Related papers: On real chains of evolution algebras

Evolutionary algorithms (EAs) are general-purpose problem solvers that usually perform an unbiased search. This is reasonable and desirable in a black-box scenario. For combinatorial optimization problems, often more knowledge about the…

Evolutionary algorithms (EAs) are population-based metaheuristics, originally inspired by aspects of natural evolution. Modern varieties incorporate a broad mixture of search mechanisms, and tend to blend inspiration from nature with…

Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly…

While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based…

The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $\sigma(a,b,c)=(ab,ac,a)$. In this note, we get the explicit expressions of all squares, and then establish the tree structure of the positions of repeated squares…

Recently, by A. Elduque and A. Labra a new technique and a type of an evolution algebra are introduced. Several nilpotent evolution algebras defined in terms of bilinear forms and symmetric endomorphisms are constructed. The technique then…

Let $\beta$ be any permutation on $n$ symbols and let $c(k, \beta)$ be the number of permutations that $k$-commute with $\beta$. The cycle type of a permutation $\beta$ is a vector $(c_1, \dots, c_n)$ such that $\beta$ has exactly $c_i$…

We consider finite-dimensional complex Lie algebras admitting a periodic derivation, i.e., a nonsingular derivation which has finite multiplicative order. We show that such Lie algebras are at most two-step nilpotent and give several…

We classify the four dimensional perfect non-simple evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.

The main result of the paper is the classification of all (nonassociative) algebras of level two, i.e. such algebras that maximal chains of nontrivial degenerations starting at them have length two. During this classification we obtain an…

Differential evolution (DE) is a well-known type of evolutionary algorithms (EA). Similarly to other EA variants it can suffer from small populations and loose diversity too quickly. This paper presents a new approach to mitigate this…

We present easily verifiable sufficient conditions of time-independence and commutativity for local and nonlocal symmetries for a large class of homogeneous (1+1)-dimensional evolution systems. In contrast with the majority of known…

Given a reduced local algebra $T$ over a suitable ring or field $k$ we study the question of whether there are nontrivial algebra surjections $R\to T$ which induce isomorphisms $\Omega_{R/k}\otimes T \to \Omega_{T/k}$. Such maps, called…

We continue the investigation of Boolean-like algebras of dimension n (nBA) having n constants e1,...,en, and an (n+1)-ary operation q (a "generalised if-then-else") that induces a decomposition of the algebra into n factors through the…

We prove that the natural permutation representation of highly transitive finite groups cannot be realized as the full automorphism group of an idempotent, finite-dimensional evolution algebra acting on the set of lines spanned by its…

We introduce a novel evolutionary algorithm (EA) with a semantic network-based representation. For enabling this, we establish new formulations of EA variation operators, crossover and mutation, that we adapt to work on semantic networks.…

Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in…

The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebra (PHA) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product(STP) of matrices are…

Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type…

In this paper, we first study derivations in non nilpotent Lie triple algebras. We determine the structure of derivation algebra according to whether the algebra admits an idempotent or a pseudo-idempotent. We study the multiplicative…