Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session Z14: Focus Session: Statistical Mechanics of Complex Networks III |
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Sponsoring Units: GSNP Chair: Adilson Motter, Northwestern University Room: D227 |
Friday, March 25, 2011 11:15AM - 11:27AM |
Z14.00001: Frequency of Relevant Nodes with Different Function Classes in Critical Boolean Networks Shabnam Hossein, Matthew Reichl, Kevin E. Bassler Boolean networks have two phases of dynamical behavior, fixed and chaotic, depending on the update functions of the nodes. Boolean functions can be categorized by their symmetry properties, which are related to their canalization properties. Canalization is a type of network robustness, which was first introduced to explain the stability of phenotype expression of biological systems. For networks with 3 inputs per node, the 256 possible Boolean functions can be divided into 14 classes that correspond to the group orbits of rotation plus parity. For critical networks at the boundary of the fixed and chaotic phases, we analytically derive the frequency of the different types of Boolean functions among the relevant nodes that control the dynamics. By setting up a set of differential equations that determines the relevant nodes through a pruning process, we can find the average number of nodes in each of the classes. Then, considering the effects of fluctuations, the probability distribution of the number of relevant nodes is accurately derived. We find that in critical networks the frequency of relevant nodes is inversely correlated with canalization. [Preview Abstract] |
Friday, March 25, 2011 11:27AM - 11:39AM |
Z14.00002: Two-Component Diffusion Anna Stephenson, Jayanta Rudra When two diffusing components propagate through the same material, the space that is occupied by one component may not be occupied by the other. This interaction, which is purely geometrical and non-chemical in nature, plays an important role in the dynamics of two-component flow. It redefines the diffusing space for each of them and each component sees its surrounding space being constrained by the other. We use a novel approach to describe the diffusion of two components through a discrete lattice of a narrow channel. Specially, we look at the influence of a fast component on a slow one and vice versa. We express the time evolution of the joint probability distribution of two diffusing components in terms of a modified Master equation such that both of these may not occupy the same lattice site at the same time. From this restricted time evolution of the joint probability distribution we then calculate relative flow rate of the component and infer whether such a channel could be used as a molecular sieve to separate a slow component from a fast one. [Preview Abstract] |
Friday, March 25, 2011 11:39AM - 11:51AM |
Z14.00003: Backbones and borders from shortest-path trees Daniel Grady, Christian Thiemann, Dirk Brockmann One of the most important tasks in complex network research is to distinguish between vertices and edges that are topologically essential and those that are not. To this end, a variety of vertex and edge centrality measures have been introduced, ranging from measuring local properties (degree, strength) to quantities that depend on the global structure of the graph (betweenness). Here we introduce a novel technique based on the family of shortest-path trees, which is applicable to strongly heterogeneous networks. This approach can identify significant edges in the network, distinct from conventional edge betweenness, and these edges make up a network backbone relevant to dynamical processes that evolve on such networks. We will show that important network structures can be extracted by investigating the similarity and differences of shortest-path trees and show that tree dissimilarity in combination with hierarchical clustering can identify communities in heterogeneous networks more successfully than ordinary reciprocal-weight distance measures. We demonstrate the success of this technique on complex multi-scale mobility networks. [Preview Abstract] |
Friday, March 25, 2011 11:51AM - 12:03PM |
Z14.00004: Interactive Network Exploration using Shortest-Path-Tree Tomography Christian Thiemann, Dirk Brockmann The shortest-path tree of a node contains information on the whole network as observed from a specific node, thus combining local and global information in a two- dimensionally embeddable sub-network. We developed new visualization software that reduces a complex network to its nodes' shortest-path trees and allows for interactive exploration of this network in a structured way. In this talk I will present various example networks and also briefly talk about off-spring projects that have been sparked by looking at networks in this way, including a simplified view on disease spreading on networks. [Preview Abstract] |
Friday, March 25, 2011 12:03PM - 12:15PM |
Z14.00005: Searching for the extreme values of the mutual information between two interacting subsystems Ilya Grigorenko, Vincent Crespi We have considered two interacting subsystems represented by classical spins with a long-range interaction immersed in a thermal reservoir. We searched for maxima and minima of the mutual information between the subsystems by tuning the interaction parameters within only one subsystem: the parameters of the second subsystem - which can be thought of as an environment for the first one - and the interaction parameters between the first subsystem and the environment remain unchanged. We have identified the conditions leading to maximisation and minimisation of the mutual information between the subsystems, and their relation to a degeneracy of the energy spectrum that is spontaneously engineered by the optimisation procedure. We interpret the spatially inhomogeneous structure of the optimised subsystem in terms of information heterogeneity. [Preview Abstract] |
Friday, March 25, 2011 12:15PM - 12:27PM |
Z14.00006: Synchronization Dynamics of Coupled Anharmonic Plasma Oscillators John Laoye, Uchechukwu Vincent, Taiwo Roy-Layinde The synchronization of two identical mutually driven coupled plasma oscillators modeled by anharmonic oscillators was investigated. Each plasma oscillator was described by a nonlinear differential equation of the form: $\ddot{x} + \epsilon (1 + x^2)\dot{x} + x + \kappa x^2 + \delta x^3 = F \cdot \cos(\omega t)$. The model employed the spring-type coupling. Numerical simulations, including Poincar\'{e} sections, time series analysis, and bifurcation diagram were performed using the fourth-order Runge-Kutta scheme. The numerical value of the threshold coupling K$_{th}$ was determined to be approximately 0.15. [Preview Abstract] |
Friday, March 25, 2011 12:27PM - 1:03PM |
Z14.00007: Visual analytics for discovering node groups in complex networks Invited Speaker: Given the abundance of relational data from a variety of sources, it is becoming increasingly more important to be able to discover hidden structures in the topology of real-world complex networks. In this talk, I will extend the usual definition of groups as densely connected sets of nodes and show that many real networks have groups distinguished by a diverse combinations of node properties, but not by the density of links alone. To overcome the virtually unlimited ways to potentially distinguish groups, we have developed an \textbf{exploratory} analysis tool that exploit human visual ability. In this visual analytical approach, the user input from \textbf{visual interaction} is integrated into the analysis to discover unknown group structures, rather than simply detecting a known type of structure. I will also address the problem of determining an appropriate number of groups, when it is not known \textit{a priori}. I will demonstrate that our method can effectively find and characterize a variety of group structures in model and real-world networks, including community and $k$-partite structures defined by link density, as well as groups distinguished by combinations of other node properties. [Preview Abstract] |
Friday, March 25, 2011 1:03PM - 1:15PM |
Z14.00008: A Network Approach to Rare Disease Modeling Susan Ghiassian, Sabrina Rabello, Amitabh Sharma, Olaf Wiest, Albert-Laszlo Barabasi Network approaches have been widely used to better understand different areas of natural and social sciences. Network Science had a particularly great impact on the study of biological systems. In this project, using biological networks, candidate drugs as a potential treatment of rare diseases were identified. Developing new drugs for more than 2000 rare diseases (as defined by ORPHANET) is too expensive and beyond expectation. Disease proteins do not function in isolation but in cooperation with other interacting proteins. Research on FDA approved drugs have shown that most of the drugs do not target the disease protein but a protein which is 2 or 3 steps away from the disease protein in the Protein-Protein Interaction (PPI) network. We identified the already known drug targets in the disease gene's PPI subnetwork (up to the 3rd neighborhood) and among them those in the same sub cellular compartment and higher coexpression coefficient with the disease gene are expected to be stronger candidates. Out of 2177 rare diseases, 1092 were found not to have any drug target. Using the above method, we have found the strongest candidates among the rest in order to further experimental validations. [Preview Abstract] |
Friday, March 25, 2011 1:15PM - 1:27PM |
Z14.00009: Flavor network and the principles of food pairing Yong-Yeol Ahn, Sebastian Ahnert, James Bagrow, Albert-Laszlo Barabasi We construct and investigate a flavor network capturing the chemical similarity between the culinary ingredients. We found that Western cuisines have a statistically significant tendency to use ingredient pairs that share many flavor compounds, in line with the food pairing hypothesis used by some chefs and molecular gastronmists. By contrast, East Asian cuisine tend to avoid compound sharing ingredients. We identify key ingredients in each cuisine that help us to explore the differences and similarities between regional cuisines. [Preview Abstract] |
Friday, March 25, 2011 1:27PM - 1:39PM |
Z14.00010: Relationship between structural and functional networks in complex systems with delay Toni Perez, Victor Eguiluz, Javier Borge-Holthoefer, Alex Arenas Functional networks of complex systems are usually obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. Here we investigate on this challenge from a fundamental physical perspective, analyzing the functional network resulting from the simplest dynamical system with delay presenting a synchronous dynamics on a given topology. We have found the conditions for the emergence of locked dynamical states and the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes), and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology, $\gamma$, is related to the exponent of the associated functional network as $\alpha =(2-\gamma)^{-1}$, for $\gamma < 2$. [Preview Abstract] |
Friday, March 25, 2011 1:39PM - 1:51PM |
Z14.00011: Why hubs may not be the most efficient spreaders Lazaros Gallos, Maksim Kitsak, Shlomo Havlin, Fredrik Liljeros, Lev Muchnik, H.E. Stanley, Hernan Makse The origin of a spreading process in a complex network can drastically influence the extent of the area that spreading can reach. In principle, the network hubs should be the most efficient spreaders. Here, we find that, in contrast to common belief, there are plausible circumstances where the best spreaders do not correspond to the best connected nodes or to the most central nodes (high betweenness centrality). Using the SIR model we find that: {\it (i)} The most efficient spreaders are those located within the core of the network as identified by the $k$-shell decomposition analysis. {\it (ii)} When multiple spreaders are considered simultaneously, the distance between them becomes the crucial parameter that determines the extent of the spreading. Similarly, we find that, in the SIS model, infections persist in the high $k$-shells of the network. Our analysis provides a plausible route for an optimal design of efficient dissemination strategies. [Preview Abstract] |
Friday, March 25, 2011 1:51PM - 2:03PM |
Z14.00012: Finite size scaling theory for discontinuous percolation transitions B. Kahng, Y.S. Cho, S.W. Kim, J.D. Noh, D. Kim Finite-size scaling (FSS) theory has been useful for characterizing phase transitions. When the phase transition is continuous, the critical behavior of a system in the thermodynamic limit can be extracted from the size-dependent behaviors of thermodynamic quantities. However, FSS approach for discontinuous transitions arising in disordered systems has not been studied yet. Here, we develop a FSS theory for the discontinuous PT in the modified Erd\"os-R\'enyi model under the Achlioptas process. A scaling function is derived based on the observed fact that the derivative of the curve of the order parameter at the critical point $t_c $ diverges with system size in a power-law manner, which is different from that for continuous percolation transitions. Numerical simulation data for different system sizes are well collapsed onto a scaling function. [Preview Abstract] |
Friday, March 25, 2011 2:03PM - 2:15PM |
Z14.00013: Monte Carlo Simulations of Metastable Decay in the Ising Model on the Hyperbolic Plane Howard L. Richards, Mallory A. Price, Julie E. Lang Consider a regular network of Ising spins with short-ranged, ferromagnetic interactions and a weak, negative magnetic field. The system evolves under single-spin-flip Metropolis dynamics from an initial state of all spins ``up'' ($s_i = +1$, $\forall i$). For Euclidean networks in less than 6 dimensions, decay from the ``metastable'' state occurs in a finite time (measured in Monte Carlo steps per spin) through the nucleation and growth of one or more finite critical droplets. For networks on the hyperbolic plane, however, we show that the size of a critical droplet diverges at a nonzero magnetic field -- the spinodal field. We then use Monte Carlo simulations on the $\{5, 4\}$ grid to demonstrate the divergence of the lifetime of the metastable state at nonzero spinodal fields. [Preview Abstract] |
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