Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session P39: Applications of Complex Networks |
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Sponsoring Units: GSNP Chair: Narayan Menon, University of Massachusetts, Amherst Room: Morial Convention Center 231 |
Wednesday, March 12, 2008 8:00AM - 8:12AM |
P39.00001: Effects of quenched randomness on predator-prey interactions in a stochastic Lotka-Volterra lattice model Uwe C. Tauber, Ulrich Dobramysl We study the influence of spatially varying reaction rates (i.e., quenched randomness) on a stochastic two-species Lotka-Volterra lattice model for predator-prey interactions using Monte Carlo simulations. The effects on the asymptotic population densities, transient oscillations, spatial distributions, and on traveling wave and invasion front speed velocities are investigated. We find that spatial variability in the predation rate yields an increase in the asymptotic population densities of {\em both} predators and prey. [Preview Abstract] |
Wednesday, March 12, 2008 8:12AM - 8:24AM |
P39.00002: Dynamical Clustering in Reaction-Dispersal Processes on Complex Networks Vincent David, Marc Timme, Theo Geisel, Dirk Brockmann We investigate nonlinear annihilation processes (e.g., $A+A\rightarrow \emptyset $) of particles that perform random walks on complex networks. In well mixed populations (mean field) this process exhibits $t^{-1}$ decay behavior in the total number of particles. Additional dispersal of particles adds a second time scale and drastically changes the decay behavior. Here we study these changes for two types of hopping processes. First, if particles independently select one of the possible exit channels at each node their exit rates are given by the sum of all outgoing weights such that the waiting times are degree-dependent. We compare this to the popular ansatz of a uniform waiting time process. Derived mean field equations show that for large numbers of particles per node both processes exhibit nearly identical relaxation properties. However, below a critical particle number the processes deviate not only from mean field predictions but, more importantly, by orders of magnitude from one another. We attribute this to dynamical clustering effects in the uniform waiting time model, that is absent in the independent channel dynamics. [Preview Abstract] |
Wednesday, March 12, 2008 8:24AM - 8:36AM |
P39.00003: Fluctuations and Food-web Structures in Individual-based Models of Biological Coevolution Per Arne Rikvold, Volkan Sevim We report very long kinetic Monte Carlo simulations of eco- systems generated by individual-based models of biological co-evolution, emphasizing the temporal fluctuations in community structure, diversity, and population sizes [1-3]. These multispecies coevolution models contain both producers that directly utilize an external resource, and consumers that must consume one or more other species for support. Time series of diversities and population sizes over tens of millions of generations display highly correlated fluctuations that give rise to power spectra of $1/f$ form. These model-intrinsic dynamic features correspond to large, correlated extinction events and similarly correlated bursts of new species, without the need for external catastrophic events. The communities generated by the evolution process take the form of simple food webs, whose species abundance distributions and degree distributions are consistent with data from real food webs.\newline [1] P. A. Rikvold, {\it J. Math. Biol\/} {\bf 55}, 653-677 (2007).\newline [2] P. A. Rikvold and V. Sevim, {\it Phys.\ Rev.\ E\/} {\bf 75}, 051920 (2007) (17 pages).\newline [3] P. A. Rikvold, arXiv:q-bio.PE/0609013. [Preview Abstract] |
Wednesday, March 12, 2008 8:36AM - 8:48AM |
P39.00004: Metabolic disease network and its implication for disease comorbidity Deok-Sun Lee, Zoltan Oltvai, Nicholas Christakis, Albert-Laszlo Barabasi Given that most diseases are the result of the breakdown of some cellular processes, a key aim of modern medicine is to establish the relationship between disease phenotypes and the various disruptions in the underlying cellular networks. Here we show that our current understanding of the structure of the human metabolic network can provide insight into potential relationships among often distinct disease phenotypes. Using the known enzyme-disease associations, we construct a human metabolic disease network in which nodes are diseases and two diseases are linked if the enzymes associated with them catalyze adjacent metabolic reactions. We find that the more connected a disease is, the higher is its prevalence and the chance that it is associated with a high mortality. The results indicate that the cellular network-level relationships between metabolic pathways and the associated disease provide insights into disease comorbidity, with potential important consequences on disease diagnosis and prevention. [Preview Abstract] |
Wednesday, March 12, 2008 8:48AM - 9:00AM |
P39.00005: The Human Phenotypic Disease Network Cesar Hidalgo, Nicholas Blumm, Albert-Laszlo Barabasi, Nicholas Christakis We study the evolution of patient illness using a network summarizing the disease associations extracted from 32 million Medicare claims recorded from 13 million elders using the ICD9-CM format. We find that the evolution of patients' illness is accurately described by a process in which once a patient develops a particular disease, subsequent disease are seen to occur among diseases lying close by in the network. In addition, we find that patients affected with diseases with high network connectivity are more likely to die during a follow-up period of eight years. [Preview Abstract] |
Wednesday, March 12, 2008 9:00AM - 9:12AM |
P39.00006: Bilateral interactions in disease dynamics - Decreasing epidemic thresholds with facilitated contact rates Alejandro Morales Gallardo, Dirk Brockmann, Theo Geisel Compartmental epidemiological models are very successful modeling paradigms in epidemiology. Typically, they are employed for quantitative assessments of key parameters such as the basic reproduction number $R_0$. These models rest on two key assumptions: 1.) a population is well mixed 2.) transmission is triggered by a population averaged contact rate. However, experimental evidence shows that contact rates vary substantially, and it has been hypothesized that this variability can change the dynamics of population relevant disease dynamics. However, for inhomogeneous populations the translation of distributed contact rates into effective disease transmission events is non-trivial. Transmission may either depend only on the contact rate of the transmitting individual alone (unilateral transmission), or on the contact rates of transmitting and receiving individual (bilateral transmission). In the SIS model we show that in either systems the endemic state of a disease can be stable for values of $R_0<1$ unlike homogeneous systems with a critical value $R_0=1$. Furthermore, bilateral contact dynamics entail parameter regimes in which a stable endemic state can cease to exist if the mean contact rate is increased, an unexpected effect absent in homogeneous populations. [Preview Abstract] |
Wednesday, March 12, 2008 9:12AM - 9:24AM |
P39.00007: Single species victory in a two-site, two-species model of population dispersion Jack Waddell, Len Sander, David Kessler We study the behavior of two species, differentiated only by their dispersal rates in an environment providing heterogeneous growth rates. Previous deterministic studies have shown that the slower-dispersal species always drives the faster species to extinction, while stochastic studies show that the opposite case can occur given small enough population and spatial heterogeneity. Other models of similar systems demonstrate the existence of an optimum dispersal rate, suggesting that distinguishing the species as faster or slower is insufficient. We here study the interface of these models for a small spatial system and determine the conditions of stability for a single species outcome. [Preview Abstract] |
Wednesday, March 12, 2008 9:24AM - 9:36AM |
P39.00008: Color Triads in Complex Networks: Uncovering Racial Segregation Patterns in US High Schools Julian Candia, Marta Gonzalez Introducing color subgraph analysis as a novel tool for characterizing complex network structures, we identify the basic racial patterns in a nationally representative sample of all public and private High Schools in the US. We apply this method on color triad subgraphs and obtain quantitative measurements on racial homophily effects, as well as on interracial mixing patterns. Strongest homophily phenomena are observed within the white student population, followed in decreasing order by black, hispanic and asian students. Racial reciprocity measurements reveal that white students tend to form triads in which they constitute a racial majority. Black-hispanic triads are also observed to be non-reciprocal, while black-asian and hispanic-asian triads show a stronger tendency towards symmetric ties. Racial preference measurements show a rather weak white-black affinity. Since both white and black triad majorities prefer a hispanic third party, hispanic students may play the role of a bridge between white and black students. In order to design better integration strategies, quantitative observations on homophily and interracial mixing patterns could be used to redefine school organizational features. Moreover, the color subgraph analysis method can be applied to a large variety of complex network systems on other interdisciplinary fields of science. [Preview Abstract] |
Wednesday, March 12, 2008 9:36AM - 9:48AM |
P39.00009: A Bayesian approach to network modularity Jake Hofman, Chris Wiggins We present an efficient, principled, and interpretable technique for inferring module assignments and identifying the optimal number of modules in a given network. Our approach is based on a probabilistic network model equivalent to an infinite-range spin-glass Potts model on the irregular lattice defined by a given network; the problem of identifying modules is then tantamount to inferring distributions over both the module assignments (i.e. spin states) and the model parameters (i.e. coupling constants) while also identifying the number of modules (i.e. number of occupied spin states) in the network. Using a variational approximation we derive a mean-field free energy, the minimization of which provides controlled approximations to the distributions of interest. We show how several existing methods for finding modules can be described as variant, special, or limiting cases of our work, and how related methods for complexity control -- identification of the true number of modules -- are outperformed. We apply the technique to synthetic and real networks and outline how the method naturally allows selection among competing network models. [Preview Abstract] |
Wednesday, March 12, 2008 9:48AM - 10:00AM |
P39.00010: Distribution of Node Characteristics in Complex Networks Juyong Park, A.-L. Barabasi Our enhanced ability to map the structure of various complex networks is accompanied by the capability to independently identify the functional characteristics of each node, leading to the observation that nodes with similar characteristics show tendencies to link to each other. Examples can be easily found in biological, technological, and social networks. Here we propose a tool to quantify the interplay between node properties and the structure of the underlying network. We show that when nodes in a network belong to two distinct classes, two independent parameters are needed. We find that the network structure limits the values of these parameters, requiring a phase diagram to uniquely characterize the configurations available to the system. The phase diagram shows independence from the network size, a finding that allows us to estimate its shape for large networks from their samples. We study biological and socioeconomic systems, finding that the proposed parameters have a strong discriminating power.~\footnote{J. Park and A.-L. Barab\'asi, \textit{Proc. Nat. Acad. Sci.} \textbf{104}, pp. 17916--17920 (2007)} [Preview Abstract] |
Wednesday, March 12, 2008 10:00AM - 10:12AM |
P39.00011: The Modular Structure of Protein Networks Hern\'an D. Rozenfeld, Diego Rybski, Shlomo Havlin, Hern\'an A. Makse The evolution of the human protein homology network (H-PHN) has led to a complex network that exhibits a surprisingly high level of modularity. Topologically, the H-PHN presents well connected groups (conformed by proteins of similar aminoacid structure) and weak connectivities between the groups. Here, we perform an empirical study of the H-PHN to characterize the degree of modularity in terms of scale-invariant laws using recently introduced box covering algorithms. We find that the exponent that determines the scale-invariance of the modularity is unexpectedly higher than the box dimension of the network. In addition, we perform a percolation analysis that gives insight into the evolutionary process that led to the modular organization and dynamics of the present H-PHN. [Preview Abstract] |
Wednesday, March 12, 2008 10:12AM - 10:24AM |
P39.00012: Synchronization behavior in linear arrays of negative differential resistance circuit elements Huidong Xu, Stephen Teitsworth We study the electronic transport properties in a linear array of nonlinear circuit elements that exhibit negative differential resistance, and find that state-cluster synchronization emerges when there is heterogeneity in the element properties. This type of synchronization is associated with a non-uniform spatial distribution of total applied voltage across the array elements, as well as the formation of multiple stable branches in computed current-voltage curves for the entire array. Unlike most synchronizing systems studied previously [1], this system possesses coupling between elements that displays both positive and negative feedback depending on the state of each element. An empirical order parameter is defined which quantifies the degree of synchronization. We also find that the degree of synchronization is strongly dependent on the \textit{ramping rate} of the total applied voltage to the array, with complete synchronization observed in the limit of small ramping rate. This model provides a basis for describing related nonlinear phenomena in more complex electronic structures such as semiconductor superlattices [2]. [1] A. Pikovsky, M. Rosenbaum, and J\"{u}rgen Kurths, \textit{Synchronization: a universal concept in nonlinear sciences} (Cambridge University Press, Cambridge, 2001). [2] M. Rogozia, S. W. Teitsworth, H. T Grahn, and K. H. Ploog, Phys. Rev. B\textbf{65}, 205303 (2002). [Preview Abstract] |
Wednesday, March 12, 2008 10:24AM - 10:36AM |
P39.00013: Hierarchical, 4-connected Small-World Graph Bruno Goncalves, Stefan Boettcher A new sequences of graphs are introduced that mimic small-world properties. The graphs are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical sequence of long-distance links in a pattern reminiscent of the tower-of-hanoi sequence. These 4-regular graphs are non-planar, have a diameter growing as 2$^{\sqrt{\log_{2}N^{2}}}$ (or as $\left[\log_{2}N\right]^{\alpha}$ with $\alpha\sim\sqrt{\log_{2}N^{2}}/\log_{2}\log_{2}N^{2}$), and a nontrivial phase transition T$_{c}>0$, for the Ising ferromagnet. These results suggest that these graphs are similar to small-world graphs with mean-field-like properties. [Preview Abstract] |
Wednesday, March 12, 2008 10:36AM - 10:48AM |
P39.00014: Exact Renormalization of Super-Diffusion on the Tower-of-Hanoi Network Stefan Boettcher, Bruno Goncalves We propose the Tower-of-Hanoi network as a hierarchical, small-world network possessing both, geometric and long-range links. Modeling diffusion via a random walk on this network provides a mean-square displacement with an exact, anomalous exponent $d_{w}=2-\ln(\phi)/\ln(2)=1.30576\ldots$. Here, $\phi=\left(1+\sqrt{5}\right)/2$ is the ``golden ratio'' that is intimately related to Fibonacci sequences. This may be the first solvable model with super-diffusion for any fractal structure. This appears to be also the first known instance of any physical exponent containing $\phi$. It originates from an unusual renormalization group fixed point with a subtle boundary layer. The connection between network geometry and the emergence of $\phi$ in this context is still elusive. [Preview Abstract] |
Wednesday, March 12, 2008 10:48AM - 11:00AM |
P39.00015: Scaling behavior of the non-affine deformation of random fiber networks Hamed Hatami-Marbini, Catalin Picu Random fiber networks exhibit non-affine deformation on multiple scales. This controls to a large extent their ``homogenized'' behavior on the macroscopic (system level) scale. It is currently believed that denser networks and networks in which the fibers have vanishing bending stiffness deform affinely. Here we show that these conclusions depend on the nature of the measure used to probe the non-affinity. If a strain based measure is used, it can be shown that all networks, irrespective of the axial or bending behavior of their fibers are non-affine. Furthermore, the non-affinity decreases with the observation scale, exhibiting a universal power law scaling. The behavior of dense and sparse networks is shown to be similar if a scale renormalization is applied. [Preview Abstract] |
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