Related papers: Self-Organized States in Cellular Automata: Exact …
We define the notion of stochastic stability, already present in the literature in the context of smooth dynamical systems, for invariant measures of cellular automata perturbed by a random noise, and the notion of strongly stochastically…
We study a Life-like cellular automaton rule $B2/S2345$ where a cell in state `0' takes state `1' if it has exactly two neighbors in state `1' and the cell remains in the state `1' if it has between two and five neighbors in state `1.' This…
We address the problem of verifying timed properties of Markovian models of large populations of interacting agents, modelled as finite state automata. In particular, we focus on time-bounded properties of (random) individual agents…
We consider a model for which every site of $\mathbb{N}$ is assigned a fitness in $[0,1]$. At every discrete time all the sites are updated and each site samples a uniform on $[0,1]$, independently of everything else. At every discrete time…
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…
We consider exchangeable Markov multi-state survival processes -- temporal processes taking values over a state-space$\mathcal{S}$ with at least one absorbing failure state $\flat \in \mathcal{S}$ that satisfy natural invariance properties…
We consider the question of whether thermodynamic macrostates are objective consequences of dynamics, or subjective reflections of our ignorance of a physical system. We argue that they are both; more specifically, that the set of…
The one-parameter two-dimensional cellular automaton with the Margolus neighbourhood is analyzed based on the considering the projection of the stochastic movements of a single particle. Introducing the auxiliary random variable associated…
A simple one-dimensional cellular automaton model with threshold dynamics is introduced. The cumulative distribution of the size of the relaxations is analytically computed and behaves as a power law with an exponent equal to -1. This…
The behavior and architecture of large scale discrete state systems found in computer software and hardware can be specified and analyzed using a particular class of primitive recursive functions. This paper begins with an illustration of…
In this report proofs are presented for a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing…
We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to non-zero probability transitions in single…
A method is proposed to identify target states that optimize a metastability index amongst a set of trial states and use these target states as milestones (or core sets) to build Markov State Models (MSMs). If the optimized metastability…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely-dimensional system. While it is well known that this approximation works surprisingly well for some cellular automata,…
Large dynamical fluctuations - atypical realizations of the dynamics sustained over long periods of time - can play a fundamental role in determining the properties of collective behavior of both classical and quantum non-equilibrium…
We focus on a family of one-dimensional probabilistic cellular automata with memory two: the dynamics is such that the value of a given cell at time $t+1$ is drawn according to a distribution which is a function of the states of its two…
We study a cellular automaton model, which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each timestep. Unit amount of energy is randomly added…
Several stochastic processes modeling molecular motors on a linear track are given by random walks (not necessarily Markovian) on quasi 1d lattices and share a common regenerative structure. Analyzing this abstract common structure, we…
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…