonly used numeral systems include:
The octal and hexadecimal systems are often used in computing because of their ease as shorthand for binary. Every hexadecimal digit corresponds to a sequence of four binary digits, since sixteen is the fourth power of two; for example, hexadecimal 7816is binary11110002. Similarly, every octal digit corresponds to a unique sequence of three binary digits, since eight is the cube of two.
This representation is unique. Letbbe a positive integer greater than 1. Then every positive integeracan be expressed uniquely in the form
wheremis a nonnegative integer and ther's are integers such that
Radices are usuallynatural numbers. However, other positional systems are possible, for example,golden ratio base(whose radix is a non-integeralgebraic number),[5]andnegative base(whose radix is negative).[6]A negative base allows the representation of negative numbers without the use of a minus sign. For example, letb= −10. Then a string of digits such as 19 denotes the (decimal) number1 × (−10)1+ 9 × (−10)0= −1.
Different bases are especially used in connection with computers.
The commonly used bases are 10 (decimal), 2 (binary), 8 (octal), and 16 (hexadecimal).
Abytewith 8bitscan represent values from 0 to 255, often expressed withleading zerosin base 2, 8 or 16 to give the same length.[7]
The first row in the tables is the base written in decimal.
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https://en.wikipedia.org/wiki/Number_base
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National security, ornational defence(national defenseinAmerican English), is thesecurityanddefenceof asovereign state, including itscitizens,economy, andinstitutions, which is regarded as a duty ofgovernment. Originally conceived as protection againstmilitary attack, national security is widely understood to include also non-military dimensions, such as the security fromterrorism, minimization ofcrime,economic security,energy security,environmental security,food security, andcyber-security. Similarly, national security risks include, in addition to the actions of otherstates, action byviolent non-state actors, bynarcotic cartels,organized crime, bymultinational corporations, and also the effects ofnatural disasters.
Governments rely on a range of measures, includingpolitical,economic, andmilitarypower, as well asdiplomacy, to safeguard the security of a state. They may also act to build the conditions of security regionally and internationally by reducingtransnationalcauses of insecurity, such asclimate change,economic inequality,political exclusion, andnuclear proliferation.
The concept of national security remains ambiguous, having evolved from simpler definitions which emphasised freedom from military threat and from political coercion.[1]: 1–6[2]: 52–54Among the many definitions proposed to date are the following, which show how the concept has evolved to encompass non-military concerns:
Potential causes of national insecurity include actions by other states (e.g.militaryorcyber attack),violent non-state actors(e.g.terrorist attack),organised criminal groupssuch asnarcotic cartels, and also the effects ofnatural disasters(e.g. flooding, earthquakes).[3]: v, 1–8[8][9]Systemic drivers of insecurity, which may betransnational, includeclimate change,economic inequalityandmarginalisation,political exclusion, andnuclear proliferation.[8]: 3[9]
In view of the wide range of risks, the security of a state has several dimensions, includingeconomic security,energy security,physical security,environmental security,food security,border security, andcyber security. These dimensions correlate closely withelements of national power.
Increasingly, governments organise theirsecurity policiesinto a national security strategy (NSS);[10]as of 2017, Spain, Sweden, the United Kingdom, and the United States are among the states to have done so.[11][12][13][14]Some states also appoint aNational Security Counciland/or aNational Security Advisorwhich is an executive government agency, it feeds the head of the state on topics concerning national security and strategic interest. The national security council/advisor strategies long term, short term, contingency national security plans.Indiaholds one such system in current, which was established on 19 November 1998.
Although states differ in their approach, various forms of coercive power predominate, particularlymilitary capabilities.[8]The scope of these capabilities has developed. Traditionally, military capabilities were mainly land- or sea-based, and in smaller countries, they still are. Elsewhere, the domains of potential warfare now include theair,space,cyberspace, andpsychological operations.[15]Military capabilities designed for these domains may be used for national security, or equally for offensive purposes, for example to conquer and annex territory and resources.
In practice, national security is associated primarily with managing physical threats and with themilitarycapabilities used for doing so.[11][13][14]That is, national security is often understood as the capacity of a nation to mobilise military forces to guarantee its borders and to deter or successfully defend against physical threats includingmilitary aggressionand attacks bynon-state actors, such asterrorism. Most states, such as South Africa and Sweden,[16][12]configure their military forces mainly for territorial defence; others, such as France, Russia, the UK and the US,[17][18][13][14]invest in higher-costexpeditionary capabilities, which allow their armed forces toproject powerand sustainmilitary operationsabroad.
Infrastructure security is thesecurityprovided to protectinfrastructure, especiallycritical infrastructure, such asairports,highways,[19]rail transport,hospitals,bridges,transport hubs, network communications,media, theelectricity grid,dams,power plants,seaports,oil refineries, andwater systems. Infrastructure security seeks to limit vulnerability of these structures and systems tosabotage,terrorism, andcontamination.[20]
Many countries have established government agencies to directly manage the security of critical infrastructure, usually, through the Ministry of Interior/Home Affairs, dedicated security agencies to protect facilities such as United StatesFederal Protective Service, and also dedicated transport police such as theBritish Transport Police. There are also commercial transportation security units such as theAmtrak Policein the United States. Critical infrastructure is vital for the essential functioning of a country. Incidental or deliberate damage can have a serious impact on the economy and essential services. Some of the threats to infrastructure include:
Computer security, also known as cybersecurity or IT security, refers to the security of computing devices such ascomputersand smartphones, as well ascomputer networkssuch as private and public networks, and theInternet. It concerns the protection of hardware, software, data, people, and also the procedures by which systems are accessed, and the field has growing importance due to the increasing reliance on computer systems in most societies.[21]Since unauthorized access to critical civil and military infrastructure is now considered a major threat, cyberspace is now recognised as a domain of warfare. One such example is the use ofStuxnetby the US and Israel against theIranian nuclear programme.[15]
Barry Buzan,Ole Wæver,Jaap de Wildeand others have argued that national security depends onpolitical security: the stability of the social order.[22]Others, such as Paul Rogers, have added that the equitability of the international order is equally vital.[9]Hence, political security depends on the rule ofinternational law(including thelaws of war), the effectiveness ofinternational political institutions, as well asdiplomacyandnegotiationbetween nations and other security actors.[22]It also depends on, among other factors, effective political inclusion of disaffected groups and thehuman securityof the citizenry.[9][8][23]
Economic security, in the context ofinternational relations, is the ability of anation stateto maintain and develop the national economy, without which other dimensions of national security cannot be managed. Economic capability largely determines the defence capability of a nation, and thus a sound economic security directly influences the national security of a nation. That is why we see countries with sound economy, happen to have sound security setup too, such asThe United States,China,Indiaamong others. In larger countries, strategies for economic security expect to access resources and markets in other countries and to protect their own markets at home.Developing countriesmay be less secure than economically advanced states due to high rates of unemployment and underpaid work.[citation needed]
Environmental security, also known as ecological security, refers to the integrity ofecosystemsand thebiosphere, particularly in relation to their capacity to sustain adiversity of life-forms(including human life). The security of ecosystems has attracted greater attention as the impact of ecological damage by humans has grown.[24]The degradation of ecosystems, includingtopsoil erosion,deforestation,biodiversity loss, andclimate change, affect economic security and can precipitatemass migration, leading to increased pressure on resources elsewhere. Ecological security is also important since most of the countries in the world are developing and dependent onagricultureand agriculture gets affected largely due to climate change. This effect affects the economy of the nation, which in turn affects national security.
The scope and nature of environmental threats to national security and strategies to engage them are a subject of debate.[3]: 29–33Romm (1993) classifies the major impacts of ecological changes on national security as:[3]: 15
Resources include water, sources of energy, land, and minerals. Availability of adequate natural resources is important for a nation to develop its industry and economic power. For example, in thePersian Gulf Warof 1991,IraqcapturedKuwaitpartly in order to secure access to its oil wells, and one reason for the US counter-invasion was the value of the same wells to its own economy.[citation needed]Water resources are subject to disputes between many nations, includingIndiaandPakistan, and in theMiddle East.
The interrelations between security, energy, natural resources, and their sustainability is increasingly acknowledged in national security strategies and resource security is now included among theUN Sustainable Development Goals.[12][11][27][14][28]In the US, for example, the military has installedsolar photovoltaicmicrogridson their bases in case ofpower outage.[29][30]
The dimensions of national security outlined above are frequently in tension with one another. For example:
If tensions such as these are mismanaged, national security policies and actions may be ineffective or counterproductive.
Increasingly, national security strategies have begun to recognise that nations cannot provide for their own security without also developing the security of their regional and international context.[14][27][11][12]For example, Sweden's national security strategy of 2017 declared:
"Wider security measures must also now encompass protection against epidemics and infectious diseases, combating terrorism and organised crime, ensuring safe transport and reliable food supplies, protecting against energy supply interruptions, countering devastating climate change, initiatives for peace and global development, and much more."[12]
The extent to which this matters, and how it should be done, is the subject of debate. Some argue that the principal beneficiary of national security policy should be the nation state itself, which should centre its strategy on protective and coercive capabilities in order to safeguard itself in a hostile environment (and potentially to project that power into its environment, and dominate it to the point ofstrategic supremacy).[35][36][37]Others argue that security depends principally on building the conditions in which equitable relationships between nations can develop, partly by reducing antagonism between actors, ensuring that fundamental needs can be met, and also that differences of interest can be negotiated effectively.[38][8][9]In the UK, for example, Malcolm Chalmers argued in 2015 that the heart of the UK's approach should be support for the Western strategic military alliance led throughNATOby the United States, as "the key anchor around which international order is maintained".[39]
Approaches to national security can have a complex impact onhuman rightsandcivil liberties. For example, the rights and liberties of citizens are affected by the use ofmilitary personnelandmilitarised police forcesto control public behaviour; the use ofsurveillance, includingmass surveillanceincyberspace, which has implications forprivacy;military recruitmentandconscriptionpractices; and the effects ofwarfareonciviliansandcivil infrastructure. This has led to adialecticalstruggle, particularly inliberal democracies, between governmentauthorityand the rights and freedoms of the general public.
Even where the exercise of national security is subject togood governance, and therule of law, a risk remains that the termnational securitymay become apretextfor suppressingunfavorable political and social views. In the US, for example, the controversialUSA Patriot Actof 2001, and the revelation byEdward Snowdenin 2013 that theNational Security Agencyharvests the personal data of the general public, brought these issues to wide public attention. Among the questions raised are whether and how national security considerations at times of war should lead to the suppression of individual rights and freedoms, and whether such restrictions are necessary when a state is at peace.
National security ideology as taught by theUS Army School of the Americasto military personnel was vital in causing the military coup of 1964 in Brazil and the 1976 one in Argentina. The military dictatorships were installed on the claim by the military that Leftists were an existential threat to the national interests.[40]
China's military is thePeople's Liberation Army(PLA). The military is the largest in the world, with 2.3 million active troops in 2005.
TheMinistry of State Securitywas established in 1983 to ensure "the security of the state through effective measures against enemy agents, spies, and counterrevolutionary activities designed to sabotage or overthrow China's socialist system."[41]
ForSchengen area[42]some parts of national security and external border control are enforced byFrontex[43]according to theTreaty of Lisbon. Thesecurity policy of the European Unionis set byHigh Representative of the Union for Foreign Affairs and Security Policyand assisted byEuropean External Action Service.[44]Europolis one of theagencies of the European Unionresponsible for combating various forms ofcrimein the European Union through coordinating law enforcement agencies of the EU member states.[45]
European Union national security has been accused of insufficiently preventing foreign threats.[46]
The state of the Republic of India's national security is determined by its internal stability and geopolitical interests. While Islamic upsurge in Indian State of Jammu and Kashmir demanding secession and far left-wing terrorism in India'sred corridorremain some key issues in India's internal security,terrorism from Pakistan-based militant groupshas been emerging as a major concern for New Delhi.
TheNational Security Advisor of Indiaheads theNational Security Council of India, receives all kinds of intelligence reports, and is chief advisor to thePrime Minister of Indiaover national and international security policy. The National Security Council has India'sdefence,foreign,home,financeministers and deputy chairman ofNITI Aayogas its members and is responsible for shaping strategies for India's security in all aspects.[47]
A lawyer Ashwini Upadhyay filed aPublic interest litigation(PIL) in the "Supreme Court of India" (SC) to identify and deport illegal immigrants. Responding to this PIL,Delhi Policetold the SC in July 2019 that nearly 500 illegal Bangladeshi immigrants have been deported in the preceding 28 months.[48]There are estimated 600,000 to 700,000 illegal Bangladeshi andRohingyaimmigrants inNational Capital Region(NCR) region specially in the districts ofGurugram,Faridabad, andNuh(Mewatregion), as well as interior villages ofBhiwaniandHisar. Most of them are Muslims who have acquired fake Hindu identity, and under questioning, they pretend to be from West Bengal. In September 2019, theChief Minister of Haryana,Manohar Lal Khattarannounced the implementation ofNRC for Haryanaby setting up a legal framework under the former judge of the Punjab and Haryana High Court, Justice HS Bhalla for updating NRC which will help in weeding out these illegal immigrants.[49]
In the years 1997 and 2000, Russia adopted documents titled "National Security Concept" that described Russia's global position, the country's interests, listed threats to national security, and described the means to counter those threats. In 2009, these documents were superseded by the "National Security Strategy to 2020". The key body responsible for coordinating policies related to Russia's national security is theSecurity Council of Russia.
According to provision 6 of theNational Security Strategy to 2020, national security is "the situation in which the individual, the society and the state enjoy protection from foreign and domestic threats to the degree that ensures constitutional rights and freedoms, decent quality of life for citizens, as well as sovereignty, territorial integrity and stable development of the Russian Federation, the defence and security of the state."
Total Defence is Singapore'swhole-of-societynational defence concept[50]based on the premise that the strongest defence of a nation is collective defence[51]– when every aspect of society stays united for the defence of the country.[52]Adopted from the national defence strategies of Sweden and Switzerland,[53]Total Defence was introduced in Singapore in 1984. Then, it was recognised that military threats to a nation can affect the psyche and social fabric of its people.[54]Therefore, the defence and progress of Singapore are dependent on all of its citizens' resolve, along with the government and armed forces.[55]Total Defence has since evolved to take into consideration threats and challenges outside of the conventional military domain.
National security of Ukraine is defined in Ukrainian law as "a set of legislative and organisational measures aimed at permanent protection of vital interests of man and citizen, society and the state, which ensure sustainable development of society, timely detection, prevention and neutralisation of real and potential threats to national interests in areas of law enforcement, fight against corruption, border activities and defence, migration policy, health care, education and science, technology and innovation policy, cultural development of the population, freedom of speech andinformation security, social policy and pension provision, housing and communal services, financial services market, protection of property rights, stock markets and circulation of securities, fiscal and customs policy, trade and business, banking services, investment policy, auditing, monetary and exchange rate policy, information security, licensing, industry and agriculture, transport and communications, information technology, energy and energy saving, functioning of natural monopolies, use ofsubsoil, land and water resources, minerals, protection of ecology and environment and other areas of public administration, in the event of emergence of negative trends towards the creation of potential or real threats to national interests."[56]
The primary body responsible for coordinating national security policy in Ukraine is theNational Security and Defense Council of Ukraine.
It is an advisory state agency to thePresident of Ukraine, tasked with developing a policy of national security on domestic and international matters. All sessions of the council take place in thePresidential Administration Building. The council was created by the provision ofSupreme Council of Ukraine#1658-12 on October 11, 1991. It was defined as the highest state body of collegiate governing on matters of defence and security of Ukraine with the following goals:
The primary body responsible for coordinating national security policy in the UK is theNational Security Council (United Kingdom)which helps produce and enact theUK's National Security Strategy. It was created in May 2010 by the newcoalition governmentof theConservative Party (UK)andLiberal Democrats. The National Security Council is a committee of theCabinet of the United Kingdomand was created as part of a wider reform of the nationalsecurity apparatus. This reform also included the creation of aNational Security Adviserand aNational Security Secretariatto support the National Security Council.[57]
The concept of national security became an official guiding principle offoreign policy in the United Stateswhen theNational Security Act of 1947was signed on July 26, 1947, byU.S. PresidentHarry S. Truman.[3]: 3As amended in 1949, this Act:
Notably, the Act didnotdefine national security, which was conceivably advantageous, as its ambiguity made it a powerful phrase to invoke against diverse threats to interests of the state, such as domestic concerns.[3]: 3–5
The notion that national security encompasses more than just military security was present, though understated, from the beginning. The Act established the National Security Council so as to "advise the President on the integration of domestic, military and foreign policies relating to national security".[2]: 52
The act establishes, within the National Security Council, the Committee on Foreign Intelligence, whose duty is to conduct an annual review "identifying the intelligence required to address the national security interests of the United Statesas specified by the President" (emphasis added).[59]
In Gen.Maxwell Taylor's 1974 essay "The Legitimate Claims of National Security", Taylor states:[60]
The national valuables in this broad sense include current assets and national interests, as well as the sources of strength upon which our future as a nation depends. Some valuables are tangible and earthy; others are spiritual or intellectual. They range widely from political assets such as the Bill of Rights, our political institutions, and international friendships to many economic assets which radiate worldwide from a highly productive domestic economy supported by rich natural resources. It is the urgent need to protect valuables such as these which legitimizes and makes essential the role of national security.
To address the institutionalisation of new bureaucracies and government practices in the post–World War II period in the U.S., the culture of semi-permanent military mobilisation joined the National Security Council (NSC), the Central Intelligence Agency (CIA), the Department of Defense (DoD), and the Joint Chiefs of Staff (JCS) for the practical application of the concept of thenational security state:[61][62][63]
During and after World War II, U.S. leaders expanded the concept of national security, and used its terminology for the first time to explain America's relationship to the world. For most of U.S. history, the continental United States was secure. But, by 1945, it had become rapidly vulnerable with the advent of long-range bombers, atom bombs, and ballistic missiles. A general perception grew that future mobilization would be insufficient and that preparation must be constant. For the first time, American leaders dealt with the essential paradox of national security faced by the Roman Empire and subsequent great powers:Si vis pacem, para bellum— "If you want peace, prepare for war."[64]
Jack Nelson-Pallmeyeroffers a seven-characteristic definition for 'national security state' as where the military and broader national security establishment, e.g., exert influence over political and economic affairs; hold ultimate power while maintaining an appearance of democracy; are preoccupied with external and/or internal enemies; define policies in secret and implement those policies through covert channels.[65]
The U.S.Joint Chiefs of Staffdefines national security of the United States in the following manner :[66]
A collective term encompassing both national defense and foreign relations of the United States. Specifically, the condition provided by: a. a military or defense advantage over any foreign nation or group of nations; b. a favorable foreign relations position; or c. a defense posture capable of successfully resisting hostile or destructive action from within or without, overt or covert.
In 2010, theWhite Houseincluded an all-encompassing world-view in a national security strategy which identified "security" as one of the country's "four enduring national interests" that were "inexorably intertwined":[67]
"To achieve the world we seek, the United States must apply our strategic approach in pursuit of four enduring national interests:
Each of these interests is inextricably linked to the others: no single interest can be pursued in isolation, but at the same time, positive action in one area will help advance all four."
U.S. Secretary of StateHillary Clintonhas said that, "The countries that threaten regional and global peace are the very places where women and girls are deprived of dignity and opportunity".[68]She has noted that countries, where women are oppressed, are places where the "rule of law and democracy are struggling to take root",[68]and that, when women's rights as equals in society are upheld, the society as a whole changes and improves, which in turn enhances stability in that society, which in turn contributes to global society.[68]
The Bush administration in January 2008 initiated the Comprehensive National Cybersecurity Initiative (CNCI). It introduced a differentiated approach, such as identifying existing and emerging cybersecurity threats, finding and plugging existing cyber vulnerabilities and apprehending those trying to access federal information systems.[69]
President Obama said the "cyber threat is one of the most serious economic and national security challenges we face as a nation" and that "America's economic prosperity in the 21st century will depend on cybersecurity".[70]
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Instatistical analysis,Freedman's paradox,[1][2]named afterDavid Freedman, is a problem inmodel selectionwherebypredictor variableswith no relationship to the dependent variable can pass tests of significance – both individually via a t-test, and jointly via an F-test for the significance of the regression. Freedman demonstrated (through simulation and asymptotic calculation) that this is a common occurrence when the number of variables is similar to the number of data points.
Specifically, if the dependent variable andkregressors are independent normal variables, and there arenobservations, then askandnjointly go to infinity in the ratiok/n=ρ,
More recently, newinformation-theoreticestimators have been developed in an attempt to reduce this problem,[3]in addition to the accompanying issue of model selection bias,[4]whereby estimators of predictor variables that have a weak relationship with the response variable are biased.
Thisstatistics-related article is astub. You can help Wikipedia byexpanding it.
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Cluster analysisorclusteringis the data analyzing technique in which task of grouping a set of objects in such a way that objects in the same group (called acluster) are moresimilar(in some specific sense defined by the analyst) to each other than to those in other groups (clusters). It is a main task ofexploratory data analysis, and a common technique forstatisticaldata analysis, used in many fields, includingpattern recognition,image analysis,information retrieval,bioinformatics,data compression,computer graphicsandmachine learning.
Cluster analysis refers to a family of algorithms and tasks rather than one specificalgorithm. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with smalldistancesbetween cluster members, dense areas of the data space, intervals or particularstatistical distributions. Clustering can therefore be formulated as amulti-objective optimizationproblem. The appropriate clustering algorithm and parameter settings (including parameters such as thedistance functionto use, a density threshold or the number of expected clusters) depend on the individualdata setand intended use of the results. Cluster analysis as such is not an automatic task, but an iterative process ofknowledge discoveryor interactive multi-objective optimization that involves trial and failure. It is often necessary to modifydata preprocessingand model parameters until the result achieves the desired properties.
Besides the termclustering, there are a number of terms with similar meanings, includingautomaticclassification,numerical taxonomy,botryology(fromGreek:βότρυς'grape'),typological analysis, andcommunity detection. The subtle differences are often in the use of the results: while in data mining, the resulting groups are the matter of interest, in automatic classification the resulting discriminative power is of interest.
Cluster analysis originated in anthropology by Driver and Kroeber in 1932[1]and introduced to psychology byJoseph Zubinin 1938[2]andRobert Tryonin 1939[3]and famously used byCattellbeginning in 1943[4]for trait theory classification inpersonality psychology.
The notion of a "cluster" cannot be precisely defined, which is one of the reasons why there are so many clustering algorithms.[5]There is a common denominator: a group of data objects. However, different researchers employ different cluster models, and for each of these cluster models again different algorithms can be given. The notion of a cluster, as found by different algorithms, varies significantly in its properties. Understanding these "cluster models" is key to understanding the differences between the various algorithms. Typical cluster models include:
A "clustering" is essentially a set of such clusters, usually containing all objects in the data set. Additionally, it may specify the relationship of the clusters to each other, for example, a hierarchy of clusters embedded in each other. Clusterings can be roughly distinguished as:
There are also finer distinctions possible, for example:
As listed above, clustering algorithms can be categorized based on their cluster model. The following overview will only list the most prominent examples of clustering algorithms, as there are possibly over 100 published clustering algorithms. Not all provide models for their clusters and can thus not easily be categorized. An overview of algorithms explained in Wikipedia can be found in thelist of statistics algorithms.
There is no objectively "correct" clustering algorithm, but as it was noted, "clustering is in the eye of the beholder."[5]In fact, an axiomatic approach to clustering demonstrates that it is impossible for any clustering method to meet three fundamental properties simultaneously:scale invariance(results remain unchanged under proportional scaling of distances),richness(all possible partitions of the data can be achieved), andconsistencybetween distances and the clustering structure.[7]The most appropriate clustering algorithm for a particular problem often needs to be chosen experimentally, unless there is a mathematical reason to prefer one cluster model over another. An algorithm that is designed for one kind of model will generally fail on a data set that contains a radically different kind of model.[5]For example, k-means cannot find non-convex clusters.[5]Most traditional clustering methods assume the clusters exhibit a spherical, elliptical or convex shape.[8]
Connectivity-based clustering, also known ashierarchical clustering, is based on the core idea of objects being more related to nearby objects than to objects farther away. These algorithms connect "objects" to form "clusters" based on their distance. A cluster can be described largely by the maximum distance needed to connect parts of the cluster. At different distances, different clusters will form, which can be represented using adendrogram, which explains where the common name "hierarchical clustering" comes from: these algorithms do not provide a single partitioning of the data set, but instead provide an extensive hierarchy of clusters that merge with each other at certain distances. In a dendrogram, the y-axis marks the distance at which the clusters merge, while the objects are placed along the x-axis such that the clusters don't mix.
Connectivity-based clustering is a whole family of methods that differ by the way distances are computed. Apart from the usual choice ofdistance functions, the user also needs to decide on the linkage criterion (since a cluster consists of multiple objects, there are multiple candidates to compute the distance) to use. Popular choices are known assingle-linkage clustering(the minimum of object distances),complete linkage clustering(the maximum of object distances), andUPGMAorWPGMA("Unweighted or Weighted Pair Group Method with Arithmetic Mean", also known as average linkage clustering). Furthermore, hierarchical clustering can be agglomerative (starting with single elements and aggregating them into clusters) or divisive (starting with the complete data set and dividing it into partitions).
These methods will not produce a unique partitioning of the data set, but a hierarchy from which the user still needs to choose appropriate clusters. They are not very robust towards outliers, which will either show up as additional clusters or even cause other clusters to merge (known as "chaining phenomenon", in particular withsingle-linkage clustering). In the general case, the complexity isO(n3){\displaystyle {\mathcal {O}}(n^{3})}for agglomerative clustering andO(2n−1){\displaystyle {\mathcal {O}}(2^{n-1})}fordivisive clustering,[9]which makes them too slow for large data sets. For some special cases, optimal efficient methods (of complexityO(n2){\displaystyle {\mathcal {O}}(n^{2})}) are known: SLINK[10]for single-linkage and CLINK[11]for complete-linkage clustering.
In centroid-based clustering, each cluster is represented by a central vector, which is not necessarily a member of the data set. When the number of clusters is fixed tok,k-means clusteringgives a formal definition as an optimization problem: find thekcluster centers and assign the objects to the nearest cluster center, such that the squared distances from the cluster are minimized.
The optimization problem itself is known to beNP-hard, and thus the common approach is to search only for approximate solutions. A particularly well-known approximate method isLloyd's algorithm,[12]often just referred to as "k-means algorithm" (althoughanother algorithm introduced this name). It does however only find alocal optimum, and is commonly run multiple times with different random initializations. Variations ofk-means often include such optimizations as choosing the best of multiple runs, but also restricting the centroids to members of the data set (k-medoids), choosingmedians(k-medians clustering), choosing the initial centers less randomly (k-means++) or allowing a fuzzy cluster assignment (fuzzy c-means).
Mostk-means-type algorithms require thenumber of clusters–k– to be specified in advance, which is considered to be one of the biggest drawbacks of these algorithms. Furthermore, the algorithms prefer clusters of approximately similar size, as they will always assign an object to the nearest centroid; often yielding improperly cut borders of clusters. This happens primarily because the algorithm optimizes cluster centers, not cluster borders. Steps involved in the centroid-based clustering algorithm are:
K-means has a number of interesting theoretical properties. First, it partitions the data space into a structure known as aVoronoi diagram. Second, it is conceptually close to nearest neighbor classification, and as such is popular inmachine learning. Third, it can be seen as a variation of model-based clustering, and Lloyd's algorithm as a variation of theExpectation-maximization algorithmfor this model discussed below.
Centroid-based clustering problems such ask-means andk-medoids are special cases of the uncapacitated, metricfacility location problem, a canonical problem in the operations research and computational geometry communities. In a basic facility location problem (of which there are numerous variants that model more elaborate settings), the task is to find the best warehouse locations to optimally service a given set of consumers. One may view "warehouses" as cluster centroids and "consumer locations" as the data to be clustered. This makes it possible to apply the well-developed algorithmic solutions from the facility location literature to the presently considered centroid-based clustering problem.
The clustering framework most closely related to statistics ismodel-based clustering, which is based ondistribution models. This approach models the data as arising from a mixture of probability distributions. It has the advantages of providing principled statistical answers to questions such as how many clusters there are, what clustering method or model to use, and how to detect and deal with outliers.
While the theoretical foundation of these methods is excellent, they suffer fromoverfittingunless constraints are put on the model complexity. A more complex model will usually be able to explain the data better, which makes choosing the appropriate model complexity inherently difficult. Standardmodel-based clusteringmethods include more parsimonious models based on theeigenvalue decompositionof the covariance matrices, that provide a balance between overfitting and fidelity to the data.
One prominent method is known as Gaussian mixture models (using theexpectation-maximization algorithm). Here, the data set is usually modeled with a fixed (to avoid overfitting) number ofGaussian distributionsthat are initialized randomly and whose parameters are iteratively optimized to better fit the data set. This will converge to alocal optimum, so multiple runs may produce different results. In order to obtain a hard clustering, objects are often then assigned to the Gaussian distribution they most likely belong to; for soft clusterings, this is not necessary.
Distribution-based clustering produces complex models for clusters that can capturecorrelation and dependencebetween attributes. However, these algorithms put an extra burden on the user: for many real data sets, there may be no concisely defined mathematical model (e.g. assuming Gaussian distributions is a rather strong assumption on the data).
In density-based clustering,[13]clusters are defined as areas of higher density than the remainder of the data set. Objects in sparse areas – that are required to separate clusters – are usually considered to be noise and border points.
The most popular[14]density-based clustering method isDBSCAN.[15]In contrast to many newer methods, it features a well-defined cluster model called "density-reachability". Similar to linkage-based clustering, it is based on connecting points within certain distance thresholds. However, it only connects points that satisfy a density criterion, in the original variant defined as a minimum number of other objects within this radius. A cluster consists of all density-connected objects (which can form a cluster of an arbitrary shape, in contrast to many other methods) plus all objects that are within these objects' range. Another interesting property of DBSCAN is that its complexity is fairly low – it requires a linear number of range queries on the database – and that it will discover essentially the same results (it isdeterministicfor core and noise points, but not for border points) in each run, therefore there is no need to run it multiple times.OPTICS[16]is a generalization of DBSCAN that removes the need to choose an appropriate value for the range parameterε{\displaystyle \varepsilon }, and produces a hierarchical result related to that oflinkage clustering. DeLi-Clu,[17]Density-Link-Clustering combines ideas fromsingle-linkage clusteringand OPTICS, eliminating theε{\displaystyle \varepsilon }parameter entirely and offering performance improvements over OPTICS by using anR-treeindex.
The key drawback ofDBSCANandOPTICSis that they expect some kind of density drop to detect cluster borders. On data sets with, for example, overlapping Gaussian distributions – a common use case in artificial data – the cluster borders produced by these algorithms will often look arbitrary, because the cluster density decreases continuously. On a data set consisting of mixtures of Gaussians, these algorithms are nearly always outperformed by methods such asEM clusteringthat are able to precisely model this kind of data.
Mean-shiftis a clustering approach where each object is moved to the densest area in its vicinity, based onkernel density estimation. Eventually, objects converge to local maxima of density. Similar to k-means clustering, these "density attractors" can serve as representatives for the data set, but mean-shift can detect arbitrary-shaped clusters similar to DBSCAN. Due to the expensive iterative procedure and density estimation, mean-shift is usually slower than DBSCAN or k-Means. Besides that, the applicability of the mean-shift algorithm to multidimensional data is hindered by the unsmooth behaviour of the kernel density estimate, which results in over-fragmentation of cluster tails.[17]
The grid-based technique is used for amulti-dimensionaldata set.[18]In this technique, we create a grid structure, and the comparison is performed on grids (also known as cells). The grid-based technique is fast and has low computational complexity. There are two types of grid-based clustering methods: STING and CLIQUE. Steps involved in the grid-based clusteringalgorithmare:
In recent years, considerable effort has been put into improving the performance of existing algorithms.[19][20]Among them areCLARANS,[21]andBIRCH.[22]With the recent need to process larger and larger data sets (also known asbig data), the willingness to trade semantic meaning of the generated clusters for performance has been increasing. This led to the development of pre-clustering methods such ascanopy clustering, which can process huge data sets efficiently, but the resulting "clusters" are merely a rough pre-partitioning of the data set to then analyze the partitions with existing slower methods such ask-means clustering.
Forhigh-dimensional data, many of the existing methods fail due to thecurse of dimensionality, which renders particular distance functions problematic in high-dimensional spaces. This led to newclustering algorithms for high-dimensional datathat focus onsubspace clustering(where only some attributes are used, and cluster models include the relevant attributes for the cluster) andcorrelation clusteringthat also looks for arbitrary rotated ("correlated") subspace clusters that can be modeled by giving acorrelationof their attributes.[23]Examples for such clustering algorithms are CLIQUE[24]andSUBCLU.[25]
Ideas from density-based clustering methods (in particular theDBSCAN/OPTICSfamily of algorithms) have been adapted to subspace clustering (HiSC,[26]hierarchical subspace clustering and DiSH[27]) and correlation clustering (HiCO,[28]hierarchical correlation clustering, 4C[29]using "correlation connectivity" and ERiC[30]exploring hierarchical density-based correlation clusters).
Several different clustering systems based onmutual informationhave been proposed. One is Marina Meilă'svariation of informationmetric;[31]another provides hierarchical clustering.[32]Using genetic algorithms, a wide range of different fit-functions can be optimized, including mutual information.[33]Alsobelief propagation, a recent development incomputer scienceandstatistical physics, has led to the creation of new types of clustering algorithms.[34]
Evaluation (or "validation") of clustering results is as difficult as the clustering itself.[35]Popular approaches involve "internal" evaluation, where the clustering is summarized to a single quality score, "external" evaluation, where the clustering is compared to an existing "ground truth" classification, "manual" evaluation by a human expert, and "indirect" evaluation by evaluating the utility of the clustering in its intended application.[36]
Internal evaluation measures suffer from the problem that they represent functions that themselves can be seen as a clustering objective. For example, one could cluster the data set by the Silhouette coefficient; except that there is no known efficient algorithm for this. By using such an internal measure for evaluation, one rather compares the similarity of the optimization problems,[36]and not necessarily how useful the clustering is.
External evaluation has similar problems: if we have such "ground truth" labels, then we would not need to cluster; and in practical applications we usually do not have such labels. On the other hand, the labels only reflect one possible partitioning of the data set, which does not imply that there does not exist a different, and maybe even better, clustering.
Neither of these approaches can therefore ultimately judge the actual quality of a clustering, but this needs human evaluation,[36]which is highly subjective. Nevertheless, such statistics can be quite informative in identifying bad clusterings,[37]but one should not dismiss subjective human evaluation.[37]
When a clustering result is evaluated based on the data that was clustered itself, this is called internal evaluation. These methods usually assign the best score to the algorithm that produces clusters with high similarity within a cluster and low similarity between clusters. One drawback of using internal criteria in cluster evaluation is that high scores on an internal measure do not necessarily result in effective information retrieval applications.[38]Additionally, this evaluation is biased towards algorithms that use the same cluster model. For example, k-means clustering naturally optimizes object distances, and a distance-based internal criterion will likely overrate the resulting clustering.
Therefore, the internal evaluation measures are best suited to get some insight into situations where one algorithm performs better than another, but this shall not imply that one algorithm produces more valid results than another.[5]Validity as measured by such an index depends on the claim that this kind of structure exists in the data set. An algorithm designed for some kind of models has no chance if the data set contains a radically different set of models, or if the evaluation measures a radically different criterion.[5]For example, k-means clustering can only find convex clusters, and many evaluation indexes assume convex clusters. On a data set with non-convex clusters neither the use ofk-means, nor of an evaluation criterion that assumes convexity, is sound.
More than a dozen of internal evaluation measures exist, usually based on the intuition that items in the same cluster should be more similar than items in different clusters.[39]: 115–121For example, the following methods can be used to assess the quality of clustering algorithms based on internal criterion:
TheDavies–Bouldin indexcan be calculated by the following formula:DB=1n∑i=1nmaxj≠i(σi+σjd(ci,cj)){\displaystyle DB={\frac {1}{n}}\sum _{i=1}^{n}\max _{j\neq i}\left({\frac {\sigma _{i}+\sigma _{j}}{d(c_{i},c_{j})}}\right)}wherenis the number of clusters,ci{\displaystyle c_{i}}is thecentroidof clusteri{\displaystyle i},σi{\displaystyle \sigma _{i}}is the average distance of all elements in clusteri{\displaystyle i}to centroidci{\displaystyle c_{i}}, andd(ci,cj){\displaystyle d(c_{i},c_{j})}is the distance between centroidsci{\displaystyle c_{i}}andcj{\displaystyle c_{j}}. Since algorithms that produce clusters with low intra-cluster distances (high intra-cluster similarity) and high inter-cluster distances (low inter-cluster similarity) will have a low Davies–Bouldin index, the clustering algorithm that produces a collection of clusters with the smallestDavies–Bouldin indexis considered the best algorithm based on this criterion.
The Dunn index aims to identify dense and well-separated clusters. It is defined as the ratio between the minimal inter-cluster distance to maximal intra-cluster distance. For each cluster partition, the Dunn index can be calculated by the following formula:[40]
whered(i,j) represents the distance between clustersiandj, andd'(k) measures the intra-cluster distance of clusterk. The inter-cluster distanced(i,j) between two clusters may be any number of distance measures, such as the distance between thecentroidsof the clusters. Similarly, the intra-cluster distanced'(k) may be measured in a variety of ways, such as the maximal distance between any pair of elements in clusterk. Since internal criterion seek clusters with high intra-cluster similarity and low inter-cluster similarity, algorithms that produce clusters with high Dunn index are more desirable.
The silhouette coefficient contrasts the average distance to elements in the same cluster with the average distance to elements in other clusters. Objects with a high silhouette value are considered well clustered, objects with a low value may be outliers. This index works well withk-means clustering, and is also used to determine the optimal number of clusters.[41]
In external evaluation, clustering results are evaluated based on data that was not used for clustering, such as known class labels and external benchmarks. Such benchmarks consist of a set of pre-classified items, and these sets are often created by (expert) humans. Thus, the benchmark sets can be thought of as agold standardfor evaluation.[35]These types of evaluation methods measure how close the clustering is to the predetermined benchmark classes. However, it has recently been discussed whether this is adequate for real data, or only on synthetic data sets with a factual ground truth, since classes can contain internal structure, the attributes present may not allow separation of clusters or the classes may containanomalies.[42]Additionally, from aknowledge discoverypoint of view, the reproduction of known knowledge may not necessarily be the intended result.[42]In the special scenario ofconstrained clustering, where meta information (such as class labels) is used already in the clustering process, the hold-out of information for evaluation purposes is non-trivial.[43]
A number of measures are adapted from variants used to evaluate classification tasks. In place of counting the number of times a class was correctly assigned to a single data point (known astrue positives), suchpair countingmetrics assess whether each pair of data points that is truly in the same cluster is predicted to be in the same cluster.[35]
As with internal evaluation, several external evaluation measures exist,[39]: 125–129for example:
Purity is a measure of the extent to which clusters contain a single class.[38]Its calculation can be thought of as follows: For each cluster, count the number of data points from the most common class in said cluster. Now take the sum over all clusters and divide by the total number of data points. Formally, given some set of clustersM{\displaystyle M}and some set of classesD{\displaystyle D}, both partitioningN{\displaystyle N}data points, purity can be defined as:
This measure doesn't penalize having many clusters, and more clusters will make it easier to produce a high purity. A purity score of 1 is always possible by putting each data point in its own cluster. Also, purity doesn't work well for imbalanced data, where even poorly performing clustering algorithms will give a high purity value. For example, if a size 1000 dataset consists of two classes, one containing 999 points and the other containing 1 point, then every possible partition will have a purity of at least 99.9%.
The Rand index[44]computes how similar the clusters (returned by the clustering algorithm) are to the benchmark classifications. It can be computed using the following formula:
whereTP{\displaystyle TP}is the number of true positives,TN{\displaystyle TN}is the number oftrue negatives,FP{\displaystyle FP}is the number offalse positives, andFN{\displaystyle FN}is the number offalse negatives. The instances being counted here are the number of correctpairwiseassignments. That is,TP{\displaystyle TP}is the number of pairs of points that are clustered together in the predicted partition and in the ground truth partition,FP{\displaystyle FP}is the number of pairs of points that are clustered together in the predicted partition but not in the ground truth partition etc. If the dataset is of size N, thenTP+TN+FP+FN=(N2){\displaystyle TP+TN+FP+FN={\binom {N}{2}}}.
One issue with theRand indexis thatfalse positivesandfalse negativesare equally weighted. This may be an undesirable characteristic for some clustering applications. The F-measure addresses this concern,[citation needed]as does the chance-correctedadjusted Rand index.
The F-measure can be used to balance the contribution offalse negativesby weightingrecallthrough a parameterβ≥0{\displaystyle \beta \geq 0}. Letprecisionandrecall(both external evaluation measures in themselves) be defined as follows:P=TPTP+FP{\displaystyle P={\frac {TP}{TP+FP}}}R=TPTP+FN{\displaystyle R={\frac {TP}{TP+FN}}}whereP{\displaystyle P}is theprecisionrate andR{\displaystyle R}is therecallrate. We can calculate the F-measure by using the following formula:[38]Fβ=(β2+1)⋅P⋅Rβ2⋅P+R{\displaystyle F_{\beta }={\frac {(\beta ^{2}+1)\cdot P\cdot R}{\beta ^{2}\cdot P+R}}}Whenβ=0{\displaystyle \beta =0},F0=P{\displaystyle F_{0}=P}. In other words,recallhas no impact on the F-measure whenβ=0{\displaystyle \beta =0}, and increasingβ{\displaystyle \beta }allocates an increasing amount of weight to recall in the final F-measure.
AlsoTN{\displaystyle TN}is not taken into account and can vary from 0 upward without bound.
The Jaccard index is used to quantify the similarity between two datasets. TheJaccard indextakes on a value between 0 and 1. An index of 1 means that the two dataset are identical, and an index of 0 indicates that the datasets have no common elements. The Jaccard index is defined by the following formula:J(A,B)=|A∩B||A∪B|=TPTP+FP+FN{\displaystyle J(A,B)={\frac {|A\cap B|}{|A\cup B|}}={\frac {TP}{TP+FP+FN}}}This is simply the number of unique elements common to both sets divided by the total number of unique elements in both sets.
Note thatTN{\displaystyle TN}is not taken into account.
The Dice symmetric measure doubles the weight onTP{\displaystyle TP}while still ignoringTN{\displaystyle TN}:DSC=2TP2TP+FP+FN{\displaystyle DSC={\frac {2TP}{2TP+FP+FN}}}
The Fowlkes–Mallows index[45]computes the similarity between the clusters returned by the clustering algorithm and the benchmark classifications. The higher the value of the Fowlkes–Mallows index the more similar the clusters and the benchmark classifications are. It can be computed using the following formula:FM=TPTP+FP⋅TPTP+FN{\displaystyle FM={\sqrt {{\frac {TP}{TP+FP}}\cdot {\frac {TP}{TP+FN}}}}}whereTP{\displaystyle TP}is the number oftrue positives,FP{\displaystyle FP}is the number offalse positives, andFN{\displaystyle FN}is the number offalse negatives. TheFM{\displaystyle FM}index is the geometric mean of theprecisionandrecallP{\displaystyle P}andR{\displaystyle R}, and is thus also known as theG-measure, while the F-measure is their harmonic mean.[46][47]Moreover,precisionandrecallare also known as Wallace's indicesBI{\displaystyle B^{I}}andBII{\displaystyle B^{II}}.[48]Chance normalized versions of recall, precision and G-measure correspond toInformedness,MarkednessandMatthews Correlationand relate strongly toKappa.[49]
The Chi index[50]is an external validation index that measure the clustering results by applying thechi-squared statistic. This index scores positively the fact that the labels are as sparse as possible across the clusters, i.e., that each cluster has as few different labels as possible. The higher the value of the Chi Index the greater the relationship between the resulting clusters and the label used.
The mututal information is aninformation theoreticmeasure of how much information is shared between a clustering and a ground-truth classification that can detect a non-linear similarity between two clusterings.Normalized mutual informationis a family of corrected-for-chance variants of this that has a reduced bias for varying cluster numbers.[35]
A confusion matrix can be used to quickly visualize the results of a classification (or clustering) algorithm. It shows how different a cluster is from the gold standard cluster.
The validity measure (short v-measure) is a combined metric for homogeneity and completeness of the clusters[51]
To measure cluster tendency is to measure to what degree clusters exist in the data to be clustered, and may be performed as an initial test, before attempting clustering. One way to do this is to compare the data against random data. On average, random data should not have clusters[verification needed].
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Insoftware engineering,double-checked locking(also known as "double-checked locking optimization"[1]) is asoftware design patternused to reduce the overhead of acquiring alockby testing the locking criterion (the "lock hint") before acquiring the lock. Locking occurs only if the locking criterion check indicates that locking is required.
The original form of the pattern, appearing inPattern Languages of Program Design 3,[2]hasdata races, depending on thememory modelin use, and it is hard to get right. Some consider it to be ananti-pattern.[3]There are valid forms of the pattern, including the use of thevolatilekeyword in Java and explicit memory barriers in C++.[4]
The pattern is typically used to reduce locking overhead when implementing "lazy initialization" in a multi-threaded environment, especially as part of theSingleton pattern. Lazy initialization avoids initializing a value until the first time it is accessed.
Consider, for example, this code segment in theJava programming language:[4]
The problem is that this does not work when using multiple threads. Alockmust be obtained in case two threads callgetHelper()simultaneously. Otherwise, either they may both try to create the object at the same time, or one may wind up getting a reference to an incompletely initialized object.
Synchronizing with a lock can fix this, as is shown in the following example:
This is correct and will most likely have sufficient performance. However, the first call togetHelper()will create the object and only the few threads trying to access it during that time need to be synchronized; after that all calls just get a reference to the member variable. Since synchronizing a method could in some extreme cases decrease performance by a factor of 100 or higher,[5]the overhead of acquiring and releasing a lock every time this method is called seems unnecessary: once the initialization has been completed, acquiring and releasing the locks would appear unnecessary. Many programmers, including the authors of the double-checked locking design pattern, have attempted to optimize this situation in the following manner:
Intuitively, this algorithm is an efficient solution to the problem. But if the pattern is not written carefully, it will have adata race. For example, consider the following sequence of events:
Most runtimes havememory barriersor other methods for managing memory visibility across execution units. Without a detailed understanding of the language's behavior in this area, the algorithm is difficult to implement correctly. One of the dangers of using double-checked locking is that even a naive implementation will appear to work most of the time: it is not easy to distinguish between a correct implementation of the technique and one that has subtle problems. Depending on thecompiler, the interleaving of threads by theschedulerand the nature of otherconcurrent system activity, failures resulting from an incorrect implementation of double-checked locking may only occur intermittently. Reproducing the failures can be difficult.
For the singleton pattern, double-checked locking is not needed:
If control enters the declaration concurrently while the variable is being initialized, the concurrent execution shall wait for completion of the initialization.
C++11 and beyond also provide a built-in double-checked locking pattern in the form ofstd::once_flagandstd::call_once:
If one truly wishes to use the double-checked idiom instead of the trivially working example above (for instance because Visual Studio before the 2015 release did not implement the C++11 standard's language about concurrent initialization quoted above[7]), one needs to use acquire and release fences:[8]
pthread_once()must be used
to initialize library (or sub-module) code when its API does not have a dedicated initialization
procedure required to be called in single-threaded mode.
As ofJ2SE 5.0, thevolatilekeyword is defined to create a memory barrier. This allows a solution that ensures that multiple threads handle the singleton instance correctly. This new idiom is described in[3]and[4].
Note the local variable "localRef", which seems unnecessary. The effect of this is that in cases wherehelperis already initialized (i.e., most of the time), the volatile field is only accessed once (due to "return localRef;" instead of "return helper;"), which can improve the method's overall performance by as much as 40 percent.[9]
Java 9 introduced theVarHandleclass, which allows use of relaxed atomics to access fields, giving somewhat faster reads on machines with weak memory models, at the cost of more difficult mechanics and loss of sequential consistency (field accesses no longer participate in the synchronization order, the global order of accesses to volatile fields).[10]
If the helper object is static (one per class loader), an alternative is theinitialization-on-demand holder idiom[11](See Listing 16.6[12]from the previously cited text.)
This relies on the fact that nested classes are not loaded until they are referenced.
Semantics offinalfield in Java 5 can be employed to safely publish the helper object without usingvolatile:[13]
The local variabletempWrapperis required for correctness: simply usinghelperWrapperfor both null checks and the return statement could fail due to read reordering allowed under the Java Memory Model.[14]Performance of this implementation is not necessarily better than thevolatileimplementation.
In .NET Framework 4.0, theLazy<T>class was introduced, which internally uses double-checked locking by default (ExecutionAndPublication mode) to store either the exception that was thrown during construction, or the result of the function that was passed toLazy<T>:[15]
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chmodis ashellcommandfor changingaccess permissionsand special mode flags offiles(includingspecial filessuch asdirectories). The name is short forchangemodewheremoderefers to the permissions and flags collectively.[1][2]
The command originated inAT&T Unixversion 1 and was exclusive toUnixandUnix-likeoperating systemsuntil it was ported to other operating systems such asWindows(inUnxUtils)[3]andIBM i.[4]
InUnixandUnix-likeoperating systems, asystem callwith the same name as the command,chmod(), provides access to the underlying access control data. The command exposes the capabilities of the system call to a shell user.
As the need for enhancedfile-system permissionsgrew,access-control lists[5]were added to many file systems to augment the modes controlled viachmod.
The implementation ofchmodbundled inGNU coreutilswas written by David MacKenzie and Jim Meyering.[6]
Although the syntax of the command varies somewhat by implementation, it generally accepts either a single octal value (which specifiesallthe mode bits on each file), or a comma-delimited list of symbolic specifiers (which describes how to change the existing mode bits of each file). The remaining arguments are a list of paths to files to be modified.[7]
Changing permissions is only allowed for the superuser (root) and the owner of a file.
If asymbolic linkis specified, the target of the link has its mode bits adjusted. Permissions directly associated with a symbolic link file system entry are typically not used.
Optional, command-line options may include:
Given a numeric permissions argument, thechmodcommand treats it as anoctalnumber, and replacesallthe mode bits for each file. (Although 4 digits are specified, leading0digits can be elided.)[8]
Why octal rather than decimal?[9]
There are twelve standard mode bits, comprising 3 special bits (setuid,setgid, andsticky), and 3 permission groups (controlling access byuser,group, andother) of 3 bits each (read,write, andexec/scan); each permission bit grants access if set (1) or denies access if clear (0).
As an octal digit represents a 3-bit value, the twelve mode bits can be represented as four octal digits.chmodaccepts up to four digits and uses 0 for left digits not specified (as is normal for numeric representation). In practice, 3 digits are commonly specified since the special modes are rarely used and the user class is usually specified.
In the context of an octal digit, each operation bit represents a numeric value: read: 4, write: 2 and execute: 1. The following table relates octal digit values to a class operations value.
The commandstatcan report a file's permissions as octal. For example:
The reported value,754indicates the following permissions:
A code permits execution if and only if it isodd(i.e. 1, 3, 5, or 7). A code permits read if and only if it is greater than or equal to 4 (i.e. 4, 5, 6, or 7). A code permits write if and only if it is 2, 3, 6, or 7.
Thechmodcommand accepts symbolic notation that specifies how to modify the existing permissions.[10]The command accepts a comma-separate list of specifiers like:[classes]+|-|=operations
Classes map permissions to users. A change specifier can select one class by including its symbol, multiple by including each class's symbol with no delimiter or if not specified, then all classes are selected and further the bits ofumaskmask will be unchanged.[11]Class specifiers include:
As ownership is key to access control, and since the symbolic specification uses the abbreviationo, some incorrectly think that it meansowner, when, in fact, it is short forothers.
The change operators include:
Operations can be specified as follows:
Mostchmodimplementations support the specification of the special modes in octal, but some do not which requires using the symbolic notation.
Thelscommand can report file permissions in a symbolic notation that is similar to the notation used withchmod.ls -lreports permissions in a notation that consists of 10 letters. The first indicates the type of the file system entry, such as dash for regular file and 'd' for directory. Following that are three sets of three letters that indicate read, write and execute permissions grouped by user, group and others classes. Each position is either dash to indicate lack of permission or the single-letter abbreviation for the permission to indicate that it's granted. For example:
The permission specifier-rwxr-xr--starts with a dash which indicates thatfindPhoneNumbers.shis a regular file; not a directory. The next three lettersrwxindicate that the file can be read, written, and executed by the owning userdgerman. The next three lettersr-xindicate that the file can be read and executed by members of thestaffgroup. And the last three lettersr--indicate that the file is read-only for other users.
Addwrite permission to thegroup class of a directory, allowing users in the same group to add files:
Removewrite permission forall classes, preventing anyone from writing to the file:
Set the permissions for theuser andgroup classes toread and execute only; nowrite permission; preventing anyone from adding files:
Enablewrite for theuser class while making itread-only forgroup and others:
To recursively set access for the directorydocs/and its contained files:
chmod -R u+w docs/
To set user and group for read and write only and set others for read only:
chmod 664 file
To set user for read, write, and execute only and group and others for read only:
chmod 744 file
To set the sticky bit in addition to user, group and others permissions:
chmod 1755 file
To set UID in addition to user, group and others permissions:
chmod 4755 file
To set GID in addition to user, group and others permissions:
chmod 2755 file
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Inlinguistics,agreementorconcord(abbreviatedagr) occurs when awordchanges form depending on the other words to which it relates.[1]It is an instance ofinflection, and usually involves making the value of somegrammatical category(such asgenderorperson) "agree" between varied words or parts of thesentence.
For example, inStandard English, one may sayI amorhe is, but not "I is" or "he am". This is becauseEnglish grammarrequires that the verb and itssubjectagree inperson. ThepronounsIandheare first and third person respectively, as are theverb formsamandis. The verb form must be selected so that it has the same person as the subject in contrast tonotional agreement, which is based on meaning.[2][3]
Agreement generally involves matching the value of somegrammatical categorybetween differentconstituentsof a sentence (or sometimes between sentences, as in some cases where apronounis required to agree with itsantecedentorreferent). Some categories that commonly trigger grammatical agreement are noted below.
Agreement based ongrammatical personis found mostly betweenverbandsubject. An example from English (I amvs.he is) has been given in the introduction to this article.
Agreement between pronoun (or correspondingpossessive adjective) and antecedent also requires the selection of the correct person. For example, if the antecedent is the first person noun phraseMary and I, then a first person pronoun (we/us/our) is required; however, most noun phrases (the dog,my cats,Jack and Jill, etc.) are third person, and are replaced by a third person pronoun (he/she/it/theyetc.).
Agreement based ongrammatical numbercan occur between verb and subject, as in the case of grammatical person discussed above. In fact the two categories are often conflated withinverb conjugationpatterns: there are specific verb forms for first person singular, second person plural and so on. Some examples:
Again as with person, there is agreement in number between pronouns (or their corresponding possessives) and antecedents:
Agreement also occurs between nouns and theirspecifierandmodifiers, in some situations. This is common in languages such as French and Spanish, wherearticles,determinersandadjectives(both attributive and predicative) agree in number with the nouns they qualify:
In English this is not such a common feature, although there are certain determiners that occur specifically with singular or plural nouns only:
In languages in whichgrammatical genderplays a significant role, there is often agreement in gender between a noun and its modifiers. For example, inFrench:
Such agreement is also found withpredicate adjectives:l'homme est grand("the man is big") vs.la chaise est grande("the chair is big"). However, in some languages, such asGerman, this is not the case; only attributive modifiers show agreement:
In the case of verbs, gender agreement is less common, although it may still occur, for example inArabic verbswhere the second and third persons take different inflections for masculine and feminine subjects. In theFrenchcompound past tense, the past participle – formally an adjective – agrees in certain circumstances with the subject or with an object (seepassé composéfor details). InRussianand most otherSlavic languages, the form of the past tense agrees in gender with the subject, again due to derivation from an earlier adjectival construction.
There is also agreement in gender between pronouns and their antecedents. Examples of this can be found in English (although English pronouns principally follow natural gender rather than grammatical gender):
For more detail seeGender in English.
In languages that have a system ofcases, there is often agreement by case between a noun and its modifiers. For example, inGerman:
In fact, the modifiers of nouns in languages such as German andLatinagree with their nouns in number, gender and case; all three categories are conflated together in paradigms ofdeclension.
Case agreement is not a significant feature of English (onlypersonal pronounsand the pronounwhohave any case marking). Agreement between such pronouns can sometimes be observed:
A rare type of agreement that phonologically copies parts of the head rather than agreeing with agrammatical category.[4]For example, inBainouk:
katama-ŋɔ
river-prox.
in-ka
this
/
/
katama-ā-ŋɔ
river-pl-prox.
in-ka-ā
these
katama-ŋɔ in-ka/katama-ā-ŋɔ in-ka-ā
river-prox. this / river-pl-prox. these
In this example, what is copied is not a prefix, but rather the initial syllable of the head "river".
Languages can have no conventional agreement whatsoever, as inJapaneseorMalay; barely any, as inEnglish; a small amount, as in spokenFrench; a moderate amount, as inGreekorLatin; or a large amount, as inSwahili.
Modern English does not have a particularly large amount of agreement, although it is present.
Apart from verbs, the main examples are the determiners “this” and “that”, which become “these” and “those” respectively when the following noun is plural:
Allregular verbs(and nearly allirregularones) in English agree in the third-person singular of the presentindicativeby adding asuffixof either-sor-es. The latter is generally used after stems ending in thesibilantssh,ch,ss,orzz(e.g.he rushes,it lurches,she amasses,it buzzes.)
Present tense ofto love:
In the present tense (indicative mood), the following verbs have irregular conjugations for the third-person singular:
Note that there is a distinction between irregular verb conjugations in the spoken language and irregular spellings of words in the written language. Linguistics generally concerns itself with the natural, spoken language, and not with spelling conventions in the written language. The verbto gois often given as an example of a verb with an irregular present tense conjugation, on account of adding "-es" instead of just "-s" for the third person singular conjugation. However, this is merely an arbitrary spelling convention. In the spoken language, the present tense conjugation ofto gois entirely regular. If we were to classifyto goas irregular based on the spelling ofgoes, then by the same reasoning, we would have to include other regular verbs with irregular spelling conventions such asto veto/vetoes,to echo/echoes,to carry/carries,to hurry/hurries, etc. In contrast, the verbto dois actually irregular in its spoken third-person singular conjugation, in addition to having a somewhat irregular spelling. While the verbdorhymes withshoe, its conjugationdoesdoes not rhyme withshoes; the verbdoesrhymes withfuzz.
Conversely, the verbto say, while it may appear to be regular based on its spelling, is in fact irregular in its third person singular present tense conjugation:Sayis pronounced /seɪ/, butsaysis pronounced /sɛz/.Sayrhymes withpay, butsaysdoes not rhyme withpays.
The highly irregular verbto beis the only verb with more agreement than this in the present tense.
Present tense ofto be:
In English,defective verbsgenerally show no agreement for person or number, they include themodal verbs:can,may,shall,will,must,should,ought.
InEarly Modern Englishagreement existed for the second person singular of all verbs in the present tense, as well as in the past tense of some common verbs. This was usually in the form-est, but-stand-talso occurred. Note that this does not affect the endings for other persons and numbers.
Example present tense forms:thou wilt,thou shalt,thou art,thou hast,thou canst.
Example past tense forms:thou wouldst,thou shouldst,thou wast,thou hadst,thou couldst
Note also the agreement shown byto beeven in thesubjunctive mood.
However, for nearly all regular verbs, a separatethouform was no longer commonly used in the past tense. Thus theauxiliary verbto dois used, e.g.thou didst help, not*thou helpedst.
Here are some special cases for subject–verb agreement in English:
Always Singular
-All's well that ends well.
-One sows, another reaps.
-Together Everyone Achieves More–that's why we're a TEAM.
- If wealth is lost, nothing is lost. If health is lost, something is lost. If the character is lost, everything is lost.
- Nothing succeeds like success.
Exceptions:Noneis construed in the singular or plural as the sense may require, though the plural is commonly used.[5]Whennoneis clearly intended to meannot one, it should be followed by a singular verb. The SAT testing service, however, considersnoneto be strictly singular.[6]
- None so deaf as those who don't hear.
-None prosper by begging.
-Every dog is a lion at home.
- Many a penny makes a pound.
-Each man and each woman has a vote.
Exceptions: When the subject is followed byeach,the verb agrees to the original subject.
- Double coincidence of wants occurs when two parties each desire to sell what the other exactly wants to buy.
-Thousand dollars is a high price to pay.
Exceptions:Ten dollars were scattered on the floor. (= Ten dollar bills)
Exceptions: Fraction or percentage can be singular or plural based on the noun that follows it.
- Half a loaf is better than no bread.
- One in three people globally do not have access to safe drinking water.
- Who is to bell the cat?
- A food web is a graphical representation of what-eats-what in an ecosystem.
-Two and two is four.
Always Plural
-The MD and the CEO of the company have arrived.
-Time and tide wait for none.
-Weal and woe come by turns.
-Day and night are alike to a blind man.
Exceptions: If the nouns, however, suggest one idea or refer to the same thing or person, the verb is singular.[5]
-The good and generous thinks the whole world is friendly.
-The new bed and breakfast opens this week.
-The MD and CEO has arrived.
Exceptions: Words joined to a subject bywith,in addition to,along with,as well (as), together with, besides, not,etc. are parenthetical and the verb agrees with the original subject.[5]
-One cow breaks the fence, and a dozen leap it.
-A dozen of eggs cost around $1.5.
-1 mole of oxygen react with 2 moles of hydrogen gas to form water.
-The rich plan for tomorrow, the poor for today.
-Where the cattle stand together, the lion lies down hungry.
Singular or Plural
-Success or failure depends on individuals.
-Neither I nor you are to blame.
-Either you or he has to go.
(But at times, it is considered better to reword such grammatically correct but awkward sentences.)
- The jury has arrived at a unanimous decision.
- The committee are divided in their opinion.
- His family is quite large.
- His family have given him full support in his times of grief.
-There's a huge audience in the gallery today.
-The audience are requested to take their seats.
Exceptions: British English, however, tends to treat team and company names as plural.
-India beat Sri Lanka by six wickets in a pulsating final to deliver World Cup glory to their cricket-mad population for the first time since 1983. (BBC)[7]
-India wins cricket World Cup for 1st time in 28 years. (Washington Post)[8]
- There's more than one way to skin a cat.
Compared with English, Latin is an example of a highlyinflectedlanguage. The consequences for agreement are thus:
Verbs must agree in person and number, and sometimes in gender, with their subjects. Articles and adjectives must agree in case, number and gender with the nouns they modify.
Sample Latin verb: the present indicative active ofportare(portar), to carry:
In Latin, a pronoun such as "ego" and "tu" is only inserted for contrast and selection. Proper nouns and common nouns functioning as subject are nonetheless frequent. For this reason, Latin is described as anull-subject language.
Spoken French always distinguishes the second person plural, and the first person plural in formal speech, from each other and from the rest of the present tense in all verbs in the first conjugation (infinitives in -er) other thanaller. The first person plural form and pronoun (nous) are now usually replaced by the pronounon(literally: "one") and a third person singular verb form in Modern French. Thus,nous travaillons(formal) becomeson travaille. In most verbs from the other conjugations, each person in the plural can be distinguished among themselves and from the singular forms, again, when using the traditional first person plural. The other endings that appear in written French (i.e.: all singular endings, and also the third person plural of verbs other than those with infinitives in -er) are often pronounced the same, except inliaisoncontexts. Irregular verbs such asêtre,faire,aller, andavoirpossess more distinctly pronounced agreement forms than regular verbs.
An example of this is the verbtravailler, which goes as follows (the single words in italic type are pronounced /tʁa.vaj/):
On the other hand, a verb likepartirhas (the single words in italic type are pronounced /paʁ/):
The final S or T is silent, and the other three forms sound different from one another and from the singular forms.
Adjectives agree in gender and number with the nouns that they modify in French. As with verbs, the agreements are sometimes only shown in spelling since forms that are written with different agreement suffixes are sometimes pronounced the same (e.g.joli,jolie); although in many cases the final consonant is pronounced in feminine forms, but silent in masculine forms (e.g.petitvs.petite). Most plural forms end in-s, but this consonant is only pronounced in liaison contexts, and it is determinants that help understand if the singular or plural is meant. Theparticiplesof verbs agree in gender and number with the subject or object in some instances.
Articles, possessives and other determinants also decline for number and (only in the singular) for gender, with plural determinants being the same for both genders. This normally produces three forms: one for masculine singular nouns, one for feminine singular nouns, and another for plural nouns of either gender:
Notice that some of the above also change (in the singular) if the following word begins with a vowel:leandlabecomel′,duandde labecomede l′,mabecomesmon(as if the noun were masculine) andcebecomescet.
InHungarian, verbs havepolypersonal agreement, which means they agree with more than one of the verb'sarguments: not only its subject but also its (accusative) object. Difference is made between the case when there is a definite object and the case when the object is indefinite or there is no object at all. (The adverbs do not affect the form of the verb.) Examples:Szeretek(I love somebody or something unspecified),szeretem(I love him, her, it, or them, specifically),szeretlek(I love you);szeret(he loves me, us, you, someone, or something unspecified),szereti(he loves her, him, it, or them specifically). Of course, nouns or pronouns may specify the exact object. In short, there is agreement between a verb and the person and number of its subject and the specificity of its object (which often refers to the person more or less exactly).
Thepredicateagrees in number with the subject and if it iscopulative(i.e., it consists of a noun/adjective and a linking verb), both parts agree in number with the subject. For example:A könyvekérdekesekvoltak"The books were interesting" ("a": the, "könyv": book, "érdekes": interesting, "voltak": were): the plural is marked on the subject as well as both the adjectival and the copulative part of the predicate.
Within noun phrases, adjectives do not show agreement with the noun, though pronouns do. e.g.a szép könyveitekkel"with your nice books" ("szép": nice): the suffixes of the plural, the possessive "your" and the case marking "with" are only marked on the noun.
In theScandinavian languages, adjectives (bothattributiveandpredicative) are declined according to thegender,number, anddefinitenessof the noun they modify. InIcelandicandFaroese, adjectives are also declined according togrammatical case, unlike the other Scandinavian languages.
In some cases inSwedish,NorwegianandDanish, adjectives and participles aspredicatesappear to disagree with their subjects. This phenomenon is referred to aspancake sentences.
InNorwegian nynorsk,Swedish,IcelandicandFaroesethe past participle must agree in gender, number and definiteness when the participle is in anattributiveorpredicativeposition. In Icelandic and Faroese, past participles would also have to agree in grammatical case.
InNorwegian bokmålandDanishit is only required to decline past participles in number and definiteness when in anattributiveposition.
MostSlavic languagesare highly inflected, except forBulgarianandMacedonian. The agreement is similar to Latin, for instance between adjectives and nouns in gender, number, case andanimacy(if counted as a separate category). The following examples are fromSerbo-Croatian:
Verbs have 6 different forms in the present tense, for three persons in singular and plural. As in Latin, subject is frequently dropped.
Another characteristic is agreement in participles, which have different forms for different genders:
Swahili, like all otherBantu languages, has numerousnoun classes. Verbs must agree in class with their subjects and objects, and adjectives with the nouns that they qualify. For example:Kitabukimojakitatosha(One book will be enough),Mchungwammojautatosha(One orange-tree will be enough),Chungwa mojalitatosha(One orange will be enough).
There is also agreement in number. For example:Vitabuviwilivitatosha(Two books will be enough),Michungwamiwiliitatosha(Two orange-trees will be enough),Machungwamawiliyatatosha(Two oranges will be enough).
Class and number are indicated with prefixes (or sometimes their absence), which are not always the same for nouns, adjectives and verbs, as illustrated by the examples.
Manysign languageshave developed verb agreement with person. TheASLverb for "see" (V handshape), moves from the subject to the object. In the case of a third person subject, it goes from a locationindexedto the subject to the object, and vice versa. Also, inGerman Sign Languagenot all verbs are capable of subject/object verb agreement, so anauxiliary verbis used to convey this, carrying the meaning of the previous verb while still inflecting for person.
In addition, some verbs also agree with theclassifierthe subject takes. In theAmerican Sign Languageverb for "to be under", the classifier a verb takes goes under a downward-facing B handshape (palm facing downward). For example, if a person or an animal was crawled under something, a V handshape with bent fingers would go under the palm, but if it was a pencil, an 1-handshape (pointer finger out) would go under the palm.
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Inlinguistics,case governmentis a type ofgovernmentwherein a verb oradpositionimposesgrammatical caserequirements on its noun phrase complement. For example, inGermanthe prepositionfür'for' governs theaccusative case:für mich'for me-accusative'.[1]Case government may modify the meaning of the verb substantially, even to meanings that are unrelated.
Case government is an important notion in languages with many case distinctions, such asRussianandFinnish. It plays less of a role in English, because English does not rely on grammatical cases, except for distinguishing subject pronouns (I, he, she, we, they) from other pronouns (me, him, her, us, them). In English, true case government is absent, but if the aforementioned subject pronouns are understood as regular pronouns in theaccusative case, it occurs in sentences such asHe found me(not for example *He found I).
InStandard German, there areprepositionswhich govern each of the three oblique cases:Accusative,Dative, andGenitive. Case marking in German is largely observed on elements which modify the noun (e.g. determiners, adjectives). In the following table, examples ofLöffel'spoon' (Masculine),Messer'knife' (Neuter), andGabel'fork' (Feminine) are in definite noun phrases for each of the four cases. In the oblique cases (i.e. non-Nominative), the prepositions supplied dictate different cases:ohne'without' governs the accusative,mit'with' governs the dative, andwegen'because of' governs the genitive:[2]
der
the.M.NOM.SG
Löffel
spoon.NOM.SG
der Löffel
the.M.NOM.SG spoon.NOM.SG
'the spoon'
das
the.N.NOM.SG
Messer
knife.NOM.SG
das Messer
the.N.NOM.SG knife.NOM.SG
'the knife'
die
the.F.NOM.SG
Gabel
fork.NOM.SG
die Gabel
the.F.NOM.SG fork.NOM.SG
'the fork'
ohne
without
den
the.M.ACC.SG
Löffel
spoon.ACC.SG
ohne den Löffel
without the.M.ACC.SG spoon.ACC.SG
'without the spoon'
ohne
without
das
the.N.ACC.SG
Messer
knife.ACC.SG
ohne das Messer
without the.N.ACC.SG knife.ACC.SG
'without the knife'
ohne
without
die
the.F.ACC.SG
Gabel
fork.ACC.SG
ohne die Gabel
without the.F.ACC.SG fork.ACC.SG
'without the fork'
mit
with
dem
the.M.DAT.SG
Löffel
spoon.DAT.SG
mit dem Löffel
with the.M.DAT.SG spoon.DAT.SG
'with the spoon'
mit
with
dem
the.N.DAT.SG
Messer
knife.DAT.SG
mit dem Messer
with the.N.DAT.SG knife.DAT.SG
'with the knife'
mit
with
der
the.F.DAT.SG
Gabel
fork.DAT.SG
mit der Gabel
with the.F.DAT.SG fork.DAT.SG
'with the fork'
wegen
because of
des
the.M.GEN.SG
Löffels
spoon-M.GEN.SG
wegen des Löffels
{because of} the.M.GEN.SG spoon-M.GEN.SG
'because of the spoon'
wegen
because of
des
the.N.GEN.SG
Messer-s
knife-N.GEN.SG
wegen des Messer-s
{because of} the.N.GEN.SG knife-N.GEN.SG
'because of the knife'
wegen
because of
der
the.F.GEN.SG
Gabel
fork.F.GEN.SG
wegen der Gabel
{because of} the.F.GEN.SG fork.F.GEN.SG
'because of the fork'
There are also two-way prepositions which govern the dative when the prepositional phrase denoteslocation(where at?), but the accusative when it denotesdirection(to/from where?).
in
in
seinem
his.M.DAT.SG
Palast
palace.DAT.SG
in seinem Palast
in his.M.DAT.SG palace.DAT.SG
'in his palace'
in
in
seinen
his.M.ACC.SG
Palast
palace.ACC.SG
in seinen Palast
in his.M.ACC.SG palace.ACC.SG
'into his palace'
In Finnish, certain verbs or groups of verbs require associated objects to employ particular cases or case-like suffixes regardless of the circumstances in which a case is normally used. For example, certain verbs expressing emotions such asrakastaa(to love),inhota(to hate), andpelätä(to fear) require the use of thepartitive case: thus, "Minä rakastan sinua" (I love you), in which "sinua" is partitive although a complete concrete entity as object would normally take thegenitive. A number of verbs associated with sensory perception such asmaistua(to taste) andkuulostaa(to sound) employ theablative-like suffix-lta/-ltä: "Jäätelö maistuu hyvältä" (Ice cream tastes good). And certain verbs referring to interests or hobbies such aspitää(to like) andnauttia(to enjoy) use theelative-like suffix-sta/-stä.[3]
In books on Finnish grammar written in Finnish the phenomenon of case government is usually referred to as "rektio", from theLatinrēctiō(control or governance).
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XOR DDoSis a Linux Trojan malware with rootkit capabilities that was used to launch large-scale DDoS attacks. Its name stems from the heavy usage of XOR encryption in both malware and network communication to the C&Cs. It is built for multiple Linux architectures like ARM, x86 and x64. Noteworthy about XOR DDoS is the ability to hide itself with an embedded rootkit component which is obtained by multiple installation steps.[1]It was discovered in September 2014 byMalwareMustDie, awhite hatmalware research group.[2][3][4]From November 2014 it was involved in massive brute force campaign that lasted at least for three months.[5]
In order to gain access it launches a brute force attack in order to discover the password to Secure Shell services on Linux.[6]Once Secure Shell credentials are acquired and login is successful, it uses root privileges to run a script that downloads and installs XOR DDoS.[7]It is believed to be of Asian origin based on its targets, which tend to be located in Asia.[8]
Thismalware-related article is astub. You can help Wikipedia byexpanding it.
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https://en.wikipedia.org/wiki/Xor_DDoS
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Instatistics,correlationordependenceis any statistical relationship, whethercausalor not, between tworandom variablesorbivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables arelinearlyrelated.
Familiar examples of dependent phenomena include the correlation between theheightof parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in thedemand curve.
Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is acausal relationship, becauseextreme weathercauses people to use more electricity for heating or cooling. However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e.,correlation does not imply causation).
Formally, random variables aredependentif they do not satisfy a mathematical property ofprobabilistic independence. In informal parlance,correlationis synonymous withdependence. However, when used in a technical sense, correlation refers to any of several specific types of mathematical relationship betweenthe conditional expectation of one variable given the other is not constant as the conditioning variable changes; broadly correlation in this specific sense is used whenE(Y|X=x){\displaystyle E(Y|X=x)}is related tox{\displaystyle x}in some manner (such as linearly, monotonically, or perhaps according to some particular functional form such as logarithmic). Essentially, correlation is the measure of how two or more variables are related to one another. There are severalcorrelation coefficients, often denotedρ{\displaystyle \rho }orr{\displaystyle r}, measuring the degree of correlation. The most common of these is thePearson correlation coefficient, which is sensitive only to a linear relationship between two variables (which may be present even when one variable is a nonlinear function of the other). Other correlation coefficients – such asSpearman's rank correlation coefficient– have been developed to be morerobustthan Pearson's and to detect less structured relationships between variables.[1][2][3]Mutual informationcan also be applied to measure dependence between two variables.
The most familiar measure of dependence between two quantities is thePearson product-moment correlation coefficient(PPMCC), or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". It is obtained by taking the ratio of the covariance of the two variables in question of our numerical dataset, normalized to the square root of their variances. Mathematically, one simply divides thecovarianceof the two variables by the product of theirstandard deviations.Karl Pearsondeveloped the coefficient from a similar but slightly different idea byFrancis Galton.[4]
A Pearson product-moment correlation coefficient attempts to establish a line of best fit through a dataset of two variables by essentially laying out the expected values and the resulting Pearson's correlation coefficient indicates how far away the actual dataset is from the expected values. Depending on the sign of our Pearson's correlation coefficient, we can end up with either a negative or positive correlation if there is any sort of relationship between the variables of our data set.[citation needed]
The population correlation coefficientρX,Y{\displaystyle \rho _{X,Y}}between tworandom variablesX{\displaystyle X}andY{\displaystyle Y}withexpected valuesμX{\displaystyle \mu _{X}}andμY{\displaystyle \mu _{Y}}andstandard deviationsσX{\displaystyle \sigma _{X}}andσY{\displaystyle \sigma _{Y}}is defined as:
ρX,Y=corr(X,Y)=cov(X,Y)σXσY=E[(X−μX)(Y−μY)]σXσY,ifσXσY>0.{\displaystyle \rho _{X,Y}=\operatorname {corr} (X,Y)={\operatorname {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={\operatorname {E} [(X-\mu _{X})(Y-\mu _{Y})] \over \sigma _{X}\sigma _{Y}},\quad {\text{if}}\ \sigma _{X}\sigma _{Y}>0.}
whereE{\displaystyle \operatorname {E} }is theexpected valueoperator,cov{\displaystyle \operatorname {cov} }meanscovariance, andcorr{\displaystyle \operatorname {corr} }is a widely used alternative notation for the correlation coefficient. The Pearson correlation is defined only if both standard deviations are finite and positive. An alternative formula purely in terms ofmomentsis:
ρX,Y=E(XY)−E(X)E(Y)E(X2)−E(X)2⋅E(Y2)−E(Y)2{\displaystyle \rho _{X,Y}={\operatorname {E} (XY)-\operatorname {E} (X)\operatorname {E} (Y) \over {\sqrt {\operatorname {E} (X^{2})-\operatorname {E} (X)^{2}}}\cdot {\sqrt {\operatorname {E} (Y^{2})-\operatorname {E} (Y)^{2}}}}}
It is a corollary of theCauchy–Schwarz inequalitythat theabsolute valueof the Pearson correlation coefficient is not bigger than 1. Therefore, the value of a correlation coefficient ranges between −1 and +1. The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship (anti-correlation),[5]and some value in theopen interval(−1,1){\displaystyle (-1,1)}in all other cases, indicating the degree oflinear dependencebetween the variables. As it approaches zero there is less of a relationship (closer to uncorrelated). The closer the coefficient is to either −1 or 1, the stronger the correlation between the variables.
If the variables areindependent, Pearson's correlation coefficient is 0. However, because the correlation coefficient detects only linear dependencies between two variables, the converse is not necessarily true. A correlation coefficient of 0 does not imply that the variables are independent[citation needed].
X,Yindependent⇒ρX,Y=0(X,Yuncorrelated)ρX,Y=0(X,Yuncorrelated)⇏X,Yindependent{\displaystyle {\begin{aligned}X,Y{\text{ independent}}\quad &\Rightarrow \quad \rho _{X,Y}=0\quad (X,Y{\text{ uncorrelated}})\\\rho _{X,Y}=0\quad (X,Y{\text{ uncorrelated}})\quad &\nRightarrow \quad X,Y{\text{ independent}}\end{aligned}}}
For example, suppose the random variableX{\displaystyle X}is symmetrically distributed about zero, andY=X2{\displaystyle Y=X^{2}}. ThenY{\displaystyle Y}is completely determined byX{\displaystyle X}, so thatX{\displaystyle X}andY{\displaystyle Y}are perfectly dependent, but their correlation is zero; they areuncorrelated. However, in the special case whenX{\displaystyle X}andY{\displaystyle Y}arejointly normal, uncorrelatedness is equivalent to independence.
Even though uncorrelated data does not necessarily imply independence, one can check if random variables are independent if theirmutual informationis 0.
Given a series ofn{\displaystyle n}measurements of the pair(Xi,Yi){\displaystyle (X_{i},Y_{i})}indexed byi=1,…,n{\displaystyle i=1,\ldots ,n}, thesample correlation coefficientcan be used to estimate the population Pearson correlationρX,Y{\displaystyle \rho _{X,Y}}betweenX{\displaystyle X}andY{\displaystyle Y}. The sample correlation coefficient is defined as
wherex¯{\displaystyle {\overline {x}}}andy¯{\displaystyle {\overline {y}}}are the samplemeansofX{\displaystyle X}andY{\displaystyle Y}, andsx{\displaystyle s_{x}}andsy{\displaystyle s_{y}}are thecorrected sample standard deviationsofX{\displaystyle X}andY{\displaystyle Y}.
Equivalent expressions forrxy{\displaystyle r_{xy}}are
wheresx′{\displaystyle s'_{x}}andsy′{\displaystyle s'_{y}}are theuncorrectedsample standard deviationsofX{\displaystyle X}andY{\displaystyle Y}.
Ifx{\displaystyle x}andy{\displaystyle y}are results of measurements that contain measurement error, the realistic limits on the correlation coefficient are not −1 to +1 but a smaller range.[6]For the case of a linear model with a single independent variable, thecoefficient of determination (R squared)is the square ofrxy{\displaystyle r_{xy}}, Pearson's product-moment coefficient.
Consider thejoint probability distributionofXandYgiven in the table below.
For this joint distribution, themarginal distributionsare:
This yields the following expectations and variances:
Therefore:
Rank correlationcoefficients, such asSpearman's rank correlation coefficientandKendall's rank correlation coefficient (τ)measure the extent to which, as one variable increases, the other variable tends to increase, without requiring that increase to be represented by a linear relationship. If, as the one variable increases, the otherdecreases, the rank correlation coefficients will be negative. It is common to regard these rank correlation coefficients as alternatives to Pearson's coefficient, used either to reduce the amount of calculation or to make the coefficient less sensitive to non-normality in distributions. However, this view has little mathematical basis, as rank correlation coefficients measure a different type of relationship than thePearson product-moment correlation coefficient, and are best seen as measures of a different type of association, rather than as an alternative measure of the population correlation coefficient.[7][8]
To illustrate the nature of rank correlation, and its difference from linear correlation, consider the following four pairs of numbers(x,y){\displaystyle (x,y)}:
As we go from each pair to the next pairx{\displaystyle x}increases, and so doesy{\displaystyle y}. This relationship is perfect, in the sense that an increase inx{\displaystyle x}isalwaysaccompanied by an increase iny{\displaystyle y}. This means that we have a perfect rank correlation, and both Spearman's and Kendall's correlation coefficients are 1, whereas in this example Pearson product-moment correlation coefficient is 0.7544, indicating that the points are far from lying on a straight line. In the same way ify{\displaystyle y}alwaysdecreaseswhenx{\displaystyle x}increases, the rank correlation coefficients will be −1, while the Pearson product-moment correlation coefficient may or may not be close to −1, depending on how close the points are to a straight line. Although in the extreme cases of perfect rank correlation the two coefficients are both equal (being both +1 or both −1), this is not generally the case, and so values of the two coefficients cannot meaningfully be compared.[7]For example, for the three pairs (1, 1) (2, 3) (3, 2) Spearman's coefficient is 1/2, while Kendall's coefficient is 1/3.
The information given by a correlation coefficient is not enough to define the dependence structure between random variables. The correlation coefficient completely defines the dependence structure only in very particular cases, for example when the distribution is amultivariate normal distribution. (See diagram above.) In the case ofelliptical distributionsit characterizes the (hyper-)ellipses of equal density; however, it does not completely characterize the dependence structure (for example, amultivariate t-distribution's degrees of freedom determine the level of tail dependence).
For continuous variables, multiple alternative measures of dependence were introduced to address the deficiency of Pearson's correlation that it can be zero for dependent random variables (see[9]and reference references therein for an overview). They all share the important property that a value of zero implies independence. This led some authors[9][10]to recommend their routine usage, particularly ofdistance correlation.[11][12]Another alternative measure is the Randomized Dependence Coefficient.[13]The RDC is a computationally efficient,copula-based measure of dependence between multivariate random variables and is invariant with respect to non-linear scalings of random variables.
One important disadvantage of the alternative, more general measures is that, when used to test whether two variables are associated, they tend to have lower power compared to Pearson's correlation when the data follow a multivariate normal distribution.[9]This is an implication of theNo free lunch theorem. To detect all kinds of relationships, these measures have to sacrifice power on other relationships, particularly for the important special case of a linear relationship with Gaussian marginals, for which Pearson's correlation is optimal. Another problem concerns interpretation. While Person's correlation can be interpreted for all values, the alternative measures can generally only be interpreted meaningfully at the extremes.[14]
For twobinary variables, theodds ratiomeasures their dependence, and takes range non-negative numbers, possibly infinity:[0,+∞]{\displaystyle [0,+\infty ]}. Related statistics such asYule'sYandYule'sQnormalize this to the correlation-like range[−1,1]{\displaystyle [-1,1]}. The odds ratio is generalized by thelogistic modelto model cases where the dependent variables are discrete and there may be one or more independent variables.
Thecorrelation ratio,entropy-basedmutual information,total correlation,dual total correlationandpolychoric correlationare all also capable of detecting more general dependencies, as is consideration of thecopulabetween them, while thecoefficient of determinationgeneralizes the correlation coefficient tomultiple regression.
The degree of dependence between variablesXandYdoes not depend on the scale on which the variables are expressed. That is, if we are analyzing the relationship betweenXandY, most correlation measures are unaffected by transformingXtoa+bXandYtoc+dY, wherea,b,c, anddare constants (banddbeing positive). This is true of some correlationstatisticsas well as theirpopulationanalogues. Some correlation statistics, such as the rank correlation coefficient, are also invariant tomonotone transformationsof the marginal distributions ofXand/orY.
Most correlation measures are sensitive to the manner in whichXandYare sampled. Dependencies tend to be stronger if viewed over a wider range of values. Thus, if we consider the correlation coefficient between the heights of fathers and their sons over all adult males, and compare it to the same correlation coefficient calculated when the fathers are selected to be between 165 cm and 170 cm in height, the correlation will be weaker in the latter case. Several techniques have been developed that attempt to correct for range restriction in one or both variables, and are commonly used in meta-analysis; the most common are Thorndike's case II and case III equations.[15]
Various correlation measures in use may be undefined for certain joint distributions ofXandY. For example, the Pearson correlation coefficient is defined in terms ofmoments, and hence will be undefined if the moments are undefined. Measures of dependence based onquantilesare always defined. Sample-based statistics intended to estimate population measures of dependence may or may not have desirable statistical properties such as beingunbiased, orasymptotically consistent, based on the spatial structure of the population from which the data were sampled.
Sensitivity to the data distribution can be used to an advantage. For example,scaled correlationis designed to use the sensitivity to the range in order to pick out correlations between fast components oftime series.[16]By reducing the range of values in a controlled manner, the correlations on long time scale are filtered out and only the correlations on short time scales are revealed.
The correlation matrix ofn{\displaystyle n}random variablesX1,…,Xn{\displaystyle X_{1},\ldots ,X_{n}}is then×n{\displaystyle n\times n}matrixC{\displaystyle C}whose(i,j){\displaystyle (i,j)}entry is
Thus the diagonal entries are all identicallyone. If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as thecovariance matrixof thestandardized random variablesXi/σ(Xi){\displaystyle X_{i}/\sigma (X_{i})}fori=1,…,n{\displaystyle i=1,\dots ,n}. This applies both to the matrix of population correlations (in which caseσ{\displaystyle \sigma }is the population standard deviation), and to the matrix of sample correlations (in which caseσ{\displaystyle \sigma }denotes the sample standard deviation). Consequently, each is necessarily apositive-semidefinite matrix. Moreover, the correlation matrix is strictlypositive definiteif no variable can have all its values exactly generated as a linear function of the values of the others.
The correlation matrix is symmetric because the correlation betweenXi{\displaystyle X_{i}}andXj{\displaystyle X_{j}}is the same as the correlation betweenXj{\displaystyle X_{j}}andXi{\displaystyle X_{i}}.
A correlation matrix appears, for example, in one formula for thecoefficient of multiple determination, a measure of goodness of fit inmultiple regression.
Instatistical modelling, correlation matrices representing the relationships between variables are categorized into different correlation structures, which are distinguished by factors such as the number of parameters required to estimate them. For example, in anexchangeablecorrelation matrix, all pairs of variables are modeled as having the same correlation, so all non-diagonal elements of the matrix are equal to each other. On the other hand, anautoregressivematrix is often used when variables represent a time series, since correlations are likely to be greater when measurements are closer in time. Other examples include independent, unstructured, M-dependent, andToeplitz.
Inexploratory data analysis, theiconography of correlationsconsists in replacing a correlation matrix by a diagram where the "remarkable" correlations are represented by a solid line (positive correlation), or a dotted line (negative correlation).
In some applications (e.g., building data models from only partially observed data) one wants to find the "nearest" correlation matrix to an "approximate" correlation matrix (e.g., a matrix which typically lacks semi-definite positiveness due to the way it has been computed).
In 2002, Higham[17]formalized the notion of nearness using theFrobenius normand provided a method for computing the nearest correlation matrix using theDykstra's projection algorithm, of which an implementation is available as an online Web API.[18]
This sparked interest in the subject, with new theoretical (e.g., computing the nearest correlation matrix with factor structure[19]) and numerical (e.g. usage theNewton's methodfor computing the nearest correlation matrix[20]) results obtained in the subsequent years.
Similarly for two stochastic processes{Xt}t∈T{\displaystyle \left\{X_{t}\right\}_{t\in {\mathcal {T}}}}and{Yt}t∈T{\displaystyle \left\{Y_{t}\right\}_{t\in {\mathcal {T}}}}: If they are independent, then they are uncorrelated.[21]: p. 151The opposite of this statement might not be true. Even if two variables are uncorrelated, they might not be independent to each other.
The conventional dictum that "correlation does not imply causation" means that correlation cannot be used by itself to infer a causal relationship between the variables.[22]This dictum should not be taken to mean that correlations cannot indicate the potential existence of causal relations. However, the causes underlying the correlation, if any, may be indirect and unknown, and high correlations also overlap withidentityrelations (tautologies), where no causal process exists (e.g., between two variables measuring the same construct). Consequently, a correlation between two variables is not a sufficient condition to establish a causal relationship (in either direction).
A correlation between age and height in children is fairly causally transparent, but a correlation between mood and health in people is less so. Does improved mood lead to improved health, or does good health lead to good mood, or both? Or does some other factor underlie both? In other words, a correlation can be taken as evidence for a possible causal relationship, but cannot indicate what the causal relationship, if any, might be.
The Pearson correlation coefficient indicates the strength of alinearrelationship between two variables, but its value generally does not completely characterize their relationship. In particular, if theconditional meanofY{\displaystyle Y}givenX{\displaystyle X}, denotedE(Y∣X){\displaystyle \operatorname {E} (Y\mid X)}, is not linear inX{\displaystyle X}, the correlation coefficient will not fully determine the form ofE(Y∣X){\displaystyle \operatorname {E} (Y\mid X)}.
The adjacent image showsscatter plotsofAnscombe's quartet, a set of four different pairs of variables created byFrancis Anscombe.[23]The foury{\displaystyle y}variables have the same mean (7.5), variance (4.12), correlation (0.816) and regression line (y=3+0.5x{\textstyle y=3+0.5x}). However, as can be seen on the plots, the distribution of the variables is very different. The first one (top left) seems to be distributed normally, and corresponds to what one would expect when considering two variables correlated and following the assumption of normality. The second one (top right) is not distributed normally; while an obvious relationship between the two variables can be observed, it is not linear. In this case the Pearson correlation coefficient does not indicate that there is an exact functional relationship: only the extent to which that relationship can be approximated by a linear relationship. In the third case (bottom left), the linear relationship is perfect, except for oneoutlierwhich exerts enough influence to lower the correlation coefficient from 1 to 0.816. Finally, the fourth example (bottom right) shows another example when one outlier is enough to produce a high correlation coefficient, even though the relationship between the two variables is not linear.
These examples indicate that the correlation coefficient, as asummary statistic, cannot replace visual examination of the data. The examples are sometimes said to demonstrate that the Pearson correlation assumes that the data follow anormal distribution, but this is only partially correct.[4]The Pearson correlation can be accurately calculated for any distribution that has a finitecovariance matrix, which includes most distributions encountered in practice. However, the Pearson correlation coefficient (taken together with the sample mean and variance) is only asufficient statisticif the data is drawn from amultivariate normal distribution. As a result, the Pearson correlation coefficient fully characterizes the relationship between variables if and only if the data are drawn from a multivariate normal distribution.
If a pair(X,Y){\displaystyle \ (X,Y)\ }of random variables follows abivariate normal distribution, the conditional meanE(X∣Y){\displaystyle \operatorname {\boldsymbol {\mathcal {E}}} (X\mid Y)}is a linear function ofY{\displaystyle Y}, and the conditional meanE(Y∣X){\displaystyle \operatorname {\boldsymbol {\mathcal {E}}} (Y\mid X)}is a linear function ofX.{\displaystyle \ X~.}The correlation coefficientρX,Y{\displaystyle \ \rho _{X,Y}\ }betweenX{\displaystyle \ X\ }andY,{\displaystyle \ Y\ ,}and themarginalmeans and variances ofX{\displaystyle \ X\ }andY{\displaystyle \ Y\ }determine this linear relationship:
whereE(X){\displaystyle \operatorname {\boldsymbol {\mathcal {E}}} (X)}andE(Y){\displaystyle \operatorname {\boldsymbol {\mathcal {E}}} (Y)}are the expected values ofX{\displaystyle \ X\ }andY,{\displaystyle \ Y\ ,}respectively, andσX{\displaystyle \ \sigma _{X}\ }andσY{\displaystyle \ \sigma _{Y}\ }are the standard deviations ofX{\displaystyle \ X\ }andY,{\displaystyle \ Y\ ,}respectively.
The empirical correlationr{\displaystyle r}is anestimateof the correlation coefficientρ.{\displaystyle \ \rho ~.}A distribution estimate forρ{\displaystyle \ \rho \ }is given by
whereFHyp{\displaystyle \ F_{\mathsf {Hyp}}\ }is theGaussian hypergeometric function.
This density is both a Bayesianposteriordensity and an exact optimalconfidence distributiondensity.[24][25]
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Incomputer security, "dancing pigs" is a term or problem that explains computer users' attitudes towards computer security. It states that users will continue to pick an amusing graphic even if they receive a warning from security software that it is potentially dangerous.[1]In other words, users choose their primary desire features without considering the security. "Dancing pigs" is generally used by tech experts and can be found in IT articles.
The term originates from a remark made byEdward Felten, an associate professor at Princeton University:
Given a choice between dancing pigs and security, users will pick dancing pigs every time.[2]
Bruce Schneierstates:
The user's going to pick dancing pigs over security every time.[3]
Bruce Schneier expands on this remark as follows:
IfJ. Random Websurferclicks on a button that promises dancing pigs on his computer monitor, and instead gets a hortatory message describing the potential dangers of the applet—he's going to choose dancing pigs over computer security any day. If the computer prompts him with a warning screen like: "The applet DANCING PIGS could contain malicious code that might do permanent damage to your computer, steal your life's savings, and impair your ability to have children," he'll click OK without even reading it. Thirty seconds later he won't even remember that the warning screen even existed.[4]
TheMozillaSecurity Reviewers' Guide states:
Many of our potential users are inexperienced computer users, who do not understand the risks involved in using interactive Web content. This means we must rely on the user's judgement as little as possible.[5]
A widely publicized 2009 paper[6]directly addresses the dancing pigs quotation and argues that users' behavior is plausibly rational:
While amusing, this is unfair: users are never offered security, either on its own or as an alternative to anything else. They are offered long, complex and growing sets of advice, mandates, policy updates and tips. These sometimes carry vague and tentative suggestions of reduced risk, never security.[7]
One study ofphishingfound that people really do prefer dancing animals to security. The study showed participants a number of phishing sites, including one that copied theBank of the Westhome page:[8]
For many participants the "cute" design, the level of detail and the fact that the site does not ask for a great deal of information were the most convincing factors. Two participants mentioned the animated bear video that appears on the page, (e.g., "because that would take a lot of effort to copy"). Participants in general found this animation appealing and many reloaded the page just to see the animation again.
Schneier believes the dancing pigs problem will lead to crime, a key threat. He said: "The tactics might change ... as security measures make some tactics harder and others easier, but the underlying issue is constant." Ignoring computer security can inflict various types of damage resulting in significant losses.[9]
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In mathematics, acomplex numberis an element of anumber systemthat extends thereal numberswith a specific element denotedi, called theimaginary unitand satisfying the equationi2=−1{\displaystyle i^{2}=-1}; every complex number can be expressed in the forma+bi{\displaystyle a+bi}, whereaandbare real numbers. Because no real number satisfies the above equation,iwas called animaginary numberbyRené Descartes. For the complex numbera+bi{\displaystyle a+bi},ais called thereal part, andbis called theimaginary part. The set of complex numbers is denoted by either of the symbolsC{\displaystyle \mathbb {C} }orC. Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world.[1][2]
Complex numbers allow solutions to allpolynomial equations, even those that have no solutions in real numbers. More precisely, thefundamental theorem of algebraasserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number. For example, the equation(x+1)2=−9{\displaystyle (x+1)^{2}=-9}has no real solution, because the square of a real number cannot be negative, but has the two nonreal complex solutions−1+3i{\displaystyle -1+3i}and−1−3i{\displaystyle -1-3i}.
Addition, subtraction and multiplication of complex numbers can be naturally defined by using the rulei2=−1{\displaystyle i^{2}=-1}along with theassociative,commutative, anddistributive laws. Every nonzero complex number has amultiplicative inverse. This makes the complex numbers afieldwith the real numbers as a subfield. Because of these properties,a+bi=a+ib{\displaystyle a+bi=a+ib}, and which form is written depends upon convention and style considerations.
The complex numbers also form areal vector spaceofdimension two, with{1,i}{\displaystyle \{1,i\}}as astandard basis. This standard basis makes the complex numbers aCartesian plane, called the complex plane. This allows a geometric interpretation of the complex numbers and their operations, and conversely some geometric objects and operations can be expressed in terms of complex numbers. For example, the real numbers form thereal line, which is pictured as the horizontal axis of the complex plane, while real multiples ofi{\displaystyle i}are the vertical axis. A complex number can also be defined by its geometricpolar coordinates: the radius is called theabsolute valueof the complex number, while the angle from the positive real axis is called the argument of the complex number. The complex numbers of absolute value one form theunit circle. Adding a fixed complex number to all complex numbers defines atranslationin the complex plane, and multiplying by a fixed complex number is asimilaritycentered at the origin (dilating by the absolute value, and rotating by the argument). The operation ofcomplex conjugationis thereflection symmetrywith respect to the real axis.
The complex numbers form a rich structure that is simultaneously analgebraically closed field, acommutative algebraover the reals, and aEuclidean vector spaceof dimension two.
A complex number is an expression of the forma+bi, whereaandbare real numbers, andiis an abstract symbol, the so-called imaginary unit, whose meaning will be explained further below. For example,2 + 3iis a complex number.[3]
For a complex numbera+bi, the real numberais called itsreal part, and the real numberb(not the complex numberbi) is itsimaginary part.[4][5]The real part of a complex numberzis denotedRe(z),Re(z){\displaystyle {\mathcal {Re}}(z)}, orR(z){\displaystyle {\mathfrak {R}}(z)}; the imaginary part isIm(z),Im(z){\displaystyle {\mathcal {Im}}(z)}, orI(z){\displaystyle {\mathfrak {I}}(z)}: for example,Re(2+3i)=2{\textstyle \operatorname {Re} (2+3i)=2},Im(2+3i)=3{\displaystyle \operatorname {Im} (2+3i)=3}.
A complex numberzcan be identified with theordered pairof real numbers(ℜ(z),ℑ(z)){\displaystyle (\Re (z),\Im (z))}, which may be interpreted as coordinates of a point in a Euclidean plane with standard coordinates, which is then called thecomplex planeorArgand diagram.[6][7][a]The horizontal axis is generally used to display the real part, with increasing values to the right, and the imaginary part marks the vertical axis, with increasing values upwards.
A real numberacan be regarded as a complex numbera+ 0i, whose imaginary part is 0. A purely imaginary numberbiis a complex number0 +bi, whose real part is zero. It is common to writea+ 0i=a,0 +bi=bi, anda+ (−b)i=a−bi; for example,3 + (−4)i= 3 − 4i.
Thesetof all complex numbers is denoted byC{\displaystyle \mathbb {C} }(blackboard bold) orC(upright bold).
In some disciplines such as electromagnetism and electrical engineering,jis used instead ofi, asifrequently represents electric current,[8][9]and complex numbers are written asa+bjora+jb.
Two complex numbersa=x+yi{\displaystyle a=x+yi}andb=u+vi{\displaystyle b=u+vi}areaddedby separately adding their real and imaginary parts. That is to say:
a+b=(x+yi)+(u+vi)=(x+u)+(y+v)i.{\displaystyle a+b=(x+yi)+(u+vi)=(x+u)+(y+v)i.}Similarly,subtractioncan be performed asa−b=(x+yi)−(u+vi)=(x−u)+(y−v)i.{\displaystyle a-b=(x+yi)-(u+vi)=(x-u)+(y-v)i.}
The addition can be geometrically visualized as follows: the sum of two complex numbersaandb, interpreted as points in the complex plane, is the point obtained by building aparallelogramfrom the three verticesO, and the points of the arrows labeledaandb(provided that they are not on a line). Equivalently, calling these pointsA,B, respectively and the fourth point of the parallelogramXthetrianglesOABandXBAarecongruent.
The product of two complex numbers is computed as follows:
For example,(3+2i)(4−i)=3⋅4−(2⋅(−1))+(3⋅(−1)+2⋅4)i=14+5i.{\displaystyle (3+2i)(4-i)=3\cdot 4-(2\cdot (-1))+(3\cdot (-1)+2\cdot 4)i=14+5i.}In particular, this includes as a special case the fundamental formula
This formula distinguishes the complex numberifrom any real number, since the square of any (negative or positive) real number is always a non-negative real number.
With this definition of multiplication and addition, familiar rules for the arithmetic of rational or real numbers continue to hold for complex numbers. More precisely, thedistributive property, thecommutative properties(of addition and multiplication) hold. Therefore, the complex numbers form an algebraic structure known as afield, the same way as the rational or real numbers do.[10]
Thecomplex conjugateof the complex numberz=x+yiis defined asz¯=x−yi.{\displaystyle {\overline {z}}=x-yi.}[11]It is also denoted by some authors byz∗{\displaystyle z^{*}}. Geometrically,zis the"reflection"ofzabout the real axis. Conjugating twice gives the original complex number:z¯¯=z.{\displaystyle {\overline {\overline {z}}}=z.}A complex number is real if and only if it equals its own conjugate. Theunary operationof taking the complex conjugate of a complex number cannot be expressed by applying only the basic operations of addition, subtraction, multiplication and division.
For any complex numberz=x+yi, the product
is anon-negative realnumber. This allows to define theabsolute value(ormodulusormagnitude) ofzto be the square root[12]|z|=x2+y2.{\displaystyle |z|={\sqrt {x^{2}+y^{2}}}.}ByPythagoras' theorem,|z|{\displaystyle |z|}is the distance from the origin to the point representing the complex numberzin the complex plane. In particular, thecircle of radius onearound the origin consists precisely of the numberszsuch that|z|=1{\displaystyle |z|=1}. Ifz=x=x+0i{\displaystyle z=x=x+0i}is a real number, then|z|=|x|{\displaystyle |z|=|x|}: its absolute value as a complex number and as a real number are equal.
Using the conjugate, thereciprocalof a nonzero complex numberz=x+yi{\displaystyle z=x+yi}can be computed to be
1z=z¯zz¯=z¯|z|2=x−yix2+y2=xx2+y2−yx2+y2i.{\displaystyle {\frac {1}{z}}={\frac {\bar {z}}{z{\bar {z}}}}={\frac {\bar {z}}{|z|^{2}}}={\frac {x-yi}{x^{2}+y^{2}}}={\frac {x}{x^{2}+y^{2}}}-{\frac {y}{x^{2}+y^{2}}}i.}More generally, the division of an arbitrary complex numberw=u+vi{\displaystyle w=u+vi}by a non-zero complex numberz=x+yi{\displaystyle z=x+yi}equalswz=wz¯|z|2=(u+vi)(x−iy)x2+y2=ux+vyx2+y2+vx−uyx2+y2i.{\displaystyle {\frac {w}{z}}={\frac {w{\bar {z}}}{|z|^{2}}}={\frac {(u+vi)(x-iy)}{x^{2}+y^{2}}}={\frac {ux+vy}{x^{2}+y^{2}}}+{\frac {vx-uy}{x^{2}+y^{2}}}i.}This process is sometimes called "rationalization" of the denominator (although the denominator in the final expression may be an irrational real number), because it resembles the method to remove roots from simple expressions in a denominator.[13][14]
Theargumentofz(sometimes called the "phase"φ)[7]is the angle of theradiusOzwith the positive real axis, and is written asargz, expressed inradiansin this article. The angle is defined only up to adding integer multiples of2π{\displaystyle 2\pi }, since a rotation by2π{\displaystyle 2\pi }(or 360°) around the origin leaves all points in the complex plane unchanged. One possible choice to uniquely specify the argument is to require it to be within the interval(−π,π]{\displaystyle (-\pi ,\pi ]}, which is referred to as theprincipal value.[15]The argument can be computed from the rectangular formx + yiby means of thearctan(inverse tangent) function.[16]
For any complex numberz, with absolute valuer=|z|{\displaystyle r=|z|}and argumentφ{\displaystyle \varphi }, the equation
holds. This identity is referred to as the polar form ofz. It is sometimes abbreviated asz=rcisφ{\textstyle z=r\operatorname {\mathrm {cis} } \varphi }.
In electronics, one represents aphasorwith amplituderand phaseφinangle notation:[17]z=r∠φ.{\displaystyle z=r\angle \varphi .}
If two complex numbers are given in polar form, i.e.,z1=r1(cosφ1+isinφ1)andz2=r2(cosφ2+isinφ2), the product and division can be computed asz1z2=r1r2(cos(φ1+φ2)+isin(φ1+φ2)).{\displaystyle z_{1}z_{2}=r_{1}r_{2}(\cos(\varphi _{1}+\varphi _{2})+i\sin(\varphi _{1}+\varphi _{2})).}z1z2=r1r2(cos(φ1−φ2)+isin(φ1−φ2)),ifz2≠0.{\displaystyle {\frac {z_{1}}{z_{2}}}={\frac {r_{1}}{r_{2}}}\left(\cos(\varphi _{1}-\varphi _{2})+i\sin(\varphi _{1}-\varphi _{2})\right),{\text{if }}z_{2}\neq 0.}(These are a consequence of thetrigonometric identitiesfor the sine and cosine function.)
In other words, the absolute values aremultipliedand the arguments areaddedto yield the polar form of the product. The picture at the right illustrates the multiplication of(2+i)(3+i)=5+5i.{\displaystyle (2+i)(3+i)=5+5i.}Because the real and imaginary part of5 + 5iare equal, the argument of that number is 45 degrees, orπ/4(inradian). On the other hand, it is also the sum of the angles at the origin of the red and blue triangles arearctan(1/3) and arctan(1/2), respectively. Thus, the formulaπ4=arctan(12)+arctan(13){\displaystyle {\frac {\pi }{4}}=\arctan \left({\frac {1}{2}}\right)+\arctan \left({\frac {1}{3}}\right)}holds. As thearctanfunction can be approximated highly efficiently, formulas like this – known asMachin-like formulas– are used for high-precision approximations ofπ:[18]π4=4arctan(15)−arctan(1239){\displaystyle {\frac {\pi }{4}}=4\arctan \left({\frac {1}{5}}\right)-\arctan \left({\frac {1}{239}}\right)}
Then-th power of a complex number can be computed usingde Moivre's formula, which is obtained by repeatedly applying the above formula for the product:zn=z⋅⋯⋅z⏟nfactors=(r(cosφ+isinφ))n=rn(cosnφ+isinnφ).{\displaystyle z^{n}=\underbrace {z\cdot \dots \cdot z} _{n{\text{ factors}}}=(r(\cos \varphi +i\sin \varphi ))^{n}=r^{n}\,(\cos n\varphi +i\sin n\varphi ).}For example, the first few powers of the imaginary unitiarei,i2=−1,i3=−i,i4=1,i5=i,…{\displaystyle i,i^{2}=-1,i^{3}=-i,i^{4}=1,i^{5}=i,\dots }.
Thennth rootsof a complex numberzare given byz1/n=rn(cos(φ+2kπn)+isin(φ+2kπn)){\displaystyle z^{1/n}={\sqrt[{n}]{r}}\left(\cos \left({\frac {\varphi +2k\pi }{n}}\right)+i\sin \left({\frac {\varphi +2k\pi }{n}}\right)\right)}for0 ≤k≤n− 1. (Herern{\displaystyle {\sqrt[{n}]{r}}}is the usual (positive)nth root of the positive real numberr.) Because sine and cosine are periodic, other integer values ofkdo not give other values. For anyz≠0{\displaystyle z\neq 0}, there are, in particularndistinct complexn-th roots. For example, there are 4 fourth roots of 1, namely
In general there isnonatural way of distinguishing one particular complexnth root of a complex number. (This is in contrast to the roots of a positive real numberx, which has a unique positive realn-th root, which is therefore commonly referred to asthen-th root ofx.) One refers to this situation by saying that thenth root is an-valued functionofz.
Thefundamental theorem of algebra, ofCarl Friedrich GaussandJean le Rond d'Alembert, states that for any complex numbers (calledcoefficients)a0, ...,an, the equationanzn+⋯+a1z+a0=0{\displaystyle a_{n}z^{n}+\dotsb +a_{1}z+a_{0}=0}has at least one complex solutionz, provided that at least one of the higher coefficientsa1, ...,anis nonzero.[19]This property does not hold for thefield of rational numbersQ{\displaystyle \mathbb {Q} }(the polynomialx2− 2does not have a rational root, because√2is not a rational number) nor the real numbersR{\displaystyle \mathbb {R} }(the polynomialx2+ 4does not have a real root, because the square ofxis positive for any real numberx).
Because of this fact,C{\displaystyle \mathbb {C} }is called analgebraically closed field. It is a cornerstone of various applications of complex numbers, as is detailed further below.
There are various proofs of this theorem, by either analytic methods such asLiouville's theorem, ortopologicalones such as thewinding number, or a proof combiningGalois theoryand the fact that any real polynomial ofodddegree has at least one real root.
The solution inradicals(withouttrigonometric functions) of a generalcubic equation, when all three of its roots are real numbers, contains the square roots ofnegative numbers, a situation that cannot be rectified by factoring aided by therational root test, if the cubic isirreducible; this is the so-calledcasus irreducibilis("irreducible case"). This conundrum led Italian mathematicianGerolamo Cardanoto conceive of complex numbers in around 1545 in hisArs Magna,[20]though his understanding was rudimentary; moreover, he later described complex numbers as being "as subtle as they are useless".[21]Cardano did use imaginary numbers, but described using them as "mental torture."[22]This was prior to the use of the graphical complex plane. Cardano and other Italian mathematicians, notablyScipione del Ferro, in the 1500s created an algorithm for solving cubic equations which generally had one real solution and two solutions containing an imaginary number. Because they ignored the answers with the imaginary numbers, Cardano found them useless.[23]
Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra, which shows that with complex numbers, a solution exists to everypolynomial equationof degree one or higher. Complex numbers thus form analgebraically closed field, where any polynomial equation has aroot.
Many mathematicians contributed to the development of complex numbers. The rules for addition, subtraction, multiplication, and root extraction of complex numbers were developed by the Italian mathematicianRafael Bombelli.[24]A more abstract formalism for the complex numbers was further developed by the Irish mathematicianWilliam Rowan Hamilton, who extended this abstraction to the theory ofquaternions.[25]
The earliest fleeting reference tosquare rootsofnegative numberscan perhaps be said to occur in the work of the Greek mathematicianHero of Alexandriain the 1st centuryAD, where in hisStereometricahe considered, apparently in error, the volume of an impossiblefrustumof apyramidto arrive at the term81−144{\displaystyle {\sqrt {81-144}}}in his calculations, which today would simplify to−63=3i7{\displaystyle {\sqrt {-63}}=3i{\sqrt {7}}}.[b]Negative quantities were not conceived of inHellenistic mathematicsand Hero merely replaced the negative value by its positive144−81=37.{\displaystyle {\sqrt {144-81}}=3{\sqrt {7}}.}[27]
The impetus to study complex numbers as a topic in itself first arose in the 16th century whenalgebraic solutionsfor the roots ofcubicandquarticpolynomialswere discovered by Italian mathematicians (Niccolò Fontana TartagliaandGerolamo Cardano). It was soon realized (but proved much later)[28]that these formulas, even if one were interested only in real solutions, sometimes required the manipulation of square roots of negative numbers. In fact, it was proved later that the use of complex numbersis unavoidablewhen all three roots are real and distinct.[c]However, the general formula can still be used in this case, with some care to deal with the ambiguity resulting from the existence of three cubic roots for nonzero complex numbers. Rafael Bombelli was the first to address explicitly these seemingly paradoxical solutions of cubic equations and developed the rules for complex arithmetic, trying to resolve these issues.
The term "imaginary" for these quantities was coined byRené Descartesin 1637, who was at pains to stress their unreal nature:[29]
... sometimes only imaginary, that is one can imagine as many as I said in each equation, but sometimes there exists no quantity that matches that which we imagine.[... quelquefois seulement imaginaires c'est-à-dire que l'on peut toujours en imaginer autant que j'ai dit en chaque équation, mais qu'il n'y a quelquefois aucune quantité qui corresponde à celle qu'on imagine.]
A further source of confusion was that the equation−12=−1−1=−1{\displaystyle {\sqrt {-1}}^{2}={\sqrt {-1}}{\sqrt {-1}}=-1}seemed to be capriciously inconsistent with the algebraic identityab=ab{\displaystyle {\sqrt {a}}{\sqrt {b}}={\sqrt {ab}}}, which is valid for non-negative real numbersaandb, and which was also used in complex number calculations with one ofa,bpositive and the other negative. The incorrect use of this identity in the case when bothaandbare negative, and the related identity1a=1a{\textstyle {\frac {1}{\sqrt {a}}}={\sqrt {\frac {1}{a}}}}, even bedeviledLeonhard Euler. This difficulty eventually led to the convention of using the special symboliin place of−1{\displaystyle {\sqrt {-1}}}to guard against this mistake.[30][31]Even so, Euler considered it natural to introduce students to complex numbers much earlier than we do today. In his elementary algebra text book,Elements of Algebra, he introduces these numbers almost at once and then uses them in a natural way throughout.
In the 18th century complex numbers gained wider use, as it was noticed that formal manipulation of complex expressions could be used to simplify calculations involving trigonometric functions. For instance, in 1730Abraham de Moivrenoted that the identities relating trigonometric functions of an integer multiple of an angle to powers of trigonometric functions of that angle could be re-expressed by the followingde Moivre's formula:
(cosθ+isinθ)n=cosnθ+isinnθ.{\displaystyle (\cos \theta +i\sin \theta )^{n}=\cos n\theta +i\sin n\theta .}
In 1748, Euler went further and obtainedEuler's formulaofcomplex analysis:[32]
eiθ=cosθ+isinθ{\displaystyle e^{i\theta }=\cos \theta +i\sin \theta }
by formally manipulating complexpower seriesand observed that this formula could be used to reduce any trigonometric identity to much simpler exponential identities.
The idea of a complex number as a point in the complex plane was first described byDanish–NorwegianmathematicianCaspar Wesselin 1799,[33]although it had been anticipated as early as 1685 inWallis'sA Treatise of Algebra.[34]
Wessel's memoir appeared in the Proceedings of theCopenhagen Academybut went largely unnoticed. In 1806Jean-Robert Argandindependently issued a pamphlet on complex numbers and provided a rigorous proof of thefundamental theorem of algebra.[35]Carl Friedrich Gausshad earlier published an essentiallytopologicalproof of the theorem in 1797 but expressed his doubts at the time about "the true metaphysics of the square root of −1".[36]It was not until 1831 that he overcame these doubts and published his treatise on complex numbers as points in the plane,[37]largely establishing modern notation and terminology:[38]
If one formerly contemplated this subject from a false point of view and therefore found a mysterious darkness, this is in large part attributable to clumsy terminology. Had one not called +1, −1,−1{\displaystyle {\sqrt {-1}}}positive, negative, or imaginary (or even impossible) units, but instead, say, direct, inverse, or lateral units, then there could scarcely have been talk of such darkness.
In the beginning of the 19th century, other mathematicians discovered independently the geometrical representation of the complex numbers: Buée,[39][40]Mourey,[41]Warren,[42][43][44]Françaisand his brother,Bellavitis.[45][46]
The English mathematicianG.H. Hardyremarked that Gauss was the first mathematician to use complex numbers in "a really confident and scientific way" although mathematicians such as NorwegianNiels Henrik AbelandCarl Gustav Jacob Jacobiwere necessarily using them routinely before Gauss published his 1831 treatise.[47]
Augustin-Louis CauchyandBernhard Riemanntogether brought the fundamental ideas ofcomplex analysisto a high state of completion, commencing around 1825 in Cauchy's case.
The common terms used in the theory are chiefly due to the founders. Argand calledcosφ+isinφthedirection factor, andr=a2+b2{\displaystyle r={\sqrt {a^{2}+b^{2}}}}themodulus;[d][48]Cauchy (1821) calledcosφ+isinφthereduced form(l'expression réduite)[49]and apparently introduced the termargument; Gauss usedifor−1{\displaystyle {\sqrt {-1}}},[e]introduced the termcomplex numberfora+bi,[f]and calleda2+b2thenorm.[g]The expressiondirection coefficient, often used forcosφ+isinφ, is due to Hankel (1867),[53]andabsolute value,formodulus,is due to Weierstrass.
Later classical writers on the general theory includeRichard Dedekind,Otto Hölder,Felix Klein,Henri Poincaré,Hermann Schwarz,Karl Weierstrassand many others. Important work (including a systematization) in complex multivariate calculus has been started at beginning of the 20th century. Important results have been achieved byWilhelm Wirtingerin 1927.
While the above low-level definitions, including the addition and multiplication, accurately describe the complex numbers, there are other, equivalent approaches that reveal the abstract algebraic structure of the complex numbers more immediately.
One approach toC{\displaystyle \mathbb {C} }is viapolynomials, i.e., expressions of the formp(X)=anXn+⋯+a1X+a0,{\displaystyle p(X)=a_{n}X^{n}+\dotsb +a_{1}X+a_{0},}where thecoefficientsa0, ...,anare real numbers. The set of all such polynomials is denoted byR[X]{\displaystyle \mathbb {R} [X]}. Since sums and products of polynomials are again polynomials, this setR[X]{\displaystyle \mathbb {R} [X]}forms acommutative ring, called thepolynomial ring(over the reals). To every such polynomialp, one may assign the complex numberp(i)=anin+⋯+a1i+a0{\displaystyle p(i)=a_{n}i^{n}+\dotsb +a_{1}i+a_{0}}, i.e., the value obtained by settingX=i{\displaystyle X=i}. This defines a function
This function issurjectivesince every complex number can be obtained in such a way: the evaluation of alinear polynomiala+bX{\displaystyle a+bX}atX=i{\displaystyle X=i}isa+bi{\displaystyle a+bi}. However, the evaluation of polynomialX2+1{\displaystyle X^{2}+1}atiis 0, sincei2+1=0.{\displaystyle i^{2}+1=0.}This polynomial isirreducible, i.e., cannot be written as a product of two linear polynomials. Basic facts ofabstract algebrathen imply that thekernelof the above map is anidealgenerated by this polynomial, and that the quotient by this ideal is a field, and that there is anisomorphism
between the quotient ring andC{\displaystyle \mathbb {C} }. Some authors take this as the definition ofC{\displaystyle \mathbb {C} }.[54]
Accepting thatC{\displaystyle \mathbb {C} }is algebraically closed, because it is analgebraic extensionofR{\displaystyle \mathbb {R} }in this approach,C{\displaystyle \mathbb {C} }is therefore thealgebraic closureofR.{\displaystyle \mathbb {R} .}
Complex numbersa+bican also be represented by2 × 2matricesthat have the form(a−bba).{\displaystyle {\begin{pmatrix}a&-b\\b&\;\;a\end{pmatrix}}.}Here the entriesaandbare real numbers. As the sum and product of two such matrices is again of this form, these matrices form asubringof the ring of2 × 2matrices.
A simple computation shows that the mapa+ib↦(a−bba){\displaystyle a+ib\mapsto {\begin{pmatrix}a&-b\\b&\;\;a\end{pmatrix}}}is aring isomorphismfrom the field of complex numbers to the ring of these matrices, proving that these matrices form a field. This isomorphism associates the square of the absolute value of a complex number with thedeterminantof the corresponding matrix, and the conjugate of a complex number with thetransposeof the matrix.
The geometric description of the multiplication of complex numbers can also be expressed in terms ofrotation matricesby using this correspondence between complex numbers and such matrices. The action of the matrix on a vector(x,y)corresponds to the multiplication ofx+iybya+ib. In particular, if the determinant is1, there is a real numbertsuch that the matrix has the form
(cost−sintsintcost).{\displaystyle {\begin{pmatrix}\cos t&-\sin t\\\sin t&\;\;\cos t\end{pmatrix}}.}In this case, the action of the matrix on vectors and the multiplication by the complex numbercost+isint{\displaystyle \cos t+i\sin t}are both therotationof the anglet.
The study of functions of a complex variable is known ascomplex analysisand has enormous practical use inapplied mathematicsas well as in other branches of mathematics. Often, the most natural proofs for statements inreal analysisor evennumber theoryemploy techniques from complex analysis (seeprime number theoremfor an example).
Unlike real functions, which are commonly represented as two-dimensional graphs,complex functionshave four-dimensional graphs and may usefully be illustrated by color-coding athree-dimensional graphto suggest four dimensions, or by animating the complex function's dynamic transformation of the complex plane.
The notions ofconvergent seriesandcontinuous functionsin (real) analysis have natural analogs in complex analysis. A sequence of complex numbers is said toconvergeif and only if its real and imaginary parts do. This is equivalent to the(ε, δ)-definition of limits, where the absolute value of real numbers is replaced by the one of complex numbers. From a more abstract point of view,C{\displaystyle \mathbb {C} }, endowed with themetricd(z1,z2)=|z1−z2|{\displaystyle \operatorname {d} (z_{1},z_{2})=|z_{1}-z_{2}|}is a completemetric space, which notably includes thetriangle inequality|z1+z2|≤|z1|+|z2|{\displaystyle |z_{1}+z_{2}|\leq |z_{1}|+|z_{2}|}for any two complex numbersz1andz2.
Like in real analysis, this notion of convergence is used to construct a number ofelementary functions: theexponential functionexpz, also writtenez, is defined as theinfinite series, which can be shown toconvergefor anyz:expz:=1+z+z22⋅1+z33⋅2⋅1+⋯=∑n=0∞znn!.{\displaystyle \exp z:=1+z+{\frac {z^{2}}{2\cdot 1}}+{\frac {z^{3}}{3\cdot 2\cdot 1}}+\cdots =\sum _{n=0}^{\infty }{\frac {z^{n}}{n!}}.}For example,exp(1){\displaystyle \exp(1)}isEuler's numbere≈2.718{\displaystyle e\approx 2.718}.Euler's formulastates:exp(iφ)=cosφ+isinφ{\displaystyle \exp(i\varphi )=\cos \varphi +i\sin \varphi }for any real numberφ. This formula is a quick consequence of general basic facts about convergent power series and the definitions of the involved functions as power series. As a special case, this includesEuler's identityexp(iπ)=−1.{\displaystyle \exp(i\pi )=-1.}
For any positive real numbert, there is a unique real numberxsuch thatexp(x)=t{\displaystyle \exp(x)=t}. This leads to the definition of thenatural logarithmas theinverseln:R+→R;x↦lnx{\displaystyle \ln \colon \mathbb {R} ^{+}\to \mathbb {R} ;x\mapsto \ln x}of the exponential function. The situation is different for complex numbers, since
by the functional equation and Euler's identity.
For example,eiπ=e3iπ= −1, so bothiπand3iπare possible values for the complex logarithm of−1.
In general, given any non-zero complex numberw, any numberzsolving the equation
is called acomplex logarithmofw, denotedlogw{\displaystyle \log w}. It can be shown that these numbers satisfyz=logw=ln|w|+iargw,{\displaystyle z=\log w=\ln |w|+i\arg w,}wherearg{\displaystyle \arg }is theargumentdefinedabove, andln{\displaystyle \ln }the (real)natural logarithm. As arg is amultivalued function, unique only up to a multiple of2π, log is also multivalued. Theprincipal valueof log is often taken by restricting the imaginary part to theinterval(−π,π]. This leads to the complex logarithm being abijectivefunction taking values in the stripR++i(−π,π]{\displaystyle \mathbb {R} ^{+}+\;i\,\left(-\pi ,\pi \right]}(that is denotedS0{\displaystyle S_{0}}in the above illustration)ln:C×→R++i(−π,π].{\displaystyle \ln \colon \;\mathbb {C} ^{\times }\;\to \;\;\;\mathbb {R} ^{+}+\;i\,\left(-\pi ,\pi \right].}
Ifz∈C∖(−R≥0){\displaystyle z\in \mathbb {C} \setminus \left(-\mathbb {R} _{\geq 0}\right)}is not a non-positive real number (a positive or a non-real number), the resultingprincipal valueof the complex logarithm is obtained with−π<φ<π. It is ananalytic functionoutside the negative real numbers, but it cannot be prolongated to a function that is continuous at any negative real numberz∈−R+{\displaystyle z\in -\mathbb {R} ^{+}}, where the principal value islnz= ln(−z) +iπ.[h]
Complexexponentiationzωis defined aszω=exp(ωlnz),{\displaystyle z^{\omega }=\exp(\omega \ln z),}and is multi-valued, except whenωis an integer. Forω= 1 /n, for some natural numbern, this recovers the non-uniqueness ofnth roots mentioned above. Ifz> 0is real (andωan arbitrary complex number), one has a preferred choice oflnx{\displaystyle \ln x}, the real logarithm, which can be used to define a preferred exponential function.
Complex numbers, unlike real numbers, do not in general satisfy the unmodified power and logarithm identities, particularly when naïvely treated as single-valued functions; seefailure of power and logarithm identities. For example, they do not satisfyabc=(ab)c.{\displaystyle a^{bc}=\left(a^{b}\right)^{c}.}Both sides of the equation are multivalued by the definition of complex exponentiation given here, and the values on the left are a subset of those on the right.
The series defining the real trigonometric functionssineandcosine, as well as thehyperbolic functionssinh and cosh, also carry over to complex arguments without change. For the other trigonometric and hyperbolic functions, such astangent, things are slightly more complicated, as the defining series do not converge for all complex values. Therefore, one must define them either in terms of sine, cosine and exponential, or, equivalently, by using the method ofanalytic continuation.
A functionf:C{\displaystyle f:\mathbb {C} }→C{\displaystyle \mathbb {C} }is calledholomorphicorcomplex differentiableat a pointz0{\displaystyle z_{0}}if the limit
exists (in which case it is denoted byf′(z0){\displaystyle f'(z_{0})}). This mimics the definition for real differentiable functions, except that all quantities are complex numbers. Loosely speaking, the freedom of approachingz0{\displaystyle z_{0}}in different directions imposes a much stronger condition than being (real) differentiable. For example, the function
is differentiable as a functionR2→R2{\displaystyle \mathbb {R} ^{2}\to \mathbb {R} ^{2}}, but isnotcomplex differentiable.
A real differentiable function is complex differentiableif and only ifit satisfies theCauchy–Riemann equations, which are sometimes abbreviated as
Complex analysis shows some features not apparent in real analysis. For example, theidentity theoremasserts that two holomorphic functionsfandgagree if they agree on an arbitrarily smallopen subsetofC{\displaystyle \mathbb {C} }.Meromorphic functions, functions that can locally be written asf(z)/(z−z0)nwith a holomorphic functionf, still share some of the features of holomorphic functions. Other functions haveessential singularities, such assin(1/z)atz= 0.
Complex numbers have applications in many scientific areas, includingsignal processing,control theory,electromagnetism,fluid dynamics,quantum mechanics,cartography, andvibration analysis. Some of these applications are described below.
Complex conjugation is also employed ininversive geometry, a branch of geometry studying reflections more general than ones about a line. In thenetwork analysis of electrical circuits, the complex conjugate is used in finding the equivalent impedance when themaximum power transfer theoremis looked for.
Threenon-collinearpointsu,v,w{\displaystyle u,v,w}in the plane determine theshapeof the triangle{u,v,w}{\displaystyle \{u,v,w\}}. Locating the points in the complex plane, this shape of a triangle may be expressed by complex arithmetic asS(u,v,w)=u−wu−v.{\displaystyle S(u,v,w)={\frac {u-w}{u-v}}.}The shapeS{\displaystyle S}of a triangle will remain the same, when the complex plane is transformed by translation or dilation (by anaffine transformation), corresponding to the intuitive notion of shape, and describingsimilarity. Thus each triangle{u,v,w}{\displaystyle \{u,v,w\}}is in asimilarity classof triangles with the same shape.[55]
TheMandelbrot setis a popular example of a fractal formed on the complex plane. It is defined by plotting every locationc{\displaystyle c}where iterating the sequencefc(z)=z2+c{\displaystyle f_{c}(z)=z^{2}+c}does notdivergewheniteratedinfinitely. Similarly,Julia setshave the same rules, except wherec{\displaystyle c}remains constant.
Every triangle has a uniqueSteiner inellipse– anellipseinside the triangle and tangent to the midpoints of the three sides of the triangle. Thefociof a triangle's Steiner inellipse can be found as follows, according toMarden's theorem:[56][57]Denote the triangle's vertices in the complex plane asa=xA+yAi,b=xB+yBi, andc=xC+yCi. Write thecubic equation(x−a)(x−b)(x−c)=0{\displaystyle (x-a)(x-b)(x-c)=0}, take its derivative, and equate the (quadratic) derivative to zero. Marden's theorem says that the solutions of this equation are the complex numbers denoting the locations of the two foci of the Steiner inellipse.
As mentioned above, any nonconstant polynomial equation (in complex coefficients) has a solution inC{\displaystyle \mathbb {C} }.A fortiori, the same is true if the equation has rational coefficients. The roots of such equations are calledalgebraic numbers– they are a principal object of study inalgebraic number theory. Compared toQ¯{\displaystyle {\overline {\mathbb {Q} }}}, the algebraic closure ofQ{\displaystyle \mathbb {Q} }, which also contains all algebraic numbers,C{\displaystyle \mathbb {C} }has the advantage of being easily understandable in geometric terms. In this way, algebraic methods can be used to study geometric questions and vice versa. With algebraic methods, more specifically applying the machinery offield theoryto thenumber fieldcontainingroots of unity, it can be shown that it is not possible to construct a regularnonagonusing only compass and straightedge– a purely geometric problem.
Another example is theGaussian integers; that is, numbers of the formx+iy, wherexandyare integers, which can be used to classifysums of squares.
Analytic number theory studies numbers, often integers or rationals, by taking advantage of the fact that they can be regarded as complex numbers, in which analytic methods can be used. This is done by encoding number-theoretic information in complex-valued functions. For example, theRiemann zeta functionζ(s)is related to the distribution ofprime numbers.
In applied fields, complex numbers are often used to compute certain real-valuedimproper integrals, by means of complex-valued functions. Several methods exist to do this; seemethods of contour integration.
Indifferential equations, it is common to first find all complex rootsrof thecharacteristic equationof alinear differential equationor equation system and then attempt to solve the system in terms of base functions of the formf(t) =ert. Likewise, indifference equations, the complex rootsrof the characteristic equation of the difference equation system are used, to attempt to solve the system in terms of base functions of the formf(t) =rt.
SinceC{\displaystyle \mathbb {C} }is algebraically closed, any non-empty complexsquare matrixhas at least one (complex)eigenvalue. By comparison, real matrices do not always have real eigenvalues, for examplerotation matrices(for rotations of the plane for angles other than 0° or 180°) leave no direction fixed, and therefore do not have anyrealeigenvalue. The existence of (complex) eigenvalues, and the ensuing existence ofeigendecompositionis a useful tool for computing matrix powers andmatrix exponentials.
Complex numbers often generalize concepts originally conceived in the real numbers. For example, theconjugate transposegeneralizes thetranspose,hermitian matricesgeneralizesymmetric matrices, andunitary matricesgeneralizeorthogonal matrices.
Incontrol theory, systems are often transformed from thetime domainto the complexfrequency domainusing theLaplace transform. The system'szeros and polesare then analyzed in thecomplex plane. Theroot locus,Nyquist plot, andNichols plottechniques all make use of the complex plane.
In the root locus method, it is important whether zeros and poles are in the left or right half planes, that is, have real part greater than or less than zero. If a linear, time-invariant (LTI) system has poles that are
If a system has zeros in the right half plane, it is anonminimum phasesystem.
Complex numbers are used insignal analysisand other fields for a convenient description for periodically varying signals. For given real functions representing actual physical quantities, often in terms of sines and cosines, corresponding complex functions are considered of which the real parts are the original quantities. For asine waveof a givenfrequency, the absolute value|z|of the correspondingzis theamplitudeand theargumentargzis thephase.
IfFourier analysisis employed to write a given real-valued signal as a sum of periodic functions, these periodic functions are often written as complex-valued functions of the form
x(t)=Re{X(t)}{\displaystyle x(t)=\operatorname {Re} \{X(t)\}}
and
X(t)=Aeiωt=aeiϕeiωt=aei(ωt+ϕ){\displaystyle X(t)=Ae^{i\omega t}=ae^{i\phi }e^{i\omega t}=ae^{i(\omega t+\phi )}}
where ω represents theangular frequencyand the complex numberAencodes the phase and amplitude as explained above.
This use is also extended intodigital signal processinganddigital image processing, which use digital versions of Fourier analysis (andwaveletanalysis) to transmit,compress, restore, and otherwise processdigitalaudiosignals, still images, andvideosignals.
Another example, relevant to the two side bands ofamplitude modulationof AM radio, is:
cos((ω+α)t)+cos((ω−α)t)=Re(ei(ω+α)t+ei(ω−α)t)=Re((eiαt+e−iαt)⋅eiωt)=Re(2cos(αt)⋅eiωt)=2cos(αt)⋅Re(eiωt)=2cos(αt)⋅cos(ωt).{\displaystyle {\begin{aligned}\cos((\omega +\alpha )t)+\cos \left((\omega -\alpha )t\right)&=\operatorname {Re} \left(e^{i(\omega +\alpha )t}+e^{i(\omega -\alpha )t}\right)\\&=\operatorname {Re} \left(\left(e^{i\alpha t}+e^{-i\alpha t}\right)\cdot e^{i\omega t}\right)\\&=\operatorname {Re} \left(2\cos(\alpha t)\cdot e^{i\omega t}\right)\\&=2\cos(\alpha t)\cdot \operatorname {Re} \left(e^{i\omega t}\right)\\&=2\cos(\alpha t)\cdot \cos \left(\omega t\right).\end{aligned}}}
Inelectrical engineering, theFourier transformis used to analyze varyingelectric currentsandvoltages. The treatment ofresistors,capacitors, andinductorscan then be unified by introducing imaginary, frequency-dependent resistances for the latter two and combining all three in a single complex number called theimpedance. This approach is calledphasorcalculus.
In electrical engineering, the imaginary unit is denoted byj, to avoid confusion withI, which is generally in use to denote electric current, or, more particularly,i, which is generally in use to denote instantaneous electric current.
Because the voltage in an AC circuit is oscillating, it can be represented as
V(t)=V0ejωt=V0(cosωt+jsinωt),{\displaystyle V(t)=V_{0}e^{j\omega t}=V_{0}\left(\cos \omega t+j\sin \omega t\right),}
To obtain the measurable quantity, the real part is taken:
v(t)=Re(V)=Re[V0ejωt]=V0cosωt.{\displaystyle v(t)=\operatorname {Re} (V)=\operatorname {Re} \left[V_{0}e^{j\omega t}\right]=V_{0}\cos \omega t.}
The complex-valued signalV(t)is called theanalyticrepresentation of the real-valued, measurable signalv(t).[58]
Influid dynamics, complex functions are used to describepotential flow in two dimensions.
The complex number field is intrinsic to themathematical formulations of quantum mechanics, where complexHilbert spacesprovide the context for one such formulation that is convenient and perhaps most standard. The original foundation formulas of quantum mechanics – theSchrödinger equationand Heisenberg'smatrix mechanics– make use of complex numbers.
Inspecial relativityandgeneral relativity, some formulas for the metric onspacetimebecome simpler if one takes the time component of the spacetime continuum to be imaginary. (This approach is no longer standard in classical relativity, but isused in an essential wayinquantum field theory.) Complex numbers are essential tospinors, which are a generalization of thetensorsused in relativity.
The fieldC{\displaystyle \mathbb {C} }has the following three properties:
It can be shown that any field having these properties isisomorphic(as a field) toC.{\displaystyle \mathbb {C} .}For example, thealgebraic closureof the fieldQp{\displaystyle \mathbb {Q} _{p}}of thep-adic numberalso satisfies these three properties, so these two fields are isomorphic (as fields, but not as topological fields).[59]Also,C{\displaystyle \mathbb {C} }is isomorphic to the field of complexPuiseux series. However, specifying an isomorphism requires theaxiom of choice. Another consequence of this algebraic characterization is thatC{\displaystyle \mathbb {C} }contains many proper subfields that are isomorphic toC{\displaystyle \mathbb {C} }.
The preceding characterization ofC{\displaystyle \mathbb {C} }describes only the algebraic aspects ofC.{\displaystyle \mathbb {C} .}That is to say, the properties ofnearnessandcontinuity, which matter in areas such asanalysisandtopology, are not dealt with. The following description ofC{\displaystyle \mathbb {C} }as atopological field(that is, a field that is equipped with atopology, which allows the notion of convergence) does take into account the topological properties.C{\displaystyle \mathbb {C} }contains a subsetP(namely the set of positive real numbers) of nonzero elements satisfying the following three conditions:
Moreover,C{\displaystyle \mathbb {C} }has a nontrivialinvolutiveautomorphismx↦x*(namely the complex conjugation), such thatx x*is inPfor any nonzeroxinC.{\displaystyle \mathbb {C} .}
Any fieldFwith these properties can be endowed with a topology by taking the setsB(x,p) = {y|p− (y−x)(y−x)* ∈P}as abase, wherexranges over the field andpranges overP. With this topologyFis isomorphic as atopologicalfield toC.{\displaystyle \mathbb {C} .}
The onlyconnectedlocally compacttopological fieldsareR{\displaystyle \mathbb {R} }andC.{\displaystyle \mathbb {C} .}This gives another characterization ofC{\displaystyle \mathbb {C} }as a topological field, becauseC{\displaystyle \mathbb {C} }can be distinguished fromR{\displaystyle \mathbb {R} }because the nonzero complex numbers areconnected, while the nonzero real numbers are not.[60]
The process of extending the fieldR{\displaystyle \mathbb {R} }of reals toC{\displaystyle \mathbb {C} }is an instance of theCayley–Dickson construction. Applying this construction iteratively toC{\displaystyle \mathbb {C} }then yields thequaternions, theoctonions,[61]thesedenions, and thetrigintaduonions. This construction turns out to diminish the structural properties of the involved number systems.
Unlike the reals,C{\displaystyle \mathbb {C} }is not anordered field, that is to say, it is not possible to define a relationz1<z2that is compatible with the addition and multiplication. In fact, in any ordered field, the square of any element is necessarily positive, soi2= −1precludes the existence of anorderingonC.{\displaystyle \mathbb {C} .}[62]Passing fromC{\displaystyle \mathbb {C} }to the quaternionsH{\displaystyle \mathbb {H} }loses commutativity, while the octonions (additionally to not being commutative) fail to be associative. The reals, complex numbers, quaternions and octonions are allnormed division algebrasoverR{\displaystyle \mathbb {R} }. ByHurwitz's theoremthey are the only ones; thesedenions, the next step in the Cayley–Dickson construction, fail to have this structure.
The Cayley–Dickson construction is closely related to theregular representationofC,{\displaystyle \mathbb {C} ,}thought of as anR{\displaystyle \mathbb {R} }-algebra(anR{\displaystyle \mathbb {R} }-vector space with a multiplication), with respect to the basis(1,i). This means the following: theR{\displaystyle \mathbb {R} }-linear mapC→Cz↦wz{\displaystyle {\begin{aligned}\mathbb {C} &\rightarrow \mathbb {C} \\z&\mapsto wz\end{aligned}}}for some fixed complex numberwcan be represented by a2 × 2matrix (once a basis has been chosen). With respect to the basis(1,i), this matrix is(Re(w)−Im(w)Im(w)Re(w)),{\displaystyle {\begin{pmatrix}\operatorname {Re} (w)&-\operatorname {Im} (w)\\\operatorname {Im} (w)&\operatorname {Re} (w)\end{pmatrix}},}that is, the one mentioned in the section on matrix representation of complex numbers above. While this is alinear representationofC{\displaystyle \mathbb {C} }in the 2 × 2 real matrices, it is not the only one. Any matrixJ=(pqr−p),p2+qr+1=0{\displaystyle J={\begin{pmatrix}p&q\\r&-p\end{pmatrix}},\quad p^{2}+qr+1=0}has the property that its square is the negative of the identity matrix:J2= −I. Then{z=aI+bJ:a,b∈R}{\displaystyle \{z=aI+bJ:a,b\in \mathbb {R} \}}is also isomorphic to the fieldC,{\displaystyle \mathbb {C} ,}and gives an alternative complex structure onR2.{\displaystyle \mathbb {R} ^{2}.}This is generalized by the notion of alinear complex structure.
Hypercomplex numbersalso generalizeR,{\displaystyle \mathbb {R} ,}C,{\displaystyle \mathbb {C} ,}H,{\displaystyle \mathbb {H} ,}andO.{\displaystyle \mathbb {O} .}For example, this notion contains thesplit-complex numbers, which are elements of the ringR[x]/(x2−1){\displaystyle \mathbb {R} [x]/(x^{2}-1)}(as opposed toR[x]/(x2+1){\displaystyle \mathbb {R} [x]/(x^{2}+1)}for complex numbers). In this ring, the equationa2= 1has four solutions.
The fieldR{\displaystyle \mathbb {R} }is the completion ofQ,{\displaystyle \mathbb {Q} ,}the field ofrational numbers, with respect to the usualabsolute valuemetric. Other choices ofmetricsonQ{\displaystyle \mathbb {Q} }lead to the fieldsQp{\displaystyle \mathbb {Q} _{p}}ofp-adic numbers(for anyprime numberp), which are thereby analogous toR{\displaystyle \mathbb {R} }. There are no other nontrivial ways of completingQ{\displaystyle \mathbb {Q} }thanR{\displaystyle \mathbb {R} }andQp,{\displaystyle \mathbb {Q} _{p},}byOstrowski's theorem. The algebraic closuresQp¯{\displaystyle {\overline {\mathbb {Q} _{p}}}}ofQp{\displaystyle \mathbb {Q} _{p}}still carry a norm, but (unlikeC{\displaystyle \mathbb {C} }) are not complete with respect to it. The completionCp{\displaystyle \mathbb {C} _{p}}ofQp¯{\displaystyle {\overline {\mathbb {Q} _{p}}}}turns out to be algebraically closed. By analogy, the field is calledp-adic complex numbers.
The fieldsR,{\displaystyle \mathbb {R} ,}Qp,{\displaystyle \mathbb {Q} _{p},}and their finite field extensions, includingC,{\displaystyle \mathbb {C} ,}are calledlocal fields.
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In probability theory and statistics, aMarkov chainorMarkov processis astochastic processdescribing asequenceof possible events in which theprobabilityof each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairsnow." Acountably infinitesequence, in which the chain moves state at discrete time steps, gives adiscrete-time Markov chain(DTMC). Acontinuous-timeprocess is called acontinuous-time Markov chain(CTMC). Markov processes are named in honor of theRussianmathematicianAndrey Markov.
Markov chains have many applications asstatistical modelsof real-world processes.[1]They provide the basis for general stochastic simulation methods known asMarkov chain Monte Carlo, which are used for simulating sampling from complexprobability distributions, and have found application in areas includingBayesian statistics,biology,chemistry,economics,finance,information theory,physics,signal processing, andspeech processing.[1][2][3]
The adjectivesMarkovianandMarkovare used to describe something that is related to a Markov process.[4]
A Markov process is astochastic processthat satisfies theMarkov property(sometimes characterized as "memorylessness"). In simpler terms, it is a process for which predictions can be made regarding future outcomes based solely on its present state and—most importantly—such predictions are just as good as the ones that could be made knowing the process's full history.[5]In other words,conditionalon the present state of the system, its future and past states areindependent.
A Markov chain is a type of Markov process that has either a discretestate spaceor a discrete index set (often representing time), but the precise definition of a Markov chain varies.[6]For example, it is common to define a Markov chain as a Markov process in eitherdiscrete or continuous timewith a countable state space (thus regardless of the nature of time),[7][8][9][10]but it is also common to define a Markov chain as having discrete time in either countable or continuous state space (thus regardless of the state space).[6]
The system'sstate spaceand time parameter index need to be specified. The following table gives an overview of the different instances of Markov processes for different levels of state space generality and for discrete time v. continuous time:
Note that there is no definitive agreement in the literature on the use of some of the terms that signify special cases of Markov processes. Usually the term "Markov chain" is reserved for a process with a discrete set of times, that is, adiscrete-time Markov chain (DTMC),[11]but a few authors use the term "Markov process" to refer to acontinuous-time Markov chain (CTMC)without explicit mention.[12][13][14]In addition, there are other extensions of Markov processes that are referred to as such but do not necessarily fall within any of these four categories (seeMarkov model). Moreover, the time index need not necessarily be real-valued; like with the state space, there are conceivable processes that move through index sets with other mathematical constructs. Notice that the general state space continuous-time Markov chain is general to such a degree that it has no designated term.
While the time parameter is usually discrete, thestate spaceof a Markov chain does not have any generally agreed-on restrictions: the term may refer to a process on an arbitrary state space.[15]However, many applications of Markov chains employ finite orcountably infinitestate spaces, which have a more straightforward statistical analysis. Besides time-index and state-space parameters, there are many other variations, extensions and generalizations (seeVariations). For simplicity, most of this article concentrates on the discrete-time, discrete state-space case, unless mentioned otherwise.
The changes of state of the system are called transitions. The probabilities associated with various state changes are called transition probabilities. The process is characterized by a state space, atransition matrixdescribing the probabilities of particular transitions, and an initial state (or initial distribution) across the state space. By convention, we assume all possible states and transitions have been included in the definition of the process, so there is always a next state, and the process does not terminate.
A discrete-time random process involves a system which is in a certain state at each step, with the state changing randomly between steps. The steps are often thought of as moments in time, but they can equally well refer to physical distance or any other discrete measurement. Formally, the steps are theintegersornatural numbers, and the random process is a mapping of these to states. The Markov property states that theconditional probability distributionfor the system at the next step (and in fact at all future steps) depends only on the current state of the system, and not additionally on the state of the system at previous steps.
Since the system changes randomly, it is generally impossible to predict with certainty the state of a Markov chain at a given point in the future. However, the statistical properties of the system's future can be predicted. In many applications, it is these statistical properties that are important.
Andrey Markovstudied Markov processes in the early 20th century, publishing his first paper on the topic in 1906.[16][17][18]Markov Processes in continuous time were discovered long before his work in the early 20th century in the form of thePoisson process.[19][20][21]Markov was interested in studying an extension of independent random sequences, motivated by a disagreement withPavel Nekrasovwho claimed independence was necessary for theweak law of large numbersto hold.[22]In his first paper on Markov chains, published in 1906, Markov showed that under certain conditions the average outcomes of the Markov chain would converge to a fixed vector of values, so proving a weak law of large numbers without the independence assumption,[16][17][18]which had been commonly regarded as a requirement for such mathematical laws to hold.[18]Markov later used Markov chains to study the distribution of vowels inEugene Onegin, written byAlexander Pushkin, and proved acentral limit theoremfor such chains.[16]
In 1912Henri Poincaréstudied Markov chains onfinite groupswith an aim to study card shuffling. Other early uses of Markov chains include a diffusion model, introduced byPaulandTatyana Ehrenfestin 1907, and a branching process, introduced byFrancis GaltonandHenry William Watsonin 1873, preceding the work of Markov.[16][17]After the work of Galton and Watson, it was later revealed that their branching process had been independently discovered and studied around three decades earlier byIrénée-Jules Bienaymé.[23]Starting in 1928,Maurice Fréchetbecame interested in Markov chains, eventually resulting in him publishing in 1938 a detailed study on Markov chains.[16][24]
Andrey Kolmogorovdeveloped in a 1931 paper a large part of the early theory of continuous-time Markov processes.[25][26]Kolmogorov was partly inspired by Louis Bachelier's 1900 work on fluctuations in the stock market as well asNorbert Wiener's work on Einstein's model of Brownian movement.[25][27]He introduced and studied a particular set of Markov processes known as diffusion processes, where he derived a set of differential equations describing the processes.[25][28]Independent of Kolmogorov's work,Sydney Chapmanderived in a 1928 paper an equation, now called theChapman–Kolmogorov equation, in a less mathematically rigorous way than Kolmogorov, while studying Brownian movement.[29]The differential equations are now called the Kolmogorov equations[30]or the Kolmogorov–Chapman equations.[31]Other mathematicians who contributed significantly to the foundations of Markov processes includeWilliam Feller, starting in 1930s, and then laterEugene Dynkin, starting in the 1950s.[26]
Suppose that there is a coin purse containing five coins worth 25¢, five coins worth 10¢ and five coins worth 5¢, and one by one, coins are randomly drawn from the purse and are set on a table. IfXn{\displaystyle X_{n}}represents the total value of the coins set on the table afterndraws, withX0=0{\displaystyle X_{0}=0}, then the sequence{Xn:n∈N}{\displaystyle \{X_{n}:n\in \mathbb {N} \}}isnota Markov process.
To see why this is the case, suppose that in the first six draws, all five nickels and a quarter are drawn. ThusX6=$0.50{\displaystyle X_{6}=\$0.50}. If we know not justX6{\displaystyle X_{6}}, but the earlier values as well, then we can determine which coins have been drawn, and we know that the next coin will not be a nickel; so we can determine thatX7≥$0.60{\displaystyle X_{7}\geq \$0.60}with probability 1. But if we do not know the earlier values, then based only on the valueX6{\displaystyle X_{6}}we might guess that we had drawn four dimes and two nickels, in which case it would certainly be possible to draw another nickel next. Thus, our guesses aboutX7{\displaystyle X_{7}}are impacted by our knowledge of values prior toX6{\displaystyle X_{6}}.
However, it is possible to model this scenario as a Markov process. Instead of definingXn{\displaystyle X_{n}}to represent thetotal valueof the coins on the table, we could defineXn{\displaystyle X_{n}}to represent thecountof the various coin types on the table. For instance,X6=1,0,5{\displaystyle X_{6}=1,0,5}could be defined to represent the state where there is one quarter, zero dimes, and five nickels on the table after 6 one-by-one draws. This new model could be represented by6×6×6=216{\displaystyle 6\times 6\times 6=216}possible states, where each state represents the number of coins of each type (from 0 to 5) that are on the table. (Not all of these states are reachable within 6 draws.) Suppose that the first draw results in stateX1=0,1,0{\displaystyle X_{1}=0,1,0}. The probability of achievingX2{\displaystyle X_{2}}now depends onX1{\displaystyle X_{1}}; for example, the stateX2=1,0,1{\displaystyle X_{2}=1,0,1}is not possible. After the second draw, the third draw depends on which coins have so far been drawn, but no longer only on the coins that were drawn for the first state (since probabilistically important information has since been added to the scenario). In this way, the likelihood of theXn=i,j,k{\displaystyle X_{n}=i,j,k}state depends exclusively on the outcome of theXn−1=ℓ,m,p{\displaystyle X_{n-1}=\ell ,m,p}state.
A discrete-time Markov chain is a sequence ofrandom variablesX1,X2,X3, ... with theMarkov property, namely that the probability of moving to the next state depends only on the present state and not on the previous states:
The possible values ofXiform acountable setScalled the state space of the chain.
A continuous-time Markov chain (Xt)t≥ 0is defined by a finite or countable state spaceS, atransition rate matrixQwith dimensions equal to that of the state space and initial probability distribution defined on the state space. Fori≠j, the elementsqijare non-negative and describe the rate of the process transitions from stateito statej. The elementsqiiare chosen such that each row of the transition rate matrix sums to zero, while the row-sums of a probability transition matrix in a (discrete) Markov chain are all equal to one.
There are three equivalent definitions of the process.[40]
LetXt{\displaystyle X_{t}}be the random variable describing the state of the process at timet, and assume the process is in a stateiat timet.
Then, knowingXt=i{\displaystyle X_{t}=i},Xt+h=j{\displaystyle X_{t+h}=j}is independent of previous values(Xs:s<t){\displaystyle \left(X_{s}:s<t\right)}, and ash→ 0 for alljand for allt,Pr(X(t+h)=j∣X(t)=i)=δij+qijh+o(h),{\displaystyle \Pr(X(t+h)=j\mid X(t)=i)=\delta _{ij}+q_{ij}h+o(h),}whereδij{\displaystyle \delta _{ij}}is theKronecker delta, using thelittle-o notation.
Theqij{\displaystyle q_{ij}}can be seen as measuring how quickly the transition fromitojhappens.
Define a discrete-time Markov chainYnto describe thenth jump of the process and variablesS1,S2,S3, ... to describe holding times in each of the states whereSifollows theexponential distributionwith rate parameter −qYiYi.
For any valuen= 0, 1, 2, 3, ... and times indexed up to this value ofn:t0,t1,t2, ... and all states recorded at these timesi0,i1,i2,i3, ... it holds that
wherepijis the solution of theforward equation(afirst-order differential equation)
with initial condition P(0) is theidentity matrix.
If the state space isfinite, the transition probability distribution can be represented by amatrix, called the transition matrix, with the (i,j)thelementofPequal to
Since each row ofPsums to one and all elements are non-negative,Pis aright stochastic matrix.
A stationary distributionπis a (row) vector, whose entries are non-negative and sum to 1, is unchanged by the operation of transition matrixPon it and so is defined by
By comparing this definition with that of aneigenvectorwe see that the two concepts are related and that
is a normalized (∑iπi=1{\textstyle \sum _{i}\pi _{i}=1}) multiple of a left eigenvectoreof the transition matrixPwith aneigenvalueof 1. If there is more than one unit eigenvector then a weighted sum of the corresponding stationary states is also a stationary state. But for a Markov chain one is usually more interested in a stationary state that is the limit of the sequence of distributions for some initial distribution.
The values of a stationary distributionπi{\displaystyle \textstyle \pi _{i}}are associated with the state space ofPand its eigenvectors have their relative proportions preserved. Since the components of π are positive and the constraint that their sum is unity can be rewritten as∑i1⋅πi=1{\textstyle \sum _{i}1\cdot \pi _{i}=1}we see that thedot productof π with a vector whose components are all 1 is unity and that π lies on asimplex.
If the Markov chain is time-homogeneous, then the transition matrixPis the same after each step, so thek-step transition probability can be computed as thek-th power of the transition matrix,Pk.
If the Markov chain is irreducible and aperiodic, then there is a unique stationary distributionπ.[41]Additionally, in this casePkconverges to a rank-one matrix in which each row is the stationary distributionπ:
where1is the column vector with all entries equal to 1. This is stated by thePerron–Frobenius theorem. If, by whatever means,limk→∞Pk{\textstyle \lim _{k\to \infty }\mathbf {P} ^{k}}is found, then the stationary distribution of the Markov chain in question can be easily determined for any starting distribution, as will be explained below.
For some stochastic matricesP, the limitlimk→∞Pk{\textstyle \lim _{k\to \infty }\mathbf {P} ^{k}}does not exist while the stationary distribution does, as shown by this example:
(This example illustrates a periodic Markov chain.)
Because there are a number of different special cases to consider, the process of finding this limit if it exists can be a lengthy task. However, there are many techniques that can assist in finding this limit. LetPbe ann×nmatrix, and defineQ=limk→∞Pk.{\textstyle \mathbf {Q} =\lim _{k\to \infty }\mathbf {P} ^{k}.}
It is always true that
SubtractingQfrom both sides and factoring then yields
whereInis theidentity matrixof sizen, and0n,nis thezero matrixof sizen×n. Multiplying together stochastic matrices always yields another stochastic matrix, soQmust be astochastic matrix(see the definition above). It is sometimes sufficient to use the matrix equation above and the fact thatQis a stochastic matrix to solve forQ. Including the fact that the sum of each the rows inPis 1, there aren+1equations for determiningnunknowns, so it is computationally easier if on the one hand one selects one row inQand substitutes each of its elements by one, and on the other one substitutes the corresponding element (the one in the same column) in the vector0, and next left-multiplies this latter vector by the inverse of transformed former matrix to findQ.
Here is one method for doing so: first, define the functionf(A) to return the matrixAwith its right-most column replaced with all 1's. If [f(P−In)]−1exists then[42][41]
One thing to notice is that ifPhas an elementPi,ion its main diagonal that is equal to 1 and theith row or column is otherwise filled with 0's, then that row or column will remain unchanged in all of the subsequent powersPk. Hence, theith row or column ofQwill have the 1 and the 0's in the same positions as inP.
As stated earlier, from the equationπ=πP,{\displaystyle {\boldsymbol {\pi }}={\boldsymbol {\pi }}\mathbf {P} ,}(if exists) the stationary (or steady state) distributionπis a left eigenvector of rowstochastic matrixP. Then assuming thatPis diagonalizable or equivalently thatPhasnlinearly independent eigenvectors, speed of convergence is elaborated as follows. (For non-diagonalizable, that is,defective matrices, one may start with theJordan normal formofPand proceed with a bit more involved set of arguments in a similar way.[43])
LetUbe the matrix of eigenvectors (each normalized to having an L2 norm equal to 1) where each column is a left eigenvector ofPand letΣbe the diagonal matrix of left eigenvalues ofP, that is,Σ= diag(λ1,λ2,λ3,...,λn). Then byeigendecomposition
Let the eigenvalues be enumerated such that:
SincePis a row stochastic matrix, its largest left eigenvalue is 1. If there is a unique stationary distribution, then the largest eigenvalue and the corresponding eigenvector is unique too (because there is no otherπwhich solves the stationary distribution equation above). Letuibe thei-th column ofUmatrix, that is,uiis the left eigenvector ofPcorresponding to λi. Also letxbe a lengthnrow vector that represents a valid probability distribution; since the eigenvectorsuispanRn,{\displaystyle \mathbb {R} ^{n},}we can write
If we multiplyxwithPfrom right and continue this operation with the results, in the end we get the stationary distributionπ. In other words,π=a1u1←xPP...P=xPkask→ ∞. That means
Sinceπis parallel tou1(normalized by L2 norm) andπ(k)is a probability vector,π(k)approaches toa1u1=πask→ ∞ with a speed in the order ofλ2/λ1exponentially. This follows because|λ2|≥⋯≥|λn|,{\displaystyle |\lambda _{2}|\geq \cdots \geq |\lambda _{n}|,}henceλ2/λ1is the dominant term. The smaller the ratio is, the faster the convergence is.[44]Random noise in the state distributionπcan also speed up this convergence to the stationary distribution.[45]
Many results for Markov chains with finite state space can be generalized to chains with uncountable state space throughHarris chains.
The use of Markov chains in Markov chain Monte Carlo methods covers cases where the process follows a continuous state space.
"Locally interacting Markov chains" are Markov chains with an evolution that takes into account the state of other Markov chains. This corresponds to the situation when the state space has a (Cartesian-) product form.
Seeinteracting particle systemandstochastic cellular automata(probabilistic cellular automata).
See for instanceInteraction of Markov Processes[46]or.[47]
Two states are said tocommunicatewith each other if both are reachable from one another by a sequence of transitions that have positive probability. This is an equivalence relation which yields a set of communicating classes. A class isclosedif the probability of leaving the class is zero. A Markov chain isirreducibleif there is one communicating class, the state space.
A stateihas periodkifkis thegreatest common divisorof the number of transitions by whichican be reached, starting fromi. That is:
The state isperiodicifk>1{\displaystyle k>1}; otherwisek=1{\displaystyle k=1}and the state isaperiodic.
A stateiis said to betransientif, starting fromi, there is a non-zero probability that the chain will never return toi. It is calledrecurrent(orpersistent) otherwise.[48]For a recurrent statei, the meanhitting timeis defined as:
Stateiispositive recurrentifMi{\displaystyle M_{i}}is finite andnull recurrentotherwise. Periodicity, transience, recurrence and positive and null recurrence are class properties — that is, if one state has the property then all states in its communicating class have the property.[49]
A stateiis calledabsorbingif there are no outgoing transitions from the state.
Since periodicity is a class property, if a Markov chain is irreducible, then all its states have the same period. In particular, if one state is aperiodic, then the whole Markov chain is aperiodic.[50]
If a finite Markov chain is irreducible, then all states are positive recurrent, and it has a unique stationary distribution given byπi=1/E[Ti]{\displaystyle \pi _{i}=1/E[T_{i}]}.
A stateiis said to beergodicif it is aperiodic and positive recurrent. In other words, a stateiis ergodic if it is recurrent, has a period of 1, and has finite mean recurrence time.
If all states in an irreducible Markov chain are ergodic, then the chain is said to be ergodic. Equivalently, there exists some integerk{\displaystyle k}such that all entries ofMk{\displaystyle M^{k}}are positive.
It can be shown that a finite state irreducible Markov chain is ergodic if it has an aperiodic state. More generally, a Markov chain is ergodic if there is a numberNsuch that any state can be reached from any other state in any number of steps less or equal to a numberN. In case of a fully connected transition matrix, where all transitions have a non-zero probability, this condition is fulfilled withN= 1.
A Markov chain with more than one state and just one out-going transition per state is either not irreducible or not aperiodic, hence cannot be ergodic.
Some authors call any irreducible, positive recurrent Markov chains ergodic, even periodic ones.[51]In fact, merely irreducible Markov chains correspond toergodic processes, defined according toergodic theory.[52]
Some authors call a matrixprimitiveif there exists some integerk{\displaystyle k}such that all entries ofMk{\displaystyle M^{k}}are positive.[53]Some authors call itregular.[54]
Theindex of primitivity, orexponent, of a regular matrix, is the smallestk{\displaystyle k}such that all entries ofMk{\displaystyle M^{k}}are positive. The exponent is purely a graph-theoretic property, since it depends only on whether each entry ofM{\displaystyle M}is zero or positive, and therefore can be found on a directed graph withsign(M){\displaystyle \mathrm {sign} (M)}as its adjacency matrix.
There are several combinatorial results about the exponent when there are finitely many states. Letn{\displaystyle n}be the number of states, then[55]
If a Markov chain has a stationary distribution, then it can be converted to ameasure-preserving dynamical system: Let the probability space beΩ=ΣN{\displaystyle \Omega =\Sigma ^{\mathbb {N} }}, whereΣ{\displaystyle \Sigma }is the set of all states for the Markov chain. Let the sigma-algebra on the probability space be generated by the cylinder sets. Let the probability measure be generated by the stationary distribution, and the Markov chain transition. LetT:Ω→Ω{\displaystyle T:\Omega \to \Omega }be the shift operator:T(X0,X1,…)=(X1,…){\displaystyle T(X_{0},X_{1},\dots )=(X_{1},\dots )}. Similarly we can construct such a dynamical system withΩ=ΣZ{\displaystyle \Omega =\Sigma ^{\mathbb {Z} }}instead.[57]
SinceirreducibleMarkov chains with finite state spaces have a unique stationary distribution, the above construction is unambiguous for irreducible Markov chains.
Inergodic theory, a measure-preserving dynamical system is calledergodicif any measurable subsetS{\displaystyle S}such thatT−1(S)=S{\displaystyle T^{-1}(S)=S}impliesS=∅{\displaystyle S=\emptyset }orΩ{\displaystyle \Omega }(up to a null set).
The terminology is inconsistent. Given a Markov chain with a stationary distribution that is strictly positive on all states, the Markov chain isirreducibleif its corresponding measure-preserving dynamical system isergodic.[52]
In some cases, apparently non-Markovian processes may still have Markovian representations, constructed by expanding the concept of the "current" and "future" states. For example, letXbe a non-Markovian process. Then define a processY, such that each state ofYrepresents a time-interval of states ofX. Mathematically, this takes the form:
IfYhas the Markov property, then it is a Markovian representation ofX.
An example of a non-Markovian process with a Markovian representation is anautoregressivetime seriesof order greater than one.[58]
Thehitting timeis the time, starting in a given set of states, until the chain arrives in a given state or set of states. The distribution of such a time period has a phase type distribution. The simplest such distribution is that of a single exponentially distributed transition.
For a subset of statesA⊆S, the vectorkAof hitting times (where elementkiA{\displaystyle k_{i}^{A}}represents theexpected value, starting in stateithat the chain enters one of the states in the setA) is the minimal non-negative solution to[59]
For a CTMCXt, the time-reversed process is defined to beX^t=XT−t{\displaystyle {\hat {X}}_{t}=X_{T-t}}. ByKelly's lemmathis process has the same stationary distribution as the forward process.
A chain is said to bereversibleif the reversed process is the same as the forward process.Kolmogorov's criterionstates that the necessary and sufficient condition for a process to be reversible is that the product of transition rates around a closed loop must be the same in both directions.
One method of finding thestationary probability distribution,π, of anergodiccontinuous-time Markov chain,Q, is by first finding itsembedded Markov chain (EMC). Strictly speaking, the EMC is a regular discrete-time Markov chain, sometimes referred to as ajump process. Each element of the one-step transition probability matrix of the EMC,S, is denoted bysij, and represents theconditional probabilityof transitioning from stateiinto statej. These conditional probabilities may be found by
From this,Smay be written as
whereIis theidentity matrixand diag(Q) is thediagonal matrixformed by selecting themain diagonalfrom the matrixQand setting all other elements to zero.
To find the stationary probability distribution vector, we must next findφ{\displaystyle \varphi }such that
withφ{\displaystyle \varphi }being a row vector, such that all elements inφ{\displaystyle \varphi }are greater than 0 and‖φ‖1{\displaystyle \|\varphi \|_{1}}= 1. From this,πmay be found as
(Smay be periodic, even ifQis not. Onceπis found, it must be normalized to aunit vector.)
Another discrete-time process that may be derived from a continuous-time Markov chain is a δ-skeleton—the (discrete-time) Markov chain formed by observingX(t) at intervals of δ units of time. The random variablesX(0),X(δ),X(2δ), ... give the sequence of states visited by the δ-skeleton.
Markov models are used to model changing systems. There are 4 main types of models, that generalize Markov chains depending on whether every sequential state is observable or not, and whether the system is to be adjusted on the basis of observations made:
ABernoulli schemeis a special case of a Markov chain where the transition probability matrix has identical rows, which means that the next state is independent of even the current state (in addition to being independent of the past states). A Bernoulli scheme with only two possible states is known as aBernoulli process.
Note, however, by theOrnstein isomorphism theorem, that every aperiodic and irreducible Markov chain is isomorphic to a Bernoulli scheme;[60]thus, one might equally claim that Markov chains are a "special case" of Bernoulli schemes. The isomorphism generally requires a complicated recoding. The isomorphism theorem is even a bit stronger: it states thatanystationary stochastic processis isomorphic to a Bernoulli scheme; the Markov chain is just one such example.
When the Markov matrix is replaced by theadjacency matrixof afinite graph, the resulting shift is termed atopological Markov chainor asubshift of finite type.[60]A Markov matrix that is compatible with the adjacency matrix can then provide ameasureon the subshift. Many chaoticdynamical systemsare isomorphic to topological Markov chains; examples includediffeomorphismsofclosed manifolds, theProuhet–Thue–Morse system, theChacon system,sofic systems,context-free systemsandblock-coding systems.[60]
Markov chains have been employed in a wide range of topics across the natural and social sciences, and in technological applications. They have been used for forecasting in several areas: for example, price trends,[61]wind power,[62]stochastic terrorism,[63][64]andsolar irradiance.[65]The Markov chain forecasting models utilize a variety of settings, from discretizing the time series,[62]to hidden Markov models combined with wavelets,[61]and the Markov chain mixture distribution model (MCM).[65]
Markovian systems appear extensively inthermodynamicsandstatistical mechanics, whenever probabilities are used to represent unknown or unmodelled details of the system, if it can be assumed that the dynamics are time-invariant, and that no relevant history need be considered which is not already included in the state description.[66][67]For example, a thermodynamic state operates under a probability distribution that is difficult or expensive to acquire. Therefore, Markov Chain Monte Carlo method can be used to draw samples randomly from a black-box to approximate the probability distribution of attributes over a range of objects.[67]
Markov chains are used inlattice QCDsimulations.[68]
A reaction network is a chemical system involving multiple reactions and chemical species. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transitions of the chain.[69]Markov chains and continuous-time Markov processes are useful in chemistry when physical systems closely approximate the Markov property. For example, imagine a large numbernof molecules in solution in state A, each of which can undergo a chemical reaction to state B with a certain average rate. Perhaps the molecule is an enzyme, and the states refer to how it is folded. The state of any single enzyme follows a Markov chain, and since the molecules are essentially independent of each other, the number of molecules in state A or B at a time isntimes the probability a given molecule is in that state.
The classical model of enzyme activity,Michaelis–Menten kinetics, can be viewed as a Markov chain, where at each time step the reaction proceeds in some direction. While Michaelis-Menten is fairly straightforward, far more complicated reaction networks can also be modeled with Markov chains.[70]
An algorithm based on a Markov chain was also used to focus the fragment-based growth of chemicalsin silicotowards a desired class of compounds such as drugs or natural products.[71]As a molecule is grown, a fragment is selected from the nascent molecule as the "current" state. It is not aware of its past (that is, it is not aware of what is already bonded to it). It then transitions to the next state when a fragment is attached to it. The transition probabilities are trained on databases of authentic classes of compounds.[72]
Also, the growth (and composition) ofcopolymersmay be modeled using Markov chains. Based on the reactivity ratios of the monomers that make up the growing polymer chain, the chain's composition may be calculated (for example, whether monomers tend to add in alternating fashion or in long runs of the same monomer). Due tosteric effects, second-order Markov effects may also play a role in the growth of some polymer chains.
Similarly, it has been suggested that the crystallization and growth of some epitaxialsuperlatticeoxide materials can be accurately described by Markov chains.[73]
Markov chains are used in various areas of biology. Notable examples include:
Several theorists have proposed the idea of the Markov chain statistical test (MCST), a method of conjoining Markov chains to form a "Markov blanket", arranging these chains in several recursive layers ("wafering") and producing more efficient test sets—samples—as a replacement for exhaustive testing.[citation needed]
Solar irradiancevariability assessments are useful forsolar powerapplications. Solar irradiance variability at any location over time is mainly a consequence of the deterministic variability of the sun's path across the sky dome and the variability in cloudiness. The variability of accessible solar irradiance on Earth's surface has been modeled using Markov chains,[76][77][78][79]also including modeling the two states of clear and cloudiness as a two-state Markov chain.[80][81]
Hidden Markov modelshave been used inautomatic speech recognitionsystems.[82]
Markov chains are used throughout information processing.Claude Shannon's famous 1948 paperA Mathematical Theory of Communication, which in a single step created the field ofinformation theory, opens by introducing the concept ofentropyby modeling texts in a natural language (such as English) as generated by an ergodic Markov process, where each letter may depend statistically on previous letters.[83]Such idealized models can capture many of the statistical regularities of systems. Even without describing the full structure of the system perfectly, such signal models can make possible very effectivedata compressionthroughentropy encodingtechniques such asarithmetic coding. They also allow effectivestate estimationandpattern recognition. Markov chains also play an important role inreinforcement learning.
Markov chains are also the basis for hidden Markov models, which are an important tool in such diverse fields as telephone networks (which use theViterbi algorithmfor error correction), speech recognition andbioinformatics(such as in rearrangements detection[84]).
TheLZMAlossless data compression algorithm combines Markov chains withLempel-Ziv compressionto achieve very high compression ratios.
Markov chains are the basis for the analytical treatment of queues (queueing theory).Agner Krarup Erlanginitiated the subject in 1917.[85]This makes them critical for optimizing the performance of telecommunications networks, where messages must often compete for limited resources (such as bandwidth).[86]
Numerous queueing models use continuous-time Markov chains. For example, anM/M/1 queueis a CTMC on the non-negative integers where upward transitions fromitoi+ 1 occur at rateλaccording to aPoisson processand describe job arrivals, while transitions fromitoi– 1 (fori> 1) occur at rateμ(job service times are exponentially distributed) and describe completed services (departures) from the queue.
ThePageRankof a webpage as used byGoogleis defined by a Markov chain.[87][88][89]It is the probability to be at pagei{\displaystyle i}in the stationary distribution on the following Markov chain on all (known) webpages. IfN{\displaystyle N}is the number of known webpages, and a pagei{\displaystyle i}haski{\displaystyle k_{i}}links to it then it has transition probabilityαki+1−αN{\displaystyle {\frac {\alpha }{k_{i}}}+{\frac {1-\alpha }{N}}}for all pages that are linked to and1−αN{\displaystyle {\frac {1-\alpha }{N}}}for all pages that are not linked to. The parameterα{\displaystyle \alpha }is taken to be about 0.15.[90]
Markov models have also been used to analyze web navigation behavior of users. A user's web link transition on a particular website can be modeled using first- or second-order Markov models and can be used to make predictions regarding future navigation and to personalize the web page for an individual user.[citation needed]
Markov chain methods have also become very important for generating sequences of random numbers to accurately reflect very complicated desired probability distributions, via a process calledMarkov chain Monte Carlo(MCMC). In recent years this has revolutionized the practicability ofBayesian inferencemethods, allowing a wide range ofposterior distributionsto be simulated and their parameters found numerically.[citation needed]
In 1971 aNaval Postgraduate SchoolMaster's thesis proposed to model a variety of combat between adversaries as a Markov chain "with states reflecting the control, maneuver, target acquisition, and target destruction actions of a weapons system" and discussed the parallels between the resulting Markov chain andLanchester's laws.[91]
In 1975 Duncan and Siverson remarked that Markov chains could be used to model conflict between state actors, and thought that their analysis would help understand "the behavior of social and political organizations in situations of conflict."[92]
Markov chains are used in finance and economics to model a variety of different phenomena, including the distribution of income, the size distribution of firms, asset prices and market crashes.D. G. Champernownebuilt a Markov chain model of the distribution of income in 1953.[93]Herbert A. Simonand co-author Charles Bonini used a Markov chain model to derive a stationary Yule distribution of firm sizes.[94]Louis Bachelierwas the first to observe that stock prices followed a random walk.[95]The random walk was later seen as evidence in favor of theefficient-market hypothesisand random walk models were popular in the literature of the 1960s.[96]Regime-switching models of business cycles were popularized byJames D. Hamilton(1989), who used a Markov chain to model switches between periods of high and low GDP growth (or, alternatively, economic expansions and recessions).[97]A more recent example is theMarkov switching multifractalmodel ofLaurent E. Calvetand Adlai J. Fisher, which builds upon the convenience of earlier regime-switching models.[98][99]It uses an arbitrarily large Markov chain to drive the level of volatility of asset returns.
Dynamic macroeconomics makes heavy use of Markov chains. An example is using Markov chains to exogenously model prices of equity (stock) in ageneral equilibriumsetting.[100]
Credit rating agenciesproduce annual tables of the transition probabilities for bonds of different credit ratings.[101]
Markov chains are generally used in describingpath-dependentarguments, where current structural configurations condition future outcomes. An example is the reformulation of the idea, originally due toKarl Marx'sDas Kapital, tyingeconomic developmentto the rise ofcapitalism. In current research, it is common to use a Markov chain to model how once a country reaches a specific level of economic development, the configuration of structural factors, such as size of themiddle class, the ratio of urban to rural residence, the rate ofpoliticalmobilization, etc., will generate a higher probability of transitioning fromauthoritariantodemocratic regime.[102]
Markov chains are employed inalgorithmic music composition, particularly insoftwaresuch asCsound,Max, andSuperCollider. In a first-order chain, the states of the system become note or pitch values, and aprobability vectorfor each note is constructed, completing a transition probability matrix (see below). An algorithm is constructed to produce output note values based on the transition matrix weightings, which could beMIDInote values, frequency (Hz), or any other desirable metric.[103]
A second-order Markov chain can be introduced by considering the current stateandalso the previous state, as indicated in the second table. Higher,nth-order chains tend to "group" particular notes together, while 'breaking off' into other patterns and sequences occasionally. These higher-order chains tend to generate results with a sense ofphrasalstructure, rather than the 'aimless wandering' produced by a first-order system.[104]
Markov chains can be used structurally, as in Xenakis's Analogique A and B.[105]Markov chains are also used in systems which use a Markov model to react interactively to music input.[106]
Usually musical systems need to enforce specific control constraints on the finite-length sequences they generate, but control constraints are not compatible with Markov models, since they induce long-range dependencies that violate the Markov hypothesis of limited memory. In order to overcome this limitation, a new approach has been proposed.[107]
Markov chains can be used to model many games of chance. The children's gamesSnakes and Laddersand "Hi Ho! Cherry-O", for example, are represented exactly by Markov chains. At each turn, the player starts in a given state (on a given square) and from there has fixed odds of moving to certain other states (squares).[citation needed]
Markov chain models have been used in advanced baseball analysis since 1960, although their use is still rare. Each half-inning of a baseball game fits the Markov chain state when the number of runners and outs are considered. During any at-bat, there are 24 possible combinations of number of outs and position of the runners. Mark Pankin shows that Markov chain models can be used to evaluate runs created for both individual players as well as a team.[108]He also discusses various kinds of strategies and play conditions: how Markov chain models have been used to analyze statistics for game situations such asbuntingandbase stealingand differences when playing on grass vs.AstroTurf.[109]
Markov processes can also be used togenerate superficially real-looking textgiven a sample document. Markov processes are used in a variety of recreational "parody generator" software (seedissociated press, Jeff Harrison,[110]Mark V. Shaney,[111][112]and Academias Neutronium). Several open-source text generation libraries using Markov chains exist.
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Inprobability theoryandstatistics, thebinomial distributionwith parametersnandpis thediscrete probability distributionof the number of successes in a sequence ofnindependentexperiments, each asking ayes–no question, and each with its ownBoolean-valuedoutcome:success(with probabilityp) orfailure(with probabilityq= 1 −p). A single success/failure experiment is also called aBernoulli trialor Bernoulli experiment, and a sequence of outcomes is called aBernoulli process; for a single trial, i.e.,n= 1, the binomial distribution is aBernoulli distribution. The binomial distribution is the basis for thebinomial testofstatistical significance.[1]
The binomial distribution is frequently used to model the number of successes in a sample of sizendrawnwith replacementfrom a population of sizeN. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is ahypergeometric distribution, not a binomial one. However, forNmuch larger thann, the binomial distribution remains a good approximation, and is widely used.
If therandom variableXfollows the binomial distribution with parametersn∈N{\displaystyle \mathbb {N} }andp∈[0, 1], we writeX~B(n,p). The probability of getting exactlyksuccesses innindependent Bernoulli trials (with the same ratep) is given by theprobability mass function:
fork= 0, 1, 2, ...,n, where
is thebinomial coefficient. The formula can be understood as follows:pkqn−kis the probability of obtaining the sequence ofnindependent Bernoulli trials in whichktrials are "successes" and the remainingn−ktrials result in "failure". Since the trials are independent with probabilities remaining constant between them, any sequence ofntrials withksuccesses (andn−kfailures) has the same probability of being achieved (regardless of positions of successes within the sequence). There are(nk){\textstyle {\binom {n}{k}}}such sequences, since the binomial coefficient(nk){\textstyle {\binom {n}{k}}}counts the number of ways to choose the positions of theksuccesses among thentrials. The binomial distribution is concerned with the probability of obtaininganyof these sequences, meaning the probability of obtaining one of them (pkqn−k) must be added(nk){\textstyle {\binom {n}{k}}}times, hencePr(X=k)=(nk)pk(1−p)n−k{\textstyle \Pr(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}}.
In creating reference tables for binomial distribution probability, usually, the table is filled in up ton/2values. This is because fork>n/2, the probability can be calculated by its complement as
Looking at the expressionf(k,n,p)as a function ofk, there is akvalue that maximizes it. Thiskvalue can be found by calculating
and comparing it to 1. There is always an integerMthat satisfies[2]
f(k,n,p)is monotone increasing fork<Mand monotone decreasing fork>M, with the exception of the case where(n+ 1)pis an integer. In this case, there are two values for whichfis maximal:(n+ 1)pand(n+ 1)p− 1.Mis themost probableoutcome (that is, the most likely, although this can still be unlikely overall) of the Bernoulli trials and is called themode.
Equivalently,M−p<np≤M+ 1 −p. Taking thefloor function, we obtainM= floor(np).[note 1]
Suppose abiased coincomes up heads with probability 0.3 when tossed. The probability of seeing exactly 4 heads in 6 tosses is
Thecumulative distribution functioncan be expressed as:
where⌊k⌋{\displaystyle \lfloor k\rfloor }is the "floor" underk, i.e. thegreatest integerless than or equal tok.
It can also be represented in terms of theregularized incomplete beta function, as follows:[3]
which is equivalent to thecumulative distribution functionsof thebeta distributionand of theF-distribution:[4]
Some closed-form bounds for the cumulative distribution function are givenbelow.
IfX~B(n,p), that is,Xis a binomially distributed random variable,nbeing the total number of experiments andpthe probability of each experiment yielding a successful result, then theexpected valueofXis:[5]
This follows from the linearity of the expected value along with the fact thatXis the sum ofnidentical Bernoulli random variables, each with expected valuep. In other words, ifX1,…,Xn{\displaystyle X_{1},\ldots ,X_{n}}are identical (and independent) Bernoulli random variables with parameterp, thenX=X1+ ... +Xnand
Thevarianceis:
This similarly follows from the fact that the variance of a sum of independent random variables is the sum of the variances.
The first 6central moments, defined asμc=E[(X−E[X])c]{\displaystyle \mu _{c}=\operatorname {E} \left[(X-\operatorname {E} [X])^{c}\right]}, are given by
The non-central moments satisfy
and in general[6][7]
where{ck}{\displaystyle \textstyle \left\{{c \atop k}\right\}}are theStirling numbers of the second kind, andnk_=n(n−1)⋯(n−k+1){\displaystyle n^{\underline {k}}=n(n-1)\cdots (n-k+1)}is thek{\displaystyle k}thfalling powerofn{\displaystyle n}.
A simple bound[8]follows by bounding the Binomial moments via thehigher Poisson moments:
This shows that ifc=O(np){\displaystyle c=O({\sqrt {np}})}, thenE[Xc]{\displaystyle \operatorname {E} [X^{c}]}is at most a constant factor away fromE[X]c{\displaystyle \operatorname {E} [X]^{c}}
Usually themodeof a binomialB(n,p)distribution is equal to⌊(n+1)p⌋{\displaystyle \lfloor (n+1)p\rfloor }, where⌊⋅⌋{\displaystyle \lfloor \cdot \rfloor }is thefloor function. However, when(n+ 1)pis an integer andpis neither 0 nor 1, then the distribution has two modes:(n+ 1)pand(n+ 1)p− 1. Whenpis equal to 0 or 1, the mode will be 0 andncorrespondingly. These cases can be summarized as follows:
Proof:Let
Forp=0{\displaystyle p=0}onlyf(0){\displaystyle f(0)}has a nonzero value withf(0)=1{\displaystyle f(0)=1}. Forp=1{\displaystyle p=1}we findf(n)=1{\displaystyle f(n)=1}andf(k)=0{\displaystyle f(k)=0}fork≠n{\displaystyle k\neq n}. This proves that the mode is 0 forp=0{\displaystyle p=0}andn{\displaystyle n}forp=1{\displaystyle p=1}.
Let0<p<1{\displaystyle 0<p<1}. We find
From this follows
So when(n+1)p−1{\displaystyle (n+1)p-1}is an integer, then(n+1)p−1{\displaystyle (n+1)p-1}and(n+1)p{\displaystyle (n+1)p}is a mode. In the case that(n+1)p−1∉Z{\displaystyle (n+1)p-1\notin \mathbb {Z} }, then only⌊(n+1)p−1⌋+1=⌊(n+1)p⌋{\displaystyle \lfloor (n+1)p-1\rfloor +1=\lfloor (n+1)p\rfloor }is a mode.[9]
In general, there is no single formula to find themedianfor a binomial distribution, and it may even be non-unique. However, several special results have been established:
Fork≤np, upper bounds can be derived for the lower tail of the cumulative distribution functionF(k;n,p)=Pr(X≤k){\displaystyle F(k;n,p)=\Pr(X\leq k)}, the probability that there are at mostksuccesses. SincePr(X≥k)=F(n−k;n,1−p){\displaystyle \Pr(X\geq k)=F(n-k;n,1-p)}, these bounds can also be seen as bounds for the upper tail of the cumulative distribution function fork≥np.
Hoeffding's inequalityyields the simple bound
which is however not very tight. In particular, forp= 1, we have thatF(k;n,p) = 0(for fixedk,nwithk<n), but Hoeffding's bound evaluates to a positive constant.
A sharper bound can be obtained from theChernoff bound:[15]
whereD(a∥p)is therelative entropy (or Kullback-Leibler divergence)between ana-coin and ap-coin (i.e. between theBernoulli(a)andBernoulli(p)distribution):
Asymptotically, this bound is reasonably tight; see[15]for details.
One can also obtainlowerbounds on the tailF(k;n,p), known as anti-concentration bounds. By approximating the binomial coefficient withStirling's formulait can be shown that[16]
which implies the simpler but looser bound
Forp= 1/2andk≥ 3n/8for evenn, it is possible to make the denominator constant:[17]
Whennis known, the parameterpcan be estimated using the proportion of successes:
This estimator is found usingmaximum likelihood estimatorand also themethod of moments. This estimator isunbiasedand uniformly withminimum variance, proven usingLehmann–Scheffé theorem, since it is based on aminimal sufficientandcompletestatistic (i.e.:x). It is alsoconsistentboth in probability and inMSE. This statistic isasymptoticallynormalthanks to thecentral limit theorem, because it is the same as taking themeanover Bernoulli samples. It has a variance ofvar(p^)=p(1−p)n{\displaystyle var({\widehat {p}})={\frac {p(1-p)}{n}}}, a property which is used in various ways, such as inWald's confidence intervals.
A closed formBayes estimatorforpalso exists when using theBeta distributionas aconjugateprior distribution. When using a generalBeta(α,β){\displaystyle \operatorname {Beta} (\alpha ,\beta )}as a prior, theposterior meanestimator is:
The Bayes estimator isasymptotically efficientand as the sample size approaches infinity (n→ ∞), it approaches theMLEsolution.[18]The Bayes estimator isbiased(how much depends on the priors),admissibleandconsistentin probability. Using the Bayesian estimator with the Beta distribution can be used withThompson sampling.
For the special case of using thestandard uniform distributionas anon-informative prior,Beta(α=1,β=1)=U(0,1){\displaystyle \operatorname {Beta} (\alpha =1,\beta =1)=U(0,1)}, the posterior mean estimator becomes:
(Aposterior modeshould just lead to the standard estimator.) This method is called therule of succession, which was introduced in the 18th century byPierre-Simon Laplace.
When relying onJeffreys prior, the prior isBeta(α=12,β=12){\displaystyle \operatorname {Beta} (\alpha ={\frac {1}{2}},\beta ={\frac {1}{2}})},[19]which leads to the estimator:
When estimatingpwith very rare events and a smalln(e.g.: ifx= 0), then using the standard estimator leads top^=0,{\displaystyle {\widehat {p}}=0,}which sometimes is unrealistic and undesirable. In such cases there are various alternative estimators.[20]One way is to use the Bayes estimatorp^b{\displaystyle {\widehat {p}}_{b}}, leading to:
Another method is to use the upper bound of theconfidence intervalobtained using therule of three:
Even for quite large values ofn, the actual distribution of the mean is significantly nonnormal.[21]Because of this problem several methods to estimate confidence intervals have been proposed.
In the equations for confidence intervals below, the variables have the following meaning:
Acontinuity correctionof0.5/nmay be added.[clarification needed]
[22]
Here the estimate ofpis modified to
This method works well forn> 10andn1≠ 0,n.[23]See here forn≤10{\displaystyle n\leq 10}.[24]Forn1= 0,nuse the Wilson (score) method below.
[25]
The notation in the formula below differs from the previous formulas in two respects:[26]
The so-called "exact" (Clopper–Pearson) method is the most conservative.[21](Exactdoes not mean perfectly accurate; rather, it indicates that the estimates will not be less conservative than the true value.)
The Wald method, although commonly recommended in textbooks, is the most biased.[clarification needed]
IfX~ B(n,p)andY~ B(m,p)are independent binomial variables with the same probabilityp, thenX+Yis again a binomial variable; its distribution isZ=X+Y~ B(n+m,p):[28]
A Binomial distributed random variableX~ B(n,p)can be considered as the sum ofnBernoulli distributed random variables. So the sum of two Binomial distributed random variablesX~ B(n,p)andY~ B(m,p)is equivalent to the sum ofn+mBernoulli distributed random variables, which meansZ=X+Y~ B(n+m,p). This can also be proven directly using the addition rule.
However, ifXandYdo not have the same probabilityp, then the variance of the sum will besmaller than the variance of a binomial variabledistributed asB(n+m,p).
The binomial distribution is a special case of thePoisson binomial distribution, which is the distribution of a sum ofnindependent non-identicalBernoulli trialsB(pi).[29]
This result was first derived by Katz and coauthors in 1978.[30]
LetX~ B(n,p1)andY~ B(m,p2)be independent. LetT= (X/n) / (Y/m).
Then log(T) is approximately normally distributed with mean log(p1/p2) and variance((1/p1) − 1)/n+ ((1/p2) − 1)/m.
IfX~ B(n,p) andY|X~ B(X,q) (the conditional distribution ofY, givenX), thenYis a simple binomial random variable with distributionY~ B(n,pq).
For example, imagine throwingnballs to a basketUXand taking the balls that hit and throwing them to another basketUY. Ifpis the probability to hitUXthenX~ B(n,p) is the number of balls that hitUX. Ifqis the probability to hitUYthen the number of balls that hitUYisY~ B(X,q) and thereforeY~ B(n,pq).
SinceX∼B(n,p){\displaystyle X\sim B(n,p)}andY∼B(X,q){\displaystyle Y\sim B(X,q)}, by thelaw of total probability,
Since(nk)(km)=(nm)(n−mk−m),{\displaystyle {\tbinom {n}{k}}{\tbinom {k}{m}}={\tbinom {n}{m}}{\tbinom {n-m}{k-m}},}the equation above can be expressed as
Factoringpk=pmpk−m{\displaystyle p^{k}=p^{m}p^{k-m}}and pulling all the terms that don't depend onk{\displaystyle k}out of the sum now yields
After substitutingi=k−m{\displaystyle i=k-m}in the expression above, we get
Notice that the sum (in the parentheses) above equals(p−pq+1−p)n−m{\displaystyle (p-pq+1-p)^{n-m}}by thebinomial theorem. Substituting this in finally yields
and thusY∼B(n,pq){\displaystyle Y\sim B(n,pq)}as desired.
TheBernoulli distributionis a special case of the binomial distribution, wheren= 1. Symbolically,X~ B(1,p)has the same meaning asX~ Bernoulli(p). Conversely, any binomial distribution,B(n,p), is the distribution of the sum ofnindependentBernoulli trials,Bernoulli(p), each with the same probabilityp.[31]
Ifnis large enough, then the skew of the distribution is not too great. In this case a reasonable approximation toB(n,p)is given by thenormal distribution
and this basic approximation can be improved in a simple way by using a suitablecontinuity correction.
The basic approximation generally improves asnincreases (at least 20) and is better whenpis not near to 0 or 1.[32]Variousrules of thumbmay be used to decide whethernis large enough, andpis far enough from the extremes of zero or one:
This can be made precise using theBerry–Esseen theorem.
The rulenp±3np(1−p)∈(0,n){\displaystyle np\pm 3{\sqrt {np(1-p)}}\in (0,n)}is totally equivalent to request that
Moving terms around yields:
Since0<p<1{\displaystyle 0<p<1}, we can apply the square power and divide by the respective factorsnp2{\displaystyle np^{2}}andn(1−p)2{\displaystyle n(1-p)^{2}}, to obtain the desired conditions:
Notice that these conditions automatically imply thatn>9{\displaystyle n>9}. On the other hand, apply again the square root and divide by 3,
Subtracting the second set of inequalities from the first one yields:
and so, the desired first rule is satisfied,
Assume that both valuesnp{\displaystyle np}andn(1−p){\displaystyle n(1-p)}are greater than 9. Since0<p<1{\displaystyle 0<p<1}, we easily have that
We only have to divide now by the respective factorsp{\displaystyle p}and1−p{\displaystyle 1-p}, to deduce the alternative form of the 3-standard-deviation rule:
The following is an example of applying acontinuity correction. Suppose one wishes to calculatePr(X≤ 8)for a binomial random variableX. IfYhas a distribution given by the normal approximation, thenPr(X≤ 8)is approximated byPr(Y≤ 8.5). The addition of 0.5 is the continuity correction; the uncorrected normal approximation gives considerably less accurate results.
This approximation, known asde Moivre–Laplace theorem, is a huge time-saver when undertaking calculations by hand (exact calculations with largenare very onerous); historically, it was the first use of the normal distribution, introduced inAbraham de Moivre's bookThe Doctrine of Chancesin 1738. Nowadays, it can be seen as a consequence of thecentral limit theoremsinceB(n,p)is a sum ofnindependent, identically distributedBernoulli variableswith parameterp. This fact is the basis of ahypothesis test, a "proportion z-test", for the value ofpusingx/n, the sample proportion and estimator ofp, in acommon test statistic.[35]
For example, suppose one randomly samplesnpeople out of a large population and ask them whether they agree with a certain statement. The proportion of people who agree will of course depend on the sample. If groups ofnpeople were sampled repeatedly and truly randomly, the proportions would follow an approximate normal distribution with mean equal to the true proportionpof agreement in the population and with standard deviation
The binomial distribution converges towards thePoisson distributionas the number of trials goes to infinity while the productnpconverges to a finite limit. Therefore, the Poisson distribution with parameterλ=npcan be used as an approximation toB(n,p)of the binomial distribution ifnis sufficiently large andpis sufficiently small. According to rules of thumb, this approximation is good ifn≥ 20andp≤ 0.05[36]such thatnp≤ 1, or ifn> 50andp< 0.1such thatnp< 5,[37]or ifn≥ 100andnp≤ 10.[38][39]
Concerning the accuracy of Poisson approximation, see Novak,[40]ch. 4, and references therein.
The binomial distribution and beta distribution are different views of the same model of repeated Bernoulli trials. The binomial distribution is thePMFofksuccesses givennindependent events each with a probabilitypof success.
Mathematically, whenα=k+ 1andβ=n−k+ 1, the beta distribution and the binomial distribution are related by[clarification needed]a factor ofn+ 1:
Beta distributionsalso provide a family ofprior probability distributionsfor binomial distributions inBayesian inference:[41]
Given a uniform prior, the posterior distribution for the probability of successpgivennindependent events withkobserved successes is a beta distribution.[42]
Methods forrandom number generationwhere themarginal distributionis a binomial distribution are well-established.[43][44]One way to generaterandom variatessamples from a binomial distribution is to use an inversion algorithm. To do so, one must calculate the probability thatPr(X=k)for all valueskfrom0throughn. (These probabilities should sum to a value close to one, in order to encompass the entire sample space.) Then by using apseudorandom number generatorto generate samples uniformly between 0 and 1, one can transform the calculated samples into discrete numbers by using the probabilities calculated in the first step.
This distribution was derived byJacob Bernoulli. He considered the case wherep=r/(r+s)wherepis the probability of success andrandsare positive integers.Blaise Pascalhad earlier considered the case wherep= 1/2, tabulating the corresponding binomial coefficients in what is now recognized asPascal's triangle.[45]
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In the mathematical field ofgraph theory, theErdős–Rényi modelrefers to one of two closely related models for generatingrandom graphsor theevolution of a random network. These models are named afterHungarianmathematiciansPaul ErdősandAlfréd Rényi, who introduced one of the models in 1959.[1][2]Edgar Gilbertintroduced the other model contemporaneously with and independently of Erdős and Rényi.[3]In the model of Erdős and Rényi, all graphs on a fixed vertex set with a fixed number of edges are equally likely. In the model introduced by Gilbert, also called theErdős–Rényi–Gilbert model,[4]each edge has a fixed probability of being present or absent,independentlyof the other edges. These models can be used in theprobabilistic methodto prove the existence of graphs satisfying various properties, or to provide a rigorous definition of what it means for a property to hold foralmost allgraphs.
There are two closely related variants of the Erdős–Rényi random graph model.
The behavior of random graphs are often studied in the case wheren{\displaystyle n}, the number of vertices, tends to infinity. Althoughp{\displaystyle p}andM{\displaystyle M}can be fixed in this case, they can also be functions depending onn{\displaystyle n}. For example, the statement that almost every graph inG(n,2ln(n)/n){\displaystyle G(n,2\ln(n)/n)}is connected means that, asn{\displaystyle n}tends to infinity, the probability that a graph onn{\displaystyle n}vertices with edge probability2ln(n)/n{\displaystyle 2\ln(n)/n}is connected tends to1{\displaystyle 1}.
The expected number of edges inG(n,p) is(n2)p{\displaystyle {\tbinom {n}{2}}p}, with a standard deviation asymptotic tos(n)=np(1−p){\displaystyle s(n)=n{\sqrt {p(1-p)}}}. Therefore, a rough heuristic is that if some property ofG(n,M) withM=(n2)p{\displaystyle M={\tbinom {n}{2}}p}does not significantly change in behavior ifMis changed by up tos(n), thenG(n,p) should share that behavior.
This is formalized in a result of Łuczak.[5]Suppose thatPis a graph property such that for every sequenceM=M(n) with|M−(n2)p|=O(s(n)){\displaystyle |M-{\tbinom {n}{2}}p|=O(s(n))}, the probability that a graph sampled fromG(n,M) has propertyPtends toaasn→ ∞. Then the probability thatG(n,p) has propertyPalso tends toa.
Implications in the other direction are less reliable, but a partial converse (also shown by Łuczak) is known whenPismonotonewith respect to the subgraph ordering (meaning that ifAis a subgraph ofBandBsatisfiesP, thenAwill satisfyPas well). Letε(n)≫s(n)/n3{\displaystyle \varepsilon (n)\gg s(n)/n^{3}}, and suppose that a monotone propertyPis true of bothG(n,p–ε) andG(n,p+ε) with a probability tending to the same constantaasn→ ∞. Then the probability thatG(n,(n2)p){\displaystyle G(n,{\tbinom {n}{2}}p)}has propertyPalso tends toa.
For example, both directions of equivalency hold ifPis the property of beingconnected, or ifPis the property of containing aHamiltonian cycle. However, properties that are not monotone (e.g. the property of having an even number of edges) or that change too rapidly (e.g. the property of having at least12(n2){\displaystyle {\tfrac {1}{2}}{\tbinom {n}{2}}}edges) may behave differently in the two models.
In practice, theG(n,p) model is the one more commonly used today, in part due to the ease of analysis allowed by the independence of the edges.
With the notation above, a graph inG(n,p) has on average(n2)p{\displaystyle {\tbinom {n}{2}}p}edges. The distribution of thedegreeof any particular vertex isbinomial:[6]
wherenis the total number of vertices in the graph. Since
this distribution isPoissonfor largenandnp= const.
In a 1960 paper, Erdős and Rényi[7]described the behavior ofG(n,p) very precisely for various values ofp. Their results included that:
Thuslnnn{\displaystyle {\tfrac {\ln n}{n}}}is a sharp threshold for the connectedness ofG(n,p).
Further properties of the graph can be described almost precisely asntends to infinity. For example, there is ak(n) (approximately equal to 2log2(n)) such that the largestcliqueinG(n, 0.5) has almost surely either sizek(n) ork(n) + 1.[8]
Thus, even though finding the size of the largest clique in a graph isNP-complete, the size of the largest clique in a "typical" graph (according to this model) is very well understood.
Edge-dual graphs of Erdos-Renyi graphs are graphs with nearly the same degree distribution, but with degree correlations and a significantly higherclustering coefficient.[9]
Inpercolation theoryone examines a finite or infinite graph and removes edges (or links) randomly. Thus the Erdős–Rényi process is in fact unweighted link percolation on thecomplete graph. (One refers to percolation in which nodes and/or links are removed with heterogeneous weights as weighted percolation). As percolation theory has much of its roots inphysics, much of the research done was on thelatticesin Euclidean spaces. The transition atnp= 1 from giant component to small component has analogs for these graphs, but for lattices the transition point is difficult to determine. Physicists often refer to study of the complete graph as amean field theory. Thus the Erdős–Rényi process is the mean-field case of percolation.
Some significant work was also done on percolation on random graphs. From a physicist's point of view this would still be a mean-field model, so the justification of the research is often formulated in terms of the robustness of the graph, viewed as a communication network. Given a random graph ofn≫ 1 nodes with an average degree⟨k⟩{\displaystyle \langle k\rangle }. Remove randomly a fraction1−p′{\displaystyle 1-p'}of nodes and leave only a fractionp′{\displaystyle p'}from the network. There exists a critical percolation thresholdpc′=1⟨k⟩{\displaystyle p'_{c}={\tfrac {1}{\langle k\rangle }}}below which the network becomes fragmented while abovepc′{\displaystyle p'_{c}}a giant connected component of ordernexists. The relative size of the giant component,P∞, is given by[7][1][2][10]
Both of the two major assumptions of theG(n,p) model (that edges are independent and that each edge is equally likely) may be inappropriate for modeling certain real-life phenomena. Erdős–Rényi graphs have low clustering, unlike many social networks.[11]Some modeling alternatives includeBarabási–Albert modelandWatts and Strogatz model. These alternative models are not percolation processes, but instead represent a growth and rewiring model, respectively. Another alternative family of random graph models, capable of reproducing many real-life phenomena, areexponential random graph models.
TheG(n,p) model was first introduced byEdgar Gilbertin a 1959 paper studying the connectivity threshold mentioned above.[3]TheG(n,M) model was introduced by Erdős and Rényi in their 1959 paper. As with Gilbert, their first investigations were as to the connectivity ofG(n,M), with the more detailed analysis following in 1960.
A continuum limit of the graph was obtained whenp{\displaystyle p}is of order1/n{\displaystyle 1/n}.[12]Specifically, consider the sequence of graphsGn:=G(n,1/n+λn−43){\displaystyle G_{n}:=G(n,1/n+\lambda n^{-{\frac {4}{3}}})}forλ∈R{\displaystyle \lambda \in \mathbb {R} }. The limit object can be constructed as follows:
Applying this procedure, one obtains a sequence of random infinite graphs of decreasing sizes:(Γi)i∈N{\displaystyle (\Gamma _{i})_{i\in \mathbb {N} }}. The theorem[12]states that this graph corresponds in a certain sense to the limit object ofGn{\displaystyle G_{n}}asn→+∞{\displaystyle n\to +\infty }.
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Greenwashing(acompound wordmodeled on "whitewash"), also calledgreen sheen,[1][2]is a form ofadvertisingormarketing spinthat deceptively usesgreen PRandgreen marketingto persuade the public that an organization's products, goals, orpoliciesareenvironmentally friendly.[3][4][5]Companies that intentionally adopt greenwashing communication strategies often do so to distance themselves from their environmental lapses or those of their suppliers.[6]Firms engage in greenwashing for two primary reasons: to appear legitimate and to project an image of environmental responsibility to the public.[7]Because there "is no harmonised definition of greenwashing", a determination that this is occurring in a given instance may be subjective.[8]
Greenwashing occurs when an organization spends significantly more resources on "green" advertising than on environmentally sound practices.[9]Many corporations use greenwashing to improvepublic opinionof their brands. Complex corporate structures can further obscure the bigger picture.[10]Corporations attempt to capitalize on consumers' environmental guilt.[11]Critics of the practice suggest that the rise of greenwashing, paired with ineffective regulation, contributes to consumer skepticism of all green claims and diminishes the power of the consumer to drive companies toward greenermanufacturing processesand business operations.[12]Greenwashing covers up unsustainable corporate agendas and policies.[13]Highly public accusations of greenwashing have contributed to the term's increasing use.[14]
Greenwashing has recently increased to meet consumer demand for environmentally-friendly goods and services. New regulations, laws, and guidelines put forward by organizations such as theCommittee of Advertising Practicein the UK aim to discourage companies from using greenwashing to deceive consumers.[15]At the same time, activists have been increasingly inclined to accuse companies of greenwashing, with inconsistent standards as to what activities merit such an accusation.[8]
Activities deemed to be characteristic of greenwashing can vary by time and place, product, and the opinions or expectations of the person making the determination.[8]
According to theUnited Nations, greenwashing can present itself in many ways:
TerraChoice, an environmental consulting division ofUL, described "seven sins of greenwashing" in 2007 to "help consumers identify products that made misleading environmental claims":[17]
The organization noted that by 2010, approximately 95% of consumer products in the U.S. claiming to be green were discovered to commit at least one of these sins.[18][19]
The origins of greenwashing can be traced to several different moments. For example,Keep America Beautifulwas a campaign founded by beverage manufacturers and others in 1953.[20]The campaign focused on recycling and littering, diverting attention away from corporate responsibility to protect the environment. The objective was to forestall the regulation of disposable containers such as the one established by Vermont.[21]
In the mid-1960s, the environmental movement gained momentum, particularly after the publication of the landmarkSilent Springby Rachel Carson. The book marked a turning point about the environment and inspired citizen action. It prompted many companies to seek a new cleaner or greener image through advertising.Jerry Mander, a formerMadison Avenueadvertising executive, called this new form of advertising "ecopornography."[22]
The firstEarth Daywas held on 22 April 1970. Most companies did not actively participate in the initial Earth Day events because environmental issues were not a major corporate priority, and there was a sense of skepticism or resistance to the movement's message. Nevertheless, some industries began to advertise themselves as friendly to the environment. For example, public utilities were estimated to have spent around $300 million advertising themselves as clean and green companies, which was eight times what they spent on pollution reduction research.[23][24]
The term "greenwashing" was coined by New YorkenvironmentalistJay Westerveldin a 1986 essay about thehotel industry'spractice of placing notices in bedrooms promoting the reuse of towels to "save the environment". He noted that these institutions often made little or no effort toward reducing energy waste, although towel reuse saved them laundry costs. He concluded that the fundamental objective was most frequently increased profit. He labeled this and other profitable-but-ineffective "environmentally-conscientious" acts as "greenwashing".[25]
In 1991, a study published in the "Journal of Public Policy and Marketing" (American Marketing Association) found that 58% of environmental ads had at least one deceptive claim. Another study found that 77% of people said a company's environmental reputation affected whether they would buy its products. One-fourth of all household products marketed around Earth Day advertised themselves as being green and environmentally friendly. In 1998, theFederal Trade Commissioncreated the "Green Guidelines", which defined terms used in environmental marketing. The following year, the FTC found the Nuclear Energy Institute's environmentally clean claims invalid. The FTC did nothing about the ads because they were out of the agency's jurisdiction. This caused the FTC to realize they needed new, clear, enforceable standards. In 1999, the word "greenwashing" was added to the "Oxford English Dictionary".[23][24]
Days before the 1992 Earth Summit in Rio de Janeiro, Greenpeace released the Greenpeace Book on Greenwash, which described the corporate takeover of the UN conference and provided case studies of the contrast between corporate polluters and their rhetoric. Third World Network published an expanded version of that report, "Greenwash: The Reality Behind Corporate Environmentalism."
In 2002, during theWorld Summit on Sustainable Developmentin Johannesburg, the Greenwashing Academy hosted the Greenwash Academy Awards. The ceremony awarded companies likeBP,ExxonMobil, and even theU.S. Governmentfor their elaborate greenwashing ads and support for greenwashing.[23][24]A European Union study from 2020 found that over 50% of examined environmental claims in the EU were vague, misleading or unfounded and 40% were unsubstantiated.[26]
Many companies have committed to lessen their greenhouse gas emissions to a net zero due to theParis Agreementbeing established in 2015. A net zero emissions level means that any emissions given off by a company would be offset by carbon eliminators in the natural world (otherwise known as carbon sinks). However, companies are not actually cutting emissions, but are creating infeasible plans and trying to improve other things rather than their emissions. Therefore, most companies are not actually upholding their agreements and ultimately continue not to cause any positive change.[16]
Some companies communicate and publicize unsubstantiated ethical claims or social responsibility, and practice greenwashing, which increases consumer cynicism and mistrust.[85]By using greenwashing, companies can present their business as more ecologically sustainable than it is. According to a policy report, greenwashing includes risks such as misleading advertisements and public communications, misleading ESG credentials, and false or deceiving carbon credit claims.[86]
After a legal analysis, the corruption and integrity risks in climate solutions reports show that regulations are significantly weaker for misleading ESG credentials than for climate washing and advertising standards. Despite imposed obligations, ESG rating agencies or ESG auditors are not regulated in any reviewed jurisdictions. Factors such as the lack of oversight by third-party environmental service providers, the opacity of internal scoring methodologies, and the lack of alignment and consistency around ESG assessments can create opportunities for misleading or unsubstantiated claims and, worst cases, bribery or fraud.[86]
Greenwashing is a relatively new area of research within psychology, and there needs to be more consensus among studies on how greenwashing affects consumers and stakeholders. Because of the variance in country and geography in recently published studies, the discrepancy between consumer behavior in studies could be attributed to cultural or geographic differences.
Researchers found that consumers significantly favor environmentally friendly products over their greenwashed counterparts.[87]A survey by LendingTree found that 55% of Americans are willing to spend more money on products they perceive to be more sustainable and eco-friendly.[88]
Consumer perceptions of greenwashing are also mediated by the level of greenwashing they are exposed to.[89]Other research suggests that few consumers notice greenwashing, particularly when they perceive the company or brand as reputable. When consumers perceive green advertising as credible, they develop more positive attitudes towards the brand, even when the advertising is greenwashed.[90]
Other research suggests that consumers with more green concern are more able to tell the difference between honest green marketing and greenwashed advertising; the more green concern, the stronger the intention not to purchase from companies from which they perceive greenwashing advertising behavior. When consumers use word-of-mouth to communicate about a product, green concern strengthens the negative relationship between the consumer's intent to purchase and the perception of greenwashing.[91]
Research suggests that consumers distrust companies that greenwash because they view the act as deceptive. If consumers perceive that a company would realistically benefit from a green marketing claim being true, then it is more likely that the claim and the company will be seen as genuine.[92]
Consumers' willingness to purchase green products decreases when they perceive that green attributes compromise product quality, making greenwashing potentially risky, even when the consumer or stakeholder is not skeptical of green messaging. Words and phrases often used in green messaging and greenwashing, such as "gentle," can lead consumers to believe the green product is less effective than a non-green option.[93]
Eco-labelscan be given to a product from an external organization and the company itself. This has raised concerns because companies can label a product as green or environmentally friendly by selectively disclosing positive attributes of the product while not disclosing environmental harms.[94]Consumers expect to see eco-labels from both internal and external sources but perceive labels from external sources to be more trustworthy. Researchers from the University of Twente found that uncertified or greenwashed internal eco-labels may still contribute to consumer perceptions of a responsible company, with consumers attributing internal motivation to a company's internal eco-labeling.[95]Other research connecting attribution theory and greenwashing found that consumers often perceive green advertising as greenwashing when companies use green advertisements, attributing the green messaging to corporate self-interest. Green advertising can backfire, particularly when the advertised environmental claim does not match a company's environmental engagement.[96]
Researchers working with consumer perception, psychology, and greenwashing note that companies should "walk the walk" regarding green advertising and behavior to avoid the negative connotations and perceptions of greenwashing. Green marketing, labeling, and advertising are most effective when they match a company's environmental engagement. This is also mediated by the visibility of those environmental engagements, meaning that if consumers are unaware of a company's commitment to sustainability or environmentally-conscious ethos, they cannot factor greenness in their assessment of the company or product.[97]
Exposure to greenwashing can make consumers indifferent to or generate negative feelings toward green marketing. Thus, genuinely green businesses must work harder to differentiate themselves from those who use false claims. Nevertheless, consumers may react negatively to valid sustainability claims because of negative experiences with greenwashing.[98]
Conversely, concerns about the perception of genuine efforts to develop more environmentally friendly practices can lead to "greenhushing", where a company avoids publicizing these efforts out of concern that they will be accused of greenwashing anyway.[8]
Companies may pursueenvironmental certificationto avoid greenwashing through independent verification of their green claims. For example, theCarbon TrustStandard launched in 2007 with the stated aim "to end 'greenwash' and highlight firms that are genuine about their commitment to the environment."[99]
There have been attempts to reduce the impact of greenwashing by exposing it to the public.[100]The Greenwashing Index, created by theUniversity of Oregonin partnership with EnviroMedia Social Marketing, allowed the public to upload and rate examples of greenwashing, but it was last updated in 2012.[101]
Research published in the Journal of Business Ethics in 2011 shows that Sustainability Ratings might deter greenwashing. Results concluded that higher sustainability ratings lead to significantly higher brand reputation than lower sustainability ratings. This same trend was found regardless of the company's level ofcorporate social responsibility(CSR) communications. This finding establishes that consumers pay more attention to sustainability ratings than CSR communications or greenwashing claims.[102]
The World Federation of Advertisers released six new guidelines for advertisers in 2022 to prevent greenwashing. These approaches encourage credible environmental claims and more sustainable outcomes.[103]
Worldwide regulations on misleading environmental claims vary from criminal liability to fines or voluntary guidelines.
The AustralianTrade Practices Actpunishes companies that provide misleading environmental claims. Any organization found guilty of such could face upA$6 millionin fines.[104]In addition, the guilty party must pay for all expenses incurred while setting the record straight about their product or company's actualenvironmental impact.[105]
Canada'sCompetition Bureau, along with theCanadian Standards Association, discourage companies from making "vague claims" about their products' environmental impact. Any claims must be backed up by "readily available data."[105]
TheEuropean Anti-Fraud Office(OLAF) handles investigations that have an environmental or sustainability element, such as the misspending of EU funds intended for green products and the counterfeiting and smuggling of products with the potential to harm the environment and health. It also handlesillegal loggingand smuggling of precious wood and timber into the EU (wood laundering).[106]
In January 2021, the European Commission, in cooperation with nationalconsumer protectionauthorities, published a report on its annual survey of consumer websites investigated for violations of EU consumer protection law.[107]The study examined green claims across a wide range of consumer products, concluding that for 42 percent of the websites examined, the claims were likely false and misleading and could well constitute actionable claims for unfair commercial practices.[108]
In the context of escalating concerns regarding the authenticity of corporate ecological sustainability claims, greenwashing has emerged as a significant issue and poses a real challenge tosustainable financeregulations gaps. ESMA outlined the correlation between the growth of ESG-related funds and greenwashing. The exponential rise of funds integrating vague ESG-related language in their names started since theParis Agreement(2015), and is effective in deceivingly attracting more investors.[109]
The 2020-2024 agenda ofDG FISMAconcern about greenwashing reconciles two objectives: increasing capital for sustainable investments and bolstering trust and investor protection in European financial markets.[110]
The European Union struck a provisional agreement to mandate new reporting rules for companies with over 250 staff and a turnover of€40 million. They must disclose environmental, social, and governance (ESG) information, which will help combat greenwashing. These requirements go into effect in 2024.[111]The European Commission has introduced a proposal ofESG regulationaimed at bolstering transparency and integrity within ESG rating in 2023.[112]
In June 2024, theFederal Constitutional Courtof Germany ruled that companies that use "climate neutral" in advertising must define what the term means or use of the phrase would not continue to be permitted due to the phrase being too vague.[113]
Norway's consumer ombudsmanhas targeted automakers who claim their cars are "green," "clean," or "environmentally friendly," with some of the world's strictest advertising guidelines. Consumer Ombudsman official Bente Øverli said: "Cars cannot do anything good for the environment except less damage than others." Manufacturers risk fines if they fail to drop misleading advertisements. Øverli said she did not know of other countries going so far in cracking down on cars and the environment.[114][115][116][117]
The Green Leaf Certification is an evaluation method created by theAssociation of Southeast Asian Nations(ASEAN) as a metric that rates the hotels' environmental efficiency of environmental protection.[118]In Thailand, this certification is believed to help regulate greenwashing phenomena associated with green hotels.Eco hotelor "green hotel" are hotels that have adopted sustainable, environmentally-friendly practices in hospitality business operations.[119]Since the development of the tourism industry in the ASEAN, Thailand superseded its neighboring countries in inbound tourism, with 9 percent of Thailand's direct GDP contributions coming from the travel and tourism industry in 2015.[120]Because of the growth and reliance on tourism as an economic pillar, Thailand developed "responsible tourism" in the 1990s to promote the well-being of local communities and the environment affected by the industry.[118]However, studies show the green hotel companies' principles and environmental perceptions contradict the basis of corporate social responsibilities in responsible tourism.[118][121]Against this context, the Green Leaf Certification issuance aims to keep the hotel industry and supply chains accountable for corporate social responsibilities regarding sustainability by having an independent international organization evaluate a hotel and rate it one through five leaves.[122]
TheCompetition and Markets Authorityis the UK's primary competition and consumer authority. In September 2021, it published a Green Claims Code to protect consumers from misleading environmental claims and businesses from unfair competition.[123]In May 2024, theFinancial Conduct Authorityintroduced anti-greenwashing rules covering sustainability claims made by regulated firms that market financial products or services.[124]
TheFederal Trade Commission(FTC) provides voluntary guidelines for environmental marketing claims. These guidelines give the FTC the right to prosecute false and misleading claims. These guidelines are not enforceable but instead were intended to be followed voluntarily:
The FTC announced in 2010 that it would update its guidelines for environmental marketing claims in an attempt to reduce greenwashing.[126]The revision to the FTC's Green Guides covers a wide range of public input, including hundreds of consumer and industry comments on previously proposed revisions, offering clear guidance on what constitutes misleading information and demanding clear factual evidence.[108]
According to FTC ChairmanJon Leibowitz, "The introduction of environmentally-friendly products into the marketplace is a win for consumers who want to purchase greener products and producers who want to sell them." Leibowitz also says such a win-win can only operate if marketers' claims are straightforward and proven.[127]
In 2013, the FTC began enforcing these revisions. It cracked down on six different companies; five of the cases concerned false or misleading advertising surrounding thebiodegradabilityof plastics. The FTC charged ECM Biofilms, American Plastic Manufacturing, CHAMP, Clear Choice Housewares, and Carnie Cap, for misrepresenting the biodegradability of their plastics treated with additives.[128]
The FTC charged a sixth company, AJM Packaging Corporation, with violating a commission consent order prohibiting companies from using advertising claims based on the product or packaging being "degradable, biodegradable, or photodegradable" without reliable scientific information.[128]The FTC now requires companies to disclose and provide the information that qualifies their environmental claims to ensure transparency.
The issue of green marketing andconsumerismin China has gained significant attention as the country faces environmental challenges. According to "Green Marketing and Consumerism in China: Analyzing the Literature" by Qingyun Zhu and Joseph Sarkis, China has implemented environmental protection laws to regulate the business and commercial sector. Regulations such as the Environmental Protection Law and the Circular Economy Promotion Law contain provisions prohibiting false advertising (known as greenwashing).[129][130]TheChinese governmenthas issued regulations and standards to regulate green advertising and labeling, including the Guidelines for Green Advertising Certification, the Guidelines for Environmental Labeling and Eco-Product Certification, and the Standards for Environmental Protection Product Declaration. These guidelines promote transparency in green marketing and prevent false or misleading claims. The Guidelines for Green Advertising Certification require that green advertising claims should be truthful, accurate, and verifiable.[131]These guidelines and certifications require that eco-labels should be based on scientific and technical evidence, and should not contain false or misleading information. The standards also require that eco-labels be easy to understand and not confuse or deceive consumers. The regulations that are set in place for greenwashing, green advertising, and labeling in China are designed to protect consumers and prevent misleading claims. China's climate crisis, sustainability, and greenwashing remain critical and require ongoing attention. The implementation of regulations and guidelines for green advertising and labeling in China aims to promote transparency and prevent false or misleading claims.
In efforts to stop this practice, in November 2016, the General Office of the State Council introduced legislation to promote the development of green products, encourage companies to adopt sustainable practices, and mention the need for a unified standard for what was to be labeled green.[132]This was a general plan or opinion on the matter, with no specifics on its implementation, however with similarly worded legislation and plans out at that time there was a push toward a unified green product standard.[133]Until then, green products had various standards and guidelines developed by different government agencies or industry associations, resulting in a lack of consistency and coherence. One example of guidelines set then was from the Ministry of Environmental Protection of China (now known as the Ministry of Ecology and Environment). They issued specifications in 2000, but these guidelines were limited and not widely recognized by industry or consumers. It was not until 2017, with the launch of GB/T (a set of national standards and recommendations), that a widespread guideline was set for what would constitute green manufacturing and a green supply chain.[134][135]Expanding on these guidelines in 2019 the State Administration for Market Regulation (SAMR) created regulations for Green Product Labels, which are symbols used on products to mark that they meet certain environmentally friendly criteria, and certification agencies have verified their manufacturing process.[136][137]The standards and coverage for green products have increased as time passes, with changes and improvements to green product standardization still occurring in 2023.[135]
In China, the Greenpeace Campaign focuses on the pain point of air pollution. The campaign aims to address the severe air pollution problem prevalent in many Chinese communities. The campaign has been working to raise awareness about air pollution's health and environmental impacts, advocate for more robust government policies and regulations to reduce emissions, and encourage a shift toward clean and renewable energy sources.[138]"From 2011 to 2016, we linked global fast fashion brands to toxic chemical pollution in China through their manufacturers. Many multinational companies and local suppliers have stopped using toxic and harmful chemicals. They included Adidas, Benetton, Burberry, Esprit, H&M, Puma, and Zara, among others." The Greenpeace Campaign in China has involved various activities, including scientific research, public education, and advocacy efforts. The campaign has organized public awareness events to engage both consumers and policymakers, urging them to take action to improve air quality. "In recent years,Chinese Communist Partygeneral secretaryXi Jinpinghas committed to controlling the expansion of coal power plants. He has also pledged to stop building new coal power abroad". The campaign seeks to drive public and government interest toward more strict air pollution control measures, promote more clean energy technology, and contribute to health, wellness, and sustainability in China. However, the health of Chinese citizens is at the forefront of this issue, as air pollution is a critical issue in the nation. The article emphasizes that China has prioritized putting people front and center on environmental issues. China's Greenpeace campaigns and those in other countries are a part of their global efforts to address environmental challenges and promote sustainability.
"Bluewashing" is a similar term. However, instead of falsely advertising environmentally friendly practices, companies are advertising corporate social responsibility. For example, companies are saying they are fighting for human rights while practicing very unethical production practices such as paying factory employees next to nothing.[139]
Carbon emission tradingcan be similar to greenwashing in that it gives an environmentally-friendly impression, but can be counterproductive if carbon is priced too low, or if large emitters are given "free credits." For example,Bank of AmericasubsidiaryMBNAoffers "Eco-Logique"MasterCardsthat reward Canadian customers withcarbon offsetswhen they use them. Customers may feel that they are nullifying theircarbon footprintby purchasing goods with these, but only 0.5% of the purchase price goes to buy carbon offsets; the rest of theinterchange feestill goes to the bank.[140]
Greenscamming describes an organization or product taking on a name that falsely implies environmental friendliness. It is related to both greenwashing andgreenspeak.[141]This is analogous toaggressive mimicryin biology.[142][143]
Greenscamming is used in particular by industrial companies and associations that deployastroturfingorganisations to try to dispute scientific findings that threaten their business model. One example is thedenial of man-made global warmingby companies in thefossil energy sector, also driven by specially-founded greenscamming organizations.[citation needed]
One reason to establish greenscamming organizations is that openly communicating the benefits of activities that damage the environment is difficult. Sociologist Charles Harper stresses that marketing a group called "Coalition to Trash the Environment for Profit" would be difficult. Anti-environment initiatives, therefore, must give theirfront organizationsdeliberately deceptive names if they want to be successful, as surveys[citation needed]show that environmental protection has a social consensus. However, the danger of being exposed as an anti-environmental initiative entails a considerable risk that the greenscamming activities will backfire and be counterproductive for the initiators.[144]
Greenscamming organizations are active in organizedclimate denial.[142]An important financier of greenscamming organizations was the oil companyExxonMobil, which financially supported more than 100 climate denial organizations and spent about 20 million U.S. dollars on greenscamming groups.[145]James Lawrence Powellidentified the "admirable" designations of many of these organizations as the most striking common feature, which for the most part sounded very rational. He quotes a list of climate denial organizations drawn up by theUnion of Concerned Scientists, which includes 43 organizations funded byExxon. None had a name that would lead one to infer that climate change denial was their "raison d'être". The list is headed byAfrica Fighting Malaria, whose website features articles and commentaries opposing ambitiousclimate mitigationconcepts, even though the dangers ofmalariacould be exacerbated byglobal warming.[146]
Examples of greenscamming organizations include theNational Wetlands Coalition, Friends of Eagle Mountain, The Sahara Club, The Alliance for Environment and Resources, The Abundant Wildlife Society of North America, theGlobal Climate Coalition, the National Wilderness Institute, the Environmental Policy Alliance of theCenter for Organizational Research and Education, and theAmerican Council on Science and Health.[143][147]Behind these ostensible environmental protection organizations lie the interests of business sectors. For example, oil drilling companies and real estate developers support the National Wetlands Coalition. In contrast, the Friends of Eagle Mountain is backed by a mining company that wants to convert open-cast mines into landfills. The Global Climate Coalition was backed by commercial enterprises that fought against government-imposed climate protection measures. Other Greenscam organizations include the U.S. Council for Energy Awareness, backed by the nuclear industry; the Wilderness Impact Research Foundation, representing the interests of loggers and ranchers; and the American Environmental Foundation, representing the interests of landowners.[148]
Another Greenscam organization is the Northwesterners for More Fish, which had a budget of $2.6 million in 1998. This group opposed conservation measures for endangered fish that restricted the interests of energy companies, aluminum companies, and the region's timber industry and tried to discredit environmentalists who promoted fish habitats.[143]TheCenter for the Study of Carbon Dioxide and Global Change, the National Environmental Policy Institute, and theInformation Council on the Environmentfunded by thecoal industryare also greenscamming organizations.[145]
In Germany, this form of mimicry or deception is used by the "European Institute for Climate and Energy" (EIKE), which suggests by its name that it is an important scientific research institution.[149]In fact, EIKE is not a scientific institution at all, but alobby organizationthat neither has an office nor employs climate scientists, but instead disseminates fake news on climate issues on its website.[150]
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Instatisticsandeconometrics, theADF-GLS test(orDF-GLS test) is a test for aunit rootin an economictime seriessample. It was developed by Elliott, Rothenberg and Stock (ERS) in 1992 as a modification of theaugmented Dickey–Fuller test(ADF).[1]
A unit root test determines whether a time series variable is non-stationary using an autoregressive model. For series featuring deterministic components in the form of a constant or a linear trend then ERS developed an asymptotically point optimal test to detect a unit root. This testing procedure dominates other existing unit root tests in terms of power. It locally de-trends (de-means) data series to efficiently estimate the deterministic parameters of the series, and use the transformed data to perform a usual ADF unit root test. This procedure helps to remove the means and linear trends for series that are not far from the non-stationary region.[2]
Consider a simple time series modelyt=dt+ut{\displaystyle y_{t}=d_{t}+u_{t}\,}withut=ρut−1+et{\displaystyle u_{t}=\rho u_{t-1}+e_{t}\,}wheredt{\displaystyle d_{t}\,}is the deterministic part andut{\displaystyle u_{t}\,}is the stochastic part ofyt{\displaystyle y_{t}\,}. When the true value ofρ{\displaystyle \rho \,}is close to 1, estimation of the model, i.e.dt{\displaystyle d_{t}\,}will pose efficiency problems because theyt{\displaystyle y_{t}\,}will be close to nonstationary. In this setting, testing for the stationarity features of the given times series will also be subject to general statistical problems. To overcome such problems ERS suggested to locally difference the time series.
Consider the case where closeness to 1 for the autoregressive parameter is modelled asρ=1−cT{\displaystyle \rho =1-{\frac {c}{T}}\,}whereT{\displaystyle T\,}is the number of observations. Now consider filtering the series using1−c¯TL{\displaystyle 1-{\frac {\bar {c}}{T}}L\,}withL{\displaystyle L\,}being a standard lag operator, i.e.y¯t=yt−(c¯/T)yt−1{\displaystyle {\bar {y}}_{t}=y_{t}-({\bar {c}}/T)y_{t-1}\,}. Working withy¯t{\displaystyle {\bar {y}}_{t}\,}would result in power gain, as ERS show, when testing the stationarity features ofyt{\displaystyle y_{t}\,}using the augmented Dickey-Fuller test. This is a point optimal test for whichc¯{\displaystyle {\bar {c}}\,}is set in such a way that the test would have a 50 percent power when the alternative is characterized byρ=1−c/T{\displaystyle \rho =1-c/T\,}forc=c¯{\displaystyle c={\bar {c}}\,}. Depending on the specification ofdt{\displaystyle d_{t}\,},c¯{\displaystyle {\bar {c}}\,}will take different values.
A Primer on Unit Root Tests, P.C.B. Phillips and Z. Xiao
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Time-triggered architecture(abbreviated asTTA), also known as atime-triggered system, is a computer system that executes one or more sets of tasks according to a predetermined and set task schedule.[1]Implementation of a TT system will typically involve use of a single interrupt that is linked to the periodic overflow of a timer. This interrupt may drive a task scheduler (a restricted form ofreal-time operating system). The scheduler will—in turn—release the system tasks at predetermined points in time.[1]
Because they have highly deterministic timing behavior, TT systems have been used for many years to developsafety-criticalaerospace and related systems.[2]
An early text that sets forth the principles of time triggered architecture, communications, and sparse time approaches isReal-Time Systems: Design Principles for Distributed Embedded Applicationsin 1997.[3]
Use of TT systems was popularized by the publication ofPatterns for Time-Triggered Embedded Systems(PTTES) in 2001[1]and the related introductory bookEmbedded Cin 2002.[4]The PTTES book also introduced the concepts of time-triggered hybrid schedulers (an architecture for time-triggered systems that require task pre-emption) and shared-clock schedulers (an architecture for distributed time-triggered systems involving multiple, synchronized, nodes).[1]
Since publication of PTTES, extensive research work on TT systems has been carried out.[5][6][7][8][9][10]
Time-triggered systems are now commonly associated with international safety standards such asIEC 61508(industrial systems),ISO 26262(automotive systems),IEC 62304(medical systems) andIEC 60730(household goods).
Time-triggered systems can be viewed as a subset of a more general event-triggered (ET) system architecture (seeevent-driven programming).
Implementation of an ET system will typically involve use of multiple interrupts, each associated with specific periodic events (such as timer overflows) or aperiodic events (such as the arrival of messages over a communication bus at random points in time). ET designs are traditionally associated with the use of what is known as areal-time operating system(or RTOS), though use of such a software platform is not a defining characteristic of an ET architecture.[1]
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Avulnerability database(VDB) is a platform aimed at collecting, maintaining, and disseminating information about discoveredcomputer security vulnerabilities. Thedatabasewill customarily describe the identified vulnerability, assess the potential impact on affected systems, and any workarounds or updates to mitigate the issue. A VDB will assign a unique identifier to each vulnerability cataloged such as a number (e.g. 123456) oralphanumericdesignation (e.g. VDB-2020-12345). Information in the database can be made available via web pages, exports, orAPI. A VDB can provide the information for free, for pay, or a combination thereof.
The first vulnerability database was the "Repaired Security Bugs in Multics", published by February 7, 1973 by Jerome H. Saltzer. He described the list as "a list of all known ways in which a user may break down or circumvent the protection mechanisms ofMultics".[1]The list was initially kept somewhat private with the intent of keeping vulnerability details until solutions could be made available. The published list contained two local privilege escalation vulnerabilities and three local denial of service attacks.[2]
Major vulnerability databases such as the ISS X-Force database, Symantec / SecurityFocus BID database, and theOpen Source Vulnerability Database(OSVDB)[a]aggregate a broad range of publicly disclosed vulnerabilities, including Common Vulnerabilities and Exposures (CVE). The primary purpose of CVE, run byMITRE, is to attempt to aggregate public vulnerabilities and give them a standardized format unique identifier.[3]Many vulnerability databases develop the received intelligence from CVE and investigate further providing vulnerability risk scores, impact ratings, and the requisite workaround. In the past, CVE was paramount for linking vulnerability databases so critical patches and debugs can be shared to inhibit hackers from accessing sensitive information on private systems.[4]TheNational Vulnerability Database(NVD), run by theNational Institute of Standards and Technology(NIST), is operated separately from the MITRE-run CVE database, but only includes vulnerability information from CVE. NVD serves as an enhancement to that data by providingCommon Vulnerability Scoring System(CVSS) risk scoring andCommon Platform Enumeration(CPE) data.
TheOpen Source Vulnerability Databaseprovides an accurate, technical and unbiased index on vulnerability security. The comprehensive database cataloged over 121,000 vulnerabilities. The OSVDB was founded in August 2002 and was launched in March 2004. In its primitive beginning, newly identified vulnerabilities were investigated by site members and explanations were detailed on the website. However, as the necessity for the service thrived, the need for dedicated staff resulted in the inception of the Open Security Foundation (OSF) which was founded as a non-profit organisation in 2005 to provide funding for security projects and primarily the OSVDB.[5]The OSVDB closed in April 2016.[6]
The U.S.National Vulnerability Databaseis a comprehensive cyber security vulnerability database formed in 2005 that reports on CVE.[7]The NVD is a primary cyber security referral tool for individuals and industries alike providing informative resources on current vulnerabilities. The NVD holds in excess of 100,000 records. Similar to the OSVDB, the NVD publishes impact ratings and categorises material into an index to provide users with an intelligible search system.[8]Other countries have their own vulnerability databases, such as theChinese National Vulnerability Databaseand Russia'sData Security Threats Database.
A variety of commercial companies also maintain their own vulnerability databases, offering customers services which deliver new and updated vulnerability data in machine-readable format as well as through web portals. Examples include A.R.P. Syndicate's Exploit Observer, Symantec's DeepSight[9]portal and vulnerability data feed, Secunia's (purchased by Flexera) vulnerability manager[10]and Accenture's vulnerability intelligence service[11](formerly iDefense).
Exploit Observer[12]uses its Vulnerability & Exploit Data Aggregation System (VEDAS) to collect exploits & vulnerabilities from a wide array of global sources, including Chinese and Russian databases.[13]
Vulnerability databases advise organisations to develop, prioritize, and execute patches or other mitigations which attempt to rectify critical vulnerabilities. However, this can often lead to the creation of additional susceptibilities as patches are created hastily to thwart further system exploitations and violations. Depending upon the level of a user or organisation, they warrant appropriate access to a vulnerability database which provides the user with disclosure of known vulnerabilities that may affect them. The justification for limiting access to individuals is to impede hackers from being versed in corporation system vulnerabilities which could potentially be further exploited.[14]
Vulnerability databases contain a vast array of identified vulnerabilities. However, few organisations possess the expertise, staff, and time to revise and remedy all potential system susceptibilities hence vulnerability scoring is a method of quantitatively determining the severity of a system violation. A multitude of scoring methods exist across vulnerability databases such as US-CERT and SANS Institute'sCritical Vulnerability Analysis Scalebut theCommon Vulnerability Scoring System(CVSS) is the prevailing technique for most vulnerability databases including OSVDB, vFeed[15]and NVD. The CVSS is based upon three primary metrics: base, temporal and environmental which each provide a vulnerability rating.[16]
This metric covers the immutable properties of a vulnerability such as the potential impact of the exposure of confidential information, the accessibility of information and the aftermath of the irretrievable deletion of information.
The temporal metrics denote the mutable nature of a vulnerability for example the credibility of an exploitability, the current state of a system violation and the development of any workarounds that could be applied.[17]
This aspect of the CVSS rates the potential loss to individuals or organisations from a vulnerability. Furthermore, it details the primary target of a vulnerability ranging from personal systems to large organisations and the number of potentially affected individuals.[18]
The complication with utilising different scoring systems it that there is no consensus on the severity of a vulnerability thus different organisations may overlook critical system exploitations. The key benefit of a standardised scoring system like CVSS is that published vulnerability scores can be assessed, pursued and remedied rapidly. Organisations and individuals alike can determine the personal impact of a vulnerability on their system. The benefits derived from vulnerability databases to consumers and organisations are exponential as information systems become increasingly embedded, our dependency and reliance on them grows, as does the opportunity for data exploitation.[19]
Although the functionality of a database may appear unblemished, without rigorous testing, the exiguous flaws can allow hackers to infiltrate a system's cyber security. Frequently, databases are published without stringent security controls hence the sensitive material is easily accessible.[20]
Database attacks are the most recurrent form of cyber security breaches recorded on vulnerability databases. SQL and NoSQL injections penetrate traditional information systems and big data platforms respectively and interpolate malicious statements allowing the hackers unregulated system access.[21]
Established databases ordinarily fail to implement crucial patches suggested by vulnerability databases due to an excessive workload and the necessity for exhaustive trialling to ensure the patches update the defective system vulnerability. Database operators concentrate their efforts into major system deficiencies which offers hackers unmitigated system access through neglected patches.[22]
All databases require audit tracks to record when data is amended or accessed. When systems are created without the necessary auditing system, the exploitation of system vulnerabilities are challenging to identify and resolve. Vulnerability databases promulgate the significance of audit tracking as a deterrent of cyber attacks.[23]
Data protection is essential to any business as personal and financial information is a key asset and the purloining of sensitive material can discredit the reputation of a firm. The implementation of data protection strategies is imperative to guard confidential information. Some hold the view that is it the initial apathy of software designers that in turn, necessitates the existence of vulnerability databases. If systems were devised with greater diligence, they may be impenetrable from SQL and NoSQL injections making vulnerability databases redundant.[24]
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https://en.wikipedia.org/wiki/Vulnerability_database
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Aflight computeris a form ofslide ruleused inaviationand one of a very fewanalog computersin widespread use in the 21st century. Sometimes it is called by the make or model name likeE6B, CR, CRP-5 or in German, as theDreieckrechner.[1]
They are mostly used inflight training, but many professional pilots still carry and use flight computers. They are used during flight planning (on the ground before takeoff) to aid in calculating fuel burn, wind correction, time en route, and other items. In the air, the flight computer can be used to calculate ground speed, estimated fuel burn and updated estimated time of arrival. The back is designed for wind correction calculations, i.e., determining how much the wind is affecting one's speed and course.
One of the most useful parts of the E6B, is the technique of finding distance over time. Take the number 60 on the inner circle which usually has an arrow, and sometimes says rate on it. 60 is used in reference to the number of minutes in an hour, by placing the 60 on the airspeed in knots, on the outer ring the pilot can find how far the aircraft will travel in any given number of minutes. Looking at the inner ring for minutes traveled and the distance traveled will be above it on the outer ring. This can also be done backwards to find the amount of time the aircraft will take to travel a given number of nautical miles. On the main body of the flight computer it will find the wind component grid, which it will use to find how much crosswind the aircraft will actually have to correct for.
The crosswind component is the amount of crosswind in knots that is being applied to the airframe and can be less than the actual speed of the wind because of the angle. Below that the pilot will find a grid called crosswind correction, this grid shows the difference the pilot needs to correct for because of wind. On either side of the front it will have rulers, one for statute miles and one for nautical miles on their sectional map.
Another very useful part is the conversion scale on the front outer circle, which helps convert between Fahrenheit and Celsius. The back of the E6B is used to find ground speed and determine how much wind correction it needs.[2]
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https://en.wikipedia.org/wiki/Flight_computer
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Logologyis the study of all things related toscienceand itspractitioners—philosophical, biological,psychological,societal,historical,political,institutional,financial. The term "logology" isback-formedfrom the suffix "-logy", as in "geology", "anthropology", etc., in the sense of the "study of science".[1][2]
The word "logology" provides grammatical variants not available with the earlier terms "science of science" and "sociology of science", such as "logologist", "logologize", "logological", and "logologically".[a]The emerging field ofmetascienceis a subfield of logology.
The early 20th century brought calls, initially fromsociologists, for the creation of a new, empirically basedsciencethat would study thescientific enterpriseitself.[5]The early proposals were put forward with some hesitancy and tentativeness.[6][b]The newmeta-sciencewould be given a variety of names,[8]including "science of knowledge", "science of science", "sociology of science", and "logology".
Florian Znaniecki, who is considered to be the founder of Polish academic sociology, and who in 1954 also served as the 44th president of theAmerican Sociological Association, opened a 1923 article:[9]
[T]hough theoretical reflection onknowledge—which arose as early asHeraclitusand theEleatics—stretches... unbroken... through the history of human thought to the present day... we are now witnessing the creation of a newscience of knowledge[author's emphasis] whose relation to the old inquiries may be compared with the relation of modernphysicsandchemistryto the 'natural philosophy' that preceded them, or of contemporarysociologyto the 'political philosophy' ofantiquityand theRenaissance. [T]here is beginning to take shape a concept of a single, general theory of knowledge... permitting of empirical study.... This theory... is coming to be distinguished clearly fromepistemology, from normativelogic, and from a strictly descriptivehistory of knowledge."[10]
A dozen years later, Polish husband-and-wife sociologistsStanisław OssowskiandMaria Ossowska(theOssowscy) took up the same subject in an article on "The Science of Science"[11]whose 1935 English-language version first introduced the term "science of science" to the world.[12]The article postulated that the new discipline would subsume such earlier ones asepistemology, thephilosophy of science, thepsychology of science, and thesociology of science.[13]The science of science would also concern itself with questions of a practical character such associal and state policyin relation to science, such as the organization of institutions of higher learning, of research institutes, and of scientific expeditions, and theprotection of scientific workers, etc. It would concern itself as well with historical questions: the history of the conception of science, of the scientist, of the various disciplines, and of learning in general.[14]
In their 1935 paper, theOssowscymentioned the German philosopherWerner Schingnitz(1899–1953) who, in fragmentary 1931 remarks, had enumerated some possible types of research in the science of science and had proposed his own name for the new discipline: scientiology. TheOssowscytook issue with the name:
Those who wish to replace the expression 'science of science' by a one-word term [that] sound[s] international, in the belief that only after receiving such a name [will] a given group of [questions be] officially dubbed an autonomous discipline, [might] be reminded of the name 'mathesiology', proposed long ago for similar purposes [by the French mathematician and physicistAndré-Marie Ampère(1775–1836)]."[15]
Yet, before long, in Poland, the unwieldy three-word termnauka o nauce, or science of science, was replaced by the more versatile one-word termnaukoznawstwo, or logology, and its natural variants:naukoznawcaor logologist,naukoznawczyor logological, andnaukoznawczoor logologically. And just afterWorld War II, only 11 years after theOssowscy's landmark 1935 paper, the year 1946 saw the founding of thePolish Academy of Sciences' quarterlyZagadnienia Naukoznawstwa(Logology) –— long before similar journals in many other countries.[16][c]
The new discipline also took root elsewhere—in English-speaking countries, without the benefit of a one-word name.
The word "science", from theLatin"scientia" (meaning "knowledge"), signifies somewhat different things in different languages. InEnglish, "science", when unqualified, generally refers to theexact,natural, orhard sciences.[18]The corresponding terms in other languages, for exampleFrench,German, andPolish, refer to a broader domain that includes not only the exact sciences (logicandmathematics) and the natural sciences (physics,chemistry,biology,Earth sciences,astronomy, etc.) but also theengineering sciences,social sciences(human geography,psychology,cultural anthropology,sociology,political science,economics,linguistics,archaeology, etc.), andhumanities(philosophy,history,classics,literary theory, etc.).[19][d]
University of Amsterdamhumanities professorRens Bodpoints out that science—defined as a set ofmethodsthat describes and interpretsobservedorinferredphenomena, past or present, aimed at testinghypothesesand buildingtheories—applies to such humanities fields asphilology,art history,musicology,philosophy,religious studies,historiography, andliterary studies.[19]
Bod gives a historic example of scientifictextual analysis. In 1440 the Italian philologistLorenzo Vallaexposed theLatindocumentDonatio Constantini, or The Donation of Constantine – which was used by theCatholic Churchto legitimize its claim to lands in theWestern Roman Empire– as aforgery. Valla used historical, linguistic, and philological evidence, includingcounterfactual reasoning, to rebut the document. Valla found words and constructions in the document that could not have been used by anyone in the time ofEmperor Constantine I, at the beginning of the fourth century C.E. For example, thelate Latinwordfeudum, meaning fief, referred to thefeudal system, which would not come into existence until themedievalera, in the seventh century C.E. Valla's methods were those of science, and inspired the later scientifically-minded work of Dutch humanistErasmus of Rotterdam(1466–1536),Leiden UniversityprofessorJoseph Justus Scaliger(1540–1609), and philosopherBaruch Spinoza(1632–1677).[19]Here it is not theexperimental methoddominant in theexactandnatural sciences, but thecomparative methodcentral to thehumanities, that reigns supreme.
Science's search for thetruthabout various aspects ofrealityentails the question of the veryknowabilityof reality. PhilosopherThomas Nagelwrites: "[In t]he pursuit ofscientific knowledgethrough the interaction betweentheoryandobservation... we test theories against their observational consequences, but we also question or reinterpret our observations in light of theory. (The choice betweengeocentricandheliocentric theoriesat the time of theCopernican Revolutionis a vivid example.) ...
How things seem is the starting point for all knowledge, and its development through further correction, extension, and elaboration is inevitably the result of more seemings—consideredjudgmentsabout the plausibility and consequences of different theoreticalhypotheses. The only way to pursue the truth is to consider what seems true, after careful reflection of a kind appropriate to the subject matter, in light of all the relevant data, principles, and circumstances."[21]
The question of knowability is approached from a different perspective by physicist-astronomerMarcelo Gleiser: "What we observe is notnatureitself but nature as discerned throughdatawe collect frommachines. In consequence, the scientificworldviewdepends on theinformationwe can acquire through ourinstruments. And given that our tools are limited, our view of theworldis necessarilymyopic. We can see only so far into the nature of things, and our ever shifting scientific worldview reflects this fundamental limitation on how we perceivereality." Gleiser cites the condition ofbiologybefore and after the invention of themicroscopeorgene sequencing; ofastronomybefore and after thetelescope; ofparticle physicsbefore and aftercollidersor fast electronics. "[T]he theories we build and the worldviews we construct change as our tools of exploration transform. This trend is the trademark of science."[22]
Writes Gleiser: "There is nothing defeatist in understanding the limitations of the scientific approach to knowledge.... What should change is a sense of scientific triumphalism—the belief that no question is beyond the reach of scientific discourse.[22][e]
"There are clear unknowables in science—reasonable questions that, unless currently accepted laws of nature are violated, we cannot find answers to. One example is themultiverse: the conjecture that ouruniverseis but one among a multitude of others, each potentially with a different set oflaws of nature. Other universes lie outside our causal horizon, meaning that we cannot receive or send signals to them. Any evidence for their existence would be circumstantial: for example, scars in the radiation permeating space because of a past collision with a neighboring universe."[24]
Gleiser gives three further examples of unknowables, involving the origins of theuniverse; oflife; and ofmind:[24][f]
"Scientific accounts of the origin of theuniverseare incomplete because they must rely on a conceptual framework to even begin to work:energy conservation,relativity,quantum physics, for instance. Why does the universe operate under these laws and not others?[24]
"Similarly, unless we can prove that only one or very fewbiochemical pathwaysexist from nonlife tolife, we cannot know for sure how life originated on Earth.[24]
"Forconsciousness, the problem is the jump from thematerialto thesubjective—for example, from firingneuronsto theexperienceofpainor thecolorred. Perhaps some kind of rudimentary consciousness could emerge in a sufficiently complex machine. But how could we tell? How do we establish—as opposed to conjecture—that something is conscious?"[24]Paradoxically, writes Gleiser, it is through our consciousness that we make sense of the world, even if imperfectly. "Can we fully understand something of which we are a part?"[24]
Among all the sciences (i.e.,disciplinesof learning, writ large) there seems to exist an inverse relation betweenprecisionandintuitiveness. The most intuitive of the disciplines, aptly termed the "humanities", relate to common human experience and, even at their most exact, are thrown back on thecomparative method; less intuitive and more precise than the humanities are thesocial sciences; while, at the base of the inverted pyramid of the disciplines,physics(concerned withmattergy– thematterandenergycomprising theuniverse) is, at its deepest, the most precise discipline and at the same time utterly non-intuitive.[g][h]
Theoretical physicist and mathematicianFreeman Dysonexplains that "[s]cience consists offactsandtheories":
"Facts are supposed to be true or false. They are discovered by observers or experimenters. A scientist who claims to have discovered a fact that turns out to be wrong is judged harshly....
"Theories have an entirely different status. They are free creations of the human mind, intended to describe our understanding of nature. Since our understanding is incomplete, theories are provisional. Theories are tools of understanding, and a tool does not need to be precisely true in order to be useful. Theories are supposed to be more-or-less true... A scientist who invents a theory that turns out to be wrong is judged leniently."[26]
Dyson cites a psychologist's description of how theories are born: "We can't live in a state of perpetual doubt, so we make up the best story possible and we live as if the story were true." Dyson writes: "The inventor of a brilliant idea cannot tell whether it is right or wrong." The passionate pursuit of wrong theories is a normal part of the development of science.[27]Dyson cites, afterMario Livio, five famous scientists who made major contributions to the understanding of nature but also believed firmly in a theory that proved wrong.[27]
Charles Darwinexplained theevolution of lifewith histheory of natural selectionof inherited variations, but he believed in a theory of blending inheritance that made the propagation of new variations impossible.[27]He never readGregor Mendel's studies that showed that thelaws of inheritancewould become simple when inheritance was considered as arandomprocess. Though Darwin in 1866 did the same experiment that Mendel had, Darwin did not get comparable results because he failed to appreciate thestatisticalimportance of using very large experimentalsamples. Eventually,Mendelian inheritanceby random variation would, no thanks to Darwin, provide the raw material for Darwinian selection to work on.[28]
William Thomson (Lord Kelvin)discovered basic laws ofenergyandheat, then used these laws to calculate an estimate of theage of the Earththat was too short by a factor of fifty. He based his calculation on the belief that theEarth's mantlewas solid and could transfer heat from the interior to the surface only byconduction. It is now known that the mantle is partly fluid and transfers most of the heat by the far more efficient process ofconvection, which carries heat by a massive circulation of hot rock moving upward and cooler rock moving downward. Kelvin could see the eruptions ofvolcanoesbringing hot liquid from deep underground to the surface; but his skill in calculation blinded him to processes, such asvolcanic eruptions, that could not be calculated.[27]
Linus Paulingdiscovered the chemical structure ofproteinand proposed a completely wrong structure forDNA, which carries hereditary information from parent to offspring. Pauling guessed a wrong structure for DNA because he assumed that a pattern that worked for protein would also work for DNA. He overlooked the gross chemical differences between protein and DNA.Francis CrickandJames Watsonpaid attention to the differences and found the correct structure for DNA that Pauling had missed a year earlier.[27]
AstronomerFred Hoylediscovered the process by which the heavierelementsessential tolifeare created bynuclear reactionsin the cores of massivestars. He then proposed a theory of the history of the universe known assteady-state cosmology, which has theuniverseexisting forever without an initialBig Bang(as Hoyle derisively dubbed it). He held his belief in the steady state long after observations proved that the Big Bang had happened.[27]
Albert Einsteindiscovered the theory of space, time, and gravitation known asgeneral relativity, and then added acosmological constant, later known asdark energy. Subsequently, Einstein withdrew his proposal of dark energy, believing it unnecessary. Long after his death, observations suggested that dark energy really exists, so that Einstein's addition to the theory may have been right; and his withdrawal, wrong.[27]
To Mario Livio's five examples of scientists who blundered, Dyson adds a sixth: himself. Dyson had concluded, on theoretical principles, that what was to become known as theW-particle, a chargedweak boson, could not exist. An experiment conducted atCERN, inGeneva, later proved him wrong. "With hindsight I could see several reasons why my stability argument would not apply to W-particles. [They] are too massive and too short-lived to be a constituent of anything that resembles ordinary matter."[29]
Harvard Universityhistorian of scienceNaomi Oreskespoints out that thetruthof scientific findings can never be assumed to be finally, absolutely settled.[30]The history of science offers many examples of matters that scientists once thought to be settled and which have proven not to be, such as the concepts ofEarthbeing the center of theuniverse, the absolute nature oftimeandspace, the stability ofcontinents, and the cause ofinfectious disease.[30]
Science, writes Oreskes, is not a fixed, immutable set of discoveries but "aprocessof learning and discovery [...]. Science can also be understood as an institution (or better, a set of institutions) that facilitates this work.[30]
It is often asserted that scientific findings are true because scientists use "thescientific method". But, writes Oreskes, "we can never actually agree on what that method is. Some will say it isempiricism:observationand description of the world. Others will say it is theexperimental method: the use of experience and experiment to testhypotheses. (This is cast sometimes as thehypothetico-deductive method, in which the experiment must be framed as a deduction from theory, and sometimes asfalsification, where the point of observation and experiment is to refute theories, not to confirm them.) Recently a prominent scientist claimed the scientific method was to avoid fooling oneself into thinking something is true that is not, and vice versa."[30]
In fact, writes Oreskes, the methods of science have varied between disciplines and across time. "Many scientific practices, particularlystatistical tests of significance, have been developed with the idea of avoiding wishful thinking and self-deception, but that hardly constitutes 'the scientific method.'"[30]
Science, writes Oreskes, "isnotsimple, and neither is thenatural world; therein lies the challenge of science communication. [...] Our efforts to understand and characterize the natural world are just that: efforts. Because we're human, we often fall flat."[30]
"Scientific theories", according to Oreskes, "are not perfect replicas ofreality, but we have good reason to believe that they capture significant elements of it."[30]
Steven Weinberg, 1979Nobel laureate in physics, and ahistorian of science, writes that the core goal of science has always been the same: "to explain the world"; and in reviewing earlier periods of scientific thought, he concludes that only sinceIsaac Newtonhas that goal been pursued more or less correctly. He decries the "intellectual snobbery" thatPlatoandAristotleshowed in their disdain for science's practical applications, and he holdsFrancis BaconandRené Descartesto have been the "most overrated" among the forerunners of modern science (they tried to prescribe rules for conducting science, which "never works").[31]
Weinberg draws parallels between past and present science, as when a scientific theory is "fine-tuned" (adjusted) to make certain quantities equal, without any understanding of why theyshouldbe equal. Such adjusting vitiated the celestial models of Plato's followers, in which different spheres carrying theplanetsandstarswere assumed, with no good reason, to rotate in exact unison. But, Weinberg writes, a similar fine-tuning also besets current efforts to understand the "dark energy" that isspeeding up the expansion of the universe.[32]
Ancient science has been described as having gotten off to a good start, then faltered. The doctrine ofatomism, propounded by thepre-SocraticphilosophersLeucippusandDemocritus, was naturalistic, accounting for the workings of the world by impersonal processes, not by divine volitions. Nevertheless, these pre-Socratics come up short for Weinberg as proto-scientists, in that they apparently never tried to justify their speculations or to test them against evidence.[32]
Weinberg believes that science faltered early on due to Plato's suggestion that scientific truth could be attained by reason alone, disregardingempirical observation, and due to Aristotle's attempt to explain natureteleologically—in terms of ends and purposes. Plato's ideal of attaining knowledge of the world by unaided intellect was "a false goal inspired by mathematics"—one that for centuries "stood in the way of progress that could be based only on careful analysis of careful observation." And it "never was fruitful" to ask, as Aristotle did, "what is the purpose of this or that physical phenomenon."[32]
A scientific field in which theGreekandHellenisticworld did make progress was astronomy. This was partly for practical reasons: the sky had long served as compass, clock, and calendar. Also, the regularity of the movements of heavenly bodies made them simpler to describe than earthly phenomena. But nottoosimple: though the sun, moon and "fixed stars" seemed regular in their celestial circuits, the "wandering stars"—the planets—were puzzling; they seemed to move at variable speeds, and even to reverse direction. Writes Weinberg: "Much of the story of the emergence of modern science deals with the effort, extending over two millennia, to explain the peculiar motions of the planets."[33]
The challenge was to make sense of the apparently irregular wanderings of the planets on the assumption that all heavenly motion is actually circular and uniform in speed. Circular, because Plato held thecircleto be the most perfect and symmetrical form; and therefore circular motion, at uniform speed, was most fitting for celestial bodies. Aristotle agreed with Plato. In Aristotle'scosmos, everything had a "natural" tendency to motion that fulfilled its inner potential. For the cosmos' sublunary part (the region below the Moon), the natural tendency was to move in a straight line: downward, for earthen things (such as rocks) and water; upward, for air and fiery things (such as sparks). But in thecelestialrealm things were not composed of earth, water, air, or fire, but of a "fifth element", or "quintessence," which was perfect and eternal. And its natural motion was uniformly circular. The stars, the Sun, the Moon, and the planets were carried in their orbits by a complicated arrangement of crystalline spheres, all centered around an immobile Earth.[34]
The Platonic-Aristotelian conviction that celestial motions must be circular persisted stubbornly. It was fundamental to the astronomerPtolemy's system, which improved on Aristotle's in conforming to the astronomical data by allowing the planets to move in combinations of circles called "epicycles".[34]
It even survived theCopernican Revolution. Copernicus was conservative in his Platonic reverence for the circle as the heavenly pattern. According to Weinberg, Copernicus was motivated to dethrone the Earth in favor of the Sun as the immobile center of the cosmos largely by aesthetic considerations: he objected to the fact that Ptolemy, though faithful to Plato's requirement that heavenly motion be circular, had departed from Plato's other requirement that it be of uniform speed. By putting the sun at the center—actually, somewhat off-center—Copernicus sought to honor circularity while restoring uniformity. But to make his system fit the observations as well as Ptolemy's system, Copernicus had to introduce still more epicycles. That was a mistake that, writes Weinberg, illustrates a recurrent theme in the history of science: "A simple and beautiful theory that agrees pretty well with observation is often closer to the truth than a complicated ugly theory that agrees better with observation."[34]
The planets, however, do not move in perfect circles but inellipses. It wasJohannes Kepler, about a century after Copernicus, who reluctantly (for he too had Platonic affinities) realized this. Thanks to his examination of the meticulous observations compiled by astronomerTycho Brahe, Kepler "was the first to understand the nature of the departures from uniform circular motion that had puzzled astronomers since the time of Plato."[34]
The replacement of circles by supposedly ugly ellipses overthrew Plato's notion ofperfectionas the celestial explanatory principle. It also destroyed Aristotle's model of the planets carried in their orbits by crystalline spheres; writes Weinberg, "there is no solid body whose rotation can produce an ellipse." Even if a planet were attached to an ellipsoid crystal, that crystal's rotation would still trace a circle. And if the planets were pursuing their elliptical motion through empty space, then what was holding them in their orbits?[34]
Science had reached the threshold of explaining the world notgeometrically, according to shape, but dynamically, according toforce. It wasIsaac Newtonwho finally crossed that threshold. He was the first to formulate, in his "laws of motion", the concept of force. He demonstrated that Kepler's ellipses were the very orbits the planets would take if they were attracted toward the Sun by a force that decreased as the square of the planet's distance from the Sun. And by comparing the Moon's motion in its orbit around the Earth to the motion of, perhaps, an apple as it falls to the ground, Newton deduced that the forces governing them were quantitatively the same. "This," writes Weinberg, "was the climactic step in the unification of the celestial and terrestrial in science."[34]
By formulating a unified explanation of the behavior of planets, comets, moons, tides, and apples, writes Weinberg, Newton "provided an irresistible model for what aphysical theoryshould be"—a model that fit no preexistingmetaphysicalcriterion. In contrast to Aristotle, who claimed to explain the falling of a rock by appeal to its inner striving, Newton was unconcerned with finding a deeper cause forgravity.[34]He declared in a postscript to the second, 1713 edition of hisPhilosophiæ Naturalis Principia Mathematica: "I have not as yet been able to deduce from phenomena the reason for these properties of gravity, and I do not feign hypotheses. It is enough that gravity really exists and acts according to the laws that we have set forth."[35]What mattered were his mathematically stated principles describing this force, and their ability to account for a vast range of phenomena.[34]
About two centuries later, in 1915, a deeper explanation for Newton's law of gravitation was found inAlbert Einstein'sgeneral theory of relativity: gravity could be explained as a manifestation of the curvature inspacetimeresulting from the presence ofmatterandenergy. Successful theories like Newton's, writes Weinberg, may work for reasons that their creators do not understand—reasons that deeper theories will later reveal. Scientific progress is not a matter of building theories on a foundation ofreason, but of unifying a greater range ofphenomenaunder simpler and more general principles.[34]
Naomi Oreskescautions against making "the classic error of conflatingabsence of evidencewithevidence of absence[emphases added]." She cites two examples of this error that were perpetrated in 2016 and 2023.[36]
In 2016 theCochrane Library, a collection of databases in medicine and other healthcare specialties, published a report that was widely understood to indicate thatflossingone's teeth confers no advantage todental health. But theAmerican Academy of Periodontology, dental professors, deans of dental schools, and clinical dentists all held that clinical practice shows differences in tooth and gum health between those who floss and those who don't.[37]
Oreskes explains that "Cochrane Reviewsbase their findings onrandomized controlled trials(RCTs), often called the 'gold standard' of scientific evidence." But many questions can't be answered well using thismethod, and some can't be answered at all. "Nutritionis a case in point. [Y]ou can't control what people eat, and when you ask... what they have eaten, many people lie. Flossing is similar. One survey concluded that one in four Americans who claimed to floss regularly was fibbing."[38]
In 2023 Cochrane published a report determining that wearingsurgical masks"probably makes little or no difference" in slowing the spread of respiratory illnesses such asCOVID-19.Mass mediareduced this to the claim that masks did not work. The Cochrane Library's editor-in-chief objected to such characterizations of the review; she said the report hadnotconcluded that "masks don't work", but rather that the "results were inconclusive." The report had made clear that its conclusions were about thequalityandcapaciousnessof available evidence, which the authors felt were insufficient to prove that masking was effective. The report's authors were "uncertain whether wearing [surgical] masks or N95/P2 respirators helps to slow the spread of respiratory viruses." Still, they were alsouncertain about that uncertainty[emphasis added], stating that their confidence in their conclusion was "low to moderate."[39]
Subsequently the report's lead author confused the public by stating that mask-wearing "Makes no difference – none of it", and that Covid policies were "evidence-free": he thus perpetrated what Oreskes calls "the [...] error of conflating absence of evidence with evidence of absence." Studies have in fact shown that U.S. states with mask mandates saw a substantial decline in Covid spread within days of mandate orders being signed; in the period from 31 March to 22 May 2020, more than 200,000 cases were avoided.[40]
Oreskes calls the Cochrane report's neglect of theepidemiologicalevidence – because it didn't meet Cochrane's rigid standard – "methodological fetishism," when scientists "fixate on a preferredmethodologyand dismiss studies that don't follow it."[41]
The term "artificial intelligence" (AI) was coined in 1955 byJohn McCarthywhen he and othercomputer scientistswere planning a workshop and did not want to inviteNorbert Wiener, the brilliant, pugnacious, and increasingly philosophical (rather than practical) author onfeedback mechanismswho had coined the term "cybernetics". The new termartificial intelligence, writesKenneth Cukier, "set in motion decades of semantic squabbles ('Can machines think?') and fueled anxieties over malicious robots... If McCarthy... had chosen a blander phrase—say, 'automation studies'—the concept might not have appealed as much toHollywood[movie] producers and [to] journalists..."[42]SimilarlyNaomi Oreskeshas commented: "[M]achine 'intelligence'... isn't intelligence at all but something more like 'machine capability.'"[43]
As machines have become increasingly capable, specific tasks considered to require "intelligence", such asoptical character recognition, have often been removed from the definition of AI, a phenomenon known as the "AI effect". It has been quipped that "AI is whatever hasn't been done yet."[44][i]
Since 1950, whenAlan Turingproposed what has come to be called the "Turing test," there has been speculation whether machines such as computers can possess intelligence; and, if so,whether intelligent machines could become a threat to human intellectual and scientific ascendancy—or even an existential threat to humanity.[46]John Searlepoints out common confusion about the correct interpretation of computation and information technology. "For example, one routinely reads that in exactly the same sense in whichGarry Kasparov… beatAnatoly Karpovinchess, the computer calledDeep Blueplayed and beat Kasparov.... [T]his claim is [obviously] suspect. In order for Kasparov to play and win, he has to be conscious that he is playing chess, and conscious of a thousand other things... Deep Blue is conscious of none of these things because it is not conscious of anything at all. Why isconsciousnessso important? You cannot literally play chess or do much of anything else cognitive if you are totally disassociated from consciousness."[46]
Searle explains that, "in the literal, real, observer-independent sense in which humans compute, mechanical computers do not compute. They go through a set of transitions in electronic states that we can interpret computationally. The transitions in those electronic states are absolute or observer-independent, butthe computation is observer-relative. The transitions in physical states are just electrical sequences unless some conscious agent can give them a computational interpretation.... There is no psychological reality at all to what is happening in the [computer]."[47]
"[A] digital computer", writes Searle, "is a syntactical machine. It manipulates symbols and does nothing else. For this reason, the project of creating human intelligence by designing a computer program that will pass theTuring Test... is doomed from the start. The appropriately programmed computer has asyntax[rules for constructing or transforming the symbols and words of a language] but nosemantics[comprehension of meaning].... Minds, on the other hand, have mental or semantic content."[48]
Like Searle,Christof Koch, chief scientist and president of theAllen Institute for Brain Science, inSeattle, is doubtful about the possibility of "intelligent" machines attainingconsciousness, because "[e]ven the most sophisticatedbrain simulationsare unlikely to produce consciousfeelings." According to Koch,
Whether machines can becomesentient[is important] forethicalreasons. If computers experience life through their own senses, they cease to be purely a means to an end determined by their usefulness to... humans. Per GNW [theGlobal Neuronal Workspacetheory], they turn from mere objects into subjects... with apoint of view.... Once computers'cognitive abilitiesrival those of humanity, their impulse to push for legal and politicalrightswill become irresistible – the right not to be deleted, not to have their memories wiped clean, not to sufferpainand degradation. The alternative, embodied by IIT [Integrated Information Theory], is that computers will remain only supersophisticated machinery, ghostlike empty shells, devoid of what we value most: the feeling of life itself."[49]
Professor of psychology and neural scienceGary Marcuspoints out a so far insuperable stumbling block to artificial intelligence: an incapacity for reliabledisambiguation. "[V]irtually every sentence [that people generate] isambiguous, often in multiple ways. Our brain is so good at comprehendinglanguagethat we do not usually notice."[50]A prominent example is known as the "pronoun disambiguation problem" ("PDP"): a machine has no way of determining to whom or what apronounin a sentence—such as "he", "she" or "it"—refers.[51]
Marcus has described currentlarge language modelsas "approximations to [...] language use rather than language understanding".[52]
Computer scientistPedro Domingoswrites: "AIs are likeautistic savantsand will remain so for the foreseeable future.... AIs lackcommon senseand can easily make errors that a human never would... They are also liable to take our instructions too literally, giving us precisely what we asked for instead of what we actually wanted.[53]
Kai-Fu Lee, aBeijing-basedventure capitalist,artificial-intelligence(AI) expert with aPh.D.incomputer sciencefromCarnegie Mellon University, and author of the 2018 book,AI Superpowers: China, Silicon Valley, and the New World Order,[54]emphasized in a 2018PBSAmanpourinterview withHari SreenivasanthatAI, with all its capabilities, will never be capable ofcreativityorempathy.[55]Bill Gates, interviewed in 2025 byWalter IsaacsononAmanpour and Company, similarly said that artificial intelligence possesses nosentienceand is incapable of human feeling or understanding.[56]
Paul Scharre writes inForeign Affairsthat "Today's AI technologies are powerful but unreliable."[57][j]George Dyson, historian of computing, writes (in what might be called "Dyson's Law") that "Any system simple enough to be understandable will not be complicated enough to behave intelligently, while any system complicated enough to behave intelligently will be too complicated to understand."[59]Computer scientistAlex Pentlandwrites: "CurrentAI machine-learningalgorithmsare, at their core, dead simple stupid. They work, but they work by brute force."[60]
"Artificial intelligence" is synonymous with "machine intelligence." The more perfectly adapted an AI program is to a given task, the less applicable it will be to other specific tasks. An abstracted, AIgeneral intelligenceis a remote prospect, if feasible at all.Melanie Mitchellnotes that an AI program calledAlphaGobested one of the world's bestGoplayers, but that its "intelligence" is nontransferable: it cannot "think" about anything except Go. Mitchell writes: "We humans tend to overestimate AI advances and underestimate the complexity of our own intelligence."[61]Writes Paul Taylor: "Perhaps there is a limit to what a computer can do without knowing that it is manipulating imperfect representations of an external reality."[62]
Humankind may not be able to outsource, to machines, its creative efforts in the sciences, technology, and culture.
Gary Marcuscautions against being taken in by deceptive claims aboutartificial general intelligencecapabilities that are put out inpress releasesby self-interested companies which tell the press and public "only what the companies want us to know."[63]Marcus writes:
Althoughdeep learninghas advanced the ability of machines torecognize patterns in data, it has three major flaws. The patterns that it learns are, ironically, superficial notconceptual; the results it creates are hard tointerpret; and the results are difficult to use in the context of other processes, such asmemoryandreasoning. AsHarvard Universitycomputer scientistLes Valiantnoted, "The central challenge [going forward] is to unify the formulation of...learningand reasoning."[64]
James Gleickwrites: "Agencyis what distinguishes us from machines. For biological creatures,reasonandpurposecome from acting in the world and experiencing the consequences. Artificial intelligences – disembodied, strangers to blood, sweat, and tears – have no occasion for that."[65]
A central concern for science and scholarship is thereliabilityandreproducibilityof their findings. Of all fields of study, none is capable of such precision asphysics. But even there the results of studies, observations, andexperimentscannot be considered absolutely certain and must be treatedprobabilistically; hence,statistically.[66]
In 1925 British geneticist and statisticianRonald FisherpublishedStatistical Methods for Research Workers, which established him as the father of modern statistics. He proposed a statistical test that summarized the compatibility of data with a given proposed model and produced a "pvalue". He counselled pursuing results withpvalues below 0.05 and not wasting time on results above that. Thus arose the idea that apvalue less than 0.05 constitutes "statistical significance" – a mathematical definition of "significant" results.[67]
The use ofpvalues, ever since, to determine the statistical significance of experimental results has contributed to an illusion ofcertaintyand toreproducibility crisesin manyscientific fields,[68]especially inexperimental economics,biomedical research, andpsychology.[69]
Every statistical model relies on a set of assumptions about how data are collected and analyzed and about how researchers decide to present their results. These results almost always center onnull-hypothesissignificance testing, which produces apvalue. Such testing does not address the truth head-on but obliquely: significance testing is meant to indicate only whether a given line of research is worth pursuing further. It does not say how likely the hypothesis is to be true, but instead addresses an alternative question: if the hypothesis were false, how unlikely would the data be? The importance of "statistical significance", reflected in thepvalue, can be exaggerated or overemphasized – something that readily occurs with small samples. That has causedreplication crises.[66]
Some scientists have advocated "redefining statistical significance", shifting its threshold from 0.05 to 0.005 for claims of new discoveries. Others say such redefining does no good because the real problem is the very existence of a threshold.[70]
Some scientists prefer to useBayesian methods, a more direct statistical approach which takes initial beliefs, adds in new evidence, and updates the beliefs. Another alternative procedure is to use thesurprisal, a mathematical quantity that adjustpvalues to produce bits – as in computer bits – of information; in that perspective, 0.05 is a weak standard.[70]
When Ronald Fisher embraced the concept of "significance" in the early 20th century, it meant "signifying" but not "important". Statistical "significance" has, since, acquired am excessive connotation of confidence in the validity of the experimental results. Statistician Andrew Gelman says, "The original sin is people wantingcertaintywhen it's not appropriate." "Ultimately", writes Lydia Denworth, "a successful theory is one that stands up repeatedly to decades of scrutiny."[70]
Increasingly, attention is being given to the principles ofopen science, such as publishing more detailed research protocols and requiring authors to follow prespecified analysis plans and to report when they deviate from them.[70]
Fifty years beforeFlorian Znanieckipublished his 1923 paper proposing the creation of an empirical field of study to study the field ofscience, Aleksander Głowacki (better known by his pen name,Bolesław Prus) had made the same proposal. In an 1873 public lecture "On Discoveries and Inventions",[71]Prus said:
Until now there has been no science that describes the means for making discoveries and inventions, and the generality of people, as well as many men of learning, believe that there never will be. This is an error. Someday a science of making discoveries and inventions will exist and will render services. It will arise not all at once; first only its general outline will appear, which subsequent researchers will correct and elaborate, and which still later researchers will apply to individual branches of knowledge.[72]
Prus defines"discovery"as "the finding out of a thing that has existed and exists in nature, but which was previously unknown to people";[73]and"invention"as "the making of a thing that has not previously existed, and which nature itself cannot make."[74]
He illustrates the concept of "discovery":
Until 400 years ago, people thought that the Earth comprised just three parts: Europe, Asia, and Africa; it was only in 1492 that the Genoese,Christopher Columbus, sailed out from Europe into the Atlantic Ocean and, proceeding ever westward, after [10 weeks] reached a part of the world that Europeans had never known. In that new land he found copper-colored people who went about naked, and he found plants and animals different from those in Europe; in short, he had discovered a new part of the world that others would later name "America." We say that Columbus haddiscoveredAmerica, because America had already long existed on Earth.[75]
Prus illustrates the concept of "invention":
[As late as] 50 years ago,locomotiveswere unknown, and no one knew how to build one; it was only in 1828 that the English engineer Stephenson built the first locomotive and set it in motion. So we say that Stephensoninventedthe locomotive, because this machine had not previously existed and could not by itself have come into being in nature; it could only have been made by man.[74]
According to Prus, "inventions and discoveries are natural phenomena and, as such, are subject to certain laws." Those are the laws of "gradualness", "dependence", and "combination".[76]
1.The law of gradualness.No discovery or invention arises at once perfected, but is perfected gradually; likewise, no invention or discovery is the work of a single individual but of many individuals, each adding his little contribution.[77]
2.The law of dependence.An invention or discovery is conditional on the prior existence of certain known discoveries and inventions. ...If the rings ofSaturncan [only] be seen through telescopes, then the telescope had to have been invented before the rings could have been seen. [...][78]
3.The law of combination.Any new discovery or invention is a combination of earlier discoveries and inventions, or rests on them. When I study a new mineral, I inspect it, I smell it, I taste it ... I combine the mineral with a balance and with fire...in this way I learn ever more of its properties.[79][k]
Each of Prus' three "laws" entails important corollaries. The law of gradualness implies the following:[81]
a) Since every discovery and invention requires perfecting, let us not pride ourselves only on discovering or inventing somethingcompletely new, but let us also work to improve or get to know more exactly things that are already known and already exist. [...][81]b) The same law of gradualness demonstrates the necessity ofexpert training. Who can perfect a watch, if not a watchmaker with a good comprehensive knowledge of his métier? Who can discover new characteristics of an animal, if not a naturalist?[81]
From the law of dependence flow the following corollaries:[81]
a) No invention or discovery, even one seemingly without value, should be dismissed, because that particular trifle may later prove very useful. There would seem to be no simpler invention than the needle, yet the clothing of millions of people, and the livelihoods of millions of seamstresses, depend on the needle's existence. Even today's beautiful sewing machine would not exist, had the needle not long ago been invented.[82]b) The law of dependence teaches us that what cannot be done today, might be done later. People give much thought to the construction of a flying machine that could carry many persons and parcels. The inventing of such a machine will depend, among other things, on inventing a material that is, say, as light as paper and as sturdy and fire-resistant as steel.[83]
Finally, Prus' corollaries to his law of combination:[83]
a) Anyone who wants to be a successful inventor, needs to know a great many things—in the most diverse fields. For if a new invention is a combination of earlier inventions, then the inventor's mind is the ground on which, for the first time, various seemingly unrelated things combine. Example: The steam engine combines the kettle for cookingRumford's Soup, the pump, and the spinning wheel.[83]
[...] What is the connection among zinc, copper, sulfuric acid, a magnet, a clock mechanism, and an urgent message? All these had to come together in the mind of the inventor of the telegraph... [...][84]
The greater the number of inventions that come into being, the more things a new inventor must know; the first, earliest and simplest inventions were made by completely uneducated people—but today's inventions, particularly scientific ones, are products of the most highly educated minds. [...][85]
b) A second corollary concerns societies that wish to have inventors. I said that a new invention is created by combining the most diverse objects; let us see where this takes us.[85]
Suppose I want to make an invention, and someone tells me: Take 100 different objects and bring them into contact with one another, first two at a time, then three at a time, finally four at a time, and you will arrive at a new invention. Imagine that I take a burning candle, charcoal, water, paper, zinc, sugar, sulfuric acid, and so on, 100 objects in all, and combine them with one another, that is, bring into contact first two at a time: charcoal with flame, water with flame, sugar with flame, zinc with flame, sugar with water, etc. Each time, I shall see a phenomenon: thus, in fire, sugar will melt, charcoal will burn, zinc will heat up, and so on. Now I will bring into contact three objects at a time, for example, sugar, zinc and flame; charcoal, sugar and flame; sulfuric acid, zinc and water; etc., and again I shall experience phenomena. Finally I bring into contact four objects at a time, for example, sugar, zinc, charcoal, and sulfuric acid. Ostensibly this is a very simple method, because in this fashion I could make not merely one but a dozen inventions. But will such an effort not exceed my capability? It certainly will. A hundred objects, combined in twos, threes and fours, will make over4 millioncombinations; so if I made 100 combinations a day, it would take me over 110 years to exhaust them all![86]
But if by myself I am not up to the task, a sizable group of people will be. If 1,000 of us came together to produce the combinations that I have described, then any one person would only have to carry out slightly more than 4,000 combinations. If each of us performed just 10 combinations a day, together we would finish them all in less than a year and a half: 1,000 people would make an invention which a single man would have to spend more than 110 years to make…[87][l]
The conclusion is quite clear: a society that wants to win renown with its discoveries and inventions has to have a great many persons working in every branch of knowledge. One or a few men of learning and genius mean nothing today, or nearly nothing, because everything is now done by large numbers. I would like to offer the following simile: Inventions and discoveries are like a lottery; not every player wins, but from among the many players a fewmustwin. The point is not that John or Paul, because they want to make an invention and because they work for it, shall make an invention; but where thousands want an invention and work for it, the invention must appear, as surely as an unsupported rock must fall to the ground.[87][m]
But, asks Prus, "What force drives [the] toilsome, often frustrated efforts [of the investigators]? What thread will clew these people through hitherto unexplored fields of study?"[88][n]
[T]he answer is very simple: man is driven to efforts, including those of making discoveries and inventions, byneeds; and the thread that guides him isobservation: observation of the works of nature and of man.[88]
I have said that the mainspring of all discoveries and inventions is needs. In fact, is there any work of man that does not satisfy some need? We build railroads because we need rapid transportation; we build clocks because we need to measure time; we build sewing machines because the speed of [unaided] human hands is insufficient. We abandon home and family and depart for distant lands because we are drawn by curiosity to see what lies elsewhere. We forsake the society of people and we spend long hours in exhausting contemplation because we are driven by a hunger for knowledge, by a desire to solve the challenges that are constantly thrown up by the world and by life![88]
Needs never cease; on the contrary, they are always growing. While the pauper thinks about a piece of bread for lunch, the rich man thinks about wine after lunch. The foot traveler dreams of a rudimentary wagon; the railroad passenger demands a heater. The infant is cramped in its cradle; the mature man is cramped in the world. In short, everyone has his needs, and everyone desires to satisfy them, and that desire is an inexhaustible source of new discoveries, new inventions, in short, of all progress.[89]
But needs aregeneral, such as the needs for food, sleep and clothing; andspecial, such as needs for a new steam engine, a new telescope, a new hammer, a new wrench. To understand the former needs, it suffices to be a human being; to understand the latter needs, one must be aspecialist—anexpert worker. Who knows better than a tailor what it is that tailors need, and who better than a tailor knows how to find the right way to satisfy the need?[90]
Now consider how observation can lead man to new ideas; and to that end, as an example, let us imagine how, more or less, clay products came to be invented.[90]
Suppose that somewhere there lived on clayey soil a primitive people who already knew fire. When rain fell on the ground, the clay turned doughy; and if, shortly after the rain, a fire was set on top of the clay, the clay under the fire became fired and hardened. If such an event occurred several times, the people might observe and thereafter remember that fired clay becomes hard like stone and does not soften in water. One of the primitives might also, when walking on wet clay, have impressed deep tracks into it; after the sun had dried the ground and rain had fallen again, the primitives might have observed that water remains in those hollows longer than on the surface. Inspecting the wet clay, the people might have observed that this material can be easily kneaded in one's fingers and accepts various forms.[91]
Some ingenious persons might have started shaping clay into various animal forms [...] etc., including something shaped like a tortoise shell, which was in use at the time. Others, remembering that clay hardens in fire, might have fired the hollowed-out mass, thereby creating the first [clay] bowl.[92]
After that, it was a relatively easy matter to perfect the new invention; someone else could discover clay more suitable for such manufactures; someone else could invent a glaze, and so on, with nature and observation at every step pointing out to man the way to invention. [...][92]
[This example] illustrates how people arrive at various ideas:by closely observing all things and wondering about all things.[92]
Take another example. [S]ometimes, in a pane of glass, we find disks and bubbles, looking through which we see objects more distinctly than with the naked eye. Suppose that an alert person, spotting such a bubble in a pane, took out a piece of glass and showed it to others as a toy. Possibly among them there was a man with weak vision who found that, through the bubble in the pane, he saw better than with the naked eye. Closer investigation showed that bilaterally convex glass strengthens weak vision, and in this way eyeglasses were invented. People may first have cut glass for eyeglasses from glass panes, but in time others began grinding smooth pieces of glass into convex lenses and producing proper eyeglasses.[93]
The art of grinding eyeglasses was known almost 600 years ago. A couple of hundred years later, the children of a certain eyeglass grinder, while playing with lenses, placed one in front of another and found that they could see better through two lenses than through one. They informed their father about this curious occurrence, and he began producing tubes with two magnifying lenses and selling them as a toy. Galileo, the great Italian scientist, on learning of this toy, used it for a different purpose and built the first telescope.[94]
This example, too, shows us that observation leads man by the hand to inventions. This example again demonstrates the truth of gradualness in the development of inventions, but above all also the fact that education amplifies man's inventiveness. A simple lens-grinder formed two magnifying glasses into a toy—while Galileo, one of the most learned men of his time, made a telescope. As Galileo's mind was superior to the craftsman's mind, so the invention of the telescope was superior to the invention of a toy.[94][...]
The three laws [that have been discussed here] are immensely important and do not apply only to discoveries and inventions, but they pervade all of nature. An oak does not immediately become an oak but begins as an acorn, then becomes a seedling, later a little tree, and finally a mighty oak: we see here the law of gradualness. A seed that has been sown will not germinate until it finds sufficient heat, water, soil and air: here we see the law of dependence. Finally, no animal or plant, or even stone, is something homogeneous and simple but is composed of various organs: here we see the law of combination.[95]
Prus holds that, over time, the multiplication of discoveries and inventions has improved the quality of people's lives and has expanded their knowledge. "This gradual advance of civilized societies, this constant growth in knowledge of the objects that exist in nature, this constant increase in the number of tools and useful materials, is termedprogress, or thegrowth of civilization."[96]Conversely, Prus warns, "societies and people that do not make inventions or know how to use them, lead miserable lives and ultimately perish."[97][o]
A fundamental feature of the scientific enterprise isreproducibilityof results. "For decades", writes Shannon Palus, "it has been... anopen secretthat a [considerable part] of the literature in some fields is plain wrong." This effectively sabotages the scientific enterprise and costs the world many billions of dollars annually in wasted resources. Militating against reproducibility is scientists' reluctance to share techniques, for fear of forfeiting one's advantage to other scientists. Also,scientific journalsandtenurecommittees tend to prize impressive new results rather than gradual advances that systematically build on existing literature. Scientists who quietly fact-check others' work or spend extra time ensuring that their ownprotocolsare easy for other researchers to understand, gain little for themselves.[98]
With a view to improving reproducibility of scientific results, it has been suggested that research-funding agencies finance only projects that include a plan for making their worktransparent. In 2016 the U.S.National Institutes of Healthintroduced new application instructions and review questions to encourage scientists to improve reproducibility. The NIH requests more information on how the study builds on previous work, and a list of variables that could affect the study, such as the sex of animal subjects—a previously overlooked factor that led many studies to describe phenomena found in male animals as universal.[99]
Likewise, the questions that a funder can ask in advance could be asked by journals and reviewers. One solution is "registered reports", a preregistration of studies whereby a scientist submits, for publication, research analysis and design plans before actually doing the study.Peer reviewersthen evaluate themethodology, and the journal promises to print the results, no matter what they are. In order to prevent over-reliance on preregistered studies—which could encourage safer, less venturesome research, thus over-correcting the problem—the preregistered-studies model could be operated in tandem with the traditional results-focused model, which may sometimes be more friendly toserendipitousdiscoveries.[99]
The "replication crisis" is compounded by a finding, published in a study summarized in 2021 by historian of scienceNaomi Oreskes, that nonreplicable studies are cited oftener than replicable ones: in other words, that bad science seems to get more attention than good science. If a substantial proportion of science is unreplicable, it will not provide a valid basis for decision-making and may delay the use of science for developing new medicines and technologies. It may also undermine the public's trust, making it harder to get peoplevaccinatedor act againstclimate change.[100]
The study tracked papers – in psychology journals, economics journals, and inScienceandNature– with documented failures of replication. The unreplicable papers were cited more than average, even after news of their unreplicability had been published.[100]
"These results," writes Oreskes, "parallel those of a 2018 study. An analysis of 126,000 rumor cascades onTwittershowed that false news spread faster and reached more people than verified true claims. [I]t was people, not [ro]bots, who were responsible for the disproportionate spread of falsehoods online."[100]
A 2016Scientific Americanreport highlights the role ofrediscoveryin science.Indiana University Bloomingtonresearchers combed through 22 million scientific papers published over the previous century and found dozens of "Sleeping Beauties"—studies that lay dormant for years before getting noticed.[101]The top finds, which languished longest and later received the most intense attention from scientists, came from the fields of chemistry, physics, and statistics. The dormant findings were wakened by scientists from other disciplines, such asmedicine, in search of fresh insights, and by the ability to test once-theoretical postulations.[101]Sleeping Beauties will likely become even more common in the future because of increasing accessibility of scientific literature.[101]TheScientific Americanreport lists the top 15 Sleeping Beauties: 7 inchemistry, 5 inphysics, 2 instatistics, and 1 inmetallurgy.[101]Examples include:
Herbert Freundlich's "Concerning Adsorption in Solutions" (1906), the first mathematical model ofadsorption, whenatomsormoleculesadhere to a surface. Today bothenvironmental remediationanddecontaminationin industrial settings rely heavily on adsorption.[101]
A. Einstein,B. PodolskyandN. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"Physical Review, vol. 47 (May 15, 1935), pp. 777–780. This famousthought experimentinquantum physics—now known as theEPR paradox, after the authors' surname initials—was discussedtheoreticallywhen it first came out. It was not until the 1970s thatphysicshad the experimental means to testquantum entanglement.[101]
J[ohn] Turkevich, P. C. Stevenson, J. Hillier, "A Study of the Nucleation and Growth Processes in the Synthesis of Colloidal Gold",Discuss. Faraday. Soc., 1951, 11, pp. 55–75, explains how to suspendgold nanoparticlesin liquid. It owes its awakening tomedicine, which now employs gold nanoparticles to detecttumorsand deliver drugs.[101]
William S. Hummers and Richard E Offeman, "Preparation of Graphitic Oxide",Journal of the American Chemical Society, vol. 80, no. 6 (March 20, 1958), p. 1339, introducedHummers' Method, a technique for makinggraphite oxide. Recent interest ingraphene's potential has brought the 1958 paper to attention. Graphite oxide could serve as a reliable intermediate for the 2-D material.[101]
Historians and sociologists have remarked the occurrence, inscience, of "multiple independent discovery". SociologistRobert K. Mertondefined such "multiples" as instances in which similardiscoveriesare made by scientists working independently of each other.[102]"Sometimes the discoveries are simultaneous or almost so; sometimes a scientist will make a new discovery which, unknown to him, somebody else has made years before."[103][104]Commonly cited examples of multiple independent discovery are the 17th-century independent formulation ofcalculusbyIsaac Newton,Gottfried Wilhelm Leibniz, and others;[105]the 18th-century independent discovery ofoxygenbyCarl Wilhelm Scheele,Joseph Priestley,Antoine Lavoisier, and others; and the 19th-century independent formulation of thetheory of evolutionofspeciesbyCharles DarwinandAlfred Russel Wallace.[106]
Merton contrasted a "multiple" with a "singleton" — a discovery that has been made uniquely by a single scientist or group of scientists working together.[107]He believed that it is multiple discoveries, rather than unique ones, that represent thecommonpattern in science.[108]
Multiple discoveries in the history of science provide evidence forevolutionarymodels of science and technology, such asmemetics(the study of self-replicating units of culture),evolutionary epistemology(which applies the concepts ofbiological evolutionto study of the growth of human knowledge), andcultural selection theory(which studies sociological and cultural evolution in a Darwinian manner). Arecombinant-DNA-inspired "paradigmof paradigms", describing a mechanism of "recombinant conceptualization", predicates that a newconceptarises through the crossing of pre-existing concepts andfacts. This is what is meant when one says that a scientist, scholar, or artist has been "influenced by" another —etymologically, that a concept of the latter's has "flowed into" the mind of the former.[109]
The phenomenon of multiple independent discoveries and inventions can be viewed as a consequence ofBolesław Prus' three laws of gradualness, dependence, and combination (see "Discoveries and inventions", above). The first two laws may, in turn, be seen as corollaries to the third law, since the laws of gradualness and dependence imply the impossibility of certain scientific or technological advances pending the availability of certain theories, facts, or technologies that must be combined to produce a given scientific or technological advance.
Technology– the application of discoveries to practical matters – showed a remarkable acceleration in what economistRobert J. Gordonhas identified as "the special century" that spanned the period up to 1970. By then, he writes, all the key technologies of modern life were in place:sanitation,electricity,mechanized agriculture,highways,air travel,telecommunications, and the like. The one signature technology of the 21st century has been theiPhone. Meanwhile, a long list of much-publicized potential major technologies remain in theprototypephase, includingself-driving cars,flying cars,augmented-reality glasses,gene therapy, andnuclear fusion. An urgent goal for the 21st century, writes Gordon, is to undo some of the consequences of the last great technology boom by developing affordablezero- and negative-emissions technologies.[110]
Technologyis the sum oftechniques,skills,methods, andprocessesused in the production ofgoodsorservicesor in the accomplishment of objectives, such asscientific investigation. Paradoxically, technology, so conceived, has sometimes been noted to take primacy over the ends themselves – even to their detriment. Laura Grego and David Wright, writing in 2019 inScientific American, observe that "Current U.S.missile defenseplans are being driven largely bytechnology,politicsandfear. Missile defenses will not allow us to escape our vulnerability tonuclear weapons. Instead large-scale developments will create barriers to taking real steps towardreducing nuclear risks—by blocking further cuts innuclear arsenalsand potentially spurring new deployments."[111]
Yale Universityphysicist-astronomerPriyamvada Natarajan, writing of the virtually-simultaneous 1846 discovery of the planetNeptunebyUrbain Le VerrierandJohn Couch Adams(after other astronomers, as early asGalileo Galileiin 1612, had unwittinglyobservedthe planet), comments:
The episode is but one of many that proves science is not a dispassionate, neutral, and objective endeavor but rather one in which the violent clash of ideas and personal ambitions often combines withserendipityto propel new discoveries.[112]
A practical question concerns the traits that enable some individuals to achieve extraordinary results in their fields of work—and how suchcreativitycan be fostered.Melissa Schilling, a student ofinnovationstrategy, has identified some traits shared by eight major innovators innatural scienceortechnology:Benjamin Franklin(1706–90),Thomas Edison(1847–1931),Nikola Tesla(1856–1943),Maria Skłodowska Curie(1867–1934),Dean Kamen(born 1951),Steve Jobs(1955–2011),Albert Einstein(1879–1955), andElon Musk(born 1971).[113]
Schilling chose innovators in natural science and technology rather than in other fields because she found much more consensus about important contributions to natural science and technology than, for example, to art or music.[114]She further limited the set to individuals associated withmultipleinnovations. "When an individual is associated with only a single major invention, it is much harder to know whether the invention was caused by the inventor's personal characteristics or by simply being at the right place at the right time."[115]
The eight individuals were all extremely intelligent, but "that is not enough to make someone a serial breakthrough innovator."[113]Nearly all these innovators showed very high levels ofsocial detachment, or separateness (a notable exception being Benjamin Franklin).[116]"Their isolation meant that they were less exposed to dominant ideas and norms, and their sense of not belonging meant that even when exposed to dominant ideas and norms, they were often less inclined to adopt them."[117]From an early age, they had all shown extreme faith in their ability to overcome obstacles—whatpsychologycalls "self-efficacy".[117]
"Most [of them, writes Schilling] were driven byidealism, a superordinate goal that was more important than their own comfort, reputation, or families. Nikola Tesla wanted to free mankind from labor through unlimited freeenergyand to achieve internationalpeacethrough globalcommunication. Elon Musk wants to solve the world's energy problems and colonizeMars. Benjamin Franklin was seeking greater social harmony and productivity through the ideals ofegalitarianism,tolerance, industriousness, temperance, and charity. Marie Curie had been inspired byPolish Positivism's argument thatPoland, which was under Tsarist Russian rule, could be preserved only through the pursuit of education and technological advance by all Poles—including women."[118]
Most of the innovators also worked hard and tirelessly because they found work extremely rewarding. Some had an extremely high need for achievement. Many also appeared to find workautotelic—rewarding for its own sake.[119]A surprisingly large portion of the breakthrough innovators have beenautodidacts—self-taught persons—and excelled much more outside the classroom than inside.[120]
"Almost all breakthrough innovation," writes Schilling, "starts with an unusual idea or with beliefs that break withconventional wisdom.... However, creative ideas alone are almost never enough. Many people have creative ideas, even brilliant ones. But usually we lack the time, knowledge, money, or motivation to act on those ideas." It is generally hard to get others' help in implementing original ideas because the ideas are often initially hard for others to understand and value. Thus each of Schilling's breakthrough innovators showedextraordinaryeffort and persistence.[121]Even so, writes Schilling, "being at the right place at the right time still matter[ed]."[122]
When Swiss botanistSimon Schwendenerdiscovered in the 1860s thatlichenswere asymbioticpartnership between afungusand analga, his finding at first met with resistance from the scientific community. After his discovery that the fungus—which cannot make its own food—provides the lichen's structure, while the alga's contribution is itsphotosyntheticproduction of food, it was found that in some lichens acyanobacteriumprovides the food—and a handful of lichen species containbothan alga and a cyanobacterium, along with the fungus.[123]
A self-taught naturalist,Trevor Goward, has helped create aparadigm shiftin the study of lichens and perhaps of all life-forms by doing something that people did in pre-scientific times: going out into nature and closely observing. His essays about lichens were largely ignored by most researchers because Goward has no scientific degrees and because some of his radical ideas are not supported by rigorous data.[124]
When Goward toldToby Spribille, who at the time lacked a high-school education, about some of his lichenological ideas, Goward recalls, "He said I was delusional." Ultimately Spribille passed a high-school equivalency examination, obtained a Ph.D. in lichenology at theUniversity of Grazin Austria, and became an assistant professor of the ecology and evolution of symbiosis at theUniversity of Alberta. In July 2016 Spribille and his co-authors published a ground-breaking paper inSciencerevealing that many lichens contain a second fungus.
Spribille credits Goward with having "a huge influence on my thinking. [His essays] gave me license to think about lichens in [an unorthodox way] and freed me to see the patterns I worked out inBryoriawith my co-authors." Even so, "one of the most difficult things was allowing myself to have an open mind to the idea that 150 years of literature may have entirely missed the theoretical possibility that there would be more than one fungal partner in the lichen symbiosis." Spribille says that academia's emphasis on the canon of what others have established as important is inherently limiting.[125]
Contrary to previous studies indicating that higherintelligencemakes for betterleadersin various fields of endeavor, later research suggests that, at a certain point, a higherIQcan be viewed as harmful.[126]Decades ago, psychologistDean Simontonsuggested that brilliant leaders' words may go over people's heads, their solutions could be more complicated to implement, and followers might find it harder to relate to them. At last, in the July 2017Journal of Applied Psychology, he and two colleagues published the results of actual tests of the hypothesis.[126][127]
Studied were 379 men and women business leaders in 30 countries, including the fields of banking, retail, and technology. The managers took IQ tests—an imperfect but robust predictor of performance in many areas—and each was rated on leadership style and effectiveness by an average of 8 co-workers. IQ correlated positively with ratings of leadership effectiveness,strategyformation,vision, and several other characteristics—up to a point. The ratings peaked at an IQ of about 120, which is higher than some 80% of office workers. Beyond that, the ratings declined. The researchers suggested that the ideal IQ could be higher or lower in various fields, depending on whether technical orsocial skillsare more valued in a given work culture.[126]
Psychologist Paul Sackett, not involved in the research, comments: "To me, the right interpretation of the work would be that it highlights a need to understand what high-IQ leaders do that leads to lower perceptions by followers. The wrong interpretation would be,'Don't hire high-IQ leaders.'"[126]The study'slead author, psychologistJohn Antonakis, suggests that leaders should use their intelligence to generate creativemetaphorsthat will persuade and inspire others. "I think the only way a smart person can signal their intelligence appropriately and still connect with the people," says Antonakis, "is to speak incharismaticways."[126]
Academic specializationproduces great benefits for science and technology by focusing effort on discrete disciplines. But excessively narrow specialization can act as a roadblock to productive collaboration between traditional disciplines.
In 2017, inManhattan,James Harris Simons, a noted mathematician and retired founder of one of the world's largesthedge funds, inaugurated theFlatiron Institute, a nonprofit enterprise whose goal is to apply his hedge fund's analytical strategies to projects dedicated to expanding knowledge and helping humanity.[128]He has established computational divisions for research in astrophysics, biology, and quantum physics,[129]and an interdisciplinary division forclimate modellingthat interfaces geology, oceanography, atmospheric science, biology, and climatology.[130]
The latter, fourth Flatiron Institute division was inspired by a 2017 presentation to the institute's leadership byJohn Grotzinger, a "bio-geoscientist" from theCalifornia Institute of Technology, who explained the challenges of climate modelling. Grotzinger was a specialist in historical climate change—specifically, what had caused the greatPermian extinction, during which virtually all species died. To properly assess this cataclysm, one had to understand both the rock record and the ocean's composition, butgeologistsdid not interact much withphysical oceanographers. Grotzinger's own best collaboration had resulted from a fortuitous lunch with an oceanographer. Climate modelling was an intrinsically difficult problem made worse by theinformation silosofacademia. "If you had it all under one umbrella... it could result [much sooner] in a major breakthrough." Simons and his team found Grotzinger's presentation compelling, and the Flatiron Institute decided to establish its fourth and final computational division.[130]
SociologistHarriet Zuckerman, in her 1977 study of natural-scienceNobel laureatesin the United States, was struck by the fact that more than half (48) of the 92 laureates who did their prize-winning research in the U.S. by 1972 had worked either as students, postdoctorates, or junior collaborators under older Nobel laureates. Furthermore, those 48 future laureates had worked under a total of 71 laureate masters.[131][p]
Social viscosity ensures that not every qualified novice scientist attains access to the most productive centers of scientific thought. Nevertheless, writes Zuckerman, "To some extent, students of promise can choose masters with whom to work and masters can choose among the cohorts of students who present themselves for study. This process of bilateral assortative selection is conspicuously at work among the ultra-elite of science. Actual and prospective members of that elite select their scientist parents and therewith their scientist ancestors just as later they select their scientist progeny and therewith their scientist descendants."[133]
Zuckerman writes: "[T]he lines of elite apprentices to elite masters who had themselves been elite apprentices, and so on indefinitely, often reach far back into thehistory of science, long before 1900, when [Alfred] Nobel's will inaugurated what now amounts to the International Academy of Sciences. As an example of the many long historical chains of elite masters and apprentices, consider the German-born English laureateHans Krebs(1953), who traces his scientific lineage [...] back through his master, the 1931 laureateOtto Warburg. Warburg had studied withEmil Fis[c]her[1852–1919], recipient of a prize in 1902 at the age of 50, three years before it was awarded [in 1905] tohisteacher,Adolf von Baeyer[1835–1917], at age 70. This lineage of four Nobel masters and apprentices has its own pre-Nobelian antecedents. Von Baeyer had been the apprentice ofF[riedrich] A[ugust] Kekulé[1829–1896], whose ideas ofstructural formulaerevolutionizedorganic chemistryand who is perhaps best known for the often retold story about his having hit upon the ring structure ofbenzenein a dream (1865). Kekulé himself had been trained by the greatorganic chemistJustus von Liebig(1803–1873), who had studied at theSorbonnewith the masterJ[oseph] L[ouis] Gay-Lussac(1778–1850), himself once apprenticed toClaude Louis Berthollet(1748–1822). Among his many institutional and cognitive accomplishments, Berthollet helped found theÉcole Polytechnique, served as science advisor toNapoleoninEgypt, and, more significant for our purposes here, worked with[Antoine] Lavoisier[1743–1794] to revise the standard system ofchemical nomenclature."[134]
Sociologist Michael P. Farrell has studied close creative groups and writes: "Most of the fragile insights that laid the foundation of a new vision emerged not when the whole group was together, and not when members worked alone, but when they collaborated and repsonded to one another in pairs."[135]François Jacob, who, withJacques Monod, pioneered the study ofgene regulation, notes that by the mid-20th century, most research inmolecular biologywas conducted by twosomes. "Two are better than one for dreaming up theories and constructing models," writes Jacob. "For with two minds working on a problem, ideas fly thicker and faster. They are bounced from partner to partner.... And in the process, illusions are sooner nipped in the bud." As of 2018, in the previous 35 years, some half ofNobel Prizes in Physiology or Medicinehad gone to scientific partnerships.[136]James Somers describes a remarkable partnership betweenGoogle's topsoftware engineers,Jeff DeanandSanjay Ghemawat.[137]
Twosome collaborations have also been prominent in creative endeavors outside thenatural sciencesandtechnology; examples areClaude Monet's andPierre-Auguste Renoir's 1869 joint creation ofImpressionism,Pablo Picasso's andGeorges Braque's six-year collaborative creation ofCubism, andJohn Lennon's andPaul McCartney's collaborations onBeatlessongs. "Everyone", writes James Somers, "falls into creative ruts, but two people rarely do so at the same time."[138]
The same point was made byFrancis Crick, member of a famous scientific duo, Francis Crick andJames Watson, who together discovered the structure of thegeneticmaterial,DNA. At the end of aPBStelevision documentary on James Watson, in a video clipping Crick explains to Watson that their collaboration had been crucial to their discovery because, when one of them was wrong, the other would set him straight.[139]
What has been dubbed "Big Science" emerged from the United States'World War IIManhattan Projectthat produced the world's firstnuclear weapons; and Big Science has since been associated withphysics, which requires massiveparticle accelerators. Inbiology, Big Science debuted in 1990 with theHuman Genome Projectto sequence humanDNA. In 2013neurosciencebecame a Big Science domain when the U.S. announced aBRAIN Initiativeand theEuropean Unionannounced aHuman Brain Project. Major new brain-research initiatives were also announced by Israel, Canada, Australia, New Zealand, Japan, and China.[140]
Earlier successful Big Science projects had habituated politicians,mass media, and the public to view Big Science programs with sometimes uncritical favor.[141]
The U.S.'s BRAIN Initiative was inspired by concern about the spread and cost ofmental disordersand by excitement about new brain-manipulation technologies such asoptogenetics.[142]After some early false starts, the U.S.National Institute of Mental Healthlet the country's brain scientists define the BRAIN Initiative, and this led to an ambitious interdisciplinary program to develop new technological tools to better monitor, measure, and simulate the brain. Competition in research was ensured by the National Institute of Mental Health'speer-review process.[141]
In the European Union, theEuropean Commission's Human Brain Project got off to a rockier start because political and economic considerations obscured questions concerning the feasibility of the Project's initial scientific program, based principally oncomputer modelingofneural circuits. Four years earlier, in 2009, fearing that the European Union would fall further behind the U.S. in computer and other technologies, the European Union had begun creating a competition for Big Science projects, and the initial program for the Human Brain Project seemed a good fit for a European program that might take a lead in advanced and emerging technologies.[142]Only in 2015, after over 800 European neuroscientists threatened to boycott the European-wide collaboration, were changes introduced into the Human Brain Project, supplanting many of the original political and economic considerations with scientific ones.[143]
As of 2019, theEuropean Union'sHuman Brain Projecthad not lived up to its extravagant promise.[144]
Nathan Myhrvold, formerMicrosoftchief technology officer and founder ofMicrosoft Research, argues that the funding ofbasic sciencecannot be left to theprivate sector—that "without government resources, basic science will grind to a halt."[145]He notes thatAlbert Einstein'sgeneral theory of relativity, published in 1915, did not spring full-blown from his brain in a eureka moment; he worked at it for years—finally driven to complete it by a rivalry with mathematicianDavid Hilbert.[145]The history of almost any iconic scientific discovery or technological invention—thelightbulb, thetransistor,DNA, even theInternet—shows that the famous names credited with the breakthrough "were only a few steps ahead of a pack of competitors." Some writers and elected officials have used this phenomenon of "parallel innovation" to argue against public financing of basic research: government, they assert, should leave it to companies to finance the research they need.[145]
Myhrvold writes that such arguments are dangerously wrong: without government support, most basic scientific research will never happen. "This is most clearly true for the kind of pure research that has delivered... great intellectual benefits but no profits, such as the work that brought us theHiggs boson, or the understanding that a supermassiveblack holesits at the center of theMilky Way, or the discovery ofmethaneseas on the surface ofSaturn's moonTitan. Company research laboratories used to do this kind of work: experimental evidence for theBig Bangwas discovered atAT&T'sBell Labs, resulting in aNobel Prize. Now those days are gone."[145]
Even in applied fields such asmaterials scienceandcomputer science, writes Myhrvold, "companies now understand that basic research is a form ofcharity—so they avoid it." Bell Labs scientists created thetransistor, but that invention earned billions forIntelandMicrosoft.Xerox PARCengineers invented the moderngraphical user interface, butAppleand Microsoft profited most.IBMresearchers pioneered the use of giantmagnetoresistanceto boosthard-diskcapacity but soon lost the disk-drive business toSeagateandWestern Digital.[145]
Company researchers now have to focus narrowly on innovations that can quickly bring revenue; otherwise the research budget could not be justified to the company's investors. "Those who believe profit-driven companies will altruistically pay for basic science that has wide-ranging benefits—but mostly to others and not for a generation—are naive.... Ifgovernmentwere to leave it to theprivate sectorto pay forbasic research, mostsciencewould come to a screeching halt. What research survived would be done largely in secret, for fear of handing the next big thing to a rival."[145]
Governmental investment is equally vital in the field of biological research. According toWilliam A. Haseltine, a formerHarvard Medical Schoolprofessor and founder of that university's cancer and HIV / AIDS research departments, early efforts to control theCOVID-19 pandemicwere hampered by governments and industry everywhere having "pulled the plug oncoronavirusresearch funding in 2006 after the firstSARS[...] pandemic faded away and again in the years immediately following theMERS[outbreak, also caused by a coronavirus] when it seemed to be controllable.[146][...] The development of promising anti-SARS and MERS drugs, which might have been active against SARS–CoV-2 [in the Covid-19 pandemic] as well, was left unfinished for lack of money."[147]Haseltine continues:
We learned from theHIVcrisis that it was important to have research pipelines already established. [It was c]ancer research in the 1950s, 1960s and 1970s [that] built a foundation for HIV / Aids studies. [During those decades t]he government [had] responded to public concerns, sharply increasing federal funding of cancer research [...]. These efforts [had] culminated in Congress's approval of PresidentRichard Nixon'sNational Cancer Actin 1971. This [had] built the science we needed to identify and understand HIV in the 1980s, although of course no one knew that payoff was coming.[147]
In the 1980s theReagan administrationdid not want to talk about AIDS or commit much funding to HIV research. [But o]nce the news broke that actorRock Hudsonwas seriously ill with AIDS, [...] $320 million [were added to] the fiscal 1986 budget for AIDS research. [...] I helped [...] design this first congressionally funded AIDS research program withAnthony Fauci, the doctor now leading [the U.S.] fight against COVID-19.[147][...]
[The] tool set for virus and pharmaceutical research has improved enormously in the past 36 years since HIV was discovered. What used to take five or 10 years in the 1980s and 1990s in many cases now can be done in five or 10 months. We can rapidly identify and synthesize chemicals to predict which drugs will be effective. We can docryoelectron microscopyto probe virus structures and simulate molecule-by-molecule interactions in a matter of weeks – something that used to take years. The lesson is to never let down our guard when it comes to funding antiviral research. We would have no hope of beating COVID-19 if it were not for the molecular biology gains we made during earlier virus battles. What we learn this time around will help us [...] during the next pandemic, but we must keep the money coming.[147]
A complementary perspective on the funding of scientific research is given by D.T. Max, writing about theFlatiron Institute, a computational center set up in 2017 inManhattanto provide scientists with mathematical assistance. The Flatiron Institute was established byJames Harris Simons, a mathematician who had used mathematicalalgorithmsto make himself aWall Streetbillionaire. The institute has three computational divisions dedicated respectively toastrophysics,biology, andquantum physics, and is working on a fourth division forclimate modelingthat will involve interfaces ofgeology,oceanography,atmospheric science,biology, andclimatology.[130]
The Flatiron Institute is part of a trend in the sciences toward privately funded research. In the United States,basic sciencehas traditionally been financed by universities or the government, but private institutes are often faster and more focused. Since the 1990s, whenSilicon Valleybegan producing billionaires, private institutes have sprung up across the U.S. In 1997Larry Ellisonlaunched theEllison Medical Foundationto study the biology ofaging. In 2003Paul Allenfounded theAllen Institute for Brain Science. In 2010Eric Schmidtfounded theSchmidt Ocean Institute.[148]
These institutes have done much good, partly by providing alternatives to more rigid systems. Butprivate foundationsalso have liabilities. Wealthy benefactors tend to direct their funding toward their personal enthusiasms. And foundations are not taxed; much of the money that supports them would otherwise have gone to the government.[148]
John P.A. Ioannidis, ofStanford University Medical School, writes that "There is increasing evidence that some of the ways we conduct, evaluate, report and disseminate research are miserably ineffective. A series of papers in 2014 inThe Lancet... estimated that 85 percent of investment inbiomedical researchis wasted. Many other disciplines have similar problems."[149]Ioannidis identifies some science-funding biases that undermine the efficiency of the scientific enterprise, and proposes solutions:
Funding too few scientists: "[M]ajor success [in scientific research] is largely the result of luck, as well as hard work. The investigators currently enjoying huge funding are not necessarily genuine superstars; they may simply be the best connected." Solutions: "Use alotteryto decide whichgrant applicationsto fund (perhaps after they pass a basic review).... Shift... funds from senior people to younger researchers..."[149]
No reward fortransparency: "Many scientific protocols, analysis methods, computational processes and data are opaque. [M]any top findings cannot bereproduced. That is the case for two out of three top psychology papers, one out of three top papers in experimental economics and more than 75 percent of top papers identifying new cancer drug targets. [S]cientists are not rewarded for sharing their techniques." Solutions: "Create better infrastructure for enabling transparency, openness and sharing. Make transparency a prerequisite for funding. [P]referentially hire, promote or tenure... champions of transparency."[149]
No encouragement forreplication: Replication is indispensable to thescientific method. Yet, under pressure to produce newdiscoveries, researchers tend to have little incentive, and much counterincentive, to try replicating results of previous studies. Solutions: "Funding agencies must pay for replication studies. Scientists' advancement should be based not only on their discoveries but also on their replication track record."[149]
No funding for young scientists: "Werner Heisenberg,Albert Einstein,Paul DiracandWolfgang Paulimade their top contributions in their mid-20s." But the average age of biomedical scientists receiving their first substantial grant is 46. The average age for a full professor in the U.S. is 55. Solutions: "A larger proportion of funding should be earmarked for young investigators. Universities should try to shift the aging distribution of their faculty by hiring more young investigators."[149]
Biased funding sources: "Most funding forresearch and developmentin the U.S. comes not from the government but from private, for-profit sources, raising unavoidableconflicts of interestand pressure to deliver results favorable to the sponsor." Solutions: "Restrict or even ban funding that has overt conflicts of interest.Journalsshould not accept research with such conflicts. For less conspicuous conflicts, at a minimum ensure transparent and thorough disclosure."[150][q]
Funding the wrong fields: "Well-funded fields attract more scientists to work for them, which increases their lobbying reach, fueling avicious circle. Some entrenched fields absorb enormous funding even though they have clearly demonstrated limited yield or uncorrectable flaws." Solutions: "Independent, impartial assessment of output is necessary for lavishly funded fields. More funds should be earmarked for new fields and fields that are high risk. Researchers should be encouraged to switch fields, whereas currently they are incentivized to focus in one area."[150]
Not spending enough: The U.S. military budget ($886 billion) is 24 times the budget of theNational Institutes of Health($37 billion). "Investment in science benefits society at large, yet attempts to convince the public often make matters worse when otherwise well-intentioned science leaders promise the impossible, such as promptly eliminating all cancer orAlzheimer's disease." Solutions: "We need to communicate how science funding is used by making the process of science clearer, including the number of scientists it takes to make major accomplishments.... We would also make a more convincing case for science if we could show that we do work hard on improving how we run it."[150]
Rewarding big spenders: "Hiring, promotion andtenuredecisions primarily rest on a researcher's ability to secure high levels of funding. But the expense of a project does not necessarily correlate with its importance. Such reward structures select mostly for politically savvy managers who know how to absorb money." Solutions: "We should reward scientists for high-quality work, reproducibility and social value rather than for securing funding. Excellent research can be done with little to no funding other than protected time. Institutions should provide this time and respect scientists who can do great work without wasting tons of money."[150]
No funding for high-risk ideas: "The pressure that taxpayer money be 'well spent' leads government funders to back projects most likely to pay off with a positive result, even if riskier projects might lead to more important, but less assured, advances. Industry also avoids investing in high-risk projects...Innovationis extremely difficult, if not impossible, to predict..." Solutions: "Fund excellent scientists rather than projects and give them freedom to pursue research avenues as they see fit. Some institutions such asHoward Hughes Medical Institutealready use this model with success." It must be communicated to the public and to policy-makers that science is a cumulative investment, that no one can know in advance which projects will succeed, and that success must be judged on the total agenda, not on a single experiment or result.[150]
Lack of good data: "There is relatively limited evidence about which scientific practices work best. We need more research on research ('meta-research') to understand how to best perform, evaluate, review, disseminate and reward science." Solutions: "We should invest in studying how to get the best science and how to choose and reward the best scientists."[150]
Naomi Oreskes, professor of thehistory of scienceatHarvard University, writes about the desirability of diversity in the backgrounds of scientists.
The history of science is rife with [...] cases ofmisogyny,prejudiceandbias. For centuries biologists promoted false theories of female inferiority, and scientific institutions typically barred women's participation. Historian of science [...]Margaret Rossiterhas documented how, in the mid-19th century, female scientists created their own scientific societies to compensate for their male colleagues' refusal to acknowledge their work.Sharon Bertsch McGraynefilled an entire volume with the stories of women who should have been awarded theNobel Prizefor work that they did in collaboration with male colleagues – or, worse, that they had stolen by them. [...]Racial biashas been at least as pernicious asgender bias; it was scientists, after all, who codified the concept ofraceas a biological category that was not simply descriptive but also hierarchical.[152]
[...][C]ognitive scienceshows that humans are prone to bias, misperception, motivated reasoning and other intellectual pitfalls. Because reasoning is slow and difficult, we rely onheuristics– intellectual shortcuts that often work but sometimes fail spectacularly. (Believing that men are, in general, better than women in math is one tiring example.) [...][152]
[...] Science is a collective effort, and it works best when scientific communities are diverse. [H]eterogeneous communities are more likely than homogeneous ones to be able to identify blind spots and correct them. Science does not correct itself; scientists correct one another through critical interrogation. And that means being willing to interrogate not just claims about the external world but claims about [scientists'] own practices and processes as well.[152]
Claire Pomeroy, president of theLasker Foundation, which is dedicated to advancingmedical research, points out thatwomen scientistscontinue to be subjected todiscriminationin professional advancement.[153]
Though the percentage of doctorates awarded to women inlife sciencesin the United States increased from 15 to 52 percent between 1969 and 2009, only a third of assistant professors and less than a fifth of full professors in biology-related fields in 2009 were women. Women make up only 15 percent of permanent department chairs inmedical schoolsand barely 16 percent of medical-school deans.[153]
The problem is a culture of unconsciousbiasthat leaves many women feeling demoralized and marginalized. In one study, science faculty were given identicalrésumésin which the names and genders of two applicants were interchanged; both maleandfemale faculty judged the male applicant to be more competent and offered him a higher salary.[153]
Unconscious bias also appears as "microassaults" againstwomen scientists: purportedly insignificantsexistjokes and insults that accumulate over the years and undermine confidence and ambition. Writes Claire Pomeroy: "Each time it is assumed that the only woman in the lab group will play the role of recording secretary, each time a research plan becomes finalized in the men's lavatory between conference sessions, each time a woman is not invited to go out for a beer after the plenary lecture to talk shop, the damage is reinforced."[153]
"When I speak to groups of women scientists," writes Pomeroy, "I often ask them if they have ever been in a meeting where they made a recommendation, had it ignored, and then heard a man receive praise and support for making the same point a few minutes later. Each time the majority of women in the audience raise their hands. Microassaults are especially damaging when they come from ahigh-schoolscience teacher, collegementor, university dean or a member of the scientific elite who has been awarded a prestigious prize—the very people who should be inspiring and supporting the next generation of scientists."[153]
Sexual harassmentis more prevalent inacademiathan in any other social sector except themilitary. A June 2018 report by theNational Academies of Sciences, Engineering, and Medicinestates that sexual harassment hurts individuals, diminishes the pool of scientific talent, and ultimately damages the integrity of science.[154]
Paula Johnson, co-chair of the committee that drew up the report, describes some measures for preventing sexual harassment in science. One would be to replace trainees' individualmentoringwith group mentoring, and to uncouple the mentoring relationship from the trainee's financial dependence on the mentor. Another way would be to prohibit the use ofconfidentiality agreementsin connection with harassment cases.[154]
A novel approach to the reporting of sexual harassment, dubbedCallisto, that has been adopted by some institutions of higher education, lets aggrieved persons record experiences of sexual harassment, date-stamped, without actually formally reporting them. This program lets people see if others have recorded experiences of harassment from the same individual, and share information anonymously.[154]
PsychologistAndrei Cimpian andphilosophyprofessorSarah-Jane Lesliehave proposed a theory to explain why American women andAfrican-Americansare often subtly deterred from seeking to enter certain academic fields by a misplaced emphasis ongenius.[155]Cimpian and Leslie had noticed that their respective fields are similar in their substance but hold different views on what is important for success. Much more than psychologists, philosophers value a certainkind of person: the "brilliant superstar" with an exceptional mind. Psychologists are more likely to believe that the leading lights in psychology grew to achieve their positions through hard work and experience.[156]In 2015, women accounted for less than 30% of doctorates granted in philosophy; African-Americans made up only 1% of philosophy Ph.D.s. Psychology, on the other hand, has been successful in attracting women (72% of 2015 psychology Ph.D.s) and African-Americans (6% of psychology Ph.D.s).[157]
An early insight into these disparities was provided to Cimpian and Leslie by the work of psychologistCarol Dweck. She and her colleagues had shown that a person's beliefs aboutabilitymatter a great deal for that person's ultimate success. A person who sees talent as a stable trait is motivated to "show off this aptitude" and to avoid makingmistakes. By contrast, a person who adopts a "growthmindset" sees his or her current capacity as a work in progress: for such a person, mistakes are not an indictment but a valuable signal highlighting which of their skills are in need of work.[158]Cimpian and Leslie and their collaborators tested the hypothesis that attitudes, about "genius" and about the unacceptability of making mistakes, within various academic fields may account for the relative attractiveness of those fields for American women and African-Americans. They did so by contacting academic professionals from a wide range of disciplines and asking them whether they thought that some form of exceptional intellectual talent was required for success in their field. The answers received from almost 2,000 academics in 30 fields matched the distribution of Ph.D.s in the way that Cimpian and Leslie had expected: fields that placed more value on brilliance also conferred fewer Ph.D.s on women and African-Americans. The proportion of women and African-American Ph.D.s in psychology, for example, was higher than the parallel proportions for philosophy, mathematics, or physics.[159]
Further investigation showed that non-academics share similar ideas of which fields require brilliance. Exposure to these ideas at home or school could discourage young members ofstereotypedgroups from pursuing certain careers, such as those in the natural sciences or engineering. To explore this, Cimpian and Leslie asked hundreds of five-, six-, and seven-year-old boys and girls questions that measured whether they associated being "really, really smart" (i.e., "brilliant") with their sex. The results, published in January 2017 inScience, were consistent with scientific literature on the early acquisition of sex stereotypes. Five-year-old boys and girls showed no difference in their self-assessment; but by age six, girls were less likely to think that girls are "really, really smart." The authors next introduced another group of five-, six-, and seven-year-olds to unfamiliar gamelike activities that the authors described as being "for children who are really, really smart." Comparison of boys' and girls' interest in these activities at each age showed no sex difference at age five but significantly greater interest from boys at ages six and seven—exactly the ages when stereotypes emerge.[160]
Cimpian and Leslie conclude that, "Given current societal stereotypes, messages that portray [genius or brilliance] as singularly necessary [for academic success] may needlessly discourage talented members of stereotyped groups."[160]
Largely as a result of his growing popularity, astronomer and science popularizerCarl Sagan, creator of the 1980PBSTVCosmosseries, came to be ridiculed by scientist peers and failed to receive tenure atHarvard Universityin the 1960s and membership in theNational Academy of Sciencesin the 1990s. Theeponymous"Sagan effect" persists: as a group, scientists still discourage individual investigators from engaging with the public unless they are already well-established senior researchers.[161][162]
The operation of the Sagan effect deprives society of the full range of expertise needed to make informed decisions about complex questions, includinggenetic engineering,climate change, andenergyalternatives. Fewer scientific voices mean fewer arguments to counterantiscienceorpseudoscientificdiscussion. The Sagan effect also creates the false impression that science is the domain of older white men (who dominate the senior ranks), thereby tending to discourage women and minorities from considering science careers.[161]
A number of factors contribute to the Sagan effect's durability. At the height of theScientific Revolutionin the 17th century, many researchers emulated the example ofIsaac Newton, who dedicated himself to physics and mathematics and never married. These scientists were viewed as pure seekers of truth who were not distracted by more mundane concerns. Similarly, today anything that takes scientists away from their research, such as having a hobby or taking part in public debates, can undermine their credibility as researchers.[163]
Another, more prosaic factor in the Sagan effect's persistence may be professionaljealousy.[163]
However, there appear to be some signs that engaging with the rest of society is becoming less hazardous to a career in science. So many people have social-media accounts now that becoming a public figure is not as unusual for scientists as previously. Moreover, as traditional funding sources stagnate, going public sometimes leads to new, unconventional funding streams. A few institutions such asEmory Universityand theMassachusetts Institute of Technologymay have begun to appreciate outreach as an area of academic activity, in addition to the traditional roles of research, teaching, and administration. Exceptional among federal funding agencies, theNational Science Foundationnow officially favors popularization.[164][162]
Likeinfectious diseases, ideas inacademiaare contagious. But why some ideas gain great currency while equally good ones remain in relative obscurity had been unclear. A team ofcomputer scientistshas used anepidemiological modelto simulate how ideas move from one academic institution to another. The model-based findings, published in October 2018, show that ideas originating at prestigious institutions cause bigger "epidemics" than equally good ideas from less prominent places. The finding reveals a big weakness in how science is done. Many highly trained people with good ideas do not obtain posts at the most prestigious institutions; much good work published by workers at less prestigious places is overlooked by other scientists and scholars because they are not paying attention.[165]
Naomi Oreskesremarks on another drawback to deprecatingpublic universitiesin favor ofIvy Leagueschools: "In 1970 most jobs did not require a college degree. Today nearly all well-paying ones do. With the rise ofartificial intelligenceand the continuedoutsourcingof low-skilled and de-skilled jobs overseas, that trend most likely will accelerate. Those who care aboutequityofopportunityshould pay less attention to the lucky few who get intoHarvardor other highly selective private schools and more to public education, because for most Americans, the road to opportunity runs through public schools."[166]
Resistance, among some of the public, to acceptingvaccinationand the reality ofclimate changemay be traceable partly to several decades of partisan attacks on government, leading to distrust of government science and then of science generally.[167]
Many scientists themselves have been loth to involve themselves in public policy debates for fear of losing credibility: they worry that if they participate in public debate on a contested question, they will be viewed as biased and discounted as partisan. However, studies show that most people want to hear from scientists on matters within their areas of expertise. Research also suggests that scientists can feel comfortable offering policy advice within their fields. "Theozonestory", writesNaomi Oreskes, "is a case in point: no one knew better than ozone scientists about the cause of the dangerous hole and therefore what needed to be done to fix it."[168]
Oreskes, however, identifies a factor that does "turn off" the public: scientists' frequent use ofjargon– of expressions that tend to be misinterpreted by, or incomprehensible to, laypersons.[167]
Inclimatologicalparlance, "positive feedback" refers to amplifyingfeedback loops, such as the ice-albedofeedback. ("Albedo", another piece of jargon, simply means "reflectivity".) The positive loop in question develops whenglobal warmingcausesArctic iceto melt, exposing water that is darker and reflects less of the sun's warming rays, leading to more warming, which leads to more melting... and so on. In climatology, such positive feedback is a bad thing; but for most laypersons, "it conjures reassuring images, such as receiving praise from your boss.".[167]
When astronomers say "metals," they mean anyelementheavier thanhelium, which includesoxygenandnitrogen, a usage that is massively confusing not just to laypersons but also tochemists. [To astronomers] [t]heBig Dipperisn't aconstellation[...] it is an "asterism" [...] InAI, there is machine "intelligence," which isn't intelligence at all but something more like "machine capability." Inecology, there are "ecosystem services," which you might reasonably think refers to companies that clean upoil spills, but it is [actually] ecological jargon for all the good things that thenatural worlddoes for us. [T]hen there's [...] the theory of "communication accommodation," which means speaking so that the listener can understand.[167]
"[R]esearchers," writesNaomi Oreskes, "are often judged more by the quantity of their output than its quality. Universities [emphasize] metrics such as the numbers of published papers andcitationswhen they make hiring,tenureand promotion decisions."[169]
When – for a number of possible reasons – publication in legitimatepeer-reviewed journalsis not feasible, this often creates aperverse incentiveto publish in "predatory journals", which do not uphold scientific standards. Some 8,000 such journals publish 420,000 papers annually – nearly a fifth of the scientific community's annual output of 2.5 million papers. The papers published in a predatory journal are listed in scientific databases alongside legitimate journals, making it hard to discern the difference.[170]
One reason why some scientists publish in predatory journals is that prestigious scientific journals may charge scientists thousands of dollars for publishing, whereas a predatory journal typically charges less than $200. (Hence authors of papers in the predatory journals are disproportionately located in less wealthy countries and institutions.)[171]
Publishing in predatory journals can be life-threatening when physicians and patients accept spurious claims about medical treatments; and invalid studies can wrongly influence public policy. More such predatory journals are appearing every year. In 2008Jeffrey Beall, aUniversity of Coloradolibrarian, developed a list of predatory journals which he updated for several years.[172]
Naomi Oreskes argues that, "[t]o put an end to predatory practices, universities and other research institutions need to find ways to correct the incentives that lead scholars to prioritize publication quantity... Setting a maximum limit on the number of articles that hiring or funding committees can consider might help... as could placing less importance on the number of citations an author gets. After all, the purpose of science is not merely to produce papers. It is to produce papers that tell us something truthful and meaningful about the world."[173]
Theperverse incentiveto "publish or perish" is often facilitated bythe fabrication of data. A classic example is the identical-twin-studies results ofCyril Burt, which – soon after Burt's death – were found to have been based on fabricated data.
Writes Gideon Lewish-Kraus:
"One of the confounding things about thesocial sciencesis thatobservational evidencecan produce onlycorrelations. [For example, t]o what extent isdishonesty[which is the subject of a number of social-science studies] a matter ofcharacter, and to what extent a matter of situation?Research misconductis sometimes explained away byincentives– thepublishingrequirements for thejobmarket, or the acclaim that can lead toconsultingfees andDavosappearances. [...] The differences betweenp-hackingandfraudis one of degree. And once it becomes customary within a field to inflate results, the field selects for researchers inclined to do so."[174]
Joe Simmons, abehavioral-scienceprofessor, writes:
"[A] field cannot rewardtruthif it does not or cannot decipher it, so it rewards other things instead. Interestingness.Novelty. Speed. Impact. Fantasy. And it effectively punishes the opposite.Intuitive Findings. Incremental Progress. Care.Curiosity.Reality."[175]
Harvard Universityhistorian of scienceNaomi Oreskeswrites that a theme at the 2024World Economic ForuminDavos, Switzerland, was a "perceived need to 'accelerate breakthroughs in research and technology.'"[176]
"[R]ecent years", however, writes Oreskes, "[have] seen important papers, written by prominent scientists and published in prestigious journals,retractedbecause of questionable data or methods." For example, the Davos meeting took place after the resignations – over questionably reliable academic papers – in 2023 ofStanford UniversitypresidentMarc Tessier-Lavigneand, in 2024, ofHarvard UniversitypresidentClaudine Gay. "In one interesting case,Frances H. Arnoldof theCalifornia Institute of Technology, who shared the 2018Nobel Prize in Chemistry, voluntarily retracted a paper when her lab was unable toreplicateher results – but after the paper had been published." Such incidents, suggests Oreskes, are likely to erode public trust in science and in experts generally.[177]
Academics at leading universities in the United States and Europe are subject toperverse incentivesto produce results – andlotsof them –quickly. A study has put the number of papers published around 2023 by scientists and other scholars at over seven million annually, compared with less than a million in 1980. Another study found 265 authors – two-thirds in the medical and life sciences – who published on average a paperevery five days.[178]
"Good science [and scholarship take] time", writes Oreskes. "More than 50 years elapsed between the 1543 publication ofCopernicus's magnum opus... and the broad scientific acceptance of theheliocentric model... Nearly a century passed between biochemistFriedrich Miescher's identification of theDNAmolecule and suggestion that it might be involved in inheritance and the elucidation of itsdouble-helixstructure in the 1950s. And it took just about half a century for geologists and geophysicists to accept geophysicistAlfred Wegener's idea ofcontinental drift."[179]
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