Related papers: Dynamical Mean-Field Theory of Complex Systems on …
Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type (During, Coolen and Sherrington, 1998) is extended and analized here for a symmetrically diluted network with finite connectivity…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for…
Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners…
Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced…
Large-scale systems with inherent heterogeneity often exhibit complex dynamics that are crucial for their functional properties. However, understanding how such heterogeneity shapes these dynamics remains a significant challenge,…
Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for…
This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…
The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
We report about the main dynamical features of a model of leaky-integrate-and fire excitatory neurons with short term plasticity defined on random massive networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation of…
We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modeling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an…
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that…
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…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…