相关论文: Algebraic computation of genetic patterns related …

We present a general formalism which allows us to derive the evolution equations describing one-dimensional (1D) and isotropic 2D interfacelike systems, that is based on symmetries, conservation laws, multiple scale arguments, and exploits…

Evolution of genetic code is studied as the change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states…

We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…

In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…

Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…

In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine…

Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and…

In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…

We showed that isomorphism classes of idempotent evolution algebras are in bijection with the orbits of the semidirect product group of the symmetric group and the torus, considered the combinatoric problem of enumeration of isomorphism…

Genetic Programming is an evolutionary algorithm that generates computer programs, or mathematical expressions, to solve complex problems. In this Guide, we demonstrate how to use Genetic Programming to develop surrogate models to mitigate…

Here we introduce researchers in algebraic biology to the exciting new field of cophylogenetics. Cophylogenetics is the study of concomitantly evolving organisms (or genes), such as host and parasite species. Thus the natural objects of…

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…

Cell type (e.g. pluripotent cell, fibroblast) is the end result of many complex processes that unfold due to evolutionary, developmental, and transformational stimuli. A cell's phenotype and the discrete, a priori states that define various…

In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type of algebra, the seed algebra, which describes exactly the behavior of a process within a…

Development combines three basic processes asymmetric --- cell division, signaling and gene regulation --- in a multitude of ways to create an overwhelming diversity of multicellular life-forms. Here, we attempt to chart this diversity…

We present an intriguing and precise interplay between algebraic geometry and the phenomenology of generations of particles. Using the electroweak sector of the MSSM as a testing ground, we compute the moduli space of vacua as an algebraic…

In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…

An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist…

Much of the genome is expressed in the vertebrate brain, with individual genes exhibiting different spatially-varying patterns of expression. These variations are not independent, with pairs of genes exhibiting complex patterns of…