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Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…

Adaptive control in biological systems, such as intestinal immunity, remains poorly understood despite detailed knowledge of underlying regulatory networks. We propose an alternative framework based on stochastic martingale turnover, in…

In an attempt to explain the uniqueness of the coding mechanism of living cells as contrasted with multi-species structure of ecosystems we examine two models of individuals with some replicative properties. In the first model the system…

A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and…

In exponentially proliferating populations of microbes, the population typically doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of…

Cells with the same genome can exist in different phenotypes. and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming…

In many biological processes heterogeneity within cell populations is an important issue. In this work we consider populations where the behavior of every single cell can be described by a system of ordinary differential equations.…

Investigations of natural variation in cell mechanics within a cell population are essential to understand the stochastic nature of soft-network deformation. Striking commonalities have been found concerning the average values and…

Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms…

Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies specific inequalities…

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical…

We investigate the scaling properties of the Penna model, which has become a popular tool for the study of population dynamics and evolutionary problems in recent years. We find that the model generates a normalised age distribution for…

Cellular heterogeneity is an immanent property of biological systems that covers very different aspects of life ranging from genetic diversity to cell-to-cell variability driven by stochastic molecular interactions, and noise induced cell…

Biological cells are built up from many different constituents of varying size and stiffness which all contribute to the cell's mechanical properties. Despite this heterogeneity, in the analysis of experimental measurements such as atomic…

I present a simple numerical model based on iteratively updating subgroups of a population, individually modeled by nonnegative real numbers, by a constant decay factor; however, at each iteration, one group is selected to instead be…

Results from molecular dynamics simulations of simple, structured particles capable of self-assembling into polyhedral shells are described. The analysis focuses on the growth histories of individual shells in the presence of an explicit…

By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…

We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the…

We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…

Neurons in the brain are often finely tuned for specific task variables. Moreover, such disentangled representations are highly sought after in machine learning. Here we mathematically prove that simple biological constraints on neurons,…