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An evolutionary tree is a cascade of bifurcations starting from a single common root, generating a growing set of daughter species as time goes by. Species here is a general denomination for biological species, spoken languages or any other…
We will study evolution algebras $A$ which are free modules of dimension $2$ over domains. Furthermore, we will assume that these algebras are perfect, that is $A^2=A$. We start by making some general considerations about algebras over…
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…
In our article "A tree of linearisable second-order evolution equations by generalised hodograph transformations" [J. Nonlin. Math. Phys. {\bf 8} (2001), 342-362] we presented a tree of linearisable (C-integrable) second-order evolution…
Given a finite-dimensional noncommutative semisimple algebra $A$ with involution, we show that $A$ always has an RBA-basis. We look for an RBA-basis that has integral or rational structure constants, and ask if the RBA admits a positive…
Any finite-dimensional commutative (associative) graded algebra with all nonzero homogeneous subspaces one-dimensional is defined by a symmetric coefficient matrix. This algebraic structure gives a basic kind of $A$-graded algebras…
We study polynomial identities of algebras with involution of nonassociative algebras over a field of characteristic zero. We prove that the growth of the sequence of $*$-codimensions of a finite-dimensional algebra is exponentially…
The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence…
The emergent dynamics in spacetime diagrams of cellular automata (CAs) is often organised by means of a number of behavioural classes. Whilst classification of elementary CAs is feasible and well-studied, non-elementary CAs are generally…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
We study extended associative semigroups (briefly, EAS), an algebraic structure used to define generalizations of the operad of associative algebras, and the subclass of commutative extended diassociative semigroups (briefly, CEDS), which…
Chain Event Graphs (CEGs) are a family of event-based graphical models that represent context-specific conditional independences typically exhibited by asymmetric state space problems. The class of continuous time dynamic CEGs (CT-DCEGs)…
Zero-curvature representations (ZCRs) are one of the main tools in the theory of integrable PDEs. In particular, Lax pairs for $(1+1)$-dimensional PDEs can be interpreted as ZCRs. In [arXiv:1303.3575], for any $(1+1)$-dimensional scalar…
The 4-dimensional Sklyanin algebras are a well-studied 2-parameter family of non-commutative graded algebras, often denoted A(E,tau), that depend on a quartic elliptic curve E in P^3 and a translation automorphism tau of E. They are graded…
Various variants of the well known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) have been proposed recently, which improve the empirical performance of the original algorithm by structural modifications. However, in practice it…
The construction of the C*-algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. These C*-algebras $C^*(E,C)$ are analyzed in…
An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of…
Generative AI (GenAI) has achieved remarkable success across a range of domains, but its capabilities remain constrained to statistical models of finite training sets and learning based on local gradient signals. This often results in…
We classify extensions of certain classifiable C*-algebras using the six term exact sequence in K-theory together with the positive cone of the K_0-groups of the distinguished ideal and quotient. We then apply our results to a class of…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…