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George H. Weiss

Bio: George H. Weiss is an academic researcher from Center for Information Technology. The author has contributed to research in topics: Random walk & Photon. The author has an hindex of 22, co-authored 61 publications receiving 6490 citations. Previous affiliations of George H. Weiss include University of Maryland, College Park & Silver Spring Networks.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the mean first passage times and their dispersion in random walks from the origin to an arbitrary lattice point on a periodic space lattice with periodic boundary conditions have been derived by the method of Green's functions.
Abstract: Formulas are obtained for the mean first passage times (as well as their dispersion) in random walks from the origin to an arbitrary lattice point on a periodic space lattice with periodic boundary conditions. Generally this time is proportional to the number of lattice points.The number of distinct points visited after n steps on a k‐dimensional lattice (with k ≥ 3) when n is large is a1n + a2n½ + a3 + a4n−½ + …. The constants a1 − a4 have been obtained for walks on a simple cubic lattice when k = 3 and a1 and a2 are given for simple and face‐centered cubic lattices. Formulas have also been obtained for the number of points visited r times in n steps as well as the average number of times a given point has been visited.The probability F(c) that a walker on a one‐dimensional lattice returns to his starting point before being trapped on a lattice of trap concentration c is F(c) = 1 + [c/(1 − c)] log c.Most of the results in this paper have been derived by the method of Green's functions.

2,280 citations

Book
31 Mar 1994
TL;DR: In this article, the ubiquitous characteristic function asymptotic properties and the diffusion limit lattice walks boundaries and constraints multistate random walks selected applications are discussed and discussed in detail.
Abstract: Introductory comments the ubiquitous characteristic function asymptotic properties and the diffusion limit lattice walks boundaries and constraints multistate random walks selected applications.

916 citations

Journal ArticleDOI
TL;DR: It is shown that the depth dependence of the distribution of photon absorption events can be inferred from measured parameters of the surface emission profile, and illustrative experimental data are shown to be in accord with the theory.
Abstract: Various characteristics of photon diffusion in turbid biological media are examined. Applications include the interpretation of data acquired with laser Doppler blood-flow monitors and the design of protocols for therapeutic excitation of tissue chromophores. Incident radiation is assumed to be applied at an interface between a turbid tissue and a transparent medium, and the reemission of photons from that interface is analyzed. Making use of a discrete lattice model, we derive an expression for the joint probability Γ(n, ρ)d2ρ that a photon will be emitted in the infinitesimal area d2ρ centered at surface point ρ = (x, y), having made n collisions with the tissue. Mathematical expressions are obtained for the intensity distribution of diffuse surface emission, the probability of photon absorption in the interior as a function of depth, and the mean path length of detected photons as a function of the distance between the site of the incident radiation and the location of the detector. We show that the depth dependence of the distribution of photon absorption events can be inferred from measured parameters of the surface emission profile. Results of relevant computer simulations are presented, and illustrative experimental data are shown to be in accord with the theory.

335 citations

Journal ArticleDOI
TL;DR: The formalism of the continuous-time random walk is applied to data on the U.S. dollar-deutsche mark future exchange, finding good agreement between theory and the observed data.
Abstract: We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollar-deutsche mark future exchange, finding good agreement between theory and the observed data.

165 citations


Cited by
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TL;DR: It is found that in most cases the estimated ‘log probability of data’ does not provide a correct estimation of the number of clusters, K, and using an ad hoc statistic ΔK based on the rate of change in the log probability between successive K values, structure accurately detects the uppermost hierarchical level of structure for the scenarios the authors tested.
Abstract: The identification of genetically homogeneous groups of individuals is a long standing issue in population genetics. A recent Bayesian algorithm implemented in the software STRUCTURE allows the identification of such groups. However, the ability of this algorithm to detect the true number of clusters (K) in a sample of individuals when patterns of dispersal among populations are not homogeneous has not been tested. The goal of this study is to carry out such tests, using various dispersal scenarios from data generated with an individual-based model. We found that in most cases the estimated 'log probability of data' does not provide a correct estimation of the number of clusters, K. However, using an ad hoc statistic DeltaK based on the rate of change in the log probability of data between successive K values, we found that STRUCTURE accurately detects the uppermost hierarchical level of structure for the scenarios we tested. As might be expected, the results are sensitive to the type of genetic marker used (AFLP vs. microsatellite), the number of loci scored, the number of populations sampled, and the number of individuals typed in each sample.

18,572 citations

Journal ArticleDOI
TL;DR: If enough data are available, genetic distance between any pair of organisms can be measured in terms of D, and this measure is applicable to any kind of organism without regard to ploidy or mating scheme.
Abstract: A measure of genetic distance (D) based on the identity of genes between populations is formulated. It is defined as D = -logeI, where I is the normalized identity of genes between two populations. This genetic distance measures the accumulated allele differences per locus. If the rate of gene substitution per year is constant, it is linearly related to the divergence time between populations under sexual isolation. It is also linearly related to geographical distance or area in some migration models. Since D is a measure of the accumulated number of codon differences per locus, it can also be estimated from data on amino acid sequences in proteins even for a distantly related species. Thus, if enough data are available, genetic distance between any pair of organisms can be measured in terms of D. This measure is applicable to any kind of organism without regard to ploidy or mating scheme.

8,801 citations

Journal ArticleDOI
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.

7,412 citations

Journal ArticleDOI
01 Dec 1992-Ecology
TL;DR: The second volume in a series on terrestrial and marine comparisons focusing on the temporal complement of the earlier spatial analysis of patchiness and pattern was published by Levin et al..
Abstract: This book is the second of two volumes in a series on terrestrial and marine comparisons, focusing on the temporal complement of the earlier spatial analysis of patchiness and pattern (Levin et al. 1993). The issue of the relationships among pattern, scale, and patchiness has been framed forcefully in John Steele’s writings of two decades (e.g., Steele 1978). There is no pattern without an observational frame. In the words of Nietzsche, “There are no facts… only interpretations.”

5,833 citations

Book
01 Jan 1979
TL;DR: In this article, a brief description is given of the various manifestations of the universal fractional power law relaxation processes, which are contrasted with the classical or Debye law, and a novel very general approach based on the so-called energy criterion is introduced.
Abstract: A brief description is given of the various manifestations of the universal fractional power law relaxation processes, which are contrasted with the classical or Debye law. It is shown that the universal law is indeed found in a remarkable variety of physical and chemical situations, and this is deemed to merit a special attempt at finding a suitably general theoretical model. Several such models are briefly described, and a novel very general approach based on the so-called energy criterion is introduced. It is concluded that it is not yet possible to establish with certainty the validity of any of the models. >

4,012 citations