arXiv subjects

Damian H. Zanette

Publications and source records attributed to Damian H. Zanette.

At least 37 records · Page 2Linked to original sources

arXiv2005

Synchronization and frustration in oscillator networks with attractive and repulsive interactions

We study, numerically and analytically, the stability of synchronization for an ensemble of coupled phase oscillators with attractive and repulsive interactions, as a function of the number of repulsive couplings and their intensity. Scaling properties of the desynchronization transition are disclosed, and it is shown that unsynchronized configurations have different symmetries depending on the intensity of the repulsive interaction. The concept of frustration minimization helps understanding the main features observed in the collective dynamics of the oscillator network.

cond-mat.stat-mech↗

arXiv2005

Optimal disorder for segregation in annealed small worlds

We study a model for microscopic segregation in a homogeneous system of particles moving on a one-dimensional lattice. Particles tend to separate from each other, and evolution ceases when at least one empty site is found between any two particles. Motion is a mixture of diffusion to nearest-neighbour sites and long-range jumps, known as annealed small-world propagation. The long-range jump probability plays the role of the small-world disorder. We show that there is an optimal value of this probability, for which the segregation process is fastest. Moreover, above a critical probability, the time needed to reach a fully segregated state diverges for asymptotically large systems. These special values of the long-range jump probability depend crucially on the particle density. Our system is a novel example of the rare dynamical processes with critical behaviour at a finite value of the small-world disorder.

nlin.AO↗

arXiv2004

Propagation of small perturbations in synchronized oscillator networks

We study the propagation of a harmonic perturbation of small amplitude on a network of coupled identical phase oscillators prepared in a state of full synchronization. The perturbation is externally applied to a single oscillator, and is transmitted to the other oscillators through coupling. Numerical results and an approximate analytical treatment, valid for random and ordered networks, show that the response of each oscillator is a rather well-defined function of its distance from the oscillator where the external perturbation is applied. For small distances, the system behaves as a dissipative linear medium: the perturbation amplitude decreases exponentially with the distance, while propagating at constant speed. We suggest that the pattern of interactions may be deduced from measurements of the response of individual oscillators to perturbations applied at different nodes of the network.

cond-mat.stat-mech↗

arXiv2004

Zipf's law and the creation of musical context

This article discusses the extension of the notion of context from linguistics to the domain of music. In language, the statistical regularity known as Zipf's law -which concerns the frequency of usage of different words- has been quantitatively related to the process of text generation. This connection is established by Simon's model, on the basis of a few assumptions regarding the accompanying creation of context. Here, it is shown that the statistics of note usage in musical compositions are compatible with the predictions of Simon's model. This result, which gives objective support to the conceptual likeness of context in language and music, is obtained through automatic analysis of the digital versions of several compositions. As a by-product, a quantitative measure of context definiteness is introduced and used to compare tonal and atonal works.

cs.CL↗

arXiv2004

A note on non-thermodynamical applications of non-extensive statistics

It is pointed out that the constraint to be imposed to the maximization of the entropy for processes outside the class of thermodynamical systems, is generally not well defined. In fact, any probability distribution can be derived from Jaynes's principle with a suitable choice of the constraint. In the case of Tsallis's non-extensive formalism, this implies that it is not possible to establish any connection between specific non-thermodynamical processes and non-extensive mechanisms and, in particular, to assign any unambiguous non-extensivity index q to those processes.

cond-mat.stat-mech↗

arXiv2004

Dynamical systems with time-dependent coupling: Clustering and critical behaviour

We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with autonomous dynamics. The system exhibits different dynamical regimes, with various forms of collective organization, controlled by the range of interactions and the dispersion of time scales in the evolution of the internal variables. In the limit of large interaction ranges, it reduces to an ensemble of coupled identical phase oscillators and, to some extent, admits to be treated analytically. We find and characterize a transition between ordered and disordered states, mediated by a regime of dynamical clustering.

cond-mat.stat-mech↗

arXiv2003

Minorities in a model for opinion formation

We study a model for social influence in which the agents' opinion is a continuous variable [G. Weisbuch et al., Complexity \textbf{7}, 2, 55 (2002)]. The convergent opinion adjustment process takes place as a result of random binary encounters whenever the difference between agents' opinions is below a given threshold. The inhomogeneity in the dynamics gives rise to a complex steady state structure, which is also highly dependent on the threshold and on the convergence parameter of the model.

cond-mat.stat-mech↗

arXiv2003

Vector opinion dynamics in a model for social influence

We present numerical simulations of a model of social influence, where the opinion of each agent is represented by a binary vector. Agents adjust their opinions as a result of random encounters, whenever the difference between opinions is below a given threshold. Evolution leads to a steady state, which highly depends on the threshold and a convergence parameter of the model. We analyze the transition between clustered and homogeneous steady states. Results of the cases of complete mixing and small-world networks are compared.

cond-mat.stat-mech↗

arXiv2003

Thermal measurements of stationary nonequilibrium systems: A test for generalized thermostatistics

We show that a gas thermometer in contact with a stationary classical system out of thermal (Boltzmann) equilibrium evolves, under very general conditions, towards a state characterized by a Levy velocity distribution. Our approach is based on a kinetic-like equation that applies to a wide class of models for the system-thermometer interaction. The results clarify the role of non-exponential energy distributions as possible generalizations of the Boltzmann distribution for systems where the usual formulation of thermostatistics may not apply. In particular, they show that the power-law distributions derived from Tsallis's nonextensive formalism are irrelevant to the stationary state of the thermometer, thus failing to give a consistent description of the system-thermometer equilibrium. We point out the need of a generalized thermostatistical formulation able to give a unified frame to Levy and Maxwell distributions.

cond-mat.stat-mech↗

arXiv2003

Dynamical clustering in oscillator ensembles with time-dependent interactions

We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so that the ensemble is inhomogeneous with respect to the internal variable. Interactions between oscillators depend on this variable and thus vary with time. We show that as the inhomogeneity of time scales in the internal evolution grows, the system undergoes a critical transition between ordered and incoherent states. This transition is mediated by a regime of dynamical clustering, where the ensemble recurrently splits into groups formed by varying subpopulations.

cond-mat.stat-mech↗

arXiv2002

Two-dimensional projections of an hypercube

We present a method to project a hypercube of arbitrary dimension on the plane, in such a way as to preserve, as well as possible, the distribution of distances between vertices. The method relies on a Montecarlo optimization procedure that minimizes the squared difference between distances in the plane and in the hypercube, appropriately weighted. The plane projections provide a convenient way of visualization for dynamical processes taking place on the hypercube.

physics.comp-ph↗

arXiv2002

Dynamics and nonequilibrium states in the Hamiltonian mean-field model: A closer look

We critically revisit the evidence for the existence of quasistationary states in the globally coupled XY (or Hamiltonian mean-field) model. A slow-relaxation regime at long times is clearly revealed by numerical realizations of the model, but no traces of quasistationarity are found during the earlier stages of the evolution. We point out the nonergodic properties of this system in the short-time range, which makes a standard statistical description unsuitable. New aspects of the evolution during the nonergodic regime, and of the energy distribution function in the final approach to equilibrium, are disclosed.

cond-mat.stat-mech↗

arXiv2002

Non-monotonic dependence on disorder in biased diffusion on small-world networks

We report numerical simulations of a strongly biased diffusion process on a one-dimensional substrate with directed shortcuts between randomly chosen sites, i.e. with a small-world-like structure. We find that, unlike many other dynamical phenomena on small-world networks, this process exhibits non-monotonic dependence on the density of shortcuts. Specifically, the diffusion time over a finite length is maximal at an intermediate density. This density scales with the length in a nontrivial manner, approaching zero as the length grows. Longer diffusion times for intermediate shortcut densities can be ascribed to the formation of cyclic paths where the diffusion process becomes occasionally trapped.

cond-mat.stat-mech↗

arXiv2002

At the boundary between biological and cultural evolution: The origin of surname distributions

Surnames and nonrecombining alleles are inherited from a single parent in a highly similar way. A simple birth-death model with mutations can accurately describe this process. Exponentially growing and constant populations are investigated, and we study how different compositions of the founder populations can be observed in present-day diversity distributions. We analyse different quantities in the statistically stationary state, both through analytic and numerical methods. Our results compare favourably to field data for family sizes in several countries. We discuss the relationship between the distribution of surnames and the genetic diversity of a population.

cond-mat.stat-mech↗

arXiv2001

Dynamics of rumor propagation on small-world networks

We study the dynamics of an epidemic-like model for the spread of a rumor on a small-world network. It has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network randomness. Here, by numerical means, we perform a quantitative characterization of the evolution in the two regimes. The variant of dynamic small worlds, where the quenched disorder of small-world networks is replaced by randomly changing connections between individuals, is also analyzed in detail and compared with a mean-field approximation.

cond-mat.stat-mech↗

arXiv2001

Self-similarity in the taxonomic classification of human languages

Statistical properties of the taxonomic classification of human languages are studied. It is shown that, at the highest levels of the taxonomic hierarchy, the frequency of taxon members as a function of the number of languages belonging to each member decays as a power law. This feature reveals that a self-similar structure underlies the taxonomy of languages, exactly as observed in the taxonomic classification of biological species. Such an analogy is a clue to the evolutionary foundation of language classification based on long-range comparison.

nlin.AO↗

arXiv2001

Effects of immunization in small-world epidemics

The propagation of model epidemics on a small-world network under the action of immunization is studied. Although the connectivity in this kind of networks is rather uniform, a vaccination strategy focused on the best connected individuals yields a considerable improvement of disease control. The model exhibits a transition from disease localization to propagation as the disorder of the underlying network grows. As a consequence, for fixed disorder, a threshold immunization level exists above which the disease remains localized.

cond-mat.stat-mech↗

arXiv2001

Entropic analysis of the role of words in literary texts

Beyond the local constraints imposed by grammar, words concatenated in long sequences carrying a complex message show statistical regularities that may reflect their linguistic role in the message. In this paper, we perform a systematic statistical analysis of the use of words in literary English corpora. We show that there is a quantitative relation between the role of content words in literary English and the Shannon information entropy defined over an appropriate probability distribution. Without assuming any previous knowledge about the syntactic structure of language, we are able to cluster certain groups of words according to their specific role in the text.

cond-mat.stat-mech↗