相关论文: Optimal Randomness in Swarm-Based Search

We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by L\'evy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary…

The L\'evy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, L\'evy walks with power…

We compute exactly the full distribution of the number $m$ of local minima in a one-dimensional landscape generated by a random walk or a L\'evy flight. We consider two different ensembles of landscapes, one with a fixed number of steps $N$…

We propose a swarm-based optimization algorithm inspired by air currents of a tornado. Two main air currents - spiral and updraft - are mimicked. Spiral motion is designed for exploration of new search areas and updraft movements is…

With the advent of Genome Sequencing, the field of Personalized Medicine has been revolutionized. From drug testing and studying diseases and mutations to clan genomics, studying the genome is required. However, genome sequence assembly is…

In this study, we present a novel hybrid algorithm, combining Levy Flight (LF) and Particle Swarm Optimization (PSO) (LF-PSO), tailored for efficient multi-robot exploration in unknown environments with limited communication and no global…

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…

In this work, we present a novel distributed method for constructing an occupancy grid map of an unknown environment using a swarm of robots with global localization capabilities and limited inter-robot communication. The robots explore the…

Target shape, not just size, plays a pivotal role in determining detectability during random search. We analyze intermittent L\'evy walks in three dimensions, and mathematically prove that the widely observed Cauchy strategy (L\'evy…

Consider a critical branching L\'{e}vy process $\{X_t, t\ge 0\}$ with branching rate $\beta>0, $ offspring distribution $\{p_k:k\geq 0\}$ and spatial motion $\{\xi_t, \Pi_x\}$. For any $t\ge 0$, let $N_t$ be the collection of particles…

Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for…

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…

We consider a one-dimensional search process under stochastic resetting conditions. A target is located at $b\geq0$ and a searcher, starting from the origin, performs a discrete-time random walk with independent jumps drawn from a…

The L\'evy flight foraging hypothesis states that organisms must have evolved adaptations to exploit L\'evy walk search strategies. Indeed, it is widely accepted that inverse square L\'evy walks optimize the search efficiency in foraging…

1. Understanding how to find targets with very limited information is a topic of interest in many disciplines. In ecology, such research has often focused on the development of two movement models: i) the L\'evy walk and; ii) the composite…

This research investigates the performance and efficiency of Unmanned Surface Vehicles (USVs) in multi-target tracking scenarios using the Adaptive Particle Swarm Optimization with k-Nearest Neighbors (APSO-kNN) algorithm. The study…

This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…

We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at $x_0\geq0$, where successive jumps are drawn independently…

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics…

The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and L\'evy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back…