Related papers: Kinetic Equations for Processes on Co-evolving Net…
We study the dynamics of the processes in the small-world networks with a power-law degree distribution where every node is considered to be in one of the two available statuses. We present an algorithm for generation of such network and…
Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
The dynamics of fluctuations is considered for electrons near a positive ion or for charges in a confining trap. The stationary nonuniform equilibrium densities are discussed and contrasted. The linear response function for small…
Inertial lift forces are exploited within inertial microfluidic devices to position, segregate, and sort particles or droplets. However the forces and their focusing positions can currently only be predicted by numerical simulations, making…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…
A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean-field…
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…
This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a…
We generalize the equivalence between off-equilibrium state and gravitational perturbation of equilibrium state from dynamics of macroscopic quantities to that of microscopic particles. We also generalize the equivalence to incorporate…
Non-equilibrium steady states (NESS) of Markov processes give rise to non-trivial cyclic probability fluxes. Cycle decompositions of the steady state offer an effective description of such fluxes. Here, we present an iterative cycle…
In this paper we establish the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces. As applications, we study the nonlinear filtering problem for a…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…
We consider the averaging process on a graph, that is the evolution of a mass distribution undergoing repeated averages along the edges of the graph at the arrival times of independent Poisson processes. We establish cutoff phenomena for…
We propose a model for social dynamics on a network. In this model each actor holds a position on some issue, actors and their opinions being associated to vertices of the graph, and, additionally, the actors hold opinions of one another,…
Two different solutions of the linearized Vlasov equation for finite systems, characterized by fixed and moving-surface boundary conditions, are discussed in a unified perspective. A condition determining the eigenfrequencies of collective…
Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…
Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…