Related papers: On linear non-uniform cellular automata: duality a…
This investigation studies the ergodic properties of reversible linear cellular automata over $\mathbb{Z}_m$ for $m \in \mathbb{N}$. We show that a reversible linear cellular automaton is either a Bernoulli automorphism or non-ergodic. This…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be…
The computational capabilities of a neural network are widely assumed to be determined by its static architecture. Here we challenge this view by establishing that a fixed neural structure can operate in fundamentally different…
Based on the assumption that the target space duality ($T\to 1/T$) is preserved even nonperturbatively, the properties of static string vacua are studied. A discussion of the effective four-dimensional supergravity action based on…
Let us consider the simplest model of one-dimensional probabilistic cellular automata (PCA). The cells are indexed by the integers, the alphabet is {0, 1}, and all the cells evolve synchronously. The new content of a cell is randomly…
One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics,…
This paper studies reachability and null-controllability for difference inclusions involving convex processes. Such difference inclusions arise, for instance, in the study of linear discrete-time systems whose inputs and/or states are…
Neural Cellular Automata (NCAs) are bio-inspired dynamical systems in which identical cells iteratively apply a learned local update rule to self-organize into complex patterns, exhibiting regeneration, robustness, and spontaneous dynamics.…
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…
Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…
Simultaneous two-state lasing is a unique property of semiconductor quantum-dot (QD) lasers. This not only changes steady-state characteristics of the laser device but also its dynamic response to perturbations. In this paper we investigate…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
This paper studies the $\alpha$-stability property of differentially flat nonlinear dynamical systems. The results build off the recently introduced notion of $\alpha$-stability, which is particularly amenable to characterize the ability of…
Despite significant progress on stability analysis of conventional multiagent networked systems with weakly coupled state-network dynamics, most of the existing results have shortcomings in addressing multiagent systems with highly coupled…
In line with the stability theory of continuous dynamical systems, Lyapunov exponents of cellular automata (CAs) have been conceived two decades ago to quantify to what extent their dynamics changes following a perturbation of their initial…
Following ideas developed by Misha Gromov, we investigate surjunctivity and reversibility properties of cellular automata defined over certain concrete categories.
The quest for Continual Learning (CL) seeks to empower neural networks with the ability to learn and adapt incrementally. Central to this pursuit is addressing the stability-plasticity dilemma, which involves striking a balance between two…
In this paper we investigate the following questions. Let $\mu, \nu$ be two regular Borel measures of finite total variation. When do we have a constant $C$ satisfying $$\int f d\nu \le C \int f d\mu$$ whenever $f$ is a continuous…