Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session Z29: Complex Networks and Their Applications II |
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Sponsoring Units: GSNP Chair: Erin Rericha, Vanderbilt University Room: 337 |
Friday, March 22, 2013 11:15AM - 11:27AM |
Z29.00001: Consensus and transitions in coupled Sznajd networks Matthew Ludden In this work we investigate two coupled square lattice networks undergoing Sznajd model dynamics. The coupling between the networks is quantified by a coupling strength $p$. Monte Carlo simulations indicate that the exit probability of each network (to reach either all spins up or all down) depends on $p$ and the initial density of up spins $d$ in the other network. For fixed initial densities, we find a critical coupling $p_c$, above which no further changes in the exit probability are observed. We also find $p_c$ to decrease linearly with increasing $d$. The consensus time scales with system size as $L^{\alpha}$, where $\alpha$ = $\alpha$($p$,$d$). The conditions that must be met for the two networks to reach consensus are also considered. [Preview Abstract] |
Friday, March 22, 2013 11:27AM - 11:39AM |
Z29.00002: Topological Influence On Network Of Coupled Chemical Oscillators Jie Zhao, Erin Rericha Networks of interacting nodes are ubiquitous in biological and communication systems. Recently the manner of the network connections, be it through of activator or inhibitor signals, and the topology of the network has received theoretical attention with the goal of finding networks with optimal synchronization and information transmission properties. In preparation for building an experimental system to examine these predictions, we numerically explore networks of Belousov-Zhabotinsky oscillatory nodes connected through unidirectional links of activator species. We measure the time required for the nodes to synchronize as a function of the network topology. While we observe a trend of smaller synchronization times with increasing first non-zero eigen values, we find that the most important factor in determining synchronization time is the initial phase difference between the oscillators. We find that the synchronization times for a given network topology, as determined from a uniform distribution of initial phase differences, is best described with a skewed Gaussian. To better understand the factors underlying this distribution, we look at the synchronization times in a three-node network as a function of both initial conditions and model parameters. [Preview Abstract] |
Friday, March 22, 2013 11:39AM - 11:51AM |
Z29.00003: Extreme Fluctuations in Stochastic Network Synchronization with Time Delays D. Hunt, B.K. Szymanski, G. Korniss We study the effects of nonzero time delay on the extreme fluctuations about the mean in complex networks with local relaxation dynamics in the presence of noise. This extends our previous results for average fluctuations \footnote{D. Hunt, G. Korniss, B.K. Szymanski, PRL \textbf{105}, 068701 (2010)}$^,$\footnote{D. Hunt, B.K. Szymanski, G. Korniss, http://arxiv.org/abs/1209.4240} by considering the typical behavior of the worst-case node as the system evolves in the steady state. Within our previously established framework of the synchronizability of such systems, we consider the changes in the distribution of extremes for various delays in particular networks and the scaling behavior of the average extremal values vs. system size across ensembles of similar networks. For networks with sufficient randomness in their structure, the distribution of the global extreme is in the same universality class as that of an ensemble of independent variables, similarly to the case of zero time delay. Specifically, it asymptotically approaches the Fisher-Tippet-Gumbel extreme-value limit distribution. The local trends for individual nodes (esp. those of high degree) within the network, as well as the scaling behavior of the global extreme, however, can be adversely affected by large time delays. [Preview Abstract] |
Friday, March 22, 2013 11:51AM - 12:03PM |
Z29.00004: The Joint Effect of Network Topology and Update Functions on the Stability of Boolean Networks Shane Squires, Andrew Pomerance, Edward Ott, Michelle Girvan Boolean networks are dynamical systems commonly used to model biological systems such as gene regulatory networks and neural networks. In a Boolean network, the state of each node can take one of two values, which is updated at discrete time steps using an update function that depends only on the states of its inputs on the previous time step. We study the stability of attractors in a Boolean network with respect to small perturbations. While recent past work has addressed the separate effects on stability of nontrivial network topology and update functions, only very crude information exists on how these effects interact. We present a general solution for finding the stability of Boolean networks, considering the joint effects of network topology and update functions. In particular, we show that the predictions of our approach agree with simulations of Boolean networks with threshold update functions. [Preview Abstract] |
Friday, March 22, 2013 12:03PM - 12:15PM |
Z29.00005: Asymptotically inspired moment-closure approximation for adaptive networks Maxim Shkarayev Dynamics of adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a systematic approach to moment closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the mean-field prediction and simulations of the full network system. [Preview Abstract] |
Friday, March 22, 2013 12:15PM - 12:27PM |
Z29.00006: Optimizing Nutrient Uptake in Biological Transport Networks Henrik Ronellenfitsch, Eleni Katifori Many biological systems employ complex networks of vascular tubes to facilitate transport of solute nutrients, examples include the vascular system of plants (phloem), some fungi, and the slime-mold \emph{Physarum}. It is believed that such networks are optimized through evolution for carrying out their designated task. We propose a set of hydrodynamic governing equations for solute transport in a complex network, and obtain the optimal network architecture for various classes of optimizing functionals. We finally discuss the topological properties and statistical mechanics of the resulting complex networks, and examine correspondence of the obtained networks to those found in actual biological systems. [Preview Abstract] |
Friday, March 22, 2013 12:27PM - 12:39PM |
Z29.00007: Paradoxical Behavior of Granger Causality Annette Witt, Demian Battaglia, Alexander Gail Granger causality is a standard tool for the description of directed interaction of network components and is popular in many scientific fields including econometrics, neuroscience and climate science. For time series that can be modeled as bivariate auto-regressive processes we analytically derive an expression for spectrally decomposed Granger Causality (SDGC) and show that this quantity depends only on two out of four groups of model parameters. Then we present examples of such processes whose SDGC expose paradoxical behavior in the sense that causality is high for frequency ranges with low spectral power. For avoiding misinterpretations of Granger causality analysis we propose to complement it by partial spectral analysis. Our findings are illustrated by an example from brain electrophysiology. Finally, we draw implications for the conventional definition of Granger causality. [Preview Abstract] |
Friday, March 22, 2013 12:39PM - 12:51PM |
Z29.00008: Direct and indirect effects in causal networks Andreas Kr\"amer Literature-derived networks of biomolecular interactions representing cause-effect relationships generally contain many indirect relationships where the actually observed causal effect results from a sequence of events represented in the same network. A statistical method is developed, based on an Ising-like spin model operating on the edges of the network, to distinguish between direct and indirect effects using only the network structure itself. This allows to identify paths representing likely causation mechanisms. [Preview Abstract] |
Friday, March 22, 2013 12:51PM - 1:03PM |
Z29.00009: Extraction of hidden information by efficient community detection in networks Jooyoung Lee, Juyong Lee, Steven Gross Currently, we are overwhelmed by a deluge of experimental data, and network physics has the potential to become an invaluable method to increase our understanding of large interacting datasets. However, this potential is often unrealized for two reasons: uncovering the hidden community structure of a network, known as community detection, is difficult, and further, even if one has an idea of this community structure, it is not a priori obvious how to efficiently use this information. Here, to address both of these issues, we, first, identify optimal community structure of given networks in terms of modularity by utilizing a recently introduced community detection method. Second, we develop an approach to use this community information to extract hidden information from a network. When applied to a protein-protein interaction network, the proposed method outperforms current state-of-the-art methods that use only the local information of a network. The method is generally applicable to networks from many areas. [Preview Abstract] |
Friday, March 22, 2013 1:03PM - 1:15PM |
Z29.00010: Scaling of Minimum Dominating Sets in Various Scale-Free Network Ensembles F. Molnar, S. Sreenivasan, B.K. Szymanski, G. Korniss We study the scaling behavior of the size of minimum dominating sets (MDS) in scale-free networks, with respect to network size $N$ and power-law exponent $\gamma $ [Nacher et al., NJP 073005 (2012)]. Network samples are constructed by either the configuration model (CM) via multigraphs, or exact degree sequence sampling methods. The MDS is found by a sequential greedy algorithm. We control the average degree by setting an appropriate lower degree cutoff $k_{\min } $. Two subtypes of networks are studied according to the maximum degree cutoff $k_{\max } $. Our results show that when $k_{\max } =\sqrt N $ all networks have similar scaling. The size of MDS is linear with respect to $N$, and for a given $N$, it increases for low $\gamma $ values. When $k_{\max } =N-1$, we find a structural difference between CM networks, and networks constructed by exact sampling methods. For the latter, we find a scaling transition of the MDS size from O(N) to O(1) at approximately $\gamma \approx 1.9$, due to the appearance of star subgraphs with O(N) central degree. For a given $N$, the size of MDS increases for higher $\gamma $ values. However, in CM networks the MDS scales linearly with $N$, and for a given $N$, it is non-monotonic with respect to $\gamma $. Finally, we find that a partial MDS, which dominates only a certain fraction of the network, has the same scaling as full domination, even for as low as $30\% $ dominated fraction. [Preview Abstract] |
Friday, March 22, 2013 1:15PM - 1:27PM |
Z29.00011: ABSTRACT WITHDRAWN |
Friday, March 22, 2013 1:27PM - 1:39PM |
Z29.00012: Graphicality of random scale-free networks with general degree cutoffs Yongjoo Baek, Daniel Kim, Meesoon Ha, Hawoong Jeong We study graphicality of random scale-free networks with arbitrary degree cutoffs in the thermodynamic limit, which refers to realizability of degree sequences randomly generated with the degree exponent $\gamma$ and the upper degree cutoff $k_c$ as the number of nodes $N$ goes to infinity. While a recent study\footnote{C. I. Del Genio, T. Gross, and K. E. Bassler, Phys. Rev. Lett. {\bf 107}, 178701 (2011).} found that only degree sequences with $\gamma > 2$ or $\gamma < 0$ are graphical if $k_c = N-1$ using the graphicality criterion proved by Erd\H{o}s and Gallai,\footnote{P. Erd\H{o}s and T. Gallai, Matematikai lapok {\bf 11}, 264 (1960).} we generalize the study to different upper cutoffs. To ensure graphicality of degree sequences, it is found that the upper cutoff must be lower than $k_c \sim N^{1/\gamma}$ for $\gamma < 2$, whereas any upper cutoff is allowed for $\gamma > 2$. This is also numerically verified, using both random and deterministic sampling of degree sequences. Our result can be interpreted as giving a fundamental constraint on the structure of random scale-free networks. [Preview Abstract] |
Friday, March 22, 2013 1:39PM - 1:51PM |
Z29.00013: Phase transition of biconnected components in scale-free networks Purin Kim, Deok-Sun Lee, Byungnam Kahng In information-transport and biological systems, there can be more than one pathway between two nodes, so that there is a backup in case one pathway is inactive. The size of such biconnected nodes can be an important measure of the robustness of a system. The giant biconnected components of diverse real-world networks suggest the importance of scale-free topology in the biconnectivity. Thus, here, we consider a critical behavior of the largest biconnected component as links are added and form a random scale-free network. The critical exponents $\beta_{\rm (BC)}$ and $\beta_{\rm (SC)}$ associated with the order parameter of the percolation transition of biconnected and single-connected components, respectively, are compared. We obtain that $\beta_{\rm (BC)}/\beta_{\rm (SC)}=\lambda-1$ for $2 < \lambda < 3$ and 2 for $\lambda > 3$, where $\lambda$ is the exponent of the degree distribution in scale-free networks. We also obtain the finite-size scaling behavior of the order parameter analytically and numerically. [Preview Abstract] |
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