Showing papers by "Vito Latora published in 2002"

Is the Boston subway a small-world network ?

Abstract: The mathematical study of the small-world concept has fostered quite some interest, showing that small-world features can be identified for some abstract classes of networks. However, passing to real complex systems, as for instance transportation networks, shows a number of new problems that make current analysis impossible. In this paper we show how a more refined kind of analysis, relying on transportation efficiency, can in fact be used to overcome such problems, and to give precious insights on the general characteristics of real transportation networks, eventually providing a picture where the small-world comes back as underlying construction principle.

Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system

Abstract: We study the dynamics of a Hamiltonian system of N classical spins with infinite-range interaction. We present numerical results which confirm the existence of metaequilibrium quasi stationary states (QSS), characterized by non-Gaussian velocity distributions, anomalous diffusion, Levy walks and dynamical correlation in phase-space. We show that the thermodynamic limit (TL) and the infinite-time limit (ITL) do not commute. Moreover, if the TL is taken before the ITL the system does not relax to the Boltzmann–Gibbs equilibrium, but remains in this new equilibrium state where nonextensive thermodynamics seems to apply.

Lévy Scaling: The Diffusion Entropy Analysis Applied to DNA Sequences

Abstract: We address the problem of the statistical analysis of a time series generated by complex dynamics with the diffusion entropy analysis (DEA) [N. Scafetta, P. Hamilton, and P. Grigolini, Fractals 9, 193 (2001)]. This method is based on the evaluation of the Shannon entropy of the diffusion process generated by the time series imagined as a physical source of fluctuations, rather than on the measurement of the variance of this diffusion process, as done with the traditional methods. We compare the DEA to the traditional methods of scaling detection and prove that the DEA is the only method that always yields the correct scaling value, if the scaling condition applies. Furthermore, DEA detects the real scaling of a time series without requiring any form of detrending. We show that the joint use of DEA and variance method allows to assess whether a time series is characterized by Levy or Gauss statistics. We apply the DEA to the study of DNA sequences and prove that their large-time scales are characterized by Levy statistics, regardless of whether they are coding or noncoding sequences. We show that the DEA is a reliable technique and, at the same time, we use it to confirm the validity of the dynamic approach to the DNA sequences, proposed in earlier work.

The Hamiltonian Mean Field Model: From Dynamics to Statistical Mechanics and Back

Abstract: The thermodynamics and the dynamics of particle systems with infiniterange coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a paradigmatic example of this class of systems. The present study addresses both attractive and repulsive interactions, with a particular emphasis on the description of clustering phenomena from a thermodynamical as well as from a dynamical point of view. The observed clustering transition can be first or second order, in the usual thermodynamical sense. In the former case, ensemble inequivalence naturally arises close to the transition, i.e. canonical and microcanonical ensembles give different results. In particular, in the microcanonical ensemble negative specific heat regimes and temperature jumps are observed. Moreover, having access to dynamics one can study non-equilibrium processes. Among them, the most striking is the emergence of coherent structures in the repulsive model, whose formation and dynamics can be studied either by using the tools of statistical mechanics or as a manifestation of the solutions of an associated Vlasov equation. The chaotic character of the HMF model has been also analyzed in terms of its Lyapunov spectrum.

The Hamiltonian Mean Field Model: from Dynamics to Statistical Mechanics and back

Abstract: The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a paradigmatic example of this class of systems. The present study addresses both attractive and repulsive interactions, with a particular emphasis on the description of clustering phenomena from a thermodynamical as well as from a dynamical point of view. The observed clustering transition can be first or second order, in the usual thermodynamical sense. In the former case, ensemble inequivalence naturally arises close to the transition, i.e. canonical and microcanonical ensembles give different results. In particular, in the microcanonical ensemble negative specific heat regimes and temperature jumps are observed. Moreover, having access to dynamics one can study non-equilibrium processes. Among them, the most striking is the emergence of coherent structures in the repulsive model, whose formation and dynamics can be studied either by using the tools of statistical mechanics or as a manifestation of the solutions of an associated Vlasov equation. The chaotic character of the HMF model has been also analyzed in terms of its Lyapunov spectrum.

The Architecture of Complex Systems

Abstract: At the present time, the most commonly accepted definition of a complex system is that of a system containing many interdependent constituents which interact nonlinearly . Therefore, when we want to model a complex system, the first issue has to do with the connectivity properties of its network, the architecture of the wirings between the constituents. In fact, we have recently learned that the network structure can be as important as the nonlinear interactions between elements, and an accurate description of the coupling architecture and a characterization of the structural properties of the network can be of fundamental importance also to understand the dynamics of the system.

Time evolution of thermodynamic entropy for conservative and dissipative chaotic maps

Abstract: We consider several low-dimensional chaotic maps started in far-from-equilibrium initial conditions and we study the process of relaxation to equilibrium. In the case of conservative maps the Boltzmann–Gibbs entropy S ( t ) increases linearly in time with a slope equal to the Kolmogorov–Sinai entropy rate. The same result is obtained also for a simple case of dissipative system, the logistic map, when considered in the chaotic regime. A very interesting results is found at the chaos threshold. In this case, the usual Boltzmann–Gibbs is not appropriate and in order to have a linear increase, as for the chaotic case, we need to use the generalized q -dependent Tsallis entropy S q ( t ) with a particular value of a q different from 1 (when q =1 the generalized entropy reduces to the Boltzmann–Gibbs). The entropic index q appears to be characteristic of the dynamical system.

Nonextensivity: From Low-Dimensional Maps to Hamiltonian Systems

Abstract: We present a brief pedagogical guided tour of the most recent applications of non-extensive statistical mechanics to well defined nonlinear dynamical systems, ranging from one-dimensional dissipative maps to many-body Hamiltonian systems.

Dynamical quasi-stationary states in a system with long-range forces

Abstract: The Hamiltonian Mean Field (HMF) model describes a system of N fully coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the critical point. In particular, when the particles are prepared in a “water bag” initial state, the relaxation to equilibrium is very slow. In the transient time the system lives in a dynamical quasi-stationary state and exhibits anomalous (enhanced) diffusion and Levy walks. In this paper we study temperature and velocity distribution of the quasi-stationary state and we show that the lifetime of such a state increases with N . In particular when the N →∞ limit is taken before the t →∞ limit, the results obtained are different from the expected canonical predictions. This scenario seems to confirm a recent conjecture proposed by Tsallis [C. Tsallis, in: S.R.A. Salinas, C. Tsallis (Eds.), Nonextensive statistical mechanics and thermodynamics, Braz. J. Phys. 29 (1999) 1 cond-mat/9903356 and contribution to this conference.

Nonextensivity: from low-dimensional maps to Hamiltonian systems

Abstract: We present a brief pedagogical guided tour of the most recent applications of nextensive statistical mechanics to well defined nonlinear dynamical systems, ranging from one-dimensional dissipative maps to many-body Hamiltonian systems.

Negative specific heat in out-of-equilibrium nonextensive systems

Abstract: We discuss the occurrence of negative specific heat in a nonextensive system which has an equilibrium second-order phase transition.The specific heat is negative only in a transient regime before equilibration, in correspondence to long-lasting metastable states. For these states standard equilibrium Bolzmann-Gibbs thermodynamics does not apply and the system shows non-Gaussian velocity distributions, anomalous diffusion and correlation in phase space. Similar results have recently been found also in several other nonextensive systems, supporting the general validity of this scenario. These models seem also to support the conjecture that a nonexstensive statistical formalism, like the one proposed by Tsallis, should be applied in such cases. The theoretical scenario is not completely clear yet, but there are already many strong theoretical indications suggesting that, it can be wrong to consider the observation of an experimental negative specific heat as an unique and unambiguous signature of a standard equilibrium first-order phase transition.

Negative specific heat in out-of-equilibrium nonextensive systems

Abstract: We discuss the occurrence of negative specific heat in a nonextensive system which has an equilibrium second-order phase transition.The specific heat is negative only in a transient regime before equilibration, in correspondence to long-lasting metastable states. For these states standard equilibrium Bolzmann-Gibbs thermodynamics does not apply and the system shows non-Gaussian velocity distributions, anomalous diffusion and correlation in phase space. Similar results have recently been found also in several other nonextensive systems, supporting the general validity of this scenario. These models seem also to support the conjecture that a nonexstensive statistical formalism, like the one proposed by Tsallis, should be applied in such cases. The theoretical scenario is not completely clear yet, but there are already many strong theoretical indications suggesting that, it can be wrong to consider the observation of an experimental negative specific heat as an unique and unambiguous signature of a standard equilibrium first-order phase transition.

Efficiency of Scale-Free Networks: Error and Attack Tolerance

Abstract: The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e. networks with power law P(k), are considered: 1) scale-free networks with no local clustering produced by the Barabasi-Albert model and 2) scale-free networks with high clustering properties as in the model by Klemm and Eguiluz, and their properties are compared to the properties of random graphs (exponential graphs). By using as mathematical measures the global and the local efficiency we investigate the effects of errors and attacks both on the global and the local properties of the network. We show that the global efficiency is a better measure than the characteristic path length to describe the response of complex networks to external factors. We find that, at variance with random graphs, scale-free networks display, both on a global and on a local scale, a high degree of error tolerance and an extreme vulnerability to attacks. In fact, the global and the local efficiency are unaffected by the failure of some randomly chosen nodes, though they are extremely sensititive to the removal of the few nodes which play a crucial role in maintaining the network's connectivity.