Edmilson Roque

Street networks are important infrastructural transportation systems that cover a great part of the planet. It is now widely accepted that transportation properties of street networks are better understood in the interplay between the street network itself and the so called \textit{information} or \textit{dual network}, which embeds the topology of the street network navigation system. In this work, we present a novel robustness analysis, based on the interaction between the primal and the dual transportation layer for two large metropolis, London and Chicago, thus considering the structural differences to intentional attacks for \textit{self-organized} and planned cities. We elaborate the results through an accurate closeness centrality analysis in the Euclidean space and in the relationship between primal and dual space. Interestingly enough, we find that even if the considered planar graphs display very distinct properties, the information space induce them to converge toward systems which are similar in terms of transportation properties.

Donate to arXiv

We discuss a strategy of sparse approximation that is based on the use of an overcomplete basis, and evaluate its performance when a random matrix is used as this basis. A small combination of basis vectors is chosen from a given overcomplete basis, according to a given compression rate, such that they compactly represent the target data with as small a distortion as possible. As a selection method, we study the $\ell_0$- and $\ell_1$-based methods, which employ the exhaustive search and $\ell_1$-norm regularization techniques, respectively. The performance is assessed in terms of the trade-off relation between the representation distortion and the compression rate. First, we evaluate the performance analytically in the case that the methods are carried out ideally, using methods of statistical mechanics. Our result clarifies the fact that the $\ell_0$-based method greatly outperforms the $\ell_1$-based one. Second, we examine the practical performances of two well-known algorithms, orthogonal matching pursuit and approximate message passing, when they are used to execute the $\ell_0$- and $\ell_1$-based methods, respectively. Our examination shows that orthogonal matching pursuit achieves a much better performance than the exact execution of the $\ell_1$-based method, as well as approximate message passing. However, regarding the $\ell_0$-based method, there is still room to design more effective greedy algorithms than orthogonal matching pursuit. Finally, we evaluate the performances of the algorithms when they are applied to image data compression.

Donate to arXiv

We study the correlation functions of su(2) invariant spin-s chains in the thermodynamic limit. We derive non-linear integral equations for an auxiliary correlation function $\omega$ for any spin s and finite temperature T. For the spin-3/2 chain for arbitrary temperature and zero magnetic field we obtain algebraic expressions for the reduced density matrix of two-sites. In the zero temperature limit, the density matrix elements are evaluated analytically and appear to be given in terms of Riemann's zeta function values of even and odd arguments.

Donate to arXiv

Publication date: 5 April 2016
Source:Physics Reports, Volume 624
Author(s): György Szabó, István Borsos
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide scale of biological objects, human individuals, or even their associations. In these systems the interactions are characterized by matrices that can be decomposed into elementary matrices (games) and classified into four types. The concept of decomposition helps the identification of potential games and also the evaluation of the potential that plays a crucial role in the determination of the preferred Nash equilibrium, and defines the Boltzmann distribution towards which these systems evolve for suitable types of dynamical rules. This survey draws parallel between the potential games and the kinetic Ising type models which are investigated for a wide scale of connectivity structures. We discuss briefly the applicability of the tools and concepts of statistical physics and thermodynamics. Additionally the general features of ordering phenomena, phase transitions and slow relaxations are outlined and applied to evolutionary games. The discussion extends to games with three or more strategies. Finally we discuss what happens when the system is weakly driven out of the “equilibrium state” by adding non-potential components representing games of cyclic dominance.

We adapt Forman's discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow in random and small-world networks, while the distribution is broad in scale-free and real-world networks. In most networks, Forman curvature is found to display significant negative correlation with degree and centrality measures. However, Forman curvature is uncorrelated with clustering coefficient in most networks. Importantly, we find that both model and real networks are vulnerable to targeted deletion of nodes with highly negative Forman curvature. Our results suggest that Forman curvature can be employed to gain novel insights on the organization of complex networks.

Donate to arXiv

This paper firstly show that 2 Dimensional Intelligent Driver Model (Jiang et al., PloS one, 9(4), e94351, 2014) is not able to replicate the synchronized traffic flow. Then we propose an improved model by considering the difference between the driving behaviors at high speeds and that at low speeds. Simulations show that the improved model can reproduce the phase transition from synchronized flow to wide moving jams, the spatiotemporal patterns of traffic flow induced by traffic bottleneck, and the evolution concavity of traffic oscillations (i.e. the standard deviation of the velocities of vehicles increases in a concave/linear way along the platoon). Validating results show that the empirical time series of traffic speed obtained from Floating Car Data can be well simulated as well.

Donate to arXiv

The SW has undeniably been one of the most popular network descriptors in the neuroscience literature. Two main reasons for its lasting popularity are its apparent ease of computation and the intuitions it is thought to provide on how networked systems operate. Over the last few years, some pitfalls of the SW construct and, more generally, of network summary measures, have widely been acknowledged.

Donate to arXiv

Author(s): M. I. Bolotov, G. V. Osipov, and A. Pikovsky

We consider two coupled populations of leaky integrate-and-fire neurons. Depending on the coupling strength, mean fields generated by these populations can have incommensurate frequencies or become frequency locked. In the observed 2:1 locking state of the mean fields, individual neurons in one popu…

[Phys. Rev. E 93, 032202] Published Wed Mar 02, 2016

Author(s): Davide Cellai and Ginestra Bianconi

In multiplex networks with a large number of layers, the nodes can have different activities, indicating the total number of layers in which the nodes are present. Here we model multiplex networks with heterogeneous activity of the nodes and we study their robustness properties. We introduce a perco…

[Phys. Rev. E 93, 032302] Published Wed Mar 02, 2016

Social networks: Better together

Nature. doi:10.1038/531S14a

Author: Chelsea Wald

Social ties go hand-in-hand with cognitive health. Now researchers are trying to determine why engaging with others helps to keep the brain healthy.

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We analyse chimera states in networks of Van der Pol oscillators with hierarchical coupling topology. We investigate the stepwise transition from a nonlocal to a hierarchical topology, and propose the network clustering coefficient as a measure to establish a link between the existence of chimera states and the compactness of the initial base pattern of a hierarchical topology; we show that a large clustering coefficient promotes the occurrence of chimeras. Depending on the level of hierarchy and base pattern, we obtain chimera states with different numbers of incoherent domains. We investigate the chimera regimes as a function of coupling strength and nonlinearity parameter of the individual oscillators. The analysis of a network with larger base pattern resulting in larger clustering coefficient reveals two different types of chimera states and highlights the increasing role of amplitude dynamics.

Donate to arXiv

The SW has undeniably been one of the most popular network descriptors in the neuroscience literature. Two main reasons for its lasting popularity are its apparent ease of computation and the intuitions it is thought to provide on how networked systems operate. Over the last few years, some pitfalls of the SW construct and, more generally, of network summary measures, have widely been acknowledged.

Donate to arXiv

We adapt Forman's discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow in random and small-world networks, while the distribution is broad in scale-free and real-world networks. In most networks, Forman curvature is found to display significant negative correlation with degree and centrality measures. However, Forman curvature is uncorrelated with clustering coefficient in most networks. Importantly, we find that both model and real networks are vulnerable to targeted deletion of nodes with highly negative Forman curvature. Our results suggest that Forman curvature can be employed to gain novel insights on the organization of complex networks.

Donate to arXiv

We study the theoretical conditions to excite a stable self-oscillation in a spin torque oscillator with an in-plane magnetized free layer and a perpendicularly magnetized pinned layer in the presence of magnetic field pointing in an arbitrary direction. The linearized Landau-Lifshitz-Gilbert (LLG) equation is found to be inapplicable to evaluate the threshold between the stable and self-oscillation states because the critical current density estimated from the linearized equation is considerably larger than that found in the numerical simulation. We derive a theoretical formula of the threshold current density by focusing on the energy gain of the magnetization from the spin torque during a time shorter than a precession period. A good agreement between the derived formula and the numerical simulation is obtained. The condition to stabilize the out-of-plane self-oscillation above the threshold is also discussed.

On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxilic acid cycle). For the first time, we consider its consistency and stability, which depend on the dissipation of a transmembrane potential formed by the respiratory chain in the plasmatic membrane of a cell. The phase-parametric characteristic of the dynamics of the ATP level depending on a given parameter is constructed. The scenario of formation of multiple autoperiodic and chaotic modes is presented. Poincar\'{e} sections and mappings are constructed. The stability of modes and the fractality of the obtained bifurcations are studied. The full spectra of Lyapunov indices, divergences, KS-entropies, horizons of predictability, and Lyapunov dimensionalities of strange attractors are calculated. Some conclusions about the structural-functional connections determining the dependence of the cell respiration cyclicity on the synchronization of the functioning of the tricarboxilic acid cycle and the electron transport chain are presented.

Donate to arXiv

"Stiff" differential equations are commonplace in engineering and dynamical systems. To solve them we need flexible integrators that can deal with rapidly-changing righthand sides. This tutorial describes the application of "adaptive" [ variable timestep ] integrators to "stiff" mechanical problems encountered in modern applications of Gibbs' 1902 statistical mechanics. Linear harmonic oscillators subject to nonlinear thermal constraints can exhibit either stiff or smooth dynamics. Two closely-related examples, Nos\'e's 1984 dynamics and Nos\'e-Hoover 1985 dynamics, are both based on Hamiltonian mechanics, as was ultimately clarified by Dettmann and Morriss in 1996. Both these dynamics are consistent with Gibbs' canonical ensemble. Nos\'e's dynamics is "stiff" and can present severe numerical difficulties. Nos\'e-Hoover dynamics, though it follows exactly the same trajectory, is "smooth" and relatively trouble-free. Our tutorial emphasises the power of adaptive integrators to resolve stiff problems like the Nos\'e oscillator. The solutions obtained illustrate the power of computer graphics to enrich numerical solutions. Adaptive integration with computer graphics are basic to an understanding of dynamical systems and statistical mechanics. These tools lead naturally into the visualization of intricate fractal structures formed by chaos as well as elaborate knots tied by regular nonchaotic dynamics. This work was invited by the American Journal of Physics.

Donate to arXiv

We introduce a new, reduced nonlinear oscillator model governing the spontaneous creation of sharp pulses in a damped, driven, cubic nonlinear Schroedinger equation. The reduced model embodies the fundamental connection between mode synchronization and spatiotemporal pulse formation. We identify attracting solutions corresponding to stable cavity solitons and Turing patterns. Viewed in the optical context, our results explain the recently reported $\pi$ and $\pi/2$ steps in the phase spectrum of microresonator-based optical frequency combs.

Donate to arXiv

"Stiff" differential equations are commonplace in engineering and dynamical systems. To solve them we need flexible integrators that can deal with rapidly-changing righthand sides. This tutorial describes the application of "adaptive" [ variable timestep ] integrators to "stiff" mechanical problems encountered in modern applications of Gibbs' 1902 statistical mechanics. Linear harmonic oscillators subject to nonlinear thermal constraints can exhibit either stiff or smooth dynamics. Two closely-related examples, Nos\'e's 1984 dynamics and Nos\'e-Hoover 1985 dynamics, are both based on Hamiltonian mechanics, as was ultimately clarified by Dettmann and Morriss in 1996. Both these dynamics are consistent with Gibbs' canonical ensemble. Nos\'e's dynamics is "stiff" and can present severe numerical difficulties. Nos\'e-Hoover dynamics, though it follows exactly the same trajectory, is "smooth" and relatively trouble-free. Our tutorial emphasises the power of adaptive integrators to resolve stiff problems like the Nos\'e oscillator. The solutions obtained illustrate the power of computer graphics to enrich numerical solutions. Adaptive integration with computer graphics are basic to an understanding of dynamical systems and statistical mechanics. These tools lead naturally into the visualization of intricate fractal structures formed by chaos as well as elaborate knots tied by regular nonchaotic dynamics. This work was invited by the American Journal of Physics.

We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and time, mimicking the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale-invariance for geometric random graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behaviour. These properties are similar to those of empirically observed web graphs.

Donate to arXiv

Multiplex networks are generalized network structures that are able to describe networks in which the same set of nodes are connected by links that have different connotations. Multiplex networks are ubiquitous since they describe social, financial, engineering and biological networks as well. Extending our ability to analyze complex networks to multiplex network structures increases greatly the level of information that is possible to extract from Big Data. For these reasons characterizing the centrality of nodes in multiplex networks and finding new ways to solve challenging inference problems defined on multiplex networks are fundamental questions of network science. In this paper we discuss the relevance of the Multiplex PageRank algorithm for measuring the centrality of nodes in multilayer networks and we characterize the utility of the recently introduced indicator function $\widetilde{\Theta}^{S}$ for describing their mesoscale organization and community structure. As working examples for studying these measures we consider three multiplex network datasets coming for social science.

We present a simple order book mechanism that regulates an artificial financial market with self-organized criticality dynamics and fat tails of returns distribution. The model shows the role played by individual imitation in determining trading decisions, while fruitfully replicates typical aggregate market behavior as the "self-fulfilling prophecy". We also address the role of random traders as a possible decentralized solution to dampen market fluctuations.

Donate to arXiv

Author(s): Swadhin Taneja, Arnold B. Mitnitski, Kenneth Rockwood, and Andrew D. Rutenberg

How long people live depends on their health, and how it changes with age. Individual health can be tracked by the accumulation of age-related health deficits. The fraction of age-related deficits is a simple quantitative measure of human aging. This quantitative frailty index (F) is as good as chro…

[Phys. Rev. E 93, 022309] Published Mon Feb 29, 2016

Author(s): Tomohiro Fukunaga, Tomoaki Imasaka, Akira Ito, Yoshiki Sugitani, Keiji Konishi, and Naoyuki Hara

This paper investigates dynamics of a management system for controlling a pair of energy storages. The system involves the following two characteristics: each storage behaves in a manner that reduces the number of charge noncharge cycles and begins to be charged when the price of power is lower than…

[Phys. Rev. E 93, 022220] Published Mon Feb 29, 2016

Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled, symmetric (sub)populations with unimodal frequency distributions and show that the resulting synchronization patterns may resemble those of a single population with bimodally distributed frequencies. Our proof of the equivalence of their stability, dynamics, and bifurcations, is based on an Ott-Antonsen ansatz. The generalization to networks consisting of multiple (sub)populations vis-\`a-vis networks with multimodal frequency distributions, however, appears impossible.

Donate to arXiv

Author(s): Hyunsuk Hong, Kevin P. O'Keeffe, and Steven H. Strogatz

We consider a mean-field model of coupled phase oscillators with quenched disorder in the coupling strengths and natural frequencies. When these two kinds of disorder are uncorrelated (and when the positive and negative couplings are equal in number and strength), it is known that phase coherence ca…

[Phys. Rev. E 93, 022219] Published Fri Feb 26, 2016

Author(s): G. Nikoghosyan, R. Nigmatullin, and M. B. Plenio

When traversing a symmetry-breaking second-order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such scaling laws that is based on the analytical transformation …

[Phys. Rev. Lett. 116, 080601] Published Fri Feb 26, 2016

Author(s): A. V. Brantov, E. A. Govras, V. F. Kovalev, and V. Yu. Bychenkov

An effective scheme of synchronized laser-triggered ion acceleration and the corresponding theoretical model are proposed for a slow light pulse of relativistic intensity, which penetrates into a near-critical-density plasma, strongly slows, and then increases its group velocity during propagation w…

[Phys. Rev. Lett. 116, 085004] Published Fri Feb 26, 2016

We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm designed for practical use both because of its ability to generate very large graphs (efficiency) and because it is easy to implement (simplicity). We focus on a family of heuristics for which we introduce optimality conditions, and show how this optimality can be reached in practice. We then propose a different approach, specifically designed for real-world degree distributions, which outperforms the first one. Based on a conjecture which we argue rigorously and which was confirmed by strong empirical evidence, we finally reduce the best asymptotic complexity bound known so far.

In previous work, we developed the scaled SIS process, which models the dynamics of SIS epidemics over networks. We derived for the scaled SIS process a closed-form expression for the time-asymptotic probability distribution of the configurations of all the agents in the network, which explicitly exhibits the underlying network topology through its adjacency matrix. This is accomplished for networks that are of finite-size and of arbitrary topology. This paper determines which network configuration is the most probable. We prove that, for a range of epidemic parameters, this combinatorial inference problem leads to a submodular optimization problem, which can be solved in polynomial time. We relate the most-probable configuration to the network structure, and in particular to the existence of high-density subgraphs. Depending on the model parameters, subset of agents may be more likely to be infected than others; these more vulnerable agents form subgraphs that are denser than the overall network. We illustrate our results with a 193 node social network of drug users and with the 4941 node Western US power grid under different model parameters.

Author(s): Wesley F. C. Cota, Silvio C. Ferreira, and Géza Ódor

We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects…

[Phys. Rev. E] Published Wed Feb 24, 2016