Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session Y29: Complex Networks and Their Applications I |
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Sponsoring Units: GSNP Chair: Greg Morrison, Harvard University Room: 337 |
Friday, March 22, 2013 8:00AM - 8:12AM |
Y29.00001: Phase transition and Self-Organized Criticality in the Brain Marzieh Zare, Malgorzata Turalska, Paolo Grigolini Empirical evidence for a scale free distribution of avalanche sizes in the brain as a manifestation of self-organized criticality (SOC) suggests that the brain operates near criticality. Simulations in the literature also show the optimal function of the brain at criticality. However, due to the lack of sufficient set of conditions in the SOC hypothesis for the classification of a system, there is no clear connection between the phase transition and SOC. Here we study a set of cooperative neurons in a two-dimensional regular network. Using a leaky integrate-and-fire model, we analyze the temporal complexity and find a phase transition from Poisson to periodic process for a specific value of the cooperation parameter. We also evaluate the efficiency of information transfer between two networks and find the maximum at the same critical value. To study the connection between phase transition and SOC, we measure the avalanche size distribution at the critical point.~Our results show no evidence on scaling to the popular inverse power law of 1.5 in size, while we observe this scaling in the supercritical regime. Overall, based on these results, we propose that an epileptic brain can generate power law scaling while a healthy brain works in an intermediate regime. [Preview Abstract] |
Friday, March 22, 2013 8:12AM - 8:24AM |
Y29.00002: An application of a measure for organization of complex networks Georgi Georgiev, Michael Daly In order to measure self-organization in complex networks a quantitative measure for organization is necessary. This will allow us to measure their degree of organization and rate of self-organization. We apply as a measure for quantity of organization the inverse of the average sum of physical actions of all elements in a system per unit motion multiplied by the Planck's constant, using the principle of least action. The meaning of quantity of organization here is the inverse of average number of quanta of action per one node crossing of an element of the system. We apply this measure to the central processing unit (CPU) of computers. The organization for several generations of CPUs shows a double exponential rate of change of organization with time. The exact functional dependence has, S-shaped structure, suggesting some of the mechanisms of self-organization. We also study the dependence of organization on the number of transistors. This method helps us explain the mechanism of increase of organization through quantity accumulation and constraint and curvature minimization with an attractor, the least average sum of actions of all elements and for all motions. This approach can help to describe, quantify, measure, manage, design and predict future behavior of complex systems to achieve the highest rates of self-organization to improve their quality. [Preview Abstract] |
Friday, March 22, 2013 8:24AM - 8:36AM |
Y29.00003: Phase Transitions in the Quadratic Contact Process on Complex Networks Chris Varghese, Rick Durrett The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where a single infected (1) individual can infect a susceptible (0) neighbor and infected individuals are allowed to recover ($1 \rightarrow 0$). In the QCP, a combination of two 1's is required to effect a $0 \rightarrow 1$ change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks as a model for the change in a population via sexual reproduction and death. We define two versions of the QCP -- vertex centered (VQCP) and edge centered (EQCP) with birth events $1-0-1 \rightarrow 1-1-1$ and $1-1-0 \rightarrow 1-1-1$ respectively, where `$-$' represents an edge. We investigate the effects of network topology by considering the QCP on regular, Erd\H{o}s-R\'{e}nyi and power law random graphs. We perform mean field calculations as well as simulations to find the steady state fraction of occupied vertices as a function of the birth rate. We find that on the homogeneous graphs (regular and Erd\H{o}s-R\'{e}nyi ) there is a discontinuous phase transition with a region of bistability, whereas on the heavy tailed power law graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter. [Preview Abstract] |
Friday, March 22, 2013 8:36AM - 8:48AM |
Y29.00004: Two-dimensional classical XY model by HOTRG Ji-Feng Yu, Zhiyuan Xie, Tao Xiang Two-dimensional (2D) classical XY model has a special phase transition, the so-called Kosterlitz-Thouless (KT) transition. Below the transtion temperature, the system has quasi long range order with all spins aligned, and the correlation function decays as power law, while the other unordered phase is exponential. Large size system study by numerical simulation is necessary, but pratically difficult.In this work, we applied a newly well-developed method: high-order tensor renormalization group (HOTRG) to investigate this model. This method is verified by 2D Ising model, and thoretially, it can deal with infinite system size. Some thermodynamic quantities such as entropy, specific heat and magnetic susceptibility etc., are computed, which may be used to find Fisher's zero of the partition function, and then to characterize the transition. [Preview Abstract] |
Friday, March 22, 2013 8:48AM - 9:00AM |
Y29.00005: Optimal Phase Oscillatory Network Rosangela Follmann Important topics as preventive detection of epidemics, collective self-organization, information flow and systemic robustness in clusters are typical examples of processes that can be studied in the context of the theory of complex networks. It is an emerging theory in a field, which has recently attracted much interest, involving the synchronization of dynamical systems associated to nodes, or vertices, of the network. Studies have shown that synchronization in oscillatory networks depends not only on the individual dynamics of each element, but also on the combination of the topology of the connections as well as on the properties of the interactions of these elements. Moreover, the response of the network to small damages, caused at strategic points, can enhance the global performance of the whole network. In this presentation we explore an optimal phase oscillatory network altered by an additional term in the coupling function. The application to associative-memory network shows improvement on the correct information retrieval as well as increase of the storage capacity. The inclusion of some small deviations on the nodes, when solutions are attracted to a false state, results in additional enhancement of the performance of the associative-memory network. [Preview Abstract] |
Friday, March 22, 2013 9:00AM - 9:12AM |
Y29.00006: The Dynamics of Network Coupled Phase Oscillators: An Ensemble Approach Gilad Barlev, Thomas Antonsen, Edward Ott We consider the dynamics of phase oscillators that interact through a coupling network. We further consider an ensemble of such systems where, for each ensemble member, the set of oscillator frequencies is randomly chosen according to a given distribution function. We then seek a statistical description of the dynamics of this ensemble. This approach allows us to apply the ansatz of Ott and Antonsen to the marginal distribution of the ensemble of states at each node. This results in a reduced set of ordinary differential equations determining these marginal distribution functions. The new set facilitates the analysis of network dynamics in several ways: (i) the time evolution of the reduced system of equations is smoother, and thus numerical solutions can be obtained much faster; (ii) the new set of equations can be used to obtaining analytical result; and (iii) for a certain type of network, a reduction to a low dimensional description of the entire network dynamics is possible. We illustrate our approach with numerical experiments on a network version of the classic Kuramoto problem, with both unimodal and bimodal frequency distributions. In the bimodal case, the dynamics are characterized by bifurcations and hysteresis involving a variety of steady and periodic attractors. [Preview Abstract] |
Friday, March 22, 2013 9:12AM - 9:24AM |
Y29.00007: Core percolation on complex networks Yang-Yu Liu, Endre Cs\'{o}ka, Haijun Zhou, M\'{a}rton P\'{o}sfai As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems, including combinatorial optimizations and network controllability. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi random networks with Poisson degree distribution, which are quite unlike many real-world networks with scale-free or fat-tailed degree distributions. Here we show that core percolation can be analytically studied for complex networks with arbitrary degree distributions. We derive the condition for core percolation and find that purely scale-free networks have no core for any degree exponents. We show that for undirected networks if core percolation occurs then it is always continuous while for directed networks it becomes discontinuous (and hybrid) if the in- and out-degree distributions differ. We also find that core percolations on undirected and directed networks have completely different critical exponents associated with their critical singularities. Finally, we apply our theory to real-world directed networks and find, surprisingly, that they often have much larger core sizes as compared to random models. [Preview Abstract] |
Friday, March 22, 2013 9:24AM - 9:36AM |
Y29.00008: Devil's Staircases, Crackling Noise and Phase Transitions in Percolation Jan Nagler We identify and study certain phenomena in percolation that can subvert predictability and controllability in networked systems. We establish devil's staircase phase transitions, non-self-averaging, and power-law fluctuations in percolation. We provide exact conditions for percolation that exhibits multiple discontinuous jumps in the order parameter where the position and magnitude of the jumps are randomly distributed - characteristic of crackling noise. The framework can be linked to magnetic effects and fragmentation processes. [Preview Abstract] |
Friday, March 22, 2013 9:36AM - 9:48AM |
Y29.00009: Explosive percolation transitions in Euclidean space Young Sul Cho, Sungmin Hwang, Hans J\"urgen Herrmann, Byungnam Kahng Since the explosive percolation transition was discovered in a random graph model in the Achlioptas process, whether the explosive percolation transition is indeed discontinuous or continuous has been controversial. Even though extensive studies have been focused on the mean-field behavior of the type of the explosive percolation transition, only a few studies are carried out in Euclidean space, Here, we show that depending on a parameter we introduce, the explosive percolation transition can be either discontinuous or continuous transition in Euclidean space, and is reduced to be continuous in the mean-field limit, which can be shown using an analytic approach. [Preview Abstract] |
Friday, March 22, 2013 9:48AM - 10:00AM |
Y29.00010: Effective spectral dimension in heterogeneous networks Sungmin Hwang, Deok-Sun Lee, Byungnam Kahng Random walks(RWs) approach is the simplest but the most fundamental method which encapsulates essential properties of diffusive dynamic process. Here, we study the two basic quantities, the return to origin probability and the first passage time distribution of random walks on scale-free networks. The behaviors of those quantities as a function of time typically depend on the spectral dimension $d_s$ in disordered fractal systems. However, we show that in scale-free networks, due to the heterogeneity of connectivities of each node in scale-free networks, those quantities display a crossover decay behavior from $\sim t^{-d_s^{\rm (hub)}/2}$ in early time regime to $\sim t^{-d_s/2}$ in later time regime, where $d_s^{\rm (hub)} \to 0$ as the degree exponent $\lambda$ approaches 2. This result implies that a random walker can be trapped effectively at the hub when $\lambda \to 2$. Next, we discuss the origin of the $d_s^{\rm (hub)}$ by applying the renormalization group transformation to deterministic hierarchical networks. [Preview Abstract] |
Friday, March 22, 2013 10:00AM - 10:12AM |
Y29.00011: Natural emergence of clusters and bursts in network evolution James Bagrow, Dirk Brockmann Network models with \emph{preferential attachment}, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced where nodes attach proportional to arbitrary fitness functions. However, in these models attaching to a node increases the ability of that node to gain more links in the future. We study network growth where nodes attach proportional to the clustering coefficients, or local densities of triangles, of existing nodes. Attaching to a node typically lowers its clustering coefficient, in contrast to preferential attachment or rich-get-richer models. This simple modification naturally leads to a variety of rich phenomena, including non-poissonian bursty dynamics, community formation, aging and renewal. This shows that complex network structure can be modeled without artificially imposing multiple dynamical mechanisms. [Preview Abstract] |
Friday, March 22, 2013 10:12AM - 10:24AM |
Y29.00012: Walking and searching in time-varying networks Nicola Perra, Andrea Baronchelli, Delia Mocanu, Bruno Goncalves, Romualdo Pastor-Satorras, Alessandro Vespignani The random walk process lies underneath the description of a large number or real world phenomena. Here we provide a general framework for the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time varying networks created from the activity potential of the nodes, and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval and diffusion processes in time-varying networks. [Preview Abstract] |
Friday, March 22, 2013 10:24AM - 10:36AM |
Y29.00013: Measuring importance in complex networks Greg Morrison, Levi Dudte, L. Mahadevan A variety of centrality measures can be defined on a network to determine the global `importance' of a node $i$. However, the inhomogeneity of complex networks implies that not all nodes $j$ will consider $i$ equally important. In this talk, we use a linearized form of the Generalized Erdos numbers [Morrison and Mahadevan EPL 93 40002 (2011)] to define a pairwise measure of the importance of a node $i$ from the perspective of node $j$ which incorporates the global network topology. This localized importance can be used to define a global measure of centrality that is consistent with other well-known centrality measures. We illustrate the use of the localized importance in both artificial and real-world networks with a complex global topology. [Preview Abstract] |
Friday, March 22, 2013 10:36AM - 10:48AM |
Y29.00014: Sequential detection of temporal communities in evolving networks by estrangement confinement Sameet Sreenivasan, Vikas Kawadia Temporal communities are the result of a consistent partitioning of nodes across multiple snapshots of an evolving network, and they provide insights into how dense clusters in a network emerge, combine, split and decay over time. Reliable detection of temporal communities requires finding a good community partition in a given snapshot while simultaneously ensuring that it bears some similarity to the partition(s) found in the previous snapshot(s). This is a particularly difficult task given the extreme sensitivity of community structure yielded by current methods to changes in the network structure. Motivated by the inertia of inter-node relationships, we present a new measure of partition distance called estrangement, and show that constraining estrangement enables the detection of meaningful temporal communities at various degrees of temporal smoothness in diverse real-world datasets. Estrangement confinement consequently provides a principled approach to uncovering temporal communities in evolving networks. (V. Kawadia and S. Sreenivasan, http://arxiv.org/abs/1203.5126) [Preview Abstract] |
Friday, March 22, 2013 10:48AM - 11:00AM |
Y29.00015: Bimodality in Network Control Tao Jia, Yang-yu Liu, Marton Posfai, Jean-Jacques Slotine, Albert-Laszlo Barabasi Controlling complex systems is a fundamental challenge of network science. Recent tools enable us to identify the minimum driver nodes, from which we can control a system. They also indicate a multiplicity of minimum driver node sets (MDS's): multiple combinations of the same number of nodes can achieve control over the system. This multiplicity allows us to classify individual nodes as critical if they are involved in all control configurations, intermittent if they occasionally act as driver nodes and redundant if they do not play any role in control. We develop computational and analytical framework analyzing nodes in each category in both model and real networks. We find that networks with identical degree distribution can be in two distinct control modes, ``centralized" or ``distributed", with drastic change on the role of each node in maintaining the controllability and orders of magnitude difference in the number of MDS's. In analyzing both model and real networks, we find that the two modes can be inferred directly from the network's degree distribution. Finally we show that the two control modes can be switched by small structural perturbations, leading to potential applications of control theory in real systems. [Preview Abstract] |
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