Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session Q44: Networks and their applications 
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Sponsoring Units: GSNP Chair: Danielle Bassett, University of Pennsylvania Room: 214D 
Wednesday, March 4, 2015 2:30PM  2:42PM 
Q44.00001: Topological Phenotypes in Complex Leaf Venation Networks Henrik Ronellenfitsch, Jana Lasser, Douglas Daly, Eleni Katifori The leaves of vascular plants contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We analyze the topology of the venation of leaves from ca. 200 species belonging to ca. 10 families, defining topological metrics that quantify the hierarchical nestedness of the network cycles. We find that most of the venation variability can be described by a two dimensional phenotypic space, where one dimension consists of a linear combination of geometrical metrics and the other dimension of topological, previously uncharacterized metrics. We show how this new topological dimension in the phenotypic space significantly improves identification of leaves from fragments, by calculating a ``leaf fingerprint'' from the topology and geometry of the higher order veins. Further, we present a simple model suggesting that the topological phenotypic traits can be explained by noise effects and variations in the timing of higher order vein developmental events. This work opens the path to (a) new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and (b) topological quantification of other planar or almost planar networks such as arterial vaculature in the neocortex and lung tissue. [Preview Abstract] 
Wednesday, March 4, 2015 2:42PM  2:54PM 
Q44.00002: Nonlinear Dynamics and Control in Microfluidic Networks Daniel Case, JeanRegis Angilella, Adilson Motter Researchers currently use abundant external devices (e.g., pumps and computers) to achieve precise flow dynamics in microfluidic systems. Here, I show our use of network concepts and computational methods to design microfluidic systems that do not depend on external devices yet still exhibit a diverse range of flow dynamics. I present an example of a microfluidic channel described by a nonlinear pressureflow relation and show that complex flow behavior can emerge in systems designed around this channel. By controlling the pressure at only a single terminal in such a system, I demonstrate the ability to switch the direction of fluid flow through intermediate channels not directly connected to the controlled terminal. I also show that adding (or removing) flow channels to a system can result in unexpected changes in the total mass flow rate, depending on the network structure of the system. We expect this work to both expand the applicability of microfluidics and promote scaling up of current experiments. [Preview Abstract] 
Wednesday, March 4, 2015 2:54PM  3:06PM 
Q44.00003: Independence of bondlevel response in disordered networks Carl Goodrich, Andrea Liu, Sidney Nagel Many properties of spring networks, such as bulk elasticity, are a sum of contributions from individual bonds. For disordered systems, these contributions are often characterized by continuous distributions with tails that can be many times larger than the average, leading to the appearance of bonds that are ``stronger'' or ``weaker'' than others. However, whether a specific bond is strong or weak depends sensitively on the measurement being made; knowing how a bond responds to compression, for example, tells little about how it will respond to shear. This leads to a new principle for disordered solids: independence of bondlevel response. We will show how this principle can be exploited to construct metamaterials with unique, textured, tunable and often extreme response. [Preview Abstract] 

Q44.00004: ABSTRACT WITHDRAWN 
Wednesday, March 4, 2015 3:18PM  3:30PM 
Q44.00005: Phasespace network structure of twodimensional $\pm$J spin glasses Xin Cao, Feng Wang, Yilong Han We illustrate a complexnetwork approach to study the phase spaces of spin glasses. By exactly mapping the whole groundstate phase spaces of twodimensional EdwardsAnderson bimodal ($\pm J$) spin glasses into networks, we discovered various phasespace properties via network analysis. The Gaussian connectivity distribution of the phasespace networks demonstrates that both the number of free spins and the visiting frequency of microstates follow Gaussian distributions. The spectra of phasespace networks are Gaussian, which is proved to be exact when the system is infinitely large. The phasespace networks exhibit community structures, which enables us to construct the entropy landscape of the ground state as a network and discover its scalefree property. The phasespace networks exhibit fractal structures, as a result of the rugged entropy landscape. Moreover, we show that the connectivity distribution, the community structure and the fractal structure drastically change at the ferromagneticglass transition. These quantitative measurements of the ground states provide new insight into the studies of spin glasses. On the other hand, the phasespace networks establish a new class of complex networks with unique topology. [Preview Abstract] 
Wednesday, March 4, 2015 3:30PM  3:42PM 
Q44.00006: Thermal Transport in CayleyTree Networks Tsampikos Kottos, Huanan Li, Boris Shapiro In recent years there has been a lot of attention in the microscopic derivation of the laws that dictate heat current in low dimensional systems. However, many real structures are not simple one or twodimensional structures. Rather, they are characterized by a complex connectivity that can be easily designed and realized in the laboratory. It is therefore necessary to unveil the rules that dictate thermal transport in such networks. In this contribution we present analytical results on heat current and its thermal fluctuations for a Cayley tree consisting of two types of harmonic masses: vertex masses $M$ where phonon scattering occurs and bond masses $m$ where phonon propagation take place. The tree is coupled to thermal reservoirs consisting of onedimensional harmonic chain of masses m. We find that the heat current is a nonmonotonic function of the massratio $\mu=M/m$. In particular, there are cases when the heat current is strictly zero below some critical value $\mu^*$. The effects of imperfections (disorder) on the heat transport are also discussed and analyzed. [Preview Abstract] 
Wednesday, March 4, 2015 3:42PM  3:54PM 
Q44.00007: Fragmentation of random trees Ziya Kalay, Eli BenNaim We investigate the fragmentation of a random recursive tree by repeated removal of nodes, resulting in a forest of disjoint trees. The initial tree is generated by sequentially attaching new nodes to randomly chosen existing nodes until the tree contains $N$ nodes. As nodes are removed, one at a time, the tree dissolves into an ensemble of separate trees, namely a forest. We study the statistical properties of trees and nodes in this heterogeneous forest. In the limit $N \to \infty$, we find that the system is characterized by a single parameter: the fraction of remaining nodes $m$. We obtain analytically the size density $\phi_s$ of trees of size $s$, which has a powerlaw tail $\phi_s \sim s^{\alpha}$, with exponent $\alpha=1+1/m$. Therefore, the tail becomes steeper as further nodes are removed, producing an unusual scaling exponent that increases continuously with time. Furthermore, we investigate the fragment size distribution in a growing tree, where nodes are added as well as removed, and find that the distribution for this case is much narrower. [Preview Abstract] 
Wednesday, March 4, 2015 3:54PM  4:06PM 
Q44.00008: Cascading Failures and Stochastic Analysis for Mitigation in SpatiallyEmbedded Random Networks Noemi Derzsy, Xin Lin, Alaa Moussawi, Boleslaw K. Szymanski, Gyorgy Korniss In complex information or infrastructure networks, even small localized disruptions can give rise to congestion, largescale correlated failures [1], or cascades,  a critical vulnerability of these systems. Recent studies have demonstrated that flowdriven cascading overload failures in spatial graphs, such as the power grid, are nonselfaveraging, hence predictability is poor and conventional mitigation strategies are largely ineffective [2]. In particular, we have shown that protecting all nodes (or edges) by the same additional capacity (tolerance) can actually lead to larger global failures, i.e., ``paying more can result in less'', in terms of robustness [2]. Here, we explore stochastic methods for optimal heterogeneous distribution of resources (node or edge capacities) subject to a fixed total cost. In addition to random geometric graphs, we also investigate cascading failures on the UCTE European electrical power transmission network. [1] A. Bernstein, D. Bienstock, D. Hay, M. Uzunoglu, and G. Zussman, http://arxiv.org/abs/1206.1099 (2011). [2] A. Asztalos, S. Sreenivasan, B.K. Szymanski, and G. Korniss, PLOS One 9(1): e84563 (2014). [Preview Abstract] 
Wednesday, March 4, 2015 4:06PM  4:18PM 
Q44.00009: Cooperative SIS epidemics can lead to abrupt outbreaks Fakhteh Ghanbarnejad, Li Chen, Weiran Cai, Peter Grassberger In this paper, we study spreading of two cooperative SIS epidemics in mean field approximations and also within an agent based framework. Therefore we investigate dynamics on different topologies like ErdosRenyi networks and regular lattices. We show that cooperativity of two diseases can lead to strongly first order outbreaks, while the dynamics still might present some scaling laws typical for second order phase transitions. We argue how topological network features might be related to this interesting hybrid behaviors. [Preview Abstract] 
Wednesday, March 4, 2015 4:18PM  4:30PM 
Q44.00010: Eigenvalue Separation in the Laplacian Spectra of Random Geometric Graphs Amy Nyberg, Kevin E. Bassler The graph Laplacian spectra of networks are important for characterizing both their structural and dynamical properties. As a prototypical example of networks with strong correlations, we investigate the spectra of random geometric graphs (RGGs), which describe networks whose nodes have a random physical location and are connected to other nodes within a threshold distance $r$. RGGs model transportation grids, wireless networks, and biological processes. The spectrum consists of two parts, a discrete part consisting of a collection of integer valued delta function peaks centered about the average degree and a continuous part that exhibits the phenomenon of eigenvalue separation. We examine the behavior of eigenvalue separation for large network size $N$ in several scaling regimes based on the parameter $\alpha$ such that $N^{\alpha}r=c$ is constant. We identify a transition at $\alpha=1/3$, above which the separated peaks get closer together as $N$ increases and separation is eventually lost, but below which the peaks get farther apart. Also, an approximation for the expected number of separated peaks is given in terms of $N$ and the average degree and we show that the expected number of peaks scales as $N^{\alpha}$. [Preview Abstract] 
Wednesday, March 4, 2015 4:30PM  4:42PM 
Q44.00011: Bounds for percolation thresholds on directed and undirected graphs Kathleen Hamilton, Leonid Pryadko Percolation theory is an efficient approach to problems with strong disorder, e.g., in quantum or classical transport, composite materials, and diluted magnets. Recently, the growing role of big data in scientific and industrial applications has led to a renewed interest in graph theory as a tool for describing complex connections in various kinds of networks: social, biological, technological, etc. In particular, percolation on graphs has been used to describe internet stability, spread of contagious diseases and computer viruses; related models describe market crashes and viral spread in social networks. We consider sitedependent percolation on directed and undirected graphs, and present several exact bounds for location of the percolation transition in terms of the eigenvalues of matrices associated with graphs, including the adjacency matrix and the Hashimoto matrix used to enumerate nonbacktracking walks. These bounds correspond t0 a mean field approximation and become asymptotically exact for graphs with no short cycles. We illustrate this convergence numerically by simulating percolation on several families of graphs with different cycle lengths.\\[0pt] Reference: K. E. Hamilton and L. P. Pryadko, PRL \textbf{113}, 208701 (2014). [Preview Abstract] 
(Author Not Attending)

Q44.00012: Reconstructing Weighted Networks from Dynamics Emily S.C. Ching, P.Y. Lai, C.Y. Leung The knowledge of how the different nodes of a network interact or link with one another is crucial for the understanding of the collective behavior and the functionality of the network. We have recently developed a method that can reconstruct both the links and their relative coupling strength of bidirectional weighted networks. Our method requires only measurements of node dynamics as input and is based on a relation between the pseudoinverse of the matrix of the correlation of the node dynamics and the Laplacian matrix of the weighted network. Using several examples of different dynamics, we demonstrate that our method can accurately reconstruct the connectivity as well as the weights of the links for weighted random and weighted scalefree networks with both linear and nonlinear dynamics. [Preview Abstract] 
Wednesday, March 4, 2015 4:54PM  5:06PM 
Q44.00013: Identification of coreperiphery structure in networks Xiao Zhang, Travis Martin, Mark Newman Many networks can be decomposed into a dense core plus an outlying, looselyconnected periphery. In this talk I will describe a method for performing such a decomposition on empirical network data using methods of statistical inference. Our method fits a generative model of coreperiphery structure to observed data using a combination of an expectationmaximization algorithm for calculating the parameters of the model and a belief propagation algorithm for calculating the decomposition itself. We find the method to be efficient, scaling easily to networks with a million or more nodes and we test it on a range of networks, including realworld examples as well as computergenerated benchmarks. [Preview Abstract] 
Wednesday, March 4, 2015 5:06PM  5:18PM 
Q44.00014: SmallWorld Propensity: A novel statistic to quantify weighted networks Danielle Bassett, Sarah Muldoon, Eric Bridgeford Many realworld networks have been shown to display a smallworld structure with high local clustering yet short average path length between any two nodes. However, characterization of smallworld properties has generally relied on a binarized representation of such graphs, neglecting the important fact that, in reality, many realworld networks are actually composed of weighted connections spanning a wide range of strengths. Here, we present a generalization of the WattsStrogtaz formalism for weighted networks along with a novel statistic called the SmallWorld Propensity that quantifies both binary and weighted smallworld structure. We apply this measure to realworld brain networks and show that by retaining network weights, we are able to better understand the smallworld structure of these systems. [Preview Abstract] 
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