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Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
We present and discuss the results of an experimental analysis in the design of Boolean networks by means of genetic algorithms. A population of networks is evolved with the aim of finding a network such that the attractor it reaches is of…
We study Boolean networks which are simple spatial models of the highly conserved Delta-Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in…
The understanding of Boolean automata networks dynamics takes an important place in various domains of computer science such as computability, complexity and discrete dynamical systems. In this paper, we make a step further in this…
Neural networks are dynamical systems that compute with their dynamics. One example is the Hopfield model, forming an associative memory which stores patterns as global attractors of the network dynamics. From studies of dynamical networks…
Boolean networks have been used successfully in modeling biological networks and provide a good framework for theoretical analysis. However, the analysis of large networks is not trivial. In order to simplify the analysis of such networks,…
First-Order Boolean Networks with Non-deterministic updates (FOBNN) compute a boolean transition graph representing the absence and presence of species over time. The utility of FOBNNs has been justified by their theoretical soundness with…
Direct cell reprogramming makes it feasible to reprogram abundant somatic cells into desired cells. It has great potential for regenerative medicine and tissue engineering. In this work, we study the control of biological networks, modelled…
In previous works, we introduced the notion of dominant vertices in the context of dynamical systems on networks. This is a set of nodes in the underlying network whose evolution determines the whole network's dynamics after a transient…
This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as…
In systems biology, attractor landscape analysis of gene regulatory networks is recognized as a powerful computational tool for studying various cellular states from proliferation and differentiation to senescence and apoptosis. Therefore,…
Gene regulatory network (GRN) modeling is a well-established theoretical framework for the study of cell-fate specification during developmental processes. Recently, dynamical models of GRNs have been taken as a basis for formalizing the…
Using analytic arguments, we show that dynamical attractor periods in large critical Boolean networks are power-law distributed. Our arguments are based on the method of relevant components, which focuses on the behavior of the nodes that…
In Bounded Model Checking both the system model and the checked property are translated into a Boolean formula to be analyzed by a SAT-solver. We introduce a new encoding technique which is particularly optimized for managing quantitative…
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…
We study the class of cooperative Boolean networks whose only regulatory functions are COPY, binary AND, and binary OR. We prove that for all sufficiently large N and c < 2 there exist Boolean networks in this class that have an attractor…
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…
In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior…