The Extreme Doubly Stochastic Quadratic Operators on Two Dimensional Simplex

2015 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sherzod Turaev ◽  
Adamu Abubakar ◽  
Akram Zeki
Keyword(s):  
Two Dimensional ◽  
Dimensional Simplex ◽  
Doubly Stochastic

scholarly journals EDSQ Operator on 2DS and Limit Behavior

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 820 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Hamad Almohamedh ◽  
Badr Almutairi ◽  
Sharyar Wani ◽  
Abdullah Alharbi ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Nonlinear Model ◽  
Limit Behavior ◽  
Two Dimensional ◽  
Quadratic Operator ◽  
Dimensional Simplex ◽  
Doubly Stochastic ◽  
Nonlinear Mathematical Models ◽  
Quadratic Stochastic Operators

This paper evaluates the limit behavior for symmetry interactions networks of set points for nonlinear mathematical models. Nonlinear mathematical models are being increasingly applied to most software and engineering machines. That is because the nonlinear mathematical models have proven to be more efficient in processing and producing results. The greatest challenge facing researchers is to build a new nonlinear model that can be applied to different applications. Quadratic stochastic operators (QSO) constitute such a model that has become the focus of interest and is expected to be applicable in many biological and technical applications. In fact, several QSO classes have been investigated based on certain conditions that can also be applied in other applications such as the Extreme Doubly Stochastic Quadratic Operator (EDSQO). This paper studies the behavior limitations of the existing 222 EDSQ operators on two-dimensional simplex (2DS). The created simulation graph shows the limit behavior for each operator. This limit behavior on 2DS can be classified into convergent, periodic, and fixed.

scholarly journals Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex

2016 ◽  
Vol 14 (1) ◽  
pp. 509-519 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Farruh Shahidi ◽  
Akram Zeki ◽  
Sherzod Turaev
Keyword(s):  
Fixed Points ◽  
Extreme Points ◽  
Initial Point ◽  
Higher Dimensions ◽  
Periodic Points ◽  
Two Dimensional ◽  
Invariant Curves ◽  
Dimensional Simplex ◽  
Doubly Stochastic ◽  
Finite Dimensional

Abstract The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex.

scholarly journals Motion vector estimation using two dimensional simplex.

1988 ◽  
Vol 42 (12) ◽  
pp. 1398-1399
Author(s):  
Shun'ichi Masuda ◽  
Koichi Ohyama ◽  
Yasuo Katayama ◽  
Hiroo Uwabu
Keyword(s):  
Motion Vector ◽  
Two Dimensional ◽  
Dimensional Simplex ◽  
Vector Estimation

scholarly journals Nonlinear Convergence Algorithm: Structural Properties with Doubly Stochastic Quadratic Operators for Multi-Agent Systems

2018 ◽  
Vol 8 (1) ◽  
pp. 49-61 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sherzod Turaev ◽  
Akram Zeki ◽  
Adamu Abubaker
Keyword(s):  
Nonlinear Operator ◽  
Stochastic Matrices ◽  
Multi Agent Systems ◽  
Quadratic Operator ◽  
Dimensional Simplex ◽  
Agent Systems ◽  
Doubly Stochastic ◽  
Degroot Model ◽  
Multi Agent ◽  
Time Required

Abstract This paper proposes nonlinear operator of extreme doubly stochastic quadratic operator (EDSQO) for convergence algorithm aimed at solving consensus problem (CP) of discrete-time for multi-agent systems (MAS) on n-dimensional simplex. The first part undertakes systematic review of consensus problems. Convergence was generated via extreme doubly stochastic quadratic operators (EDSQOs) in the other part. However, this work was able to formulate convergence algorithms from doubly stochastic matrices, majorization theory, graph theory and stochastic analysis. We develop two algorithms: 1) the nonlinear algorithm of extreme doubly stochastic quadratic operator (NLAEDSQO) to generate all the convergent EDSQOs and 2) the nonlinear convergence algorithm (NLCA) of EDSQOs to investigate the optimal consensus for MAS. Experimental evaluation on convergent of EDSQOs yielded an optimal consensus for MAS. Comparative analysis with the convergence of EDSQOs and DeGroot model were carried out. The comparison was based on the complexity of operators, number of iterations to converge and the time required for convergences. This research proposed algorithm on convergence which is faster than the DeGroot linear model.

scholarly journals MORE ON GENERALIZED SIMPLICIAL CHIRAL MODELS

2001 ◽  
Vol 16 (06) ◽  
pp. 1161-1171
Author(s):  
M. ALIMOHAMMADI ◽  
KH. SAAIDI
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Density Function ◽  
Path Integration ◽  
Two Dimensional ◽  
Third Order ◽  
Dimensional Simplex ◽  
Yang Mills ◽  
Eigenvalue Density ◽  
Large N

By generalizing the auxiliary field term in the Lagrangian of simplicial chiral models on a (d-1)-dimensional simplex, the generalized simplicial chiral models has been introduced in Ref. 1. These models can be solved analytically only in d=0 and d=2 cases at large-N limit. In the d=0 case, we calculate the eigenvalue density function in strong regime and show that the partition function computed from this density function is consistent with one calculated by path integration directly. In the d=2 case, it is shown that all V= Tr (AA†)n models have a third order phase transition, the same as the two-dimensional Yang–Mills theory.

scholarly journals Diagnostic Simplexes for Dissolved-Gas Analysis

Energies ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 6459
Author(s):  
James Dukarm ◽  
Zachary Draper ◽  
Tomasz Piotrowski
Keyword(s):  
High Voltage ◽  
Equilateral Triangle ◽  
Gas Analysis ◽  
Two Dimensional ◽  
Unique Combination ◽  
Dissolved Gas ◽  
Dimensional Simplex ◽  
Dissolved Gas Analysis ◽  
Fault Type ◽  
Electrical Apparatus

A Duval triangle is a diagram used for fault type identification in dissolved-gas analysis of oil-filled high-voltage transformers and other electrical apparatus. The proportional concentrations of three fault gases (such as methane, ethylene, and acetylene) are used as coordinates to plot a point in an equilateral triangle and identify the fault zone in which it is located. Each point in the triangle corresponds to a unique combination of gas proportions. Diagnostic pentagons published by Duval and others seek to emulate the triangles while incorporating five fault gases instead of three. Unfortunately the mapping of five gas proportions to a point inside a two-dimensional pentagon is many-to-one; consequently, dissimilar combinations of gas proportions are mapped to the same point in the pentagon, resulting in mis-diagnosis. One solution is to replace the pentagon with a four-dimensional simplex, a direct generalization of the Duval triangle. In a comparison using cases confirmed by inspection, the simplex outperformed three ratio methods, Duval triangle 1, and two pentagons.

scholarly journals Onξ(s)-Quadratic Stochastic Operators on Two-Dimensional Simplex and Their Behavior

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov ◽  
Izzat Qaralleh
Keyword(s):  
Time Evolution ◽  
General Problem ◽  
Operator Theory ◽  
Nonlinear Operator ◽  
Two Dimensional ◽  
Dimensional Simplex ◽  
Nonlinear Operators ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Quadratic Stochastic Operators

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. We studyξ(s)-QSO defined on 2D simplex. We first classifyξ(s)-QSO into 20 nonconjugate classes. Further, we investigate the dynamics of three classes of such operators.

scholarly journals An Energy Efficient QAM Modulation with Multidimensional Signal Constellation

2016 ◽  
Vol 62 (2) ◽  
pp. 159-165 ◽  
Author(s):  
Tomasz G. Markiewicz
Keyword(s):  
Energy Efficient ◽  
Average Energy ◽  
Higher Dimensions ◽  
Two Dimensional ◽  
Sphere Packings ◽  
Dimensional Simplex ◽  
Signal Constellation ◽  
Multidimensional Signal ◽  
Qam Modulation ◽  
The Impact

Abstract Packing constellations points in higher dimensions, the concept of multidimensional modulation exploits the idea drawn from geometry for searching dense sphere packings in a given dimension, utilising it to minimise the average energy of the underlying constellations. The following work analyses the impact of spherical shaping of the constellations bound instead of the traditional, hyper-cubical bound. Balanced constellation schemes are obtained with the N-dimensional simplex merging algorithm. The performance of constellations of dimensions 2, 4 and 6 is compared to the performance of QAM modulations of equivalent throughputs in the sense of bits transmitted per complex (two-dimensional) symbols. The considered constellations give an approximately 0:7 dB to 1 dB gain in terms of BER over a standard QAM modulation.

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