Papers by Andrea Gabrielli
Physical review, May 1, 2020
We address the problem of community detection in networks by introducing a general definition of ... more We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The specific implementation of the quality function and the resulting optimal community structure thus become dependent both on the type of Markov process and on the specific Markov times considered. For instance, if we use a natural Markov chain dynamics and discount its stationary distribution -that is, we take as reference process the dynamics at infinite time -we obtain the standard formulation of the Markov stability. Notably, the possibility to use finite-time transition probabilities to define the reference process naturally allows detecting communities at different resolutions, without the need to consider a continuous-time Markov chain in the small time limit. The main advantage of our general formulation of Markov stability based on dynamical flows is that we work with lumped Markov chains on network partitions, having the same stationary distribution of the original process. In this way the form of the quality function becomes invariant under partitioning, leading to a self-consistent definition of community structures at different aggregation scales.
Journal of Informetrics, 2017
The Journal of Network Theory in Finance, 2018
55100 Lucca (Italy) 3 Istituto dei Sistemi Complessi (ISC)-CNR UoS "Sapienza"-00185 Rome (Italy) ... more 55100 Lucca (Italy) 3 Istituto dei Sistemi Complessi (ISC)-CNR UoS "Sapienza"-00185 Rome (Italy) 4 INFN Roma1 unit-00185 Rome (Italy) 5 CC&G S.p.A. London Stock Exchange Group-00186 Rome (Italy) In the last years, increasing efforts have been put into the development of effective stress tests to quantify the resilience of financial institutions. Here we propose a stress test methodology for central counterparties based on a network characterization of clearing members, whose links correspond to direct credits and debits. This network constitutes the ground for the propagation of financial distress: equity losses caused by an initial shock with both exogenous and endogenous components reverberate within the network and are amplified through credit and liquidity contagion channels. At the end of the dynamics, we determine the vulnerability of each clearing member, which represents its potential equity loss. We apply the proposed framework to the Fixed Income asset class of CC&G, the central counterparty operating in Italy whose main cleared securities are Italian Government Bonds. We consider two different scenarios: a distributed, plausible initial shock, as well as a shock corresponding to the cover 2 regulatory requirement (i.e., the simultaneous default of the two most exposed clearing members). Although the two situations lead to similar results after an unlimited reverberation of shocks on the network, the distress propagation is much more hasty in the latter case, with a large number of additional defaults triggered at early stages of the dynamics. Our results thus show that setting a default fund to cover insolvencies only on a cover 2 basis may not be adequate for taming systemic events, and only very conservative default fundssuch as CC&G's one-can face total losses due to the shock propagation. Overall, our network-based stress test represents a refined tool for calibrating default fund amounts.
Computer Physics Communications, 2002
The role of geometrical micro-barriers on the conversion efficiency of reactive flows in narrow t... more The role of geometrical micro-barriers on the conversion efficiency of reactive flows in narrow threedimensional channels of millimetric size is investigated. Using a Lattice-Boltzmann-Lax-Wendroff code, we show that micro-barriers have an appreciable effect on the effective reaction efficiency of the device. If extrapolated to macroscopic scales, these effects can result in a sizeable increase of the overall reaction efficiency.
Journal of Informetrics, 2016
We discuss, at the macro-level of nations, the contribution of research funding and rate of inter... more We discuss, at the macro-level of nations, the contribution of research funding and rate of international collaboration to research performance, with important implications for the "science of science policy". In particular, we cross-correlate suitable measures of these quantities with a scientometric-based assessment of scientific success, studying both the average performance of nations and their temporal dynamics in the space defined by these variables during the last decade. We find significant differences among nations in terms of efficiency in turning (financial) input into bibliometrically measurable output, and we confirm that growth of international collaboration positively correlate with scientific success-with significant benefits brought by EU integration policies. Various geo-cultural clusters of nations naturally emerge from our analysis. We critically discuss the factors that potentially determine the observed patterns.
EPL, Nov 1, 2001
This paper focuses on the statistical properties of wild-land fires and, in particular, investiga... more This paper focuses on the statistical properties of wild-land fires and, in particular, investigates if spread dynamics relates to simple invasion model. The fractal dimension and lacunarity of three fire scars classified from satellite imagery are analysed. Results indicate that the burned clusters behave similarly to percolation clusters on boundaries and look more dense in their core. We show that Dynamical Percolation reproduces this behaviour and can help to describe the fire evolution. By mapping fire dynamics onto the percolation models the strategies for fire control might be improved.
arXiv (Cornell University), 2001
In this lecture we clarify the basic difference between the correlation properties for systems ch... more In this lecture we clarify the basic difference between the correlation properties for systems characterized by small or large fluctuations. The concepts of correlation length, homogeneity scale, scale invariance and criticality are discussed as well. We relate these concepts to the interpretation of galaxy clsutering.
International Journal of Modern Physics B, May 30, 1998
The study of phenomena such as capillary displacement in porous media, fracture propagation, and ... more The study of phenomena such as capillary displacement in porous media, fracture propagation, and interface dynamics in quenched random media has attracted a great deal of interest in the last few years. This class of problems does not seem to be treatable with the standard theoretical methods, and the only analytical results come from scaling theory or mapping, for some of their properties, to other solvable models. In this paper a recently proposed approach to problems with extremal dynamics in quenched disordered media, named run time statistics ͑RTS͒ or quenched-stochastic transformation, is described in detail. This method allows us to map a quenched dynamics such as invasion percolation onto a stochastic annealed process with cognitive memory. By combining RTS with the fixed scale transformation approach, we develop a general and systematic theoretical method to compute analytically the critical exponents of invasion percolation, with and without trapping, and directed invasion percolation. In addition we can also understand and describe quantitatively the self-organized nature of the process. ͓S1063-651X͑96͒07207-8͔
Journal of Statistical Mechanics: Theory and Experiment, Jul 1, 2022
A set of discrete individual points located in an embedding continuum space can be seen as percol... more A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical ecology to analyze, e.g., the spatial percolation of a tree species in a tropical forest or a savanna. Here, we revisit the problem of aggregating random points in continuum systems (from 2 to 6−dimensional Euclidean spaces) to analyze the nature of the corresponding percolation transition in spatial point processes. This problem finds a natural description in terms of the canonical ensemble but not in the usual grand-canonical one, customarily employed to describe percolation transitions. This leads us to analyze the question of ensemble equivalence and study whether the resulting canonical continuum percolation transition shares its universal properties with standard percolation transitions, analyzing diverse homogeneous and heterogeneous spatial point processes. We, therefore, provide a powerful tool to characterize and classify a vast class of natural point patterns, revealing their fundamental properties based on percolation phase transitions.
arXiv (Cornell University), Nov 12, 2019
Rank size plots of very different systems are usually fitted with Zipf's law, however, one often ... more Rank size plots of very different systems are usually fitted with Zipf's law, however, one often observes strong deviations at large sizes. We show that these deviations contain essential and general information on the evolution and the intrinsic cutoffs of the system. In particular, if the first ranks show deviations from Zipf's law, the empirical maximum represents the intrinsic upper cutoff of the physical system. Moreover, pure Zipf's law is always present whenever the underlying power-law size distribution is undersampled.
Bulletin of the American Physical Society, Feb 27, 2012
"Quasistationary" states are approximately time-independent out of equilibrium states which have ... more "Quasistationary" states are approximately time-independent out of equilibrium states which have been observed in a variety of systems of particles interacting by longrange interactions. We investigate here the conditions of their occurrence for a generic pair interaction V (r → ∞) ∼ 1/r γ with γ > 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 γ < d − 1, the existence of quasi-stationary states is ensured by the large distance behavior of the interaction alone, while for γ > 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.
Physical Review Letters, Aug 25, 1997
We analyze the combined effect of a Laplacian field and quenched disorder for the generation of f... more We analyze the combined effect of a Laplacian field and quenched disorder for the generation of fractal structures with a study, both numerical and theoretical, of the quenched dielectric breakdown model (QDBM). The growth dynamics is shown to evolve from the avalanches of invasion percolation (IP) to the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation (DLA) and the dielectric breakdown model (DBM). The fractal dimension is strongly reduced with respect to both DBM and IP, due to the combined effect of memory and field screening. This implies a specific relation between the fractal dimension of the breakdown structures (dielectric or mechanical) and the microscopic properties of disordered materials.
arXiv (Cornell University), Mar 9, 2010
We present a new approach of topology biased random walks for undirected networks. We focus on a ... more 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 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 ad hoc algorithms for the exploration of complex networks and their communities.
Probabilistic approach to the Bak-Sneppen model
Physical review, Mar 18, 2002
Renormalization-group study of one-dimensional systems with roughening transitions
Physical review, Oct 1, 1999
Physical Review E, Sep 29, 2015
We investigate stochastic models of particles entering a channel with a random time distribution.... more We investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value N , a blockage occurs and the particle flux is definitively interrupted. By introducing an integral representation of the n particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particle and their time correlation. We generalize previous results for N = 2 to an arbitrary distribution of entry times and obtain new, exact solutions for N = 3 for a Poisson distribution and partial results for N ≥ 4.
Physical review, Sep 5, 2017
We explore the formation and relaxation of so-called quasi-stationary states (QSS) for particle d... more We explore the formation and relaxation of so-called quasi-stationary states (QSS) for particle distributions in three dimensions interacting via an attractive radial pair potential V (r → ∞) ∼ 1/r γ with γ > 0, and either a soft-core or hard-core regularization at small r. In the first part of the paper we generalize, for any spatial dimension d ≥ 2, Chandrasekhar's approach for the case of gravity to obtain analytic estimates of the rate of collisional relaxation due to two body collisions. The resultant relaxation rates indicate an essential qualitative difference depending on the integrability of the pair force at large distances: for γ > d − 1 the rate diverges in the large particle number N (mean field) limit, unless a sufficiently large soft core is present; for γ < d − 1, on the other hand, the rate vanishes in the same limit even in the absence of any regularization. In the second part of the paper we compare our analytical predictions with the results of extensive parallel numerical simulations in d = 3 performed with an appropriate modification of the GADGET code, for a range of different exponents γ and soft cores leading to the formation of QSS. We find, just as for the previously well studied case of gravity (which we also revisit), excellent agreement between the parametric dependence of the observed relaxation times and our analytic predictions. Further, as in the case of gravity, we find that the results indicate that, when large impact factors dominate, the appropriate cutoff is the size of the system (rather than, for example, the mean inter-particle distance). Our results provide strong evidence that the existence of QSS is robust only for longrange interactions with a large distance behavior γ < d − 1; for γ ≥ d − 1 the existence of such states will be conditioned strongly on the short range properties of the interaction.
Physical review research, Jan 27, 2021
The rank-size plots of a large number of different physical and socioeconomic systems are usually... more The rank-size plots of a large number of different physical and socioeconomic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a dynamical approach is crucial: during their evolution, some systems are attracted towards Zipf's law, while others present Zipf's law only temporarily and, therefore, spuriously. A truly Zipfian dynamics is characterized by a dynamical constraint, or coherence, among the parameters of the generating PDF, and the number of elements in the system. A clear-cut example of such coherence is natural language. Our framework allows us to derive some quantitative results that go well beyond the usual Zipf's law: (i) earthquakes can evolve only incoherently and thus show Zipf's law spuriously; this allows an assessment of the largest possible magnitude of an earthquake occurring in a geographical region. (ii) We prove that Zipfian dynamics are not additive, explaining analytically why US cities evolve coherently, while world cities do not. (iii) Our concept of coherence can be used for model selection, for example, the Yule-Simon process can describe the dynamics of world countries' GDP. (iv) World cities present spurious Zipf's law and we use this property for estimating the maximal population of an urban agglomeration.
arXiv (Cornell University), Dec 23, 2019
A recent paper by Hausmann and collaborators (1) reaches the important conclusion that Complexity... more A recent paper by Hausmann and collaborators (1) reaches the important conclusion that Complexity-weighted diversification is the essential element to predict country growth. We like this result because Complexity-weighted diversification is precisely the first equation of the Fitness algorithm that we introduced in 2012 (2,3). However, contrary to what is claimed in (1), it is incorrect to say that diversification is contained also in the ECI algorithm (4). We discuss the origin of this misunderstanding and show that the ECI algorithm contains exactly zero diversification. This is actually one of the reasons for the poor performances of ECI which leads to completely unrealistic results, as for instance, the derivation that Qatar or Saudi Arabia are industrially more competitive than China (5,6). Another important element of our new approach is the representation of the economic dynamics of countries as trajectories in the GDPpc-Fitness space (7-10). In some way also this has been rediscovered by Hausmann and collaborators and renamed as "Stream plots", but, given their weaker metrics and methods, they propose it to use it only for a qualitative insight, while ours led to quantitative and successful forecasting. The Fitness approach has paved the way to a robust and testable framework for Economic Complexity resulting in a highly competitive scheme for growth forecasting (7-10). According to a recent report by Bloomberg (9): The new Fitness method, "systematically outperforms standard methods, despite requiring much less data".
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Papers by Andrea Gabrielli