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Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a…
Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks…
Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied,…
In this paper, we perform a theoretical analysis of the sequential convergence of elementary cellular automata that have at least one fixed point. Our aim is to establish which elementary rules always reach fixed points under sequential…
This paper studies the dynamics of a network of diffusively-coupled bistable systems. Under mild conditions and without requiring smoothness of the vector field, we analyze the network dynamics and show that the solutions converge globally…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
The determination and classification of fixed points of large Boolean networks is addressed in terms of constraint satisfaction problem. We develop a general simplification scheme that, removing all those variables and functions belonging…
Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we…
In this paper, we give some results concerning the dynamics of double Boolean automata circuits (dbac's for short), namely, networks associated to interaction graphs composed of two side-circuits that share a node. More precisely, we give…
This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, the evolution equation of each gene switches among a collection of candidate…
Random boolean cellular automata are investigated, where each gate has two randomly chosen inputs and is randomly assigned a boolean function of its inputs. The effect of non-uniform distributions on the choice of the boolean functions is…
Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted…
The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…
The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The…
Boolean networks are one of the most studied discrete models in the context of the study of gene expression. In order to define the dynamics associated to a Boolean network, there are several \emph{update schemes} that range from parallel…
The global dynamics of gene regulatory networks are known to show robustness to perturbations in the form of intrinsic and extrinsic noise, as well as mutations of individual genes. One molecular mechanism underlying this robustness has…
Among the fundamental questions in computer science is that of the impact of synchronism/asynchronism on computations, which has been addressed in various fields of the discipline: in programming, in networking, in concurrence theory, in…
A recent article by Weidner et al. [2021] presents a method to extract graph properties that are predictive of the dynamical behavior of multivariate, discrete models of biochemical regulation. In other words, a method that uses only…
Phase transitions constitute fundamental mechanisms underlying abrupt or qualitative changes in the collective dynamics of interacting units across a wide range of natural and engineered systems. In dynamical networks, such transitions lead…
Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean…