Related papers: Mean-Field Approximation of Dynamics on Networks
As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide neural networks in the mean field regime, and hence the…
In the study of dynamics on networks, moment closure is a commonly used method to obtain low-dimensional evolution equations amenable to analysis. The variables in the evolution equations are mean counts of subgraph states and are referred…
We study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into…
Researchers have developed several theoretical methods for predicting epidemic thresholds, including the mean-field like (MFL) method, the quenched mean-field (QMF) method, and the dynamical message passing (DMP) method. When these methods…
Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent…
Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models,…
We propose a novel approximate inference algorithm that approximates a target distribution by amortising the dynamics of a user-selected MCMC sampler. The idea is to initialise MCMC using samples from an approximation network, apply the…
We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes…
The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…
We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible)…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
We consider optimizing two-layer neural networks in the mean-field regime where the learning dynamics of network weights can be approximated by the evolution in the space of probability measures over the weight parameters associated with…
An abstract network approach is proposed for the description of the dynamics in reactive processes. The phase space of the variables (concentrations in reactive systems) is partitioned into a finite number of segments, which constitute the…
Originally arising in the context of interacting particle systems in statistical physics, dynamical systems and differential equations on networks/graphs have permeated into a broad number of mathematical areas as well as into many…
New ideas and technologies adopted by a small number of individuals occasionally spread globally through a complex web of social ties. Here, we present a simple and general approximation method, namely, a message-passing approach, that…
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…
Adaptive (or co-evolutionary) network dynamics, i.e., when changes of the network/graph topology are coupled with changes in the node/vertex dynamics, can give rise to rich and complex dynamical behavior. Even though adaptivity can improve…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
Mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional defined over the space of probability distributions. MFLD has gained attention due to its connection with noisy gradient descent for mean-field…