Related papers: Emergence of L\'evy walks from second order stocha…

Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not…

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 analyze a class of linear partial differential equations that arise as deterministic descriptions of the scaling limits of L\'evy walks, in which transport is driven by a convex combination of fractional material derivatives and a source…

Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…

We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…

What is the fastest way of finding a randomly hidden target? This question of general relevance is of vital importance for foraging animals. Experimental observations reveal that the search behaviour of foragers is generally intermittent:…

Evolutionary Algorithms are naturally inspired approximation optimisation algorithms that usually interfere with science problems when common mathematical methods are unable to provide a good solution or finding the exact solution requires…

In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…

Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We…

Collective animal movement fascinates children and scientists alike. One of the most commonly given explanations for collective animal movement is improved foraging. Animals are hypothesized to gain from searching for food in groups. Here,…

We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…

We study the theoretical convergence properties of random-search methods when optimizing non-convex objective functions without having access to derivatives. We prove that standard random-search methods that do not rely on second-order…

We extend a recently introduced prototypical stochastic model describing uniformly the search and return of objects looking for new food sources around a given home. The model describes the kinematic motion of the object with constant speed…

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 $N$…

In quadruped gait learning, policy search methods that scale high dimensional continuous action spaces are commonly used. In most approaches, it is necessary to introduce prior knowledge on the gaits to limit the highly non-convex search…

Scaling mobility patterns have been widely observed for animals. In this paper, we propose a deterministic walk model to understand the scaling mobility patterns, where walkers take the least-action walks on a lattice landscape and prey.…

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…

Efficiency of an optimization process is largely determined by the search algorithm and its fundamental characteristics. In a given optimization, a single type of algorithm is used in most applications. In this paper, we will investigate…

Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce randomly distributed resources, but a less explored alternative is that this behaviour may result from the…

We study the efficiency of search processes based on Levy flights (LFs) with power-law distributed jump lengths in the presence of an external drift. While LFs turn out to be efficient search processes when relative to the starting point…