Francesca Colaiori

Preferential attachment in the growth of social networks: The internet encyclopedia Wikipedia

We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with those of the World Wide Web, despite the very different growth mechanism. In particular, we measure a scale-invariant distribution of the in and out degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users, who are responsible of its evolution, can act globally on the network.

Detecting communities in large networks

We develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and link orientation. Since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned, it turns to be specially suitable for the analysis of social and information networks. We test the algorithm on a large-scale data-set from a psychological experiment of word association. In this case, it proves to be successful both in clustering words, and in uncovering mental association patterns.

Universality Classes of Optimal Channel Networks

Energy minimization of both homogeneous and heterogeneous river networks shows that, over a range of parameter values, there are only three distinct universality classes. The exponents for all three classes of behavior are calculated.

Scaling, optimality, and landscape evolution

A nonlinear model is studied which describes the evolution of a landscape under the effects of erosion and regeneration by geologic uplift by mean of a simple differential equation. The equation, already in wide use among geomorphologists and in that context obtained phenomenologically, is here derived by reparametrization invariance arguments and exactly solved in dimension d=1. Results of numerical simulations in d=2 show that the model is able to reproduce the critical scaling characterizing landscapes associated with natural river basins. We show that configurations minimizing the rate of energy dissipation (optimal channel networks) are stationary solutions of the equation describing the landscape evolution. Numerical simulations show that a careful annealing of the equation in the presence of additive noise leads to configurations very close to the global minimum of the dissipated energy, characterized by mean field exponents. We further show that if one considers generalized river network configurations in which splitting of the flow (i.e., braiding) and loops are allowed, the minimization of the dissipated energy results in spanning loopless configurations, under the constraints imposed by the continuity equations. This is stated in the form of a general theorem applicable to generic networks, suggesting that other branching structures occurring in nature may possibly arise as optimal structures minimizing a cost function.

Signature of effective mass in crackling-noise asymmetry

Crackling noise is a common feature in many dynamic systems1,2,3,4,5,6,7,8,9, the most familiar instance of which is the sound made by a sheet of paper when crumpled into a ball. Although seemingly random, this noise contains fundamental information about the properties of the system in which it occurs. One potential source of such information lies in the asymmetric shape of noise pulses emitted by a diverse range of noisy systems8,9,10,11,12, but the cause of this asymmetry has lacked explanation1. Here we show that the leftward asymmetry observed in the Barkhausen effect2 — the noise generated by the jerky motion of domain walls as they interact with impurities in a soft magnet—is a direct consequence of a magnetic domain wall’s negative effective mass. As well as providing a means of determining domain-wall effective mass from a magnet’s Barkhausen noise, our work suggests an inertial explanation for the origin of avalanche asymmetries in crackling-noise phenomena more generally.

Exactly solvable model of avalanches dynamics for Barkhausen crackling noise

We review the present state of understanding of the Barkhausen effect in soft ferromagnetic materials. Barkhausen noise (BN) is generated by the discontinuous motion of magnetic domains as they interact with impurities and defects. BN is one of the many examples of crackling noise, arising in a variety of contexts with remarkably similar features, and occurring when a system responds in a jerky manner to a smooth external forcing. Among all crackling system, we focus on BN, where a complete and consistent picture emerges thanks to an exactly solvable model of avalanche dynamics, known as the ABBM model, which ultimately describes the system in terms of a Langevin equation for the velocity of the avalanche front. Despite its simplicity, the ABBM model is able to accurately reproduce the phenomenology observed in the experiments on a large class of magnetic materials, as long as universal properties are involved. To complete the picture and to understand the long-standing discrepancy between the ABBM theory and the experiments, which otherwise agree exceptionally well, consisting of the puzzling asymmetric shape of the noise pulses, microscopic details must be taken into account, namely the effects of eddy current retardation. These effects can be incorporated in the model, and result, to a first-order approximation, in a negative effective mass associated with the wall. The progress made in understanding BN is potentially relevant for other crackling systems: on the one hand, the ABBM model turns out to be a paradigmatic model for the universal behaviour of avalanche dynamics; on the other hand, the microscopic explanation of the asymmetry in the noise pulses suggests that inertial effects may also be at the origin of pulses asymmetry observed in other crackling systems.

ANALYTICAL AND NUMERICAL STUDY OF OPTIMAL CHANNEL NETWORKS

We analyze the optimal channel network model for river networks using both analytical and numerical approaches. This is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the optimal configurations. The fractal character of river networks is reflected in the power-law behavior of various quantities characterizing the morphology of the basin. In the context of a finite-size scaling ansatz, the exponents describing the power-law behavior are calculated exactly and show mean-field behavior, except for two limiting values of a parameter characterizing the dissipated energy, for which the system belongs to different universality classes. Two modified versions of the model, incorporating quenched disorder, are considered: the first simulates heterogeneities in the local properties of the soil and the second considers the effects of a nonuniform rainfall. In the region of mean-field behavior, the model is shown to be robust for both kinds of perturbations. In the two limiting cases the random rainfall is still irrelevant, whereas the heterogeneity in the soil properties leads to different universality classes. Results of a numerical analysis of the model are reported that confirm and complement the theoretical analysis of the global minimum. The statistics of the local minima are found to resemble more strongly observational data on real rivers.

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.

Communities Detection in Large Networks

We develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and links orientations. Since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned, it turns to be specially suitable to the analysis of social and information networks. We test the algorithm on a large-scale data-set from a psychological experiment of word association. In this case, it proves to be successful both in clustering words, and in uncovering mental association patterns.

Dynamic hysteresis in Finemet thin films

In this paper, we present a series of dynamic measurements on a set of Finemet thin films, having thickness ranging from 200 /spl Aring/ to 5 /spl mu/m, by using both magneto-optical Kerr effect (MOKE) and the fluxmetric inductive method. Unexpectedly, the data show two completely different hysteresis behavior, showing relevant differences in their frequency dependences. In particular, optical hysteresis is easily explained by a simple depinning model which can be solved analytically.