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Inmetadata, the termdata elementis an atomic unit of data that has precise meaning or precise semantics. A data element has:
Data elements usage can be discovered by inspection ofsoftware applicationsor applicationdata filesthrough a process of manual or automatedApplication Discovery and Understanding. Once data elements are discovered they can be registered in ametadata registry.
Intelecommunications, the termdata elementhas the following components:
In the areas ofdatabasesanddata systemsmore generally a data element is a concept forming part of adata model. As an element of data representation, a collection of data elements forms adata structure.[1]
In practice, data elements (fields, columns, attributes, etc.) are sometimes "overloaded", meaning a given data element will have multiple potential meanings. While a known bad practice, overloading is nevertheless a very real factor or barrier to understanding what a system is doing.
Thisdatabase-related article is astub. You can help Wikipedia byexpanding it.
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In themathematicalfield ofFourier analysis, theconjugate Fourier seriesarises by realizing the Fourier series formally as the boundary values of thereal partof aholomorphic functionon theunit disc. Theimaginary partof that function then defines the conjugate series.Zygmund (1968)studied the delicate questions of convergence of this series, and its relationship with theHilbert transform.
In detail, consider atrigonometric seriesof the form
in which the coefficientsanandbnarereal numbers. This series is the real part of thepower series
along theunit circlewithz=eiθ{\displaystyle z=e^{i\theta }}. The imaginary part ofF(z) is called theconjugate seriesoff, and is denoted
Thismathematical analysis–related article is astub. You can help Wikipedia byexpanding it.
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Intraditional logic, acontradictionoccurs when apropositionconflicts either with itself or establishedfact. It is often used as a tool to detectdisingenuousbeliefs andbias. Illustrating a general tendency in applied logic,Aristotle'slaw of noncontradictionstates that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."[1]
In modernformal logicandtype theory, the term is mainly used instead for asingleproposition, often denoted by thefalsumsymbol⊥{\displaystyle \bot }; a proposition is a contradiction iffalsecan be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition).[2][3]This can be generalized to a collection of propositions, which is then said to "contain" a contradiction.
By creation of aparadox,Plato'sEuthydemusdialogue demonstrates the need for the notion ofcontradiction. In the ensuing dialogue,Dionysodorusdenies the existence of "contradiction", all the while thatSocratesis contradicting him:
... I in my astonishment said: What do you mean Dionysodorus? I have often heard, and have been amazed to hear, this thesis of yours, which is maintained and employed by the disciples of Protagoras and others before them, and which to me appears to be quite wonderful, and suicidal as well as destructive, and I think that I am most likely to hear the truth about it from you. The dictum is that there is no such thing as a falsehood; a man must either say what is true or say nothing. Is not that your position?
Indeed, Dionysodorus agrees that "there is no such thing as false opinion ... there is no such thing as ignorance", and demands of Socrates to "Refute me." Socrates responds "But how can I refute you, if, as you say, to tell a falsehood is impossible?".[4]
In classical logic, particularly inpropositionalandfirst-order logic, a propositionφ{\displaystyle \varphi }is a contradictionif and only ifφ⊢⊥{\displaystyle \varphi \vdash \bot }. Since for contradictoryφ{\displaystyle \varphi }it is true that⊢φ→ψ{\displaystyle \vdash \varphi \rightarrow \psi }for allψ{\displaystyle \psi }(because⊥⊢ψ{\displaystyle \bot \vdash \psi }), one may prove any proposition from a set of axioms which contains contradictions. This is called the "principle of explosion", or "ex falso quodlibet" ("from falsity, anything follows").[5]
In acompletelogic, a formula is contradictory if and only if it isunsatisfiable.
For a set of consistent premisesΣ{\displaystyle \Sigma }and a propositionφ{\displaystyle \varphi }, it is true inclassical logicthatΣ⊢φ{\displaystyle \Sigma \vdash \varphi }(i.e.,Σ{\displaystyle \Sigma }provesφ{\displaystyle \varphi }) if and only ifΣ∪{¬φ}⊢⊥{\displaystyle \Sigma \cup \{\neg \varphi \}\vdash \bot }(i.e.,Σ{\displaystyle \Sigma }and¬φ{\displaystyle \neg \varphi }leads to a contradiction). Therefore, aproofthatΣ∪{¬φ}⊢⊥{\displaystyle \Sigma \cup \{\neg \varphi \}\vdash \bot }also proves thatφ{\displaystyle \varphi }is true under the premisesΣ{\displaystyle \Sigma }. The use of this fact forms the basis of aproof techniquecalledproof by contradiction, which mathematicians use extensively to establish the validity of a wide range of theorems. This applies only in a logic where thelaw of excluded middleA∨¬A{\displaystyle A\vee \neg A}is accepted as an axiom.
Usingminimal logic, a logic with similar axioms to classical logic but withoutex falso quodlibetand proof by contradiction, we can investigate the axiomatic strength and properties of various rules that treat contradiction by considering theorems of classical logic that are not theorems of minimal logic.[6]Each of these extensions leads to anintermediate logic:
In mathematics, the symbol used to represent a contradiction within a proof varies.[7]Some symbols that may be used to represent a contradiction include ↯, Opq,⇒⇐{\displaystyle \Rightarrow \Leftarrow }, ⊥,↔{\displaystyle \leftrightarrow \ \!\!\!\!\!\!\!}/ , and ※; in any symbolism, a contradiction may be substituted for the truth value "false", as symbolized, for instance, by "0" (as is common inBoolean algebra). It is not uncommon to seeQ.E.D., or some of its variants, immediately after a contradiction symbol. In fact, this often occurs in a proof by contradiction to indicate that the original assumption was proved false—and hence that its negation must be true.
In general, aconsistency proofrequires the following two things:
But by whatever method one goes about it, all consistency proofs wouldseemto necessitate the primitive notion ofcontradiction.Moreover, itseemsas if this notion would simultaneously have to be "outside" the formal system in the definition of tautology.
WhenEmil Post, in his 1921 "Introduction to a General Theory of Elementary Propositions", extended his proof of the consistency of thepropositional calculus(i.e. the logic) beyond that ofPrincipia Mathematica(PM), he observed that with respect to ageneralizedset of postulates (i.e. axioms), he would no longer be able to automatically invoke the notion of "contradiction"—such a notion might not be contained in the postulates:
The prime requisite of a set of postulates is that it be consistent. Since the ordinary notion of consistency involves that of contradiction, which again involves negation, and since this function does not appear in general as a primitive in [thegeneralizedset of postulates] a new definition must be given.[8]
Post's solution to the problem is described in the demonstration "An Example of a Successful Absolute Proof of Consistency", offered byErnest NagelandJames R. Newmanin their 1958Gödel's Proof. They too observed a problem with respect to the notion of "contradiction" with its usual "truth values" of "truth" and "falsity". They observed that:
The property of being a tautology has been defined in notions of truth and falsity. Yet these notions obviously involve a reference to somethingoutsidethe formula calculus. Therefore, the procedure mentioned in the text in effect offers aninterpretationof the calculus, by supplying a model for the system. This being so, the authors have not done what they promised, namely, "to define a property of formulas in terms of purely structural features of the formulas themselves". [Indeed] ... proofs of consistency which are based on models, and which argue from the truth of axioms to their consistency, merely shift the problem.[9]
Given some "primitive formulas" such as PM's primitives S1V S2[inclusive OR] and ~S (negation), one is forced to define the axioms in terms of these primitive notions. In a thorough manner, Post demonstrates in PM, and defines (as do Nagel and Newman, see below) that the property oftautologous– as yet to be defined – is "inherited": if one begins with a set of tautologous axioms (postulates) and adeduction systemthat containssubstitutionandmodus ponens, then aconsistentsystem will yield only tautologous formulas.
On the topic of the definition oftautologous, Nagel and Newman create twomutually exclusiveandexhaustiveclasses K1and K2, into which fall (the outcome of) the axioms when their variables (e.g. S1and S2are assigned from these classes). This also applies to the primitive formulas. For example: "A formula having the form S1V S2is placed into class K2, if both S1and S2are in K2; otherwise it is placed in K1", and "A formula having the form ~S is placed in K2, if S is in K1; otherwise it is placed in K1".[10]
Hence Nagel and Newman can now define the notion oftautologous: "a formula is a tautology if and only if it falls in the class K1, no matter in which of the two classes its elements are placed".[11]This way, the property of "being tautologous" is described—without reference to a model or an interpretation.
For example, given a formula such as ~S1V S2and an assignment of K1to S1and K2to S2one can evaluate the formula and place its outcome in one or the other of the classes. The assignment of K1to S1places ~S1in K2, and now we can see that our assignment causes the formula to fall into class K2. Thus by definition our formula is not a tautology.
Post observed that, if the system were inconsistent, a deduction in it (that is, the last formula in a sequence of formulas derived from the tautologies) could ultimately yield S itself. As an assignment to variable S can come from either class K1or K2, the deduction violates the inheritance characteristic of tautology (i.e., the derivation must yield an evaluation of a formula that will fall into class K1). From this, Post was able to derive the following definition of inconsistency—without the use of the notion of contradiction:
Definition.A system will be said to be inconsistent if it yields the assertion of the unmodified variable p [S in the Newman and Nagel examples].
In other words, the notion of "contradiction" can be dispensed when constructing a proof of consistency; what replaces it is the notion of "mutually exclusive and exhaustive" classes. An axiomatic system need not include the notion of "contradiction".[12]: 177
Adherents of theepistemologicaltheory ofcoherentismtypically claim that as a necessary condition of the justification of abelief, that belief must form a part of a logically non-contradictorysystemof beliefs. Somedialetheists, includingGraham Priest, have argued that coherence may not require consistency.[13]
A pragmatic contradiction occurs when the very statement of the argument contradicts the claims it purports. An inconsistency arises, in this case, because the act of utterance, rather than the content of what is said, undermines its conclusion.[14]
Indialectical materialism: Contradiction—as derived fromHegelianism—usually refers to an opposition inherently existing within one realm, one unified force or object. This contradiction, as opposed to metaphysical thinking, is not an objectively impossible thing, because these contradicting forces exist in objective reality, not cancelling each other out, but actually defining each other's existence. According toMarxist theory, such a contradiction can be found, for example, in the fact that:
Hegelian and Marxist theories stipulate that thedialecticnature of history will lead to thesublation, orsynthesis, of its contradictions. Marx therefore postulated that history would logically makecapitalismevolve into asocialistsociety where themeans of productionwould equally serve theworking and producing classof society, thus resolving the prior contradiction between (a) and (b).[15]
Colloquial usagecan label actions or statements as contradicting each other when due (or perceived as due) topresuppositionswhich are contradictory in the logical sense.
Proof by contradictionis used inmathematicsto constructproofs.
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Inmathematics, aquotient categoryis acategoryobtained from another category by identifying sets ofmorphisms. Formally, it is aquotient objectin thecategory of (locally small) categories, analogous to aquotient grouporquotient space, but in the categorical setting.
LetCbe a category. Acongruence relationRonCis given by: for each pair of objectsX,YinC, anequivalence relationRX,Yon Hom(X,Y), such that the equivalence relations respect composition of morphisms. That is, if
are related in Hom(X,Y) and
are related in Hom(Y,Z), theng1f1andg2f2are related in Hom(X,Z).
Given a congruence relationRonCwe can define thequotient categoryC/Ras the category whose objects are those ofCand whose morphisms areequivalence classesof morphisms inC. That is,
Composition of morphisms inC/Riswell-definedsinceRis a congruence relation.
There is a natural quotientfunctorfromCtoC/Rwhich sends each morphism to its equivalence class. This functor is bijective on objects and surjective on Hom-sets (i.e. it is afull functor).
Every functorF:C→Ddetermines a congruence onCby sayingf~giffF(f) =F(g). The functorFthen factors through the quotient functorC→C/~ in a unique manner. This may be regarded as the "first isomorphism theorem" for categories.
IfCis anadditive categoryand we require the congruence relation ~ onCto be additive (i.e. iff1,f2,g1andg2are morphisms fromXtoYwithf1~f2andg1~g2, thenf1+g1~f2+g2), then the quotient categoryC/~ will also be additive, and the quotient functorC→C/~ will be an additive functor.
The concept of an additive congruence relation is equivalent to the concept of atwo-sided ideal of morphisms: for any two objectsXandYwe are given an additive subgroupI(X,Y) of HomC(X,Y) such that for allf∈I(X,Y),g∈ HomC(Y,Z) andh∈ HomC(W,X), we havegf∈I(X,Z) andfh∈I(W,Y). Two morphisms in HomC(X,Y) are congruent iff their difference is inI(X,Y).
Every unitalringmay be viewed as an additive category with a single object, and the quotient of additive categories defined above coincides in this case with the notion of aquotient ringmodulo a two-sided ideal.
Thelocalization of a categoryintroduces new morphisms to turn several of the original category's morphisms into isomorphisms. This tends to increase the number of morphisms between objects, rather than decrease it as in the case of quotient categories. But in both constructions it often happens that two objects become isomorphic that weren't isomorphic in the original category.
TheSerre quotientof anabelian categoryby aSerre subcategoryis a new abelian category which is similar to a quotient category but also in many cases has the character of a localization of the category.
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"Talking past each other" is an English phrase describing the situation where two or more people talk about different subjects, while believing that they are talking about the same thing.[1]
David Horton writes that when characters in fiction talk past each other, the effect is to expose "an unbridgeable gulf between their respective perceptions and intentions. The result is an exchange, but never an interchange, of words in fragmented and cramped utterances whose subtext often reveals more than their surface meaning."[2]
The phrase is used in widely varying contexts. For example, in 1917,Albert EinsteinandDavid Hilberthad dawn-to-dusk discussions of physics; and they continued their debate in writing, althoughFelix Kleinrecords that they "talked past each other, as happens not infrequently between simultaneously producing mathematicians."[3]
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Astardateis a fictional system of time measurement developed for the television and film seriesStar Trek. In the series, use of this date system is commonly heard at the beginning of avoice-overlog entry, such as "Captain's log, stardate 41153.7. Our destination is planet Deneb IV …". While the original method was inspired by theModified Julian date[1][2][3]system currently used by astronomers, the writers and producers have selected numbers using different methods over the years, some more arbitrary than others. This makes it impossible to convert all stardates into equivalent calendar dates, especially since stardates were originally intended to avoid specifying exactly whenStar Trektakes place.[4]
The original 1967Star Trek Guide(April 17, 1967, p. 25) instructed writers forthe originalStar TrekTV serieson how to select stardates for their scripts. Writers could pick any combination of four numbers plus a decimal point, and aim for consistency within a single script, but not necessarily between different scripts. This was to "avoid continually mentioningStar Trek's century" and avoid "arguments about whether this or that would have developed by then".[5]Though the guide sets the series "about two hundred years from now", the few references within the show itself were contradictory, and later productions and reference materials eventually placed the series between the years 2265 and 2269. The second pilot begins on stardate 1312.4 and the last-produced episode on stardate 5928.5.[6]Though the dating system was revised forStar Trek: The Next Generation, the pilot ofStar Trek: Discoveryfollows the original series' dating system, starting on stardate 1207.3, which is stated precisely to be Sunday, May 11, 2256.[7]
SubsequentStar Trekseries followed a new numerical convention.Star Trek: The Next Generation(TNG) revised the stardate system in the 1987Star Trek: The Next Generation Writer's/Director's Guide, to five digits and one decimal place. According to the guide, the first digit "4" should represent the 24th century, with the second digit representing thetelevision season. The remaining digits can progress unevenly, with the decimal representing the time as fractional days. Stardates ofStar Trek: Deep Space Ninebegan with 46379.1, corresponding to the sixth season ofTNGwhich was also set in the year 2369.Star Trek: Voyagerbegan with stardate 48315.6 (2371), one season afterTNGhad finished its seventh and final season. As inTNG, the second digit would increase by one every season, while the initial two digits eventually rolled over from 49 to 50, despite the year 2373 still being in the 24th century.Star Trek: Nemesiswas set around stardate 56844.9.Star Trek: Discoverytraveled to the year 3188, giving a stardate of 865211.3, corresponding to that year in this system of stardates.
On March 9, 2023,Star Trek: Picardgave a stardate of 78183.10. This indicates a continuity withTNG. Each stardate increment represents one milliyear, with 78 years in 2401, counted from 2323. The decimal represents a fractional day. Thus, stardates are a composition of two types ofdecimal time. In the twenty-first century, this would indicate 78 years from 1945.
Stardates usually are expressed with a single decimal digit, but sometimes with more than one. For instance,The Next Generationepisode,"The Child", displays the stardate 42073.1435. According toThe Star Trek Guide, the official writers' guide for the original series:
Likewise, page 32 of the 1988Star Trek: The Next Generation Writer's/Director's Guidefor season two states:
This was demonstrated by the ship's chronometer in theTOS-Remasteredepisode, "The Naked Time," and by Captain Varley's video logs in theTNGepisode "Contagion". The latter displays several stardates with two decimal digits next to corresponding times.
AdditionalStar Trekmedia have generated their own numbering systems. The 2009MMORPGStar Trek Onlinebegan on stardate 86088.58, in the in-game year 2409, counting 1000 stardates per year from May 25, 1922.[8]WriterRoberto Orcirevised the system for the2009 filmStar Trekso that the first four digits correspond to the year, while the remainder was intended to stand for the day of the year, in effect representing anordinal date.[9][10][11]In the first installment of the movie trilogy,Spockmakes his log of the destruction of Vulcan on stardate 2258.42, or February 11, 2258.Star Trek Into Darknessbegins on stardate 2259.55, or February 24, 2259.[12]Star Trek Beyondbegins on stardate 2263.02, or January 2, 2263. InThe Big Bang Theoryepisode, "The Adhesive Duck Deficiency",Sheldon Coopergives the stardate 63345.3, corresponding with the date of theLeonid meteor showerthat year, November 17, 2009.[13]
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Game Description Language(GDL) is a specializedlogicprogramming languagedesigned byMichael Genesereth. The goal of GDL is to allow the development of AI agents capable ofgeneral game playing. It is part of the General Game Playing Project atStanford University.
GDL is a tool for expressing the intricacies of game rules and dynamics in a form comprehensible to AI systems through a combination of logic-based constructs and declarative principles.
In practice, GDL is often used for General Game Playing competitions and research endeavors. In these contexts, GDL is used to specify the rules of games that AI agents are expected to play. AI developers and researchers harness GDL to create algorithms that can comprehend and engage with games based on their rule descriptions. The use of GDL paves the way for the development of highly adaptable AI agents, capable of competing and excelling in diverse gaming scenarios.
This innovation is a testament to the convergence of logic-based formalism and the world of games, opening new horizons for AI's potential in understanding and mastering a multitude of games. Game Description Language equips AI with a universal key to unlock the mysteries of diverse game environments and strategies.
Quoted in an article inNew Scientist, Genesereth pointed out that althoughDeep Bluecan play chess at agrandmasterlevel, it is incapable of playingcheckersat all because it is a specialized game player.[1]Both chess and checkers can be described in GDL. This enables general game players to be built that can play both of these games and any other game that can be described using GDL.
GDL is a variant ofDatalog, and thesyntaxis largely the same. It is usually given inprefix notation. Variables begin with "?".[2]
The following is the list of keywords in GDL, along with brief descriptions of their functions:
A game description in GDL provides complete rules for each of the following elements of a game.
Facts that define the roles in a game. The following example is from a GDL description of the two-player gameTic-tac-toe:
Rules that entail all facts about the initial game state. An example is:
Rules that describe each move by the conditions on the current position under which it can be taken by a player. An example is:
Rules that describe all facts about the next state relative to the current state and the moves taken by the players. An example is:
Rules that describe the conditions under which the current state is a terminal one. An example is:
The goal values for each player in a terminal state. An example is:
With GDL, one can describe finite games with an arbitrary number of players. However, GDL cannot describe games that contain an element of chance (for example, rolling dice) or games where players have incomplete information about the current state of the game (for example, in many card games the opponents' cards are not visible).GDL-II, theGame Description Language for Incomplete Information Games, extends GDL by two keywords that allow for the description of elements of chance and incomplete information:[3]
The following is an example from a GDL-II description of the card gameTexas hold 'em:
Michael Thielscher also created a further extension,GDL-III, a general game description language withimperfect informationandintrospection, that supports the specification ofepistemic games— ones characterised by rules that depend on the knowledge of players.[4]
In classical game theory, games can be formalised inextensiveandnormalforms. Forcooperative game theory, games are represented using characteristic functions. Some subclasses of games allow special representations in smaller sizes also known assuccinct games.
Some of the newer developments of formalisms and languages for the representation of some subclasses of games or representations adjusted to the needs of interdisciplinary research are summarized as the following table.[5]Some of these alternative representations also encode time-related aspects:
A 2016 paper "describes a multilevel algorithm compiling a general game description in GDL into an optimized reasoner in a low level language".[19]
A 2017 paper uses GDL to model the process of mediating a resolution to a dispute between two parties and presented an algorithm that uses available information efficiently to do so.[20]
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Harrison Colyar White(March 21, 1930 – May 18, 2024) was an American sociologist who was the Giddings Professor of Sociology atColumbia University. White played an influential role in the “Harvard Revolution” insocial networks[1]and theNew York School of relational sociology.[2]He is credited with the development of a number of mathematical models of social structure includingvacancy chainsandblockmodels. He has been a leader of a revolution insociologythat is still in process, using models of social structure that are based onpatterns of relationsinstead of the attributes and attitudes of individuals.[3]
Among social network researchers, White is widely respected. For instance, at the 1997International Network of Social Network Analysisconference, the organizer held a special “White Tie” event, dedicated to White.[4]Social network researcher Emmanuel Lazega refers to him as both “Copernicus and Galileo” because he invented both the vision and the tools.
The most comprehensive documentation of his theories can be found in the bookIdentity and Control, first published in 1992. A major rewrite of the book appeared in June 2008. In 2011, White received the W.E.B. DuBois Career of Distinguished Scholarship Award from theAmerican Sociological Association, which honors "scholars who have shown outstanding commitment to the profession of sociology and whose cumulative work has contributed in important ways to the advancement of the discipline."[5]Before his retirement to live inTucson, Arizona, White was interested in sociolinguistics and business strategy as well as sociology.
White was born on March 21, 1930, inWashington, D.C.He had three siblings and his father was a doctor in the US Navy. Although moving around to different Naval bases throughout his adolescence, he considered himself Southern, andNashville, TNto be his home. At the age of 15, he entered theMassachusetts Institute of Technology(MIT), receiving his undergraduate degree at 20 years of age; five years later, in 1955, he received a doctorate intheoretical physics, also from MIT withJohn C. Slateras his advisor.[6]His dissertation was titledA quantum-mechanical calculation of inter-atomic force constants in copper.[7]This was published in thePhysical Reviewas "Atomic Force Constants of Copper from Feynman's Theorem" (1958).[8]While at MIT he also took a course with the political scientistKarl Deutsch, who White credits with encouraging him to move toward the social sciences.[9]
After receiving his PhD in theoretical physics, he received a Fellowship from the Ford Foundation to begin his second doctorate in sociology atPrinceton University. His dissertation advisor wasMarion J. Levy. White also worked withWilbert Moore,Fred Stephan, andFrank W. Notesteinwhile at Princeton.[10]His cohort was very small, with only four or five other graduate students includingDavid Matza, andStanley Udy.
At the same time, he took up a position as an operations analyst at theOperations Research Office,Johns Hopkins Universityfrom 1955 to 1956.[11]During this period, he worked with Lee S. Christie onQueuing with Preemptive Priorities or with Breakdown, which was published in 1958.[12]Christie previously worked alongside mathematical psychologistR. Duncan Lucein the Small Group Laboratory at MIT while White was completing his first PhD in physics also at MIT.
While continuing his studies at Princeton, White also spent a year as a fellow at theCenter for Advanced Study in the Behavioral Sciences,Stanford University, California where he metHarold Guetzkow. Guetzkow was a faculty member at the Carnegie Institute of Technology, known for his application of simulations to social behavior and long-time collaborator with many other pioneers in organization studies, includingHerbert A. Simon,James March, andRichard Cyert.[13]Upon meeting Simon through his mutual acquaintance with Guetzkow, White received an invitation to move from California to Pittsburgh to work as an assistant professor of Industrial Administration and Sociology at theGraduate School of Industrial Administration, Carnegie Institute of Technology (laterCarnegie-Mellon University), where he stayed for a couple of years, between 1957 and 1959. In an interview, he claimed to have fought with the dean,Leyland Bock, to have the word "sociology" included in his title.
It was also during his time at the Stanford Center for Advanced Study that White met his first wife, Cynthia A. Johnson, who was a graduate ofRadcliffe College, where she had majored in art history. The couple's joint work on the French Impressionists,Canvases and Careers(1965) and “Institutional Changes in the French Painting World” (1964), originally grew out of a seminar on art in 1957 at the Center for Advanced Study led by Robert Wilson. White originally hoped to use sociometry to map the social structure of French art to predict shifts, but he had an epiphany that it was not social structure but institutional structure which explained the shift.
It was also during these years that White, still a graduate student in sociology, wrote and published his first social scientific work, "Sleep: A Sociological Interpretation" inActa Sociologicain 1960, together withVilhelm Aubert, a Norwegian sociologist. This work was a phenomenological examination of sleep which attempted to "demonstrate that sleep was more than a straightforward biological activity... [but rather also] a social event".[14]
For his dissertation, White carried out empirical research on a research and development department in a manufacturing firm, consisting of interviews and a 110-item questionnaire with managers. He specifically used sociometric questions, which he used to model the "social structure" of relationships between various departments and teams in the organization. In May 1960 he submitted as his doctoral dissertation, titledResearch and Development as a Pattern in Industrial Management: A Case Study in Institutionalisation and Uncertainty,[15]earning a PhD in sociology fromPrinceton University. His first publication based on his dissertation was ''Management conflict and sociometric structure'' in theAmerican Journal of Sociology.[16]
In 1959James Colemanleft the University of Chicago to found a new department of social relations at Johns Hopkins University, this left a vacancy open for a mathematical sociologist like White. He moved to Chicago to start working as an associate professor at the Department of Sociology. At that time, highly influential sociologists, such asPeter Blau,Mayer Zald,Elihu Katz,Everett Hughes,Erving Goffmanwere there. As Princeton only required one year in residence, and White took the opportunity to take positions at Johns Hopkins, Stanford, and Carnegie while still working on his dissertation, it was at Chicago that White credits as being his "real socialization in a way, into sociology."[17]It was here that White advised his first two graduate students Joel H. Levine andMorris Friedell, both who went on to make contributions to social network analysis in sociology. While at the Center for Advanced Study, White began learning anthropology and became fascinated with kinship. During his stay at theUniversity of ChicagoWhite was able to finishAn Anatomy of Kinship, published in 1963 within the Prentice-Hall series in Mathematical Analysis of Social Behavior, withJames ColemanandJames Marchas chief editors. The book received significant attention from many mathematical sociologists of the time, and contributed greatly to establish White as a model builder.[18]
In 1963, White left Chicago to be an associate professor of sociology at theHarvard Department of Social Relations—the same department founded by Talcott Parsons and still heavily influenced by the structural-functionalist paradigm of Parsons. As White previously only taught graduate courses at Carnegie and Chicago, his first undergraduate course wasAn Introduction to Social Relations(see Influence) at Harvard, which became infamous among network analysts. As he "thought existing textbooks were grotesquely unscientific,"[19]the syllabus of the class was noted for including few readings by sociologists, and comparatively more readings by anthropologists, social psychologists, and historians.[20]White was also a vocal critic of what he called the "attributes and attitudes" approach of Parsonsian sociology, and came to be the leader of what has been variously known as the “Harvard Revolution," the "Harvard breakthrough," or the "Harvard renaissance" in social networks. He worked closely with small group researchersGeorge C. HomansandRobert F. Bales, which was largely compatible with his prior work in organizational research and his efforts to formalize network analysis. Overlapping White's early years,Charles Tilly, a graduate of the Harvard Department of Social Relations, was a visiting professor at Harvard and attended some of White's lectures - network thinking heavily influenced Tilly's work.
White remained at Harvard until 1986. In addition to a divorce from his wife, Cynthia, (with whom he published several works) and wanting a change, the sociology department at the University of Arizona offer him the position as department chair.[21]He remained at Arizona for two years.
In 1988, White joined Columbia University as a professor of sociology and was the director of thePaul F. Lazarsfeld Center for the Social Sciences. This was at the early stages of what is perhaps the second major revolution in network analysis, the so-called "New York School of relational sociology." This invisible college included Columbia as well as the New School for Social Research and New York University. While the Harvard Revolution involved substantial advances in methods for measuring and modeling social structure, the New York School involved the merging of cultural sociology with network-structural sociology, two traditions which had previously been antagonistic. White stood at the heart of this, and his magnum opusIdentity and Controlwas a testament to this new relational sociology.
In 1992, White received the named position of Giddings Professor of Sociology and was the chair of the department of sociology for various years until his retirement. He resided in Tucson, Arizona.
A good summary of White's sociological contributions is provided by his former student and collaborator,Ronald Breiger:
White addresses problems of social structure that cut across the range of the social sciences. Most notably, he has contributed (1) theories of role structures encompassing classificatory kinship systems of native Australian peoples and institutions of the contemporary West; (2) models based on equivalences of actors across networks of multiple types of social relation; (3) theorization of social mobility in systems of organizations; (4) a structural theory of social action that emphasizes control, agency, narrative, and identity; (5) a theory of artistic production; (6) a theory of economic production markets leading to the elaboration of a network ecology for market identities and new ways of accounting for profits, prices, and market shares; and (7) a theory of language use that emphasizes switching between social, cultural, and idiomatic domains within networks of discourse. His most explicit theoretical statement isIdentity and Control: A Structural Theory of Social Action(1992), although several of the major components of his theory of the mutual shaping of networks, institutions, and agency are also readily apparent inCareers and Creativity: Social Forces in the Arts(1993), written for a less-specialized audience.[22]
More generally, White and his students sparked interest in looking at society as networks rather than as aggregates of individuals.[23]
This view is still controversial. In sociology and organizational science, it is difficult to measure cause and effect in a systematic way. Because of that, it is common to use sampling techniques to discover some sort of average in a population.
For instance, we are told almost daily how the average European or American feels about a topic. It allows social scientists and pundits to make inferences about cause and say “people are angry at the current administration because the economy is doing poorly.” This kind of generalization certainly makes sense, but it does not tell us anything about an individual. This leads to the idea of an idealized individual, something that is the bedrock of modern economics.[24]Most modern economic theories look at social formations, like organizations, as products of individuals all acting in their own best interest.[25]
While this has proved to be useful in some cases, it does not account well for the knowledge that is required for the structures to sustain themselves. White and his students (and his students' students) have been developing models that incorporate the patterns of relationships into descriptions of social formations. This line of work includes: economic sociology, network sociology and structuralist sociology.
White's most comprehensive work isIdentity and Control. The first edition came out in 1992 and the second edition appeared in June 2008.
In this book, White discusses the social world, including “persons,” as emerging from patterns of relationships. He argues that it is a default human heuristic to organize the world in terms of attributes, but that this can often be a mistake. For instance, there are countless books on leadership that look for the attributes that make a good leader. However, no one is a leader without followers; the term describes a relationship one has with others. Without the relationships, there would be no leader. Likewise, an organization can be viewed as patterns of relationships. It would not “exist” if people did not honor and maintain specific relationships. White avoids giving attributes to things that emerge from patterns of relationships, something that goes against our natural instincts and requires some thought to process.[26]
Identity and Controlhas seven chapters. The first six are about social formations that control us and how our own judgment organizes our experience in ways that limit our actions. The final chapter is about “getting action” and how change is possible. One of the ways is by “proxy,” empowering others.
Harrison White also developed a perspective on market structure and competition in his 2002 book,Markets from Networks, based on the idea that markets are embedded insocial networks. His approach is related to economic concepts such asuncertainty(as defined byFrank Knight),monopolistic competition(Edward Chamberlin), orsignalling(Spence). This sociological perspective on markets has influenced both sociologists (seeJoel M. Podolny) and economists (seeOlivier Favereau).
White's later work discussed linguistics. InIdentity and Controlhe emphasized “switching” between network domains as a way to account for grammar in a way that does not ignore meaning as does much of standard linguistic theory. He had a long-standing interest in organizations, and before he retired, he worked on how strategy fits into the overall models of social construction he has developed.
In addition to his own publications, White is widely credited with training many influential generations of network analysts in sociology. Including the early work in the 1960s and 1970s during the Harvard Revolution, as well as the 1980s and 1990s at Columbia during the New York School of relational sociology.
White's student and teaching assistant,Michael Schwartz,took notes in the spring of 1965, known asNotes on the Constituents of Social Structure, of White's undergraduateIntroduction to Social Relations course (Soc Rel 10). These notes were circulated among network analysis students and aficionados, until finally published in 2008 in Sociologica. As popular social science blog Orgtheory.net explains, "in contemporary American sociology, there are no set of student-taken notes that have had as much underground influence as those from Harrison White’s introductorySoc Rel 10seminar at Harvard."[27]
The first generation of Harvard graduate students that trained with White during the 1960s went on to be a formidable cohort of network analytically inclined sociologists. His first graduate student at Harvard wasEdward Laumannwho went onto develop one of the most widely used methods of studying personal networks known as ego-network surveys (developed with one of Laumann's students at the University of Chicago,Ronald Burt). Several of them went on to contribute to the "Toronto school" of structural analysis.Barry Wellman, for instance, contributed heavily to the cross fertilization of network analysis and community studies, later contributing to the earliest studies of online communities. Another of White's earliest students at Harvard was Nancy Lee (now Nancy Howell) who used social network analysis in her groundbreaking study of how women seeking an abortion found willing doctors before Roe v. Wade. She found that women found doctors through links of friends and acquaintances and was four degrees separated from the doctor on average. White also trained later additions to the Toronto school, Harriet Friedmann ('77) and Bonnie Erickson ('73).
One of White's most well-known graduate students wasMark Granovetter, who attended Harvard as a Ph.D. student from 1965 to 1970. Granovetter studied how people got jobs, discovered they were more likely to get them through acquaintances than through friends. Recounting the development of his widely cited 1973 article, "The Strength of Weak Ties", Granovetter credits White's lectures and specifically White's description of sociometric work by Anatol Rapaport and William Horrath that gave him the idea. This, tied with earlier work byStanley Milgram(who was also in theHarvard Department of Social Relations1963–1967, though not one of White's students), gave scientists a better sense of how the social world was organized: into many densegroupswith “weak ties” between them. Granovetter's work provided the theoretical background forMalcolm Gladwell'sThe Tipping Point. This line of research is still actively being pursued byDuncan Watts,Albert-László Barabási,Mark Newman,Jon Kleinbergand others.
White's research on “vacancy chains” was assisted by a number of graduate students, includingMichael SchwartzandIvan Chase. The outcome of this was the bookChains of Opportunity. The book described a model of social mobility where the roles and the people that filled them were independent. The idea of a person being partially created by their position in patterns of relationships has become a recurring theme in his work. This provided a quantitative analysis of social roles, allowing scientists new ways to measure society that were not based on statistical aggregates.
During the 1970s, White work with his student'sScott Boorman,Ronald Breiger, and François Lorrain on a series of articles that introduce a procedure called "blockmodeling" and the concept of "structural equivalence." The key idea behind these articles was identifying a "position" or "role" through similarities in individuals' social structure, rather than characteristics intrinsic to the individuals ora prioridefinitions of group membership.
At Columbia, White trained a new cohort of researchers who pushed network analysis beyond methodological rigor to theoretical extension and the incorporation of previously neglected concepts, namely, culture and language.
Many of his students and mentees have had a strong impact in sociology. Other former students includeMichael Schwartzand Ivan Chase, both professors at Stony Brook; Joel Levine, who foundedDartmouth College's Math/Social Science program;Edward Laumannwho pioneered survey-based egocentric network research and became a dean and provost atUniversity of Chicago;Kathleen CarleyatCarnegie Mellon University;Ronald Breigerat theUniversity of Arizona;Barry Wellmanat theUniversity of Torontoand then the NetLab Network;Peter BearmanatColumbia University; Bonnie Erickson (Toronto);Christopher Winship(Harvard University); Joel Levine (Dartmouth College), Nicholas Mullins (Virginia Tech, deceased), Margaret Theeman (Boulder), Brian Sherman (retired, Atlanta), Nancy Howell (retired, Toronto);David R. Gibson(University of Notre Dame); Matthew Bothner (University of Chicago);Ann Mische(University of Notre Dame); Kyriakos Kontopoulos (Temple University); andFrédéric Godart(INSEAD).[28]
White died at an assisted living facility inTucson, on May 19, 2024, at the age of 94.[29]
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Incryptography, abrute-force attackconsists of an attacker submitting manypasswordsorpassphraseswith the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct one is found. Alternatively, the attacker can attempt to guess thekeywhich is typically created from the password using akey derivation function. This is known as anexhaustive key search. This approach doesn't depend on intellectual tactics; rather, it relies on making several attempts.[citation needed]
A brute-force attack is acryptanalytic attackthat can, in theory, be used to attempt to decrypt any encrypted data (except for data encrypted in aninformation-theoretically securemanner).[1]Such an attack might be used when it is not possible to take advantage of other weaknesses in an encryption system (if any exist) that would make the task easier.
When password-guessing, this method is very fast when used to check all short passwords, but for longer passwords other methods such as thedictionary attackare used because a brute-force search takes too long. Longer passwords, passphrases and keys have more possible values, making them exponentially more difficult to crack than shorter ones due to diversity of characters.[2]
Brute-force attacks can be made less effective byobfuscatingthe data to be encoded making it more difficult for an attacker to recognize when the code has been cracked or by making the attacker do more work to test each guess. One of the measures of the strength of an encryption system is how long it would theoretically take an attacker to mount a successful brute-force attack against it.[3]
Brute-force attacks are an application of brute-force search, the general problem-solving technique of enumerating all candidates and checking each one. The word 'hammering' is sometimes used to describe a brute-force attack,[4]with 'anti-hammering' for countermeasures.[5]
Brute-force attacks work by calculating every possible combination that could make up a password and testing it to see if it is the correct password. As the password's length increases, the amount of time, on average, to find the correct password increases exponentially.[6]
The resources required for a brute-force attack growexponentiallywith increasingkey size, not linearly. Although U.S. export regulations historically restricted key lengths to 56-bitsymmetric keys(e.g.Data Encryption Standard), these restrictions are no longer in place, so modern symmetric algorithms typically use computationally stronger 128- to 256-bit keys.
There is a physical argument that a 128-bit symmetric key is computationally secure against brute-force attack. TheLandauer limitimplied by the laws of physics sets a lower limit on the energy required to perform a computation ofkT·ln 2per bit erased in a computation, whereTis the temperature of the computing device inkelvins,kis theBoltzmann constant, and thenatural logarithmof 2 is about 0.693 (0.6931471805599453). No irreversible computing device can use less energy than this, even in principle.[7]Thus, in order to simply flip through the possible values for a 128-bit symmetric key (ignoring doing the actual computing to check it) would, theoretically, require2128− 1bit flips on a conventional processor. If it is assumed that the calculation occurs near room temperature (≈300 K), the Von Neumann-Landauer Limit can be applied to estimate the energy required as ≈1018joules, which is equivalent to consuming 30gigawattsof power for one year. This is equal to 30×109W×365×24×3600 s = 9.46×1017J or 262.7 TWh (about 0.1% of theyearly world energy production). The full actual computation – checking each key to see if a solution has been found – would consume many times this amount. Furthermore, this is simply the energy requirement for cycling through the key space; the actual time it takes to flip each bit is not considered, which is certainly greater than 0 (seeBremermann's limit).[citation needed]
However, this argument assumes that the register values are changed using conventional set and clear operations, which inevitably generateentropy. It has been shown that computational hardware can be designed not to encounter this theoretical obstruction (seereversible computing), though no such computers are known to have been constructed.[citation needed]
As commercial successors of governmentalASICsolutions have become available, also known ascustom hardware attacks, two emerging technologies have proven their capability in the brute-force attack of certain ciphers. One is moderngraphics processing unit(GPU) technology,[8][page needed]the other is thefield-programmable gate array(FPGA) technology. GPUs benefit from their wide availability and price-performance benefit, FPGAs from theirenergy efficiencyper cryptographic operation. Both technologies try to transport the benefits of parallel processing to brute-force attacks. In case of GPUs some hundreds, in the case of FPGA some thousand processing units making them much better suited to cracking passwords than conventional processors. For instance in 2022, 8Nvidia RTX 4090GPU were linked together to test password strength by using the softwareHashcatwith results that showed 200 billion eight-characterNTLMpassword combinations could be cycled through in 48 minutes.[9][10]
Various publications in the fields of cryptographic analysis have proved the energy efficiency of today's FPGA technology, for example, the COPACOBANA FPGA Cluster computer consumes the same energy as a single PC (600 W), but performs like 2,500 PCs for certain algorithms. A number of firms provide hardware-based FPGA cryptographic analysis solutions from a single FPGAPCI Expresscard up to dedicated FPGA computers.[citation needed]WPAandWPA2encryption have successfully been brute-force attacked by reducing the workload by a factor of 50 in comparison to conventional CPUs[11][12]and some hundred in case of FPGAs.
Advanced Encryption Standard(AES) permits the use of 256-bit keys. Breaking a symmetric 256-bit key by brute-force requires 2128times more computational power than a 128-bit key. One of the fastest supercomputers in 2019 has a speed of 100petaFLOPSwhich could theoretically check 100 trillion (1014) AES keys per second (assuming 1000 operations per check), but would still require 3.67×1055years to exhaust the 256-bit key space.[13]
An underlying assumption of a brute-force attack is that the complete key space was used to generate keys, something that relies on an effectiverandom number generator, and that there are no defects in the algorithm or its implementation. For example, a number of systems that were originally thought to be impossible to crack by brute-force have nevertheless beencrackedbecause thekey spaceto search through was found to be much smaller than originally thought, because of a lack of entropy in theirpseudorandom number generators. These includeNetscape's implementation ofSecure Sockets Layer(SSL) (cracked byIan GoldbergandDavid Wagnerin 1995) and aDebian/Ubuntuedition ofOpenSSLdiscovered in 2008 to be flawed.[14][15]A similar lack of implemented entropy led to the breaking ofEnigma'scode.[16][17]
Credential recycling is thehackingpractice of re-using username and password combinations gathered in previous brute-force attacks. A special form of credential recycling ispass the hash, whereunsaltedhashed credentials are stolen and re-used without first being brute-forced.[18]
Certain types of encryption, by their mathematical properties, cannot be defeated by brute-force. An example of this isone-time padcryptography, where everycleartextbit has a corresponding key from a truly random sequence of key bits. A 140 character one-time-pad-encoded string subjected to a brute-force attack would eventually reveal every 140 character string possible, including the correct answer – but of all the answers given, there would be no way of knowing which was the correct one. Defeating such a system, as was done by theVenona project, generally relies not on pure cryptography, but upon mistakes in its implementation, such as the key pads not being truly random, intercepted keypads, or operators making mistakes.[19]
In case of anofflineattack where the attacker has gained access to the encrypted material, one can try key combinations without the risk of discovery or interference. In case ofonlineattacks, database and directory administrators can deploy countermeasures such as limiting the number of attempts that a password can be tried, introducing time delays between successive attempts, increasing the answer's complexity (e.g., requiring aCAPTCHAanswer or employingmulti-factor authentication), and/or locking accounts out after unsuccessful login attempts.[20][page needed]Website administrators may prevent a particular IP address from trying more than a predetermined number of password attempts against any account on the site.[21]Additionally, the MITRE D3FEND framework provides structured recommendations for defending against brute-force attacks by implementing strategies such as network traffic filtering, deploying decoy credentials, and invalidating authentication caches.[22]
In a reverse brute-force attack (also called password spraying), a single (usually common) password is tested against multiple usernames or encrypted files.[23]The process may be repeated for a select few passwords. In such a strategy, the attacker is not targeting a specific user.
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Amobile operating systemis anoperating systemused forsmartphones,tablets,smartwatches, smartglasses, or other non-laptoppersonalmobile computing devices. While computers such aslaptopsare "mobile", the operating systems used on them are usually not considered mobile, as they were originally designed fordesktop computersthat historically did not have or need specificmobilefeatures. This "fine line" distinguishing mobile and other forms has become blurred in recent years, due to the fact that newer devices have become smaller and more mobile, unlike thehardwareof the past. Key notabilities blurring this line are the introduction oftablet computers, lightlaptops, and the hybridization of the2-in-1 PCs.
Mobile operating systems combine features of adesktop computeroperating system with other features useful for mobile or handheld use, and usually including a wireless inbuilt modem andSIMtray for telephone and data connection. In Q1 2018, over 123 million smartphones were sold (the most ever recorded) with 60.2% runningAndroidand 20.9% runningiOS.[1]Sales in 2012 were 1.56 billion; sales in 2023 were 1.43 billion[2]with 53.32% beingAndroid.[3]Android alone has more sales than the popular desktop operating systemMicrosoft Windows, and smartphone use (even without tablets) outnumbers desktop use.[4]
Mobile devices, with mobile communications abilities (for example,smartphones), contain two mobile operating systems. The main user-facing software platform is supplemented by a second low-level proprietary real-time operating system which operates the radio and other hardware. Research has shown that these low-level systems may contain a range of security vulnerabilities permitting malicious base stations to gain high levels of control over the mobile device.[5]
Mobile operating systems have had the most use of any operating system since 2017 (measured by web use).[2]
Mobile operating system milestones mirror the development ofmobile phones,PDAs, and smartphones:
These operating systems often run atopbasebandor otherreal-time operating systemsthat handle hardware aspects of the phone.
Android (based on the modifiedLinux kernel) is a mobile operating system developed by Open Handset Alliance.[118]The base system isopen-source(and only the kernelcopyleft), but the apps and drivers which provide functionality are increasingly becomingclosed-source.[119]Besides having the largest installed base worldwide on smartphones, it is also the most popular operating system forgeneral purpose computers[further explanation needed](a category that includes desktop computers and mobile devices), even though Android is not a popular operating system for regular (desktop)personal computers(PCs). Although the Android operating system isfree and open-source software,[120]in devices sold, much of the softwarebundledwith it (including Google apps and vendor-installed software) isproprietary softwareand closed-source.[121]
Android's releases before2.0(1.0,1.5,1.6) were used exclusively on mobile phones. Android 2.x releases were mostly used for mobile phones but also some tablets.Android 3.0was a tablet-oriented release and does not officially run on mobile phones. Both phone and tablet compatibility were merged withAndroid 4.0. The current Android version isAndroid 14, released on October 4, 2023.
Android One, a successor toGoogle Nexus, is a software experience that runs on the unmodified Android operating system. Unlike most of the "stock" Androids running on the market, the Android OneUser Interface(UI) closely resembles theGoogle PixelUI, due to Android One being a software experience developed by Google and distributed to partners such asNokia Mobile (HMD)andXiaomi. Thus, the UI is intended to be as clean as possible.Original equipment manufacturer(OEM) partners may tweak or add additional apps such as cameras to thefirmware, but most of the apps are handled proprietarily by Google. Operating system updates are handled by Google and internally tested by OEMs before being distributed via anOTA updatetoend users.
BharOS is a mobile operating system in India. It is an Indian government-funded project to develop a free and open-source operating system (OS) for use in government and public systems.
BlackBerry Secure is an operating system developed byBlackBerry, based on the Android Open Source Project (AOSP). BlackBerry officially announced the name for their Android-basedfront-endtouch interfacein August 2017, before which BlackBerry Secure was running on BlackBerry brand devices, such asBlackBerry Priv,DTEK 50/60andBlackBerry KeyOne. Currently, BlackBerry plans to license out the BlackBerry Secure to other OEMs.
CalyxOSis anoperating systemfor smartphones based on Android with mostlyfree and open-sourcesoftware. It is produced by theCalyx Instituteas part of its mission to "defend online privacy, security and accessibility."
Cherry OSis a customized operating system that was developed byCherry Mobile. It was first released in 2017 and has been developed with a light interface, optimized performance, tools for security, battery management, and access to localized apps.
ColorOSis a custom front-end touch interface based on the Android Open Source Project (AOSP) and developed byOPPO Electronics Corp.In 2016, OPPO officially released ColorOS with every OPPO andRealmedevice and released an officialROMfor theOnePlus One. Future Realme devices will have their own version of ColorOS.
CopperheadOSis asecurity-hardenedversion of Android.
DivestOSis a soft fork ofLineageOS.[122]Includes Monthly Updates, FOSS Focus, Deblobbing, Security and Privacy focus, and F-Droid[123]
Huawei EMUI is the front-end touch interface developed byHuawei Technologies Co. Ltd.and its sub-brandHonorwhich is based on Google's Android Open Source Project (AOSP). EMUI is preinstalled on most Huawei and Honor devices. While it was based on the open-source Android operating system, it consists of closed-source proprietary software. Since the US sanctions, it is currently a fork of Android similar to FireOS instead of a compatible one.
In mainland China, and internationally since 2020 due to U.S. sanctions, EMUI devices use Huawei Mobile Services such as Huawei AppGallery instead of Google Mobile Services. Aside from being based on Android, Huawei also bundles the HarmonyOS microkernel in the latest EMUI update inside Android, which handles other processes including security authentication such as the fingerprint authentication.[124]
/e/ is an operating systemforkedfrom the source code ofLineageOS(based on Android). /e/ targets Android smart phone devices and usesMicroGas a replacement forGoogle Play Services.[125]/e/OS is not completelyopen source software, because it comes with the proprietary Magic Earth 'Maps' app.
Amazon Fire OSis a mobile operating system forked from Android and produced byAmazonfor itsFire range of tablets,Echoand Echo Dot, and other content delivery devices likeFire TV(previously for theirFire Phone). Fire OS primarily centers on content consumption, with a customized user interface and heavy ties to content available from Amazon's own storefronts and services.
Flyme OSis an operating system developed byMeizu Technology Co., Ltd., anopen-sourceoperating system based on the Android Open Source Project (AOSP). Flyme OS is mainly installed on Meizu smartphones such as theMX series. However, it also has officialROMsupport for a few Android devices.
Funtouch OSis a custom user interface developed byVivothat is based on the Android Open Source Project. FuntouchOS 10.5 had a redesigned UI that resembled stock Androids.
iQOO UI was a custom user interface based on Vivo's FuntouchOS. The UI largely resembled its predecessor, with a customized UI on top of the FuntouchOS. It was installed on iQOO smartphones sold inChinaand later was succeeded by OriginOS
GrapheneOS is a variant of Android forPixelhardware.
Hello UI (formerly called My UI and My UX) is a custom Android UI developed by Motorola for their devices. It used to look like the stock Android user experience up until My UI 3.x.
HiOS is an Android-based operating system developed byHong Kongmobile phone manufacturerTecno Mobile, a subsidiary ofTranssion Holdings, exclusively for their smartphones. HiOS allows for a wide range of user customization without requiringrootingthe mobile device. The operating system is also bundled with utility applications that allow users to free up memory, freeze applications, limit data accessibility to applications among others. HiOS comes with features like Launcher, Private Safe, Split Screen and Lockscreen Notification.
HTC Sense is a software suite developed by HTC, used primarily on the company's Android-based devices. Serving as a successor to HTC'sTouchFLO 3Dsoftware forWindows Mobile, Sense modifies many aspects of the Androiduser experience, incorporating added features (such as an altered home screen and keyboard),widgets, HTC-developed applications, and redesigned applications. The first device with Sense, theHTC Hero, was released in 2009.
Xiaomi HyperOS or HyperOS (formerly calledMIUI[127][128]), developed by the Chinese electronic companyXiaomi, is a mobile operating system based on theAndroid Open Source Project(AOSP). It is mostly founded in Xiaomi smartphones and tablets such as the Xiaomi (formerly Mi) andRedmiSeries. However, MIUI also had official ROM support for a few Android devices. Although HyperOS is based on AOSP, which is open-source, it consisted of closed-source proprietary software.
A specific version of MIUI developed for Xiaomi sub-brand (Currently an independence brand)POCO, the overall experience of the "skin" was similar to those of standard MIUI expect during the early release of MIUI for POCO where compared to standard MIUI it has an app drawer and allowed for 3rd party Android icon customization. Whereas the current MIUI for POCO shared all the common experience with those of standard MIUI, except the icon and the POCO Launcher instead of stock MIUI Launcher. In 2024 MIUI for POCO was replaced by Xiaomi HyperOS.
Indus OS is a custom mobile operating system based on the Android Open Source Project (AOSP). It is developed by the Indus OS team based in India. No longer valid as of 2018, Indus OS is available onMicromax,Intex,Karbonn, and other Indian smartphone brands.
LG UX (formerlyOptimus UI) was a front-end touch interface developed by LG Electronics and partners, featuring a fulltouch user interface. It was not an operating system. LG UX was used internally by LG for sophisticatedfeature phonesand tablet computers, and was not available for licensing by external parties.
Optimus UI 2, based on Android 4.1.2, has been released on the Optimus K II and the Optimus Neo 3. It features a more refined user interface compared to the prior version based on Android 4.1.1, along with new functionalities such as voice shutter and quick memo.
Lineage Android Distribution is a custom mobile operating system based on the Android Open Source Project (AOSP). It serves as the successor to the highly popular custom ROM,CyanogenMod, from which it was forked in December 2016 when Cyanogen Inc. announced it was discontinuing development and shut down the infrastructure behind the project. Since Cyanogen Inc. retained the rights to the Cyanogen name, the project rebranded its fork as LineageOS.
Similar to CyanogenMod, it does not include any proprietary apps unless the user installs them. It allows Android users who can no longer obtain update support from their manufacturer to continue updating their OS version to the latest one based on official release from Google AOSP and heavy theme customization.
"MagicOS" (formerly known as Magic UI and Magic Live) is a front-end touch interface developed byHonoras a subsidiary of Huawei Technologies Co. Ltd before Honor became an independent company.
Magic UI is based on HuaweiEMUI, which is based on the Android Open Source Project (AOSP). The overall user interface looks almost identical to EMUI, even after the separation. While it was based on the open-source Android operating system, it consists of closed-source proprietary software.
Due to sanctions imposed by the US on Huawei, new devices released by both Huawei and Honor are no longer allowed to includeGoogle Mobile Services. To allow Honor to regain access to Google services, Huawei sold off Honor to become an independent company, thereby allowing them to pre-install Google Mobile Services on their latest devices.
MyOS (formerly called MiFavor) is a custom Android UI developed byZTEfor their flagship smartphones andnubiasmartphones. MyOS is based on the Android Open Source Project (AOSP). This is a redesign from their previous custom Android UI, MiFavor.
Nothing OS is a custom Android UI developed byNothingfor theirNothing Phone (1). Nothing OS design interface are identical to the stock Android and Pixel UI experience, aside from their custom font and widget which is based on dot design.
nubia UI was a custom Android UI developed byZTEandnubiafor their smartphones. nubia UI was based on the Android Open Source Project (AOSP).
One UI (formerly calledTouchWizandSamsung Experience) is a user interface developed by Samsung Electronics in 2008 with partners. It is not a true operating system, but auser experience. Samsung Experience is used internally by Samsung for smartphones,feature phones, and tablet computers. The Android version of Samsung Experience also came with Samsung-made apps preloaded until theGalaxy S6, which removed all Samsung pre-loaded apps exceptSamsung Galaxy Store(formerly Galaxy Apps) to save storage space due to the removal of itsMicroSD. With the release of Samsung Galaxy S8 and S8+, Samsung Experience 8.1 was preinstalled on it with new functions, known as Samsung DeX. Similar to the concept of Microsoft Continuum, Samsung DeX allowed high-end Galaxy devices such as S8/S8+ or Note 8 to connect into a docking station, which extends the device to allow desktop-like functionality by connecting a keyboard, mouse, and monitor. Samsung also announced "Linux on Galaxy", which allows users to use the standard Linux distribution on the DeX platform.
Additionally, starting fromGalaxy Note 3onwards. Samsung had includedKnox, a hardware-based security platform to most of their Galaxy phones as an additional security measure on top of the TEE OS. Allowing user to have a secure environment in within their Secure Folder to have more protected environment to install sensitive apps, which separated from the main homescreen.
Origin OSis a custom user interface developed by Vivo that is based on Android. It is a redesigned skin of Funtouch OS. It is currently only available in China but may someday be released globally.
OxygenOS is based on the open source Android Open Source Project (AOSP) and is developed byOnePlusto replace Cyanogen OS on OnePlus devices such as theOnePlus One. It is preinstalled on theOnePlus 2,OnePlus X,OnePlus 3,OnePlus 3T,OnePlus 5,OnePlus 5T, andOnePlus 6.[130]As stated by Oneplus, OxygenOS is focused on stabilizing and maintaining of stock Android functionalities like those found onNexusdevices. It consists of mainly Google apps and minor UI customization to maintain the sleekness of stock Android.
Google Pixel UIor Pixel Launcher is developed by Google and based on the open-source Android system. Unlike Nexus phones, where Google shipped with stock Android, the UI that came with first-generationPixelphones was slightly modified. As part of the Google Pixel software, the Pixel UI and its home launcher are closed-source and proprietary, so it is only available on Pixel family devices. However, third-party mods allow non-Pixel smartphones to install Pixel Launcher withGoogle Nowfeed integration. FromPixel 3series onwards, Google had included the Trusty OS as their TEE OS running aside Android.
realme UI is a mobile operating system developed byRealmewhich is based onOPPOColorOS, which itself is based on the Android Open Source Project (AOSP). The UI mostly resemble its predecessor, but with a custom UI on top of ColorOS to match Realme's target audience.
realme UI R edition is a custom Android skin that Realme developed for their lower-end device line with "C" and Narzo series, the Android-based line of is based onAndroid Go, hence the overall experience is tune down to allowed for smoother experience on budget Realme devices.
Red Magic OS is a mobile operating system developed by ZTE andNubiafor their Red Magic devices.
Replicant is a custom mobile operating system based on the Android with all proprietary drivers andbloatedclosed-source software removed.
TCL UI is a custom user interface developed byTCL Technologyfor their in-house smartphone series. The OS is based on the Android Open Source Project (AOSP).
VOS is a custom Android UI developed byBQ AquarisandVsmart.
XOS (formerly known as XUI) is an Android-based operating system developed byHong Kongmobile phone manufacturerInfinix Mobile, a subsidiary ofTranssion Holdings, exclusively for their smartphones. XOS allows for a wide range of user customization without requiringrootingthe mobile device. The operating system comes with utility applications that allow users to protect their privacy, improve speed, enhance their experience, etc. XOS comes with features like XTheme, Scan to Recharge, Split Screen and XManager.
Sony Xperia UI (formerly known as Sony Ericsson Timescape UI) was the front-end UI developed bySony Mobile(formerly Sony Ericsson) in 2010 for their Android-basedSony Xperiaseries. Sony Xperia UI mostly consisted of Sony's own applications such as Sony Music (formerly known as Walkman Music player), Albums and Video Player. During its time as Timescape UI, the UI differed from the standard Android UI—instead of traditional apps dock on the bottom part, they were located at the four corners of the home screen, while the middle of the screen consisted of thewidget. However, recent UI developments more closely resemble those of stock Android.
ZenUI is a front-end touch interface developed byASUSwith partners, featuring a full touch user interface. ZenUI is used by ASUS for itsAndroid phonesand tablet computers, and is not available for licensing by external parties. ZenUI also comes preloaded with ASUS-made apps like ZenLink (PC Link, Share Link, Party Link & Remote Link).
ZUI is a custom operating system originally developed byLenovosubsidiaryZUK Mobilefor their smartphones. However, after the shutting down of ZUK Mobile, Lenovo took over as the main developer of ZUI. The operating system is based on the Android Open Source Project (AOSP).
Wear OS (also known simply as Wear and formerly Android Wear) is a version of Google's Android operating system designed for smartwatches and otherwearables. By pairing with mobile phones running Android version 6.0 or newer, or iOS version 10.0 or newer with limited support from Google's pairing application, Wear OS integratesGoogle Assistanttechnology and mobile notifications into a smartwatch form factor.
In May 2021 atGoogle I/O, Google announced a major update to the platform, internally known as Wear OS 3.0. It incorporates a new visual design inspired by Android 12, and Fitbit exercise tracking features. Google also announced a partnership with Samsung Electronics, who is collaborating with Google to unify its Tizen-based smartwatch platform with Wear OS, and has committed to using Wear OS on its future smartwatch products. The underlying codebase was also upgraded to Android 11. Wear OS 3.0 will be available to Wear OS devices runningQualcomm SnapdragonWear 4100system on chip, and will be an opt-in upgrade requiring a factory reset to install.
One UI Watch is the user interface Samsung developed for their Wear OS based smartwatch, officially announced after both Google and Samsung confirmed they would unify their respective wearable operating systems (Google Wear OS 2.0 and Samsung Tizen) into Wear OS 3.0.
ChromeOS is an operating system designed by Google that is based on the Linux kernel and uses theGoogle Chromeweb browser as its principal user interface. As a result, ChromeOS primarily supportsweb applications. Google announced the project in July 2009, conceiving it as an operating system in which both applications and user data reside in thecloud: hence ChromeOS primarily runsweb applications.[132]
Due to increase of popularity with 2-in-1 PCs, most recent Chromebooks are introduced with touch screen capability, with Android applications starting to become available for the operating system in 2014. And in 2016, access to Android apps in the entireGoogle Play Storewas introduced on supported ChromeOS devices. With the support of Android applications, there are Chromebook devices that are positioned as tablet based instead of notebooks.
ChromeOS is only available pre-installed on hardware from Google manufacturing partners. An open source equivalent,ChromiumOS, can becompiledfrom downloadedsource code. Early on, Google provided design goals for ChromeOS, but has not otherwise released a technical description.
Sailfish OS is from Jolla. It is open source withGNU General Public License(GPL) for middleware stack core which comes from MER. Sailfish due to Jolla's business model and due to alliances with various partners and due to intentional design of OS internals, is capable to adopt in several layers third-party software including Jolla software e.g. Jolla's UI is proprietary software (closed source), so such components can be proprietary with many kinds of licences. However, user can replace them with open source components like e.g. NEMO UI instead Jolla's UI.
After Nokia abandoned in 2011 the MeeGo project, most of the MeeGo team left Nokia, and established Jolla as a company to use MeeGo and Mer business opportunities. The MER standard allows it to be launched on any hardware with kernel compatible with MER. In 2012, Linux Sailfish OS based on MeeGo and using middleware of MER core stack distribution was launched for public use. The first device, theJolla smartphone, was unveiled on May 20, 2013. In 2015, Jolla Tablet was launched and theBRICScountries declared it an officially supported OS there. Jolla started licensing Sailfish OS 2.0 for third parties. Some devices sold are updateable to Sailfish 2.0 with no limits.
Nemo Mobileis a community-driven OS, similar to Sailfish but attempting to replace its proprietary components, such as the user interface.[133][134][135]
SteamOS is aLinux distributiondeveloped byValve. It incorporates Valve's popular namesakeSteamvideo game storefront and is the primary operating system forSteam Machinesand theSteam Deck. SteamOS isopen sourcewith some closed source components.
SteamOS was originally built to support streaming of video games from onepersonal computerto the one running SteamOS within the same network, although the operating system can support standalone systems and was intended to be used as part of Valve'sSteam Machineplatform. SteamOS versions 1.0, released in December 2013, and 2.0 were based on theDebiandistribution of Linux withGNOMEdesktop.[136]With SteamOS, Valve encouraged developers to incorporate Linux compatibility into their releases to better support Linux gaming options.
In February 2022, Valve released thehandheldgaming computerSteam Deckrunning SteamOS 3.0. SteamOS 3 is based on theArch Linuxdistribution withKDE Plasma 5.[137][138]
Tizen (based on the Linux kernel) is a mobile operating system hosted by Linux Foundation, together with support from the Tizen Association, guided by a Technical Steering Group composed of Intel and Samsung.
Tizen is an operating system for devices including smartphones, tablets,In-Vehicle Infotainment(IVI) devices, however currently it mainly focuses on wearable and smart TVs. It is an open source system (however the SDK was closed-source and proprietary) that aims to offer a consistent user experience across devices. Tizen's main components are the Linux kernel and theWebKitruntime. According to Intel, Tizen "combines the best of LiMo and MeeGo."HTML5apps are emphasized, with MeeGo encouraging its members to transition to Tizen, stating that the "future belongs to HTML5-based applications, outside of a relatively small percentage of apps, and we are firmly convinced that our investment needs to shift toward HTML5." Tizen will be targeted at a variety of platforms such as handsets, touch pc, smart TVs and in-vehicle entertainment.[139][140]On May 17, 2013, Tizen released version 2.1, code-named Nectarine.[141]
While Tizen itself was open source, most of the UX and UI layer that was developed by Samsung was mainly closed-source and proprietary, such as the TouchWiz UI on the Samsung Z's series smartphone and One UI for their Galaxy Watch wearable lines.
Note that some refrigerators use Tizen,[142]even though they are not considered mobile devices.
Samsung has revealed plans to discontinue the Tizen operating system by the end of 2025, marking a complete halt in support for the smartwatch OS. The company ceased using Tizen OS with its Galaxy Watch4 release, favoring a hybrid OS developed with Google.
KaiOS is from Kai. It is based onFirefox OS/Boot to Gecko. Unlike most mobile operating systems which focus on smartphones, KaiOS was developed mainly for feature phones, giving these access to more advanced technologies usually found on smartphones, such as app stores and Wi-Fi/4G capabilities.[143]
It is a mix of closed-source and open-source components.[144][145]FirefoxOS/B2G was released under the permissiveMPL 2.0. It does not redistribute itself under the same license, so KaiOS is now presumably proprietary (but still mostlyopen-source, publishing its source code).[144][145]KaiOS is not entirely proprietary, as it uses the copyleftGPLLinux kernel also used in Android.[146]
Smart Feature OSis a custom version of KaiOS that was developed and solely used byHMD Globalfor their KaiOS line of Nokia feature phone. The main differences between stock KaiOS and Smart Feature OS is the aesthetics such as icons, widgets, a custom Nokia ringtone and notification tone.
Fuchsia is a capability-based, real-time operating system (RTOS) currently being developed by Google. It was first discovered as a mysterious code post on GitHub in August 2016, without any official announcement. In contrast to prior Google-developed operating systems such as ChromeOS and Android, which are based on Linux kernels, Fuchsia is based on a new microkernel called "Zircon", derived from "Little Kernel", a small operating system intended for embedded systems. This allows it to remove Linux and the copyleftGPLunder which the Linux kernel is licensed; Fuchsia is licensed under thepermissiveBSD 3-clause,Apache 2.0, andMIT licenses. Upon inspection, media outlets noted that the code post on GitHub suggested Fuchsia's capability to run on universal devices, from embedded systems to smartphones, tablets and personal computers. In May 2017, Fuchsia was updated with a user interface, along with a developer writing that the project was not a for experimental, prompting media speculation about Google's intentions with the operating system, including the possibility of it replacing Android.[147]
LiteOS is a discontinued lightweight open source real-time operating system which is part of Huawei's "1+2+1" Internet of Things solution, which is similar to Google Android Things and Samsung Tizen. It was released under thepermissiveBSD 3-clause license. LiteOS was used in the Huawei Watch GT series and their sub-brand Honor Magic Watch series.[citation needed]
OpenHarmonyis an open-source version of HarmonyOS developed and donated by Huawei to the OpenAtom Foundation. It supports devices running a mini system with memory as small as 128 KB, or running a standard system with memory greater than 128 MB. The open sourceHarmonyOSis based on the HuaweiLiteOSkernel andLinux kernelfor standard systems. OpenHarmony LiteOS Cortex-A brings small-sized, low-power, and high-performance experience and builds a unified and open ecosystem for developers. In addition, it provides rich kernel mechanisms, more comprehensive Portable Operating System Interface (POSIX), and a unified driver framework, Hardware Driver Foundation (HDF), which offers unified access for device developers and friendly development experience for application developers.[citation needed]
Fedora Mobility is under developing mobile operating system by the Fedora Project that are porting Fedora to run on portable devices such as phones and tablets.
LuneOS is a modern reimplementation of the Palm/HP webOS interface.
Manjaro ARM is a mobile operating system with Plasma Mobile desktop environment that is running and default operating system on the PinePhone, an ARM-based smartphone released by Pine64.
A mobileDebianfocused forPinePhoneand soonLibrem.[citation needed]
Plasma Mobile is a Plasma variant for smartphones.[148]Plasma Mobile runs onWaylandand it is compatible with Ubuntu Touch applications,[149]PureOSapplications,[150]and eventually Android applications[151]via KDE'sShashlikproject – also sponsored by Blue Systems,[152][153]orAnbox. It is under the copyleftGPLv2license.
TheNecunophone uses Plasma Mobile. It is entirely open-source and thus does not have a cellular modem, so it must make calls byVOIP, like a pocket computer.[154]
postmarketOS is based on theAlpine LinuxLinux distribution. It is intended to run on older phone hardware. As of 2019[update]it is inalpha.
PureOS is a Debian GNU/Linux derivative using onlyfree softwaremeeting theDebian Free Software Guidelines, mainly thecopyleftGPL. PureOS is endorsed byFree Software Foundationas one of the freedom-respecting operating systems.[155]It is developed byPurism, and was already in use on Purism's laptops before it was used on theLibrem 5smartphone. Purism, in partnership withGNOMEandKDE, aims to separate theCPUfrom thebaseband processorand include hardwarekill switchesfor the phone'sWi-Fi,Bluetooth, camera, microphone, and baseband processor, and provide both GNOME andKDE Plasma Mobileas options for the desktop environment.[156][157]
Ubuntu Touch is an open-source (GPL) mobile version of theUbuntuoperating system[112]originally developed in 2013 byCanonical Ltd.and continued by the non-profit UBports Foundation in 2017.[158][159]Ubuntu Touch can run on a pure GNU/Linux base on phones with the required drivers, such as theLibrem 5[150]and thePinePhone.[160]To enable hardware that was originally shipped with Android, Ubuntu Touch makes use of the Android Linux kernel, using Android drivers and services via anLXCcontainer, but does not use any of the Java-like code of Android.[161][162]As of February 2022, Ubuntu Touch is available on 78 phones and tablets.[112][163]The UBports Installer serves as an easy-to-use tool to allow inexperienced users to install the operating system on third-party devices without damaging their hardware.[112][164]
iOS (formerly named iPhone OS) was created byApple Inc.It has the second largest installed base worldwide on smartphones, but the largest profits, due to aggressive price competition between Android-based manufacturers.[165]It is closed-source and proprietary, and is built on the open sourceDarwinoperating system. The iPhone,iPod Touch,iPad, and second and third-generationApple TVall use iOS, which is derived frommacOS.
Native third-party applications were not officially supported until the release of iPhone OS 2.0 on July 11, 2008. Before this, "jailbreaking" allowed third-party applications to be installed. In recent years, the jailbreaking scene has changed drastically due to Apple's continued efforts to secure their operating system and prevent unauthorized modifications. Currently, jailbreaks of recent iterations of iOS are only semi-untethered, which requires a device to be re-jailbroken at every boot, and exploits for jailbreaks are becoming increasingly hard to find and use.
Currently all iOS devices are developed by Apple and manufactured byFoxconnor another of Apple's partners.
iPadOS is a tablet operating system created and developed by Apple Inc. specifically for their iPad line of tablet computers. It was announced at the company's 2019 Worldwide Developers Conference (WWDC), as a derivation from iOS but with a greater emphasis put on multitasking. It was released on September 24, 2019.
watchOS is the operating system of the Apple Watch, developed by Apple Inc. It is based on the iOS operating system and has many similar features. It was released on April 24, 2015, along with the Apple Watch, the only device that runs watchOS. It is currently the most widely used wearable operating system. It features focus on convenience, such as being able to place phone calls and send texts, and health, such as fitness and heart rate tracking.
The most current version of the watchOS operating system iswatchOS 10.
Kindle firmware is a mobile operating system specifically designed forAmazon Kindlee-readers. It is based on a custom Linux kernel, but it is mostly closed-source and proprietary.
HarmonyOS is a distributed operating system developed by Huawei that was specifically designed for smartphones, tablets, TVs, smartwatches, smart devices made by Huawei. It is based on a proprietary multi-kernel and Linux kernel subsystem. Released officially for smartphones on June 2, 2021, from its initial launch on August 9, 2019, for smart screen TVs. On August 4, 2023, Huawei announces its full stackHarmonyOS NEXTfor HarmonyOS that will replace the current multi-kernel stack that contains Linux kernel subsystem with APK apps, with only native HarmonyOS apps able to be used. On January 18, 2024, Galaxy Edition version was announced to be used for the next version of HarmonyOS.
TheNintendo Switch system software(also known by its codename Horizon) is an updatable firmware and operating system used by theNintendo Switchhybrid video game console/tablet andNintendo Switch Litehandheld game console. It is based on a proprietary microkernel. The UI includes a HOME screen, consisting of the top bar, the screenshot viewer ("Album"), and shortcuts to the Nintendo eShop, News, and Settings.
The system itself is based on theNintendo 3DS system software, additionally the networking stack in the Switch OS is derived at least in part fromFreeBSDcode while the Stagefright multimedia framework is derived fromAndroidcode.
ThePlayStation Vita system softwareis the official firmware and operating system for thePlayStation VitaandPlayStation TVvideo game consoles. It uses the LiveArea as its graphical shell. The PlayStation Vita system software has one optional add-on component, the PlayStation Mobile Runtime Package. The system is built on a Unix-base which is derived from FreeBSD and NetBSD.
Windows 10 (not to be confused with Windows 10 Mobile—see below) is a personal computer operating system developed and released by Microsoft as part of theWindows NTfamilyof operating systems. It was released on July 29, 2015, and manyeditionsandversionshave been released since then. It was designed to run across multiple Microsoft product such as PCs and Tablets. The Windows user interface was revised to handle transitions between a mouse-oriented interface and a touchscreen-optimized interface based on available input devices particularly on 2-in-1 PCs.
Windows 10 also introduced universal apps, expanding on Metro-style apps, these apps can be designed to run across multiple Microsoft product families with nearly identical code including PCs, tablets, smartphones, embedded systems, Xbox One, Surface Hub and Mixed Reality.
Windows 11 is a major version of theWindows NToperating system developed by Microsoft that was announced on June 24, 2021, and is the successor to Windows 10, which was released in 2015. Windows 11 was released on October 5, 2021, as a free upgrade viaWindows Updatefor eligible devices running Windows 10.
Microsoft promoted that Windows 11 would have improved performance and ease of use over Windows 10; it features major changes to the Windowsshellinfluenced by the canceledWindows 10X, including a redesignedStart menu, the replacement of its "live tiles" with a separate "Widgets" panel on thetaskbar, the ability to create tiled sets of windows that can be minimized and restored from thetaskbaras a group, and new gaming technologies inherited fromXbox Series X and Series Ssuch asAuto HDRandDirectStorageon compatible hardware.Internet Exploreris fully replaced by theBlink layout engine-basedMicrosoft Edge, whileMicrosoft Teamsis integrated into the Windows shell. Microsoft also announced plans to offer support for Androidappsto run on Windows 11, with support forAmazon Appstoreand manually-installedpackages. On March 5, 2024, Microsoft announced that Android apps support will be depreciated on March 5, 2025.
Similar to Windows 10, it was designed to run across multiple Microsoft product such as PCs and Tablets. The Windows user interface was further revised to combine the UI element of both mouse-oriented interface and a touchscreen-optimized interface based into a hybrid UI that combined the capabilities of touch with a traditional desktop UI.
Other than the major operating systems, some companies such as Huami (Amazfit), Huawei, realme, TCL, and Xiaomi have developed their own proprietary RTOSes specifically for their own smartbands and smartwatches that are designed for power effiency and lower battery consumption and are not based on any other operating system.
Operating System that is primarily designed for their Bip series, however, Huami is currently developing the operating system to run on other smartwatches as well.
Huawei Band Operating system is an operating system specifically designed and developed by Huawei for their fitness trackers, including smartbands fromHonor
Proprietary OS developed by Lenovo for their fitness trackers and smartwatches.
A proprietary operating system design to run on realme smartbands and smartwatches.
A proprietary RTOS powering TCL and Alcatel branded smartbands and smartwatches.
Proprietary RTOS that is developed by Huami for theXiaomi Mi Bandseries.
CyanogenMod was a custom mobile operating system based on the Android Open Source Project (AOSP). It was a custom ROM that was co-developed by the CyanogenMod community. The OS did not include any proprietary apps unless the user installed them. Due to its open source nature, CyanogenMod allowed Android users who could no longer obtain update support from their manufacturer to continue updating their OS version to the latest one based on official releases from Google AOSP and heavy theme customization. The last version of the OS was CyanogenMod 13 which was based on Android Asus.
On December 24, 2016, CyanogenMod announced on their blog that they would no longer be releasing any CyanogenMod updates. All development moved to LineageOS.
Cyanogen OS was based onCyanogenModand maintained by Cyanogen Inc; however, it included proprietary apps and it was only available for commercial uses.
Firefox OS (formerly known as "Boot to Gecko" and shortly "B2G")[166]is from Mozilla. It was an open source mobile operating system released under theMozilla Public Licensebuilt on the Android Linux kernel and used Android drivers, but did not use any Java-like code of Android.
According toArs Technica, "Mozilla says that B2G is motivated by a desire to demonstrate that the standards-based open Web has the potential to be a competitive alternative to the existing single-vendor application development stacks offered by the dominant mobile operating systems."[167]In September 2016, Mozilla announced that work on Firefox OS has ceased, and all B2G-related code would be removed from mozilla-central.[168]
MeeGowas from non-profit organizationThe Linux Foundation. It is open source and GPL. At the 2010Mobile World Congressin Barcelona, Nokia and Intel both unveiledMeeGo, a mobile operating system that combined Moblin and Maemo to create an open-sourced experience for users across all devices. In 2011 Nokia announced that it would no longer pursue MeeGo in favor of Windows Phone. Nokia announced theNokia N9on June 21, 2011, at the Nokia Connection event[169]in Singapore. LG announced its support for the platform.[170]Maemo was a platform developed by Nokia for smartphones andInternet tablets. It is open source and GPL, based onDebian GNU/Linuxand draws much of itsgraphical user interface(GUI),frameworks, andlibrariesfrom the GNOME project. It uses theMatchboxwindow manager and theGTK-basedHildonas its GUI andapplication framework.
webOS was developed by Palm. webOS is an open source mobile operating system running on the Linux kernel, initially developed by Palm, which launched with thePalm Pre. After being acquired by HP, two phones (theVeerand thePre 3) and a tablet (theTouchPad) running webOS were introduced in 2011. On August 18, 2011, HP announced that webOS hardware would be discontinued,[171]but would continue to support and update webOS software and develop the webOS ecosystem.[172]HP released webOS as open source under the name Open webOS, and plans to update it with additional features.[173]On February 25, 2013, HP announced the sale of webOS to LG Electronics, who used the operating system for its "smart" or Internet-connected TVs. However, HP retained patents underlying WebOS and cloud-based services such as the App Catalog.
Bada platform (stylized as bada; Korean: 바다) was an operating system for mobile devices such as smartphones and tablet computers. It was developed by Samsung Electronics. Its name is derived from "바다 (bada)", meaning "ocean" or "sea" in Korean. It ranges from mid- to high-end smartphones. To foster adoption of Bada OS, since 2011 Samsung reportedly has considered releasing the source code under an open-source license, and expanding device support to include Smart TVs. Samsung announced in June 2012 intentions to merge Bada into the Tizen project, but would meanwhile use its own Bada operating system, in parallel with Google Android OS and Microsoft Windows Phone, for its smartphones. All Bada-powered devices are branded under the Wave name, but not all of Samsung's Android-powered devices are branded under the name Galaxy.
On February 25, 2013, Samsung announced that it will stop developing Bada, moving development to Tizen instead. Bug reporting was finally terminated in April 2014.[174]
In 1999,Research In Motionreleased its first BlackBerry devices, providing secure real-time push-email communications on wireless devices. Services such as BlackBerry Messenger provide the integration of all communications into a single inbox. In September 2012, RIM announced that the 200 millionth BlackBerry smartphone was shipped. As of September 2014, there were around 46 million active BlackBerry service subscribers.[175]In the early 2010s, RIM underwent a platform transition, changing its company name to BlackBerry Limited and making new devices using a new operating system named "BlackBerry 10".[176]
BlackBerry 10 (based on theQNXOS) is from BlackBerry. As a smartphone OS, it is closed-source and proprietary, and only runs on phones and tablets manufactured by BlackBerry.
One of the dominant platforms in the world in the late 2000s, its global market share was reduced significantly by the mid-2010s. In late 2016, BlackBerry announced that it will continue to support the OS, with a promise to release 10.3.3.[177][178]Therefore, BlackBerry 10 would not receive any major updates as BlackBerry and its partners would focus more on their Android base development.[179]
TheNintendo 3DS system softwareis the updatable operating system used by the Nintendo 3DS.
Symbian platform was developed by Nokia for some models of smartphones. It is proprietary software, it was however used by Ericsson (Sony Ericsson), Sending and Benq. The operating system was discontinued in 2012, although a slimmed-down version for basic phones was still developed until July 2014. Microsoft officially shelved the platform in favor of Windows Phone after its acquisition of Nokia.[180]
Palm OS/Garnet OS was fromAccess Co.It is closed-source and proprietary. webOS was introduced by Palm in January 2009, as the successor to Palm OS with Web 2.0 technologies,open architectureand multitasking abilities.
Windows Mobile was a family of proprietary operating systems from Microsoft aimed at business and enterprise users, based on Windows CE and originally developed forPocket PC(PDA) devices. In 2010 it was replaced with the consumer-focused Windows Phone.[118][55]
Versions of Windows Mobile came in multiple editions, like "Pocket PC Premium", "Pocket PC Professional", "Pocket PC Phone", and "Smartphone" (Windows Mobile 2003) or "Professional", "Standard", and "Classic" (Windows Mobile 6.0). Some editions were touchscreen-only and some were keyboard-only, although there were cases where device vendors managed to graft support for one onto an edition targeted at the other. Cellular phone features were also only supported by some editions. Microsoft started work on a version of Windows Mobile that would combine all features together, but it was aborted, and instead they focused on developing the non-backward-compatible, touchscreen-only Windows Phone 7.[76]
Windows Phone is a proprietary mobile operating system developed by Microsoft for smartphones as the replacement successor to Windows Mobile andZune. Windows Phone features a new touchscreen-oriented user interface derived from Metro design language. Windows Phone was replaced by Windows 10 Mobile in 2015.
Windows 10 Mobile (formerly called Windows Phone) was from Microsoft. It was closed-source and proprietary.
Unveiled on February 15, 2010, Windows Phone included a user interface inspired by Microsoft'sMetro Design Language. It was integrated with Microsoft services such asOneDriveand Office,Xbox Music,Xbox Video,Xbox Livegames, andBing, but also integrated with many other non-Microsoft services such asFacebookandGoogle accounts. Windows Phone devices were made primarily byMicrosoft Mobile/Nokia, and also by HTC and Samsung.
On January 21, 2015, Microsoft announced that the Windows Phone brand would be phased out and replaced with Windows 10 Mobile, bringing tighter integration and unification with its PC counterpart Windows 10, and providing a platform for smartphones and tablets with screen sizes under 8 inches.
On October 8, 2017, Microsoft officially announced that they would no longer push any major updates to Windows 10 Mobile. The operating system was put in maintenance mode, where Microsoft would push bug fixes and general improvements only. Windows 10 Mobile would not receive any new feature updates.[113][114]
On January 18, 2019, Microsoft announced that support for Windows 10 Mobile wouldendon December 10, 2019, with no further security updates released after then, and that Windows 10 Mobile users should migrate to iOS or Android phones.[116][117]
The released version of Windows 10 Mobile were:
Windows 8is a major release of theWindows NToperating systemdeveloped byMicrosoft. It wasreleased to manufacturingon August 1, 2012, and was made available for download viaMSDNandTechNeton August 15, 2012.[181]Nearly three months after its initial release, it finally made its first retail appearance on October 26, 2012.[182]
Windows 8 introduced major changes to the operating system's platform anduser interfacewith the intention to improve its user experience ontablets, whereWindowscompeted with mobile operating systems such asAndroidandiOS.[183]In particular, these changes included a touch-optimizedWindows shellandstart screenbased on Microsoft'sMetrodesign language, integration with online services, theWindows Store, and a new keyboard shortcut forscreenshots.[184]Many of these features were adapted fromWindows Phone. Windows 8 also added support forUSB 3.0,Advanced Format,near-field communication, andcloud computing, as well as a new lock screen with clock and notifications and the previously released "Domino" and "Beauty and a Beat". Additional security features—including built-inantivirus software, integration withMicrosoft SmartScreenphishing filtering, and support forSecure Booton supported devices—were introduced. It was the first Windows version to support ARM architecture under theWindows RTbranding. No CPUs withoutPAE,SSE2andNXare supported in this version.
Windows 8.1is a release of theWindows NToperating systemdeveloped byMicrosoft. It wasreleased to manufacturingon August 27, 2013, and broadly released for retail sale on October 17, 2013, about a year after the retail release of its predecessor, and succeeded byWindows 10on July 29, 2015. Windows 8.1 was made available for download viaMSDNandTechnetand available as a free upgrade for retail copies ofWindows 8andWindows RTusers via theWindows Store. Aserverversion,Windows Server 2012 R2, was released on October 18, 2013.
Windows 8.1 aimed to address complaints of Windows 8 users and reviewers on launch. Enhancements include an improvedStart screen, additional snap views, additional bundled apps, tighterOneDrive(formerly SkyDrive) integration,Internet Explorer 11(IE11), aBing-powered unified search system, restoration of a visibleStart buttonon thetaskbar, and the ability to restore the previous behavior of opening the user's desktop on login instead of the Start screen.
In 2006, Android and iOS did not exist and only 64 million smartphones were sold.[185]In 2018 Q1, 183.5 million smartphones were sold and global market share was 48.9% for Android and 19.1% for iOS. Only 131,000 smartphones running other operating systems were sold, constituting 0.03% of sales.[186]
According toStatCounterweb use statistics (a proxy for all use), smartphones (alone without tablets) have majority use globally, with desktop computers used much less (and Android, in particular, more popular than Windows).[187]Use varies however by continent with smartphones way more popular in the biggest continents, i.e. Asia, and the desktop still more popular in some, though not in North America.
The desktop is still popular in many countries (while overall down to 44.9% in the first quarter of 2017[188]), smartphones are more popular even in many developed countries (or about to be in more). A few countries on any continent are desktop-minority; European countries (and some in South America, and a few, e.g. Haiti, in North America; and most in Asia and Africa) are smartphone-majority, Poland and Turkey highest with 57.68% and 62.33%, respectively. In Ireland, smartphone use at 45.55% outnumbers desktop use and mobile as a whole gains majority when including the tablet share at 9.12%.[189][188]Spain is also slightly desktop-minority.
The range of measured mobile web use varies a lot by country, and a StatCounter press release recognizes "India among world leaders in use of mobile to surf the internet"[190](of the big countries) where the share is around (or over) 80%[191]and desktop is at 19.56%, with Russia trailing with 17.8% mobile use (and desktop the rest).
Smartphones (alone, without tablets), first gained majority in December 2016 (desktop-majority was lost the month before), and it was not a Christmas-time fluke, as while close to majority after smartphone majority happened again in March 2017.[188]
In the week from November 7–13, 2016, smartphones alone (without tablets) overtook desktop, for the first time (for a short period; non-full-month).[192]Mobile-majority applies to countries such as Paraguay in South America, Poland in Europe and Turkey; and most of Asia and Africa. Some of the world is still desktop-majority, with e.g. in the United States at 54.89% (but no not on all days).[193]However, in someterritories of the United States, such asPuerto Rico,[194]desktop is way under majority, with Windows under 30% overtaken by Android.
On October 22, 2016 (and subsequent weekends), mobile showed majority.[195]Since October 27, the desktop has not shown majority, not even on weekdays. Smartphones alone have shown majority since December 23 to the end of the year, with the share topping at 58.22% on Christmas Day.[196]To the "mobile"-majority share then of smartphones, tablets could be added giving a 63.22% majority. While an unusually high top, a similarly high also happened on Monday April 17, 2017, with then only smartphones share slightly lower and tablet share slightly higher, with them combined at 62.88%.
According to a StatCounter November 1, 2016 press release[update], the world has turned desktop-minority;[197]at about 49% desktop use for the previous month, but mobile was not ranked higher, tablet share had to be added to it to exceed desktop share. By now, mobile (smartphones) have full majority, outnumbering desktop/laptop computers by a safe margin (and no longer counting tablets with desktops makes them most popular).
Notes:
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Scientific consensusis the generally held judgment, position, and opinion of themajorityor thesupermajorityofscientistsin aparticular fieldof study at any particular time.[1][2]
Consensus is achieved throughscholarly communicationatconferences, thepublicationprocess, replication ofreproducibleresults by others, scholarlydebate,[3][4][5][6]andpeer review. A conference meant to create a consensus is termed as a consensus conference.[7][8][9]Such measures lead to a situation in which those within the discipline can often recognize such a consensus where it exists; however, communicating to outsiders that consensus has been reached can be difficult, because the "normal" debates through which science progresses may appear to outsiders as contestation.[10]On occasion, scientific institutes issue position statements intended to communicate a summary of the science from the "inside" to the "outside" of the scientific community, or consensus review articles[11]orsurveys[12]may be published. In cases where there is little controversy regarding the subject under study, establishing the consensus can be quite straightforward.
Popular or political debate on subjects that are controversial within the public sphere but not necessarily controversial within the scientific community may invoke scientific consensus: note such topics asevolution,[13][14]climate change,[15]the safety ofgenetically modified organisms,[16]or the lack of a link betweenMMR vaccinations and autism.[10]
Scientific consensus is related to (and sometimes used to mean)convergent evidence, that is, the concept that independent sources of evidence converge on a conclusion.[17][18]
There are many philosophical and historical theories as to how scientific consensus changes over time. Because the history of scientific change is extremely complicated, and because there is a tendency to project "winners" and "losers" onto the past in relation to thecurrentscientific consensus, it is very difficult to come up with accurate and rigorous models for scientific change.[19]This is made exceedingly difficult also in part because each of the various branches of science functions in somewhat different ways with different forms of evidence and experimental approaches.[20][21]
Most models of scientific change rely on new data produced by scientificexperiment.Karl Popperproposed that since no amount of experiments could everprovea scientific theory, but a single experiment coulddisproveone, science should be based onfalsification.[22]Whilst this forms a logical theory for science, it is in a sense "timeless" and does not necessarily reflect a view on how science should progress over time.
Among the most influential challengers of this approach wasThomas Kuhn, who argued instead that experimentaldataalways provide some data which cannot fit completely into a theory, and that falsification alone did not result in scientific change or an undermining of scientific consensus. He proposed that scientific consensus worked in the form of "paradigms", which were interconnected theories and underlying assumptions about the nature of the theory itself which connected various researchers in a given field. Kuhn argued that only after the accumulation of many "significant" anomalies would scientific consensus enter a period of "crisis". At this point, new theories would be sought out, and eventually one paradigm would triumph over the old one – a series ofparadigm shiftsrather than a linear progression towards truth. Kuhn's model also emphasized more clearly the social and personal aspects of theory change, demonstrating through historical examples that scientific consensus was never truly a matter of pure logic or pure facts.[23]However, these periods of 'normal' and 'crisis' science are not mutually exclusive. Research shows that these are different modes of practice, more than different historical periods.[10]
Perception of whether a scientific consensus exists on a given issue, and how strong that conception is, has been described as a "gateway belief" upon which other beliefs and then action are based.[28]
In public policy debates, the assertion that there exists a consensus of scientists in a particular field is often used as an argument for the validity of a theory. Similarly arguments for alackof scientific consensus are often used to support doubt about the theory.[citation needed]
For example, thescientific consensus on the causes of global warmingis thatglobal surface temperatureshave increased in recent decades and that the trend is caused primarily by human-inducedemissions of greenhouse gases.[29][30][31]Thehistorian of scienceNaomi Oreskespublished an article inSciencereporting that a survey of the abstracts of 928 science articles published between 1993 and 2003 showed none which disagreed explicitly with the notion ofanthropogenic global warming.[29]In an editorial published inThe Washington Post, Oreskes stated that those who opposed these scientific findings are amplifying the normal range of scientific uncertainty about any facts into an appearance that there is a great scientific disagreement, or a lack of scientific consensus.[32]Oreskes's findings were replicated by other methods that require no interpretation.[10]
The theory ofevolution through natural selectionis also supported by an overwhelming scientific consensus; it is one of the most reliable and empirically tested theories in science.[33][34]Opponents of evolution claim that there is significant dissent on evolution within the scientific community.[35]Thewedge strategy, a plan to promoteintelligent design, depended greatly on seeding and building on public perceptions of absence of consensus on evolution.[36]
The inherentuncertainty in science, where theories are neverprovenbut can only bedisproven(seefalsifiability), poses a problem for politicians, policymakers, lawyers, and business professionals. Where scientific or philosophical questions can often languish in uncertainty for decades within their disciplinary settings, policymakers are faced with the problems of making sound decisions based on the currently available data, even if it is likely not a final form of the "truth". The tricky part is discerning what is close enough to "final truth". For example, social action against smoking probably came too long after science was 'pretty consensual'.[10]
Certain domains, such as the approval of certain technologies for public consumption, can have vast and far-reaching political, economic, and human effects should things run awry with the predictions of scientists. However, insofar as there is an expectation that policy in a given field reflect knowable and pertinent data and well-accepted models of the relationships between observable phenomena, there is little good alternative for policy makers than to rely on so much of what may fairly be called 'the scientific consensus' in guiding policy design and implementation, at least in circumstances where the need for policy intervention is compelling. While science cannot supply 'absolute truth' (or even its complement 'absolute error') its utility is bound up with the capacity to guide policy in the direction of increased public good and away from public harm. Seen in this way, the demand that policy rely only on what is proven to be "scientific truth" would be a prescription for policy paralysis and amount in practice to advocacy of acceptance of all of the quantified and unquantified costs and risks associated with policy inaction.[10]
No part of policy formation on the basis of the ostensible scientific consensus precludes persistent review either of the relevant scientific consensus or the tangible results of policy. Indeed, the same reasons that drove reliance upon the consensus drives the continued evaluation of this reliance over time – and adjusting policy as needed.[citation needed]
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In the field ofmultivariate statistics,kernel principal component analysis (kernel PCA)[1]is an extension ofprincipal component analysis(PCA) using techniques ofkernel methods. Using a kernel, the originally linear operations of PCA are performed in areproducing kernel Hilbert space.
Recall that conventional PCA operates on zero-centered data; that is,
wherexi{\displaystyle \mathbf {x} _{i}}is one of theN{\displaystyle N}multivariate observations.
It operates by diagonalizing thecovariance matrix,
in other words, it gives aneigendecompositionof the covariance matrix:
which can be rewritten as
(See also:Covariance matrix as a linear operator)
To understand the utility of kernel PCA, particularly for clustering, observe that, whileNpoints cannot, in general, belinearly separatedind<N{\displaystyle d<N}dimensions, they canalmost alwaysbe linearly separated ind≥N{\displaystyle d\geq N}dimensions. That is, givenNpoints,xi{\displaystyle \mathbf {x} _{i}}, if we map them to anN-dimensional space with
it is easy to construct ahyperplanethat divides the points into arbitrary clusters. Of course, thisΦ{\displaystyle \Phi }creates linearly independent vectors, so there is no covariance on which to perform eigendecompositionexplicitlyas we would in linear PCA.
Instead, in kernel PCA, a non-trivial, arbitraryΦ{\displaystyle \Phi }function is 'chosen' that is never calculated explicitly, allowing the possibility to use very-high-dimensionalΦ{\displaystyle \Phi }'s if we never have to actually evaluate the data in that space. Since we generally try to avoid working in theΦ{\displaystyle \Phi }-space, which we will call the 'feature space', we can create the N-by-N kernel
which represents the inner product space (seeGramian matrix) of the otherwise intractable feature space. The dual form that arises in the creation of a kernel allows us to mathematically formulate a version of PCA in which we never actually solve the eigenvectors and eigenvalues of the covariance matrix in theΦ(x){\displaystyle \Phi (\mathbf {x} )}-space (seeKernel trick). The N-elements in each column ofKrepresent thedot productof one point of the transformed data with respect to all the transformed points (N points). Some well-known kernels are shown in the example below.
Because we are never working directly in the feature space, the kernel-formulation of PCA is restricted in that it computes not the principal components themselves, but the projections of our data onto those components. To evaluate the projection from a point in the feature spaceΦ(x){\displaystyle \Phi (\mathbf {x} )}onto the kth principal componentVk{\displaystyle V^{k}}(where superscript k means the component k, not powers of k)
We note thatΦ(xi)TΦ(x){\displaystyle \Phi (\mathbf {x} _{i})^{T}\Phi (\mathbf {x} )}denotes dot product, which is simply the elements of the kernelK{\displaystyle K}. It seems all that's left is to calculate and normalize theaik{\displaystyle \mathbf {a} _{i}^{k}}, which can be done by solving the eigenvector equation
whereN{\displaystyle N}is the number of data points in the set, andλ{\displaystyle \lambda }anda{\displaystyle \mathbf {a} }are the eigenvalues and eigenvectors ofK{\displaystyle K}. Then to normalize the eigenvectorsak{\displaystyle \mathbf {a} ^{k}}, we require that
Care must be taken regarding the fact that, whether or notx{\displaystyle x}has zero-mean in its original space, it is not guaranteed to be centered in the feature space (which we never compute explicitly). Since centered data is required to perform an effective principal component analysis, we 'centralize'K{\displaystyle K}to becomeK′{\displaystyle K'}
where1N{\displaystyle \mathbf {1_{N}} }denotes a N-by-N matrix for which each element takes value1/N{\displaystyle 1/N}. We useK′{\displaystyle K'}to perform the kernel PCA algorithm described above.
One caveat of kernel PCA should be illustrated here. In linear PCA, we can use the eigenvalues to rank the eigenvectors based on how much of the variation of the data is captured by each principal component. This is useful for data dimensionality reduction and it could also be applied to KPCA. However, in practice there are cases that all variations of the data are same. This is typically caused by a wrong choice of kernel scale.
In practice, a large data set leads to a large K, and storing K may become a problem. One way to deal with this is to perform clustering on the dataset, and populate the kernel with the means of those clusters. Since even this method may yield a relatively large K, it is common to compute only the top P eigenvalues and eigenvectors of the eigenvalues are calculated in this way.
Consider three concentric clouds of points (shown); we wish to use kernel PCA to identify these groups. The color of the points does not represent information involved in the algorithm, but only shows how the transformation relocates the data points.
First, consider the kernel
Applying this to kernel PCA yields the next image.
Now consider aGaussian kernel:
That is, this kernel is a measure of closeness, equal to 1 when the points coincide and equal to 0 at infinity.
Note in particular that the first principal component is enough to distinguish the three different groups, which is impossible using only linear PCA, because linear PCA operates only in the given (in this case two-dimensional) space, in which these concentric point clouds are not linearly separable.
Kernel PCA has been demonstrated to be useful for novelty detection[3]and image de-noising.[4]
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This is a list of topics aroundBoolean algebraandpropositional logic.
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So help me Godis a phrase often used to give anoath, sometimes optionally as part of anoath of office. It is used in some jurisdictions as an oath for performing a public duty, such as an appearance in court. The phrase implies greater care than usual in the truthfulness of one's testimony or in the performance of one's duty.
Notably, the wordhelpinso help me Godis in thesubjunctive mood.
InAustralia, theOath of Allegianceis available in two forms, one of which contains the phrase "So help me God!"[1]
InCanada, the Oath of Office, Oath of Allegiance, and Oath of Members of the Privy Council may be sworn, and end in "So help me God." They may also be solemnly affirmed, and in such case the phrase is omitted.[2]
TheConstitution of Fiji, Chapter 17requires this phrase for theoath of allegiance, and before service to the republic from the President's office or Vice-President's office, a ministerial position, or a judicial position.
InNew ZealandtheOath of Allegianceis available in English or Māori in two forms, one an oath containing the phrase 'so help me God' and the other anaffirmationwhich does not. ThePolice Act 1958and theOaths Modernisation Billstill includes the phrase.[3][4]
TheOath of Allegianceset out in thePromissory Oaths Act 1868ends with this phrase, and is required to be taken by various office-holders.[5]
The phrase "So help me God" is prescribed in oaths as early as theJudiciary Act of 1789, for U.S. officers other than the President. The act makes the semantic distinction between anaffirmationand anoath.[6]The oath, religious in essence, includes the phrase "so help me God" and "[I] swear". The affirmation uses "[I] affirm". Both serve the same purpose and are described as one (i.e. "... solemnly swear, or affirm, that ...")[7]
In theUnited States, theNo Religious Test Clausestates that "no religious test shall ever be required as a qualification to any office or public trust under the United States." Still, there are federal oaths which do include the phrase "So help me God", such as forjusticesandjudgesin28 U.S.C.§ 453.[8]
There is no law that requires Presidents to add the words "So help me God" at the end of the oath (or to use a Bible). Some historians maintain thatGeorge Washingtonhimself added the phrase to the end of his first oath, setting a precedent for future presidents and continuing what was already established practice in his day[9]and that all Presidents since have used this phrase, according to Marvin Pinkert, executive director of theNational Archives Experience.[10]Many other historians reject this story given that "it was not until 65 years after the event that the story that Washington added this phrase first appeared in a published volume" and other witnesses, who were present for the event, did not cite him as having added the phrase.[11]These historians further note that "we have no convincing contemporary evidence that any president said "so help me God" until September 1881, when Chester A. Arthur took the oath after the death of James Garfield."[12]It is demonstrable, however, that those historians are in error regarding their claim that there is no "contemporary evidence" of a president saying "so help me God" until 1881. Richard Gardiner's research published in theWhite House History Quarterly, November 2024, offers contemporary evidence for presidents who used the phrase going back to William Henry Harrison in 1841, and Andrew Jackson.[13]
TheUnited States Oath of Citizenship(officially referred to as the "Oath of Allegiance", 8 C.F.R. Part 337 (2008)), taken by all immigrants who wish to becomeUnited States citizens, includes the phrase "so help me God"; however8 CFR337.1provides that the phrase is optional.
TheEnlistment oathand officer'sOath of Officeboth contain this phrase. A change in October 2013 to Air Force Instruction 36-2606[14]made it mandatory to include the phrase during Air Force enlistments/reenlistments. This change has made the instruction "consistent with the language mandated in 10 USC 502".[15]The Air Force announced on September 17, 2014, that it revoked this previous policy change, allowing anyone to omit "so help me God" from the oath.[16]
Some of the states have specified that the words "so help me God" were used in oath of office, and also required ofjurors, witnesses in court,notaries public, and state employees. Alabama, Connecticut, Delaware, Kentucky, Louisiana, Maine, Mississippi, New Mexico, North Carolina, Texas, and Virginia retain the required "so help me God" as part of the oath to public office. Historically, Maryland and South Carolina did include it but both have been successfully challenged in court. Other states, such as New Hampshire, North Dakota and Rhode Island allow exceptions or alternative phrases. In Wisconsin, the specific language of the oath has been repealed.[17]
InCroatia, the text of presidential oath, which is defined by the Presidential Elections Act amendments of 1997 (Article 4), ends with "Tako mi Bog pomogao" (So help me God).[18][19]
In 2009, concerns about the phrase infringing onConstitution of Croatiawere raised.Constitutional Court of Croatiaruled them out in 2017, claiming that it is compatible with constitution and secular state.[20][21][22]The court said the phrase is in neither direct nor indirect relation to any religious beliefs of theelected president. It doesn't represent a theist or religious belief and does not stop the president in any way from expressing any other religious belief. Saying the phrase while taking the presidential oath does not force a certain belief on the President and does not infringe on their religious freedoms.[22]
In the inauguration ofDutch monarchs, the phrase "zo waarlijk helpe mij God Almachtig" ("So help me God Almighty") is used at the conclusion of the monarch's oath.[23]
In theOath of Officeof thePresident of the Philippines, the phrase "So help me God" (Filipino:Kasihan nawâ akó ng Diyos) is mandatory in oaths.[24]An affirmation, however, has exactly the same legal effect as an oath.
In medieval France, tradition held that when the Duke of Brittany or other royalty entered the city ofRennes, they would proclaimEt qu'ainsi Dieu me soit en aide("And so help me God").[25]
The phraseSo wahr mir Gott helfe(literally "as true as God may help me") is an optional part in oaths of office prescribed for civil servants, soldiers, judges as well as members and high representatives of the federal and state governments such as theFederal President,Federal Chancellorand theMinister Presidents. Parties and witnesses in criminal and civil proceedings may also be placed under oath with this phrase. In such proceedings, the judge first speaks the wordsYou swear [by God Almighty and All-Knowing] that to the best of your knowledge you have spoken the pure truth and not concealed anything.The witness or party then must answerI swear it [, so help me God]. The words between brackets are added or omitted according to the preference of the person placed under oath.[26]If the person concerned raises a conscientious objection against any kind of oath, the judge may speak the wordsAware of your responsibility in court, you affirm that to the best of your knowledge you have spoken the pure truth and not concealed anythingto which the person needs to replyYes.[27]Both forms of the oath and the affirmation carry the same penalty, if the person is found to have lied. Contrary to the oath without a religious phrase, this kind of affirmation is not necessarily available outside court proceedings (e.g. for an oath of office).
The traditional oath of witnesses in Austrian courts ends with the phraseso wahr mir Gott helfe. There are, however, exemptions for witnesses of different religious denominations as well as those unaffiliated with any religion. The oath is rarely practised in civil trials and was completely abolished for criminal procedures in 2008. The phraseso wahr mir Gott helfeis also an (optional) part in the oath of surveyors who testify as expert witnesses as well as court-certified interpreters. Unlike in Germany, the phraseso wahr mir Gott helfeis not part of the oath of office of theFederal President, members of the federal government or state governors, who may or may not add a religious affirmation after the form of oath prescribed by the constitution.
ThePolishphrase is "Tak mi dopomóż Bóg" or "Tak mi, Boże, dopomóż." It has been used in most version of thePolish Army oaths, however other denominations use different phrases. President, prime minister, deputy prime ministers, ministers and members of both houses of parliament can add this phrase at the end of the oath of their office.[28]
InRomania, the oath translation is "Așa să-mi ajute Dumnezeu!", which is used in various ceremonies such as the ministers' oath in front of the president of the republic or the magistrates' oath.
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Inmathematical analysis, adomainorregionis anon-empty,connected, andopen setin atopological space. In particular, it is any non-empty connected opensubsetof thereal coordinate spaceRnor thecomplex coordinate spaceCn. A connected open subset ofcoordinate spaceis frequently used for thedomain of a function.[1]
The basic idea of a connected subset of a space dates from the 19th century, but precise definitions vary slightly from generation to generation, author to author, and edition to edition, as concepts developed and terms were translated between German, French, and English works. In English, some authors use the termdomain,[2]some use the termregion,[3]some use both terms interchangeably,[4]and some define the two terms slightly differently;[5]some avoid ambiguity by sticking with a phrase such asnon-empty connected open subset.[6]
One common convention is to define adomainas a connected open set but aregionas theunionof a domain with none, some, or all of itslimit points.[7]Aclosed regionorclosed domainis the union of a domain and all of its limit points.
Various degrees of smoothness of theboundaryof the domain are required for various properties of functions defined on the domain to hold, such as integral theorems (Green's theorem,Stokes theorem), properties ofSobolev spaces, and to definemeasureson the boundary and spaces oftraces(generalized functions defined on the boundary). Commonly considered types of domains are domains withcontinuousboundary,Lipschitz boundary,C1boundary, and so forth.
Abounded domainis a domain that isbounded, i.e., contained in some ball.Bounded regionis defined similarly. Anexterior domainorexternal domainis a domain whosecomplementis bounded; sometimes smoothness conditions are imposed on its boundary.
Incomplex analysis, acomplex domain(or simplydomain) is any connected open subset of thecomplex planeC. For example, the entire complex plane is a domain, as is the openunit disk, the openupper half-plane, and so forth. Often, a complex domain serves as thedomain of definitionfor aholomorphic function. In the study ofseveral complex variables, the definition of a domain is extended to include any connected open subset ofCn.
InEuclidean spaces,one-,two-, andthree-dimensionalregions arecurves,surfaces, andsolids, whose extent are called, respectively,length,area, andvolume.
Definition. An open set is connected if it cannot be expressed as the sum of two open sets. An open connected set is called a domain.
German:Eine offene Punktmenge heißt zusammenhängend, wenn man sie nicht als Summe von zwei offenen Punktmengen darstellen kann. Eine offene zusammenhängende Punktmenge heißt ein Gebiet.
According toHans Hahn,[8]the concept of a domain as an open connected set was introduced byConstantin Carathéodoryin his famous book (Carathéodory 1918).
In this definition, Carathéodory considers obviouslynon-emptydisjointsets.
Hahn also remarks that the word "Gebiet" ("Domain") was occasionally previously used as asynonymofopen set.[9]The rough concept is older. In the 19th and early 20th century, the termsdomainandregionwere often used informally (sometimes interchangeably) without explicit definition.[10]
However, the term "domain" was occasionally used to identify closely related but slightly different concepts. For example, in his influentialmonographsonelliptic partial differential equations,Carlo Mirandauses the term "region" to identify an open connected set,[11][12]and reserves the term "domain" to identify an internally connected,[13]perfect set, each point of which is an accumulation point of interior points,[11]following his former masterMauro Picone:[14]according to this convention, if a setAis a region then itsclosureAis a domain.[11]
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Online transaction processing(OLTP) is a type ofdatabasesystem used in transaction-oriented applications, such as many operational systems. "Online" refers to the fact that such systems are expected to respond to user requests and process them in real-time (process transactions). The term is contrasted withonline analytical processing(OLAP) which instead focuses on data analysis (for exampleplanningandmanagement systems).
The term "transaction" can have two different meanings, both of which might apply: in the realm of computers ordatabase transactionsit denotes an atomic change of state, whereas in the realm of business or finance, the term typically denotes an exchange of economic entities (as used by, e.g.,Transaction Processing Performance Councilorcommercial transactions.[1]): 50OLTP may use transactions of the first type to record transactions of the second type.
OLTP is typically contrasted toonline analytical processing(OLAP), which is generally characterized by much more complex queries, in a smaller volume, for the purpose of business intelligence or reporting rather than to process transactions. Whereas OLTP systems process all kinds of queries (read, insert, update and delete), OLAP is generally optimized for read only and might not even support other kinds of queries. OLTP also operates differently frombatch processingandgrid computing.[1]: 15
In addition, OLTP is often contrasted toonline event processing(OLEP), which is based on distributedevent logsto offer strong consistency in large-scale heterogeneous systems.[2]Whereas OLTP is associated with short atomic transactions, OLEP allows for more flexible distribution patterns and higher scalability, but with increased latency and without guaranteed upper bound to the processing time.
OLTP has also been used to refer to processing in which the system responds immediately to user requests. Anautomated teller machine(ATM) for a bank is an example of a commercial transaction processing application.[3]Online transaction processing applications have high throughput and are insert- or update-intensive in database management. These applications are used concurrently by hundreds of users. The key goals of OLTP applications are availability, speed, concurrency and recoverability (durability).[4]Reduced paper trails and the faster, more accurate forecast for revenues and expenses are both examples of how OLTP makes things simpler for businesses. However, like many modern online information technology solutions, some systems require offline maintenance, which further affects the cost-benefit analysis of an online transaction processing system.
An OLTP system is an accessible data processing system in today's enterprises. Some examples of OLTP systems include order entry, retail sales, and financial transaction systems.[5]Online transaction processing systems increasingly require support for transactions that span a network and may include more than one company. For this reason, modern online transaction processing software uses client or server processing and brokering software that allows transactions to run on different computer platforms in a network.
In large applications, efficient OLTP may depend on sophisticated transaction management software (such as IBMCICS) and/ordatabaseoptimization tactics to facilitate the processing of large numbers of concurrent updates to an OLTP-oriented database.
For even more demanding decentralized database systems, OLTP brokering programs can distribute transaction processing among multiple computers on anetwork. OLTP is often integrated intoservice-oriented architecture(SOA) andWeb services.
Online transaction processing (OLTP) involves gathering input information, processing the data and updating existing data to reflect the collected and processed information. As of today, most organizations use a database management system to support OLTP. OLTP is carried in a client-server system.
Online transaction process concerns about concurrency and atomicity. Concurrency controls guarantee that two users accessing the same data in the database system will not be able to change that data or the user has to wait until the other user has finished processing, before changing that piece of data. Atomicity controls guarantee that all the steps in a transaction are completed successfully as a group. That is, if any steps between the transaction fail, all other steps must fail also.[6]
To build an OLTP system, a designer must know that the large number of concurrent users does not interfere with the system's performance. To increase the performance of an OLTP system, a designer must avoid excessive use of indexes and clusters.
The following elements are crucial for the performance of OLTP systems:[4]
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Standard formis a way of expressingnumbersthat are too large or too small to be conveniently written indecimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to asscientific formorstandard index form, orScientific notationin the United States. Thisbase tennotation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certainarithmetic operations. Onscientific calculators, it is usually known as "SCI" display mode.
In scientific notation, nonzero numbers are written in the form
ormtimes ten raised to the power ofn, wherenis aninteger, and thecoefficientmis a nonzeroreal number(usually between 1 and 10 in absolute value, and nearly always written as aterminating decimal). The integernis called theexponentand the real numbermis called thesignificandormantissa.[1]The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of thefractional partof thecommon logarithm. If the number is negative then a minus sign precedesm, as in ordinary decimal notation. Innormalized notation, the exponent is chosen so that theabsolute value(modulus) of the significandmis at least 1 but less than 10.
Decimal floating pointis a computer arithmetic system closely related to scientific notation.
For performing calculations with aslide rule, standard form expression is required. Thus, the use of scientific notation increased as engineers and educators used that tool. SeeSlide rule#History.
Any real number can be written in the formm×10^nin many ways: for example, 350 can be written as3.5×102or35×101or350×100.
Innormalizedscientific notation (called "standard form" in the United Kingdom), the exponentnis chosen so that theabsolute valueofmremains at least one but less than ten (1 ≤ |m| < 10). Thus 350 is written as3.5×102. This form allows easy comparison of numbers: numbers with bigger exponents are (due to the normalization) larger than those with smaller exponents, and subtraction of exponents gives an estimate of the number oforders of magnitudeseparating the numbers. It is also the form that is required when using tables ofcommon logarithms. In normalized notation, the exponentnis negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as5×10−1). The 10 and exponent are often omitted when the exponent is 0. For a series of numbers that are to be added or subtracted (or otherwise compared), it can be convenient to use the same value ofmfor all elements of the series.
Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalized or differently normalized form, such asengineering notation, is desired. Normalized scientific notation is often calledexponentialnotation– although the latter term is more general and also applies whenmis not restricted to the range 1 to 10 (as in engineering notation for instance) and tobasesother than 10 (for example,3.15×2^20).
Engineering notation (often named "ENG" on scientific calculators) differs from normalized scientific notation in that the exponentnis restricted tomultiplesof 3. Consequently, the absolute value ofmis in the range 1 ≤ |m| < 1000, rather than 1 ≤ |m| < 10. Though similar in concept, engineering notation is rarely called scientific notation. Engineering notation allows the numbers to explicitly match their correspondingSI prefixes, which facilitates reading and oral communication. For example,12.5×10−9mcan be read as "twelve-point-five nanometres" and written as12.5 nm, while its scientific notation equivalent1.25×10−8mwould likely be read out as "one-point-two-five times ten-to-the-negative-eight metres".
Calculatorsandcomputer programstypically present very large or small numbers using scientific notation, and some can be configured to uniformly present all numbers that way. Becausesuperscriptexponents like 107can be inconvenient to display or type, the letter "E" or "e" (for "exponent") is often used to represent "times ten raised to the power of", so that the notationmEnfor a decimal significandmand integer exponentnmeans the same asm× 10n. For example6.022×1023is written as6.022E23or6.022e23, and1.6×10−35is written as1.6E-35or1.6e-35. While common in computer output, this abbreviated version of scientific notation is discouraged for published documents by some style guides.[2][3]
Most popular programming languages – includingFortran,C/C++,Python, andJavaScript– use this "E" notation, which comes from Fortran and was present in the first version released for theIBM 704in 1956.[4]The E notation was already used by the developers ofSHARE Operating System(SOS) for theIBM 709in 1958.[5]Later versions of Fortran (at least sinceFORTRAN IVas of 1961) also use "D" to signifydouble precisionnumbers in scientific notation,[6]and newer Fortran compilers use "Q" to signifyquadruple precision.[7]TheMATLABprogramming language supports the use of either "E" or "D".
TheALGOL 60(1960) programming language uses a subscript ten "10" character instead of the letter "E", for example:6.0221023.[8][9]This presented a challenge for computer systems which did not provide such a character, soALGOL W(1966) replaced the symbol by a single quote, e.g.6.022'+23,[10]and some Soviet ALGOL variants allowed the use of the Cyrillic letter "ю", e.g.6.022ю+23[citation needed]. Subsequently, theALGOL 68programming language provided a choice of characters:E,e,\,⊥, or10.[11]The ALGOL "10" character was included in the SovietGOST 10859text encoding (1964), and was added toUnicode5.2 (2009) asU+23E8⏨DECIMAL EXPONENT SYMBOL.[12]
Some programming languages use other symbols. For instance,Simulauses&(or&&forlong), as in6.022&23.[13]Mathematicasupports the shorthand notation6.022*^23(reserving the letterEfor themathematical constante).
The firstpocket calculatorssupporting scientific notation appeared in 1972.[14]To enter numbers in scientific notation calculators include a button labeled "EXP" or "×10x", among other variants. The displays of pocket calculators of the 1970s did not display an explicit symbol between significand and exponent; instead, one or more digits were left blank (e.g.6.022 23, as seen in theHP-25), or a pair of smaller and slightly raised digits were reserved for the exponent (e.g.6.02223, as seen in theCommodore PR100). In 1976,Hewlett-Packardcalculator user Jim Davidson coined the termdecapowerfor the scientific-notation exponent to distinguish it from "normal" exponents, and suggested the letter "D" as a separator between significand and exponent in typewritten numbers (for example,6.022D23); these gained some currency in the programmable calculator user community.[15]The letters "E" or "D" were used as a scientific-notation separator bySharppocket computersreleased between 1987 and 1995, "E" used for 10-digit numbers and "D" used for 20-digit double-precision numbers.[16]TheTexas InstrumentsTI-83andTI-84series of calculators (1996–present) use asmall capitalEfor the separator.[17]
In 1962, Ronald O. Whitaker of Rowco Engineering Co. proposed a power-of-ten system nomenclature where the exponent would be circled, e.g. 6.022 × 103would be written as "6.022③".[18]
A significant figure is a digit in a number that adds to its precision. This includes all nonzero numbers, zeroes between significant digits, and zeroesindicated to be significant. Leading and trailing zeroes are not significant digits, because they exist only to show the scale of the number. Unfortunately, this leads to ambiguity. The number1230400is usually read to have five significant figures: 1, 2, 3, 0, and 4, the final two zeroes serving only as placeholders and adding no precision. The same number, however, would be used if the last two digits were also measured precisely and found to equal 0 – seven significant figures.
When a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the placeholding zeroes are no longer required. Thus1230400would become1.2304×106if it had five significant digits. If the number were known to six or seven significant figures, it would be shown as1.23040×106or1.230400×106. Thus, an additional advantage of scientific notation is that the number of significant figures is unambiguous.
It is customary in scientific measurement to record all the definitely known digits from the measurement and to estimate at least one additional digit if there is any information at all available on its value. The resulting number contains more information than it would without the extra digit, which may be considered a significant digit because it conveys some information leading to greater precision in measurements and in aggregations of measurements (adding them or multiplying them together).
Additional information about precision can be conveyed through additional notation. It is often useful to know how exact the final digit or digits are. For instance, the accepted value of the mass of theprotoncan properly be expressed as1.67262192369(51)×10−27kg, which is shorthand for(1.67262192369±0.00000000051)×10−27kg. However it is still unclear whether the error (5.1×10−37in this case) is the maximum possible error,standard error, or some otherconfidence interval.
In normalized scientific notation, in E notation, and in engineering notation, thespace(which intypesettingmay be represented by a normal width space or athin space) that is allowedonlybefore and after "×" or in front of "E" is sometimes omitted, though it is less common to do so before the alphabetical character.[19]
Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation. None of these alter the actual number, only how it's expressed.
First, move the decimal separator point sufficient places,n, to put the number's value within a desired range, between 1 and 10 for normalized notation. If the decimal was moved to the left, append× 10n; to the right,× 10−n. To represent the number1,230,400in normalized scientific notation, the decimal separator would be moved 6 digits to the left and× 106appended, resulting in1.2304×106. The number−0.0040321would have its decimal separator shifted 3 digits to the right instead of the left and yield−4.0321×10−3as a result.
Converting a number from scientific notation to decimal notation, first remove the× 10non the end, then shift the decimal separatorndigits to the right (positiven) or left (negativen). The number1.2304×106would have its decimal separator shifted 6 digits to the right and become1,230,400, while−4.0321×10−3would have its decimal separator moved 3 digits to the left and be−0.0040321.
Conversion between different scientific notation representations of the same number with different exponential values is achieved by performing opposite operations of multiplication or division by a power of ten on the significand and an subtraction or addition of one on the exponent part. The decimal separator in the significand is shiftedxplaces to the left (or right) andxis added to (or subtracted from) the exponent, as shown below.
Given two numbers in scientific notation,x0=m0×10n0{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}}andx1=m1×10n1{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}}
Multiplicationanddivisionare performed using the rules for operation withexponentiation:x0x1=m0m1×10n0+n1{\displaystyle x_{0}x_{1}=m_{0}m_{1}\times 10^{n_{0}+n_{1}}}andx0x1=m0m1×10n0−n1{\displaystyle {\frac {x_{0}}{x_{1}}}={\frac {m_{0}}{m_{1}}}\times 10^{n_{0}-n_{1}}}
Some examples are:5.67×10−5×2.34×102≈13.3×10−5+2=13.3×10−3=1.33×10−2{\displaystyle 5.67\times 10^{-5}\times 2.34\times 10^{2}\approx 13.3\times 10^{-5+2}=13.3\times 10^{-3}=1.33\times 10^{-2}}and2.34×1025.67×10−5≈0.413×102−(−5)=0.413×107=4.13×106{\displaystyle {\frac {2.34\times 10^{2}}{5.67\times 10^{-5}}}\approx 0.413\times 10^{2-(-5)}=0.413\times 10^{7}=4.13\times 10^{6}}
Additionandsubtractionrequire the numbers to be represented using the same exponential part, so that the significand can be simply added or subtracted:
Next, add or subtract the significands:x0±x1=(m0±m1)×10n0{\displaystyle x_{0}\pm x_{1}=(m_{0}\pm m_{1})\times 10^{n_{0}}}
An example:2.34×10−5+5.67×10−6=2.34×10−5+0.567×10−5=2.907×10−5{\displaystyle 2.34\times 10^{-5}+5.67\times 10^{-6}=2.34\times 10^{-5}+0.567\times 10^{-5}=2.907\times 10^{-5}}
While base ten is normally used for scientific notation, powers of other bases can be used too,[25]base 2 being the next most commonly used one.
For example, in base-2 scientific notation, the number 1001binbinary(=9d) is written as1.001b× 2d11bor1.001b× 10b11busing binary numbers (or shorter1.001 × 1011if binary context is obvious).[citation needed]In E notation, this is written as1.001bE11b(or shorter: 1.001E11) with the letter "E" now standing for "times two (10b) to the power" here. In order to better distinguish this base-2 exponent from a base-10 exponent, a base-2 exponent is sometimes also indicated by using the letter "B" instead of "E",[26]a shorthand notation originally proposed byBruce Alan MartinofBrookhaven National Laboratoryin 1968,[27]as in1.001bB11b(or shorter: 1.001B11). For comparison, the same number indecimal representation:1.125 × 23(using decimal representation), or 1.125B3 (still using decimal representation). Some calculators use a mixed representation for binary floating point numbers, where the exponent is displayed as decimal number even in binary mode, so the above becomes1.001b× 10b3dor shorter 1.001B3.[26]
This is closely related to the base-2floating-pointrepresentation commonly used in computer arithmetic, and the usage of IECbinary prefixes(e.g. 1B10 for 1×210(kibi), 1B20 for 1×220(mebi), 1B30 for 1×230(gibi), 1B40 for 1×240(tebi)).
Similar to "B" (or "b"[28]), the letters "H"[26](or "h"[28]) and "O"[26](or "o",[28]or "C"[26]) are sometimes also used to indicatetimes 16 or 8 to the poweras in 1.25 =1.40h× 10h0h= 1.40H0 = 1.40h0, or 98000 =2.7732o× 10o5o= 2.7732o5 = 2.7732C5.[26]
Another similar convention to denote base-2 exponents is using a letter "P" (or "p", for "power"). In this notation the significand is always meant to be hexadecimal, whereas the exponent is always meant to be decimal.[29]This notation can be produced by implementations of theprintffamily of functions following theC99specification and (Single Unix Specification)IEEE Std 1003.1POSIXstandard, when using the%aor%Aconversion specifiers.[29][30][31]Starting withC++11,C++I/O functions could parse and print the P notation as well. Meanwhile, the notation has been fully adopted by the language standard sinceC++17.[32]Apple'sSwiftsupports it as well.[33]It is also required by theIEEE 754-2008binary floating-point standard. Example: 1.3DEp42 represents1.3DEh× 242.
Engineering notationcan be viewed as a base-1000 scientific notation.
Sayre, David, ed. (1956-10-15).The FORTRAN Automatic Coding System for the IBM 704 EDPM: Programmer's Reference Manual(PDF). New York: Applied Science Division and Programming Research Department,International Business Machines Corporation. pp. 9, 27. Retrieved2022-07-04.(2+51+1 pages)
"6. Extensions: 6.1 Extensions implemented in GNU Fortran: 6.1.8 Q exponent-letter".The GNU Fortran Compiler. 2014-06-12. Retrieved2022-12-21.
"The Unicode Standard"(v. 7.0.0 ed.). Retrieved2018-03-23.
Vanderburgh, Richard C., ed. (November 1976)."Decapower"(PDF).52-Notes – Newsletter of the SR-52 Users Club.1(6). Dayton, OH: 1. V1N6P1. Retrieved2017-05-28.Decapower– In the January 1976 issue of65-Notes(V3N1p4) Jim Davidson (HP-65Users Club member #547) suggested the term "decapower" as a descriptor for the power-of-ten multiplier used in scientific notation displays. I'm going to begin using it in place of "exponent" which is technically incorrect, and the letter D to separate the "mantissa" from the decapower for typewritten numbers, as Jim also suggests. For example,123−45[sic] which is displayed in scientific notation as1.23 -43will now be written1.23D-43. Perhaps, as this notation gets more and more usage, the calculator manufacturers will change their keyboard abbreviations. HP's EEX and TI's EE could be changed to ED (for enter decapower).[1]"Decapower".52-Notes – Newsletter of the SR-52 Users Club. Vol. 1, no. 6. Dayton, OH. November 1976. p. 1. Retrieved2018-05-07.(NB. The termdecapowerwas frequently used in subsequent issues of this newsletter up to at least 1978.)
電言板6 PC-U6000 PROGRAM LIBRARY[Telephone board 6 PC-U6000 program library] (in Japanese). Vol. 6. University Co-op. 1993.
"TI-83 Programmer's Guide"(PDF). Retrieved2010-03-09.
"INTOUCH 4GL a Guide to the INTOUCH Language". Archived fromthe originalon 2015-05-03.
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Inquantum computing, aquantum algorithmis analgorithmthat runs on a realistic model ofquantum computation, the most commonly used model being thequantum circuitmodel of computation.[1][2]A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classicalcomputer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on aquantum computer. Although all classical algorithms can also be performed on a quantum computer,[3]: 126the term quantum algorithm is generally reserved for algorithms that seem inherently quantum, or use some essential feature of quantum computation such asquantum superpositionorquantum entanglement.
Problems that areundecidableusing classical computers remain undecidable using quantum computers.[4]: 127What makes quantum algorithms interesting is that they might be able to solve some problems faster than classical algorithms because the quantum superposition and quantum entanglement that quantum algorithms exploit generally cannot be efficiently simulated on classical computers (seeQuantum supremacy).
The best-known algorithms areShor's algorithmfor factoring andGrover's algorithmfor searching an unstructured database or an unordered list. Shor's algorithm runs much (almost exponentially) faster than the most efficient known classical algorithm for factoring, thegeneral number field sieve.[5]Grover's algorithm runs quadratically faster than the best possible classical algorithm for the same task,[6]alinear search.
Quantum algorithms are usually described, in the commonly used circuit model of quantum computation, by aquantum circuitthat acts on some inputqubitsand terminates with ameasurement. A quantum circuit consists of simplequantum gates, each of which acts on some finite number of qubits. Quantum algorithms may also be stated in other models of quantum computation, such as theHamiltonian oracle model.[7]
Quantum algorithms can be categorized by the main techniques involved in the algorithm. Some commonly used techniques/ideas in quantum algorithms includephase kick-back,phase estimation, thequantum Fourier transform,quantum walks,amplitude amplificationandtopological quantum field theory. Quantum algorithms may also be grouped by the type of problem solved; see, e.g., the survey on quantum algorithms for algebraic problems.[8]
Thequantum Fourier transformis the quantum analogue of thediscrete Fourier transform, and is used in several quantum algorithms. TheHadamard transformis also an example of a quantum Fourier transform over an n-dimensional vector space over the fieldF2. The quantum Fourier transform can be efficiently implemented on a quantum computer using only a polynomial number ofquantum gates.[citation needed]
The Deutsch–Jozsa algorithm solves ablack-boxproblem that requires exponentially many queries to the black box for any deterministic classical computer, but can be done with a single query by a quantum computer. However, when comparing bounded-error classical and quantum algorithms, there is no speedup, since a classical probabilistic algorithm can solve the problem with a constant number of queries with small probability of error. The algorithm determines whether a functionfis either constant (0 on all inputs or 1 on all inputs) or balanced (returns 1 for half of the input domain and 0 for the other half).
The Bernstein–Vazirani algorithm is the first quantum algorithm that solves a problem more efficiently than the best known classical algorithm. It was designed to create anoracle separationbetweenBQPandBPP.
Simon's algorithm solves a black-box problem exponentially faster than any classical algorithm, including bounded-error probabilistic algorithms. This algorithm, which achieves an exponential speedup over all classical algorithms that we consider efficient, was the motivation forShor's algorithmfor factoring.
Thequantum phase estimation algorithmis used to determine the eigenphase of an eigenvector of a unitary gate, given a quantum state proportional to the eigenvector and access to the gate. The algorithm is frequently used as a subroutine in other algorithms.
Shor's algorithm solves thediscrete logarithmproblem and theinteger factorizationproblem in polynomial time,[9]whereas the best known classical algorithms take super-polynomial time. It is unknown whether these problems are inPorNP-complete. It is also one of the few quantum algorithms that solves a non-black-box problem in polynomial time, where the best known classical algorithms run in super-polynomial time.
Theabelianhidden subgroup problemis a generalization of many problems that can be solved by a quantum computer, such as Simon's problem, solvingPell's equation, testing theprincipal idealof aringR andfactoring. There are efficient quantum algorithms known for the Abelian hidden subgroup problem.[10]The more general hidden subgroup problem, where the group is not necessarily abelian, is a generalization of the previously mentioned problems, as well asgraph isomorphismand certainlattice problems. Efficient quantum algorithms are known for certain non-abelian groups. However, no efficient algorithms are known for thesymmetric group, which would give an efficient algorithm for graph isomorphism[11]and thedihedral group, which would solve certain lattice problems.[12]
AGauss sumis a type ofexponential sum. The best known classical algorithm for estimating these sums takes exponential time. Since the discrete logarithm problem reduces to Gauss sum estimation, an efficient classical algorithm for estimating Gauss sums would imply an efficient classical algorithm for computing discrete logarithms, which is considered unlikely. However, quantum computers can estimate Gauss sums to polynomial precision in polynomial time.[13]
Consider anoracleconsisting ofnrandom Boolean functions mappingn-bit strings to a Boolean value, with the goal of finding nn-bit stringsz1,...,znsuch that for the Hadamard-Fourier transform, at least 3/4 of the strings satisfy
and at least 1/4 satisfy
This can be done inbounded-error quantum polynomial time(BQP).[14]
Amplitude amplificationis a technique that allows the amplification of a chosen subspace of a quantum state. Applications of amplitude amplification usually lead to quadratic speedups over the corresponding classical algorithms. It can be considered as a generalization of Grover's algorithm.[citation needed]
Grover's algorithm searches an unstructured database (or an unordered list) with N entries for a marked entry, using onlyO(N){\displaystyle O({\sqrt {N}})}queries instead of theO(N){\displaystyle O({N})}queries required classically.[15]Classically,O(N){\displaystyle O({N})}queries are required even allowing bounded-error probabilistic algorithms.
Theorists have considered a hypothetical generalization of a standard quantum computer that could access the histories of the hidden variables inBohmian mechanics. (Such a computer is completely hypothetical and wouldnotbe a standard quantum computer, or even possible under the standard theory of quantum mechanics.) Such a hypothetical computer could implement a search of an N-item database in at mostO(N3){\displaystyle O({\sqrt[{3}]{N}})}steps. This is slightly faster than theO(N){\displaystyle O({\sqrt {N}})}steps taken by Grover's algorithm. However, neither search method would allow either model of quantum computer to solveNP-completeproblems in polynomial time.[16]
Quantum countingsolves a generalization of the search problem. It solves the problem of counting the number of marked entries in an unordered list, instead of just detecting whether one exists. Specifically, it counts the number of marked entries in anN{\displaystyle N}-element list with an error of at mostε{\displaystyle \varepsilon }by making onlyΘ(ε−1N/k){\displaystyle \Theta \left(\varepsilon ^{-1}{\sqrt {N/k}}\right)}queries, wherek{\displaystyle k}is the number of marked elements in the list.[17][18]More precisely, the algorithm outputs an estimatek′{\displaystyle k'}fork{\displaystyle k}, the number of marked entries, with accuracy|k−k′|≤εk{\displaystyle |k-k'|\leq \varepsilon k}.
A quantum walk is the quantum analogue of a classicalrandom walk. A classical random walk can be described by aprobability distributionover some states, while a quantum walk can be described by aquantum superpositionover states. Quantum walks are known to give exponential speedups for some black-box problems.[19][20]They also provide polynomial speedups for many problems. A framework for the creation of quantum walk algorithms exists and is a versatile tool.[21]
The Boson Sampling Problem in an experimental configuration assumes[22]an input ofbosons(e.g., photons) of moderate number that are randomly scattered into a large number of output modes, constrained by a definedunitarity. When individual photons are used, the problem is isomorphic to a multi-photon quantum walk.[23]The problem is then to produce a fair sample of theprobability distributionof the output that depends on the input arrangement of bosons and the unitarity.[24]Solving this problem with a classical computer algorithm requires computing thepermanentof the unitary transform matrix, which may take a prohibitively long time or be outright impossible. In 2014, it was proposed[25]that existing technology and standard probabilistic methods of generating single-photon states could be used as an input into a suitable quantum computablelinear optical networkand that sampling of the output probability distribution would be demonstrably superior using quantum algorithms. In 2015, investigation predicted[26]the sampling problem had similar complexity for inputs other thanFock-statephotons and identified a transition incomputational complexityfrom classically simulable to just as hard as the Boson Sampling Problem, depending on the size of coherent amplitude inputs.
The element distinctness problem is the problem of determining whether all the elements of a list are distinct. Classically,Ω(N){\displaystyle \Omega (N)}queries are required for a list of sizeN{\displaystyle N}; however, it can be solved inΘ(N2/3){\displaystyle \Theta (N^{2/3})}queries on a quantum computer. The optimal algorithm was put forth byAndris Ambainis,[27]andYaoyun Shifirst proved a tight lower bound when the size of the range is sufficiently large.[28]Ambainis[29]and Kutin[30]independently (and via different proofs) extended that work to obtain the lower bound for all functions.
The triangle-finding problem is the problem of determining whether a given graph contains a triangle (acliqueof size 3). The best-known lower bound for quantum algorithms isΩ(N){\displaystyle \Omega (N)}, but the best algorithm known requires O(N1.297) queries,[31]an improvement over the previous best O(N1.3) queries.[21][32]
A formula is a tree with a gate at each internal node and an input bit at each leaf node. The problem is to evaluate the formula, which is the output of the root node, given oracle access to the input.
A well studied formula is the balanced binary tree with only NAND gates.[33]This type of formula requiresΘ(Nc){\displaystyle \Theta (N^{c})}queries using randomness,[34]wherec=log2(1+33)/4≈0.754{\displaystyle c=\log _{2}(1+{\sqrt {33}})/4\approx 0.754}. With a quantum algorithm, however, it can be solved inΘ(N1/2){\displaystyle \Theta (N^{1/2})}queries. No better quantum algorithm for this case was known until one was found for the unconventional Hamiltonian oracle model.[7]The same result for the standard setting soon followed.[35]
Fast quantum algorithms for more complicated formulas are also known.[36]
The problem is to determine if ablack-box group, given bykgenerators, iscommutative. A black-box group is a group with an oracle function, which must be used to perform the group operations (multiplication, inversion, and comparison with identity). The interest in this context lies in the query complexity, which is the number of oracle calls needed to solve the problem. The deterministic and randomized query complexities areΘ(k2){\displaystyle \Theta (k^{2})}andΘ(k){\displaystyle \Theta (k)}, respectively.[37]A quantum algorithm requiresΩ(k2/3){\displaystyle \Omega (k^{2/3})}queries, while the best-known classical algorithm usesO(k2/3logk){\displaystyle O(k^{2/3}\log k)}queries.[38]
Thecomplexity classBQP(bounded-error quantum polynomial time) is the set ofdecision problemssolvable by aquantum computerinpolynomial timewith error probability of at most 1/3 for all instances.[39]It is the quantum analogue to the classical complexity classBPP.
A problem isBQP-complete if it is inBQPand any problem inBQPcan bereducedto it inpolynomial time. Informally, the class ofBQP-complete problems are those that are as hard as the hardest problems inBQPand are themselves efficiently solvable by a quantum computer (with bounded error).
Witten had shown that theChern-Simonstopological quantum field theory(TQFT) can be solved in terms ofJones polynomials. A quantum computer can simulate a TQFT, and thereby approximate the Jones polynomial,[40]which as far as we know, is hard to compute classically in the worst-case scenario.[citation needed]
The idea that quantum computers might be more powerful than classical computers originated in Richard Feynman's observation that classical computers seem to require exponential time to simulate many-particle quantum systems, yet quantum many-body systems are able to "solve themselves."[41]Since then, the idea that quantum computers can simulate quantum physical processes exponentially faster than classical computers has been greatly fleshed out and elaborated. Efficient (i.e., polynomial-time) quantum algorithms have been developed for simulating both Bosonic and Fermionic systems,[42]as well as the simulation of chemical reactions beyond the capabilities of current classical supercomputers using only a few hundred qubits.[43]Quantum computers can also efficiently simulate topological quantum field theories.[44]In addition to its intrinsic interest, this result has led to efficient quantum algorithms for estimatingquantum topological invariantssuch asJones[45]andHOMFLY polynomials,[46]and theTuraev-Viro invariantof three-dimensional manifolds.[47]
In 2009,Aram Harrow, Avinatan Hassidim, andSeth Lloyd, formulated a quantum algorithm for solvinglinear systems. Thealgorithmestimates the result of a scalar measurement on the solution vector to a given linear system of equations.[48]
Provided that the linear system issparseand has a lowcondition numberκ{\displaystyle \kappa }, and that the user is interested in the result of a scalar measurement on the solution vector (instead of the values of the solution vector itself), then the algorithm has a runtime ofO(log(N)κ2){\displaystyle O(\log(N)\kappa ^{2})}, whereN{\displaystyle N}is the number of variables in the linear system. This offers an exponential speedup over the fastest classical algorithm, which runs inO(Nκ){\displaystyle O(N\kappa )}(orO(Nκ){\displaystyle O(N{\sqrt {\kappa }})}for positive semidefinite matrices).
Hybrid Quantum/Classical Algorithms combine quantum state preparation and measurement with classical optimization.[49]These algorithms generally aim to determine the ground-state eigenvector and eigenvalue of a Hermitian operator.
Thequantum approximate optimization algorithmtakes inspiration from quantum annealing, performing a discretized approximation of quantum annealing using a quantum circuit. It can be used to solve problems in graph theory.[50]The algorithm makes use of classical optimization of quantum operations to maximize an "objective function."
Thevariational quantum eigensolver(VQE) algorithm applies classical optimization to minimize the energy expectation value of anansatz stateto find the ground state of a Hermitian operator, such as a molecule's Hamiltonian.[51]It can also be extended to find excited energies of molecular Hamiltonians.[52]
The contracted quantum eigensolver (CQE) algorithm minimizes the residual of a contraction (or projection) of the Schrödinger equation onto the space of two (or more) electrons to find the ground- or excited-state energy and two-electron reduced density matrix of a molecule.[53]It is based on classical methods for solving energies and two-electron reduced density matrices directly from the anti-Hermitian contracted Schrödinger equation.[54]
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In computer terminology, ahoneypotis acomputer securitymechanism set to detect, deflect, or, in some manner, counteract attempts at unauthorized use ofinformation systems. Generally, a honeypot consists ofdata(for example, in a network site) that appears to be a legitimate part of the site which contains information or resources of value to attackers. It is actually isolated, monitored, and capable of blocking or analyzing the attackers. This is similar to policesting operations, colloquially known as "baiting" a suspect.[1]
The main use for this network decoy is to distract potential attackers from more important information and machines on the real network, learn about the forms of attacks they can suffer, and examine such attacks during and after the exploitation of a honeypot.
It provides a way to prevent and see vulnerabilities in a specific network system. A honeypot is a decoy used to protect a network from present or future attacks.[2][3]Honeypots derive their value from the use by attackers. If not interacted with, the honeypot has little to no value. Honeypots can be used for everything from slowing down or stopping automated attacks, capturing new exploits, to gathering intelligence on emerging threats or early warning and prediction.[4]
Honeypots can be differentiated based on whether they are physical or virtual:[2][3]
Honeypots can be classified based on their deployment (use/action) and based on their level of involvement. Based on deployment, honeypots may be classified as:[5]
Production honeypotsare easy to use, capture only limited information, and are used primarily by corporations. Production honeypots are placed inside the production network with other production servers by an organization to improve their overall state of security. Normally, production honeypots are low-interaction honeypots, which are easier to deploy. They give less information about the attacks or attackers than research honeypots.[5]
Research honeypotsare run to gather information about the motives and tactics of theblack hatcommunity targeting different networks. These honeypots do not add direct value to a specific organization; instead, they are used to research the threats that organizations face and to learn how to better protect against those threats.[6]Research honeypots are complex to deploy and maintain, capture extensive information, and are used primarily by research, military, or government organizations.[7]
Based on design criteria, honeypots can be classified as:[5]
Pure honeypotsare full-fledged production systems. The activities of the attacker are monitored by using a bug tap that has been installed on the honeypot's link to the network. No other software needs to be installed. Even though a pure honeypot is useful, the stealthiness of the defense mechanisms can be ensured by a more controlled mechanism.
High-interaction honeypotsimitate the activities of the production systems that host a variety of services and, therefore, an attacker may be allowed a lot of services to waste their time. By employingvirtual machines, multiple honeypots can be hosted on a single physical machine. Therefore, even if the honeypot is compromised, it can be restored more quickly. In general, high-interaction honeypots provide more security by being difficult to detect, but they are expensive to maintain. If virtual machines are not available, one physical computer must be maintained for each honeypot, which can be exorbitantly expensive. Example:Honeynet.
Low-interaction honeypotssimulate only the services frequently requested by attackers.[8]Since they consume relatively few resources, multiple virtual machines can easily be hosted on one physical system, the virtual systems have a short response time, and less code is required, reducing the complexity of the virtual system's security. Example:Honeyd. This type of honeypot was one of the first types being created in the late nineties and was mainly used for detecting attacks, not studying them.[9]
Sugarcaneis a type of honeypot that masquerades as an open proxy.[10]It can often take form as a server designed to look like a misconfigured HTTP proxy.[11]Probably the most famous open proxy was the default configuration ofsendmail(before version 8.9.0 in 1998) which would forward email to and from any destination.[12]
Recently, a new market segment calleddeception technologyhas emerged using basic honeypot technology with the addition of advanced automation for scale. Deception technology addresses the automated deployment of honeypot resources over a large commercial enterprise or government institution.[13]
A malware honeypot is a decoy designed to intentionally attract malicious software. It does this by imitating a vulnerable system or network, such as a web server. The honeypot is intentionally set up with security flaws that look to invite these malware attacks. Once attacked IT teams can then analyze the malware to better understand where it comes from and how it acts.[14]
Spammersabuse vulnerable resources such asopen mail relaysandopen proxies. These are servers that accept e-mail from anyone on the Internet—including spammers—and send it to its destination. Some system administrators have created honeypot programs that masquerade as these abusable resources to discover spammer activity.
There are several capabilities such honeypots provide to these administrators, and the existence of such fake abusable systems makes abuse more difficult or risky. Honeypots can be a powerful countermeasure to abuse from those who rely on very high-volume abuse (e.g., spammers).
These honeypots can reveal the abuser'sIP addressand provide bulk spam capture (which enables operators to determine spammers'URLsand response mechanisms). As described by M. Edwards at ITPRo Today:
Typically, spammers test a mail server for open relaying by simply sending themselves an email message. If the spammer receives the email message, the mail server obviously allows open relaying. Honeypot operators, however, can use the relay test to thwart spammers. The honeypot catches the relay test email message, returns the test email message, and subsequently blocks all other email messages from that spammer. Spammers continue to use the antispam honeypot for spamming, but the spam is never delivered. Meanwhile, the honeypot operator can notify spammers' ISPs and have their Internet accounts canceled. If honeypot operators detect spammers who use open-proxy servers, they can also notify the proxy server operator to lock down the server to prevent further misuse.[15]
The apparent source may be another abused system. Spammers and other abusers may use a chain of such abused systems to make detection of the original starting point of the abuse traffic difficult.
This in itself is indicative of the power of honeypots asanti-spamtools. In the early days of anti-spam honeypots, spammers, with little concern for hiding their location, felt safe testing for vulnerabilities and sending spam directly from their own systems. Honeypots made the abuse riskier and more difficult.
Spam still flows through open relays, but the volume is much smaller than in 2001-02. While most spam originates in the U.S.,[16]spammers hop through open relays across political boundaries to mask their origin. Honeypot operators may use intercepted relay tests to recognize and thwart attempts to relay spam through their honeypots. "Thwart" may mean "accept the relay spam but decline to deliver it." Honeypot operators may discover other details concerning the spam and the spammer by examining the captured spam messages.
Open-relay honeypots include Jackpot, written inJavaby Jack Cleaver;smtpot.py, written inPythonby Karl A. Krueger;[17]and spamhole, written inC.[18]TheBubblegum Proxypotis an open-source honeypot (or "proxypot").[19]
An email address that is not used for any other purpose than to receive spam can also be considered a spam honeypot. Compared with the term "spamtrap", the term "honeypot" might be more suitable for systems and techniques that are used to detect or counterattack probes. With a spamtrap, spam arrives at its destination "legitimately"—exactly as non-spam email would arrive.
An amalgam of these techniques isProject Honey Pot, a distributed, open-source project that uses honeypot pages installed on websites around the world. These honeypot pages disseminate uniquely tagged spamtrap email addresses andspammerscan then be tracked—the corresponding spam mail is subsequently sent to these spamtrap e-mail addresses.[20]
Databases often get attacked by intruders usingSQL injection. As such activities are not recognized by basic firewalls, companies often use database firewalls for protection. Some of the availableSQL databasefirewalls provide/support honeypot architectures so that the intruder runs against a trap database while the web application remains functional.[21]
Industrial Control Systems(ICS) are often the target of cyberattacks.[22]One of the main targets within ICS areProgrammable Logic Controllers.[23]In order to understand intruders' techniques in this context, several honeypots have been proposed. Conpot[24][25]is a low interaction honeypot capable of simulation Siemens PLCs. HoneyPLC is a medium interaction honeypot that can simulate Siemens, Rockwell and other PLC brands.[26][27]
Just as honeypots are weapons against spammers, honeypot detection systems are spammer-employed counter-weapons. As detection systems would likely use unique characteristics of specific honeypots to identify them, such as the property-value pairs of default honeypot configuration,[28]many honeypots in use utilise a set of unique characteristics larger and more daunting to those seeking to detect and thereby identify them. This is an unusual circumstance in software; a situation in which"versionitis"(a large number of versions of the same software, all differing slightly from each other) can be beneficial. There's also an advantage in having some easy-to-detect honeypots deployed.Fred Cohen, the inventor of theDeception Toolkit, argues that every system running his honeypot should have a deception port which adversaries can use to detect the honeypot.[29]Cohen believes that this might deter adversaries. Honeypots also allow for early detection of legitimate threats. No matter how the honeypot detects the exploit, it can alert you immediately to the attempted attack.[30]
The goal of honeypots is to attract and engage attackers for a sufficiently long period to obtain high-levelIndicators of Compromise(IoC) such as attack tools andTactics, Techniques, and Procedures(TTPs). Thus, a honeypot needs to emulate essential services in the production network and grant the attacker the freedom to perform adversarial activities to increase its attractiveness to the attacker. Although the honeypot is a controlled environment and can be monitored by using tools such as honeywall,[31]attackers may still be able to use some honeypots as pivot nodes to penetrate production systems.[32]
The second risk of honeypots is that they may attract legitimate users due to a lack of communication in large-scale enterprise networks. For example, the security team who applies and monitors the honeypot may not disclose the honeypot location to all users in time due to the lack of communication or the prevention of insider threats.[33][34]
"A 'honey net' is a network of high interaction honeypots that simulates a production network and configured such that all activity is monitored, recorded and in a degree, discreetly regulated."
Two or more honeypots on a network form ahoney net. Typically, a honey net is used for monitoring a larger and/or more diverse network in which one honeypot may not be sufficient. Honey nets and honeypots are usually implemented as parts of largernetwork intrusion detection systems. Ahoney farmis a centralized collection of honeypots and analysis tools.[35]
The concept of the honey net first began in 1999 when Lance Spitzner, founder of theHoneynet Project, published the paper "To Build a Honeypot".[36]
An early formulation of the concept, called "entrapment", is defined inFIPS39 (1976) as "the deliberate planting of apparent flaws in a system for the purpose of detecting attempted penetrations or confusing an intruder about which flaws to exploit".[37]
The earliest honeypot techniques are described inClifford Stoll's 1989 bookThe Cuckoo's Egg.
One of the earliest documented cases of the cybersecurity use of a honeypot began in January 1991. On January 7, 1991, while he worked at AT&T Bell Laboratories Cheswick observed a criminal hacker, known as acracker, attempting to obtain a copy of a password file. Cheswick wrote that he and colleagues constructed a "chroot "Jail" (or "roach motel")" which allowed them to observe their attacker over a period of several months.[38]
In 2017,Dutch policeused honeypot techniques to track down users of thedarknet marketHansa.
The metaphor of a bear being attracted to and stealing honey is common in many traditions, including Germanic, Celtic, and Slavic. A common Slavic word for the bear ismedved"honey eater". The tradition of bears stealing honey has been passed down through stories and folklore, especially the well knownWinnie the Pooh.[39][40]
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