相关论文: A Counterexample to the L\'evy Flight Foraging Hyp…

We consider a forager diffusing via a fractional heat equation and we introduce several efficiency functionals whose optimality is discussed in relation to the L\'evy exponent of the evolution equation. Several biological scenarios, such as…

Optimal random foraging strategy has gained increasing concentrations. It is shown that L\'evy flight is more efficient compared with the Brownian motion when the targets are sparse. However, standard L\'evy flight generally cannot be…

We study the efficiency of random search processes based on L{\'e}vy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the bias of the searcher…

A combined dynamics consisting of Brownian motion and L\'evy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of…

In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…

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…

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…

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…

This book chapter introduces to the problem to which extent search strategies of foraging biological organisms can be identified by statistical data analysis and mathematical modeling. A famous paradigm in this field is the Levy Flight…

It is widely accepted that inverse square L\'evy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets when the search restarts in the vicinity of the…

Brownian motion is widely used as a paradigmatic model of diffusion in equilibrium media throughout the physical, chemical, and biological sciences. However, many real world systems, particularly biological ones, are intrinsically…

We investigated the relationships between search efficiency, movement strategy, and non-local communication in the biological context of animal foraging. We considered situations where the members of a population of foragers perform either…

In natural foraging, many organisms seem to perform two different types of motile search: directed search (taxis) and random search. The former is observed when the environment provides cues to guide motion towards a target. The latter…

Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of L\'evy walks, a specific range of optimal efficiencies was suggested under variation of search…

In this paper we propose and advocate the use of the so called L\'evy flights as a driving mechanism for a class of stochastic optimization computations. This proposal, for some reasons overlooked until now, is - in author's opinion - very…

We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with L\'evy search based on…

The L\'evy hypothesis states that inverse square L\'evy walks are optimal search strategies because they maximise the encounter rate with sparse, randomly distributed, replenishable targets. It has served as a theoretical basis to interpret…

The competition between two ecologically similar species that use the same resources and differ from each other only in the type of spatial motion they undergo is studied. The latter is assumed to be described either by Brownian motion or…

Recent analysis of empirical data [F. Radicchi, A. Baronchelli & L.A.N. Amaral. PloS ONE 7, e029910 (2012)] showed that humans adopt L\'evy flight strategies when exploring the bid space in on-line auctions. A game theoretical model proved…

L\'evy walks are random walk processes whose step-lengths follow a long-tailed power-law distribution. Due to their abundance as movement patterns of biological organisms, significant theoretical efforts have been devoted to identifying the…