Code is available. See the HOWTO.}, keywords = {Condensed Matter - Statistical Mechanics, Physics - Data Analysis, Statistics and Probability, Statistics - Machine Learning}, file = {arXiv\:1705.10225 PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/EQFK6NP5/Peixoto - 2017 - Bayesian stochastic blockmodeling.pdf:application/pdf;arXiv.org Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/G73CQIS5/1705.html:text/html} }, @article{valles-catala_consistency_2017, title = {On the consistency between model selection and link prediction in networks}, url = {http://arxiv.org/abs/1705.07967}, abstract = {A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand, discounting statistical fluctuations. This problem can be approached using two principled criteria that at first may seem equivalent: selecting the most plausible model in terms of its posterior probability; or selecting the model with the highest predictive performance in terms of identifying missing links. Here we show that while these two approaches yield consistent results in most of cases, there are also notable instances where they do not, that is, where the most plausible model is not the most predictive. We show that in the latter case the improvement of predictive performance can in fact lead to overfitting both in artificial and empirical settings. Furthermore, we show that, in general, the predictive performance is higher when we average over collections of models that are individually less plausible, than when we consider only the single most plausible model.}, urldate = {2017-05-25}, number = {}, journal = {}, author = {Vallès-Català, Toni and Peixoto, Tiago P. and Guimerà, Roger and Sales-Pardo, Marta}, month = may, year = {2017}, annote = {1705.07967}, comments = {Code is available. See the HOWTO.}, keywords = {Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Statistics - Machine Learning}, file = {arXiv\:1705.07967 PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/DEDP84K2/Vallès-Català et al. - 2017 - On the consistency between model selection and lin.pdf:application/pdf;arXiv.org Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/JEWH7RWB/1705.html:text/html} }, @article{peixoto_modelling_2017, type = {{arXiv} e-print}, title = {Modeling sequences and temporal networks with dynamic community structures}, url = {http://arxiv.org/abs/1509.04740}, abstract = {In evolving complex systems such as air traffic and social organisations, collective effects emerge from their many components’ dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and links that change over time, they remain highly complex. It is therefore often necessary to use methods that extract the temporal networks’ large-scale dynamic community structure. However, such methods are subject to overfitting or suffer from effects of arbitrary, a priori-imposed timescales, which should instead be extracted from data. Here we simultaneously address both problems and develop a principled data-driven method that determines relevant timescales and identifies patterns of dynamics that take place on networks, as well as shape the networks themselves. We base our method on an arbitrary-order Markov chain model with community structure, and develop a nonparametric Bayesian inference framework that identifies the simplest such model that can explain temporal interaction data.}, number = {}, urldate = {2017-09-19}, author = {Peixoto, Tiago P. and Rosvall, Martin}, month = sep, year = {2017}, keywords = {}, annote = {1509.04740}, doi = {10.1038/s41467-017-00148-9}, journal = {Nature Communications 8, 582}, file = {} }, @article{peixoto_nonparametric_2016, title = {Nonparametric Bayesian inference of the microcanonical stochastic block model}, url = {http://arxiv.org/abs/1610.02703}, abstract = {A principled approach to characterize the hidden modular structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: 1. Deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, that not only remove limitations that seriously degrade the inference on large networks, but also reveal structures at multiple scales; 2. A very efficient inference algorithm that scales well not only for networks with a large number of nodes and edges, but also with an unlimited number of modules. We show also how this approach can be used to sample modular hierarchies from the posterior distribution, as well as to perform model selection. Furthermore, we expose a direct equivalence between our microcanonical approach and alternative derivations based on the canonical SBM.}, number = {95}, pages = {012317}, urldate = {2016-10-12}, author = {Peixoto, Tiago P.}, month = oct, year = {2017}, annote = {1610.02703}, doi = {10.1103/PhysRevE.95.012317}, journal = {Phys. Rev. E}, comments = {Code is available. See the HOWTO.}, keywords = {}, file = {} }, @article{de_arruda_disease_2017, title = {Disease localization in multilayer networks}, volume = {7}, url = {http://link.aps.org/doi/10.1103/PhysRevX.7.011014}, doi = {10.1103/PhysRevX.7.011014}, abstract = {We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptible-infected-recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we report on an interesting phenomenon, the barrier effect; i.e., for a three-layer configuration, when the layer with the lowest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems, opening new possibilities for the study of spreading processes.}, number = {1}, annote = {1509.07054}, urldate = {2017-02-11}, journal = {Phys. Rev. X}, author = {de Arruda, Guilherme Ferraz and Cozzo, Emanuele and Peixoto, Tiago P. and Rodrigues, Francisco A. and Moreno, Yamir}, month = feb, year = {2017}, pages = {011014}, file = {APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/4BND9TJF/PhysRevX.7.html:text/html;Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/B5C6PFRC/de Arruda et al. - 2017 - Disease Localization in Multilayer Networks.pdf:application/pdf} }, @article{hric_network_2016, title = {Network structure, metadata, and the prediction of missing nodes and annotations}, volume = {6}, url = {http://link.aps.org/doi/10.1103/PhysRevX.6.031038}, doi = {10.1103/PhysRevX.6.031038}, abstract = {The empirical validation of community detection methods is often based on available annotations on the nodes that serve as putative indicators of the large-scale network structure. Most often, the suitability of the annotations as topological descriptors itself is not assessed, and without this it is not possible to ultimately distinguish between actual shortcomings of the community detection algorithms, on one hand, and the incompleteness, inaccuracy, or structured nature of the data annotations themselves, on the other. In this work, we present a principled method to access both aspects simultaneously. We construct a joint generative model for the data and metadata, and a nonparametric Bayesian framework to infer its parameters from annotated data sets. We assess the quality of the metadata not according to their direct alignment with the network communities, but rather in their capacity to predict the placement of edges in the network. We also show how this feature can be used to predict the connections to missing nodes when only the metadata are available, as well as predicting missing metadata. By investigating a wide range of data sets, we show that while there are seldom exact agreements between metadata tokens and the inferred data groups, the metadata are often informative of the network structure nevertheless, and can improve the prediction of missing nodes. This shows that the method uncovers meaningful patterns in both the data and metadata, without requiring or expecting a perfect agreement between the two.}, number = {3}, urldate = {2016-09-29}, journal = {Phys. Rev. X}, author = {Hric, Darko and Peixoto, Tiago P. and Fortunato, Santo}, month = sep, year = {2016}, pages = {031038}, annote = {1604.00255}, file = {} }, @article{newman_generalized_2015, type = {{arXiv} e-print}, title = {Generalized communities in networks}, url = {http://arxiv.org/abs/1505.07478}, abstract = {A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that encompasses traditional communities but includes a wide range of generalized structural patterns as well. We describe a principled method for detecting this generalized structure in empirical network data and demonstrate with real-world examples how it can be used to learn new things about the shape and meaning of networks.}, number = {115, 088701}, urldate = {2015-05-27}, author = {Newman, M. E. J. and Peixoto, Tiago P.}, month = may, year = {2015}, keywords = {Computer Science - Social and Information Networks, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Physics - Data Analysis, Statistics and Probability, Physics - Physics and Society, Statistics - Machine Learning}, annote = {1505.07478}, doi = {10.1103/PhysRevLett.115.088701}, journal = {Phys. Rev. Lett.}, comments = {Cover of the PRL issue!}, file = {} }, @article{fisher_sampling_2015, type = {{arXiv} e-print}, title = {Sampling motif-constrained ensembles of networks}, url = {http://arxiv.org/abs/1507.08696}, abstract = {The statistical significance of network properties is conditioned on null models which satisfy specified properties but that are otherwise random. Exponential random graph models are a principled theoretical framework to generate such constrained ensembles, but which often fail in practice, either due to model inconsistency, or due to the impossibility to sample networks from them. These problems affect the important case of networks with prescribed clustering coefficient or number of small connected subgraphs (motifs). In this paper we use the Wang-Landau method to obtain a multicanonical sampling that overcomes both these problems. We sample, in polynomial time, networks with arbitrary degree sequences from ensembles with imposed motifs counts. Applying this method to social networks, we investigate the relation between transitivity and homophily, and we quantify the correlation between different types of motifs, finding that single motifs can explain up to 60\% of the variation of motif profiles.}, number = {115, 188701}, urldate = {2015-07-30}, author = {Fisher, Rico and Leitão, Jorge C. and Peixoto, Tiago P. and Altmann, Eduardo G.}, month = jul, year = {2015}, keywords = {}, annote = {1507.08696}, doi = {10.1103/PhysRevLett.115.188701}, journal = {Phys. Rev. Lett.}, file = {} }, @article{peixoto_inferring_2015, type = {{arXiv} e-print}, title = {Inferring the mesoscale structure of layered, edge-valued and time-varying networks}, url = {http://arxiv.org/abs/1504.02381}, abstract = {Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges or as a time-dependence of the network structure. Although they are crucial for a more comprehensive scientific understanding, these representations offer substantial challenges. Namely, it is an open problem how to precisely characterize the large or mesoscale structure of network systems in relation to these additional aspects. Furthermore, the direct incorporation of these features invariably increases the effective dimension of the network description, and hence aggravates the problem of overfitting, i.e. the use of overly-complex characterizations that mistake purely random fluctuations for actual structure. In this work, we propose a robust and principled method to tackle these problems, by constructing generative models of modular network structure, incorporating layered, attributed and time-varying properties, as well as a Bayesian methodology to infer the parameters from data and select the most appropriate model according to statistical evidence. We show that the method is capable of revealing hidden structure in layered, edge-valued and time-varying networks, and that the most appropriate level of granularity with respect to the additional dimensions can be reliably identified. We illustrate our approach on a variety of empirical systems, including a social network of physicians, the voting correlations of deputies in the Brazilian national congress, the global airport network, and a proximity network of high-school students.}, number = {92, 042807}, urldate = {2014-09-11}, author = {Peixoto, Tiago P.}, month = sep, year = {2015}, keywords = {Computer Science - Social and Information Networks, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Physics - Data Analysis, Statistics and Probability, Physics - Physics and Society, Statistics - Machine Learning}, annote = {1504.02381}, doi = {10.1103/PhysRevE.92.042807}, journal = {Phys. Rev. E}, comments = {Code is available. See the HOWTO.}, file = {} }, @article{peixoto_model_2015, type = {{arXiv} e-print}, title = {Model selection and hypothesis testing for large-scale network models with overlapping groups}, url = {http://arxiv.org/abs/1409.3059}, abstract = {The desire to understand network systems in increasing detail has resulted in the development of a diversity of generative models that describe large-scale structure in a variety of ways, and allow its characterization in a principled and powerful manner. Current models include features such as degree correction, where nodes with arbitrary degrees can belong to the same group, and community overlap, where nodes are allowed to belong to more than one group. However, such elaborations invariably result in an increased number of parameters, which make these model variants prone to overfitting. Without properly accounting for the increased model complexity, one should naturally expect these larger models to "better" fit empirical networks, regardless of the actual statistical evidence supporting them. Here we propose a principled method of model selection based on the minimum description length principle and posterior odds ratios that is capable of fully accounting for the increased degrees of freedom of the larger models, and selects the best model according to the statistical evidence available in the data. Contrary to other alternatives such as likelihood ratios and parametric bootstrapping, this method scales very well, and combined with efficient inference methods recently developed, allows for the analysis of very large networks with an arbitrarily large number of groups. In applying this method to many empirical datasets from different fields, we observed that while degree correction tends to provide better fits for a majority of networks, community overlap does not, and is selected as better model only for a minority of them.}, number = {5, 011033}, urldate = {2014-09-11}, author = {Peixoto, Tiago P.}, month = sep, year = {2015}, keywords = {Computer Science - Social and Information Networks, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Physics - Data Analysis, Statistics and Probability, Physics - Physics and Society, Statistics - Machine Learning}, annote = {1409.3059}, doi = {10.1103/PhysRevX.5.011033}, journal = {Phys. Rev. X}, comments = {Code is available. See the HOWTO.}, file = {} }, @article{moller_maximum-entropy_2015, type = {{arXiv} e-print}, title = {Maximum-entropy large-scale structures of Boolean networks optimized for criticality}, url = {http://dx.doi.org/10.1088/1367-2630/17/4/043021}, abstract = {We construct statistical ensembles of modular Boolean networks that are constrained to lie at the critical line between frozen and chaotic dynamic regimes. The ensembles are maximally random given the imposed constraints, and thus represent null models of critical networks. By varying the network density and the entropic cost associated with biased Boolean functions, the ensembles undergo several phase transitions. The observed structures range from fully random to several ordered ones, including a prominent core–periphery-like structure, and an 'attenuated' two-group structure, where the network is divided in two groups of nodes, and one of them has Boolean functions with very low sensitivity. This shows that such simple large-scale structures are the most likely to occur when optimizing for criticality, in the absence of any other constraint or competing optimization criteria.}, number = {17 043021}, urldate = {2014-09-11}, author = {Möller, Marco and Peixoto, Tiago P.}, month = sep, year = {2015}, doi = {10.1088/1367-2630/17/4/043021}, journal = {New J. Phys.}, file = {} }, @article{prister_limits_2014, type = {{arXiv} e-print}, title = {Limits and Trade-Offs of Topological Network Robustness}, url = {http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0108215#pone-0108215-g006}, abstract = {We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale structures. We present results from numerical two-objective optimization simulations for networks with various fixed mean degree and number of blocks. The results provide strong evidence that three different blocks are sufficient to realize the best trade-off between the two measures of robustness, i.e. to obtain the complete front of Pareto-optimal networks. For all values of the mean degree, a characteristic three block structure emerges over large parts of the Pareto-optimal front. This structure can be often characterized as a core-periphery structure, composed of a group of core nodes with high degree connected among themselves and to a periphery of low-degree nodes, in addition to a third group of nodes which is disconnected from the periphery, and weakly connected to the core. Only at both extremes of the Pareto-optimal front, corresponding to maximal robustness against random and targeted node removal, a two-block core-periphery structure or a one-block fully random network are found, respectively.}, number = {9(9): e108215}, urldate = {2014-09-11}, author = {Priester, Christopher and Schmitt, Sebastian and Peixoto, Tiago P.}, month = sep, year = {2014}, keywords = {}, doi = {10.1371/journal.pone.0108215}, journal = {PLoS ONE}, file = {} }, @article{peixoto_hierarchical_2013, type = {{arXiv} e-print}, title = {Hierarchical block structures and high-resolution model selection in large networks}, url = {http://arxiv.org/abs/1310.4377}, abstract = {Discovering the large-scale topological features in empirical networks is a crucial tool in understanding how complex systems function. However most existing methods used to obtain the modular structure of networks suffer from serious problems, such as the resolution limit on the size of communities, where smaller but well-defined clusters are not detectable when the network becomes large. This phenomenon occurs for the very popular approach of modularity optimization, but also for more principled ones based on statistical inference and model selection. Here we construct a nested generative model which, through a complete description of the entire network hierarchy at multiple scales, is capable of avoiding this limitation, and enables the detection of modular structure at levels far beyond those possible by current approaches. Even with this increased resolution, the method is based on the principle of parsimony, and is capable of separating signal from noise, and thus will not lead to the identification of spurious modules even on sparse networks. Furthermore, it fully generalizes other approaches in that it is not restricted to purely assortative mixing patterns, directed or undirected graphs, and ad hoc hierarchical structures such as binary trees. Despite its general character, the approach is tractable, and can be combined with advanced techniques of community detection to yield an efficient algorithm which scales well for very large networks.}, number = {}, urldate = {2013-10-17}, author = {Peixoto, Tiago P.}, month = oct, year = {2014}, keywords = {Computer Science - Social and Information Networks, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Physics - Data Analysis, Statistics and Probability, Physics - Physics and Society, Statistics - Machine Learning}, annote = {1310.4377}, doi = {10.1103/PhysRevX.4.011047}, journal = {Phys. Rev. X 4, 011047}, comments = {Code is available. See the HOWTO.}, file = {1310.4377 PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/JNT8XUZK/Peixoto - 2013 - Hierarchical block structures and high-resolution .pdf:application/pdf;arXiv.org Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/H3Q6PNHG/1310.html:text/html} }, @article{peixoto_efficient_2013, type = {{arXiv} e-print}, title = {Efficient Monte Carlo and greedy heuristic for the inference of stochastic block models}, url = {http://arxiv.org/abs/1310.4378}, abstract = {We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo ({MCMC)} method, with a fast mixing time and a much reduced susceptibility to getting trapped in metastable states, or as a greedy agglomerative heuristic, with an almost linear {\$O(N{\textbackslash}ln{\textasciicircum}2N)\$} complexity, where {\$N\$} is the number of nodes in the network, independent on the number of blocks being inferred. We show that the heuristic is capable of delivering results which are indistinguishable from the more exact and numerically expensive {MCMC} method in many artificial and empirical networks, despite being much faster. The method is entirely unbiased towards any specific mixing pattern, and in particular it does not favor assortative community structures.}, number = {}, urldate = {2013-10-17}, author = {Peixoto, Tiago P.}, month = oct, year = {2014}, keywords = {Computer Science - Social and Information Networks, Condensed Matter - Statistical Mechanics, Physics - Computational Physics, Physics - Data Analysis, Statistics and Probability, Statistics - Machine Learning}, annote = {1310.4378}, doi = {10.1103/PhysRevE.89.012804}, journal = {Phys. Rev. E 89, 012804}, comments = {Code is available. See the HOWTO.}, file = {1310.4378 PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/9DI9P5SU/Peixoto - 2013 - Efficient Monte Carlo and greedy heuristic for the.pdf:application/pdf;arXiv.org Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/6EB52TNK/1310.html:text/html} }, @article{peixoto_eigenvalue_2013, title = {Eigenvalue Spectra of Modular Networks}, volume = {111}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.111.098701}, doi = {10.1103/PhysRevLett.111.098701}, abstract = {A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often, such spectral features are theoretically obtained by considering only local node properties, such as degree distributions. Many networks, however, possess large-scale modular structures that can drastically influence their spectral characteristics and which are neglected in such simplified descriptions. Here, we obtain in a unified fashion the spectrum of a large family of operators, including the adjacency, Laplacian, and normalized Laplacian matrices, for networks with generic modular structure, in the limit of large degrees. We focus on the conditions necessary for the merging of the isolated eigenvalues with the continuous band of the spectrum, after which the planted modular structure can no longer be easily detected by spectral methods. This is a crucial transition point which determines when a modular structure is strong enough to affect a given dynamical process. We show that this transition happens in general at different points for the different matrices, and hence the detectability threshold can vary significantly, depending on the operator chosen. Equivalently, the sensitivity to the modular structure of the different dynamical processes associated with each matrix will be different, given the same large-scale structure present in the network. Furthermore, we show that, with the exception of the Laplacian matrix, the different transitions coalesce into the same point for the special case where the modules are homogeneous but separate otherwise.}, number = {9}, urldate = {2013-08-27}, journal = {Phys. Rev. Lett.}, author = {Peixoto, Tiago P.}, month = aug, year = {2013}, pages = {098701}, annote = {1306.2507}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/MPFTGT95/Peixoto - 2013 - Eigenvalue Spectra of Modular Networks.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/M9MT6K5T/e098701.html:text/html} }, @article{krause_spontaneous_2013, type = {{arXiv} e-print}, title = {Spontaneous centralization of control in a network of company ownerships}, url = {http://arxiv.org/abs/1306.3422}, abstract = {We introduce a model for the adaptive evolution of a network of company ownerships. In a recent work it has been shown that the empirical global network of corporate control is marked by a central, tightly connected "core" made of a small number of large companies which control a significant part of the global economy. Here we show how a simple, adaptive "rich get richer" dynamics can account for this characteristic, which incorporates the increased buying power of more influential companies, and in turn results in even higher control. We conclude that this kind of centralized structure can emerge without it being an explicit goal of these companies, or as a result of a well-organized strategy.}, number = {}, urldate = {2013-10-17}, author = {Krause, Sebastian M. and Peixoto, Tiago P. and Bornholdt, Stefan}, month = jun, year = {2013}, keywords = {Computer Science - Social and Information Networks, Physics - Physics and Society, Quantitative Finance - General Finance}, annote = {1306.3422}, doi = {10.1371/journal.pone.0080303}, journal = {PLoS ONE 8(12): e80303}, file = {1306.3422 PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/KUPFWF23/Krause et al. - 2013 - Spontaneous centralization of control in a network.pdf:application/pdf;arXiv.org Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/Q9PPKUWP/1306.html:text/html} }, @article{peixoto_parsimonious_2013, title = {Parsimonious Module Inference in Large Networks}, volume = {110}, lccn = {0000}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.110.148701}, doi = {10.1103/PhysRevLett.110.148701}, abstract = {We investigate the detectability of modules in large networks when the number of modules is not known in advance. We employ the minimum description length principle which seeks to minimize the total amount of information required to describe the network, and avoid overfitting. According to this criterion, we obtain general bounds on the detectability of any prescribed block structure, given the number of nodes and edges in the sampled network. We also obtain that the maximum number of detectable blocks scales as {√N}, where N is the number of nodes in the network, for a fixed average degree ⟨k⟩. We also show that the simplicity of the minimum description length approach yields an efficient multilevel Monte Carlo inference algorithm with a complexity of O({τNlogN)}, if the number of blocks is unknown, and O({τN)} if it is known, where τ is the mixing time of the Markov chain. We illustrate the application of the method on a large network of actors and films with over 106 edges, and a dissortative, bipartite block structure.}, number = {}, urldate = {2013-04-13}, journal = {Phys. Rev. Lett.}, author = {Peixoto, Tiago P.}, month = apr, year = {2013}, pages = {148701}, annote = {1212.4794}, comments = {Code is available. See the HOWTO.}, file = {APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/QEHEADHE/e148701.html:text/html;PhysRevLett.110.148701.pdf:/home/count0/stuff/workspace/pesquisa/zotero/storage/7VCE6TFH/PhysRevLett.110.148701.pdf:application/pdf} }, @article{peixoto_evolution_2012, title = {Evolution of Robust Network Topologies: Emergence of Central Backbones}, volume = {109}, lccn = {0000}, shorttitle = {Evolution of Robust Network Topologies}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.109.118703}, doi = {10.1103/PhysRevLett.109.118703}, abstract = {We model the robustness against random failure or an intentional attack of networks with an arbitrary large-scale structure. We construct a block-based model which incorporates—in a general fashion—both connectivity and interdependence links, as well as arbitrary degree distributions and block correlations. By optimizing the percolation properties of this general class of networks, we identify a simple core-periphery structure as the topology most robust against random failure. In such networks, a distinct and small “core” of nodes with higher degree is responsible for most of the connectivity, functioning as a central “backbone” of the system. This centralized topology remains the optimal structure when other constraints are imposed, such as a given fraction of interdependence links and fixed degree distributions. This distinguishes simple centralized topologies as the most likely to emerge, when robustness against failure is the dominant evolutionary force.}, number = {11}, urldate = {2013-03-01}, journal = {Phys. Rev. Lett.}, author = {Peixoto, Tiago P. and Bornholdt, Stefan}, month = sep, year = {2012}, pages = {118703}, annote = {1205.2909}, comments = {Coverage: Synopsis in Physics}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/54R4CWZK/Peixoto and Bornholdt - 2012 - Evolution of Robust Network Topologies Emergence .pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/XAMJ6PI6/e118703.html:text/html} }, @article{peixoto_entropy_2012, title = {Entropy of stochastic blockmodel ensembles}, volume = {85}, url = {http://link.aps.org/doi/10.1103/PhysRevE.85.056122}, doi = {10.1103/PhysRevE.85.056122}, abstract = {Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we derive expressions for the entropy of stochastic blockmodel ensembles. We consider several ensemble variants, including the traditional model as well as the newly introduced degree-corrected version [ Karrer et al. Phys. Rev. E 83 016107 (2011)], which imposes a degree sequence on the vertices, in addition to the block structure. The imposed degree sequence is implemented both as “soft” constraints, where only the expected degrees are imposed, and as “hard” constraints, where they are required to be the same on all samples of the ensemble. We also consider generalizations to multigraphs and directed graphs. We illustrate one of many applications of this measure by directly deriving a log-likelihood function from the entropy expression, and using it to infer latent block structure in observed data. Due to the general nature of the ensembles considered, the method works well for ensembles with intrinsic degree correlations (i.e., with entropic origin) as well as extrinsic degree correlations, which go beyond the block structure.}, number = {5}, urldate = {2012-07-04}, journal = {Phys. Rev. E}, author = {Peixoto, Tiago P.}, month = may, year = {2012}, pages = {056122}, annote = {1112.6028}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/GEQW86FP/Peixoto - 2012 - Entropy of stochastic blockmodel ensembles.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/HQTQ24PG/e056122.html:text/html} }, @article{peixoto_no_2012, title = {No Need for Conspiracy: Self-Organized Cartel Formation in a Modified Trust Game}, volume = {108}, lccn = {0001}, shorttitle = {No Need for Conspiracy}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.108.218702}, doi = {10.1103/PhysRevLett.108.218702}, abstract = {We investigate the dynamics of a trust game on a mixed population, where individuals with the role of buyers are forced to play against a predetermined number of sellers whom they choose dynamically. Agents with the role of sellers are also allowed to adapt the level of value for money of their products, based on payoff. The dynamics undergoes a transition at a specific value of the strategy update rate, above which an emergent cartel organization is observed, where sellers have similar values of below-optimal value for money. This cartel organization is not due to an explicit collusion among agents; instead, it arises spontaneously from the maximization of the individual payoffs. This dynamics is marked by large fluctuations and a high degree of unpredictability for most of the parameter space and serves as a plausible qualitative explanation for observed elevated levels and fluctuations of certain commodity prices.}, number = {21}, urldate = {2013-03-01}, journal = {Phys. Rev. Lett.}, author = {Peixoto, Tiago P. and Bornholdt, Stefan}, month = may, year = {2012}, pages = {218702}, annote = {1201.3798}, comments = {Coverage: (Phys.org) High gas prices may be explained by self-organized cartel behavior, (Physics arXiv Blog) Cartels Are an Emergent Phenomenon, Say Complexity Theorists, (Jura Forum) Bremer Uni-Studie: Flächendeckend höhere Benzinpreise deuten nicht gleich auf Preisabsprachen hin, (kreiszeitung.de) Benzinpreis: Kein Hinweis auf Absprache}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/FUZPV44N/Peixoto and Bornholdt - 2012 - No Need for Conspiracy Self-Organized Cartel Form.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/NK3ZKTMX/e218702.html:text/html} }, @article{peixoto_emergence_2012, title = {Emergence of robustness against noise: A structural phase transition in evolved models of gene regulatory networks}, volume = {85}, lccn = {0003}, shorttitle = {Emergence of robustness against noise}, url = {http://link.aps.org/doi/10.1103/PhysRevE.85.041908}, doi = {10.1103/PhysRevE.85.041908}, abstract = {We investigate the evolution of Boolean networks subject to a selective pressure which favors robustness against noise, as a model of evolved genetic regulatory systems. By mapping the evolutionary process into a statistical ensemble and minimizing its associated free energy, we find the structural properties which emerge as the selective pressure is increased and identify a phase transition from a random topology to a “segregated-core” structure, where a smaller and more densely connected subset of the nodes is responsible for most of the regulation in the network. This segregated structure is very similar qualitatively to what is found in gene regulatory networks, where only a much smaller subset of genes—those responsible for transcription factors—is responsible for global regulation. We obtain the full phase diagram of the evolutionary process as a function of selective pressure and the average number of inputs per node. We compare the theoretical predictions with Monte Carlo simulations of evolved networks and with empirical data for Saccharomyces cerevisiae and Escherichia coli.}, number = {4}, urldate = {2012-05-01}, journal = {Phys. Rev. E}, author = {Peixoto, Tiago P.}, month = apr, year = {2012}, pages = {041908}, annote = {1108.4341}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/62V749FK/Peixoto - 2012 - Emergence of robustness against noise A structura.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/DHEI7N72/Peixoto - 2012 - Emergence of robustness against noise A structura.html:text/html} }, @article{ackermann_reliable_2012, title = {Reliable dynamics in Boolean and continuous networks}, volume = {14}, issn = {1367-2630}, lccn = {0001}, url = {http://iopscience.iop.org/1367-2630/14/12/123029}, doi = {10.1088/1367-2630/14/12/123029}, abstract = {We investigate the dynamical behavior of a model of robust gene regulatory networks which possess ‘entirely reliable’ trajectories. In a Boolean representation, these trajectories are characterized by being insensitive to the order in which the nodes are updated, i.e. they always go through the same sequence of states. The Boolean model for gene activity is compared with a continuous description in terms of differential equations for the concentrations of {mRNA} and proteins. We found that entirely reliable Boolean trajectories can be reproduced perfectly in the continuous model when realistic Hill coefficients are used. We investigate to what extent this high correspondence between Boolean and continuous trajectories depends on the extent of reliability of the Boolean trajectories, and we identify simple criteria that enable the faithful reproduction of the Boolean dynamics in the continuous description.}, language = {en}, number = {12}, urldate = {2013-03-01}, journal = {New J. Phys.}, author = {Ackermann, Eva and Peixoto, Tiago P. and Drossel, Barbara}, month = dec, year = {2012}, pages = {123029}, file = {Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/CZCI93KG/Ackermann et al. - 2012 - Reliable dynamics in Boolean and continuous networ.pdf:application/pdf;Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/R7D7MZPV/123029.html:text/html} }, @article{peixoto_behavior_2012, title = {The behavior of noise-resilient Boolean networks with diverse topologies}, volume = {2012}, issn = {1742-5468}, url = {http://iopscience.iop.org/1742-5468/2012/01/P01006}, doi = {10.1088/1742-5468/2012/01/P01006}, number = {01}, urldate = {2012-01-19}, journal = {J. Stat. Mech.}, author = {Peixoto, Tiago P}, month = jan, year = {2012}, pages = {P01006}, annote = {1108.4329 }, file = {IOP Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/TAFFGGTE/Peixoto - 2012 - The behavior of noise-resilient Boolean networks w.pdf:application/pdf} }, @article{richters_trust_2011, title = {Trust Transitivity in Social Networks}, volume = {6}, url = {http://dx.doi.org/10.1371/journal.pone.0018384}, doi = {10.1371/journal.pone.0018384}, abstract = {Non-centralized recommendation-based decision making is a central feature of several social and technological processes, such as market dynamics, peer-to-peer file-sharing and the web of trust of digital certification. We investigate the properties of trust propagation on networks, based on a simple metric of trust transitivity. We investigate analytically the percolation properties of trust transitivity in random networks with arbitrary in/out-degree distributions, and compare with numerical realizations. We find that the existence of a non-zero fraction of absolute trust (i.e. entirely confident trust) is a requirement for the viability of global trust propagation in large systems: The average pair-wise trust is marked by a discontinuous transition at a specific fraction of absolute trust, below which it vanishes. Furthermore, we perform an extensive analysis of the Pretty Good Privacy ({PGP)} web of trust, in view of the concepts introduced. We compare different scenarios of trust distribution: community- and authority-centered. We find that these scenarios lead to sharply different patterns of trust propagation, due to the segregation of authority hubs and densely-connected communities. While the authority-centered scenario is more efficient, and leads to higher average trust values, it favours weakly-connected “fringe” nodes, which are directly trusted by authorities. The community-centered scheme, on the other hand, favours nodes with intermediate in/out-degrees, in detriment of the authorities and its “fringe” peers.}, number = {4}, urldate = {2011-08-24}, journal = {{PLoS} {ONE}}, author = {Richters, Oliver and Peixoto, Tiago P.}, month = apr, year = {2011}, pages = {e18384}, annote = {1012.1358}, file = {PLoS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/MPKSESD5/Richters and Peixoto - 2011 - Trust Transitivity in Social Networks.pdf:application/pdf;PLoS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/STK2HRP9/infodoi10.1371journal.pone.html:text/html} }, @article{peixoto_density_2011, title = {Density profile and polymer configurations for a polymer melt in a regular array of nanotubes}, volume = {13}, issn = {1367-2630}, url = {http://iopscience.iop.org/1367-2630/13/7/073030}, doi = {10.1088/1367-2630/13/7/073030}, number = {7}, urldate = {2012-02-09}, journal = {New J. Phys.}, author = {Peixoto, Tiago P and Drossel, Barbara}, month = jul, year = {2011}, pages = {073030}, file = {IOP Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/DTEIF8XM/Peixoto and Drossel - 2011 - Density profile and polymer configurations for a p.pdf:application/pdf} }, @article{peixoto_phase_2010, title = {The phase diagram of random Boolean networks with nested canalizing functions}, volume = {78}, issn = {1434-6028, 1434-6036}, url = {http://www.springerlink.com/content/l7325318063712j7/}, doi = {10.1140/epjb/e2010-10559-0}, number = {2}, urldate = {2012-02-09}, journal = {Eur. Phys. J. B}, author = {Peixoto, T. P.}, month = nov, year = {2010}, pages = {187--192}, annote = {1007.3411}, file = {The European Physical Journal B - Condensed Matter and Complex Systems, Volume 78, Number 2 - SpringerLink:/home/count0/stuff/workspace/pesquisa/zotero/storage/7PWSPRBJ/l7325318063712j7.html:text/html} }, @article{schmal_boolean_2010, title = {Boolean networks with robust and reliable trajectories}, volume = {12}, issn = {1367-2630}, url = {http://iopscience.iop.org/1367-2630/12/11/113054/}, doi = {10.1088/1367-2630/12/11/113054}, number = {11}, urldate = {2011-07-14}, journal = {New J. Phys.}, author = {Schmal, Christoph and Peixoto, Tiago P and Drossel, Barbara}, month = nov, year = {2010}, pages = {113054}, annote = {1008.1726}, file = {1367-2630_12_11_113054.pdf:/home/count0/stuff/workspace/pesquisa/zotero/storage/BTQ56R5K/1367-2630_12_11_113054.pdf:application/pdf;Boolean networks with robust and reliable trajectories:/home/count0/stuff/workspace/pesquisa/zotero/storage/T4ER29JZ/113054.html:text/html} }, @article{peixoto_redundancy_2010, title = {Redundancy and Error Resilience in Boolean Networks}, volume = {104}, lccn = {0014}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.104.048701}, doi = {10.1103/PhysRevLett.104.048701}, abstract = {We consider the effect of noise in sparse Boolean networks with redundant functions. We show that they always exhibit a nonzero error level, and the dynamics undergoes a phase transition from nonergodicity to ergodicity, as a function of noise, after which the system is no longer capable of preserving a memory of its initial state. We obtain upper bounds on the critical value of noise for networks of different sparsity.}, number = {4}, urldate = {2010-02-15}, journal = {Phys. Rev. Lett.}, author = {Peixoto, Tiago P.}, month = jan, year = {2010}, pages = {048701}, annote = {0909.1740}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/BMDGHGDP/Peixoto - 2010 - Redundancy and Error Resilience in Boolean Network.pdf:application/pdf;APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/Q5SSCJNX/Peixoto - 2010 - Redundancy and Error Resilience in Boolean Network.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/DNM29B4P/e048701.html:text/html;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/CSQG864T/e048701.html:text/html} }, @article{peixoto_spatiotemporal_2010, title = {Spatiotemporal correlations of aftershock sequences}, volume = {115}, url = {http://www.agu.org/pubs/crossref/2010/2010JB007626.shtml}, doi = {201010.1029/2010JB007626}, urldate = {2012-02-09}, journal = {J. Geophys. Res.}, author = {Peixoto, Tiago P. and Doblhoff-Dier, Katharina and Davidsen, Jörn}, month = oct, pages = {B10309}, year = {2010}, file = {} }, @article{mahanandia_polymer_2010, title = {Polymer confinement effects in aligned carbon nanotubes arrays}, volume = {12}, issn = {1463-9076}, url = {http://pubs.rsc.org/en/Content/ArticleLanding/2010/CP/B922906J}, doi = {10.1039/b922906j}, number = {17}, urldate = {2010-08-13}, journal = {Phys. Chem. Chem. Phys.}, author = {Mahanandia, Pitamber and Schneider, Jörg J. and Khaneft, Marina and Stühn, Bernd and Peixoto, Tiago P. and Drossel, Barbara}, year = {2010}, pages = {4407}, file = {Polymer confinement effects in aligned carbon nanotubes arrays - Physical Chemistry Chemical Physics (RSC Publishing):/home/count0/stuff/workspace/pesquisa/zotero/storage/BTTPVCQ8/B922906J.html:text/html} }, @article{peixoto_boolean_2009, title = {Boolean networks with reliable dynamics}, volume = {80}, url = {http://link.aps.org/doi/10.1103/PhysRevE.80.056102}, doi = {10.1103/PhysRevE.80.056102}, abstract = {We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states, which is independent of the order in which the nodes are updated. We explored numerically the topology, the update functions, and the state space structure of these networks, which we constructed using a minimum number of links and the simplest update functions. We found that the clustering coefficient is larger than in random networks and that the probability distribution of three-node motifs is similar to that found in gene regulation networks. Among the update functions, only a subset of all possible functions occurs, and they can be classified according to their probability. More homogeneous functions occur more often, leading to a dominance of canalyzing functions. Finally, we studied the entire state space of the networks. We observed that with increasing systems size, fixed points become more dominant, moving the networks close to the frozen phase.}, number = {5}, urldate = {2010-02-15}, journal = {Phys. Rev. E}, author = {Peixoto, Tiago P. and Drossel, Barbara}, month = nov, year = {2009}, pages = {056102}, annote = {0905.0925}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/GJVWQU4R/Peixoto and Drossel - 2009 - Boolean networks with reliable dynamics.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/RC53V9UF/e056102.html:text/html} }, @article{peixoto_noise_2009, title = {Noise in random Boolean networks}, volume = {79}, url = {http://link.aps.org/doi/10.1103/PhysRevE.79.036108}, doi = {10.1103/PhysRevE.79.036108}, number = {3}, urldate = {2010-07-15}, journal = {Phys. Rev. E}, author = {Peixoto, Tiago P. and Drossel, Barbara}, month = mar, year = {2009}, pages = {036108}, annote = {0808.3087}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/5STQATSU/Peixoto and Drossel - 2009 - Noise in random Boolean networks.pdf:application/pdf;APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/8XDWANS7/Peixoto and Drossel - 2009 - Noise in random Boolean networks.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/JJGU9X5C/e036108.html:text/html;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/JCCRPBPF/e036108.html:text/html} }, @article{peixoto_network_2008, title = {Network of recurrent events for the Olami-Feder-Christensen model}, volume = {77}, url = {http://link.aps.org/doi/10.1103/PhysRevE.77.066107}, doi = {10.1103/PhysRevE.77.066107}, abstract = {We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder, and Christensen ({OFC)} to mimic earthquakes and investigate to what extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicity. Following a recently proposed method to characterize such clustering by networks of recurrent events [J. Davidsen, P. Grassberger, and M. Paczuski, Geophys. Res. Lett. 33, L11304 (2006)], we find that for synthetic catalogs generated by the {OFC} model these networks have many nontrivial statistical properties. This includes characteristic degree distributions, very similar to what has been observed for real seismicity. There are, however, also significant differences between the {OFC} model and earthquake catalogs, indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.}, number = {6}, urldate = {2010-02-15}, journal = {Phys. Rev. E}, author = {Peixoto, Tiago P. and Davidsen, Jörn}, month = jun, year = {2008}, note = {Copyright (C) 2010 The American Physical Society; Please report any problems to prola@aps.org}, pages = {066107}, annote = {0803.1404}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/TI897DWF/Peixoto and Davidsen - 2008 - Network of recurrent events for the Olami-Feder-Ch.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/8JKHCBTH/e066107.html:text/html} }, @article{peixoto_network_2006, title = {Network of epicenters of the Olami-Feder-Christensen model of earthquakes}, volume = {74}, url = {http://link.aps.org/doi/10.1103/PhysRevE.74.016126}, doi = {10.1103/PhysRevE.74.016126}, abstract = {We study the dynamics of the Olami-Feder-Christensen ({OFC)} model of earthquakes, focusing on the behavior of sequences of epicenters regarded as a growing complex network. Besides making a detailed and quantitative study of the effects of the borders (the occurrence of epicenters is dominated by a strong border effect which does not scale with system size), we examine the degree distribution and the degree correlation of the graph. We detect sharp differences between the conservative and nonconservative regimes of the model. Removing border effects, the conservative regime exhibits a Poisson-like degree statistics and is uncorrelated, while the nonconservative has a broad power-law-like distribution of degrees (if the smallest events are ignored), which reproduces the observed behavior of real earthquakes. In this regime the graph has also an unusually strong degree correlation among the vertices with higher degree, which is the result of the existence of temporary attractors for the dynamics: as the system evolves, the epicenters concentrate increasingly on fewer sites, exhibiting strong synchronization, but eventually spread again over the lattice after a series of sufficiently large earthquakes. We propose an analytical description of the dynamics of this growing network, considering a Markov process network with hidden variables, which is able to account for the mentioned properties.}, number = {1}, urldate = {2010-02-15}, journal = {Phys. Rev. E}, author = {Peixoto, Tiago P. and Prado, Carmen P. C.}, month = jul, year = {2006}, note = {Copyright (C) 2010 The American Physical Society; Please report any problems to prola@aps.org}, pages = {016126}, annote = {cond-mat/0602244}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/TM6M8Q7F/Peixoto and Prado - 2006 - Network of epicenters of the Olami-Feder-Christens.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/T9XDAZTA/e016126.html:text/html} }, @article{peixoto_statistics_2004, title = {Statistics of epicenters in the Olami-Feder-Christensen model in two and three dimensions}, volume = {342}, issn = {0378-4371}, url = {http://www.sciencedirect.com/science/article/B6TVG-4CDG0J0-4/2/560c4930fcfe0c616f8919102af78d1d}, doi = {10.1016/j.physa.2004.04.075}, abstract = {Recently, Abe and Suzuki pointed out that epicenters of earthquakes could be connected in order to generate a graph, with properties of a scale-free network. We have shown that the Olami-Feder-Christensen ({OFC)} model for the dynamics of earthquakes, defined both in square and cubic lattices, is able to reproduce this new behavior. The distribution of distances between successive earthquakes is also presented. Our results indicate the robustness of the {OFC} model to describe earthquake dynamics. Surprisingly, we found that only the non-conservative version of the {OFC} model generates a network with scale-free properties. The conservative version, instead, behaves like a random graph. The distribution of distances in 3-D and the distribution of connectivities in a 2-D lattice confirm the differences observed between the conservative and non-conservative regime.}, number = {1-2}, urldate = {2010-02-15}, journal = {Physica A}, author = {Peixoto, Tiago P. and Prado, Carmen P. C.}, month = oct, year = {2004}, keywords = {complex networks, Complex systems, Earthquake, Self-organized criticality}, pages = {171--177}, file = {ScienceDirect Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/CUGW8H79/Peixoto and Prado - 2004 - Statistics of epicenters in the Olami-Feder-Christ.pdf:application/pdf;ScienceDirect Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/J5JS9TJ3/science.html:text/html} }, @article{peixoto_distribution_2004, title = {Distribution of epicenters in the Olami-Feder-Christensen model}, volume = {69}, url = {http://link.aps.org/doi/10.1103/PhysRevE.69.025101}, doi = {10.1103/PhysRevE.69.025101}, abstract = {We show that the well established Olami-Feder-Christensen ({OFC)} model for the dynamics of earthquakes is able to reproduce a striking property of real earthquake data. Recently, it has been pointed out by Abe and Suzuki that the epicenters of earthquakes could be connected in order to generate a graph, with properties of a scale-free network of the Barabási-Albert type. However, only the nonconservative version of the Olami-Feder-Christensen model is able to reproduce this behavior. The conservative version, instead, behaves like a random graph. Besides indicating the robustness of the model to describe earthquake dynamics, those findings reinforce that conservative and nonconservative versions of the {OFC} model are qualitatively different. Also, we propose a completely different dynamical mechanism that, even without an explicit rule of preferential attachment, generates a scale-free network. The preferential attachment is in this case a “byproduct” of the long term correlations associated with the self-organized critical state.}, number = {2}, urldate = {2010-02-15}, journal = {Phys. Rev. E}, author = {Peixoto, Tiago P. and Prado, Carmen P. C.}, month = feb, year = {2004}, note = {Copyright (C) 2010 The American Physical Society; Please report any problems to prola@aps.org}, pages = {025101}, annote = {cond-mat/0310366}, file = {APS Full Text PDF:/home/count0/stuff/workspace/pesquisa/zotero/storage/R8T9N8F9/Peixoto and Prado - 2004 - Distribution of epicenters in the Olami-Feder-Chri.pdf:application/pdf;APS Snapshot:/home/count0/stuff/workspace/pesquisa/zotero/storage/7PTSQT7K/e025101.html:text/html} }