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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…
All aspects of our society, including the life sciences, need a mechanism for people working within them to represent the concepts they employ to carry out their research. For the information systems being designed and developed to support…
Cell biomechanics involve a great number of complex phenomena that are fundamental to the evolution of life itself and other associated processes, ranging from the very early stages of embryo-genesis to the maintenance of damaged structures…
Cancers remain the lead cause of disease-related, pediatric death in North America. The emerging field of complex systems has redefined cancer networks as a computational system with intractable algorithmic complexity. Herein, a tumor and…
Across biological subdisciplines, the last decade has seen an explosion of high-dimensional datasets, including datasets for cells, species, immune systems, neurons and behaviour. At the ICTS workshop 'Unifying Theories in High-Dimensional…
The traditional methods of the biology, based on illustrative descriptions and linear logic explanations, are discussed. This work aims to improve this approach by introducing alternative tools to describe and represent complex biological…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term…
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics with…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. First, we introduce a new theoretical framework, reaction-diffusion system on `chemical species…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Cells coexist together in colonies or as tissues. Their behaviour is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network…
We propose a theoretical model for species that is focused on intrinsic organization and processes. Specifically, we regard species to be networks of organisms integrated by reproductive mechanisms (e.g., conjugation, meiosis, syngamy)…
AI systems are often used to make or contribute to important decisions in a growing range of applications, including criminal justice, hiring, and medicine. Since these decisions impact human lives, it is important that the AI systems act…
The aim of this review is to present and analyze the probabilistic models of mathematical phylogenetics which have been intensively used in recent years in biology as the cornerstone of attempts to infer and reconstruct the ancestral…
Biological phenotypes are products of complex evolutionary processes in which selective forces influence multiple biological trait measurements in unknown ways. Phylogenetic factor analysis disentangles these relationships across the…
Many open problems in biology, as in the physical sciences, display nonlinear and 'chaotic' dynamics, which, to the extent possible, cannot be reasonably understood. Moreover, mathematical models which aim to predict/estimate unknown…
We propose a two-scale model to resolve essential features of developmental tissue deformations. The model couples individual cellular behavior to the mechanics at tissue scale. This is realized by a multiphase-field model addressing the…
Many biological, physical, and social interactions have a particular dependence on where they take place. In living cells, protein movement between the nucleus and cytoplasm affects cellular response (i.e., proteins must be present in the…
Cells process external and internal signals through chemical interactions. Cells that constitute the immune system (e.g., antigen presenting cell, T-cell, B-cell, mast cell) can have different functions (e.g., adaptive memory, inflammatory…