相关论文: Intermittent Cauchy walks enable optimal 3D search…

We study the polygons governing the convex hull of a point set created by the steps of $n$ independent two-dimensional random walkers. Each such walk consists of $T$ discrete time steps, where $x$ and $y$ increments are i.i.d. Gaussian. We…

Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space and a query point (image),…

Quantifying and comparing patterns of dynamical ecological systems require averaging over measurable quantities. For example, to infer variation in movement and behavior, metrics such as step length and velocity are averaged over large…

First hitting times (FHTs) describe the time it takes a random "searcher" to find a "target" and are used to study timescales in many applications. FHTs have been well-studied for diffusive search, especially for small targets, which is…

The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…

This paper focuses on Cauchy problem for the three-dimensional two-fluid type model, in which the presence of vacuum is permitted. Under some assumptions that the initial data satisfy appropriate regularity conditions and a compatibility…

Probability distributions of human displacements has been fit with exponentially truncated L\'evy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the…

A quantum walk on a lattice is a paradigm of a quantum search in a database. The database qubit strings are the lattice sites, qubit rotations are tunneling events, and the target site is tagged by an energy shift. For quantum walks on a…

In multi-agent search planning for a randomly moving and camouflaging target, we examine heterogeneous searchers that differ in terms of their endurance level, travel speed, and detection ability. This leads to a convex mixed-integer…

We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process…

A step reinforced random walk is a discrete time process with memory such that at each time step, with fixed probability $p \in (0,1)$, it repeats a previously performed step chosen uniformly at random while with complementary probability…

We propose a new model-free method to detect change points between distinct phases in a single random trajectory of an intermittent stochastic process. The local convex hull (LCH) is constructed for each trajectory point, while its…

We consider a previously devised model describing Levy random walks (Phys. Rev E 79, 011110; 80, 031148, (2009)). It is demonstrated numerically that the given model describes Levy random walks with superdiffusive, ballistic, as well as…

Scale invariant patterns have been found in different biological systems, in many cases resembling what physicists have found in other nonbiological systems. Here we describe the foraging patterns of free-ranging spider monkeys (Ateles…

We are studying the motion of a random walker in two and three dimensional continuum with uniformly distributed jump-length. This is different from conventional Lavy flight. In 2D and 3D continuum, a random walker can move in any direction,…

The Levy-type distributions are derived using the principle of maximum Tsallis nonextensive entropy both in the full and half spaces. The rates of convergence to the exact Levy stable distributions are determined by taking the N-fold…

The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so called mean first passage time (MFPT) problem. The…

Scale-invariant spatial or temporal patterns and L\'evy flight motion have been observed in a large variety of biological systems. It has been argued that animals in general might perform L\'evy flight motion with power law distribution of…

We present a new oblivious walking strategy for convex subdivisions. Our walk is faster than the straight walk and more generally applicable than the visibility walk. To prove termination of our walk we use a novel monotonically decreasing…

This paper studies optimal unmanned aerial vehicle (UAV) placement to ensure line-of-sight (LOS) communication and sensing for a cluster of ground users possibly in deep shadow, while the UAV maintains backhaul connectivity with a base…