Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Q17: Focus Session: Network of Networks 
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Chair: Antonio Scala, CNRISC Institute for Complex Systems Room: 402 
Wednesday, March 5, 2014 2:30PM  3:06PM 
Q17.00001: Multilevel Complex Networks and Systems Invited Speaker: Guido Caldarelli Network theory has been a powerful tool to model isolated complex systems. However, the classical approach does not take into account the interactions often present among different systems. Hence, the scientific community is nowadays concentrating the efforts on the foundations of new mathematical tools for understanding what happens when~multiple networks interact. The case of economic and financial networks represents a paramount example of multilevel networks. In the case of trade, trade among countries the different levels can be described by the different granularity of the trading relations. Indeed, we have now data from the scale of consumers to that of the country level. In the case of financial institutions, we have a variety of levels at the same scale. For example one bank can appear in the interbank networks, ownership network and cds networks in which the same institution can take place. In both cases the systemically important vertices need to be determined by different procedures of centrality definition and community detection. In this talk I will present some specific cases of study related to these topics and present the regularities found. [Preview Abstract] 
Wednesday, March 5, 2014 3:06PM  3:18PM 
Q17.00002: Epidemic Fault Propagation and Synchronization for Networks of Networks Gregorio D'Agostino , Huijuan Wang , Piet Van Mieghem , Shlomo Havlin , Eugene Stanley We have employed spectral methods to deal with both epidemics and diffusion processes on Networks of Networks (NoNs). Resorting to the largest eigenvalue of the adjacency matrix, we have estimated the threshold for epidemic processes. The algebraic connectivity has provided information on the slowest diffusion mode. The former quantities and their interplay are worth studying for their own sake. However, the motivation of the work arises in the context of Critical Infrastructure Protection. In fact, epidemics on NoNs provide a modeling of fault propagation on interdependent infrastructures and the diffusion processes are strictly related to their synchronization modes. Different theoretical approaches have been employed including exact bounds estimates, meanfield approximations and perturbative expansions. All these approaches provided tools to compare the resilience of NoNs with respect to both synchronization and fault propagation. We have modeled NoNs by different interdependent network models (BA, ER, RR etc) linked according to different strategies. Upon increasing the number of links among networks interesting emergent behaviors are observed. [Preview Abstract] 
Wednesday, March 5, 2014 3:18PM  3:30PM 
Q17.00003: Coexistence of critical regimes in interconnected networks Filippo Radicchi Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked systems exposed to potentially catastrophic failures. The theoretical approach to this problem is based on the study of the nature of the phase transitions associated to critical phenomena running on interconnected networks. In particular, it has been shown that many critical phenomena of continuous nature in isolated networks become instead discontinuous, and thus catastrophic, in interconnected networks when the strength of the connections between the various network layers is sufficiently large. We show that four main ingredients determine the critical features of a random interconnected network: the strength of the interconnections, the first two moments of the degree distribution of the entire network, and the correlation between intra and interlayer degrees. Different mixtures of these ingredients change the location of the critical points, and lead to the emergence a very rich scenario where phase transitions can be either discontinuous or continuous and different regimes can disappear or even coexist. [Preview Abstract] 
Wednesday, March 5, 2014 3:30PM  3:42PM 
Q17.00004: International and Domestic Business Cycles as Dynamics of a Network of Networks Yuichi Ikeda , Hiroshi Iyetomi , Hideaki Aoyama , Hiroshi Yoshikawa Synchronization in business cycles has attracted economists and physicists as selforganization in the time domain. From a different point of view, international and domestic business cycles are also interesting as dynamics of a network of networks or a multilevel network. In this paper, we analyze the Indices of Industrial Production monthly timeseries in Japan from January 1988 to December 2007 to develop a deeper understanding of domestic business cycles. The frequency entrainment and the partial phase locking were observed for the 16 sectors to be direct evidence of synchronization. We also showed that the information of the economic shock is carried by the phase timeseries. The common shock and individual shocks are separated using phase timeseries. The former dominates the economic recession in all of 1992, 1998 and 2001. In addition to the above analysis, we analyze the quarterly GDP time series for Australia, Canada, France, Italy, the United Kingdom, and the United States from Q2 1960 to Q1 2010 in order to clarify its origin. We find frequency entrainment and partial phase locking. Furthermore, a coupled limitcycle oscillator model is developed to explain the mechanism of synchronization. In this model, the interaction due to international trade is interpreted as the origin of the synchronization. The obtained results suggest that the business cycle may be described as a dynamics of the multilevel coupled oscillators exposed to random individual shocks. [Preview Abstract] 
Wednesday, March 5, 2014 3:42PM  3:54PM 
Q17.00005: Heterogeneous nodal responses in cascade dynamics on multiplex networks KyuMin Lee , Charles D. Brummitt , KwangIl Goh Structure and dynamics of multiplex network systems have been intensively studied recently, revealing nontrivial results such as facilitated cascading failures and new type of phase transitions unforeseen in the singlelevel systems. However, most studies about multilayered, network of networks have mainly considered the case of single nodal response to multiple layers, that is, every node responds to the multiple layers in identical way. Most complex systems like human society, however, function not only through various kinds of relations but also through heterogeneous response behavior across agents, indicating a new level of complexity. To address it, here we formulate a threshold cascade model on multiplex networks with a mixture of two response functions: OR and AND rules. For the OR response, nodes are activated if enough neighbors in any layer are active, whereas for the AND response, the nodes activate only if enough neighbors in all layers are active. Coexistence of these two response rules is shown to control between facilitation and inhibition of cascading failures, and moreover, it can also control the type of transitions to global cascades between continuous and discontinuous ones. We will discuss the implication of the results in the context of social dynamics. [Preview Abstract] 
Wednesday, March 5, 2014 3:54PM  4:06PM 
Q17.00006: Mutual Percolation of Multiplex Networks with Link Overlaps Sangchul Lee , Byungjoon Min , KyuMin Lee , K.I. Goh Many realworld complex systems operate through multiple layers of distinct interactions and the interplay between them. Most studies on multiplex networks, however, have largely ignored the effect of the link overlap across layers despite the strong empirical evidences for its significance. In this respect here we study the impact of link overlaps on mutual percolation of multiplex networks with two layers (duplex networks). We present the analytic solution based on the generating function approach that explicitly distinguishes the distinctive roles that the overlap and nonoverlap links play in establishing the mutual connectivity. The analytic solution is fully supported by extensive numerical simulations, thus successfully remedies the shortcoming of previously proposed theory by Cellai et al. [arXiv:1307.6359v1]. Our analytical results show that while the overlap links strongly facilitate mutual percolation by making components connected with overlap links yet it is unable to diminish the discontinuous nature of mutual percolation transition. Finally, we discuss the implication of our results to the robustness of duplex networks against link failures. [Preview Abstract] 
Wednesday, March 5, 2014 4:06PM  4:18PM 
Q17.00007: Coevolution model of multiplex networks Jinhyeon Kim , Jung Yeol Kim , K.I. Goh Many realworld complex systems can be represented as multiplex networks with multiple types of links. Each link type in the system defines network layers, which coexist and cooperate for the system's function. To understand such multiplex systems, we study a modeling framework based on coevolution of network layers. In our previous research, we introduced the coevolution of network layers as an evolutionary mechanism for the correlated multiplexity in growing networks [1]. We examined how the entangled growth of coevolving layers can shape the network structure and showed analytically and numerically that the coevolution can induce strong degree correlations across layers, as well as modulate degree distribution. In this research, we study several variants of the basic model with more realistic features such as the difference in the number of nodes and nonsimultaneous arrivals of nodes in different layers, to characterize how these features also affect the correlation property of the multiplex structure. Further, we study the effect of negative coupling between layers in multiplex network evolution. \\[4pt] [1] J. Y. Kim and K. I. Goh, Phys. Rev. Lett. 111, 058702 (2013) [Preview Abstract] 
Wednesday, March 5, 2014 4:18PM  4:30PM 
Q17.00008: Layercrossing overhead and information spreading in multiplex social networks Byungjoon Min , K.I. Goh Many realworld systems consist of multiple different layers of networks and interplay between them. Taking such multiplexity into account is important to a complete understanding of the structure and dynamics of complex systems. In this respect, we propose and study a model of information or disease spreading on multiplex social networks, in which agents interact or communicate through multiple channels (layers), and there exists a layerswitching overhead for transmission across the interaction layers. The model is characterized by the pathdependent transmissibility over a contact, which is dynamically determined, dependent on both incoming and outgoing transmission layers due to the switching overhead. We formulate a generalized theory with a mapping to deal with such a pathdependent transmissibility, and demonstrate dependency of epidemic threshold and epidemic outbreak size with respect to multiplexity characteristics such as the densities of network layers, layercrossing costs, and type of seed infections. Our results suggest that explicit consideration of multiplexity can be crucial in realistic modeling of spreading processes on social networks. [Preview Abstract] 
Wednesday, March 5, 2014 4:30PM  4:42PM 
Q17.00009: Reliability theory for diffusion processes on interconnected networks Yasamin Khorramzadeh , Mina Youssef , Stephen Eubank We present the concept of network reliability as a framework to study diffusion dynamics in interdependent networks. We illustrate how different outcomes of diffusion processes, such as cascading failure, can be studied by estimating the reliability polynomial under different reliability rules. As an example, we investigate the effect of structural properties on diffusion dynamics for a few different topologies of two coupled networks. We evaluate the effect of varying the probability of failure propagating along the edges, both within a single network as well as between the networks. We exhibit the sensitivity of interdependent network reliability and connectivity to edge failures in each topology. [Preview Abstract] 
Wednesday, March 5, 2014 4:42PM  4:54PM 
Q17.00010: Synchronization in Networks of Coupled Chemical Oscillators Kenneth Showalter , Mark Tinsley , Simbarashe Nkomo , Hua Ke We have studied networks of coupled photosensitive chemical oscillators. Experiments and simulations are carried out on networks with different topologies and modes of coupling. We describe experimental and modeling studies of chimera and phasecluster states and their relation to other synchronization states. Networks of integrateandfire oscillators are also studied in which sustained coordinated activity is exhibited. Individual nodes display incoherent firing events; however, a dominant frequency within the collective signal is exhibited. The introduction of spiketimingdependent plasticity allows the network to evolve and leads to a stable unimodal linkweight distribution. M. R. Tinsley et al., Nature Physics 8, 662 (2012); S. Nkomo et al., Phys. Rev. Lett. 110, 244102 (2013); H. Ke et al., in preparation. [Preview Abstract] 
Wednesday, March 5, 2014 4:54PM  5:06PM 
Q17.00011: Percolation of localized attack on isolated and interdependent random networks Shuai Shao , Xuqing Huang , H. Eugene Stanley , Shlomo Havlin Percolation properties of isolated and interdependent random networks have been investigated extensively. The focus of these studies has been on random attacks where each node in network is attacked with the same probability or targeted attack where each node is attacked with a probability being a function of its centrality, such as degree. Here we discuss a new type of realistic attacks which we call a localized attack where a group of neighboring nodes in the networks are attacked. We attack a randomly chosen node, its neighbors, and its neighbor of neighbors and so on, until removing a fraction ($1p$) of the network. This type of attack reflects damages due to localized disasters, such as earthquakes, floods and war zones in realworld networks. We study, both analytically and by simulations the impact of localized attack on percolation properties of random networks with arbitrary degree distributions and discuss in detail random regular (RR) networks, Erd\H{o}sR\'{e}nyi (ER) networks and scalefree (SF) networks. We extend and generalize our theoretical and simulation results of single isolated networks to networks formed of interdependent networks. [Preview Abstract] 

Q17.00012: ABSTRACT WITHDRAWN 
Wednesday, March 5, 2014 5:18PM  5:30PM 
Q17.00013: Discontinuous percolation transition at a finite threshold Byungnam Kahng , Young Sul Cho Recent interest of discontinuous percolation transitions (DPT) has been sparked by the explosive percolation model. Even though this model shows an abrupt percolation transition in finitesized systems, it reveals that the jump of the order parameter shrinks to zero as the system size is increased. To disclose the mechanism of the DPT, a spanningclusteravoiding (SCA) model in the Euclidean space was introduced and analytically understood. However, the DPT in the SCA model is trivial because the percolation threshold is one. Thus, it is timely demanding to construct a general framework, under which a nontrivial DPT can take place at a finite threshold. Here, we propose the necessary conditions for the nontrivial DPT, and classify existing percolation models according to this criterion. Moreover, a model, satisfying those conditions and showing a nontrivial DPT, is introduced and discussed in the perspective of the network of networks. We anticipate this theoretical framework to be a platform for further researches on DPT in other disciplinary systems. [Preview Abstract] 
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