Related papers: Accelerating consensus of self-driven swarm via ad…
In this paper we consider a free boundary problem which models the spreading of an invasive species whose spreading is enhanced by the changing climate. We assume that the climate is shifting with speed c and obtain a complete…
We propose a general statistical mechanics framework for the collective motion of animals. The framework considers the principle of maximum entropy, the interaction, boundary, and desire effects, as well as the time-delay effect. These…
Modern sampling-based motion planning algorithms typically take between hundreds of milliseconds to dozens of seconds to find collision-free motions for high degree-of-freedom problems. This paper presents performance improvements of more…
Collective dynamics of many interacting particles have been widely studied because of a wealth of their behavioral patterns quite different from the individual traits. A selective way of birds that reacts to their neighbors is one of the…
This study employs molecular dynamics simulations to investigate droplet dynamics when a stationary droplet on a solid surface is struck by another droplet of similar size from above. The focus is on the jumping behavior of the merged…
We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical…
We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the…
The paper treats an agent-based model with averaging dynamics to which we refer as the K-averaging model. Broadly speaking, our model can be added to the growing list of dynamics exhibiting self-organization such as the well-known…
The problem of consensus in the presence of adversarially behaving agents has been studied extensively in the literature. The proposed algorithms typically guarantee that the consensus value lies within the convex hull of initial normal…
In this paper, we give estimates for the speed of convergence towards a limiting stable law in the recently introduced setting of mod-$\phi$ convergence. Namely, we define a notion of zone of control, closely related to mod-$\phi$…
We consider collisional models for granular particles and analyze the conditions under which the restitution coefficient might be a constant. We show that these conditions are not consistent with known collision laws. From the…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
We exploit a suite of large \emph{N}-body simulations (up to N=$4096^3$) performed with \Abacus, of scale-free models with a range of spectral indices $n$, to better understand and quantify convergence of the matter power spectrum. Using…
We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…
Self-organization of a biologically motivated swarm into smaller subgroups of different velocities is found by solving a 1-dimensional adaptive-velocity swarm, in which the velocity of an agent is averaged over a finite local radius of…
We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…
In this work, the time-dependent solution for the Lotka-Volterra Predator-Prey model is derived with the help of the Lambert W function. This allows an exact analytical expression for the period of the associated limit-cycle oscillations…
The paper considers the consensus problem in large networks represented by time-varying directed graphs. A practical way of dealing with large-scale networks is to reduce their dimension by collapsing the states of nodes belonging to…
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…
Self-propelled particles with alignment, displaying ordered collective motions such as swarming, can be investigated by the well-known Vicsek model. However, challenges still remain regarding the nature of the associated phase transition.…