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Janusz A Hołyst

Publications and source records attributed to Janusz A Hołyst.

10 recordsLinked to original sources
PubMed2006

Ising model on two connected Barabasi-Albert networks.

We investigate analytically the behavior of the Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alignment of spins in both networks. A difference between critical temperatures of both phases disappears in the limit of vanishing inter-network coupling for identical networks. The analytic predictions are confirmed by numerical simulations.

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PubMed2006

Fluctuation-dissipation relations in complex networks.

In this paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing the susceptibilities of different networks to changes in external fields. In the case of networks with a given degree sequence, we argue that the scale-free topologies of real-world networks may arise as a result of the self-organization of real systems into sparse structures with low susceptibility to random external disruptions. We also show that the ensembles of networks with a given degree sequence and networks characterized by two-point correlations are equivalent to random networks with hidden variables.

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PubMed2005

Statistical analysis of 22 public transport networks in Poland.

Public transport systems in 22 Polish cities have been analyzed. The sizes of these networks range from N = 152 to 2881. Depending on the assumed definition of network topology, the degree distribution can follow a power law or can be described by an exponential function. Distributions of path lengths in all considered networks are given by asymmetric, unimodal functions. Clustering, assortativity, and betweenness are studied. All considered networks exhibit small-world behavior and are hierarchically organized. A transition between dissortative small networks N approximately < or = 500 and assortative large networks N approximately > or = 500 is observed.

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PubMed2005

Universal scaling of distances in complex networks.

Universal scaling of distances between vertices of Erdos-Rényi random graphs, scale-free Barabási-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k(i) and k(j) equals to (l(ij)) = A - B log(k(i)k(j)). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree (k)nn calculated for the nearest neighbors and on network clustering coefficients.

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PubMed2004

Average path length in random networks.

Analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found. We apply the approach to classical random graphs of Erdös and Rényi (ER), evolving networks introduced by Barabási and Albert as well as random networks with asymptotic scale-free connectivity distributions characterized by an arbitrary scaling exponent alpha>2. Our result for 2 infinity there is a saturation effect for the average path length.

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PubMed2004

Supremacy distribution in evolving networks.

We study a supremacy distribution in evolving Barabasi-Albert networks. The supremacy s(i) of a node i is defined as the total number of all nodes that are not older than i and can be linked to it by a directed path (including the node i ). The nodes form a basin connected to the node i as its in-component. For a network with a characteristic parameter m=1,2,3,... , the supremacy of an individual node increases with the network age as t((1+m)/2) in an appropriate scaling region. It follows that there is a relation s(k) approximately k(m+1) between a node degree k and its supremacy s , and the supremacy distribution P(s) scales as s(-1-2/(1+m)) . Analytic calculations basing on a continuum theory of supremacy evolution and on a corresponding rate equation have been confirmed by numerical simulations.

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PubMed2003

Mean-field theory for clustering coefficients in Barabási-Albert networks.

We applied a mean-field approach to study clustering coefficients in Barabási-Albert (BA) networks. We found that the local clustering in BA networks depends on the node degree. Analytic results have been compared to extensive numerical simulations finding a very good agreement for nodes with low degrees. Clustering coefficient of a whole network calculated from our approach perfectly fits numerical data.

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PubMed2003

Linear stability analysis in a liquid layer with a surface velocity gradient.

A case of combined planar Couette-Poiseuille flow corresponding to vanishing horizontal flux has been generalized by the introduction of a model for the surface velocity gradient. A relation corresponding to the Orr-Sommerfeld equation has been derived for this model. The critical value of the surface velocity gradient has been obtained. At the critical point, the corresponding critical Reynolds number equals infinity. Using an approximated method we estimated the behavior of the critical Reynolds number for a slightly overcritical surface velocity gradient.

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PubMed2003

Noise-level estimation of time series using coarse-grained entropy.

We present a method of noise-level estimation that is valid even for high noise levels. The method makes use of the functional dependence of coarse-grained correlation entropy K2(epsilon ) on the threshold parameter epsilon. We show that the function K2(epsilon ) depends, in a characteristic way, on the noise standard deviation sigma. It follows that observing K2 (epsilon ) one can estimate the noise level sigma. Although the theory has been developed for the Gaussian noise added to the observed variable we have checked numerically that the method is also valid for the uniform noise distribution and for the case of Langevin equation corresponding to the dynamical noise. We have verified the validity of our method by applying it to estimate the noise level in several chaotic systems and in the Chua electronic circuit contaminated by noise.

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