Related papers: The case for algebraic biology: from research to e…
The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the…
Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the past decade, multilayer network science -- the branch of the field dealing with units interacting in multiple…
Machine learning is a modern approach to problem-solving and task automation. In particular, machine learning is concerned with the development and applications of algorithms that can recognize patterns in data and use them for predictive…
The clear understanding of the non-convex landscape of neural network is a complex incomplete problem. This paper studies the landscape of linear (residual) network, the simplified version of the nonlinear network. By treating the gradient…
Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The…
In this review, we give an introduction to the structural and functional properties of the biological networks. We focus on three major themes: topology of complex biological networks like the metabolic and protein-protein interaction…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
It is a fascinating subject to explore how well we can understand the processes of life on the basis of fundamental laws of physics. It is emphasised that viewing biological processes as manipulation of information extracts their essential…
Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant…
Can the cross product be generalized? Why are the trace and determinant so important in matrix theory? What do all the coefficients of the characteristic polynomial represent? This paper describes a technique for `doodling' equations from…
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
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…
Deep learning has become a powerful tool in computational biology, revolutionising the analysis and interpretation of biological data over time. In our article review, we delve into various aspects of deep learning in computational biology.…
Quantitative methods and mathematical modeling are playing an increasingly important role across disciplines. As a result, interdisciplinary mathematics courses are increasing in popularity. However, teaching such courses at an advanced…
Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with multiplicative structures, i.e., in…
We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…
The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic…