Search results for "Lévy flights"

Time characteristics of Lévy flights in a steep potential well

2013

Using the method previously developed for ordinary Brownian diffusion, we derive a new formula to calculate the correlation time of stationary Lévy flights in a steep potential well. For the symmetric quartic potential, we obtain the exact expression of the correlation time of steady-state Lévy flights with index α = 1. The correlation time of stationary Lévy flights decreases with an increasing noise intensity and steepness of potential well.

Langevin Approach to Levy Flights in Fixed Potentials: Exact Results for Stationary Probability Distributions

2008

The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density function of Levy flights in different smooth potential profiles. We find confinement of the particle in the superdiffusion motion with a bimodal stationary distribution for all the anharmonic symmetric monostable potentials investigated. The stationary probability density functions show power-law tails, which ensure finiteness of the variance. By reviewing recent results on these statistical characteristics, the peculiarities of Levy flights in compariso…

Does the movement pattern of non-visual eye movements during episodic vs semantic memory tasks correspond to Lévy Flights?: Poster

2021

Lévy flights and Lévy-Schrödinger semigroups

2010

We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.

Lévy Flights for Ant Colony Optimization in Continuous Domains

2009

In this paper, the authors propose the use of the Levy probability distribution as leading mechanism for solutions differentiation in an efficient and bio-inspired optimization algorithm, ant colony optimization in continuous domains, ACOR. In the classical ACOR, new solutions are constructed starting from one solution, selected from an archive, where Gaussian distribution is used for parameter diversification. In the proposed approach, the Levy probability distributions are properly introduced in the solution construction step, in order to couple the ACOR algorithm with the exploration properties of the Levy distribution.

Spatial Cognition 2020/1: Book of abstracts : August 2-4, 2021, University of Latvia

2021

Spatial Cognition is concerned with the acquisition, development, representation, organization, and use of knowledge about spatial objects in real, virtual or hybrid environments and processed by human or artificial agents. Spatial Cognition includes research from different fields insofar as they are concerned with cognitive agents and space, such as cognitive and developmental psychology, linguistics, computer science, geography, cartography, philosophy, neuroscience, and education. Research issues in the field range from the investigation of human spatial cognition to mobile robot navigation, including topics such as wayfinding, spatial planning, spatial learning, internal and external re…

Does the movement pattern of non-visual eye movements during episodic vs semantic memory tasks correspond to Lévy Flights?: Oral presentation

2021