Related papers: Accelerating consensus of self-driven swarm via ad…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
A bottleneck can largely deteriorate the flow, such as a traffic light or an on-ramp at a road. To alleviate bottleneck situations, one of the important strategies is to control the input rate to suit the state of the road. In this study,…
Recently, an Enskog-type kinetic theory for Vicsek-type models for self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901 (2011)]. This theory is based on an exact equation for a Markov chain in phase space and is not…
In this paper, a distributed velocity-constrained consensus problem is studied for discrete-time multi-agent systems, where each agent's velocity is constrained to lie in a nonconvex set. A distributed constrained control algorithm is…
We develop a new statistical model to analyse time-varying ranking data. The model can be used with a large number of ranked items, accommodates exogenous time-varying covariates and partial rankings, and is estimated via the maximum…
We consider flocking of self-propelling agents in two dimensions, each of which communicates with its neighbors within a limited vision cone. Also, the communication occurs with some delay. The communication among the agents are modeled by…
Efficient collective response to external perturbations is one of the most striking abilities of a biological system. Signal propagation through the group is an important condition for the imple- mentation of such a response. Information…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
We introduce two models of consensus following a majority rule on time-evolving stochastic block models (SBM), in which the network evolution is Markovian or non-Markovian. Under the majority rule, in each round, each agent simultaneously…
The velocity relaxation of an impulsively forced spherical particle in a fluid confined by two parallel plane walls is studied using a direct numerical simulation approach. During the relaxation process, the momentum of the particle is…
In the classical herding literature, agents receive a private signal regarding a binary state of nature, and sequentially choose an action, after observing the actions of their predecessors. When the informativeness of private signals is…
Observations of the cosmic velocity field could become an important cosmological probe in the near future. To take advantage of future velocity-flow surveys we must however have the theoretical predictions under control. In many respects,…
We develop a convergence-rate analysis of momentum with cyclical step-sizes. We show that under some assumption on the spectral gap of Hessians in machine learning, cyclical step-sizes are provably faster than constant step-sizes. More…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
In this paper, we study the macroscopic limit of a new model of collective displacement. The model, called PTWA, is a combination of the Vicsek alignment model and the Persistent Turning Walker (PTW) model of motion by curvature control.…
We investigate the implementation of a new stochastic Kuramoto-Vicsek-type model for global optimization of nonconvex functions on the sphere. This model belongs to the class of Consensus-Based Optimization. In fact, particles move on the…
We show that memory, in the form of underdamped angular dynamics, is a crucial ingredient for the collective properties of self-propelled particles. Using Vicsek-style models with an Ornstein-Uhlenbeck process acting on angular velocity, we…
In this work, the orientation adapter, a species of active particles that adapt their direction of motion from the other active particles, is introduced. The orientation adapters exist besides the usual Vicsek-like particles; both are…
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…
Learning curves are a measure for how the performance of machine learning models improves given a certain volume of training data. Over a wide variety of applications and models it was observed that learning curves follow -- to a large…