Search results for "Random walk"

A Hierarchical Learning Scheme for Solving the Stochastic Point Location Problem

2012

Published version of a chapter in the book: Advanced Research in Applied Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-31087-4_78 This paper deals with the Stochastic-Point Location (SPL) problem. It presents a solution which is novel in both philosophy and strategy to all the reported related learning algorithms. The SPL problem concerns the task of a Learning Mechanism attempting to locate a point on a line. The mechanism interacts with a random environment which essentially informs it, possibly erroneously, if the unknown parameter is on the left or the right of a given point which also is the current guess. The first pioneering work […

Modeling mass transfer in fracture flows with the time domain-random walk method

2019

The time domain-random walk method was developed further for simulating mass transfer in fracture flows together with matrix diffusion in surrounding porous media. Specifically, a time domain-random walk scheme was developed for numerically approximating solutions of the advection-diffusion equation when the diffusion coefficient exhibits significant spatial variation or even discontinuities. The proposed scheme relies on second-order accurate, central-difference approximations of the advective and diffusive fluxes. The scheme was verified by comparing simulated results against analytical solutions in flow configurations involving a rectangular channel connected on one side with a porous ma…

Gradient flows in random walk spaces

2021

El món digital ha comportat l'aparició de molts tipus de dades, de mida i complexitat creixents. De fet, els dispositius moderns ens permeten obtenir fàcilment imatges de major resolució, així com recopilar dades sobre cerques a la xarxa, anàlisis sanitàries, xarxes socials, sistemes d'informació geogràfica, etc. En conseqüència, l'estudi i el tractament d'aquests grans conjunts de dades té un gran interès i valor. En aquest sentit, els grafs ponderats proporcionen un espai de treball natural i flexible on representar les dades. En aquest context, un vèrtex representa una dada concreta i a cada aresta se li assigna un pes segons alguna mesura de semblança adequadament triada entre els vèrte…

Temporal Structure of Human Gaze Dynamics Is Invariant During Free Viewing.

2015

We investigate the dynamic structure of human gaze and present an experimental study of the frequency components of the change in gaze position over time during free viewing of computer-generated fractal images. We show that changes in gaze position are scale-invariant in time with statistical properties that are characteristic of a random walk process. We quantify and track changes in the temporal structure using a well-defined scaling parameter called the Hurst exponent, H. We find H is robust regardless of the spatial complexity generated by the fractal images. In addition, we find the Hurst exponent is invariant across all participants, including those with distinct changes to higher or…

2020

Abstract This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint subsets of the exterior. Both the cases of infinitely many measurements and a single measurement are addressed. The results are based on a reduction from the fractional conductivity equation to the fractional Schrodinger equation, and as such represent extensions of previous works. Moreover, a simple application is shown in which the fractional conductivity equation is put into relation with a long jump random walk with weights.

Rectilinear evolution in arvicoline rodents and numerical dating of Iberian Early Pleistocene sites

2014

Abstract Lozano-Fernandez et al. (2013a) have recently published a method intended for numerical dating of Early Pleistocene sites, which is based on the assumption of uniform, constant rate increase through time of mean lower molar tooth length of water voles ( Mimomys savini ) in a number of levels sampled in the stratigraphic sequence of Atapuerca TD site. They suggest that the regression equation obtained in this local section for site chronology on tooth size could be useful for estimating the numerical age of other localities from southwestern Europe. However, in our opinion this biostratigraphic approach has severe conceptual and methodological problems, which discourage its use as a…

Bayesian dynamic modeling of time series of dengue disease case counts

2017

The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model’s short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order …

Structural difficulty in grammatical evolution versus genetic programming

2013

Genetic programming (GP) has problems with structural difficulty as it is unable to search effectively for solutions requiring very full or very narrow trees. As a result of structural difficulty, GP has a bias towards narrow trees which means it searches effectively for solutions requiring narrow trees. This paper focuses on the structural difficulty of grammatical evolution (GE). In contrast to GP, GE works on variable-length binary strings and uses a grammar in Backus-Naur Form (BNF) to map linear genotypes to phenotype trees. The paper studies whether and how GE is affected by structural difficulty. For the analysis, we perform random walks through the search space and compare the struc…

On the Locality of Standard Search Operators in Grammatical Evolution

2014

Offspring should be similar to their parents and inherit their relevant properties. This general design principle of search operators in evolutionary algorithms is either known as locality or geometry of search operators, respectively. It takes a geometric perspective on search operators and suggests that the distance between an offspring and its parents should be less than or equal to the distance between both parents. This paper examines the locality of standard search operators used in grammatical evolution (GE) and genetic programming (GP) for binary tree problems. Both standard GE and GP search operators suffer from low locality since a substantial number of search steps result in an o…

Fractional master equations and fractal time random walks

1995

Fractional master equations containing fractional time derivatives of order 0\ensuremath{\le}1 are introduced on the basis of a recent classification of time generators in ergodic theory. It is shown that fractional master equations are contained as a special case within the traditional theory of continuous time random walks. The corresponding waiting time density \ensuremath{\psi}(t) is obtained exactly as \ensuremath{\psi}(t)=(${\mathit{t}}^{\mathrm{\ensuremath{\omega}}\mathrm{\ensuremath{-}}1}$/C)${\mathit{E}}_{\mathrm{\ensuremath{\omega}},\mathrm{\ensuremath{\omega}}}$(-${\mathit{t}}^{\mathrm{\ensuremath{\omega}}}$/C), where ${\mathit{E}}_{\mathrm{\ensuremath{\omega}},\mathrm{\ensuremat…