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Complex dynamical networks consisting of many components that interact and produce each other are difficult to understand, especially, when new components may appear. In this paper we outline a theory to deal with such systems. The theory…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
A mathematical model of Min oscillation in Escherichia coli is numerically studied. The oscillatory state and hysteretic transition are explained with simpler coupled differential equations. Next, we propose a simple model of cell growth…
Modeling non-stationary data is a challenging problem in the field of continual learning, and data distribution shifts may result in negative consequences on the performance of a machine learning model. Classic learning tools are often…
Replication time is among the most important components of a bacterial cell's reproductive fitness. Paradoxically, larger cells replicate in less time than smaller cells despite the fact that building a larger cell requires increased…
In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell…
A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
A cell is polarised when it has developed a main axis of organisation through the reorganisation of its cytosqueleton and its intracellular organelles. Polarisation can occur spontaneously or be triggered by external signals, like gradients…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
We introduce bio-inspired artificial neural networks consisting of neurons that are additionally characterized by spatial positions. To simulate properties of biological systems we add the costs penalizing long connections and the proximity…
Nonlinear coupling between inter- and intra-element dynamics appears as a collective behaviour of elements. The elements in this paper denote symptoms such as a bacterium having an internal network of genes and proteins, a reactive droplet,…
Metabolic networks consist of linked functional components, or modules. The mechanism underlying metabolic network modularity is of great interest not only to researchers of basic science but also to those in fields of engineering. Previous…
In a range of scientific coauthorship networks, transitions emerge in degree distributions, correlations between degrees and local clustering coefficients, etc. The existence of those transitions could be regarded as a result of the…
We cast the metabolism of interacting cells within a statistical mechanics framework considering both, the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of…
This article presents a physical biology approach to understanding organization and segregation of bacterial chromosomes. The author uses a "piston" analogy for bacterial chromosomes in a cell, which leads to a phase diagram for the…