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We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis.…
Time-varying connections are crucial in understanding the structures and dynamics of complex networks. In this paper, we propose a continuous-time switching topology model for temporal networks that is driven by bursty behavior and study…
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…
Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…
Finite dynamical systems (e.g. Boolean networks and logical models) have been used in modeling biological systems to focus attention on the qualitative features of the system, such as the wiring diagram. Since the analysis of such systems…
Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally,…
The statistics of correlations are central quantities characterizing the collective dynamics of recurrent neural networks. We derive exact expressions for the statistics of correlations of nonlinear recurrent networks in the limit of a…
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…
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…
A logical function can be used to characterizing a property of a state of Boolean network (BN), which is considered as an aggregation of states. To illustrate the dynamics of a set of logical functions, which characterize our concerned…
Protein structure prediction and folding are fundamental to understanding biology, with recent deep learning advances reshaping the field. Diffusion-based generative models have revolutionized protein design, enabling the creation of novel…
Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is…
This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced…
Ever since the last two decades of the past century pioneering studies in the field of statistical physics had focused their efforts on developing models of neural networks that could display memory storage and retrieval. Though many…
Network representations can help reveal the behavior of complex systems. Useful information can be derived from the network properties and invariants, such as components, clusters or cliques, as well as from their changes over time. The…
We prove that the fully asynchronous dynamics of a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$ without negative loop can be simulated, in a very specific way, by a monotone Boolean network with $2n$ components. We then use this result to…
This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…
We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for studying the propagation of an initial…