Related papers: The case for algebraic biology: from research to e…
In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and…
Advances in deep learning models have revolutionized the study of biomolecule systems and their mechanisms. Graph representation learning, in particular, is important for accurately capturing the geometric information of biomolecules at…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…
Proteins are complex biomolecules that play a central role in various biological processes, making them critical targets for breakthroughs in molecular biology, medical research, and drug discovery. Deciphering their intricate, hierarchical…
Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
We study multivariate polynomials over `structured' grids. We begin by proposing an interpretation as to what it means for a finite subset of a field to be structured; we do so by means of a numerical parameter, the nullity. We then extend…
Understanding the structure and dynamics of biological networks is one of the important challenges in system biology. In addition, increasing amount of experimental data in biological networks necessitate the use of efficient methods to…
We consider evolution algebras and their related substructures: evolution ideals and evolution subalgebras. After exposing some of the concepts related to them in the literature, we explore the order structures that arise in the sets of…
The theory of algebras with polynomial identities has developed significantly, with special attention devoted to the classification of varieties according to the asymptotic behavior of their codimension sequences. This sequence is a…
An affine variety induces the structure of an algebraic matroid on the set of coordinates of the ambient space. The matroid has two natural decorations: a circuit polynomial attached to each circuit, and the degree of the projection map to…
I dedicated the volume $1$ of monograph 'Introduction into Noncommutative Algebra' to studying of algebra over commutative ring. The main topics that I covered in this volume: definition of module and algebra over commutative ring; linear…
In this book i treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However, noncommutativity of a product creates a…
First we shortly review the different kinds of network modelling methods for systems biology with an emphasis on the different subtypes of logical models, which we review in more detail. Then we show the advantages of Boolean networks…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
Biological systems and processes are networks of complex nonlinear regulatory interactions between nucleic acids, proteins, and metabolites. A natural way in which to represent these interaction networks is through the use of a graph. In…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…