DERIVATIONS AND AUTOMORPHISMS OF NILPOTENT EVOLUTION ALGEBRA WITH INDEX OF NILPOTENCY (n-3)

2020 ◽  
Vol 46 (1) ◽  
pp. 69-87
Author(s):  
Basma M. Al-Shutnawi
Keyword(s):  
Evolution Algebra

scholarly journals Derivations and automorphisms of nilpotent evolution algebras with maximal nilindex

2019 ◽  
Vol 18 (12) ◽  
pp. 1950233 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Otabek Khakimov ◽  
Bakhrom Omirov ◽  
Izzat Qaralleh
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Finite Dimensional ◽  
Evolution Algebra

This paper is devoted to the nilpotent finite-dimensional evolution algebras [Formula: see text] with [Formula: see text]. We describe the Lie algebra of derivations of these algebras. Moreover, in terms of these Lie algebras, we fully construct nilpotent evolution algebra with maximal index of nilpotency. Furthermore, this result allowed us fully characterize all local and 2-local derivations of the considered evolution algebras. Besides, all automorphisms and local automorphisms of these algebras are found.

CLASSIFICATION DYNAMICS OF TWO-DIMENSIONAL CHAINS OF EVOLUTION ALGEBRAS

2014 ◽  
Vol 25 (02) ◽  
pp. 1450012 ◽  
Author(s):  
SH. N. MURODOV
Keyword(s):  
Dynamical System ◽  
The State ◽  
Two Dimensional ◽  
Evolution Algebra

Recently by Casas et al. a notion of chain of evolution algebras (CEAs) is introduced. This chain is a dynamical system the state of which at each given time is an evolution algebra. It is known 25 distinct classes of chains of two-dimensional evolution algebras. In our previous paper we gave the classification of two-dimensional real evolution algebras. This classification contains seven (pairwise non-isomorphic) such algebras. For each known CEA we study its dynamics to be an element of a given class.

Hybrid QPSO-NNIA2 Algorithm for Multi-Objective Optimization Problem

2019 ◽  
Vol 33 (08) ◽  
pp. 1959025
Author(s):  
Lan Zhang
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problem ◽  
Nearest Neighbor ◽  
Superior Performance ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Evolution Algebra ◽  
Neighbor List

To improve the convergence and distribution of a multi-objective optimization algorithm, a hybrid multi-objective optimization algorithm, based on the quantum particle swarm optimization (QPSO) algorithm and adaptive ranks clone and neighbor list-based immune algorithm (NNIA2), is proposed. The contribution of this work is threefold. First, the vicinity distance was used instead of the crowding distance to update the archived optimal solutions in the QPSO algorithm. The archived optimal solutions are updated and maintained by using the dynamic vicinity distance based m-nearest neighbor list in the QPSO algorithm. Secondly, an adaptive dynamic threshold of unfitness function for constraint handling is introduced in the process. It is related to the evolution algebra and the feasible solution. Thirdly, a new metric called the distribution metric is proposed to depict the diversity and distribution of the Pareto optimal. In order to verify the validity and feasibility of the QPSO-NNIA2 algorithm, we compare it with the QPSO, NNIA2, NSGA-II, MOEA/D, and SPEA2 algorithms in solving unconstrained and constrained multi-objective problems. The simulation results show that the QPSO-NNIA2 algorithm achieves superior convergence and superior performance by three metrics compared to other algorithms.

Particle Swarm Optimization Based on Multiobjective Optimization

2012 ◽  
Vol 263-266 ◽  
pp. 2146-2149
Author(s):  
Zi Rui Ma
Keyword(s):  
Particle Swarm Optimization ◽  
Search Space ◽  
Multi Objective Optimization ◽  
Dynamic Adjustment ◽  
Swarm Optimization ◽  
Population Evolution ◽  
Flight Experience ◽  
Evolution Algebra ◽  
External Population

PSO will population each individual as the search space without a volume and quality of particle. These particles in the search space at a certain speed flight, the speed according to its own flight experience and the entire population of flight experience dynamic adjustment. We describe the standard PSO, multi-objective optimization and MOPSO. The main focus of this thesis is several PSO algorithms which are introduced in detail and studied. MOPSO algorithm introduced adaptive grid mechanism of the external population, not only to groups of particle on variation, but also to the value scope of the particles and variation, and the variation scale and population evolution algebra in proportion.

scholarly journals F-evolution algebra

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2637-2652 ◽  
Author(s):  
Uygun Jamilov ◽  
Manuel Ladra
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Necessary Conditions ◽  
Zero Point ◽  
Limit Set ◽  
Volterra Type ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Evolution Algebra ◽  
Upper Estimate

We consider the evolution algebra of a free population generated by an F-quadratic stochastic operator. We prove that this algebra is commutative, not associative and necessarily power-associative. We show that this algebra is not conservative, not stationary, not genetic and not train algebra, but it is a Banach algebra. The set of all derivations of the F-evolution algebra is described. We give necessary conditions for a state of the population to be a fixed point or a zero point of the F-quadratic stochastic operator which corresponds to the F-evolution algebra. We also establish upper estimate of the ?-limit set of the trajectory of the operator. For an F-evolution algebra of Volterra type we describe the full set of idempotent elements and the full set of absolute nilpotent elements.

scholarly journals The connection between evolution algebras, random walks and graphs

2019 ◽  
Vol 19 (02) ◽  
pp. 2050023 ◽  
Author(s):  
Paula Cadavid ◽  
Mary Luz Rodiño Montoya ◽  
Pablo M. Rodriguez
Keyword(s):  
Probability Theory ◽  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Discrete Time ◽  
Associative Algebras ◽  
Biological Phenomena ◽  
Evolution Algebra ◽  
New Type ◽  
Markov Evolution

Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov chains. The winning of this relation is that many results coming from Probability Theory may be stated in the context of Abstract Algebra. In this paper, we explore the connection between evolution algebras, random walks and graphs. More precisely, we study the relationships between the evolution algebra induced by a random walk on a graph and the evolution algebra determined by the same graph. Given that any Markov chain may be seen as a random walk on a graph, we believe that our results may add a new landscape in the study of Markov evolution algebras.

scholarly journals The Jacobson radical of an evolution algebra

2018 ◽  
Vol 9 (2) ◽  
pp. 601-634 ◽  
Author(s):  
M. Victoria Velasco
Keyword(s):  
Jacobson Radical ◽  
Evolution Algebra

scholarly journals Chains of three-dimensional evolution algebras: A description

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3175-3190
Author(s):  
Anvar Imomkulov ◽  
Victoria Velasco
Keyword(s):  
Three Dimensional ◽  
Time Dependent ◽  
Kolmogorov Equation ◽  
Natural Basis ◽  
3 Dimensional ◽  
Evolution Algebra ◽  
Fixed Rank ◽  
Weighted Digraph

In this paper we describe locally all the chains of three-dimensional evolution algebras (3-dimensional CEAs). These are families of evolution algebras with the property that their structure matrices with respect to a certain natural basis satisfy the Chapman-Kolmogorov equation. We do it by describing all 3-dimensional CEAs whose structure matrices have a fixed rank equal to 3, 2 and 1, respectively. We show that arbitrary CEAs are locally CEAs of fixed rank. Since every evolution algebra can be regarded as a weighted digraph, this allows us to understand and visualize time-dependent weighted digraphs with 3 nodes.

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