arXiv subjects

Andrea Gabrielli

Publications and source records attributed to Andrea Gabrielli.

At least 73 records · Page 4Linked to original sources

arXiv2015

Randomizing bipartite networks: the case of the World Trade Web

Within the last fifteen years, network theory has been successfully applied both to natural sciences and to socioeconomic disciplines. In particular, bipartite networks have been recognized to provide a particularly insightful representation of many systems, ranging from mutualistic networks in ecology to trade networks in economy, whence the need of a pattern detection-oriented analysis in order to identify statistically-significant structural properties. Such an analysis rests upon the definition of suitable null models, i.e. upon the choice of the portion of network structure to be preserved while randomizing everything else. However, quite surprisingly, little work has been done so far to define null models for real bipartite networks. The aim of the present work is to fill this gap, extending a recently-proposed method to randomize monopartite networks to bipartite networks. While the proposed formalism is perfectly general, we apply our method to the binary, undirected, bipartite representation of the World Trade Web, comparing the observed values of a number of structural quantities of interest with the expected ones, calculated via our randomization procedure. Interestingly, the behavior of the World Trade Web in this new representation is strongly different from the monopartite analogue, showing highly non-trivial patterns of self-organization.

physics.soc-ph↗

arXiv2015

Systemic risk analysis in reconstructed economic and financial networks

We address a fundamental problem that is systematically encountered when modeling complex systems: the limitedness of the information available. In the case of economic and financial networks, privacy issues severely limit the information that can be accessed and, as a consequence, the possibility of correctly estimating the resilience of these systems to events such as financial shocks, crises and cascade failures. Here we present an innovative method to reconstruct the structure of such partially-accessible systems, based on the knowledge of intrinsic node-specific properties and of the number of connections of only a limited subset of nodes. This information is used to calibrate an inference procedure based on fundamental concepts derived from statistical physics, which allows to generate ensembles of directed weighted networks intended to represent the real system, so that the real network properties can be estimated with their average values within the ensemble. Here we test the method both on synthetic and empirical networks, focusing on the properties that are commonly used to measure systemic risk. Indeed, the method shows a remarkable robustness with respect to the limitedness of the information available, thus representing a valuable tool for gaining insights on privacy-protected economic and financial systems.

physics.soc-ph↗

arXiv2015

The Scientific Competitiveness of Nations

We use citation data of scientific articles produced by individual nations in different scientific domains to determine the structure and efficiency of national research systems. We characterize the scientific fitness of each nation (that is, the competitiveness of its research system) and the complexity of each scientific domain by means of a non-linear iterative algorithm able to assess quantitatively the advantage of scientific diversification. We find that technological leading nations, beyond having the largest production of scientific papers and the largest number of citations, do not specialize in a few scientific domains. Rather, they diversify as much as possible their research system. On the other side, less developed nations are competitive only in scientific domains where also many other nations are present. Diversification thus represents the key element that correlates with scientific and technological competitiveness. A remarkable implication of this structure of the scientific competition is that the scientific domains playing the role of "markers" of national scientific competitiveness are those not necessarily of high technological requirements, but rather addressing the most "sophisticated" needs of the society.

physics.soc-ph↗

arXiv2014

Reconstructing topological properties of complex networks using the fitness model

A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this paper we investigate a novel method to reconstruct global topological properties of a complex network starting from limited information. This method uses the knowledge of an intrinsic property of the nodes (indicated as fitness), and the number of connections of only a limited subset of nodes, in order to generate an ensemble of exponential random graphs that are representative of the real systems and that can be used to estimate its topological properties. Here we focus in particular on reconstructing the most basic properties that are commonly used to describe a network: density of links, assortativity, clustering. We test the method on both benchmark synthetic networks and real economic and financial systems, finding a remarkable robustness with respect to the number of nodes used for calibration. The method thus represents a valuable tool for gaining insights on privacy-protected systems.

cs.SI↗

arXiv2013

Non-Markovian Models of Blocking in Concurrent and Countercurrent Flows

We investigate models in which blocking can interrupt a particulate flow process at any time. Filtration, and flow in micro/nano-channels and traffic flow are examples of such processes. We first consider concurrent flow models where particles enter a channel randomly. If at any time two particles are simultaneously present in the channel, failure occurs. The key quantities are the survival probability and the distribution of the number of particles that pass before failure. We then consider a counterflow model with two opposing Poisson streams. There is no restriction on the number of particles passing in the same direction, but blockage occurs if, at any time, two opposing particles are simultaneously present in the passage.

cond-mat.stat-mech↗

arXiv2012

Bootstrapping topology and systemic risk of complex network using the fitness model

We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network density and the degree distri- bution as a function of the size of the initial subset of nodes. Moreover, we also study the resilience of the network to distress propagation. We first test the method on ensembles of synthetic networks generated with the Exponential Random Graph model which allows to apply common tools from statistical mechanics. We then test it on the empirical case of the World Trade Web. In both cases, we find that a subset of 10 % of nodes is enough to reconstruct the main features of the network along with its resilience with an error of 5%.

physics.soc-ph↗

arXiv2012

A network analysis of countries' export flows: firm grounds for the building blocks of the economy

In this paper we analyze the bipartite network of countries and products from UN data on country production. We define the country-country and product-product projected networks and introduce a novel method of filtering information based on elements' similarity. As a result we find that country clustering reveals unexpected socio-geographic links among the most competing countries. On the same footings the products clustering can be efficiently used for a bottom-up classification of produced goods. Furthermore we mathematically reformulate the "reflections method" introduced by Hidalgo and Hausmann as a fixpoint problem; such formulation highlights some conceptual weaknesses of the approach. To overcome such an issue, we introduce an alternative methodology (based on biased Markov chains) that allows to rank countries in a conceptually consistent way. Our analysis uncovers a strong non-linear interaction between the diversification of a country and the ubiquity of its products, thus suggesting the possible need of moving towards more efficient and direct non-linear fixpoint algorithms to rank countries and products in the global market.

physics.soc-ph↗

arXiv2010

A dynamical classification of the range of pair interactions

We formalize a classification of pair interactions based on the convergence properties of the {\it forces} acting on particles as a function of system size. We do so by considering the behavior of the probability distribution function (PDF) P(F) of the force field F in a particle distribution in the limit that the size of the system is taken to infinity at constant particle density, i.e., in the "usual" thermodynamic limit. For a pair interaction potential V(r) with V(r) \rightarrow \infty) \sim 1/r^a defining a {\it bounded} pair force, we show that P(F) converges continuously to a well-defined and rapidly decreasing PDF if and only if the {\it pair force} is absolutely integrable, i.e., for a > d-1, where d is the spatial dimension. We refer to this case as {\it dynamically short-range}, because the dominant contribution to the force on a typical particle in this limit arises from particles in a finite neighborhood around it. For the {\it dynamically long-range} case, i.e., a \leq d-1, on the other hand, the dominant contribution to the force comes from the mean field due to the bulk, which becomes undefined in this limit. We discuss also how, for a \leq d-1 (and notably, for the case of gravity, a=d-2) P(F) may, in some cases, be defined in a weaker sense. This involves a regularization of the force summation which is generalization of the procedure employed to define gravitational forces in an infinite static homogeneous universe. We explain that the relevant classification in this context is, however, that which divides pair forces with a > d-2 (or a < d-2), for which the PDF of the {\it difference in forces} is defined (or not defined) in the infinite system limit, without any regularization. In the former case dynamics can, as for the (marginal) case of gravity, be defined consistently in an infinite uniform system.

cond-mat.stat-mech↗

arXiv2010

Quasi-stationary states and the range of pair interactions

"Quasi-stationary" states are approximately time-independent out of equilibrium states which have been observed in a variety of systems of particles interacting by long-range interactions. We investigate here the conditions of their occurrence for a generic pair interaction V(r \rightarrow \infty) \sim 1/r^a with a > 0, in d>1 dimensions. We generalize analytic calculations known for gravity in d=3 to determine the scaling parametric dependences of their relaxation rates due to two body collisions, and report extensive numerical simulations testing their validity. Our results lead to the conclusion that, for a < d-1, the existence of quasi-stationary states is ensured by the large distance behavior of the interaction alone, while for a > d-1 it is conditioned on the short distance properties of the interaction, requiring the presence of a sufficiently large soft-core in the interaction potential.

cond-mat.stat-mech↗

arXiv2010

Topologically biased random walk with application for community finding in networks

We present a new approach of topology biased random walks for undirected networks. We focus on a one parameter family of biases and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion (PEM) to study the features of random walks {\em vs.} parameter values. Furthermore, we show an analysis of the spectral gap maximum associated to the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow {\em ad hoc} algorithms for the exploration of complex networks and their communities.

cond-mat.stat-mech↗

arXiv2010

Gravitational force in an infinite one-dimensional Poisson distribution

We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences which arise. Deriving an exact analytic expression for the probability density function (PDF) P(F), we show that it is badly defined in the limit in which the well known Holtzmark distribution is obtained in the analogous three-dimensional case. A well defined P(F) may, however, be obtained in the infinite range limit by an appropriate renormalization of the coupling strength, giving a Gaussian form. Calculating the spatial correlation properties we show that this latter procedure has a trivial physical meaning. Finally we calculate the PDF and correlation properties of differences of forces (at separate spatial points), which are well defined without any renormalization. We explain that the convergence of these quantities is in fact sufficient to allow a physically meaningful infinite system limit to be defined for the clustering dynamics from Poissonian initial conditions.

cond-mat.stat-mech↗

arXiv2009

The Smallville Effect: Social Ties Make Mobile Networks More Secure Against the Node Capture Attack

Mobile Ad Hoc networks, due to the unattended nature of the network itself and the dispersed location of nodes, are subject to several unique security issues. One of the most vexed security threat is node capture. A few solutions have already been proposed to address this problem; however, those solutions are either centralized or focused on theoretical mobility models alone. In the former case the solution does not fit well the distributed nature of the network while, in the latter case, the quality of the solutions obtained for realistic mobility models severely differs from the results obtained for theoretical models. The rationale of this paper is inspired by the observation that re-encounters of mobile nodes do elicit a form of social ties. Leveraging these ties, it is possible to design efficient and distributed algorithms that, with a moderated degree of node cooperation, enforce the emergent property of node capture detection. In particular, in this paper we provide a proof of concept proposing a set of algorithms that leverage, to different extent, node mobility and node cooperation--that is, identifying social ties--to thwart node capture attack. In particular, we test these algorithms on a realistic mobility scenario. Extensive simulations show the quality of the proposed solutions and, more important, the viability of the proposed approach.

cs.CR↗

arXiv2009

1-d gravity in infinite point distributions

The dynamics of infinite, asymptotically uniform, distributions of self-gravitating particles in one spatial dimension provides a simple toy model for the analogous three dimensional problem. We focus here on a limitation of such models as treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e. the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by "Jeans' swindle" for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N-body simulations. For identical particles the dynamics of the simplest toy model is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss previous results in the literature, and present new results for the specific case of this simplest (static) model starting from "shuffled lattice" initial conditions. These show qualitative properties (notably its "self-similarity") of the evolution very similar to those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.

cond-mat.stat-mech↗

arXiv2008

Barabasi Queueing Model and Invasion Percolation on a tree

In this paper we study the properties of the Barabási model of queueing under the hypothesis that the number of tasks is steadily growing in time. We map this model exactly onto an Invasion Percolation dynamics on a Cayley tree. This allows to recover the correct waiting time distribution $P_W(τ)\sim τ^{-3/2}$ at the stationary state (as observed in different realistic data) and also to characterize it as a sequence of causally and geometrically connected bursts of activity. We also find that the approach to stationarity is very slow.

physics.soc-ph↗

arXiv2008

Clustering and coalescence from multiplicative noise: the Kraichnan ensemble

We study the dynamics of the two-point statistics of the Kraichnan ensemble which describes the transport of a passive pollutant by a stochastic turbulent flow characterized by scale invariant structure functions. The fundamental equation of this problem consists in the Fokker-Planck equation for the two-point correlation function of the density of particles performing spatially correlated Brownian motions with scale invariant correlations. This problem is equivalent to the stochastic motion of an effective particle driven by a generic multiplicative noise. In this paper we propose an alternative and more intuitive approach to the problem than the original one leading to the same conclusions. The general features of this new approach make possible to fit it to other more complex contexts.

cond-mat.stat-mech↗

arXiv2007

Tilings of space and superhomogeneous point processes

We consider the construction of point processes from tilings, with equal volume tiles, of d-dimensional Euclidean space. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are "superhomogeneous'' (or "hyperuniform''), i.e., for which the structure factor S(k) vanishes when the wavenumber k tends to zero. The exponent of the leading small-k behavior depends in a simple manner on the nature of the correlation properties of the specific tiling and on the conservation of the mass moments of the tiles. Assigning one point to the center of mass of each tile gives the exponent γ=4 for any tiling in which the shapes and orientations of the tiles are short-range correlated. Smaller exponents, in the range 4-d<γ<4 (and thus always superhomogeneous for d\leq 4), may be obtained in the case that the latter quantities have long-range correlations. Assigning more than one point to each tile in an appropriate way, we show that one can obtain arbitrarily higher exponents in both cases. We illustrate our results with explicit constructions using known deterministic tilings, as well as some simple stochastic tilings for which we can calculate S(k) exactly. Our results provide, we believe, the first explicit analytical construction of point processes with γ> 4. Applications to condensed matter physics, and also to cosmology, are briefly discussed.

cond-mat.stat-mech↗

arXiv2007

Two-point correlation properties of stochastic "cloud processes''

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically that there may be non-trivial correlations in the displacement fields describing the positions of the different daughters of the same "mother" particle, and then treat separately the cases in which there are, or are not, correlations also between the displacements of daughters belonging to different mothers. For both cases exact formulae are derived relating the structure factor (power spectrum) of the daughter distribution to that of the mother. These results can be considered as a generalization of the analogous equations obtained in ref. [1] (cond-mat/0409594) for the case of stochastic displacement fields applied to particle distributions. An application of the present results is that they give explicit algorithms for generating, starting from regular lattice arrays, stochastic particle distributions with an arbitrarily high degree of large-scale uniformity.

cond-mat.stat-mech↗

arXiv2007

Diffusion, super-diffusion and coalescence from single step

From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to build a velocity field. First we show that spatially uncorrelated fields $\bu(\bx)$ lead to both standard and anomalous diffusion equation. When the field $\bu(\bx)$ is spatially correlated each particle performs a simple free Brownian motion, but the trajectories of different particles result to be mutually correlated. The two-point statistical properties of the field $\bu(\bx)$ induce two-point spatial correlations in the particle distribution satisfying a simple but non-trivial diffusion-like equation. These displacement-displacement correlations lead the system to three possible regimes: coalescence, simple clustering and a combination of the two. The existence of these different regimes, in the one-dimensional system, is shown through computer simulations and a simple theoretical argument.

cond-mat.stat-mech↗