scholarly journals Weak equivalence of higher-dimensional automata

2021 ◽  
Vol vol. 23 no. 1 (Automata, Logic and Semantics) ◽  
Author(s):  
Thomas Kahl
Keyword(s):  
Tensor Product ◽  
Weak Equivalence ◽  
Higher Dimensional ◽  
Trace Language ◽  
Independence Structure

This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak equivalence focuses mainly on a traditional trace language and a new homology language, which captures the overall independence structure of an HDA. It is shown that weak equivalence is compatible with both the tensor product and the coproduct of HDAs and that, under certain conditions, HDAs may be reduced to weakly equivalent smaller ones by merging and collapsing cubes.

COMPLEXITY RELAXATION OF THE TENSOR PRODUCT MODEL TRANSFORMATION FOR HIGHER DIMENSIONAL PROBLEMS

2008 ◽  
Vol 9 (2) ◽  
pp. 195-200 ◽  
Author(s):  
Péter Baranyi ◽  
Zoltén Petres ◽  
Péter Korondi ◽  
Yeung Yam ◽  
Hideki Hashimoto
Keyword(s):  
Tensor Product ◽  
Model Transformation ◽  
Product Model ◽  
Higher Dimensional

scholarly journals Perfect hypercomplex algebras: Semi-tensor product approach

2021 ◽  
Vol 1 (4) ◽  
pp. 177-187
Author(s):  
Daizhan Cheng ◽  
◽  
Zhengping Ji ◽  
Jun-e Feng ◽  
Shihua Fu ◽  
...  
Keyword(s):  
Tensor Product ◽  
Sufficient Conditions ◽  
Characteristic Functions ◽  
Hypercomplex Numbers ◽  
3 Dimensional ◽  
Zero Sets ◽  
Higher Dimensional ◽  
Product Approach ◽  
Necessary And Sufficient

<abstract><p>The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebras (PHAs) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product (STP) of matrices are reviewed. The zero sets are defined for non-invertible hypercomplex numbers in a given PHA, and characteristic functions are proposed for calculating zero sets. Then PHA of various dimensions are considered. First, classification of $ 2 $-dimensional PHAs are investigated. Second, all the $ 3 $-dimensional PHAs are obtained and the corresponding zero sets are calculated. Finally, $ 4 $- and higher dimensional PHAs are also considered.</p></abstract>

scholarly journals THE COMBINATORICS OF TENSOR PRODUCTS OF HIGHER AUSLANDER ALGEBRAS OF TYPE A

2020 ◽  
pp. 1-21
Author(s):  
JORDAN MCMAHON ◽  
NICHOLAS J. WILLIAMS
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Type A ◽  
Coordinate Ring ◽  
Preprojective Algebra ◽  
Finite Algebras ◽  
Plücker Coordinates ◽  
Higher Dimensional ◽  
Dimensional Version

Abstract We consider maximal non-l-intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in the Grassmannian coordinate ring, as described by Scott. We extend a method of Scott for producing such collections, which are related to tensor products of higher Auslander algebras of type A. We show that a higher preprojective algebra of the tensor product of two d-representation-finite algebras has a d-precluster-tilting subcategory. Finally, we relate mutations of these collections to a form of tilting for these algebras.

scholarly journals Subdivision Depth Computation for Tensor Productn-Ary Volumetric Models

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Ghulam Mustafa ◽  
Muhammad Sadiq Hashmi
Keyword(s):  
Tensor Product ◽  
Error Bounds ◽  
Error Control ◽  
Computational Formula ◽  
Evaluation Technique ◽  
Volumetric Models ◽  
Higher Dimensional ◽  
Special Cases ◽  
Subdivision Depth ◽  
Control Tool

We offer computational formula of subdivision depth for tensor productn-ary (n⩾2) volumetric models based on error bound evaluation technique. This formula provides and error control tool in subdivision schemes over regular hexahedron lattice in higher-dimensional spaces. Moreover, the error bounds of Mustafa et al. (2006) are special cases of our bounds.

Second Order Convergence of the Interpolation based on-Element

2016 ◽  
Vol 9 (4) ◽  
pp. 595-618 ◽  
Author(s):  
Ruijian He ◽  
Xinlong Feng
Keyword(s):  
Tensor Product ◽  
Product Type ◽  
Second Order ◽  
Basis Functions ◽  
Dimensional Case ◽  
Order Convergence ◽  
Numerical Tests ◽  
Higher Dimensional ◽  
Second Order Convergence ◽  
Integral Average

AbstractIn this paper, the second order convergence of the interpolation based on-element is derived in the case ofd=1, 2 and 3. Using the integral average on each element, the new basis functions of tensor product type is builded up and we can easily extend it to the higher dimensional case. Finally, some numerical tests are made to show the analytical results of the interpolation errors.

Principles of Quantum-like Evolution

2019 ◽  
Vol 26 (02) ◽  
pp. 1950007
Author(s):  
Andrzej Wichert
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Tensor Product ◽  
Open System ◽  
Stochastic Matrix ◽  
Chaotic Behaviour ◽  
Quantum Cognition ◽  
Higher Dimensional ◽  
The Matrix

We present a case study of quantum-like probabilities that are motivated by quantum cognition. We introduce quantum-like evolution that is l2 norm preserving but in which the matrix does not need to be unitary. We show how to map any 2 × 2 stochastic matrix to an l2 norm preserving balanced phase matrix that maps real vectors of length one into complex vectors of length one. Quantum-like evolution can simulate a probability distribution of open system in which the operator is not unitary but norm preserving. Such a kind of behaviour is studied in quantum cognition. By tensor product higher dimensional balanced phase matrices can be built. Quantum-like evolution can simulate either unitary open one by coding the phase of input vector into the phase of a balanced phase matrix, a Markov chain or an alternative evolution that can lead to fixed, periodic or chaotic behaviour resulting in strange oscillations.

scholarly journals THE EQUIVALENCE PRINCIPLE AS A PROBE FOR HIGHER DIMENSIONS

2005 ◽  
Vol 14 (12) ◽  
pp. 2315-2318 ◽  
Author(s):  
PAUL S. WESSON
Keyword(s):  
General Relativity ◽  
Equivalence Principle ◽  
Particle Physics ◽  
Higher Dimensions ◽  
Weak Equivalence ◽  
Weak Equivalence Principle ◽  
Five Dimensions ◽  
Geometrical Symmetry ◽  
Higher Dimensional

Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle becomes a geometrical symmetry which can be broken, perhaps at a level detectable by new tests in space.

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