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Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…
The standard engineering approach to modelling of complex systems is highly compositional. In order to be able to understand (or to control) the behavior of a complex dynamical systems, it is often desirable, if not necessary, to view this…
Multi-agent systems in biology, society, and engineering are capable of making decisions through the dynamic interaction of their elements. Nonlinearity of the interactions is key for the speed, robustness, and flexibility of multi-agent…
Copulas are mathematical tools for modeling joint probability distributions. Since copulas enable one to conveniently treat the marginal distribution of each variable and the interdependencies among variables separately, in the past 60…
Biological adhesion is a critical mechanical function of complex organisms operating at multiple scales. At the cellular scale, cell-cell adhesion is remarkably tunable to enable both cohesion and malleability during development,…
We present a 'calculator' for constructing a homogeneous approximation of nonlinear control systems, which is based on the algebraic approach developed by the authors in their previous papers. This approach mainly uses linear algebraic and…
In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to…
Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between…
Quantum integrable systems have very strong mathematical properties that allow an exact description of their energetic spectrum. From the Bethe equations, I formulate the Baxter "T-Q" relation, that is the starting point of two…
In this paper, we develop a variational method to track and make predictions about a real-world system from continuous imperfect observations about this system, using an agent-based model that describes the system dynamics. By combining the…
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…
This paper presents a proposal of a rather new type of effective interatomic interaction for molecular dynamics and similar applications. The model consists of atoms with prescribed geometric arrangement of active orbitals, represented by…
Molecular dynamics (MD) simulation is a powerful tool for studying biomolecular structural changes, molecular recognition, transmembrane transport, and functional mechanisms. However, its practical bottleneck lies not only in software…
The purpose of this paper is to present a new approach to ecological model calibration -- an agent-based software. This agent works on three stages: 1- It builds a matrix that synthesizes the inter-variable relationships; 2- It analyses the…
Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed,…
In this work we propose and investigate a family of models, which admits as particular cases some well known mathematical models of tumor-immune system interaction, with the additional assumption that the influx of immune system cells may…
Whole-cell modelling is constrained by the laws of nature in general and the laws of thermodynamics in particular. This paper shows how one prolific source of information, stoichiometric models of biomolecular systems, can be integrated…
Systems Biology has emerged in the last years as a new holistic approach based on the global understanding of cells instead of only being focused on their individual parts (genes or proteins), to better understand the complexity of human…
We describe a process calculus featuring high level constructs for component-oriented programming in a distributed setting. We propose an extension of the higher-order pi-calculus intended to capture several important mechanisms related to…
There is little research concerning comparisons and combination of System Dynamics Simulation (SDS) and Agent Based Simulation (ABS). ABS is a paradigm used in many levels of abstraction, including those levels covered by SDS. We believe…