Biomedical subjects

Daniel ben-Avraham

Publications and source records attributed to Daniel ben-Avraham.

6 recordsLinked to original sources

PubMed2006

Kleinberg navigation in fractal small-world networks.

We study the Kleinberg problem of navigation in small-world networks when the underlying lattice is a fractal consisting of N>>1 nodes. Our extensive numerical simulations confirm the prediction that the most efficient navigation is attained when the length r of long-range links is taken from the distribution P(r) approximately r(-alpha), where alpha=d(f) is the fractal dimension of the underlying lattice. We find finite-size corrections to the exponent alpha, proportional to 1/(ln N)2.

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PubMed2005

Synchronous and asynchronous recursive random scale-free nets.

We investigate the differences between scale-free recursive nets constructed by a synchronous, deterministic updating rule (e.g., Apollonian nets), versus an asynchronous, random sequential updating rule (e.g., random Apollonian nets). We show that the dramatic discrepancies observed recently for the degree exponent in these two cases result from a biased choice of the units to be updated sequentially in the asynchronous version.

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PubMed2004

Designer nets from local strategies.

We propose a local strategy for constructing scale-free networks of arbitrary degree distributions, based on the redirection method of Krapivsky and Redner [Phys. Rev. E 63, 066123 (2001)]. Our method includes a set of external parameters that can be tuned at will to match detailed behavior at small degree k, in addition to the scale-free power-law tail signature at large k. Once achieved, the target distribution is maintained throughout the growth of the net. The method is local in that addition of a new node requires knowledge of only the immediate environs of the (randomly selected) node to which it is attached. (Global strategies require information on finite fractions of the growing net.)

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PubMed2003

Self-similarity in random collision processes.

Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long-time limit and the similarity functions have algebraic or stretched exponential tails. The characteristic exponents are roots of transcendental equations and vary continuously with the mixing parameters. In the presence of conservation laws, the velocity distributions become universal.

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PubMed2003

Large-scale simulations of diffusion-limited n-species annihilation.

We present results from computer simulations for diffusion-limited n-species annihilation, A(i)+A(j)-->0 (i,j=1,2, em leader,n;i not equal j), on the line, for lattices comprising of up to 2(28) sites, and where the process proceeds to completion (no further reactions possible), involving up to 10(15) time steps. These enormous simulations are made possible by the renormalized reaction-cell method. Our results suggest that the concentration decay exponent for n species is alpha(n)=(n-1)/2n instead of (2n-3)/(4n-4), as previously believed, and are in agreement with recent theoretical arguments of Deloubrière et al. We also propose an expression for Delta, the correction-to-scaling exponent for the concentration decay, defined by c(t) approximately t(-alpha)(A+Bt-Delta).

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PubMed2002

Asymptotic analysis of a random walk with a history-dependent step length.

We study an unbiased, discrete-time random walk on the nonnegative integers, with the origin absorbing, and a history-dependent step length. Letting y denote the maximum distance the walker has ever been from the origin, steps that do not change y have length v, while those that increase y (taking the walker to a site that has never been visited) have length n. The process serves as a simplified model of spreading in systems with an infinite number of absorbing configurations. Asymptotic analysis of the probability generating function shows that, for large t, the survival probability decays as S(t) approximately t(-delta), with delta=v/2n. Our expression for the decay exponent is in agreement with the results obtained via numerical iteration of the transition matrix.

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