Sant'Ambrogio di Torino, Italy
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Allegra M.,Institute for Scientific Interchange ISI | Allegra M.,University of Turin | Allegra M.,Polytechnic University of Turin | Giorda P.,Institute for Scientific Interchange ISI | Montorsi A.,Polytechnic University of Turin
Physical Review B - Condensed Matter and Materials Physics | Year: 2011

We study the quantum discord (QD) and the classical correlations (CC) in a reference model for strongly correlated electrons, the one-dimensional bond-charge extended Hubbard model. We show that the comparison of QD and CC and of their derivatives in the direct and reciprocal lattice allows one to efficiently inspect the structure of two-points driven quantum phase transitions, discriminating those at which off diagonal long-range order (ODLRO) is involved. Moreover, we observe that QD between pair of sites is a monotonic function of ODLRO, thus establishing a direct relation between the latter and two point quantum correlations that differ from the entanglement. The study of the ground-state properties allows us to show that for a whole class of permutation invariant (η-pair) states quantum discord can violate the monogamy property, both in presence and in absence of bipartite entanglement. In the thermodynamic limit, due to the presence of ODLRO, the violation for η-pair states is maximal, while, for the purely fermionic ground state, it is finite. From a general perspective, all our results validate the importance of the concepts of QD and CC for the study of critical condensed-matter systems. © 2011 American Physical Society.

Tria F.,Institute for Scientific Interchange ISI | Loreto V.,Institute for Scientific Interchange ISI | Loreto V.,University of Rome La Sapienza | Servedio V.D.P.,University of Rome La Sapienza | And 2 more authors.
Scientific Reports | Year: 2014

Novelties are a familiar part of daily life. They are also fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities, one novelty can pave the way for others in a process that Kauffman has called expanding the adjacent possible . The dynamics of correlated novelties, however, have yet to be quantified empirically or modeled mathematically. Here we propose a simple mathematical model that mimics the process of exploring a physical, biological, or conceptual space that enlarges whenever a novelty occurs. The model, a generalization of Polya's urn, predicts statistical laws for the rate at which novelties happen (Heaps' law) and for the probability distribution on the space explored (Zipf's law), as well as signatures of the process by which one novelty sets the stage for another. We test these predictions on four data sets of human activity: the edit events of Wikipedia pages, the emergence of tags in annotation systems, the sequence of words in texts, and listening to new songs in online music catalogues. By quantifying the dynamics of correlated novelties, our results provide a starting point for a deeper understanding of the adjacent possible and its role in biological, cultural, and technological evolution.

Balcan D.,Indiana University Bloomington | Vespignani A.,Indiana University Bloomington | Vespignani A.,Institute for Scientific Interchange ISI
Nature Physics | Year: 2011

Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumours, and emergence of consensus. These patterns however are often dominated by specific locations and recurrent flows and poorly modelled by the random diffusive dynamics generally used to study them. Here we develop a theoretical framework to analyse contagion within a network of locations where individuals recall their geographic origins. We find a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected. This transition cannot be uncovered by continuous deterministic models because of the stochastic features of the contagion process and defines an invasion threshold that depends on mobility parameters, providing guidance for controlling contagion spread by constraining mobility processes. We recover the threshold behaviour by analysing diffusion processes mediated by real human commuting data. © 2011 Macmillan Publishers Limited. All rights reserved.

Vespignani A.,Northeastern University | Vespignani A.,Institute for Scientific Interchange ISI
Nature Physics | Year: 2012

In recent years the increasing availability of computer power and informatics tools has enabled the gathering of reliable data quantifying the complexity of socio-technical systems. Data-driven computational models have emerged as appropriate tools to tackle the study of dynamical phenomena as diverse as epidemic outbreaks, information spreading and Internet packet routing. These models aim at providing a rationale for understanding the emerging tipping points and nonlinear properties that often underpin the most interesting characteristics of socio-technical systems. Here, using diffusion and contagion phenomena as prototypical examples, we review some of the recent progress in modelling dynamical processes that integrates the complex features and heterogeneities of real-world systems.

Perra N.,Indiana University Bloomington | Perra N.,Center for the Study of Complex Networks | Balcan D.,Indiana University Bloomington | Goncalves B.,Indiana University Bloomington | And 2 more authors.
PLoS ONE | Year: 2011

The last decade saw the advent of increasingly realistic epidemic models that leverage on the availability of highly detailed census and human mobility data. Data-driven models aim at a granularity down to the level of households or single individuals. However, relatively little systematic work has been done to provide coupled behavior-disease models able to close the feedback loop between behavioral changes triggered in the population by an individual's perception of the disease spread and the actual disease spread itself. While models lacking this coupling can be extremely successful in mild epidemics, they obviously will be of limited use in situations where social disruption or behavioral alterations are induced in the population by knowledge of the disease. Here we propose a characterization of a set of prototypical mechanisms for self-initiated social distancing induced by local and non-local prevalence-based information available to individuals in the population. We characterize the effects of these mechanisms in the framework of a compartmental scheme that enlarges the basic SIR model by considering separate behavioral classes within the population. The transition of individuals in/out of behavioral classes is coupled with the spreading of the disease and provides a rich phase space with multiple epidemic peaks and tipping points. The class of models presented here can be used in the case of data-driven computational approaches to analyze scenarios of social adaptation and behavioral change. © 2011 Perra et al.

Balcan D.,Lagrange Systems | Balcan D.,Indiana University Bloomington | Vespignani A.,Northeastern University | Vespignani A.,Institute for Scientific Interchange ISI
Journal of Theoretical Biology | Year: 2012

In this paper we develop a framework to analyze the behavior of contagion and spreading processes in complex subpopulation networks where individuals have memory of their subpopulation of origin. We introduce a metapopulation model in which subpopulations are connected through heterogeneous fluxes of individuals. The mobility process among communities takes into account the memory of residence of individuals and is incorporated with the classical susceptible-infectious-recovered epidemic model within each subpopulation. In order to gain analytical insight into the behavior of the system we use degree-block variables describing the heterogeneity of the subpopulation network and a time-scale separation technique for the dynamics of individuals. By considering the stochastic nature of the epidemic process we obtain the explicit expression of the global epidemic invasion threshold, below which the disease dies out before reaching a macroscopic fraction of the subpopulations. This threshold is not present in continuous deterministic diffusion models and explicitly depends on the disease parameters, the mobility rates, and the properties of the coupling matrices describing the mobility across subpopulations. The results presented here take a step further in offering insight into the fundamental mechanisms controlling the spreading of infectious diseases and other contagion processes across spatially structured communities. © 2011 Elsevier Ltd.

Campos Venuti L.,Institute for Scientific Interchange ISI | Jacobson N.T.,University of Southern California | Santra S.,University of Southern California | Zanardi P.,Institute for Scientific Interchange ISI | Zanardi P.,University of Southern California
Physical Review Letters | Year: 2011

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this Letter we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasicritical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime. © 2011 American Physical Society.

Jacobson N.T.,University of Southern California | Venuti L.C.,Institute for Scientific Interchange ISI | Zanardi P.,University of Southern California | Zanardi P.,Institute for Scientific Interchange ISI
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2011

In this work we investigate the equilibration dynamics after a sudden Hamiltonian quench of a quantum spin system initially prepared in a thermal state. To characterize the equilibration we evaluate the Loschmidt echo, a global measure for the degree of distinguishability between the initial and time-evolved quenched states. We present general results valid for small quenches and detailed analysis of the quantum XY chain. The result is that quantum criticality manifests, even at small but finite temperatures, in a universal double-peaked form of the echo statistics and poor equilibration for sufficiently relevant perturbations. In addition, for this model we find a tight lower bound on the Loschmidt echo in terms of the purity of the initial state and the more easily evaluated Hilbert-Schmidt inner product between initial and time-evolved quenched states. This bound allows us to relate the time-averaged Loschmidt echo with the purity of the time-averaged state, a quantity that has been shown to provide an upper bound on the variance of observables. © 2011 American Physical Society.

Campos Venuti L.,Institute for Scientific Interchange ISI | Zanardi P.,Institute for Scientific Interchange ISI | Zanardi P.,University of Southern California
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2010

A sudden change in the Hamiltonian parameter drives a quantum system out of equilibrium. For a finite-size system, expectations of observables start fluctuating in time without converging to a precise limit. A new equilibrium state emerges only in the probabilistic sense, when the probability distribution for the observable expectations over long times concentrates around their mean value. In this paper we study the full statistic of generic observables after a small quench. When the quench is performed around a regular (i.e., noncritical) point of the phase diagram, generic observables are expected to be characterized by Gaussian distribution functions ("good equilibration"). Instead, when quenching around a critical point a new, universal, double-peaked distribution function emerges for relevant perturbations. Our analytic predictions are numerically checked for a nonintegrable extension of the quantum Ising model. © 2010 The American Physical Society.

Mukherjee A.,Institute for Scientific Interchange ISI | Choudhury M.,Microsoft | Ganguly N.,Indian Institute of Technology Kharagpur
Physica A: Statistical Mechanics and its Applications | Year: 2011

It is a well-known fact that the degree distribution (DD) of the nodes in a partition of a bipartite network influences the DD of its one-mode projection on that partition. However, there are no studies exploring the effect of the DD of the other partition on the one-mode projection. In this article, we show that the DD of the other partition, in fact, has a very strong influence on the DD of the one-mode projection. We establish this fact by deriving the exact or approximate closed-forms of the DD of the one-mode projection through the application of generating function formalism followed by the method of iterative convolution. The results are cross-validated through appropriate simulations. © 2011 Elsevier B.V. All rights reserved.

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