Related papers: The Convergence of Bird Flocking
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
We present a simple model to study L\'{e}vy-flight foraging in a finite landscape with countable targets. In our approach, foraging is a step-based exploratory random search process with a power-law step-size distribution $P(l) \propto…
Wing articulation is critical for efficient flight of bird- and bat-sized animals. Inspired by the flight of $\textit{Cynopterus brachyotis}$, the lesser short-nosed fruit bat, we built a two-degree-of-freedom flapping wing platform with…
Diffusion models are relatively easy to train but require many steps to generate samples. Consistency models are far more difficult to train, but generate samples in a single step. In this paper we propose Multistep Consistency Models: A…
We consider discrete, iterative load balancing via matchings on arbitrary graphs. Initially each node holds a certain number of tokens, defining the load of the node, and the objective is to redistribute the tokens such that eventually each…
In swarms of flying insects, the motions of individuals are largely uncoordinated with those of their neighbors, unlike the highly ordered motion of bird flocks. However, it has been observed that insects may transiently form pairs with…
We study the stability of the ordered phase of flocking models with a scalar order parameter. Using both the active Ising model and a hydrodynamic description, we show that droplets of particles moving in the direction opposite to that of…
In the load balancing problem, each node in a network is assigned a load, and the goal is to equally distribute the loads among the nodes, by preforming local load exchanges. While load balancing was extensively studied in static networks,…
The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that…
Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the…
Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth…
In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of…
In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels $\phi(x):=|x|^{-(n+\alpha)}$ for $\alpha\in(0,2)$. The solutions describe unidirectional…
We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a…
Stability of flapping flight, a natural requirement for flying insects, is one of the major challenges for designing micro aerial vehicles (MAVs). To better understand how a flying insect could stabilize itself during hover, we have…
A simple model of the two dimensional collective motion of a group of mobile agents have been studied. Like birds, these agents travel in open free space where each of them interacts with the first $n$ neighbors determined by the…
There has been substantial work studying consensus problems for which there is a single common final state, although there are many real-world complex networks for which the complete consensus may be undesirable. More recently, the concept…
We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…