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Intersection Number (graph Theory)
In the mathematical field of graph theory, the intersection number of a graph G=(V,E) is the smallest number of elements in a representation of G as an intersection graph of finite sets. In such a representation, each vertex is represented as a set, and two vertices are connected by an edge whenever their sets have a common element. Equivalently, the intersection number is the smallest number of cliques needed to cover all of the edges of G. A set of cliques that cover all edges of a graph is called a clique edge cover or edge clique cover, or even just a clique cover, although the last term is ambiguous: a clique cover can also be a set of cliques that cover all vertices of a graph. Sometimes "covering" is used in place of "cover". As well as being called the intersection number, the minimum number of these cliques has been called the ''R''-content, edge clique cover number, or clique cover number. The problem of computing the intersection number has been called the intersect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Erdős–Faber–Lovász Conjecture
In graph theory, the Erdős–Faber–Lovász conjecture is a problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972.. It says: :If complete graphs, each having exactly vertices, have the property that every pair of complete graphs has at most one shared vertex, then the union of the graphs can be properly colored with colors. The conjecture for all sufficiently large values of was proved by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus. Equivalent formulations introduced the problem with a story about seating assignment in committees: suppose that, in a university department, there are committees, each consisting of faculty members, and that all committees meet in the same room, which has chairs. Suppose also that at most one person belongs to the intersection of any two committees. Is it possible to assign the committee members to chairs in such a way that each member si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bitwise And
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Food Web
A food web is the natural interconnection of food chains and a graphical representation of what-eats-what in an ecological community. Position in the food web, or trophic level, is used in ecology to broadly classify organisms as autotrophs or heterotrophs. This is a non-binary classification; some organisms (such as carnivorous plants) occupy the role of mixotrophs, or autotrophs that additionally obtain organic matter from non-atmospheric sources. The linkages in a food web illustrate the feeding pathways, such as where heterotrophs obtain organic matter by feeding on autotrophs and other heterotrophs. The food web is a simplified illustration of the various methods of feeding that link an ecosystem into a unified system of exchange. There are different kinds of consumer–resource interactions that can be roughly divided into herbivory, carnivory, scavenging, and parasitism. Some of the organic matter eaten by heterotrophs, such as sugars, provides energy. Autotrophs and hetero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Compact Letter Display
Compact Letter Display (CLD) is a statistical method to clarify the output of multiple hypothesis testing when using the Analysis of variance, ANOVA and Tukey's range test, Tukey's range tests. CLD can also be applied following the Duncan's new multiple range test (which is similar to Tukey's range test). CLD facilitates the identification of variables, or Factor analysis, factors, that have Statistical difference testing, statistically different means (or averages) vs. the ones that do not have statistically different means (or averages). The basic technique of compact letter display is to label variables by one or more letters, so that variables are statistically indistinguishable if and only if they share at least one letter. The problem of doing so, using as few distinct letters as possible can be represented combinatorially as the problem of computing an Intersection number (graph theory), edge clique cover of a graph representing pairs of indistinguishable variables. As we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Data Visualization
Data and information visualization (data viz/vis or info viz/vis) is the practice of designing and creating Graphics, graphic or visual Representation (arts), representations of a large amount of complex quantitative and qualitative data and information with the help of static, dynamic or interactive visual items. Typically based on data and information collected from a certain domain of expertise, these visualizations are intended for a broader audience to help them visually explore and discover, quickly understand, interpret and gain important insights into otherwise difficult-to-identify structures, relationships, correlations, local and global patterns, trends, variations, constancy, clusters, outliers and unusual groupings within data (''exploratory visualization''). When intended for the general public (mass communication) to convey a concise version of known, specific information in a clear and engaging manner (''presentational'' or ''explanatory visualization''), it is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fiber Optic
An optical fiber, or optical fibre, is a flexible glass or plastic fiber that can transmit light from one end to the other. Such fibers find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths (data transfer rates) than electrical cables. Fibers are used instead of metal wires because signals travel along them with less loss and are immune to electromagnetic interference. Fibers are also used for illumination and imaging, and are often wrapped in bundles so they may be used to carry light into, or images out of confined spaces, as in the case of a fiberscope. Specially designed fibers are also used for a variety of other applications, such as fiber optic sensors and fiber lasers. Glass optical fibers are typically made by drawing, while plastic fibers can be made either by drawing or by extrusion. Optical fibers typically include a core surrounded by a transparent cladding material with a lower index ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Independent Set (graph Theory)
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set S of vertices such that for every two vertices in S, there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in S. A set is independent if and only if it is a clique in the graph's complement. The size of an independent set is the number of vertices it contains. Independent sets have also been called "internally stable sets", of which "stable set" is a shortening. A maximal independent set is an independent set that is not a proper subset of any other independent set. A maximum independent set is an independent set of largest possible size for a given graph G. This size is called the independence number of ''G'' and is usually denoted by \alpha(G). The optimization problem of finding such a set is called the maximum independent set problem. It is a strongly NP-hard problem. As ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Integer Programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0–1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. Canonical and standard form for ILPs In integer linear programming, the ''canonical form'' is distinct from the ''standard form''. An integer linear program in canonical form is expressed thus (note that it is the \mathbf vector which is to be decided): : \begin & \underset && \mathbf^\mathrm \mathbf\\ & \text && A \mathbf \le \mathbf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Very Long Instruction Word
Very long instruction word (VLIW) refers to instruction set architectures that are designed to exploit instruction-level parallelism (ILP). A VLIW processor allows programs to explicitly specify instructions to execute in parallel, whereas conventional central processing units (CPUs) mostly allow programs to specify instructions to execute in sequence only. VLIW is intended to allow higher performance without the complexity inherent in some other designs. The traditional means to improve performance in processors include dividing instructions into sub steps so the instructions can be executed partly at the same time (termed ''pipelining''), dispatching individual instructions to be executed independently, in different parts of the processor (''superscalar architectures''), and even executing instructions in an order different from the program (''out-of-order execution''). These methods all complicate hardware (larger circuits, higher cost and energy use) because the processor mus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Compiler
In computing, a compiler is a computer program that Translator (computing), translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a lower level language, low-level programming language (e.g. assembly language, object code, or machine code) to create an executable program.Compilers: Principles, Techniques, and Tools by Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman - Second Edition, 2007 There are many different types of compilers which produce output in different useful forms. A ''cross-compiler'' produces code for a different Central processing unit, CPU or operating system than the one on which the cross-compiler itself runs. A ''bootstrap compiler'' is often a temporary compiler, used for compiling a more permanent or better optimised compiler for a language. Related software ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Scheduling
A schedule (, ) or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are intended to take place. The process of creating a schedule — deciding how to order these tasks and how to commit resources between the variety of possible tasks — is called scheduling,Ofer Zwikael, John Smyrk, ''Project Management for the Creation of Organisational Value'' (2011), p. 196: "The process is called scheduling, the output from which is a timetable of some form". and a person responsible for making a particular schedule may be called a scheduler. Making and following schedules is an ancient human activity. Some scenarios associate this kind of planning with learning life skills. Schedules are necessary, or at least useful, in situations where individuals need to know what time they must be at a specific location to rece ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
