Related papers: On the Convergence of Elementary Cellular Automata…
This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
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…
The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The…
An apparent violation of hyperscaling at the endpoint of the critical line in the Domany-Kinzel stochastic cellular automaton finds an elementary resolution upon noting that the order parameter is discontinuous at this point. We derive a…
We apply a recently proposed dynamically driven renormalization group scheme to probabilistic cellular automata having one absorbing state. We have found just one unstable fixed point with one relevant direction. In the limit of small…
This paper considers synchronous discrete-time dynamical systems on graphs based on the threshold model. It is well known that after a finite number of rounds these systems either reach a fixed point or enter a 2-cycle. The problem of…
In some situations, EM algorithm shows slow convergence problems. One possible reason is that standard procedures update the parameters simultaneously. In this paper we focus on finite mixture estimation. In this framework, we propose a…
We consider the problem of finding the density of 1's in a configuration obtained by $n$ iterations of a given cellular automaton (CA) rule, starting from disordered initial condition. While this problems is intractable in full generality…
We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing…
Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random…
Recent advances in deep learning optimization showed that, with some a-posteriori information on fully-trained models, it is possible to match the same performance by simply training a subset of their parameters. Such a discovery has a…
A novel sequential change detection problem is proposed, in which the goal is to not only detect but also accelerate the change. Specifically, it is assumed that the sequentially collected observations are responses to treatments selected…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…
Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the…
Boolean networks are discrete dynamical systems where each automaton has its own Boolean function for computing its state according to the configuration of the network. The updating mode then determines how the configuration of the network…