Related papers: Classification in chains of three-dimensional real…
Bedau has developed a general set of evolutionary statistics that quantify the adaptive component of evolutionary processes. On the basis of these measures, he has proposed a set of 4 classes of evolutionary system. All artificial life…
The growth of evolutionary computing (EC) methods in the exploration of complex potential energy landscapes of atomic and molecular clusters, as well as crystals over the last decade or so is reviewed. The trend of growth indicates that…
We introduce the abstract notion of a chain, which is a sequence of $n$ points in the plane, ordered by $x$-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general…
The history of gene families -- which are equivalent to event-labeled gene trees -- can to some extent be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes.…
Unordered feature sets are a nonstandard data structure that traditional neural networks are incapable of addressing in a principled manner. Providing a concatenation of features in an arbitrary order may lead to the learning of spurious…
This paper gives two methods for constructing associative 3-folds in R^7, based around the fundamental idea of evolution equations, and uses these methods to construct examples of these geometric objects. The paper is a generalisation of…
We study classifiers operating under severe classification time constraints, corresponding to 1-1000 CPU microseconds, using Convolutional Tables Ensemble (CTE), an inherently fast architecture for object category recognition. The…
A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of separable simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have…
An important aspect in the theory of algebras with polynomial identities is the study of the asymptotic behavior of the codimension sequence $c_n(A),\, n\geq 1,$ which measures the growth of polynomial identities of a given algebra $A$. In…
Evolutionary algorithms (EAs) are universal solvers inspired by principles of natural evolution. In many applications, EAs produce astonishingly good solutions. As they are able to deal with complex optimisation problems, they show great…
Evolution Strategies (ES) are stochastic derivative-free optimization algorithms whose most prominent representative, the CMA-ES algorithm, is widely used to solve difficult numerical optimization problems. We provide the first rigorous…
The rates-across-sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is the product of a character-specific scale factor and a…
In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the…
We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…
An algebra is called skew-symmetric if its multiplication operation is a skew-symmetric bilinear application. We determine all these algebras in dimension $3$ over a field of characteristic different from $2$. As an application, we…
For any skew symmetric matrix over complex numbers, we introduce an EALA and it is called Skew Symmetric Extended Affine Lie Algebra (SSEALA). This way we get a large class of EALAs and most often they are non-isomorphic. In this paper we…
A subspace of an algebra with involution is called a Lie skew-ideal if it is closed under Lie products with skew-symmetric elements. Lie skew-ideals are classified in central simple algebras with involution (there are eight of them for…
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…
We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of…
We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative algebra, and we apply it to obtain the classification of the $3$-dimensional Poisson algebras. In addition, we study the…