Related papers: Infinite-dimensional genetic and evolution algebra…
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…
A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…
Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue…
Evolution algebras are non-associative algebras. In this work we provide an extension of this class of algebras, in the context of Hilbert spaces, capable to deal with infinite-dimensional spaces. We illustrate the applicability of our…
We survey the development and status quo of a subject best described as "generic representation theory of finite dimensional algebras", which started taking shape in the early 1980s. Let $\Lambda$ be a finite dimensional algebra over an…
After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
Gauge symmetries generally appear as a constraint algebra, under which one expects all physical states to be singlets. However, quantum anomalies and boundary conditions introduce central charges and change this picture, thus causing…
We consider statistical mechanics models of continuous spins in a disordered environment. These models have a natural interpretation as effective interface models. It is well known that without disorder there are no interface Gibbs measures…
We study from a physics viewpoint a class of generative neural nets, Gibbs machines, designed for gradual learning. While including variational auto-encoders, they offer a broader universal platform for incrementally adding newly learned…
The type and several invariant subspaces related to the upper annihilating series of finite-dimensional nilpotent evolution algebras are introduced. These invariants can be easily computed from any natural basis. Some families of nilpotent…
Evolution algebras were introduced into Genetics to deal with the mechanism of inheritance of asexual organisms. Their distribution into isotopism classes is uniquely related with the mutation of alleles in non-Mendelian Genetics. This…
A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…
Bayesian optimal design is a well-established approach to planning experiments. A distribution for the responses, i.e. a statistical model, is assumed which is dependent on unknown parameters. A utility function is then specified giving…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
In this paper, we introduce gonosomic algebras to algebraically translate the phenomenon of genetic sterility. Gonosomic algebras extend the concept of gonosomal algebras used as algebraic model of genetic phenomena related to…
With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities)…
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
We consider the intersection $\mathfrak{M}(A)$ of all maximal ideals of an evolution algebra $A$ and study the structure of the quotient $A/\M(A)$. In a previous work, maximal ideals have been related to hereditary subsets of a graph…