Live briefing
Everything about Hypercube
Convex polytope, the n-dimensional analogue of a square and a cube
In geometry, a hypercube is an n-dimensional analogue of a square and a cube ; the special case for n = 4 is known as a tesseract. It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in n dimensions is equal to. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: HypercubeA 5-minute orientation
- Skim a recent paper: Epilepsy detection in 121 patient populations using hypercube pattern from EEG signalsInfluential work since 2022
- Pick up a classic book: Optimal cube-connected cube multiprocessorsThe most-reprinted book on the subject
- Read the landmark paper: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systemsCited 2,425 times
- Go sideways: TesseractA closely related topic
- Go sideways: DemihypercubeA closely related topic
📖 Definitions
Noun A geometric figure in four or more dimensions, which is analogous to a cube in three dimensions. Specifically, the n-dimensional equivalent of a cube for any non-negative integer n.
Noun Such a figure in four dimensions; a tesseract.
Noun A data cube with more than three dimensions.
Noun A computer architecture in which each processor is connected to n others, by analogy with a hypercube of n dimensions.
🏆 Landmark papers (most cited)
Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems
Large Sample Properties of Simulations Using Latin Hypercube Sampling
A conditioned Latin hypercube method for sampling in the presence of ancillary information
On Latin hypercube sampling for structural reliability analysis
Generalized Hypercube and Hyperbus Structures for a Computer Network
The generalization of Latin hypercube sampling
A Hypercube-Based Encoding for Evolving Large-Scale Neural Networks
Optimal Latin-hypercube designs for computer experiments
🆕 Influential since 2022
Epilepsy detection in 121 patient populations using hypercube pattern from EEG signals
Adaptive Latin Hypercube Sampling for a Surrogate-Based Optimization with Artificial Neural Network
Fatigue life uncertainty prediction using the Monte Carlo and Latin hypercube sampling techniques under uniaxial and multiaxial cyclic loading
On the efficacy of conditioned and progressive Latin hypercube sampling in supervised machine learning
SRIME: a strengthened RIME with Latin hypercube sampling and embedded distance-based selection for engineering optimization problems
📚 Books worth reading
- 📕Optimal cube-connected cube multiprocessorsXian-He Sun · 1993
- 📕Adaptive fault-tolerant routing in hypercube multicomputersMing-Syan Chen · 1990
Hypercube multiprocessors, 1986Conference on Hypercube Multiprocessors (1st 1985 Knoxville, Tenn.) · 1986- 📕The Third Conference on Hypercube Concurrent Computers and ApplicationsConference on Hypercube Multiprocessors (3rd 1988 Pasadena, Calif.), Calif.) Conference on Hypercube Multiprocessors 1988 (Pasadena · 1988
- 📕Parallelization of finite element analysis codes using heterogeneous distributed computingFüsun Özgüner · 1996
- 📕Fault-tolerant communications in parallel systemsSeungjin Park · 1993
- 📕Concurrent image processing executive (CIPE)Mih-seh Kong · 1989
- 📕A network flow model for load balancing in circuit-switched multicomputersShahid H. Bokhari · 1990
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Tesseract In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter…
- Demihypercube In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation…
- Cross-polytope In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean space…
- Regular polytope In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In…
- Duoprism In geometry of 4 dimensions or higher, a double prism or duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions…
- Truncated tesseract In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract. There are three truncations, including a…
- Cantellated tesseract In four-dimensional geometry, a cantellated tesseract is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular tesseract…
- 5-cell In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells…