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General-purpose computing on graphics processing units(GPGPU, or less oftenGPGP) is the use of agraphics processing unit(GPU), which typically handles computation only forcomputer graphics, to perform computation in applications traditionally handled by thecentral processing unit(CPU).[1][2][3][4]The use of multiplevid... | https://en.wikipedia.org/wiki/General-purpose_computing_on_graphics_processing_units |
Incomputer science, asegmented scanis a modification of theprefix sumwith an equal-sized array of flag bits to denote segment boundaries on which the scan should be performed.[1]
In the following, the '1' flag bits indicate the beginning of each segment.
An alternative method used byHigh Performance Fortranis to begi... | https://en.wikipedia.org/wiki/Segmented_scan |
Asummed-area tableis adata structureandalgorithmfor quickly and efficiently generating the sum of values in a rectangular subset of a grid. In theimage processingdomain, it is also known as anintegral image. It was introduced tocomputer graphicsin 1984 byFrank Crowfor use withmipmaps. Incomputer visionit was popularize... | https://en.wikipedia.org/wiki/Summed-area_table |
Inmathematicsandcomputer science, arecursive definition, orinductive definition, is used to define theelementsin asetin terms of other elements in the set (Aczel1977:740ff). Some examples of recursively definable objects includefactorials,natural numbers,Fibonacci numbers, and theCantor ternary set.
Arecursivedefiniti... | https://en.wikipedia.org/wiki/Recursive_definition |
Incomputer programming, especiallyfunctional programmingandtype theory, analgebraic data type(ADT) is a kind ofcomposite data type, i.e., adata typeformed by combining other types.
Two common classes of algebraic types areproduct types(i.e.,tuples, andrecords) andsum types(i.e.,taggedordisjoint unions,coproducttypes o... | https://en.wikipedia.org/wiki/Algebraic_data_type |
Intype theory, a system hasinductive typesif it has facilities for creating a new type from constants and functions that create terms of that type. The feature serves a role similar todata structuresin a programming language and allows a type theory to add concepts likenumbers,relations, andtrees. As the name suggest... | https://en.wikipedia.org/wiki/Inductive_type |
Anodeis a basic unit of adata structure, such as alinked listortreedata structure. Nodes containdataand also may link to other nodes. Links between nodes are often implemented bypointers.
Nodes are often arranged into tree structures. A node represents the information contained in a single data structure. These nodes ... | https://en.wikipedia.org/wiki/Node_(computer_science) |
Ahierarchical queryis a type ofSQL querythat handleshierarchical modeldata. They are special cases of more general recursivefixpointqueries, which computetransitive closures.
In standardSQL:1999hierarchical queries are implemented by way of recursivecommon table expressions(CTEs). Unlike Oracle's earlierconnect-by cla... | https://en.wikipedia.org/wiki/Hierarchical_and_recursive_queries_in_SQL |
Inmathematics, theKleene–Rosser paradoxis a paradox that shows that certain systems offormal logicareinconsistent, in particular the version ofHaskell Curry'scombinatory logicintroduced in 1930, andAlonzo Church's originallambda calculus, introduced in 1932–1933, both originally intended as systems of formal logic. The... | https://en.wikipedia.org/wiki/Kleene%E2%80%93Rosser_paradox |
this,self, andMearekeywordsused in some computerprogramming languagesto refer to the object, class, or other entity which the currently running code is a part of. The entity referred to thus depends on theexecution context(such as which object has its method called). Different programming languages use these keywords... | https://en.wikipedia.org/wiki/Open_recursion |
Sierpiński curvesare arecursivelydefinedsequenceofcontinuousclosed planefractal curvesdiscovered byWacław Sierpiński, which in the limitn→∞{\displaystyle n\to \infty }completely fill the unit square: thus their limit curve, also calledthe Sierpiński curve, is an example of aspace-filling curve.
Because the Sierpiński ... | https://en.wikipedia.org/wiki/Sierpi%C5%84ski_curve |
TheMcCarthy 91 functionis arecursive function, defined by thecomputer scientistJohn McCarthyas a test case forformal verificationwithincomputer science.
The McCarthy 91 function is defined as
The results of evaluating the function are given byM(n) = 91 for all integer argumentsn≤ 100, andM(n) =n− 10 forn> 100. Indeed... | https://en.wikipedia.org/wiki/McCarthy_91_function |
Inmathematical logicandcomputer science, ageneral recursive function,partial recursive function, orμ-recursive functionis apartial functionfromnatural numbersto natural numbers that is "computable" in an intuitive sense – as well as in aformal one. If the function is total, it is also called atotal recursive function(s... | https://en.wikipedia.org/wiki/%CE%9C-recursive_function |
Incomputability theory, aprimitive recursive functionis, roughly speaking, a function that can be computed by acomputer programwhoseloopsare all"for" loops(that is, an upper bound of the number of iterations of every loop is fixed before entering the loop). Primitive recursive functions form a strictsubsetof thosegener... | https://en.wikipedia.org/wiki/Primitive_recursive_function |
Incomputer science, theTak functionis arecursive function, named afterIkuo Takeuchi[ja]. It is defined as follows:
τ(x,y,z)={τ(τ(x−1,y,z),τ(y−1,z,x),τ(z−1,x,y))ify<xzotherwise{\displaystyle \tau (x,y,z)={\begin{cases}\tau (\tau (x-1,y,z),\tau (y-1,z,x),\tau (z-1,x,y))&{\text{if }}y<x\\z&{\text{otherwise}}\end{cases}}}... | https://en.wikipedia.org/wiki/Tak_(function) |
Inmathematics, specificallycategory theory, afunctoris amappingbetweencategories. Functors were first considered inalgebraic topology, where algebraic objects (such as thefundamental group) are associated totopological spaces, and maps between these algebraic objects are associated tocontinuousmaps between spaces. N... | https://en.wikipedia.org/wiki/Functor |
Infunctional programming, anapplicative functor, or an applicative for short, is an intermediate structure betweenfunctorsandmonads. Incategory theorythey are calledclosed monoidal functors. Applicative functors allow for functorial computations to be sequenced (unlike plain functors), but don't allow using results fro... | https://en.wikipedia.org/wiki/Applicative_functor |
In manycomputer programminglanguages, ado while loopis acontrol flowstatementthat executes a block of code and then either repeats the block or exits the loop depending on a givenbooleancondition.
Thedo whileconstruct consists of a process symbol and a condition. First the code within the block is executed. Then the c... | https://en.wikipedia.org/wiki/Do_while_loop |
Incomputer science, afor-looporfor loopis acontrol flowstatementfor specifyingiteration. Specifically, a for-loop functions by running a section of code repeatedly until a certain condition has been satisfied.
For-loops have two parts: a header and a body. The header defines the iteration and the body is the code exec... | https://en.wikipedia.org/wiki/For_loop |
In most computerprogramming languages, awhile loopis acontrol flowstatementthat allows code to be executed repeatedly based on a givenBooleancondition. Thewhileloop can be thought of as a repeatingif statement.
Thewhileconstruct consists of a block of code and a condition/expression.[1]The condition/expression is eval... | https://en.wikipedia.org/wiki/While_loop |
Incomputer science, aprogramming languageis said to havefirst-class functionsif it treatsfunctionsasfirst-class citizens. This means the language supports passing functions as arguments to other functions, returning them as the values from other functions, and assigning them to variables or storing them in data structu... | https://en.wikipedia.org/wiki/First-class_function |
In computer science,function-levelprogramming refers to one of the two contrastingprogramming paradigmsidentified byJohn Backusin his work on programs as mathematical objects, the other beingvalue-level programming.
In his 1977Turing Awardlecture, Backus set forth what he considered to be the need to switch to a diffe... | https://en.wikipedia.org/wiki/Function-level_programming |
Inmathematical logic,category theory, andcomputer science,kappa calculusis aformal systemfor definingfirst-orderfunctions.
Unlikelambda calculus, kappa calculus has nohigher-order functions; its functions are
notfirst class objects. Kappa-calculus can be
regarded as "a reformulation of the first-order fragment of typ... | https://en.wikipedia.org/wiki/Kappa_calculus |
Ahigher order message(HOM) in a computerprogramming languageis a form ofhigher-order programmingthat allows messages that have other messages as arguments. The concept was introduced atMacHack2003[1][2]byMarcel Weiherand presented in a more complete form in 2005 by Marcel Weiher andStéphane Ducasse.[3]Loops can be writ... | https://en.wikipedia.org/wiki/Higher_order_message |
{n∣∃k∈Z,n=2k}{\displaystyle \{n\mid \exists k\in \mathbb {Z} ,n=2k\}}
Inmathematicsand more specifically inset theory,set-builder notationis anotationfor specifying asetby a property that characterizes its members.[1]
Specifying sets by member properties is allowed by theaxiom schema of specification. This is also kn... | https://en.wikipedia.org/wiki/Set-builder_notation |
TheSQLSELECTstatement returns aresult setof rows, from one or moretables.[1][2]
A SELECT statement retrieves zero or more rows from one or moredatabase tablesor databaseviews. In most applications,SELECTis the most commonly useddata manipulation language(DML) command. As SQL is adeclarative programminglanguage,SELECTq... | https://en.wikipedia.org/wiki/Select_(SQL) |
Structured Query Language(SQL) (pronounced/ˌɛsˌkjuˈɛl/S-Q-L;or alternatively as/ˈsiːkwəl/"sequel")[4][5]is adomain-specific languageused to manage data, especially in arelational database management system(RDBMS). It is particularly useful in handlingstructured data, i.e., data incorporating relations among entities an... | https://en.wikipedia.org/wiki/SQL#Queries |
Incomputing,algorithmic skeletons, orparallelism patterns, are a high-levelparallel programming modelfor parallel and distributed computing.
Algorithmic skeletons take advantage of common programming patterns to hide the complexity of parallel and distributed applications. Starting from a basic set of patterns (skelet... | https://en.wikipedia.org/wiki/Algorithmic_skeleton |
Incomputer programming, specifically when using theimperative programmingparadigm, anassertionis apredicate(aBoolean-valued functionover thestate space, usually expressed as alogical propositionusing thevariablesof a program) connected to a point in the program, that always should evaluate to true at that point in code... | https://en.wikipedia.org/wiki/Assertion_(computing) |
TheGuarded Command Language(GCL) is aprogramming languagedefined byEdsger Dijkstraforpredicate transformer semanticsin EWD472.[1]It combines programming concepts in a compact way. It makes it easier to develop a program and its proof hand-in-hand, with the proof ideas leading the way; moreover, parts of a program can a... | https://en.wikipedia.org/wiki/Guarded_Command_Language |
Inconcurrent programming,guarded suspension[1]is asoftware design patternfor managing operations that require both alockto be acquired and apreconditionto be satisfied before the operation can be executed. The guarded suspension pattern is typically applied to method calls in object-oriented programs, and involves susp... | https://en.wikipedia.org/wiki/Guarded_suspension |
Inmathematics, theIverson bracket, named afterKenneth E. Iverson, is a notation that generalises theKronecker delta, which is the Iverson bracket of the statementx=y. It maps anystatementto afunctionof thefree variablesin that statement. This function is defined to take the value 1 for the values of the variables for w... | https://en.wikipedia.org/wiki/Iverson_bracket |
Thematerial conditional(also known asmaterial implication) is abinary operationcommonly used inlogic. When the conditional symbol→{\displaystyle \to }isinterpretedas material implication, a formulaP→Q{\displaystyle P\to Q}is true unlessP{\displaystyle P}is true andQ{\displaystyle Q}is false.
Material implication is us... | https://en.wikipedia.org/wiki/Logical_conditional |
In computer programming, asentinel nodeis a specifically designatednodeused withlinked listsandtreesas a traversal path terminator. This type of node does not hold or reference any data managed by the data structure.
Sentinels are used as an alternative over usingNULLas the path terminator in order to get one or more ... | https://en.wikipedia.org/wiki/Sentinel_node |
Incomputer programming languages, aswitch statementis a type of selection control mechanism used to allow the value of avariableor expression to change thecontrol flowof program execution via search and map.
Switch statements function somewhat similarly to theifstatement used in programming languages likeC/C++,C#,Visu... | https://en.wikipedia.org/wiki/Switch_statement |
Substructural type systemsare a family oftype systemsanalogous tosubstructural logicswhere one or more of thestructural rulesare absent or only allowed under controlled circumstances. Such systems can constrain access tosystem resourcessuch asfiles,locks, andmemoryby keeping track of changes of state and prohibiting in... | https://en.wikipedia.org/wiki/Linear_type |
Linear logicis asubstructural logicproposed by FrenchlogicianJean-Yves Girardas a refinement ofclassicalandintuitionistic logic, joining thedualitiesof the former with many of theconstructiveproperties of the latter.[1]Although the logic has also been studied for its own sake, more broadly, ideas from linear logic have... | https://en.wikipedia.org/wiki/Linear_logic |
Incomputer science,array-access analysisis acompiler analysisapproach used to decide the read and write access patterns to elements or portions of arrays.[1]
The major data type manipulated in scientific programs is the array. The define/use analysis on a whole array is insufficient for aggressivecompiler optimization... | https://en.wikipedia.org/wiki/Array_access_analysis |
Anarray database management systemorarray DBMSprovidesdatabaseservices specifically forarrays(also calledraster data), that is: homogeneous collections of data items (often calledpixels,voxels, etc.), sitting on a regular grid of one, two, or more dimensions. Often arrays are used to represent sensor, simulation, image... | https://en.wikipedia.org/wiki/Array_database_management_system |
Incomputer science,bounds-checking eliminationis acompiler optimizationuseful inprogramming languagesorruntime systemsthat enforcebounds checking, the practice of checking every index into anarrayto verify that the index is within the defined valid range of indexes.[1]Its goal is to detect which of these indexing opera... | https://en.wikipedia.org/wiki/Bounds-checking_elimination |
Formats that usedelimiter-separated values(alsoDSV)[2]: 113store two-dimensional arrays of data by separating the values in each row with specificdelimitercharacters. Mostdatabaseandspreadsheetprograms are able to read or save data in a delimited format. Due to their wide support, DSV files can be used indata exchangea... | https://en.wikipedia.org/wiki/Delimiter-separated_values |
Incomputer programming,bounds checkingis any method of detecting whether avariableis within someboundsbefore it is used. It is usually used to ensure that a number fits into a given type (range checking), or that a variable being used as anarrayindex is within the bounds of the array (index checking). A failed bounds c... | https://en.wikipedia.org/wiki/Index_checking |
Incomputing, a group ofparallel arrays(also known asstructure of arraysor SoA) is a form ofimplicit data structurethat uses multiplearraysto represent a singular array ofrecords. It keeps a separate,homogeneous dataarray for each field of the record, each having the same number of elements. Then, objects located at the... | https://en.wikipedia.org/wiki/Parallel_array |
Innumerical analysisandscientific computing, asparse matrixorsparse arrayis amatrixin which most of the elements are zero.[1]There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify assparsebut a common criterion is that the number of non-zero elements is roughly equal to th... | https://en.wikipedia.org/wiki/Sparse_array |
Incomputer programming, avariable-length array(VLA), also calledvariable-sizedorruntime-sized, is anarray data structurewhose length is determined atruntime, instead of atcompile time.[1]In the languageC, the VLA is said to have a variably modifieddata typethat depends on a value (seeDependent type).
The main purpose ... | https://en.wikipedia.org/wiki/Variable-length_array |
Incomputer science, adisjoint-set data structure, also called aunion–find data structureormerge–find set, is adata structurethat stores a collection ofdisjoint(non-overlapping)sets. Equivalently, it stores apartition of a setinto disjointsubsets. It provides operations for adding new sets, merging sets (replacing them ... | https://en.wikipedia.org/wiki/Disjoint_set_(data_structure) |
Abitstream(orbit stream), also known asbinary sequence, is asequenceofbits.
Abytestreamis a sequence ofbytes. Typically, each byte is an8-bit quantity, and so the termoctet streamis sometimes used interchangeably. An octet may be encoded as a sequence of 8 bits in multiple different ways (seebit numbering) so there is... | https://en.wikipedia.org/wiki/Bitstream |
Incomputer science,coinductionis a technique for defining and proving properties of systems ofconcurrentinteractingobjects.
Coinduction is themathematicaldualtostructural induction.[citation needed]Coinductively defineddata typesare known ascodataand are typicallyinfinitedata structures, such asstreams.
As a definiti... | https://en.wikipedia.org/wiki/Codata_(computer_science) |
Inconnection-oriented communication, adata streamis thetransmissionof a sequence ofdigitally encoded signalsto conveyinformation.[1]Typically, the transmitted symbols are grouped into a series ofpackets.[2]
Data streaming has become ubiquitous. Anything transmitted over theInternetis transmitted as a data stream. Usin... | https://en.wikipedia.org/wiki/Data_stream |
Data Stream Mining(also known asstream learning) is the process of extracting knowledge structures from continuous, rapid data records. Adata streamis an ordered sequence of instances that in many applications of data stream mining can be read only once or a small number of times using limited computing and storage cap... | https://en.wikipedia.org/wiki/Data_stream_mining |
Inpacket switchingnetworks,traffic flow,packet flowornetwork flowis a sequence ofpacketsfrom a sourcecomputerto a destination, which may be another host, amulticastgroup, or abroadcastdomain. RFC 2722 defines traffic flow as "an artificial logical equivalent to a call or connection."[1]RFC 3697 defines traffic flow as ... | https://en.wikipedia.org/wiki/Traffic_flow_(computer_networking) |
Anetwork socketis a software structure within anetwork nodeof acomputer networkthat serves as an endpoint for sending and receiving data across the network. The structure and properties of a socket are defined by anapplication programming interface(API) for the networking architecture. Sockets are created only during t... | https://en.wikipedia.org/wiki/Network_socket |
Streaming mediarefers tomultimediadelivered through anetworkfor playback using amedia player. Media is transferred in astreamofpacketsfrom aserverto aclientand is rendered in real-time;[1]this contrasts with filedownloading, a process in which the end-user obtains an entire media file before consuming the content. Stre... | https://en.wikipedia.org/wiki/Streaming_media |
Incomputing, adiscriminatoris afieldof characters designed to separate a certain element from others of the sameidentifier. As an example, suppose that a program must save two uniqueobjectsto memory, both of whose identifiers happen to befoo. To ensure the two objects are not conflated, the program may assigndiscrimina... | https://en.wikipedia.org/wiki/Discriminator |
TheCommon Object Request Broker Architecture(CORBA) is astandarddefined by theObject Management Group(OMG) designed to facilitate the communication of systems that are deployed on diverseplatforms. CORBA enables collaboration between systems on different operating systems,programming languages, and computing hardware. ... | https://en.wikipedia.org/wiki/CORBA |
Variantis adata typein certain programming languages, particularlyVisual Basic,OCaml,[1]DelphiandC++when using theComponent Object Model. It is an implementation of theeponymous conceptincomputer science.
In Visual Basic (andVisual Basic for Applications) the Variant data type is atagged unionthat can be used to repre... | https://en.wikipedia.org/wiki/Variant_type_(COM) |
Thenull coalescing operatoris abinary operatorthat is part of the syntax for a basicconditional expressionin severalprogramming languages, such as (in alphabetical order):C#[1]since version 2.0,[2]Dart[3]since version 1.12.0,[4]PHPsince version 7.0.0,[5]Perlsince version 5.10 aslogical defined-or,[6]PowerShellsince 7.0... | https://en.wikipedia.org/wiki/Null_coalescing_operator |
Incomputer programming, asemipredicate problemoccurs when asubroutineintended to return a useful value can fail, but the signalling of failure uses an otherwise validreturn value.[1]The problem is that the caller of the subroutine cannot tell what the result means in this case.
Thedivisionoperation yields areal number... | https://en.wikipedia.org/wiki/Semipredicate_problem |
Incomputer science, aunionis avaluethat may have any of multiple representations or formats within the same area ofmemory; that consists of avariablethat may hold such adata structure. Someprogramming languagessupport aunion typefor such adata type. In other words, a union type specifies the permitted types that may be... | https://en.wikipedia.org/wiki/Union_type |
In the area ofmathematical logicandcomputer scienceknown astype theory, aunit typeis atypethat allows only one value (and thus can hold no information). The carrier (underlying set) associated with a unit type can be anysingleton set. There is anisomorphismbetween any two such sets, so it is customary to talk abouttheu... | https://en.wikipedia.org/wiki/Unit_type |
On thex86computer architecture, atriple faultis a special kind ofexceptiongenerated by theCPUwhen an exception occurs while the CPU is trying to invoke thedouble faultexception handler, which itself handles exceptions occurring while trying to invoke a regular exception handler.
x86processors beginning with the80286wi... | https://en.wikipedia.org/wiki/Triple_fault |
Incomputer programming, atype systemis alogical systemcomprising a set of rules that assigns a property called atype(for example,integer,floating point,string) to everyterm(a word, phrase, or other set of symbols). Usually the terms are variouslanguage constructsof acomputer program, such asvariables,expressions,functi... | https://en.wikipedia.org/wiki/Existential_types |
Inmathematical logic,System UandSystem U−arepure type systems, i.e. special forms of atyped lambda calculuswith an arbitrary number ofsorts, axioms and rules (or dependencies between the sorts).
System U was proved inconsistent byJean-Yves Girardin 1972[1](and the question of consistency of System U−was formulated). T... | https://en.wikipedia.org/wiki/System_U |
Inmathematical logicandtype theory, theλ-cube(also writtenlambda cube) is a framework introduced byHenk Barendregt[1]to investigate the different dimensions in which thecalculus of constructionsis a generalization of thesimply typed λ-calculus. Each dimension of the cube corresponds to a new kind of dependency between ... | https://en.wikipedia.org/wiki/Lambda_cube |
Inmathematics,even and odd ordinalsextend the concept ofparityfrom thenatural numbersto theordinal numbers. They are useful in sometransfinite inductionproofs.
The literature contains a few equivalent definitions of the parity of an ordinal α:
Unlike the case of evenintegers, one cannot go on to characterize even ord... | https://en.wikipedia.org/wiki/Even_and_odd_ordinals |
Inmathematics, anorder topologyis a specifictopologythat can be defined on anytotally ordered set. It is a natural generalization of the topology of thereal numbersto arbitrary totally ordered sets.
IfXis a totally ordered set, theorder topologyonXis generated by thesubbaseof "open rays"
for alla, binX. ProvidedXhas... | https://en.wikipedia.org/wiki/Order_topology#Ordinal_space |
Inmathematics, thesurreal numbersystem is atotally orderedproper classcontaining not only thereal numbersbut alsoinfiniteandinfinitesimal numbers, respectively larger or smaller inabsolute valuethan any positive real number. Research on theGo endgamebyJohn Horton Conwayled to the original definition and construction of... | https://en.wikipedia.org/wiki/Surreal_number |
In themathematicaldiscipline ofgraph theory, a3-dimensional matchingis a generalization ofbipartite matching(also known as 2-dimensional matching) to 3-partitehypergraphs, which consist of hyperedges each of which contains 3 vertices (instead of edges containing 2 vertices in a usual graph).
3-dimensional matching, of... | https://en.wikipedia.org/wiki/3-dimensional_matching |
Ingraph theory, avertex coverin ahypergraphis a set ofvertices, such that every hyperedge of the hypergraph contains at least one vertex of that set. It is an extension of the notion ofvertex coverin a graph.[1]: 466–470[2]
An equivalent term is ahitting set: given a collection of sets, a set whichintersectsall sets i... | https://en.wikipedia.org/wiki/Vertex_cover_in_hypergraphs |
Ingraph theory, the termbipartite hypergraphdescribes several related classes ofhypergraphs, all of which are natural generalizations of abipartite graph.
The weakest definition of bipartiteness is also called2-colorability. A hypergraphH= (V,E) is called 2-colorable if its vertex setVcan be partitioned into two sets,... | https://en.wikipedia.org/wiki/Bipartite_hypergraph |
In the mathematical discipline ofgraph theory, arainbow matchingin anedge-colored graphis amatchingin which all the edges have distinct colors.
Given an edge-colored graphG= (V,E), a rainbow matchingMinGis a set of pairwise non-adjacent edges, that is, no two edges share a common vertex, such that all the edges in the... | https://en.wikipedia.org/wiki/Rainbow_matching#hypergraphs |
Ingraph theory, ad-interval hypergraphis a kind of ahypergraphconstructed usingintervalsofreal lines. The parameterdis apositive integer. Theverticesof ad-interval hypergraph are the points ofddisjointlines(thus there areuncountably manyvertices). Theedgesof the graph ared-tuplesof intervals, one interval in every real... | https://en.wikipedia.org/wiki/D-interval_hypergraph |
In mathematics, theErdős–Ko–Rado theoremlimits the number ofsetsin afamily of setsfor which every two sets have at least one element in common.Paul Erdős,Chao Ko, andRichard Radoproved the theorem in 1938, but did not publish it until 1961. It is part of the field ofcombinatorics, and one of the central results ofextre... | https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Ko%E2%80%93Rado_theorem |
Fractional coloringis a topic in a branch ofgraph theoryknown asfractional graph theory. It is a generalization of ordinarygraph coloring. In a traditional graph coloring, each vertex in a graph is assigned some color, and adjacent vertices — those connected by edges — must be assigned different colors. In a fractional... | https://en.wikipedia.org/wiki/Fractional_coloring |
Ingraph theory, apathin anedge-colored graphis said to berainbowif no color repeats on it. A graph is said to berainbow-connected(orrainbow colored) if there is a rainbow path between each pair of itsvertices. If there is a rainbowshortest pathbetween each pair of vertices, the graph is said to bestrongly rainbow-conne... | https://en.wikipedia.org/wiki/Rainbow_coloring |
Ingraph theory, the termbipartite hypergraphdescribes several related classes ofhypergraphs, all of which are natural generalizations of abipartite graph.
The weakest definition of bipartiteness is also called2-colorability. A hypergraphH= (V,E) is called 2-colorable if its vertex setVcan be partitioned into two sets,... | https://en.wikipedia.org/wiki/Rainbow-colorable_hypergraph |
Ingraph theory, arainbow-independent set(ISR) is anindependent setin agraph, in which eachvertexhas a differentcolor.
Formally, letG= (V,E)be a graph, and suppose vertex setVispartitionedintomsubsetsV1, …,Vm, called "colors". A setUof vertices is called a rainbow-independent set if it satisfies both the following cond... | https://en.wikipedia.org/wiki/Rainbow-independent_set |
Incombinatoricsandcomputer science,covering problemsare computational problems that ask whether a certain combinatorial structure 'covers' another, or how large the structure has to be to do that. Covering problems areminimization problemsand usuallyinteger linear programs, whosedual problemsare calledpacking problems.... | https://en.wikipedia.org/wiki/Rainbow_covering |
In themathematicalfield ofgraph theory,Hall-type theorems for hypergraphsare severalgeneralizationsofHall's marriage theoremfromgraphstohypergraphs. Such theorems were proved by Ofra Kessler,[1][2]Ron Aharoni,[3][4]Penny Haxell,[5][6]Roy Meshulam,[7]and others.
Hall's marriage theorem provides a condition guaranteeing... | https://en.wikipedia.org/wiki/Hall-type_theorems_for_hypergraphs |
Ineconomicsandsocial choice theory, anenvy-free matching (EFM)is a matching between people to "things", which isenvy-freein the sense that no person would like to switch their "thing" with that of another person. This term has been used in several different contexts.
In an unweightedbipartite graphG = (X+Y,E), anenvy-... | https://en.wikipedia.org/wiki/Envy-free_matching |
Inmathematics,economics, andcomputer science, thestable matching polytopeorstable marriage polytopeis aconvex polytopederived from the solutions to an instance of thestable matching problem.[1][2]
The stable matching polytope is theconvex hullof theindicator vectorsof the stable matchings of the given problem. It has ... | https://en.wikipedia.org/wiki/Stable_matching_polytope |
Inmathematics,economics, andcomputer science, thelattice of stable matchingsis adistributive latticewhose elements arestable matchings. For a given instance of the stable matching problem, this lattice provides analgebraicdescription of the family of all solutions to the problem. It was originally described in the 1970... | https://en.wikipedia.org/wiki/Lattice_of_stable_matchings |
Thesecretary problemdemonstrates a scenario involvingoptimal stoppingtheory[1][2]that is studied extensively in the fields ofapplied probability,statistics, anddecision theory. It is also known as themarriage problem, thesultan's dowry problem, thefussy suitor problem, thegoogol game, and thebest choice problem. Its so... | https://en.wikipedia.org/wiki/Secretary_problem |
Ingraph theory,graph coloringis a methodic assignment of labels traditionally called "colors" to elements of agraph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color. Graph coloring is a special case ofgraph labeling. In its simplest form, it is a way of colori... | https://en.wikipedia.org/wiki/Vertex_coloring |
Acomplex adaptive system(CAS) is asystemthat iscomplexin that it is adynamic network of interactions, but the behavior of the ensemble may not be predictable according to the behavior of the components. It isadaptivein that the individual andcollective behaviormutate andself-organizecorresponding to the change-initiati... | https://en.wikipedia.org/wiki/Complex_adaptive_system |
Dual phase evolution(DPE) is a process that drivesself-organizationwithincomplex adaptive systems.[1]It arises in response to phase changes within the network of connections formed by a system's components. DPE occurs in a wide range of physical, biological and social systems. Its applications to technology include met... | https://en.wikipedia.org/wiki/Dual-phase_evolution |
The study ofinterdependent networksis a subfield ofnetwork sciencedealing with phenomena caused by the interactions betweencomplex networks. Though there may be a wide variety of interactions between networks,dependencyfocuses on the scenario in which the nodes in one network require support from nodes in another netw... | https://en.wikipedia.org/wiki/Interdependent_networks |
Innetwork theory,multidimensional networks, a special type ofmultilayer network, are networks with multiple kinds of relations.[1][2][3][4][5][6][7]Increasingly sophisticated attempts to model real-world systems as multidimensional networks have yielded valuable insight in the fields ofsocial network analysis,[3][4][8]... | https://en.wikipedia.org/wiki/Multidimensional_network |
Inmathematics,random graphis the general term to refer toprobability distributionsovergraphs. Random graphs may be described simply by a probability distribution, or by arandom processwhich generates them.[1][2]The theory of random graphs lies at the intersection betweengraph theoryandprobability theory. From a mathem... | https://en.wikipedia.org/wiki/Random_graph |
Random graph theory of gelationis a mathematical theory forsol–gel processes. The theory is a collection of results that generalise theFlory–Stockmayer theory, and allow identification of thegel point, gel fraction, size distribution of polymers,molar mass distributionand other characteristics for a set of many polymer... | https://en.wikipedia.org/wiki/Random_graph_theory_of_gelation |
Ascale-free networkis anetworkwhosedegree distributionfollows apower law, at least asymptotically. That is, the fractionP(k) of nodes in the network havingkconnections to other nodes goes for large values ofkas
whereγ{\displaystyle \gamma }is a parameter whose value is typically in the range2<γ<3{\textstyle 2<\gamma <... | https://en.wikipedia.org/wiki/Scale-free_networks |
Asmall-world networkis agraphcharacterized by a highclustering coefficientand lowdistances. In an example of the social network, high clustering implies the high probability that two friends of one person are friends themselves. The low distances, on the other hand, mean that there is a short chain of social connection... | https://en.wikipedia.org/wiki/Small_world_networks |
Aspatial network(sometimes alsogeometric graph) is agraphin which theverticesoredgesarespatial elementsassociated withgeometricobjects, i.e., the nodes are located in a space equipped with a certainmetric.[1][2]The simplest mathematical realization of spatial network is alatticeor arandom geometric graph(see figure in ... | https://en.wikipedia.org/wiki/Spatial_network |
Trophic coherenceis a property ofdirected graphs(or directednetworks).[1]It is based on the concept oftrophic levelsused mainly inecology,[2]but which can be defined for directed networks in general and provides a measure of hierarchical structure among nodes. Trophic coherence is the tendency of nodes to fall into wel... | https://en.wikipedia.org/wiki/Trophic_coherence |
Defunct
Defunct
TheGerman nobility(deutscher Adel) androyaltywerestatus groupsof themedieval society in Central Europe, which enjoyed certainprivilegesrelative to other people under the laws and customs in theGerman-speaking area, until the beginning of the 20th century. Historically, German entities that recognized ... | https://en.wikipedia.org/wiki/German_nobility |
The concept ofGermanyas a distinct region inCentral Europecan be traced toJulius Caesar, who referred to the unconquered area east of theRhineasGermania, thus distinguishing it fromGaul. The victory of theGermanic tribesin theBattle of the Teutoburg Forest(AD9) prevented annexation by theRoman Empire, although theRoman... | https://en.wikipedia.org/wiki/History_of_Germany |
TheHoly Roman Emperor, originally and officially theEmperor of the Romans(Latin:ImperatorRomanorum;German:Kaiserder Römer) during theMiddle Ages, and also known as theRoman-German Emperorsince theearly modern period[1](Latin:Imperator Germanorum;German:Römisch-Deutscher Kaiser), was the ruler andhead of stateof theHoly... | https://en.wikipedia.org/wiki/Holy_Roman_Emperor |
This is a list of monarchs who ruled overEast Francia, and theKingdom of Germany(Latin:Regnum Teutonicum), fromthe divisionof theFrankish Empirein 843 andthe collapseof theHoly Roman Empirein 1806 untilthe collapseof theGerman Empirein 1918:
Inaccurate[a]
Non-contemporary
Non-contemporary
The title "King of the Rom... | https://en.wikipedia.org/wiki/List_of_German_monarchs |
TheImperial Diet(Latin:Dieta ImperiiorComitium Imperiale;German:Reichstag) was the deliberative body of theHoly Roman Empire. It was not alegislative bodyin the contemporary sense; its members envisioned it more like a central forum where it was more important to negotiate than to decide.[1]
Its members were theImperi... | https://en.wikipedia.org/wiki/Reichstag_(Holy_Roman_Empire) |
Amissus dominicus(pluralmissi dominici),Latinfor "envoy[s] of the lord [ruler]", also known inDutchasZendgraaf(German:Sendgraf), meaning "sentGraf", was an official commissioned by the Frankish king orHoly Roman Emperorto supervise the administration, mainly of justice, in parts of his dominions too remote for frequent... | https://en.wikipedia.org/wiki/Sendgraf |
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