Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session B56: Network Theory II |
Hide Abstracts |
Sponsoring Units: GSNP DBIO Chair: Albert-Laszlo Barabasi Room: BCEC 255 |
Monday, March 4, 2019 11:15AM - 11:27AM |
B56.00001: Distribution efficiency and structure of complex networks. Georgios Gounaris, Miguel Ruiz Garcia, Eleni Katifori Optimized transport networks play a key role in the function of various artificial and natural systems, such as plant or animal vasculature. Part of the function of these flow networks is to efficiently distribute nutrients to the organism. In the case of the animal circulatory system, the oxygen distributed to the tissues is carried by the red blood cells flowing through the capillaries in the blood plasma. The architecture of the network, as defined by its structure and topology controls both the energy dissipated in transferring the viscous fluid (e.g. the blood through the capillaries) and the efficiency of the nutrient transport (e.g. how the oxygen is distributed in the tissue). In this work, we investigate the optimal structure of networks when both energy optimization and transport efficiency are considered. We discuss how the network structure is affected by the trade-offs of different optimization functionals that compete to impose hierarchy and uniformity to the same network. |
Monday, March 4, 2019 11:27AM - 11:39AM |
B56.00002: Optimal noise-canceling networks Henrik Ronellenfitsch, Jorn Dunkel, Michael Wilczek From the cerebral cortex to large-scale power grids, natural and engineered networks face the challenge of converting noisy inputs into robust signals. The input fluctuations often exhibit complex yet statistically reproducible correlations that reflect underlying internal or environmental processes such as synaptic noise or atmospheric turbulence. This raises the practically and biophysically relevant question of whether and how noise-filtering can be hard-wired directly into a network's architecture. By considering generic phase oscillator arrays under cost constraints, we explore the design, efficiency and topology of noise-canceling networks. We find that when the input fluctuations become more correlated in space or time, optimal network architectures become sparser and more hierarchically organized, resembling the vasculature in plants or animals. Our results provide concrete guiding principles for designing more robust and efficient power grids and sensor networks. |
Monday, March 4, 2019 11:39AM - 11:51AM |
B56.00003: The fundamental advantages of temporal networks Aming Li, Sean Cornelius, Yang-Yu Liu, Long Wang, Albert Barabasi Most networked systems of scientific interest are characterized by temporal links, meaning the network’s structure changes over time. It has been shown that link temporality, by distrupting network paths, can slow down or otherwise hinder many dynamical processes, from information spreading to accessibility. Considering the ubiquity of temporal networks in nature, we ask: Are there any advantages of the networks’ temporality? Here we develop an analytical framework to study the critical process of control in temporal networks. We show that temporal networks can, compared to their static counterparts, reach controllability faster, demand orders of magnitude less control energy, and allow control trajectories that are considerably more compact than those characterizing static networks. Thus, temporality ensures a degree of flexibility that would be unattainable in static networks, enhancing our ability to control them. |
Monday, March 4, 2019 11:51AM - 12:03PM |
B56.00004: Persistence in Random and Disordered Networks. Omar Malik, Alaa M Moussawi, David Hunt, Melinda Varga, Zoltan Toroczkai, Boleslaw Szymanski, Gyorgy Korniss To better understand the lifetime and temporal dynamics of activities and trends in social networks, we initiated investigations of diffusive persistence in various graphs. Persistence is defined as the probability that the diffusive field at a given node has not changed sign up to a certain time (or in general, that node remained inactive/active). We investigated disordered networks (characterized by the fraction of removed edges) and found that the behavior of the persistence probability depended on the topology of the network. In 2D networks we have found that above the percolation threshold diffusive persistence scale scales similarly to that of the original two-dimensional regular lattice, i.e., a power law with an exponent of 0.18. At the percolation threshold, the scaling changes to one with 0.12. This new exponent is the result of the interplay of diffusive persistence and the underlying structural transition in the disordered lattice at the percolation threshold. In contrast, we found that in random networks without a regular structure, such as Erdös-Rényi networks, no simple power-law scaling behavior exists above the percolation threshold. |
Monday, March 4, 2019 12:03PM - 12:15PM |
B56.00005: Global suppression effect on the infinite-order percolation transitions in growing networks Byungnam Kahng, S. M. Oh, S.-W. Son The percolation transition in growing networks can be of infinite order, following the Berezinskii-Kosteritz-Thouless (BKT) transition. Examples can be found in diverse systems ranging from socio- to bio-networks such as the coauthorship networks and the protein interaction networks. Here we are interested in how such an infinite-order percolation transition is changed by global suppression (GS) effect. In fact, about a half century ago, Thouless showed that 1/r^{2}-type long-range interactions in the one-dimensional Ising model change the phase transition type from second order to first order. One may think that the GS dynamics plays a similar role of changing percolation transitions in complex systems. We show that the BKT transition breaks down, but the features of infinite-order, second-order, and first-order transitions all emerge in a single framework. The critical region below the BKT transition point is extended and the power-law behavior of the cluster size distribution reaches the state with the exponent two, suggesting that the system has the maximum diversity of cluster sizes. We also elucidate the underlying mechanisms and show that those features are universal. Forming such extereme diversity by the GS dynamics may be helpful for establishing stablized complex systems. |
Monday, March 4, 2019 12:15PM - 12:27PM |
B56.00006: Walks in rough energy landscapes: a network model Riccardo Giuseppe Margiotta, Reimer Kuehn, Peter Sollich A simple way to describe the slow relaxation and ageing of a glass is to consider the system as a point in configuration-space hopping between local energy minima. The associated Markov process is specified by the distribution of these minima and the transition rates between them. Previous studies have explored the analytically tractable mean-field case [Bouchaud et al, 96] where the network of allowed transitions is fully connected. We consider a more elaborate version of the model by introducing the concept of distance among minima: the evolution takes place on sparse networks. This brings the problem into the realm of sparse random matrices. We therefore base our analysis on the spectral properties of the infinitesimal generator of the process - the master operator. We use the cavity method to evaluate the average eigenvalue spectrum and degree of localisation of eigenstates in the thermodynamic limit. These quantities are key in determining the dynamics of the system and can be used to compute time-dependent observables such as the return probability. Our findings show that eigenstates have attributes arising from a non-trivial combination of the corresponding mean field and infinite temperature limits of the model, indicating the existence of three different regimes in time. |
Monday, March 4, 2019 12:27PM - 12:39PM |
B56.00007: Disintegration of Different Types of Networks by Overload under Massive Attack Gabriel Cwilich, Yosef Kornbluth, Sergey Buldyrev We discuss a network which has a fraction of its nodes fail initially , and the redistribution of the betweenness centrality of the remaining nodes leads to subsequent failures, as in the Motter and Lai model; the subsequent change of the betweenness can lead to a cascade of failures that might disintegrate the network. There is a threshold in the size of the initial attack that leads to disintegration. The transition switches from first order to second when the tolerance of the nodes increases for networks with a narrow distribution of the degrees of their nodes ( Erdös-Rényi, random regular, small-world.,In the case of broader distributions, like a power law with exponent smaller than 3, the destruction of the initial nodes tends to stabilize the network, the value of the threshold goes to zero and the transition remains second order for all tolerances . We present an analytic calculation of the behavior of the betweenness of the different nodes during the disintegration and extensive numerical simulations .We consider the influence of the localized nature of the initial attacks on the disintegration. We show that these type of networks are, surprisingly, much more resilient vis-à-vis localized attacks. |
Monday, March 4, 2019 12:39PM - 12:51PM |
B56.00008: Transfractal Stochastic Nets Christopher Diggans, Daniel Ben-Avraham, Erik Bollt A stochastic extension of the (u,v)-flower graph recursion is given for the case where u=1, which produces small-world, transfinite dimensional hierarchical graphs. Inspired by the two equivalent (for the non-stochastic case) means of propagation, two approaches are provided. Both rely on using a list of possible v values and a probability distribution, e.g. v=[v_1, v_2] and p=[p,1-p], and both converge to the same statistics for large graph order. The first, less restrictive case entails choosing a random v value for each edge at each generation; the second, producing a more symmetric result, involves choosing a random value for v at each generation to be consistent across that step. The main contribution of these constructions is the ability to tune desirable network parameters such as assortativity and the exponent of the power law degree distribution. An additional area of interest for the second method is exact eigenvalue propagation, which has been determined for the case of v=[2,3]. As part of this work, a general result was found for propagating the eigenvalues of recursive quadrangularizations of any simple graph. |
Monday, March 4, 2019 12:51PM - 1:03PM |
B56.00009: From the betweenness centrality in street networks to structural invariants in random planar graphs Alec Kirkley, Hugo Barbosa, Marc Barthelemy, Gourab Ghoshal The betweenness centrality, a path-based global measure of flow, is a static predictor of congestion and load on networks. Here we demonstrate that its statistical distribution is invariant for planar networks, that are used to model many infrastructural and biological systems. Empirical analysis of street networks from 97 cities worldwide, along with simulations of random planar graph models, indicates the observed invariance to be a consequence of a bimodal regime consisting of an underlying tree structure for high betweenness nodes, and a low betweenness regime corresponding to loops providing local path alternatives. Furthermore, the high betweenness nodes display a non-trivial spatial clustering with increasing spatial correlation as a function of the edge-density. Our results suggest that the spatial distribution of betweenness is a more accurate discriminator than its statistics for comparing static congestion patterns and its evolution across cities as demonstrated by analyzing 200 years of street data for Paris. |
Monday, March 4, 2019 1:03PM - 1:15PM |
B56.00010: Topology of tangledness of network embeddings Yanchen Liu, Nima Dehmamy, Albert-Laszlo Barabasi The force directed layout (FDL; mass and spring model) is a class of layouts in which the position of the nodes are highly correlated with the network structure. In three dimensional space, one can embed any network without link crossings. However, as in glassy systems, the number of low energy configurations in FDL is extremely large, and distinguishing between them is very difficult. Here we introduce a topological measure, which we call the graph linking number, that allows us to classify some of these energy states. |
Monday, March 4, 2019 1:15PM - 1:27PM |
B56.00011: The hidden role of coupled wave network topology on the dynamics of nonlinear lattices Sophia Sklan, Baowen Li In most systems, its division into interacting constituent elements gives rise to a natural network structure. Analyzing the dynamics of these elements and the topology of these natural graphs gave rise to the fields of (nonlinear) dynamics and network science, respectively. However, just as an object in a potential well can be described as both a particle (real space representation) and a wave (reciprocal or Fourier space representation), the ``natural'' network structure of these interacting constituent elements is not unique. In particular, in this work we develop a formalism for Fourier Transforming these networks to create a new class of interacting constituent elements - the coupled wave network - and discuss the nontrivial experimental realizations of these structures. This perspective unifies many previously distinct structures, most prominently the set of local nonlinear lattice models, and reveals new forms of order in nonlinear media. Notably, by analyzing the topological characteristics of nonlinear scattering processes, we can control the system's dynamics and isolate the different dynamical regimes that arise from this reciprocal network structure, including the bounding scattering topologies. |
Monday, March 4, 2019 1:27PM - 1:39PM |
B56.00012: Structure and Dynamics of Cultured Neuronal Networks Emily S.C. Ching We have developed a method that can reconstruct the connectivity structure of a weighted directed network using only time-series measurements of the dynamics of the nodes. Our method is guided by noise-induced mathematical relations. We apply this method to reconstruct cultured neuronal networks using the electrical signals recorded in cultures of cortices of rat embryos by multi-electrode arrays. The reconstructed neuronal networks have 4095 nodes; their connection probability and proportion of the giant strongly connected component are comparable to those of the chemical synapse network of C. Elegans, and both are small-world networks. Our method can further reconstruct the average incoming and outgoing coupling strength of each node and whether the nodes are excitatory or inhibitory. We obtain various interesting results about the distributions of the in-degree and out-degree, and the average incoming and outgoing coupling strength of the nodes. Moreover, we find that the spike rate of the nodes is related to their network properties. Using this relation, we can predict whether a node has high or low spike rate with high accuracy. |
Monday, March 4, 2019 1:39PM - 1:51PM |
B56.00013: Directed aging and memory: Teaching an old foam new tricks Nidhi Pashine, Daniel Hexner, Andrea Liu, Sidney Robert Nagel As a material ages, its physical properties change. Under an applied stress, it plastically deforms in order to relieve the internal stress in incremental steps. At each instant, it lowers the stress in the most effective way. Thus, over long times, the final state of the material depends on the external stresses it was exposed to during the aging process. A material thus has a memory of the stresses to which it was exposed during the aging process. We exploit this property and direct the aging process with specific protocols in such a way that our material reaches a distinct, final state with a prescribed and desired functionality. In order to demonstrate this behavior, we use sheets of foam that we cut with a laser cutter and place under stress in such a way that the material develops unusual elastic properties. To accelerate the aging process, we apply heat to the sample. We have been able to modify the Poisson’s ratio of our system considerably; we can make a sample that was initially nearly incompressible and make it auxetic (negative Poisson’s ratio). We can likewise take an auxetic sample and make it incompressible. We have also been able to train local behavior so that a sample responds with a prescribed local deformation in response to a global perturbation. |
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