Edmilson Roque

We present analytical results for the distribution of first hitting times of random walkers on Erd\H{o}s-R\'enyi networks. Starting from a random initial node, a random walker hops randomly between adjacent nodes on the network until it hits a node which it has already visited before. At this point, the path is terminated. The path length $d$, pursued by the random walker from the initial node up to its termination is called the first hitting time or the first intersection length. Using recursion equations, we obtain analytical results for the tail distribution of the path lengths, $P(d>\ell)$. The results are found to be in excellent agreement with simulations. It turns out that the distribution $P(d>\ell)$ follows a product of an exponential distribution and a Rayleigh distribution. We also obtain expressions for the mean, median and standard deviation of this distribution in terms of the network size and its mean degree. It is found that the first hitting time is much shorter than the last hitting time of the corresponding self-avoiding walk. The termination of the path may take place either due to a backtracking step of the random walker into the previous node or due to retracing of its path, namely stepping into a node which has been visited two or more time steps earlier. We obtain analytical results for the probabilities, $p_b$ and $p_r$, that the cause of termination will be backtracking or retracing, respectively. It is shown that in dilute networks the dominant termination scenario is backtracking while in dense networks most paths are terminated by retracing. We also obtain expressions for the conditional distributions of path lengths, $P(d=\ell|b)$ and $P(d=\ell|r)$. These results provide useful insight into the general problem of survival analysis and the statistics of mortality rates when two or more termination scenarios coexist.

With the rise of Wikipedia as a first-stop source for scientific knowledge, it is important to compare its representation of that knowledge to that of the academic literature. Here we identify the 250 most heavily used journals in each of 26 research fields (4,721 journals, 19.4M articles in total) indexed by the Scopus database, and test whether topic, academic status, and accessibility make articles from these journals more or less likely to be referenced on Wikipedia. We find that a journal's academic status (impact factor) and accessibility (open access policy) both strongly increase the probability of it being referenced on Wikipedia. Controlling for field and impact factor, the odds that an open access journal is referenced on the English Wikipedia are 47% higher compared to paywall journals. One of the implications of this study is that a major consequence of open access policies is to significantly amplify the diffusion of science, through an intermediary like Wikipedia, to a broad audience.

Network generation models provide an understanding of the dynamics behind the formation and evolution of different networks including social networks, technological networks and biological networks. Two important applications of these models are to study the evolution dynamics of network formation and to generate benchmark networks with known community structures. Research has been conducted in both these directions relatively independent of the other application area. This creates a disjunct between real world networks and the networks generated to study community detection algorithms.

In this paper, we propose to study both these application areas together i.e.\ introduce a network generation model based on evolution dynamics of real world networks and generate networks with community structures that can be used as benchmark graphs to study community detection algorithms. The generated networks possess tunable modular structures which can be used to generate networks with known community structures. We study the behaviour of different community detection algorithms based on the proposed model and compare it with other models to generate benchmark graphs. Results suggest that the networks generated using the proposed model present tougher challenges for community detection algorithms due to the topological structure introduced by evolution dynamics.

How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view. The basic idea is to envision the graph clustering as a density-cut problem, such that the vertices in the same cluster are densely connected and the vertices between clusters are sparsely connected. To identify meaningful clusters (communities) in a graph, a density-connected tree is first constructed in a local fashion. Owing to the density-connected tree, Dcut allows partitioning a graph into multiple densely tight-knit clusters directly. We demonstrate that our method has several attractive benefits: (a) Dcut provides an intuitive criterion to evaluate the goodness of a graph clustering in a more natural and precise way; (b) Built upon the density-connected tree, Dcut allows identifying the meaningful graph clusters of densely connected vertices efficiently; (c) The density-connected tree provides a connectivity map of vertices in a graph from a local density perspective. We systematically evaluate our new clustering approach on synthetic as well as real data to demonstrate its good performance.

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We investigate the time averaged squared displacement (TASD) of continuous time random walks with respect to the number of steps $N$, which the random walker performed during the data acquisition time $T$. We prove that the TASD, and as well the apparent diffusion constant, grow linearly with $N$, provided the steps possess a fourth moment and can not accumulate in small intervals. Consequently, the fluctuations of the latter are dominated by the fluctuations of $N$, and fluctuations of the walker's thermal history are irrelevant. Furthermore, we show that the relative scatter decays as $1/\sqrt{N}$, which suppresses all non-linear features in a plot of the TASD against the lag time. Parts of our arguments also hold for continuous time random walks with correlated steps.

Abstract

When designing or extending electricity grids, both frequency stability and resilience against cascading failures have to be considered amongst other aspects of energy security and economics such as construction costs due to total line length. Here, we compare an improved simulation model for cascading failures with state-of-the-art simulation models for short-term grid dynamics. Random ensembles of realistic power grid topologies are generated using a recent model that allows for a tuning of global vs local redundancy. The former can be measured by the algebraic connectivity of the network, whereas the latter can be measured by the networks transitivity. We show that, while frequency stability of an electricity grid benefits from a global form of redundancy, resilience against cascading failures rather requires a more local form of redundancy and further analyse the corresponding trade-off.

Abstract

Renewables will soon dominate energy production in our electric power system. And yet, how to integrate renewable energy into the grid and the market is still a subject of major debate. Decentral Smart Grid Control (DSGC) was recently proposed as a robust and decentralized approach to balance supply and demand and to guarantee a grid operation that is both economically and dynamically feasible. Here, we analyze the impact of network topology by assessing the stability of essential network motifs using both linear stability analysis and basin volume for delay systems. Our results indicate that if frequency measurements are averaged over sufficiently large time intervals, DSGC enhances the stability of extended power grid systems. We further investigate whether DSGC supports centralized and/or decentralized power production and find it to be applicable to both. However, our results on cycle-like systems suggest that DSGC favors systems with decentralized production. Here, lower line capacities and lower averaging times are required compared to those with centralized production.

Abstract

Extreme events are a challenge to natural as well as man-made systems. For critical infrastructure like power grids, we need to understand their resilience against large disturbances. Recently, new measures of the resilience of dynamical systems have been developed in the complex system literature. Basin stability and survivability respectively assess the asymptotic and transient behavior of a system when subjected to arbitrary, localized but large perturbations in frequency and phase. To employ these methods that assess power grid resilience, we need to choose a certain model detail of the power grid. For the grid topology we considered the Scandinavian grid and an ensemble of power grids generated with a random growth model. So far the most popular model that has been studied is the classical swing equation model for the frequency response of generators and motors. In this paper we study a more sophisticated model of synchronous machines that also takes voltage dynamics into account, and compare it to the previously studied model. This model has been found to give an accurate picture of the long term evolution of synchronous machines in the engineering literature for post fault studies. We find evidence that some stable fix points of the swing equation become unstable when we add voltage dynamics. If this occurs the asymptotic behavior of the system can be dramatically altered, and basin stability estimates obtained with the swing equation can be dramatically wrong. We also find that the survivability does not change significantly when taking the voltage dynamics into account. Further, the limit cycle type asymptotic behaviour is strongly correlated with transient voltages that violate typical operational voltage bounds. Thus, transient voltage bounds are dominated by transient frequency bounds and play no large role for realistic parameters.

It is very common to observe nonlinear features in agricultural and ecological systems. For example, in tree crop production, alternate bearing is well known phenomena caused by nonlinear dynamics. Production of single tree of Citrus Unshiu trees is recognized to be driven by a mechanistic process modeled with the so-called "resource budget model", which demonstrates phenomenon of alternate bearing. However, the term of alternative bearing is used not only for an individual tree's production but also for total production of a large sized population of trees. In this paper, we developed noise induced uncoupled dynamics model for population alternate bearing based on Isagi's resource budget model. Based on numerical experiments with the developed model, theoretical possibility of a substantial alternate bearing effect even in a national market was proposed.

Author(s): Diego Paiva Pires, Marco Cianciaruso, Lucas C. Céleri, Gerardo Adesso, and Diogo O. Soares-Pinto

Understanding the speed with which a quantum system can evolve between distinguishable states has applications in quantum technology. A new theoretical study demonstrates a general family of quantum speed limits that can be applied to any physical process.

[Phys. Rev. X 6, 021031] Published Thu Jun 02, 2016

Author: Julia Fahrenkamp-Uppenbrink

For years, scientists have debated where dogs came from. Did wolves first forge their special relationship with humans in Europe, or in Asia? The answer, according to a new study, is yes. Researchers report that genetic analysis of hundreds of canines—including a nearly 5000-year-old dog unearthed on the east coast of Ireland—reveals that dogs may have been domesticated twice, once in Asia and once in Europe or the Near East, although European ancestry has mostly vanished from today's dogs. The findings could resolve a rift that has roiled the canine origins community—but experts say a lot more work needs to be done to confirm them. Author: David Grimm

The weight of links in a network is often related to the similarity of the nodes. Here, we introduce a simple tunable measure for analysing the similarity of nodes across different link weights. In particular, we use the measure to analyze homophily in a group of 659 freshman students at a large university. Our analysis is based on data obtained using smartphones equipped with custom data collection software, complemented by questionnaire-based data. The network of social contacts is represented as a weighted multilayer network constructed from different channels of telecommunication as well as data on face-to-face contacts. We find that even strongly connected individuals are not more similar with respect to basic personality traits than randomly chosen pairs of individuals. In contrast, several socio-demographics variables have a significant degree of similarity. We further observe that similarity might be present in one layer of the multilayer network and simultaneously be absent in the other layers. For a variable such as gender, our measure reveals a transition from similarity between nodes connected with links of relatively low weight to dis-similarity for the nodes connected by the strongest links. We finally analyze the overlap between layers in the network for different levels of acquaintanceships.

We present an exhaustive mathematical analysis of the recently proposed Non-Poissonian Ac- tivity Driven (NoPAD) model [Moinet et al. Phys. Rev. Lett., 114 (2015)], a temporal network model incorporating the empirically observed bursty nature of social interactions. We focus on the aging effects emerging from the Non-Poissonian dynamics of link activation, and on their effects on the topological properties of time-integrated networks, such as the degree distribution. Analytic expressions for the degree distribution of integrated networks as a function of time are derived, ex- ploring both limits of vanishing and strong aging. We also address the percolation process occurring on these temporal networks, by computing the threshold for the emergence of a giant connected component, highlighting the aging dependence. Our analytic predictions are checked by means of extensive numerical simulations of the NoPAD model.

Author(s): Dane Taylor, Saray Shai, Natalie Stanley, and Peter J. Mucha

Many systems are naturally represented by a multilayer network in which edges exist in multiple layers that encode different, but potentially related, types of interactions, and it is important to understand limitations on the detectability of community structure in these networks. Using random matr…

[Phys. Rev. Lett. 116, 228301] Published Thu Jun 02, 2016

We show the first solvable chaotic synchronization model of unidirectionally coupled dynamical systems. We establish a new interpretation of the conditional Lyapunov exponent that characterizes chaotic synchronization completely. Moreover, we newly show how the conditional Lyapunov exponent relates to common noise-induced synchronization phenomena by the new interpretation.

The navigation satellite constellations in medium-Earth orbit exist in a background of third-body secular resonances stemming from the perturbing gravitational effects of the Moon and the Sun. The resulting chaotic motions, emanating from the overlapping of neighboring resonant harmonics, induce especially strong perturbations on the orbital eccentricity, which can be transported to large values, thereby increasing the collision risk to the constellations and possibly leading to a proliferation of space debris. We show here that this transport is of a diffusive nature and we present representative diffusion maps that are useful in obtaining a global comprehension of the dynamical structure of the navigation satellite orbits.

A major hurdle in the simulation of the steady state of epidemic processes is that the system will unavoidably visit an absorbing, disease-free state at sufficiently long times due to the finite size of the networks where epidemics evolves. In the present work, we compare different quasistationary (QS) simulation methods where the absorbing states are suitably handled and the thermodynamical limit of the original dynamics can be achieved. We analyzed the standard QS (SQS) method, where the sampling is constrained to active configurations, the reflecting boundary condition (RBC), where the dynamics returns to the pre-absorbing configuration, and hub reactivation (HR), where the most connected vertices of the network is reactivated after a visit to an absorbing state. We applied the methods to the contact process (CP) and susceptible-infected-susceptible (SIS) models on regular and scale-free networks. The investigated methods yield the same epidemic threshold for both models. For CP, that undergoes a standard collective phase transition, the methods are equivalent. For SIS, whose phase transition is ruled by the hub mutual reactivation, the SQS and HR methods were able to capture localized epidemic phases while RBC did not. We also applied auto-correlation time as a tool to characterize the phase transition and observed that this analysis provides the same finite size scaling exponents for the critical relaxation time for the investigated methods. Finally, we verified the equivalence between RBC method and a weak external field for epidemics in networks.

Concurrent enhancement of percolation and synchronization in adaptive networks

Scientific Reports, Published online: 2 June 2016; doi:10.1038/srep27111

In this work, we establish a connection between the extended Prelle-Singer procedure with other widely used analytical methods to identify integrable systems in the case of $n^{th}$-order nonlinear ordinary differential equations (ODEs). By synthesizing these methods we bring out the interlink between Lie point symmetries, contact symmetries, $\lambda$-symmetries, adjoint-symmetries, null forms, Darboux polynomials, integrating factors, Jacobi last multiplier and generalized $\lambda$-symmetries corresponding to the $n^{th}$-order ODEs. We also prove these interlinks with suitable examples. By exploiting these interconnections, the characteristic quantities associated with different methods can be deduced without solving the associated determining equations.

Author(s): Juan Carlos González-Avella and Celia Anteneodo

Coupled map lattices are paradigmatic models of many collective phenomena. However, quite different patterns can emerge depending on the updating scheme. While in early versions, maps were updated synchronously, there has been in recent years a concern to consider more realistic updating schemes whe…

[Phys. Rev. E 93, 052230] Published Tue May 31, 2016

Author(s): Victor J. Barranca, Douglas Zhou, and David Cai

Utilizing the sparsity ubiquitous in real-world network connectivity, we develop a theoretical framework for efficiently reconstructing sparse feed-froward connections in a pulse-coupled nonlinear network through its output activities. Using only a small ensemble of random inputs, we solve this inve…

[Phys. Rev. E] Published Fri May 27, 2016

Studies on how to model the interplay between diseases and behavioral responses (so-called coupled disease-behavior interaction) have attracted increasing attention. Owing to the lack of obvious clinical evidence of diseases, or the incomplete information related to the disease, the risks of infection cannot be perceived and may lead to inappropriate behavioral responses. Therefore, how to quantitatively analyze the impacts of asymptomatic infection on the interplay between diseases and behavioral responses is of particular importance. In this letter, under the complex network framework, we study the coupled disease-behavior interaction model by dividing infectious individuals into two states: U-state (without evident clinical symptoms, labelled as U) and I-state (with evident clinical symptoms, labelled as I). A susceptible individual can be infected by U- or I-nodes, however, since the U-nodes cannot be easily observed, susceptible individuals take behavioral responses only...

Author(s): Spase Petkoski, Andreas Spiegler, Timothée Proix, Parham Aram, Jean-Jacques Temprado, and Viktor K. Jirsa

Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by d…

[Phys. Rev. E] Published Tue May 31, 2016