Related papers: Levy walk with multiple internal states
L\'evy noise influences diverse non-equilibrium systems across scales, including quantum devices, active biological matter, and financial markets. While such noise is pervasive, its overall impact on activated transitions between metastable…
Two the most common tasks for autonomous mobile robots is to explore the environment and locate a target. %In the last case, the objective is either to find a target in the shortest time possible or, alternatively, to find %as many targets…
In this paper we derive explicit formulas for the densities of Levy walks. Our results cover both jump-first and wait-first scenarios. The obtained densities solve certain fractional differential equations involving fractional material…
We develop simple diffusion-advection models to estimate the average time it takes fish to reach one of the boundaries of an enclosure and the population distribution over time moving in the enclosure (such as a lake or slough). We start…
We discuss dual time evolution scenarios which, albeit running according to the same real time clock, in each considered case may be mapped among each other by means of an analytic continuation in time. This dynamical duality is a generic…
We discuss various features of the trajectories of spider monkeys looking for food in a tropical forest, as observed recently in an extensive {\it in situ} study. Some of the features observed can be interpreted as the result of social…
An important open problem in the theory of L\'evy flights concerns the analytically tractable formulation of absorbing boundary conditions. Although numerical studies using the correctly defined nonlocal approach have yielded substantial…
The idea of adaptive walks on fitness landscapes as a means of studying evolutionary processes on large time scales is extended to fitness landscapes that are slowly changing over time. The influence of ruggedness and of the amount of…
We study decentralized learning over networks where data are distributed across nodes without a central coordinator. Random walk learning is a token-based approach in which a single model is propagated across the network and updated at each…
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…
L\'evy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard…
We study the disruption process of hierarchical 3-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with 3-body numerical…
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…
One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles…
Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in…
We study a simple model of a forager as a walk that modifies a relaxing substrate. Within it simplicity, this provides an insight on a number of relevant and non-intuitive facts. Even without memory of the good places to feed and no…
Robot swarms, systems of many robots that operate in a distributed fashion, have many applications in areas such as search-and-rescue, natural disaster response, and self-assembly. Several of these applications can be abstracted to the…
We introduce a formalism of fractional diffusion on networks based on a fractional Laplacian matrix that can be constructed directly from the eigenvalues and eigenvectors of the Laplacian matrix. This fractional approach allows random walks…
Modeling how human moves in the space is useful for policy-making in transportation, public safety, and public health. Human movements can be viewed as a dynamic process that human transits between states (\eg, locations) over time. In the…
I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…