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Vito Latora

Publications and source records attributed to Vito Latora.

158 records · Page 9Linked to original sources
arXiv2003

Power-Law Time Distribution of Large Earthquakes

We study the statistical properties of time distribution of seimicity in California by means of a new method of analysis, the Diffusion Entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent $μ=2.06 \pm 0.01$. We propose the Long-Range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.

cond-mat.stat-mech↗
arXiv2002

Economic Small-World Behavior in Weighted Networks

The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation suffers from a variety of limitations, that make it unsuitable to provide a general tool of analysis for real networks, and not just for mathematical (topological) abstractions. In this paper we show where the major problems arise, and how there is therefore the need for a new reformulation of the small-world concept. Together with an analysis of the variables involved, we then propose a new theory of small-world networks based on two leading concepts: efficiency and cost. Efficiency measures how well information propagates over the network, and cost measures how expensive it is to build a network. The combination of these factors leads us to introduce the concept of {\em economic small worlds}, that formalizes the idea of networks that are "cheap" to build, and nevertheless efficient in propagating information, both at global and local scale. This new concept is shown to overcome all the limitations proper of the so-far commonly adopted formulation, and to provide an adequate tool to quantitatively analyze the behaviour of complex networks in the real world. Various complex systems are analyzed, ranging from the realm of neural networks, to social sciences, to communication and transportation networks. In each case, economic small worlds are found. Moreover, using the economic small-world framework, the construction principles of these networks can be quantitatively analyzed and compared, giving good insights on how efficiency and economy principles combine up to shape all these systems.

cond-mat.stat-mech↗
arXiv2002

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

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.

cond-mat.stat-mech↗
arXiv2002

Efficiency of Scale-Free Networks: Error and Attack Tolerance

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.

cond-mat↗
arXiv2002

Lévy scaling: the Diffusion Entropy Analysis applied to DNA sequences

We address the problem of the statistical analysis of a time series generated by complex dynamics with a new method: the Diffusion Entropy Analysis (DEA) (Fractals, {\bf 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 we 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 de-trending. We show that the joint use of DEA and variance method allows to assess whether a time series is characterized by Lévy or Gauss statistics. We apply the DEA to the study of DNA sequences, and we prove that their large-time scales are characterized by Lévy statistics, regardless of whether they are coding or non-coding 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.

cond-mat.stat-mech↗
arXiv2002

Is the Boston subway a small-world network ?

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.

cond-mat.stat-mech↗
arXiv2001

Efficient Behavior of Small-World Networks

We introduce the concept of efficiency of a network, measuring how efficiently it exchanges information. By using this simple measure small-world networks are seen as systems that are both globally and locally efficient. This allows to give a clear physical meaning to the concept of small-world, and also to perform a precise quantitative a nalysis of both weighted and unweighted networks. We study neural networks and man-made communication and transportation systems and we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency.

cond-mat↗
arXiv2001

Lévy statistics in coding and non-coding nucleotide sequences

We propose a new method of statistical analysis of nucleotide sequences yielding the true scaling without requiring any form of de-trending. With the help of artificial sequences that are proved to be statistically equivalent to the real DNA sequences we find that power-law correlations are present in both coding and non-coding sequences, in accordance with the recent work of other authors. We also afford a compelling evidence that these long-range correlations generate Lévy statistics in both types of sequences.

cond-mat.stat-mech↗
arXiv2000

Harmony in the Small-World

The Small-World phenomenon, popularly known as six degrees of separation, has been mathematically formalized by Watts and Strogatz in a study of the topological properties of a network. Small-worlds networks are defined in terms of two quantities: they have a high clustering coefficient C like regular lattices and a short characteristic path length L typical of random networks. Physical distances are of fundamental importance in the applications to real cases, nevertheless this basic ingredient is missing in the original formulation. Here we introduce a new concept, the connectivity length D, that gives harmony to the whole theory. D can be evaluated on a global and on a local scale and plays in turn the role of L and 1/C. Moreover it can be computed for any metrical network and not only for the topological cases. D has a precise meaning in term of information propagation and describes in an unified way both the structural and the dynamical aspects of a network: small-worlds are defined by a small global and local D, i.e. by a high efficiency in propagating information both on a local and on a global scale. The neural system of the nematode C. elegans, the collaboration graph of film actors, and the oldest U.S. subway system, can now be studied also as metrical networks and are shown to be small-worlds.

cond-mat.stat-mech↗
arXiv2000

Dynamical Quasi-Stationary States in a system with long-range forces

The Hamiltonian Mean Field 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 Lévy 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 $N\to \infty$ limit is taken before the $t \to \infty$ limit, the results obtained are different from the expected canonical predictions. This scenario seems to confirm a recent conjecture proposed by C.Tsallis.

cond-mat.stat-mech↗
arXiv1998

Kolmogorov-Sinai entropy-rate vs. physical entropy

This paper elucidates the connection between the KS entropy-rate kappa and the time evolution of the physical or statistical entropy S. For a large family of chaotic conservative dynamical systems including the simplest ones, the evolution of S(t) for far-from-equilibrium processes includes a stage during which S is a simple linear function of time whose slope is kappa. The paper presents numerical confirmation of this connection for a number of chaotic symplectic maps, ranging from the simplest 2-dimensional ones to a 4-dimensional and strongly nonlinear map.

chao-dyn↗
arXiv1998

Chaos and Statistical Mechanics in the Hamiltonian Mean Field Model

We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of $N$ fully-coupled rotators which shows a second order phase transition. The canonical thermodynamical solution is briefly recalled and its predictions are tested numerically at finite $N$. The Vlasov stationary solution is shown to give the same consistency equation of the canonical solution and its predictions for rotator angle and momenta distribution functions agree very well with numerical simulations. A link is established between the behavior of the maximal Lyapunov exponent and that of thermodynamical fluctuations, expressed by kinetic energy fluctuations or specific heat. The extensivity of chaos in the $N \to \infty$ limit is tested through the scaling properties of Lyapunov spectra and of the Kolmogorov-Sinai entropy. Chaotic dynamics provides the mixing property in phase space necessary for obtaining equilibration; however, the relaxation time to equilibrium grows with $N$, at least near the critical point. Our results constitute an interesting bridge between Hamiltonian chaos in many degrees of freedom systems and equilibrium thermodynamics.

chao-dyn↗
arXiv1997

Lyapunov instability and finite size effects in a system with long-range forces

We study the largest Lyapunov exponent $λ$ and the finite size effects of a system of N fully-coupled classical particles, which shows a second order phase transition. Slightly below the critical energy density $U_c$, $λ$ shows a peak which persists for very large N-values (N=20000). We show, both numerically and analytically, that chaoticity is strongly related to kinetic energy fluctuations. In the limit of small energy, $λ$ goes to zero with a N-independent power law: $λ\sim \sqrt{U}$. In the continuum limit the system is integrable in the whole high temperature phase. More precisely, the behavior $λ\sim N^{-1/3}$ is found numerically for $U > U_c$ and justified on the basis of a random matrix approximation.

chao-dyn↗