Related papers: Optimal L\'{e}vy-flight foraging in a finite lands…
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
Persistent monitoring missions require an up-to-date knowledge of the changing state of the underlying environment. UAVs can be gainfully employed to continually visit a set of targets representing tasks (and locations) in the environment…
Collective patterns of motion emerge across biological taxa: insects swarm, fish school, and birds flock. In particular, large migratory birds form strikingly ordered V-shaped formations, which experiments and direct numerical simulations…
Theory purports that animal foraging choices evolve to maximize returns, such as net energy intake. Empirical research in both human and nonhuman animals reveals that individuals often attend to the foraging choices of their competitors…
Essential to each other, growth and exploration are jointly observed in populations, be it alive such as animals and cells or inanimate such as goods and money. But their ability to move, crucial to cope with uncertainty and optimize…
In the literature, scaling laws for wireless mobile networks have been characterized under various models of node mobility and several assumptions on how communication occurs between nodes. To improve the realism in the analysis of scaling…
In this paper, preys with stochastic evasion policies are considered. The stochasticity adds unpredictable changes to the prey's path for avoiding predator's attacks. The prey's cost function is composed of two terms balancing the…
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…
The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time…
These notes from a graduate class at the Unuversidad Autonoma de Madrid analyze a search behavior known as Area Resticted Search (ARS), widespread in the animal kingdom, and optimal when the resources that one is after are "patchy". In the…
We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general L\'evy…
Collective foragers, from animals to robotic swarms, must balance exploration and exploitation to locate sparse resources efficiently. While social learning is known to facilitate this balance, how the range of information sharing shapes…
We provide a probabilistic approach to modeling the movements of subjects through multiple stages, with "stays" or survival at each stage for a random length of time, and ending at a desired final stage. We use conditional Markov chains…
L\'evy walk process is one of the most effective models to describe superdiffusion, which underlies some important movement patterns and has been widely observed in the micro and macro dynamics. From the perspective of random walk theory,…
The {\alpha}-stable L\'evy process, commonly used to describe L\'evy flight, is characterized by discontinuous jumps and is widely used to model anomalous transport phenomena. In this study, we investigate the associated exit problem and…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
1. Predicting space use patterns of animals from their interactions with the environment is fundamental for understanding the effect of habitat changes on ecosystem functioning. Recent attempts to address this problem have sought to unify…
For both Levy flight and Levy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given…
This paper presents a swarm teaming perspective that enhances the scope of classic investigations on survivable networks. A target searching generic context is considered as test-bed, in which a swarm of ground agents and a swarm of UAVs…
The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some details,…