Related papers: Fixed points of Boolean networks with sparse conne…
Single-point measurements of fluctuations in the scrape-off layer of magnetized plasmas are generally found to be dominated by large-amplitude bursts which are associated with radial motion of blob-like structures. A stochastic model for…
Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a…
We call $i$ a fixed point of a given sequence if the value of that sequence at the $i$-th position coincides with $i$. Here, we enumerate fixed points in the class of restricted growth sequences. The counting process is conducted by…
A Boolean network is a mapping $f :\{0,1\}^n \to \{0,1\}^n$, which can be used to model networks of $n$ interacting entities, each having a local Boolean state that evolves over time according to a deterministic function of the current…
We analyze the equilibrium fluctuations of the density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow…
Neural networks storing multiple discrete attractors are canonical models of biological memory. Previously, the dynamical stability of such networks could only be guaranteed under highly restrictive conditions. Here, we derive a theory of…
We examine analytically the existence and stability of phase-locked states in a weakly heterogeneous neuronal network. We consider a model of N neurons with all-to-all synaptic coupling where the heterogeneity is in the firing frequency or…
Combinatorial threshold-linear networks (CTLNs) are a special class of recurrent neural networks whose dynamics are tightly controlled by an underlying directed graph. Recurrent networks have long been used as models for associative memory…
We focus on the localized phase of pinning models with i.i.d. site disorder on which we assume only that the moment generating function is bounded in a neighborhood of the origin. We develop quantitative correlation functions estimates for…
Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study…
In stochastic evolutionary dynamics, the replacement of an existing genotype or cultural trait by a newly introduced mutant is typically characterized by the quantities of fixation probability and fixation time. But in a structured…
This contribution presents a review of our present theoretical as well as experimental knowledge of different fluctuation observables relevant to nuclear multifragmentation. The possible connection between the presence of a fluctuation peak…
We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical…
Non-linear equations describing the time evolution of frequencies and voltages in power grids exhibit fixed points of stable grid operation. The dynamical behaviour after perturbations around these fixed points can be used to characterise…
We analyze maximum entropy random graph ensembles with constrained degrees, drawn from arbitrary degree distributions, and a tuneable number of 3-loops (triangles). We find that such ensembles generally exhibit two transitions, a clustering…
We present here a study of the clustering and cycles in the graph of Internet at the Autonomous Systems level. We show that,even if the whole structure is changing with time, the statistical distributions of loops of order 3,4,5 remain…
We consider the existence of non-synchronized fixed points to the Kuramoto model defined on sparse networks: specifically, networks where each vertex has degree exactly three. We show that "most" such networks support multiple attracting…
We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal…
Thermodynamics of clusterized matter is studied in the framework of statistical models with non-interacting cluster degrees of freedom. At variance with the analytical Fisher model, exact Metropolis simulation results indicate that the…
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…