Related papers: A class of cellular automata equivalent to determi…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
For a class of particle systems in continuous space with local interactions, we show that the asymptotic diffusion matrix is an infinitely differentiable function of the density of particles. Our method allows us to identify relatively…
The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…
We introduce Neural Particle Automata (NPA), a Lagrangian generalization of Neural Cellular Automata (NCA) from static lattices to dynamic particle systems. Unlike classical Eulerian NCA where cells are pinned to pixels or voxels, NPA model…
Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
We present a novel particle management method using the Characteristic Mapping framework. In the context of explicit evolution of parametrized curves and surfaces, the surface distribution of marker points created from sampling the…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
In this exploratory paper we introduce the problem of cognitive agents that learn how to modify their environment according to local sensing to reach a global goal. We concentrate on discrete dynamics (cellular automata) on a…
Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…
Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition…
Given a matrix $A$ and vector $b$ with polynomial entries in $d$ real variables $\delta=(\delta_1,\ldots,\delta_d)$ we consider the following notion of feasibility: the pair $(A,b)$ is locally feasible if there exists an open neighborhood…
A cellular automata approach using a Directed Cyclic Graph is used to model interrelationships of fluctuating time, state and space. This model predicts phenomena including a constant and maximum speed at which any moving entity can travel,…
A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be…
A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into…
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
In this paper we consider cellular automata $(\mathfrak{G},\Phi)$ with algebraic local rules and such that $\mathfrak{G}$ is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular…
Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…
A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e.…
Methods developed in a previous paper are employed to define an exact correspondence between the states of a deterministic cellular automaton in 1+1 dimensions and those of a bosonic quantum field theory. The result may be used to argue…