arXiv subjects

Francisco A. Rodrigues

Publications and source records attributed to Francisco A. Rodrigues.

At least 55 records · Page 3Linked to original sources

arXiv2020

Universality of eigenvector delocalization and the nature of the SIS phase transition in multiplex networks

Universal spectral properties of multiplex networks allow us to assess the nature of the transition between disease-free and endemic phases in the SIS epidemic spreading model. In a multiplex network, depending on a coupling parameter, $p$, the inverse participation ratio ($IPR$) of the leading eigenvector of the adjacency matrix can be in two different structural regimes: (i) layer-localized and (ii) delocalized. Here we formalize the structural transition point, $p^*$, between these two regimes, showing that there are universal properties regarding both the layer size $n$ and the layer configurations. Namely, we show that $IPR \sim n^{-δ}$, with $δ\approx 1$, and revealed an approximately linear relationship between $p^*$ and the difference between the layers' average degrees. Furthermore, we showed that this multiplex structural transition is intrinsically connected with the nature of the SIS phase transition, allowing us to both understand and quantify the phenomenon. As these results are related to the universal properties of the leading eigenvector, we expect that our findings might be relevant to other dynamical processes in complex networks.

physics.soc-ph↗

arXiv2020

Power laws distributions in objective priors

The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the posterior distribution. However, these priors are typically improper and may lead to improper posterior. Here, we show, for a general family of distributions, that the obtained objective priors for the parameters either follow a power-law distribution or has an asymptotic power-law behavior. As a result, we observed that the exponents of the model are between 0.5 and 1. Understand these behaviors allow us to easily verify if such priors lead to proper or improper posteriors directly from the exponent of the power-law. The general family considered in our study includes essential models such as Exponential, Gamma, Weibull, Nakagami-m, Haf-Normal, Rayleigh, Erlang, and Maxwell Boltzmann distributions, to list a few. In summary, we show that comprehending the mechanisms describing the shapes of the priors provides essential information that can be used in situations where additional complexity is presented.

math.ST↗

arXiv2020

Centrality anomalies in complex networks as a result of model over-simplification

Tremendous advances have been made in our understanding of the properties and evolution of complex networks. These advances were initially driven by information-poor empirical networks and theoretical analysis of unweighted and undirected graphs. Recently, information-rich empirical data complex networks supported the development of more sophisticated models that include edge directionality and weight properties, and multiple layers. Many studies still focus on unweighted undirected description of networks, prompting an essential question: how to identify when a model is simpler than it must be? Here, we argue that the presence of centrality anomalies in complex networks is a result of model over-simplification. Specifically, we investigate the well-known anomaly in betweenness centrality for transportation networks, according to which highly connected nodes are not necessarily the most central. Using a broad class of network models with weights and spatial constraints and four large data sets of transportation networks, we show that the unweighted projection of the structure of these networks can exhibit a significant fraction of anomalous nodes compared to a random null model. However, the weighted projection of these networks, compared with an appropriated null model, significantly reduces the fraction of anomalies observed, suggesting that centrality anomalies are a symptom of model over-simplification. Because lack of information-rich data is a common challenge when dealing with complex networks and can cause anomalies that misestimate the role of nodes in the system, we argue that sufficiently sophisticated models be used when anomalies are detected.

physics.soc-ph↗

arXiv2019

A machine learning approach to predicting dynamical observables from network structure

Estimating the outcome of a given dynamical process from structural features is a key unsolved challenge in network science. The goal is hindered by difficulties associated to nonlinearities, correlations and feedbacks between the structure and dynamics of complex systems. In this work, we develop an approach based on machine learning algorithms that is shown to provide an answer to the previous challenge. Specifically, we show that it is possible to estimate the outbreak size of a disease starting from a single node as well as the degree of synchronicity of a system made up of Kuramoto oscillators. In doing so, we show which topological features of the network are key for this estimation, and provide a rank of the importance of network metrics with higher accuracy than previously done. Our approach is general and can be applied to any dynamical process running on top of complex networks. Likewise, our work constitutes an important step towards the application of machine learning methods to unravel dynamical patterns emerging in complex networked systems.

physics.soc-ph↗

arXiv2019

Epidemic spreading with awareness and different timescales in multiplex networks

One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as individuals aware of the presence of a disease can take measures to reduce their exposure to contagion. In this paper, we propose a mathematical model for the spread of diseases with awareness in complex networks. Unlike previous models, the information is propagated following a generalized Maki-Thompson rumor model. Flexibility on the timescale between information and disease spreading is also included. We verify that the velocity characterizing the diffusion of information awareness greatly influences the disease prevalence. We also show that a reduction in the fraction of unaware individuals does not always imply a decrease of the prevalence, as the relative timescale between disease and awareness spreading plays a crucial role in the systems' dynamics. This result is shown to be independent of the network topology. We finally calculate the epidemic threshold of our model, and show that it does not depend on the relative timescale. Our results provide a new view on how information influence disease spreading and can be used for the development of more efficient methods for disease control.

physics.soc-ph↗

arXiv2019

The nested structural organization of the worldwide trade multi-layer network

Nestedness has traditionally been used to detect assembly patterns in meta-communities and networks of interacting species. Attempts have also been made to uncover nested structures in international trade, typically represented as bipartite networks in which connections can be established between countries (exporters or importers) and industries. A bipartite representation of trade, however, inevitably neglects transactions between industries. To fully capture the organization of the global value chain, we draw on the World Input-Output Database and construct a multi-layer network in which the nodes are the countries, the layers are the industries, and links can be established from sellers to buyers within and across industries. We define the buyers' and sellers' participation matrices in which the rows are the countries and the columns are all possible pairs of industries, and then compute nestedness based on buyers' and sellers' involvement in transactions between and within industries. Drawing on appropriate null models that preserve the countries' or layers' degree distributions in the original multi-layer network, we uncover variations of country- and transaction-based nestedness over time, and identify the countries and industries that most contributed to nestedness. We discuss the implications of our findings for the study of the international production network and other real-world systems.

physics.soc-ph↗

arXiv2019

Collective dynamics of random Janus oscillator networks

Janus oscillators have been recently introduced as a remarkably simple phase oscillator model that exhibits non-trivial dynamical patterns -- such as chimeras, explosive transitions, and asymmetry-induced synchronization -- that once were only observed in specifically tailored models. Here we study ensembles of Janus oscillators coupled on large homogeneous and heterogeneous networks. By virtue of the Ott-Antonsen reduction scheme, we find that the rich dynamics of Janus oscillators persists in the thermodynamic limit of random regular, Erdős-Rényi and scale-free random networks. We uncover for all these networks the coexistence between partially synchronized state and a multitude of states displaying global oscillations. Furthermore, abrupt transitions of the global and local order parameters are observed for all topologies considered. Interestingly, only for scale-free networks, it is found that states displaying global oscillations vanish in the thermodynamic limit.

nlin.AO↗

arXiv2019

Fundamentals of spreading processes in single and multilayer complex networks

Spreading processes have been largely studied in the literature, both analytically and by means of large-scale numerical simulations. These processes mainly include the propagation of diseases, rumors and information on top of a given population. In the last two decades, with the advent of modern network science, we have witnessed significant advances in this field of research. Here we review the main theoretical and numerical methods developed for the study of spreading processes on complex networked systems. Specifically, we formally define epidemic processes on single and multilayer networks and discuss in detail the main methods used to perform numerical simulations. Throughout the review, we classify spreading processes (disease and rumor models) into two classes according to the nature of time: (i) continuous-time and (ii) cellular automata approach, where the second one can be further divided into synchronous and asynchronous updating schemes. Our revision includes the heterogeneous mean-field, the quenched-mean field, and the pair quenched mean field approaches, as well as their respective simulation techniques, emphasizing similarities and differences among the different techniques. The content presented here offers a whole suite of methods to study epidemic-like processes in complex networks, both for researchers without previous experience in the subject and for experts.

physics.soc-ph↗

arXiv2019

On the onset of synchronization of Kuramoto oscillators in scale-free networks

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent $2 < γ\leq 3$, in line with what has been observed for other dynamical processes in such networks. For $γ> 3$, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators.

cond-mat.stat-mech↗

arXiv2019

Multifractality in random networks with power-law decaying bond strengths

In this paper we demonstrate numerically that random networks whose adjacency matrices ${\bf A}$ are represented by a diluted version of the Power--Law Banded Random Matrix (PBRM) model have multifractal eigenfunctions. The PBRM model describes one--dimensional samples with random long--range bonds. The bond strengths of the model, which decay as a power--law, are tuned by the parameter $μ$ as $A_{mn}\propto |m-n|^{-μ}$; while the sparsity is driven by the average network connectivity $α$: for $α=0$ the vertices in the network are isolated and for $α=1$ the network is fully connected and the PBRM model is recovered. Though it is known that the PBRM model has multifractal eigenfunctions at the critical value $μ=μ_c=1$, we clearly show [from the scaling of the relative fluctuation of the participation number $I_2$ as well as the scaling of the probability distribution functions $P(\ln I_2)$] the existence of the critical value $μ_c\equiv μ_c(α)$ for $α<1$. Moreover, we characterise the multifractality of the eigenfunctions of our random network model by the use of the corresponding multifractal dimensions $D_q$, that we compute from the finite network-size scaling of the typical eigenfunction participation numbers $\exp\left\langle\ln I_q \right\rangle$.

physics.soc-ph↗

arXiv2019

Layer degradation triggers an abrupt structural transition in multiplex networks

Network robustness is a central point in network science, both from a theoretical and a practical point of view. In this paper, we show that layer degradation, understood as the continuous or discrete loss of links' weight, triggers a structural transition revealed by an abrupt change in the algebraic connectivity of the graph. Unlike traditional single layer networks, multiplex networks exist in two phases, one in which the system is protected from link failures in some of its layers and one in which all the system senses the failure happening in one single layer. We also give the exact critical value of the weight of the intra-layer links at which the transition occurs for continuous layer degradation and its relation to the value of the coupling between layers. This relation allows us to reveal the connection between the transition observed under layer degradation and the one observed under the variation of the coupling between layers.

physics.soc-ph↗

arXiv2019

Mobility helps problem-solving systems to avoid Groupthink

Groupthink occurs when everyone in a group starts thinking alike, as when people put unlimited faith in a leader. Avoiding this phenomenon is a ubiquitous challenge to problem-solving enterprises and typical countermeasures involve the mobility of group members. Here we use an agent-based model of imitative learning to study the influence of the mobility of the agents on the time they require to find the global maxima of NK-fitness landscapes. The agents cooperate by exchanging information on their fitness and use this information to copy the fittest agent in their influence neighborhoods, which are determined by face-to-face interaction networks. The influence neighborhoods are variable since the agents perform random walks in a two-dimensional space. We find that mobility is slightly harmful for solving easy problems, i.e. problems that do not exhibit suboptimal solutions or local maxima. For difficult problems, however, mobility can prevent the imitative search being trapped in suboptimal solutions and guarantees a better performance than the independent search for any system size.

physics.soc-ph↗

arXiv2018

Impact of the distribution of recovery rates on disease spreading in complex networks

We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied structural heterogeneity. Our analytical solution is able to predict the shift in the critical properties induced by heterogeneous recovery rates. Additionally, we show that the critical value of infectivity tends to be smaller than the one predicted by quenched mean-field approaches in the homogeneous case and that it can be linked to the variance of the recovery rates. We then illustrate the role of dynamical--structural correlations, which allow for a complete change in the critical behavior. We show that it is possible for a power-law network topology to behave similarly to a homogeneous structure by an appropriate tuning of its recovery rates, and vice versa. Finally, we show how heterogeneity in recovery rates affects the network localization properties of the spreading process.

physics.soc-ph↗

arXiv2018

Unfolding the complexity of the global value chain: Strengths and entropy in the single-layer, multiplex, and multi-layer international trade networks

The worldwide trade network has been widely studied through different data sets and network representations with a view to better understanding interactions among countries and products. Here we investigate international trade through the lenses of the single-layer, multiplex, and multi-layer networks. We discuss differences among the three network frameworks in terms of their relative advantages in capturing salient topological features of trade. We draw on the World Input-Output Database to build the three networks. We then uncover sources of heterogeneity in the way strength is allocated among countries and transactions by computing the strength distribution and entropy in each network. Additionally, we trace how entropy evolved, and show how the observed peaks can be associated with the onset of the global economic downturn. Findings suggest how more complex representations of trade, such as the multi-layer network, enable us to disambiguate the distinct roles of intra- and cross-industry transactions in driving the evolution of entropy at a more aggregate level. We discuss our results and the implications of our comparative analysis of networks for research on international trade and other empirical domains across the natural and social sciences.

physics.soc-ph↗

arXiv2018

Pattern Recognition Approach to Violin Shapes of MIMO database

Since the landmarks established by the Cremonese school in the 16th century, the history of violin design has been marked by experimentation. While great effort has been invested since the early 19th century by the scientific community on researching violin acoustics, substantially less attention has been given to the statistical characterization of how the violin shape evolved over time. In this paper we study the morphology of violins retrieved from the Musical Instrument Museums Online (MIMO) database -- the largest freely accessible platform providing information about instruments held in public museums. From the violin images, we derive a set of measurements that reflect relevant geometrical features of the instruments. The application of Principal Component Analysis (PCA) uncovered similarities between violin makers and their respective copyists, as well as among luthiers belonging to the same family lineage, in the context of historical narrative. Combined with a time-windowed approach, thin plate splines visualizations revealed that the average violin outline has remained mostly stable over time, not adhering to any particular trends of design across different periods in music history.

stat.AP↗

arXiv2018

A polynomial eigenvalue approach for multiplex networks

We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive interesting results based on an interpretation of the traditional eigenvalue problem. More specifically, we reduce the dimensionality of our matrices but increase the power of the characteristic polynomial, i.e, a polynomial eigenvalue problem. Such an approach may sound counterintuitive at first glance, but it allows us to relate the quadratic problem for a 2-Layer multiplex system with the spectra of the aggregated network and to derive bounds for the spectra, among many other interesting analytical insights. Furthermore, it also permits to directly obtain analytical and numerical insights on the eigenvalue behavior as a function of the coupling between layers. Our study includes the supra-adjacency, supra-Laplacian, and the probability transition matrices, which enable us to put our results under the perspective of structural phases in multiplex networks. We believe that this formalism and the results reported will make it possible to derive new results for multiplex networks in the future.

physics.soc-ph↗

arXiv2018

Spectra of random networks in the weak clustering regime

The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values of the clustering coefficient. Here we study effects of cycles of order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectral distribution of the network adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Implications to network dynamics are discussed. Our findings can shed light in the study of how particular kinds of subgraphs influence network dynamics.

physics.soc-ph↗

arXiv2017

The role of city size and urban metrics on crime modeling

Unveiling the relationships between crime and socioeconomic factors is crucial for modeling and preventing these illegal activities. Recently, a significant advance has been made in understanding the influence of urban metrics on the levels of crime in different urban systems. In this chapter, we show how the dynamics of crime growth rate and the number of crime in cities are related to cities' size. We also discuss the role of urban metrics in crime modeling within the framework of the urban scaling hypothesis, where a data-driven approach is proposed for modeling crime. This model provides several insights into the mechanism ruling the dynamics of crime and can assist policymakers in making better decisions on resource allocation and help crime prevention.

physics.soc-ph↗