Related papers: First-order aggregation models with alignment

We consider a first-order aggregation model in both discrete and continuum formulations and show rigorously how it can be obtained as zero inertia limits of second-order models. In the continuum case the procedure consists in a macroscopic…

We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighbourhood. In the first-order model the location of each…

The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…

We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second order term by a nonlinear function of the global density, with…

First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…

We extend a well-studied ODE model for collective behaviour by considering anisotropic interactions among individuals. Anisotropy is modelled by limited sensorial perception of individuals, that depends on their current direction of motion.…

In this paper a comparison between first order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number $N$ of pedestrians. The novelty is the fact of considering massive agents, namely…

This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…

We study a system of self-propelled particles which interact with their neighbors via alignment and repulsion. The particle velocities result from self-propulsion and repulsion by close neighbors. The direction of self-propulsion is…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…

We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…

Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on the density, modelled via an interaction potential. We set up…

In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field…

The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…

Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…

We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…

We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and…