Papers by Ignacio Perotti
arXiv (Cornell University), Nov 20, 2014
Interactions in time-varying complex systems are often very heterogeneous at the topological leve... more Interactions in time-varying complex systems are often very heterogeneous at the topological level (who interacts with whom) and at the temporal level (when interactions occur and how often). While it is known that temporal heterogeneities often have strong effects on dynamical processes, e.g. the burstiness of contact sequences is associated with slower spreading dynamics, the picture is far from complete. In this paper, we show that temporal heterogeneities result in temporal sparsity at the time scale of average inter-event times, and that temporal sparsity determines the amount of slowdown of Susceptible-Infectious (SI) spreading dynamics on temporal networks. This result is based on the analysis of several empirical temporal network data sets. An approximate solution for a simple network model confirms the association between temporal sparsity and slowdown of SI spreading dynamics. Since deterministic SI spreading always follows the fastest temporal paths, our results generalize-paths are slower to traverse because of temporal sparsity, and therefore all dynamical processes are slower as well.
Zipf's law states that the frequencies of word apparitions in written texts are ranked follow... more Zipf's law states that the frequencies of word apparitions in written texts are ranked following a power law. This law is a robust statistical property observed both in translated and untranslated languages. Interestingly, this law seems to be also manifested in music records where several metrics take the place of words---the canonical choice of Zipfian units in written texts---but finding an accurate analogous of the concept of words in music is difficult because lacks a functional semantic. This yields to the question of which are the proper Zipfian units in music, and even in other contexts. In particular, in written texts, several alternatives had been proposed besides the canonical use of words, seeking to extend the range of validity of Zipf's law. In this work we perform a comparative statistical analysis of musical scores and literary texts, to seek and validate a natural election of Zipfian units in music. We found that Zipf's law emerges in music when chords a...
Physical Review E, 2020
The study of network robustness focuses on the way the overall functionality of a network is affe... more The study of network robustness focuses on the way the overall functionality of a network is affected as some of its constituent parts fail. Failures can occur at random or be part of an intentional attack and, in general, networks behave differently against different removal strategies. Although much effort has been put on this topic, there is no unified framework to study the problem. While random failures have been mostly studied under percolation theory, targeted attacks have been recently restated in terms of network dismantling. In this work, we link these two approaches by performing a finite-size scaling analysis to four dismantling strategies over Erdös-Rényi networks: initial and recalculated high degree removal and initial and recalculated high betweenness removal. We find that the critical exponents associated with the initial attacks are consistent with the ones corresponding to random percolation, while the recalculated attacks are likely to belong to different universality classes. In particular, recalculated betweenness produces a very abrupt transition with a hump in the cluster size distribution near the critical point, resembling some explosive percolation processes.
arXiv: Physics and Society, 2020
Collective dynamics studies of team sports such as football is a hard task involving large amount... more Collective dynamics studies of team sports such as football is a hard task involving large amounts of data and analysis. In this contribution we aim to address a particular subject of this broad field such as the dynamics of the ball possession intervals. To this end we have analyzed a novel football database comprising one season of the five major leagues of Europe. First we obtained the key elements of ball possession dynamics from a statistical analysis of the database. Using this input we developed a simple stochastic model based on three agents, two teammates, and one defender. This model includes four parameters and can capture the main emergent statistical observables of the ball possession intervals in the database: the distribution of (i) possession time, (ii) the number of passes performed, and (iii) the ball distance traveled on passes. In the last part, we show that the dynamics of the model, can be mapped into a Wiener process with a drift and an absorbing barrier.
Many complex systems can be described by networks, in which nodes represent the constituent compo... more Many complex systems can be described by networks, in which nodes represent the constituent components and edges represent connections between them. A fundamental issue concerning networked systems is their robustness to the failure of its elements. Since the degree to which the system continues functioning, as its components are degraded, typically depends on the integrity of the underlying network, the question of system robustness can be addressed by analyzing how the network structure changes as nodes are removed. Of special importance is the case of directed attacks, where nodes are removed in decreasing order of importance. Node importance is typically identified using centrality measures, such as its degree or betweenness. Networks with a broad degree distribution are fragile against attacks on their hubs. On the other hand, homogeneous networks are expected to be more robust. There exist, nonetheless, exceptions to this rule; real systems such as power grids and road network...
Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is kno... more Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects we devise an analytically solvable model of Susceptible-Infected (SI) spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.
Physical Review E, 2020
In this contribution, we study the interaction dynamics in the game of football-soccer in the con... more In this contribution, we study the interaction dynamics in the game of football-soccer in the context of ball possession intervals. To do so, we analyze a novel database, comprising one season of the five major football leagues of Europe. Using this input, we developed a stochastic model based on three agents: two teammates and one defender. Despite its simplicity, the model is able to capture, in good approximation, the statistical behavior of possession times, passes lengths, and number of passes performed. In the last part, we show that the model's dynamics can be mapped into a Wiener process with drift and an absorbing barrier.
Chaos, Solitons & Fractals, 2021
Percolation transition on Delaunay graphs based on betweenness and range-limited betweenness cent... more Percolation transition on Delaunay graphs based on betweenness and range-limited betweenness centrality attacks. • Finite-size scaling analysis and critical exponent derivation. • Continuous and discontinuous transitions depending on the range of interactions.
Physical Review E, 2020
Complex systems often exhibit multiple levels of organization covering a wide range of physical s... more Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this phenomenon, we introduce a generalization of information theory that works with hierarchical partitions. We begin revisiting the recently introduced Hierarchical Mutual Information (HMI), and show that it can be written as a level by level summation of classical conditional mutual information terms. Then, we prove that the HMI is bounded from above by the corresponding hierarchical joint entropy. In this way, in analogy to the classical case, we derive hierarchical generalizations of many other classical information-theoretic quantities. In particular, we prove that, as opposed to its classical counterpart, the hierarchical generalization of the Variation of Information is not a metric distance, but it admits a transformation into one. Moreover, focusing on potential applications of the existing developments of the theory, we show how to adjust by chance the HMI. We also corroborate and analyze all the presented theoretical results with exhaustive numerical computations, and include an illustrative application example of the introduced formalism. Finally, we mention some open problems that should be eventually addressed for the proposed generalization of information theory to reach maturity.
Physica A: Statistical Mechanics and its Applications, 2020
Zipf's law is found when the vocabulary of long written texts is ranked according to the frequenc... more Zipf's law is found when the vocabulary of long written texts is ranked according to the frequency of word occurrences, establishing a power-law decay for the frequency vs rank relation. This law is a robust statistical property observed even in ancient untranslated languages. Interestingly, this law seems to be also manifested in music records when several metrics-functioning as words in written texts-are used. Even though music can be regarded as a language, finding an accurate equivalent of the concept of words in music is difficult because it lacks a functional semantic. This raises the question of which is the appropriate choice of Zipfian units in music, which is extensive to other contexts where this law can emerge. In particular, this is still an open question in written texts, where several alternatives have been proposed as Zipfian units besides the canonical use of words. Seeking to validate a natural election of Zipfian units in music, in this work we find that Zipf's law emerges when a combination of chords and notes are chosen as Zipfian units. Our results are grounded on a consistent analysis of the statistical properties of music and texts, complemented with theoretical considerations that combine different reference models, including a simple model inspired in the Lempel-Ziv compression algorithm that we have devised to explain the emergence of Zipfs law as the consequence of languages evolving into more efficient forms of communication.
Physical Review E, 2019
Evidence of critical dynamics has been recently found in both experiments and models of large sca... more Evidence of critical dynamics has been recently found in both experiments and models of large scale brain dynamics. The understanding of the nature and features of such critical regime is hampered by the relatively small size of the available connectome, which prevent among other things to determine its associated universality class. To circumvent that, here we study a neural model defined on a class of small-world network that share some topological features with the human connectome. We found that varying the topological parameters can give rise to a scale-invariant behavior belonging either to mean field percolation universality class or having non universal critical exponents. In addition, we found certain regions of the topological parameters space where the system presents a discontinuous (i.e., non critical) dynamical phase transition into a percolated state. Overall these results shed light on the interplay of dynamical and topological roots of the complex brain dynamics.
Physical Review E, 2018
In this work we introduce a variant of the Yule-Simon model for preferential growth by incorporat... more In this work we introduce a variant of the Yule-Simon model for preferential growth by incorporating a finite kernel to model the effects of bounded memory. We characterize the properties of the model combining analytical arguments with extensive numerical simulations. In particular, we analyze the lifetime and popularity distributions by mapping the model dynamics to corresponding Markov chains and branching processes, respectively. These distributions follow power-laws with well defined exponents that are within the range of the empirical data reported in ecologies. Interestingly, by varying the innovation rate, this simple out-of-equilibrium model exhibits many of the characteristics of a continuous phase transition and, around the critical point, it generates time series with power-law popularity, lifetime and inter-event time distributions, and non-trivial temporal correlations, such as a bursty dynamics in analogy with the activity of solar flares. Our results suggest that an appropriate balance between innovation and oblivion rates could provide an explanatory framework for many of the properties commonly observed in many complex systems.
Physical review. E, 2017
Hierarchical organization is an important, prevalent characteristic of complex systems; to unders... more Hierarchical organization is an important, prevalent characteristic of complex systems; to understand their organization, the study of the underlying (generally complex) networks that describe the interactions between their constituents plays a central role. Numerous previous works have shown that many real-world networks in social, biologic, and technical systems present hierarchical organization, often in the form of a hierarchy of community structures. Many artificial benchmark graphs have been proposed to test different community detection methods, but no benchmark has been developed to thoroughly test the detection of hierarchical community structures. In this study, we fill this vacancy by extending the Lancichinetti-Fortunato-Radicchi (LFR) ensemble of benchmark graphs, adopting the rule of constructing hierarchical networks proposed by Ravasz and Barabási. We employ this benchmark to test three of the most popular community detection algorithms and quantify their accuracy us...
Scientific reports, Jan 9, 2017
Chess is an emblematic sport that stands out because of its age, popularity and complexity. It ha... more Chess is an emblematic sport that stands out because of its age, popularity and complexity. It has served to study human behavior from the perspective of a wide number of disciplines, from cognitive skills such as memory and learning, to aspects like innovation and decision-making. Given that an extensive documentation of chess games played throughout history is available, it is possible to perform detailed and statistically significant studies about this sport. Here we use one of the most extensive chess databases in the world to construct two networks of chess players. One of the networks includes games that were played over-the-board and the other contains games played on the Internet. We study the main topological characteristics of the networks, such as degree distribution and correlations, transitivity and community structure. We complement the structural analysis by incorporating players' level of play as node metadata. Although both networks are topologically different, ...
PloS one, 2016
A series of recent works studying a database of chronologically sorted chess games-containing 1.4... more A series of recent works studying a database of chronologically sorted chess games-containing 1.4 million games played by humans between 1998 and 2007- have shown that the popularity distribution of chess game-lines follows a Zipf's law, and that time series inferred from the sequences of those game-lines exhibit long-range memory effects. The presence of Zipf's law together with long-range memory effects was observed in several systems, however, the simultaneous emergence of these two phenomena were always studied separately up to now. In this work, by making use of a variant of the Yule-Simon preferential growth model, introduced by Cattuto et al., we provide an explanation for the simultaneous emergence of Zipf's law and long-range correlations memory effects in a chess database. We find that Cattuto's Model (CM) is able to reproduce both, Zipf's law and the long-range correlations, including size-dependent scaling of the Hurst exponent for the corresponding t...
PLOS ONE, 2016
We consider a dynamical model of distress propagation on complex networks, which we apply to the ... more We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall the stability of the system increases between 2008 and 2013.
Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is kno... more Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects we devise an analytically solvable model of Susceptible-Infected (SI) spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.
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Papers by Ignacio Perotti