Biomedical subjects

János Kertész

Publications and source records attributed to János Kertész.

9 recordsLinked to original sources

PubMed2006

Scaling theory of temporal correlations and size-dependent fluctuations in the traded value of stocks.

Records of the traded value of fi stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average : sigma(i) is proportional to alpha, with a strong time scale dependence alpha(Delta(t)). The nontrivial (i.e., neither 0.5 nor 1) value of alpha may have different origins and provides information about the microscopic dynamics. We present a set of stylized facts and then show their connection to such behavior. The functional form alpha(Delta(t)) originates from two aspects of the dynamics: Stocks of larger companies both tend to be traded in larger packages and also display stronger correlations of traded value. The results are integrated into a general framework that can be applied to a wide range of complex systems.

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PubMed2005

Intensity and coherence of motifs in weighted complex networks.

The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this approach. In this paper we generalize this method for weighted networks. We introduce subgraph "intensity" as the geometric mean of its link weights "coherence" as the ratio of the geometric to the corresponding arithmetic mean. Using these measures, motif scores and clustering coefficient can be generalized to weighted networks. To demonstrate these concepts, we apply them to financial and metabolic networks and find that inclusion of weights may considerably modify the conclusions obtained from the study of unweighted characteristics.

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PubMed2005

Random walks on complex networks with inhomogeneous impact.

In many complex systems, for the activity f(i) of the constituents or nodes i a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) proportional variant alpha: universal values alpha=1/2 or 1 were found, however, with exceptions. With the help of an impact variable we present a random walk model where the activity is the product of the number of visitors at a node and their impact. If the impact depends strongly on the node connectivity and the properties of the carrying network are broadly distributed (as in a scale-free network) we find both analytically and numerically nonuniversal alpha values. The exponent always crosses over to the universal value of 1 if the external drive dominates.

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PubMed2005

Force indeterminacy in the jammed state of hard disks.

Granular packings of hard disks are investigated by means of contact dynamics which is an appropriate technique to explore the allowed force realizations in the space of contact forces. Configurations are generated for given friction coefficients, and then an ensemble of equilibrium forces is found for fixed contacts. We study the force fluctuations within this ensemble. In the limit of zero friction, the fluctuations vanish in accordance with the isostaticity of the packing. The magnitude of the fluctuations has a nonmonotonous friction dependence. The increase for small friction can be attributed to the opening of the angle of the Coulomb cone, while the decrease as friction increases is due to the reduction of connectivity of the contact network, leading to local, independent clusters of indeterminacy. We discuss the relevance of indeterminacy to packings of deformable particles and to the mechanical response properties.

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PubMed2004

Phase diagram of optimal paths.

We show that by choosing appropriate distributions of the randomness the search for optimal paths links diverse problems of disordered media, such as directed percolation, invasion percolation, and directed and nondirected spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in O(N(1+df/d)) steps, where df is the fractal dimension of the path. Using extensive simulations in two dimensions, we identify the phase boundaries of the directed polymer universality class. A new strong-disorder phase occurs where the optimum paths are self-affine with parameter-dependent scaling exponents. Furthermore, the phase diagram contains directed and nondirected percolation as well as the directed random walk models at specific points and lines.

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PubMed2003

Structural transitions in scale-free networks.

Real growing networks such as the World Wide Web or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the (Barabási-Albert) preferential attachment network growth capture all these aspects. We present a scaling theory to describe the behavior of the generalized models and the mean-field rate equation for clustering. This is solved for a specific case with the result C(k) approximately 1/k for the clustering of a node of degree k. This mean-field exponent agrees with simulations, and reproduces the clustering of many real networks.

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PubMed2003

Shearing of loose granular materials: a statistical mesoscopic model.

A two-dimensional lattice model for the formation and evolution of shear bands in granular media is proposed. Each lattice site is assigned a random variable which reflects the local density. At every time step, the strain is localized along a single shear band which is a spanning path on the lattice chosen through an extremum condition. The dynamics consists of randomly changing the "density" of the sites only along the shear band, and then repeating the procedure of locating the extremal path and changing it. Starting from an initially uncorrelated density field, it is found that this dynamics leads to a slow compaction along with a nontrivial patterning of the system, with high-density regions forming which shelter long-lived low-density valleys. Further, as a result of these large density fluctuations, the shear band, which was initially equally likely to be found anywhere on the lattice, gets progressively trapped for longer and longer periods of time. This state is, however, metastable, and the system continues to evolve slowly in a manner reminiscent of glassy dynamics. Several quantities have been studied numerically which support this picture and elucidate the unusual system-size effects involved.

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PubMed2003

Slow relaxation due to optimization and restructuring: solution on a hierarchical lattice.

Motivated by the large strain shear of loose granular materials, we introduced a model that consists of consecutive optimization and restructuring steps leading to a self-organization of a density field. The extensive connections to other models of statistical physics are discussed. We investigate our model on a hierarchical lattice that allows an exact asymptotic renormalization treatment. A surprisingly close analogy is observed between the simulation results on the regular and the hierarchical lattices. The dynamics is characterized by the breakdown of ergodicity, by unusual system size effects in the development of the average density, as well as by the age distribution, the latter showing multifractal properties.

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PubMed2002

Shortest paths and load scaling in scale-free trees.

The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the m=1 case of the Barabási-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows one to demonstrate why the distribution approaches a Gaussian in the limit of N large. The load, the number of the shortest distance paths passing through any node, is discussed in the tree presentation.

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