Biomedical subjects

Tomer Kalisky

Publications and source records attributed to Tomer Kalisky.

5 recordsLinked to original sources

PubMed2006

Width of percolation transition in complex networks.

It is known that the critical probability for the percolation transition is not a sharp threshold. Actually it is a region of nonzero width Deltap(c) for systems of finite size. Here we present evidence that for complex networks Deltap(c) approximately p(c)/l, where l approximately Nnu(opt), where is the average length of the percolation cluster, and N is the number of nodes in the network. For Erdos-Rényi graphs nu(opt)=1/3, while for scale-free networks with a degree distribution P(k) approximately k(-lambda) and 3<lambda<4, nu(opt)=(lambda-3)/(lambda-1) . We show analytically and numerically that the survivability S(p,l), which is the probability of a cluster to survive l chemical shells at probability p, behaves near criticality as S(p,l)=S(p(c),l)exp[(p-p(c))l/p(c)]. Thus for probabilities inside the region |p-p(c)|<p(c)/l the behavior of the system is indistinguishable from that of the critical point.

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PubMed2006

Scale-free networks emerging from weighted random graphs.

We study Erdös-Rényi random graphs with random weights associated with each link. We generate a "supernode network" by merging all nodes connected by links having weights below the percolation threshold (percolation clusters) into a single node. We show that this network is scale-free, i.e., the degree distribution is P(k) approximately k(-lambda) with lambda=2.5. Our results imply that the minimum spanning tree in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with lambda=2.5. We suggest that optimization causes the percolation threshold to emerge spontaneously, thus creating naturally a scale-free supernode network. We discuss the possibility that this phenomenon is related to the evolution of several real world scale-free networks.

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PubMed2005

Scaling of optimal-path-lengths distribution in complex networks.

We study the distribution of optimal path lengths in random graphs with random weights associated with each link ("disorder"). With each link i we associate a weight tau(i) = exp (a r(i)), where r(i) is a random number taken from a uniform distribution between 0 and 1, and the parameter a controls the strength of the disorder. We suggest, in an analogy with the average length of the optimal path, that the distribution of optimal path lengths has a universal form that is controlled by the expression (1/p(c)) (l(infinity)/a), where l(infinity) is the optimal path length in strong disorder (a --> infinity) and p(c) is the percolation threshold. This relation is supported by numerical simulations for Erdos-Rényi and scale-free graphs. We explain this phenomenon by showing explicitly the transition between strong disorder and weak disorder at different length scales in a single network.

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PubMed2005

Volatility of linear and nonlinear time series.

Previous studies indicated that nonlinear properties of Gaussian distributed time series with long-range correlations, u(i), can be detected and quantified by studying the correlations in the magnitude series |u(i)|, the "volatility." However, the origin for this empirical observation still remains unclear and the exact relation between the correlations in u(i) and the correlations in |u(i)| is still unknown. Here we develop analytical relations between the scaling exponent of linear series u(i) and its magnitude series |u(i)|. Moreover, we find that nonlinear time series exhibit stronger (or the same) correlations in the magnitude time series compared with linear time series with the same two-point correlations. Based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series; the nonlinear multifractal time series is generated by multiplying a long-range correlated time series (that represents the magnitude series) with uncorrelated time series [that represents the sign series sgn (u(i))]. We apply our techniques on daily deep ocean temperature records from the equatorial Pacific, the region of the El-Ninõ phenomenon, and find: (i) long-range correlations from several days to several years with 1/f power spectrum, (ii) significant nonlinear behavior as expressed by long-range correlations of the volatility series, and (iii) broad multifractal spectrum.

Biophysics↗

PubMed2004

Effect of disorder strength on optimal paths in complex networks.

We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path l(opt) in a disordered Erdos-Rényi (ER) random network and scale-free (SF) network. Each link i is associated with a weight tau(i) identical withexp (a r(i) ) , where r(i) is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder. We find that for any finite a , there is a crossover network size N* (a) at which the transition occurs. For N< /=4 , and l(opt) approximately N (lambda-3) (/ (lambda-1) ) for SF networks with 3 >N* (a) the scaling behavior is in the weak disorder regime, with l(opt) approximately ln N for ER networks and SF networks with lambda>3 . In order to study the transition we propose a measure which indicates how close or far the disordered network is from the limit of strong disorder. We propose a scaling ansatz for this measure and demonstrate its validity. We proceed to derive the scaling relation between N* (a) and a . We find that N* (a) approximately a(3) for ER networks and for SF networks with lambda>/=4 , and N* (a) approximately a (lambda-1) (/ (lambda-3) ) for SF networks with 3<lambda<4 .

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