Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session Y42: Spatiotemporal dynamics of complex networks: From mean field to large deviationsInvited

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Sponsoring Units: GSNP Chair: Ira Schwartz, Naval Research Lab Room: LACC 502B 
Friday, March 9, 2018 11:15AM  11:51AM 
Y42.00001: NoiseInduced Rare Events in Population Dynamics: The Effect of Spatial Heterogeneity Invited Speaker: Michael Assaf We study the influence of the network topology on the statistics of interest including rare events of interacting particle systems on complex graphs. As an example, we investigate the metastability and fixation properties of a set of evolutionary processes. In the framework of evolutionary game theory, where the fitness and selection are frequency dependent and vary with the population composition, we analyze the dynamics of snowdrift games (characterized by a metastable coexistence state) on scalefree networks. Using an effective diffusion theory in the weak selection limit, we demonstrate how the scalefree structure affects the system’s metastable state and leads to anomalous fixation compared to the nonspatial wellmixed case. In particular, we analytically and numerically show that the probability and mean time to fixation are characterized by stretchedexponential behaviors with exponents depending on the network’s degree distribution. 
Friday, March 9, 2018 11:51AM  12:27PM 
Y42.00002: Probabilistic stability measures and the dynamics of power grids. Invited Speaker: Frank Hellmann I present results on the impact of the topology of the underlying network on the dynamics of oscillator networks, in particular, dynamical models of power grids. In order to study such highdimensional networked systems I will introduce probabilistic stability measures that allow for sampling based estimation. By designing these measures with explicit reference to the network structure, we can uncover novel relationships between dynamical and structural properties. 
Friday, March 9, 2018 12:27PM  1:03PM 
Y42.00003: Spatiotemporal propagation of cascading failures in complex networks Invited Speaker: Michael Danziger When the functionality of a node in a complex network requires the simultaneous functioning of a node in another network, even a single failed node can lead to a cascade of failures throughout the system[1,2,3]. In spatial networks, this cascade has distinctive spatiotemporal properties, including a new kind of nucleation transition and a new metastable phase[4,5]. In this talk we will review recent advances on interdependent spatial network cascades including spatially localized attacks [6,7] and the impact of tunable embedding strength [8]. We will also compare these results with the spatiotemporal patterns of overload cascades [9]. The ubiquity of spatial networks and the distinctiveness of the cascading patterns on them, make it essential that we fully understand the fundamental cascade mechanisms underlying the observed behavior. 
Friday, March 9, 2018 1:03PM  1:39PM 
Y42.00004: Making rare events happen: prediction and control of network extinction, switching, and other extreme processes Invited Speaker: Jason Hindes Many complex networks must operate in uncertain and dynamic environments. Over long time scales, combinations of random internal interactions and dynamical perturbations can organize to drive a network from one collective state to another. Such noiseinduced large fluctuations may be associated with desirable outcomes, such as epidemic extinctions, or undesirable ones, such as switching in collective order, or loss of network synchrony. In this talk I will discuss a general formalism for predicting rare events in networks with internal and external noise, the role of topology in facilitating the most extreme network events, techniques for optimal network control that leverage uncertainty, and numerical solutions for the aforementioned when explicit formulas are unknown. Along the way, I will consider many examples: from epidemic dynamics to opinion formation and synchronization of coupled oscillators 
Friday, March 9, 2018 1:39PM  2:15PM 
Y42.00005: Densification, Emergent Modularity, and Related Mysteries of Complex Networks Invited Speaker: Sidney Redner

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