相关论文: The Mesoscopic category, Automata and Tropical Geo…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
On the basis of the qualitative analysis and numerical simulation of cosmological models with classical and phantom scalar fields with self-action there have been revealed and refined such models' distinctive features and potential…
A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…
We propose the notion of association schemoids generalizing that of association schemes from small categorical points of view. In particular, a generalization of the Bose-Mesner algebra of an association scheme appears as a subalgebra in…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
We explain a hierarchy of Friedel sum rule like formulas that help us understand response of mesoscopic systems to applied electric and magnetic fields. The formulas can be derived fully quantum mechanically and then there is a mathematical…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
In this paper we study in complete generality the family of two-state, deterministic, monotone, local, homogeneous cellular automata in $\mathbb{Z}^d$ with random initial configurations. Formally, we are given a set…
Cellular automata provide models of parallel computation based on cells, whose connectivity is given by an action of a monoid on the cells. At each step in the computation, every cell is decorated with a state that evolves in discrete steps…
We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion,…
We study generalized automata (in the sense of Ad\'amek-Trnkov\'a) in Joyal's category of (set-valued) combinatorial species, and as an important preliminary step, we study coalgebras for its derivative endofunctor $\partial$ and for the…
Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off…
For a symplectic manifold satisfying some topological condition,we define a special class of modules over the deformation quantization algebra. For any two such modules we construct an infinity local system of morphisms. We construct such…
We show how the trajectories of $d$-dimensional cellular automata (CA) can be used to determine the ground states of $(d+1)$-dimensional classical spin models, and we characterise their quantum phase transition, when in the presence of a…
Mathematical models come in many forms across biological applications. In the case of complex, spatial dynamics and pattern formation, stochastic models also face two main challenges: pattern data is largely qualitative, and model…
Multisymplectic geometry - which originates from the well known de Donder-Weyl theory - is a natural framework for the study of classical field theories. Recently, two algebraic structures have been put forward to encode a given theory…
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…
We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method…
A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity…
We introduce a mesoscopic partition function for classical many-body systems based on a combined spatial and phase-space coarse-graining, replacing the canonical phase-space integral with a discrete sum over occupation numbers. The…