Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session R43: Nonlinear Dynamics in Networks IFocus
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Sponsoring Units: GSNP Chair: Adilson Motter, Northwestern University Room: 346 |
Thursday, March 17, 2016 8:00AM - 8:36AM |
R43.00001: Collective Dynamics of Oscillator Networks: Why do we suffer from heavy jet lag? Invited Speaker: Hiroshi Kori The circadian rhythm of the entire body in mammals is orchestrated by a small tissue in the brain called the suprachiamatic nucleus (SCN). The SCN consists of a population of neurons, each of which exhibit circadian (i.e., approximately 24 h) gene expression. Neurons form a complex network and interact with each other using various types of neurotransmitters. The rhythmic gene expressions of individual cells in the SCN synchronize through such interaction. Jet-lag symptoms arise from temporal mismatch between the internal circadian clock orchestrated by the SCN and external solar time. It may take about one week or even longer to recover from jet lag after a long-distance trip. We recently found that recovery from jet lag is considerably accelerated in the knocked-out (KO) mice lacking the receptors of a certain neurotransmitter in the SCN [1]. Importantly, all other properties of mice including sleep-awake rhythms and breeding seem to be intact. Only the response to the jet lag changes. It was also found that after a few days of jet lag, cells in the SCN desynchronize in the wild type (WT) mice, whereas they do not in KO mice. This desynchrony might be a main reason for heavy jet lag symptoms. To understand the mechanism underlying jet lag, we propose a simple model of the SCN, which is a network of phase oscillators [1]. Despite its simplicity, this model can reproduce important dynamical properties of the SCN. For example, this model reproduces the desynchrony of oscillators after jet lag. Moreover, when intercellular interaction is weaker, this desynchrony is suppressed and the recover from jet lag is considerably accelerated. Our mathematical study provides a deeper understanding of jet lag and an idea how to circumvent heavy jet lag symptoms. [1] Y. Yamaguchi, T. Suzuki, Y. Mizoro, H. Kori, K. Okada, Y. Chen, J.M. Fustin, F. Yamazaki, N. Mizuguchi, J. Zhang, X. Dong, G. Tsujimoto, Y. Okuno, M. Doi, H. Okamura: Mice Genetically Deficient in Vasopressin V1a and V1b Receptors Are Resistant to Jet Lag, Science 342, pp. 85-90 (2013). [Preview Abstract] |
Thursday, March 17, 2016 8:36AM - 8:48AM |
R43.00002: Synchronization in neuronal oscillator networks with input heterogeneity and arbitrary network structure Elizabeth Davison, Biswadip Dey, Naomi Leonard Mathematical studies of synchronization in networks of neuronal oscillators offer insight into neuronal ensemble behavior in the brain. Systematic means to understand how network structure and external input affect synchronization in network models have the potential to improve methods for treating synchronization-related neurological disorders such as epilepsy and Parkinson's disease. To elucidate the complex relationships between network structure, external input, and synchronization, we investigate synchronous firing patterns in arbitrary networks of neuronal oscillators coupled through gap junctions with heterogeneous external inputs. We first apply a passivity-based Lyapunov analysis to undirected networks of homogeneous FitzHugh-Nagumo (FN) oscillators with homogeneous inputs and derive a sufficient condition on coupling strength that guarantees complete synchronization. In biologically relevant regimes, we employ Gronwall's inequality to obtain a bound tighter than those previously reported. We extend both analyses to a homogeneous FN network with heterogeneous inputs and show how cluster synchronization emerges under conditions on the symmetry of the coupling matrix and external inputs. Our results can be generalized to any network of semi-passive oscillators. [Preview Abstract] |
Thursday, March 17, 2016 8:48AM - 9:00AM |
R43.00003: Independent Noise Can Synchronize Interacting Networks of Pulse-Coupled Oscillators Hermann Riecke, John Meng Structured networks comprised of subnetwork modules are ubiquitous. Motivated by the observation of rhythms and their interaction in different brain areas, we study a network consisting of two subnetworks of pulse-coupled integrate-fire neurons. Through mutual inhibition the neurons in the individual subnetworks can become synchronized and each subnetwork can exhibit coherent oscillatory dynamics, e.g. an ING-rhythm. In the absence of coupling between the networks the rhythms will in general have different frequencies. We investigate the interaction between these different rhythms. Strikingly, we find that increasing the noise level in the input to the individual neurons can synchronize the rhythms of the two networks, even though the inputs to different neurons are uncorrelated, sharing no common component. A heuristic phase model for the coupled networks shows that this synchronization hinges on the fact that only a fraction of the neurons may spike in a given cycle. Thus, the synchronization of the network rhythms differs qualitatively from that of individual oscillators. [Preview Abstract] |
Thursday, March 17, 2016 9:00AM - 9:12AM |
R43.00004: A simple experimental realization of the Sakaguchi-Kuramoto model David Mertens, Zhuwei Zeng, Lars English We explore the collective phase dynamics of Wien-bridge oscillators coupled resistively. The dynamics of these oscillators were recently shown to follow Sakaguchi's modification to the Kuramoto model. In this talk we outline the steps of that analysis. We then examine results for a variety of experimentally obtained coupling arrangements, including all-to-all and some-to-all. In particular, we provide evidence for the emergence of synchronized clusters, a finite-size effect that is not accounted for in the traditional theories for the Sakaguchi-Kuramoto model. [Preview Abstract] |
Thursday, March 17, 2016 9:12AM - 9:24AM |
R43.00005: Experimental studies of a chain of Sakaguchi-Kuramoto oscillators Hanyu Ma, David Mertens, Lars English The collective phase dynamics of Wien-bridge oscillators, coupled resistively, were recently shown to follow the Sakaguchi-Kuramoto model. In this talk we present experimental findings for the dynamics of rings of oscillators. For identical speeds and uni-directional nearest-neighbor coupling, we find that the system quickly approaches a steady state of identical nearest-neighbor phase offsets. We then present the effects of adding disorder to the natural speeds. We also discuss the case of bi-directional coupling, in which case chimera behavior is expected. [Preview Abstract] |
Thursday, March 17, 2016 9:24AM - 9:36AM |
R43.00006: Title: Chimeras in small, globally coupled networks: Experiments and stability analysis Joseph D. Hart, Kanika Bansal, Thomas E. Murphy, Rajarshi Roy Since the initial observation of chimera states, there has been much discussion of the conditions under which these states emerge. The emphasis thus far has mainly been to analyze large networks of coupled oscillators; however, recent studies have begun to focus on the opposite limit: what is the smallest system of coupled oscillators in which chimeras can exist? We experimentally observe chimeras and other partially synchronous patterns in a network of four globally-coupled chaotic opto-electronic oscillators. By examining the equations of motion, we demonstrate that symmetries in the network topology allow a variety of synchronous states to exist, including cluster synchronous states and a chimera state. Using the group theoretical approach recently developed for analyzing cluster synchronization, we show how to derive the variational equations for these synchronous patterns and calculate their linear stability. The stability analysis gives good agreement with our experimental results. Both experiments and simulations suggest that these chimera states often appear in regions of multistability between global, cluster, and desynchronized states. [Preview Abstract] |
Thursday, March 17, 2016 9:36AM - 9:48AM |
R43.00007: ABSTRACT WITHDRAWN |
Thursday, March 17, 2016 9:48AM - 10:00AM |
R43.00008: Emerging hierarchies in dynamically adapting webs Eleni Katifori, Johannes Graewer, Marcelo Magnasco, Carl Modes Transport networks play a key role across four realms of eukaryotic life: slime molds, fungi, plants, and animals. In addition to the developmental algorithms that build them, many also employ adaptive strategies to respond to stimuli, damage, and other environmental changes. We model these adapting network architectures using a generic dynamical system on weighted graphs and find in simulation that these networks ultimately develop a hierarchical organization of the final weighted architecture accompanied by the formation of a system-spanning backbone. We quantify the hierarchical organization of the networks by developing an algorithm that decomposes the architecture to multiple scales and analyzes how the organization in each scale relates to that of the scale above and below it. The methodologies developed in this work are applicable to a wide range of systems including the slime mold physarum polycephalum, human microvasculature, and force chains in granular media. [Preview Abstract] |
Thursday, March 17, 2016 10:00AM - 10:12AM |
R43.00009: Hybrid percolation transition in complex networks Byungnam Kahng Percolation has been one of the most applied statistical models. Percolation transition is one of the most robust continuous transitions known thus far. However, recent extensive researches reveal that it exhibits diverse types of phase transitions such as discontinuous and hybrid phase transitions. Here hybrid phase transition means the phase transition exhibiting natures of both continuous and discontinuous phase transitions simultaneously. Examples include k-core percolation, cascading failures in interdependent networks, synchronization, etc. Thus far, it is not manifest if the critical behavior of hybrid percolation transitions conforms to the conventional scaling laws of second-order phase transition. Here, we investigate the critical behaviors of hybrid percolation transitions in the cascading failure model in inter-dependent networks and the restricted Erdos-Renyi model. We find that the critical behaviors of the hybrid percolation transitions contain some features that cannot be described by the conventional theory of second-order percolation transitions. [Preview Abstract] |
Thursday, March 17, 2016 10:12AM - 10:24AM |
R43.00010: Phase Transitions in Networks of Memristive Elements Forrest Sheldon, Massimiliano Di Ventra The memory features of memristive elements (resistors with memory), analogous to those found in biological synapses, have spurred the development of neuromorphic systems based on them (see, e.g., [1]). In turn, this requires a fundamental understanding of the collective dynamics of networks of memristive systems. Here, we study an experimentally-inspired model of disordered memristive networks in the limit of a slowly ramped voltage and show through simulations that these networks undergo a first-order phase transition in the conductivity for sufficiently high values of memory, as quantified by the memristive ON/OFF ratio. We provide also a mean-field theory that reproduces many features of the transition and particularly examine the role of boundary conditions and current- vs. voltage-controlled networks. The dynamics of the mean-field theory suggest a distribution of conductance jumps which may be accessible experimentally. We finally discuss the ability of these networks to support massively-parallel computation. Work supported in part by the Center for Memory and Recording Research at UCSD. [1] Y.V. Pershin and M. Di Ventra, Proc. IEEE, {\bf 100}, 2071 (2012). [Preview Abstract] |
Thursday, March 17, 2016 10:24AM - 10:36AM |
R43.00011: ABSTRACT WITHDRAWN |
Thursday, March 17, 2016 10:36AM - 10:48AM |
R43.00012: A network model of human aging: Limits, errors, and information Spencer Farrell, Arnold Mitnitski, Kenneth Rockwood, Andrew Rutenberg The Frailty Index (FI) quantifies human aging using the fraction of accumulated age-related deficits. The FI correlates strongly with mortality and accumulates non-linearly and stochastically with age. Clinical data shows a nearly universal limit of FI $\le 0.7$. We computationally model an aging population using a network model of interacting deficits. Deficits damage and repair at rates that depend upon the average damage of connected nodes. The model is parametrized to fit clinical data. We find that attribution errors, especially false negative, allow the model to recover the frailty limit. Mutual information allows us to assess how well the FI can predict mortality. Mutual information provides a non-parametric measure of how the FI predicts mortality. We find that attribution errors have a small effect on the mutual information when many deficits are included in the model. The mutual information of our model and of the clinical data are comparable. [Preview Abstract] |
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