Gábor Vattay

Public-key encryption with chaos

We propose public-key encryption algorithms based on chaotic maps, which are generalization of well-known and commercially used algorithms: Rivest-Shamir-Adleman (RSA), ElGamal, and Rabin. For the case of generalized RSA algorithm we discuss in detail its software implementation and properties. We show that our algorithm is as secure as RSA algorithm.

Giant clusters in random ad hoc networks.

The present paper introduces ad hoc communication networks as examples of large scale real networks that can be prospected by statistical means. A description of giant cluster formation based on a single parameter of node neighbor numbers is given along with the discussion of some asymptotic aspects of giant cluster sizes.

The European Traffic Observatory Measurement Infrastructure (ETOMIC): a testbed for universal active and passive measurements

The European Traffic Observatory is a European Union VI Framework Program sponsored effort, within the Integrated Project EVERGROW, that aims at providing a paneuropean traffic measurement infrastructure with high-precision, GPS-synchronized monitoring nodes. This paper describes the system and node architectures, together with the management system. On the other hand, we also present the testing platform that is currently being used for testing ETOMIC nodes before actual deployment.

Traffic Dynamics in Scale-Free Networks

We study traffic dynamics in growing scale-free networks. Both the scale-free structure of the network and the adaptive nature of the dynamics which controls traffic in the network are considered in the model. The model is investigated with computer simulations and analytically for the case of a scale-free tree. For the scale-free tree, an exact formula and its power law approximation of the complementary cumulative distribution function of link load (edge betweenness) is presented. We examine whether the scaling properties of the network affect the performance of the transport mechanism and estimate the average number of competing transport mechanisms at bottlenecks. We find that bottlenecks tend to appear on the periphery of the network as the performance increases. Various bandwidth allocation strategies are compared. We show that the best performance is achieved when capacity is distributed proportionally to the expected load of links. We demonstrate that it is necessary to study both the topology and the dynamics of the transport mechanism to understand the whole system.

Scaling and intermittency in animal behaviour

Scale-invariant spatial and temporal patterns have been observed in a large variety of biological systems. It has been argued that animals in general might perform Levy flight motion with power law distribution of times between successive changes of the direction of motion. Here we study the temporal behaviour of nesting gilts. The time spent by a gilt in a given form of activity has a power law probability distribution without a finite average. Further analysis reveals intermittent occurrence of certain periodic behavioural sequences which are responsible for the scaling behaviour and indicates the existence of a critical state. This is in close analogy with temporal sequences of velocity found in turbulent flows, where random and regular sequences alternate and form an intermittent sequence. The source of this complex behaviour can come only from the neural system forced by hormonal stimulus due to nesting instincts. This is the first carefully examined case, where complex scaling behaviour of animals is related to the self-organization and possibly to some unstable critical state of the nervous system.

Random matrix analysis of localization properties of gene coexpression network.

We analyze gene coexpression network under the random matrix theory framework. The nearest-neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral rigidity test follows random matrix prediction for a certain range and deviates afterwards. Eigenvector analysis of the network using inverse participation ratio suggests that the statistics of bulk of the eigenvalues of network is consistent with those of the real symmetric random matrix, whereas few eigenvalues are localized. Based on these IPR calculations, we can divide eigenvalues in three sets: (a) The nondegenerate part that follows RMT. (b) The nondegenerate part, at both ends and at intermediate eigenvalues, which deviates from RMT and expected to contain information about important nodes in the network. (c) The degenerate part with zero eigenvalue, which fluctuates around RMT-predicted value. We identify nodes corresponding to the dominant modes of the corresponding eigenvectors and analyze their structural properties.

A detailed path-latency model for router geolocation

This study outlines two novel techniques which can be used in the area of IP geolocation. First we introduce a detailed path-latency model to be able to determine the overall propagation delays along the network paths more accurately. This knowledge then leads to more precise geographic distance estimation between network routers and measurement nodes. In addition to the application of the detailed path-latency model, we describe a method which utilizes high-precision one-way delay measurements to further increase the accuracy of router geolocation techniques. The precise one-way delay values are used as a “path-constraint” to limit the overall geographic distance between the measurement nodes. The approach introduced in this paper can be used to localize all the network routers along the network path between the measurement nodes and can be combined with other existing geolocation techniques. The introduced techniques are validated in a wide range of experiments performed in the ETOMIC measurement infrastructure.

The European traffic observatory measurement infrastructure (ETOMIC)

The European traffic observatory is a European Union VI framework program sponsored effort, within the integrated project EVERGROW, that aims at providing an panEuropean traffic measurement infrastructure with high-precision, GPS-synchronized monitoring nodes. This paper describes the system and node architectures, together with the management system.

Spectral transitions in networks

We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erds–Renyi (E–R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brody-distribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein–protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E–R graph.

APPLICATION OF THE DIFFRACTION TRACE FORMULA TO THE THREE-DISK SCATTERING SYSTEM

The diffraction trace formula derived previously and the spectral determinant are tested on the open three-disk scattering system. The system contains a generic and exponentially growing number of diffraction periodic orbits. In spite of this it is shown that even the scattering resonances with large imaginary part can be reproduced semiclassically. The nontrivial interplay of the diffraction periodic orbits with the usual geometrical orbits produces the fine structure of the complicated spectrum of scattering resonances, which are beyond the resolution of the conventional periodic orbit theory.