Andrea Baldassarri

Collective dynamics of social annotation

The enormous increase of popularity and use of the worldwide web has led in the recent years to important changes in the ways people communicate. An interesting example of this fact is provided by the now very popular social annotation systems, through which users annotate resources (such as web pages or digital photographs) with keywords known as “tags.” Understanding the rich emergent structures resulting from the uncoordinated actions of users calls for an interdisciplinary effort. In particular concepts borrowed from statistical physics, such as random walks (RWs), and complex networks theory, can effectively contribute to the mathematical modeling of social annotation systems. Here, we show that the process of social annotation can be seen as a collective but uncoordinated exploration of an underlying semantic space, pictured as a graph, through a series of RWs. This modeling framework reproduces several aspects, thus far unexplained, of social annotation, among which are the peculiar growth of the size of the vocabulary used by the community and its complex network structure that represents an externalization of semantic structures grounded in cognition and that are typically hard to access.

EMERGENT COMMUNITY STRUCTURE IN SOCIAL TAGGING SYSTEMS

A distributed classification paradigm known as collaborative tagging has been widely adopted in new Web applications designed to manage and share online resources. Users of these applications organize resources (Web pages, digital photographs, academic papers) by associating with them freely chosen text labels, or tags. Here we leverage the social aspects of collaborative tagging and introduce a notion of resource distance based on the collective tagging activity of users. We collect data from a popular system and perform experiments showing that our definition of distance can be used to build a weighted network of resources with a detectable community structure. We show that this community structure clearly exposes the semantic relations among resources. The communities of resources that we observe are a genuinely emergent feature, resulting from the uncoordinated activity of a large number of users, and their detection paves the way for mapping emergent semantics in social tagging systems.

Fluctuation-dissipation relations in driven granular gases

We study the dynamics of a two-dimensional driven inelastic gas, by means of direct simulation Monte Carlo techniques, i.e., under the assumption of molecular chaos. Under the effect of a uniform stochastic driving in the form of a white noise plus a friction term, the gas is kept in a nonequilibrium steady state characterized by fractal density correlations and non-Gaussian distributions of velocities; the mean-squared velocity, that is the so-called granular temperature, is lower than the bath temperature. We observe that a modified form of the Kubo relation, which relates the autocorrelation and the linear response for the dynamics of a system at equilibrium, still holds for the off equilibrium, though stationary, dynamics of the systems under investigation. Interestingly, the only needed modification to the equilibrium Kubo relation is the replacement of the equilibrium temperature with an effective temperature, which results equal to the global granular temperature. We present two independent numerical experiments, where two different observables are studied: (a) the staggered density current, whose response to an impulsive shear is proportional to its autocorrelation in the unperturbed system and (b) the response of a tracer to a small constant force, switched on at time t(w), which is proportional to the mean-square displacement in the unperturbed system. Both measures confirm the validity of Kubos formula, provided that the granular temperature is used as the proportionality factor between response and autocorrelation, at least for not too large inelasticities.

Self-Stabilized Fractality of Seacoasts through Damped Erosion

Erosion of rocky coasts spontaneously creates irregular seashores. But the geometrical irregularity, in turn, damps the sea waves, decreasing the average wave amplitude. There may then exist a mutual self-stabilization of the wave amplitude together with the irregular morphology of the coast. A simple model of such stabilization is studied. It leads, through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with a dimension close to 4/3. Fractal geometry here plays the role of a morphological attractor directly related to percolation geometry.

Average shape of a fluctuation: universality in excursions of stochastic processes.

We study the average shape of a fluctuation of a time series x(t), which is the average value (T) before x(t) first returns at time T to its initial value x(0). For large classes of stochastic processes, we find that a scaling law of the form (T) = T(alpha)f(t/T) is obeyed. The scaling function f(s) is, to a large extent, independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.

Brownian Forces in Sheared Granular Matter

We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilized, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.

KINETICS MODELS OF INELASTIC GASES

In the present paper we review some recent progresses in the study of the dynamics of cooling granular gases, obtained using idealized models to address different issues of their kinetics. The inelastic Maxwell gas is studied as an introductory mean field model that has the major advantage of being exactly resoluble in the case of scalar velocities, showing an asymptotic velocity distribution with power law tails |v|-4. More realistic models can be obtained placing the same process on a spatial lattice. Two regimes are observed: an uncorrelated transient followed by a dynamical stage characterized by correlations in the velocity field in the form of shocks and vortices. The lattice models, in one and two dimensions, account for different numerical measurements: some of them agree with the already known results, while others have never been efficiently measured and shed light on the deviation from homogeneity. In particular in the velocity-correlated regime the computation of structure factors gives indication of a dynamics similar to that of a diffusion process on large scales with a more complex behavior at shorter scales.

Stochastic dynamics of a sheared granular medium

We experimentally investigate the response of a sheared granular medium in a Couette geometry. The apparatus exhibits the expected stick-slip motion and we probe it in the very intermittent regime resulting from low driving. Statistical analysis of the dynamic fluctuations reveals notable regularities. We observe a possible stability property for the torque distribution, reminiscent of the stability of Gaussian independent variables. In this case, however, the variables are correlated and the distribution is skewed. Moreover, the whole dynamical intermittent regime can be described with a simple stochastic model, finding good quantitative agreement with the experimental data. Interestingly, a similar model has been previously introduced in the study of magnetic domain wall motion, a source of Barkhausen noise. Our study suggests interesting connections between different complex phenomena and reveals some unexpected features that remain to be explained.

What is the temperature of a granular medium

In this paper we discuss whether thermodynamical concepts and in particular the notion of temperature could be relevant for the dynamics of granular systems. We briefly review how a temperature-like quantity can be defined and measured in granular media in very different regimes, namely the glassy-like, the liquidlike and the granular gas. The common denominator will be given by the fluctuation–dissipation theorem, whose validity is explored by means of both numerical and experimental techniques. It turns out that, although a definition of a temperature is possible in all cases, its interpretation is far from being obvious. We discuss the possible perspectives both from the theoretical and, more importantly, from the experimental point of view. (Some figures in this article are in colour only in the electronic version)

Cooling of a lattice granular fluid as an ordering process.

We present a microscopic model of granular medium to study the role of dynamical correlations and the onset of spatial order induced by the inelasticity of the interactions on the velocity field. In spite of its simplicity and intrinsic limitations, it features several aspects of the rich phenomenology observed in granular materials and allows to make contact with other topics of statistical mechanics such as diffusion processes, domain growth, aging phenomena. Interestingly, while local observables, being controlled by the largest wavelength fluctuations, seem to suggest a purely diffusive behavior, the formation of spatially extended structures and topological defects, such as vortices and shocks, reveals a more complex scenario. Finally, only for quasielastic systems, we observe a neat scale separation, which represents a fundamental hypothesis to develop a granular hydrodynamics.