相关论文: Stability in random Boolean cellular automata on t…
How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…
Self-stabilization is a strong property that guarantees that a network always resume correct behavior starting from an arbitrary initial state. Weaker guarantees have later been introduced to cope with impossibility results: probabilistic…
Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. Since gene expression is regulated by proteins such as…
In this paper we provide an analytical study of the theory of multi-valued and fuzzy cellular automata where the fuzziness appears as the result of the application of an underlying multi-valued or continuous logic as opposed to standard…
Probabilistic Cellular Automata are extended stochastic systems, widely used for modelling phenomena in many disciplines. The possibility of controlling their behaviour is therefore an important topic. We shall present here an approach to…
Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the r esult could actually make sense physically, as a valid quantum evolution; but…
Cell division and death can be regulated by the mechanical forces within a tissue. We study the consequences for the stability and roughness of a propagating interface, by analysing a model of mechanically-regulated tissue growth in the…
The cellular automata discrete dynamical system is considered as the two-stage process: the majority rule for the change in the automata state and the rule for the change in topological relations between automata. The influence of changing…
We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
A two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.
An analytical model based on variational principles for a thin-walled stiffened plate subjected to axial compression is presented. A system of nonlinear differential and integral equations is derived and solved using numerical continuation.…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
A one-dimensional two-state number-conserving cellular automaton (NCCA) is a cellular automaton whose states are 0 or 1 and where cells take states 0 and 1 and updated their states by the rule which keeps overall sum of states constant. It…
In this essay I aim to investigate and discuss the process through which bundles of things "self-organize" into other things. In particular, I engage in such investigation by trying to apply a framework of analysis of structural stability…
Subzero automata is a class of tree automata whose acceptance condition can express probabilistic constraints. Our main result is that the problem of determining if a subzero automaton accepts some regular tree is decidable.
We investigate number conserving cellular automata with up to five inputs and two states with the goal of comparing their dynamics with diffusion. For this purpose, we introduce the concept of decompression ratio describing expansion of…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
We characterize the stability, metastability, and the stationary regime of traffic dynamics in a single-cell uplink wireless system. The traffic is represented in terms of spatial birth-death processes, in which users arrive as a Poisson…