Related papers: A Counterexample to the L\'evy Flight Foraging Hyp…

Bayesian model-based reinforcement learning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, finding the resulting Bayes-optimal…

Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…

Recent work from the reinforcement learning community has shown that Evolution Strategies are a fast and scalable alternative to other reinforcement learning methods. In this paper we show that Evolution Strategies are a special case of…

In this paper we resolve an open problem proposed by Lai, Poor, Xin, and Georgiadis (2011, IEEE Transactions on Information Theory). Consider a sequence of Brownian Motions with unknown drift equal to one or zero, which we may be observed…

Rayleigh-L\'evy flights are simplified cosmological tools which capture certain essential statistical properties of the cosmic density field, including hierarchical structures in higher-order correlations, making them a valuable reference…

We consider a long-range version of self-avoiding walk in dimension $d > 2(\alpha \wedge 2)$, where $d$ denotes dimension and $\alpha$ the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to…

In this article it is shown that the Brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete $n$-vertex ordered graph trees whose search-depth functions converge to the Brownian…

We consider a Levy flyer of order alpha that starts from a point x0 on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it…

In this paper, we address rare-event simulation for heavy-tailed L\'evy processes with infinite activities. The presence of infinite activities poses a critical challenge, making it impractical to simulate or store the precise sample path…

I describe a framework for adaptive scientific exploration based on iterating an Observation--Inference--Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data…

Backtracking search is a powerful algorithmic paradigm that can be used to solve many problems. It is in a certain sense the dual of variable elimination; but on many problems, e.g., SAT, it is vastly superior to variable elimination in…

We investigate exploration patterns of a microswimmer, modeled as an active Brownian particle, searching for a target region located in a well of an energy landscape and separated from the initial position of the particle by high barriers.…

Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…

We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the…

We study Markovian continuous-time random walk models for L\'evy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal to zero in…

We consider the time evolution of two-dimensional Levy flights in a finite area with periodic boundary conditions. From simulations we show that the fractal path dimension d_f and thus the degree of area coverage grows in time until it…

Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually…

We formulate the problem of confined L\'evy flight on a comb. The comb represents a sawtooth-like potential field $V(x)$, with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law…

This paper provides a multivariate extension of Bertoin's pathwise construction of a L\'evy process conditioned to stay positive/negative. Thus obtained processes conditioned to stay in half-spaces are closely related to the original…

Large-scale sparse multi-objective optimization problems (LSMOPs) are prevalent in real-world applications, where optimal solutions typically contain only a few nonzero variables, such as in adversarial attacks, critical node detection, and…