hypercube


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hypercube

[′hī·pər ‚kyüb]
(computer science)
A configuration of parallel processors in which the locations of the processors correspond to the vertices of a mathematical hypercube and the links between them correspond to its edges.
(mathematics)
The analog of a cube in n dimensions (n = 2, 3, ….), with 2 n vertices, n 2 n-1edges, and 2 n cells; for an object with edges of length 2 a, the coordinates of the vertices are (± a, ± a, …, ± a).
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

hypercube

A cube of more than three dimensions. A single (2^0 = 1) point (or "node") can be considered as a zero dimensional cube, two (2^1) nodes joined by a line (or "edge") are a one dimensional cube, four (2^2) nodes arranged in a square are a two dimensional cube and eight (2^3) nodes are an ordinary three dimensional cube. Continuing this geometric progression, the first hypercube has 2^4 = 16 nodes and is a four dimensional shape (a "four-cube") and an N dimensional cube has 2^N nodes (an "N-cube"). To make an N+1 dimensional cube, take two N dimensional cubes and join each node on one cube to the corresponding node on the other. A four-cube can be visualised as a three-cube with a smaller three-cube centred inside it with edges radiating diagonally out (in the fourth dimension) from each node on the inner cube to the corresponding node on the outer cube.

Each node in an N dimensional cube is directly connected to N other nodes. We can identify each node by a set of N Cartesian coordinates where each coordinate is either zero or one. Two node will be directly connected if they differ in only one coordinate.

The simple, regular geometrical structure and the close relationship between the coordinate system and binary numbers make the hypercube an appropriate topology for a parallel computer interconnection network. The fact that the number of directly connected, "nearest neighbour", nodes increases with the total size of the network is also highly desirable for a parallel computer.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)

hypercube

A parallel processing architecture made up of binary multiples of computers (4, 8, 16, etc.). The computers are interconnected so that data travel is kept to a minimum. For example, in two eight-node cubes, each node in one cube would be connected to the counterpart node in the other.
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References in periodicals archive ?
Betweenness Centrality of Vertices in Hypercubes. The n-cube or n-dimensional hypercube [Q.sub.n] is defined recursively by [Q.sub.1] = [K.sub.2] and [Q.sub.n] = [K.sub.2] x [Q.sub.n - 1].
One can easily see that the unknown parameter vector [delta](t) belongs to the hypercube of (A.13).
Areas formed by blocks, referred to as [f.sub.111] [f.sub.211], [f.sub.112] [f.sub.211], ..., and so forth, are called receptive fields (or hypercube).
In this paper, we present a modified Latin hypercube sample called the Monte Carlo hypercube sampling method (MCHSM), and the method is presented in the next subsection.
Key words: Latin Hypercube Sampling, Sensitivity Analysis, Anchor-infill Assembly, Pull-out Response, Infill material Properties
A software reconstruction program uses prior spatial/spectral calibration information to reconstruct the measured scene into its hypercube so that every pixel in the resulting image has an associated spectrum.
More recent, animated works, such as P-1411-e, 2010, use software to picture the eleven-dimensional hypercube and other complex geometric analogues, with elements of the representations randomized.
For the MCS, the Latin Hypercube Sampling is selected due to that this technique avoids repeating samples that have been evaluated, and also forces the tails of a distribution to participate in the sampling process.
MITS, a provider of advanced reporting and analytics solutions, has announced a new inventory analysis tool for wholesale distributors using the Epicor (formerly Activant) Prelude distribution management system called the Prelude Inventory Hypercube.
US literary critic Eisenhauer presents four meditations on the work of Latin lyric poet Gaius Valerius Catullus (84-54 BC) concerned with who he thought he was, the logodaedal hypercube, the irony of how things are and non-resistance, and from libertinage to Zukofsky.