Related papers: Order Structures around Evolution Algebras
To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…
The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two…
We develop a combinatorial and order-theoretic framework for shuffles, understood as ordered concatenations of indexed families of sequences that induce total orders on the natural numbers. Motivated by the classical \v{S}arkovski\u{i}…
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…
Several general properties, concerning reduction algebras - rings of definition and algorithmic efficiency of the set of ordering relations - are discussed. For the reduction algebras, related to the diagonal embedding of the Lie algebra…
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…
The growth of science and technology is a recombinative process, wherein new discoveries and inventions are built from prior knowledge. Yet relatively little is known about the manner in which scientific and technological knowledge develop…
We study the class of idempotent-generated pseudo-composition algebras, which is a subclass of the family of axial algebras. More specifically, we utilise the group-algebra correspondence, natural to the axial framework in order to study…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
Some general criteria to produce explicit free algebras inside the division ring of fractions of skew polynomial rings are presented. These criteria are applied to some special cases of division rings with natural involutions, yielding, for…
We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the finite-dimensional representations. We also…
Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible…
We study sunflowers within the context of finitely generated substructures of ultrahomogeneous structures. In particular, we look at bounds on how large a set system is needed to guarantee the existence of sunflowers of a given size. We…
Order-sorted algebras and many sorted algebras exist in a long history with many different implementations and applications. A lot of language specifications have been defined in order-sorted algebra frameworks such as the language…
The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consider the related problems of computing all minimal overorders…
We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…