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Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a class of ' cellular networks'…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
Reduction of a two-component FitzHugh-Nagumo model to a single-component model with long-range connection is considered on general networks. The reduced model describes a single chemical species reacting on the nodes and diffusing across…
We discuss recent developments in the modeling of negative autoregulated genetic networks. In particular, we consider the temporal evolution of the population of mRNA and proteins in simple networks using rate equations. In the limit of low…
Naturally occuring or man-made systems displaying periodic spatial modulations of their properties on a nanoscale constitute superlattices. Such modulated structures are important both as prototypes of simple nanotechnological devices and…
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…
Cellular automata generate spatially extended, temporally persistent emergent structures from local update rules. No general method derives the mechanisms of that generation from the rule itself; existing tools reconstruct structure from…
Evolution produces complex and structured networks of interacting components in chemical, biological, and social systems. We describe a simple mathematical model for the evolution of an idealized chemical system to study how a network of…
This work proposes a very simple random matrix model, the Flip Matrix Model, liable to approximate the behavior of a two dimensional electron in a weak random potential. Its construction is based on a phase space analysis, a suitable…
The coupled (chaotic) map lattices (CMLs) characterizes the collective dynamics of a spatially distributed system consisting of locally or globally coupled maps. The current research on the dynamic behavior of CMLs is based on the framework…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern…
Multi-cell cooperation (MCC) is an approach for mitigating inter-cell interference in dense cellular networks. Existing studies on MCC performance typically rely on either over-simplified Wyner-type models or complex system-level…
This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…
The emergence of complex structures in the systems governed by a simple set of rules is among the most fascinating aspects of Nature. The particularly powerful and versatile model suitable for investigating this phenomenon is provided by…
We introduce various models for cellulose bio-degradation by micro-organisms. Those models rely on complex chemical mechanisms, involve the structure of the cellulose chains and are allowed to depend on the phenotypical traits of the…
We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
We investigate a system of two polarized molecules in a layered trap. The molecules reside in adjacent layers and interact purely via the dipole-dipole interaction. We determine the properties of the ground state of the system as a function…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…