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ABSTRACT: Distinct channels of interaction in a complex networked system define network
layers, which co-exist and co-operate for the system's function. Towards
realistic modeling and understanding such multiplex systems, we introduce and
study a class of growing multiplex network models in which different network
layers coevolve, and examine how the entangled growth of coevolving layers can
shape the overall network structure. We show analytically and numerically that
the coevolution can induce strong degree correlations across layers, as well as
modulate degree distributions. We further show that such a coevolution-induced
correlated multiplexity can alter the system's response to dynamical process,
exemplified by the suppressed susceptibility to a threshold cascade process.
03/2013;
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ABSTRACT: We study a random walk model in which the jumping probability to a site is
dependent on the number of previous visits to the site, as a model of the
mobility with memory. To this end we introduce two parameters called the memory
parameter alpha and the impulse parameter p. From extensive numerical
simulations, we found that various limited mobility patterns such as
sub-diffusion, trapping, and logarithmic diffusion could be observed. By the
memory, a long-ranged directional anti-correlation kinetically-induces
anomalous sub-di?usive and trapping behaviors, and transition between them.
With random jumps by the impulse parameter, a trapped walker can escape from
the trap very slowly, resulting in an ultraslow logarithmic diffusive behavior.
Our results suggest that the memory of walker's has-beens can be one mechanism
explaining many of empirical characteristics of the mobility of animated
objects.
06/2012;
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ABSTRACT: Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex networks. We generalize the threshold cascade model [Watts, Proc. Natl. Acad. Sci. USA 99, 5766 (2002)] to multiplex networks, in which a node activates if a sufficiently large fraction of neighbors in any layer are active. We show that both combining layers (i.e., realizing other interactions play a role) and splitting a network into layers (i.e., recognizing distinct kinds of interactions) facilitate cascades. Notably, layers unsusceptible to global cascades can cooperatively achieve them if coupled. On one hand, this suggests fundamental limitations on predicting cascades without full knowledge of a system's multiplexity; on the other hand, it offers feasible means to control cascades by introducing or removing sparse layers in an existing network.
Physical Review E 04/2012; 85(4 Pt 2):045102. · 2.26 Impact Factor
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ABSTRACT: The branching process (BP) approach has been successful in explaining the
avalanche dynamics in complex networks. However, its applications are mainly
focused on unipartite networks, in which all nodes are of the same type. Here,
motivated by a need to understand avalanche dynamics in metabolic networks, we
extend the BP approach to a particular bipartite network composed of Boolean
AND and OR logic gates. We reduce the bipartite network into a unipartite
network by integrating out OR gates, and obtain the effective branching ratio
for the remaining AND gates. Then the standard BP approach is applied to the
reduced network, and the avalanche size distribution is obtained. We test the
BP results with simulations on the model networks and two microbial metabolic
networks, demonstrating the usefulness of the BP approach.
03/2012;
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ABSTRACT: We introduce the sandpile model on multiplex networks with more than one type
of edge and investigate its scaling and dynamical behaviors. We find that the
introduction of multiplexity does not alter the scaling behavior of avalanche
dynamics; the system is critical with an asymptotic power-law avalanche size
distribution with an exponent $\tau = 3/2$ on duplex random networks. The
detailed cascade dynamics, however, is affected by the multiplex coupling. For
example, higher-degree nodes such as hubs in scale-free networks fail more
often in the multiplex dynamics than in the simplex network counterpart in
which different types of edges are simply aggregated. Our results suggest that
multiplex modeling would be necessary in order to gain a better understanding
of cascading failure phenomena of real-world multiplex complex systems, such as
the global economic crisis.
12/2011;
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ABSTRACT: Nodes in a complex networked system often engage in more than one type of
interactions among them; they form a multiplex network with multiple types of
links. In real-world complex systems, a node's degree for one type of links and
that for the other are not randomly distributed but correlated, which we term
correlated multiplexity. In this paper we study a simple model of multiplex
random networks and demonstrate that the correlated multiplexity can
drastically affect the properties of giant component in the network.
Specifically, when the degrees of a node for different interactions in a duplex
Erdos-Renyi network are maximally correlated, the network contains the giant
component for any nonzero link densities. In contrast, when the degrees of a
node are maximally anti-correlated, the emergence of giant component is
significantly delayed, yet the entire network becomes connected into a single
component at a finite link density. We also discuss the mixing patterns and the
cases with imperfect correlated multiplexity.
10/2011;
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ABSTRACT: We study the susceptible-infected model with power-law waiting time distributions P(τ)~τ^{-α}, as a model of spreading dynamics under heterogeneous human activity patterns. We found that the average number of new infections n(t) at time t decays as a power law in the long-time limit, n(t)~t^{-β}, leading to extremely slow prevalence decay. We also found that the exponent in the spreading dynamics β is related to that in the waiting time distribution α in a way depending on the interactions between agents but insensitive to the network topology. These observations are well supported by both the theoretical predictions and the long prevalence decay time in real social spreading phenomena. Our results unify individual activity patterns with macroscopic collective dynamics at the network level.
Physical Review E 03/2011; 83(3 Pt 2):036102. · 2.26 Impact Factor
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ABSTRACT: Most real-world complex systems can be modelled by coupled networks with multiple layers. How and to what extent the pattern of couplings between network layers may influence the interlaced structure and function of coupled networks are not clearly understood. Here we study the impact of correlated inter-layer couplings on the network robustness of coupled networks using percolation concept. We found that the positive correlated inter-layer coupling enhaces network robustness in the sense that it lowers the percolation threshold of the interlaced network than the negative correlated coupling case. At the same time, however, positive inter-layer correlation leads to smaller giant component size in the well-connected region, suggesting potential disadvantage for network connectivity, as demonstrated also with some real-world coupled network structures. Comment: 4 pages, 3 figures
10/2010;
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ABSTRACT: The rise and fall of a research field is the cumulative outcome of its intrinsic scientific value and social coordination among scientists. The structure of the social component is quantifiable by the social network of researchers linked via coauthorship relations, which can be tracked through digital records. Here, we use such coauthorship data in theoretical physics and study their complete evolutionary trail since inception, with a particular emphasis on the early transient stages. We find that the coauthorship networks evolve through three common major processes in time: the nucleation of small isolated components, the formation of a treelike giant component through cluster aggregation, and the entanglement of the network by large-scale loops. The giant component is constantly changing yet robust upon link degradations, forming the network's dynamic core. The observed patterns are successfully reproducible through a network model.
Physical Review E 08/2010; 82(2 Pt 2):026112. · 2.26 Impact Factor
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ABSTRACT: We study the effect of team and hierarchy on the waiting-time dynamics of priority-queue networks. To this end, we introduce generalized priority-queue network models incorporating interaction rules based on team-execution and hierarchy in decision making, respectively. It is numerically found that the waiting-time distribution exhibits a power law for long waiting times in both cases, yet with different exponents depending on the team size and the position of queue nodes in the hierarchy, respectively. The observed power-law behaviors have in many cases a corresponding single or pairwise-interacting queue dynamics, suggesting that the pairwise interaction may constitute a major dynamic consequence in the priority-queue networks. It is also found that the reciprocity of influence is a relevant factor for the priority-queue network dynamics.
Physical Review E 06/2010; 81(6 Pt 2):066109. · 2.26 Impact Factor
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ABSTRACT: We study the noise characteristics of stochastic oscillations in protein number dynamics of simple genetic oscillatory systems. Using the three-component negative feedback transcription regulatory system called the repressilator as a prototypical example, we quantify the degree of fluctuations in oscillation periods and amplitudes, as well as the noise propagation along the regulatory cascade in the stable oscillation regime via dynamic Monte Carlo simulations. For the single protein-species level, the fluctuation in the oscillation amplitudes is found to be larger than that of the oscillation periods, the distributions of which are reasonably described by the Weibull distribution and the Gaussian tail, respectively. Correlations between successive periods and between successive amplitudes, respectively, are measured to assess the noise propagation properties, which are found to decay faster for the amplitude than for the period. The local fluctuation property is also studied. Comment: 7 pages, 6 figures, minor changes, final published version
09/2009;
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ABSTRACT: We study the dynamics of priority-queue networks, generalizations of the binary interacting priority-queue model introduced by Oliveira and Vazquez [Physica A 388, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.
Physical Review E 06/2009; 79(5 Pt 2):056110. · 2.26 Impact Factor
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ABSTRACT: A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free (SF) networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box; thereby, vertices in preassigned boxes can divide subsequent boxes into more than one piece, but divided boxes are counted once. We find that such box-split allowance in the algorithm is a crucial ingredient necessary to obtain the fractal scaling for fractal networks; however, it is inessential for regular lattice and conventional fractal objects embedded in the Euclidean space. Next, the algorithm is viewed from the cluster-growing perspective that boxes are allowed to overlap; thereby, vertices can belong to more than one box. The number of distinct boxes a vertex belongs to is, then, distributed in a heterogeneous manner for SF fractal networks, while it is of Poisson-type for the conventional fractal objects.
Chaos An Interdisciplinary Journal of Nonlinear Science 07/2007; 17(2):026116. · 2.08 Impact Factor
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ABSTRACT: Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a box-covering algorithm that is a modified version of the original algorithm introduced by Song [Nature (London) 433, 392 (2005)]; this algorithm enables easy implementation. Fractal networks are viewed as comprising a skeleton and shortcuts. The skeleton, embedded underneath the original network, is a special type of spanning tree based on the edge betweenness centrality; it provides a scaffold for the fractality of the network. When the skeleton is regarded as a branching tree, it exhibits a plateau in the mean branching number as a function of the distance from a root. For nonfractal networks, on the other hand, the mean branching number decays to zero without forming a plateau. Based on these observations, we construct a fractal network model by combining a random branching tree and local shortcuts. The scaffold branching tree can be either critical or supercritical, depending on the small worldness of a given network. For the network constructed from the critical (supercritical) branching tree, the average number of vertices within a given box grows with the lateral size of the box according to a power-law (an exponential) form in the cluster-growing method. The critical and supercritical skeletons are observed in protein interaction networks and the World Wide Web, respectively. The distribution of box masses, i.e., the number of vertices within each box, follows a power law Pm(M) approximately M(-eta). The exponent eta depends on the box lateral size l(B). For small values of l(B), eta is equal to the degree exponent gamma of a given scale-free network, whereas eta approaches the exponent tau=gamma/(gamma-1) as l(B) increases, which is the exponent of the cluster-size distribution of the random branching tree. Finally, we study the perimeter H(alpha) of a given box alpha, i.e., the number of edges connected to different boxes from a given box alpha as a function of the box mass M(B,alpha). It is obtained that the average perimeter over the boxes with box mass M(B) is likely to scale as <H(M(B))> approximately M(B), irrespective of the box size l(B).
Physical Review E 01/2007; 75(1 Pt 2):016110. · 2.26 Impact Factor
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ABSTRACT: Fractal scaling and self-similar connectivity behaviour of scale-free (SF) networks are reviewed and investigated in diverse aspects. We first recall an algorithm of box-covering that is useful and easy to implement in SF networks, the so-called random sequential box-covering. Next, to understand the origin of the fractal scaling, fractal networks are viewed as comprising of a skeleton and shortcuts. The skeleton, embedded underneath the original network, is a spanning tree specifically based on the edge-betweenness centrality or load. We show that the skeleton is a non-causal tree, either critical or supercritical. We also study the fractal scaling property of the k-core of a fractal network and find that as k increases, not only does the fractal dimension of the k-core change but also eventually the fractality no longer holds for large enough k. Finally, we study the self-similarity, manifested as the scale-invariance of the degree distribution under coarse-graining of vertices by the box-covering method. We obtain the condition for self-similarity, which turns out to be independent of the fractality, and find that some non-fractal networks are self-similar. Therefore, fractality and self-similarity are disparate notions in SF networks.
New Journal of Physics New Journal of Physics. 01/2007; 9(177):1367-263043869.
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ABSTRACT: We study structural feature and evolution of the Internet at the autonomous systems level. Extracting relevant parameters for the growth dynamics of the Internet topology, we construct a toy model for the Internet evolution, which includes the ingredients of multiplicative stochastic evolution of nodes and edges and adaptive rewiring of edges. The model reproduces successfully structural features of the Internet at a fundamental level. We also introduce a quantity called the load as the capacity of node needed for handling the communication traffic and study its time-dependent behavior at the hubs across years. The load at hub increases with network size $N$ as $\sim N^{1.8}$. Finally, we study data packet traffic in the microscopic scale. The average delay time of data packets in a queueing system is calculated, in particular, when the number of arrival channels is scale-free. We show that when the number of arriving data packets follows a power law distribution, $\sim n^{-\lambda}$, the queue length distribution decays as $n^{1-\lambda}$ and the average delay time at the hub diverges as $\sim N^{(3-\lambda)/(\gamma-1)}$ in the $N \to \infty$ limit when $2 < \lambda < 3$, $\gamma$ being the network degree exponent.
09/2006;
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ABSTRACT: With the advancement in the information age, people are using electronic media more frequently for communications, and social relationships are also increasingly resorting to online channels. While extensive studies on traditional social networks have been carried out, little has been done on online social networks. Here we analyze the structure and evolution of online social relationships by examining the temporal records of a bulletin board system (BBS) in a university. The BBS dataset comprises of 1908 boards, in which a total of 7446 students participate. An edge is assigned to each dialogue between two students, and it is defined as the appearance of the name of a student in the from- and to-field in each message. This yields a weighted network between the communicating students with an unambiguous group association of individuals. In contrast to a typical community network, where intracommunities (intercommunities) are strongly (weakly) tied, the BBS network contains hub members who participate in many boards simultaneously but are strongly tied, that is, they have a large degree and betweenness centrality and provide communication channels between communities. On the other hand, intracommunities are rather homogeneously and weakly connected. Such a structure, which has never been empirically characterized in the past, might provide a new perspective on the social opinion formation in this digital era.
Physical Review E 07/2006; 73(6 Pt 2):066123. · 2.26 Impact Factor
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ABSTRACT: We study the origin of scale invariance (SI) of the degree distribution in scale-free (SF) networks with a degree exponent $\gamma$ under coarse graining. A varying number of vertices belonging to a community or a box in a fractal analysis is grouped into a supernode, where the box mass $M$ follows a power-law distribution, $P_m(M)\sim M^{-\eta}$. The renormalized degree $k^{\prime}$ of a supernode scales with its box mass $M$ as $k^{\prime} \sim M^{\theta}$. The two exponents $\eta$ and $\theta$ can be nontrivial as $\eta \ne \gamma$ and $\theta <1$. They act as relevant parameters in determining the self-similarity, i.e., the SI of the degree distribution, as follows: The self-similarity appears either when $\gamma \le \eta$ or under the condition $\theta=(\eta-1)/(\gamma-1)$ when $\gamma> \eta$, irrespective of whether the original SF network is fractal or non-fractal. Thus, fractality and self-similarity are disparate notions in SF networks.
06/2006;
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ABSTRACT: We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called a skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.
Physical Review Letters 02/2006; 96(1):018701. · 7.37 Impact Factor
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ABSTRACT: With the advancement in the information age, people are using electronic media more frequently for communications, and social relationships are also increasingly resorting to online channels. While extensive studies on traditional social networks have been carried out, little has been done on online social network. Here we analyze the structure and evolution of online social relationships by examining the temporal records of a bulletin board system (BBS) in a university. The BBS dataset comprises of 1,908 boards, in which a total of 7,446 students participate. An edge is assigned to each dialogue between two students, and it is defined as the appearance of the name of a student in the from- and to-field in each message. This yields a weighted network between the communicating students with an unambiguous group association of individuals. In contrast to a typical community network, where intracommunities (intercommunities) are strongly (weakly) tied, the BBS network contains hub members who participate in many boards simultaneously but are strongly tied, that is, they have a large degree and betweenness centrality and provide communication channels between communities. On the other hand, intracommunities are rather homogeneously and weakly connected. Such a structure, which has never been empirically characterized in the past, might provide a new perspective on social opinion formation in this digital era. Comment: 7 pages, 7 figures, 2 tables
01/2006;
