Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session X16: Complex NetworksLive

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Sponsoring Units: GSNP Chair: Kevin Bassler, Univ of Houston 
Friday, March 19, 2021 8:00AM  8:12AM Live 
X16.00001: Time series analysis of GDP scaling and dynamical regimes Tai YoungTaft, Harold Hastings

Friday, March 19, 2021 8:12AM  8:24AM Live 
X16.00002: Φ index: A standardized scaleindependent citation indicator Manolis Antonoyiannakis Any average quantity can experience strong fluctuations due to outliers, an effect that grows with decreasing sample size. Thus, sizenormalized quantities are not truly sizeindependent. For citation averages, such as Impact Factors (IF), this effect causes distortions that routinely plague journal IF rankings [1]. The Central Limit Theorem, which underlies this effect, also allows us to standardize citation averages and remove the scale dependence. We thus propose the Φ index, a standardized citation impact indicator that is analogous to the Zscore in statistics. Apart from being scaleindependent, the Φ index can also account for different citation practices across research areas, which allows us to compare journals of different sizes and subjects. The Φ index can be readily generalized to other citation averages used to compare research areas, university departments or countries in various types of rankings. 
Friday, March 19, 2021 8:24AM  8:36AM Live 
X16.00003: Piecemeal Model Reduction Benjamin Francis, Mark Transtrum, Andrija Sarić, Aleksandar Stanković Many systems can be modeled as a complicated network of interacting components. Often the level of detail in the model exceeds the richness of the available data, or makes the model computationally intensive to use or difficult to interpret. Such models can be improved by reducing their complexity. If a model of a network is very large, it may be desirable to split it into pieces and reduce them separately, recombining them after reduction. We discuss piecemeal reduction of a network in the context of the Manifold Boundary Approximation Method (MBAM), including its advantages over other reduction methods. We show that MBAM transforms the model reduction problem into one of selecting a model from a partially ordered set (poset). In some cases, the poset can be factored into components. This is equivalent to decomposing the model into pieces that can be reduced separately. We use this insight to propose a strategy for piecemeal reduction via MBAM. We demonstrate on a resistor network and show that MBAM finds a reduced model that introduces less bias than similar models with randomly selected reductions. 
Friday, March 19, 2021 8:36AM  8:48AM Live 
X16.00004: Dynamics of a threering BZ chemical reactiondiffusion oscillator network Maria Eleni Moustaka, Michael M Norton, Christopher Simonetti, Ian Hunter, James V Sheehy, Seth Fraden We confine the autocatalytic, lightsensitive, BelousovZhabotinsky reaction to microfabricated networks of containers of nanoliter volume constructed from the elastomer PDMS using soft lithography. Each container can be regarded as a single pointlike network node that emits and receives inhibitory and excitatory chemical signals. Here we present the dynamics of a reactiondiffusion 3ring chemical oscillator network. This network has two large stable attractors with large basins of attraction; clockwise and counterclockwise waves of excitation. In this work we discuss the role that topology has on the network dynamics and compare experiment with two theoretical phase models: the chemical VanagEpstein model and the Kuramoto model. 
Friday, March 19, 2021 8:48AM  9:00AM Live 
X16.00005: Point pattern analysis through proximity graphs Szabolcs Horvát, Carl D Modes Spatial point patterns appear in many fields of research, including physics (arrangement of atoms in solids), ecology (location of plants or animals) and biology (cells in a tissue). The proximity graph of a point set is constructed by connecting neighbouring points. βskeletons are a parametrized family of such graphs with many convenient mathematical properties, such as certain guarantees on connectedness and planarity (in the twodimensional case). We develop a new method for characterizing spatial point patterns by first constructing the points’ βskeleton, then describing its network properties. We show that this analysis technique can reveal different types of features of the point set than what common existing point pattern analysis methods are sensitive to, and demonstrate its use on biological datasets. Finally, we investigate the use of proximity graphs as null models for spatial networks. 
Friday, March 19, 2021 9:00AM  9:12AM Live 
X16.00006: Experimental Equivariant Dynamics in a Network of ReactionDiffusion Oscillators Ian Hunter, Michael M Norton, Bolun Chen, Chris Simonetti, Maria Eleni Moustaka, Jonathan Touboul, Seth Fraden Does form follow function in natural coupledoscillator networks? Symmetry controls both the steadystate and the transient spatiotemporal patterns that form in mathematically ideal networks to a remarkable degree. But what happens in the realworld networks, with imperfections in their nodes and connections? To address these questions, we developed a model experimental reactiondiffusion network formed by an oscillatory chemical reaction confined to a square symmetric ring of 4 diffusively coupled microfluidic reactors. We compared experimental dynamics to theory assuming perfect symmetry and theory incorporating slight heterogeneity. We observed that even slight heterogeneity selectively modifies and eliminates some patterns, while preserving others. This work demonstrates that a surprising degree of the natural network’s dynamics are constrained by symmetry in spite of the breakdown of the assumptions of perfect symmetry and raises the question of why heterogeneity destabilizes some symmetry predicted states, but not others. 
Friday, March 19, 2021 9:12AM  9:24AM Live 
X16.00007: Gated Recurrent Neural Networks 1: marginal stability and line attractors Kamesh Krishnamurthy, Tankut Can, David J Schwab Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) for processing sequential data. Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions. However, real neurons can have gating – i.e. multiplicative – interactions, and gating is also a central feature of the best performing RNNs in machine learning. Here, we use DMFT and random matrix theory to study the consequences of gating in RNNs. Specifically, we show that gating robustly produces marginal stability and line attractors  important mechanisms for biologicallyrelevant computations requiring long memory. Prior models for lineattractors need finetuning and their relevance has been debated. Our results suggest gating as a new paradigm for achieving lineattractor dynamics without finetuning. This ability might also underlie the superior ability of gated ML RNNs to learn tasks with longtime correlations, in line with empirical studies of trained RNNs. 
Friday, March 19, 2021 9:24AM  9:36AM Live 
X16.00008: Clusters crossed by a random walk in twodimensional systems Sam Frank, Istvan Kovacs

Friday, March 19, 2021 9:36AM  9:48AM Live 
X16.00009: Firstorder synchronization transition in a large population of strongly coupled relaxation oscillators Jan Totz, Dumitru Calugaru, Erik Martens, Harald Engel Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and manmade systems, which range from neural networks to power grids. We report on experiments with hundreds of strongly coupled photochemical relaxation oscillators that exhibit a discontinuous synchronization transition with hysteresis, as opposed to the paradigmatic continuous transition expected from the widely used weak coupling theory. The resulting firstorder transition is robust with respect to changes in network connectivity and natural frequency distribution. This allows us to identify the relaxation character of the oscillators as the essential parameter that determines the nature of the synchronization transition. We further support this hypothesis by revealing the mechanism of the transition, which cannot be accounted for by standard phase reduction techniques. 
Friday, March 19, 2021 9:48AM  10:00AM On Demand 
X16.00010: Random matrix analysis of Multilayer Networks Tanu Raghav, Sarika Jalan We investigate the spectra of adjacency matrices of multilayer networks under random matrix theory (RMT) framework. Through numerical experiments, we show that the randomness in the connection architecture of at least one layer may govern NNSD of the entire multilayer network, and in fact, can lead to a transition from the Poisson to GOE statistics or vice versa by changing random connections in only one of its layers. Additionally, one of the layers being substituted by a random network dominates the spectral fluctuations of the entire multiplex networks irrespective of network architecture or multiplexing strength of another layer. To conclude, these numerical experiments suggest that small multiplexing supports regularity in the spectra captured through NNSD whereas an increase in multiplexing leads to randomness. These investigations have implications in providing the structural and dynamical control of entire systems represented by multilayer networks due to structural perturbation in only one of the layers. 
Friday, March 19, 2021 10:00AM  10:12AM On Demand 
X16.00011: Novel Pattern Identification Means for Networks and Tabular Data based upon Lie Groups Joseph Johnson The author previously derived a decomposition of the generators of the general linear group GL(n) in n dimensions into Abelian A(n) and Markov Type MT(n^{2}1) Lie algebras where the MT generates all Markov Transformations preserving the sum of coordinates when nonnegative combinations are used giving a Markov monoid (MM). He then showed that all networks, as defined by a square matrix C of nonnegative connections among nodes are isomorphic to this MM. The resulting MM has columns that can be interpreted as probability distributions supporting n^{th} order Renyi entropy which give spectral curves supporting network expansions and a distance function between networks. The eigenvalues of the MM are shown to define novel network clusters where the eigenvectors define the contributions of each node to each cluster. We then showed that tabular data tables can be transformed into two networks, allowing novel pattern identification to also be performed on numerical tables as well as general networks. We have performed this analysis on networks of internet traffic and on tables of medical patients and their properties (blood …). It is suggested that these algorithms (ported to an AWS server) offer novel pattern recognition methods for Big Data for both networks and tabular numerical data. 
Friday, March 19, 2021 10:12AM  10:24AM On Demand 
X16.00012: True scalefree networks hidden by finite size effects Guido Caldarelli, matteo serafino, Giulio Cimini, Amos Maritan, Andrea Rinaldo, Samir suweis, Jayanth Banavar We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scalefree structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees. Specifically, we analyze by finitesize scaling analysis the datasets of real networks to check whether the purported departures from power law behavior are due to the finiteness of sample size. We find that a large number of the networks follow a finite size scaling hypothesis without any selftuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially involving infrastructure and transportation but also in social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finitesize effects due to the nature of the sample data. 
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