Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session S43: Nonlinear Dynamics in Networks IIFocus
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Sponsoring Units: GSNP Chair: Adilson Motter, Northwestern University Room: 346 |
Thursday, March 17, 2016 11:15AM - 11:51AM |
S43.00001: \textbf{Quantifying Stability in Complex Networks: From Linear to Basin Stability } Invited Speaker: J\"urgen Kurths The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is in several cases too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. Specifically, we employ a component-wise version of basin stability, a nonlinear inspection scheme, to investigate how a grid's degree of stability is influenced by certain patterns in the wiring topology. Various statistics from our ensemble simulations all support one main finding: The widespread and cheapest of all connection schemes, namely dead ends and dead trees, strongly diminish stability. For the Northern European power system we demonstrate that the inverse is also true: `Healing' dead ends by addition of transmission lines substantially enhances stability. This indicates a crucial smart-design principle for tomorrow's sustainable power grids: add just a few more lines to avoid dead ends. Further, we analyse the particular function of certain network motifs to promote the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design. Moreover, it will be shown that basin stability enables uncovering the mechanism for explosive synchronization and understanding of evolving networks. \\ \\Reference: P. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Physics 9, 89 (2013) P. Menck, J. Heitzig, J. Kurths, and H. Schellnhuber, Nature Communication 5, 3969 (2014) P. Schultz, J. Heitzig, and J. Kurths, New Journal Physics 16, 125001 (2014) V. Kohar, P. Ji, A. Choudhary, S. Sinha, and J. Kurths, Phys. Rev. E 90, 022812 (2014) Y. Zou, T. Pereira,~M. Small,~ Z. Liu, and J. Kurths, Phys. Rev. Lett. 112, 114102 (2014) [Preview Abstract] |
Thursday, March 17, 2016 11:51AM - 12:03PM |
S43.00002: Control of State Transitions in Complex and Biophysical Networks Adilson Motter, Daniel Wells, William Kath Noise is a fundamental part of intracellular processes. While the response of biological systems to noise has been studied extensively, there has been limited understanding of how to exploit it to induce a desired cell state. Here I will present a scalable, quantitative method based on the Freidlin-Wentzell action to predict and control noise-induced switching between different states in genetic networks that, conveniently, can also control transitions between stable states in the absence of noise. I will discuss applications of this methodology to predict control interventions that can induce lineage changes and to identify new candidate strategies for cancer therapy. This framework offers a systems approach to identifying the key factors for rationally manipulating network dynamics, and should also find use in controlling other classes of complex networks exhibiting multi-stability. Reference: D. K. Wells, W. L. Kath, and A. E. Motter, Phys. Rev. X 5, 031036 (2015). [Preview Abstract] |
Thursday, March 17, 2016 12:03PM - 12:15PM |
S43.00003: Landscape Construction in Dynamical Systems Ying Tang, Ruoshi Yuan, Gaowei Wang, Ping Ao The idea of landscape has been recently applied to study various of biological problems. We demonstrate that a dynamical structure built into nonlinear dynamical systems allows us to construct such a global optimization landscape, which serves as the Lyapunov function for the ordinary differential equation. We find exact constructions on the landscape for a class of dynamical systems, including a van der Pol type oscillator, competitive Lotka-Volterra systems, and a chaotic system. The landscape constructed provides a new angle for understanding and modelling biological network dynamics. [Preview Abstract] |
Thursday, March 17, 2016 12:15PM - 12:27PM |
S43.00004: Cell fate reprogramming by control of intracellular network dynamics Jorge G. T. Zanudo, Reka Albert Identifying control strategies for biological networks is paramount for practical applications that involve reprogramming a cell's fate, such as disease therapeutics and stem cell reprogramming. Although the topic of controlling the dynamics of a system has a long history in control theory, most of this work is not directly applicable to intracellular networks. Here we present a network control method that integrates the structural and functional information available for intracellular networks to predict control targets. Formulated in a logical dynamic scheme, our control method takes advantage of certain function-dependent network components and their relation to steady states in order to identify control targets, which are guaranteed to drive any initial state to the target state with 100{\%} effectiveness and need to be applied only transiently for the system to reach and stay in the desired state. We illustrate our method's potential to find intervention targets for cancer treatment and cell differentiation by applying it to a leukemia signaling network and to the network controlling the differentiation of T cells. We find that the predicted control targets are effective in a broad dynamic framework. Moreover, several of the predicted interventions are supported by experiments. [Preview Abstract] |
Thursday, March 17, 2016 12:27PM - 12:39PM |
S43.00005: Predictive Control of Large Complex Networks Aleksandar Haber, Adilson E. Motter Networks of coupled dynamical subsystems are increasingly used to represent complex natural and engineered systems. While recent technological developments give us improved means to actively control the dynamics of individual subsystems in various domains, network control remains a challenging problem due to difficulties imposed by intrinsic nonlinearities, control constraints, and the large-scale nature of the systems. In this talk, we will present a model predictive control approach that is effective while accounting for these realistic properties of complex networks. Our method can systematically identify control interventions that steer the trajectory to a desired state, even in the presence of strong nonlinearities and constraints. Numerical tests show that the method is applicable to a variety of networks, ranging from power grids to chemical reaction systems. [Preview Abstract] |
Thursday, March 17, 2016 12:39PM - 12:51PM |
S43.00006: Reconstructing Directed Networks From Noisy Dynamics Hiu Ching Tam, Emily SC Ching Complex systems can be fruitfully studied as networks of many elementary units, known as nodes, interacting with one another with the interactions being the links between the nodes. The overall behavior of the systems depends crucially on the network structure depicting how the nodes are linked with each other. It is usually possible to measure the dynamics of the individual nodes but difficult, if not impossible, to directly measure the interactions or links between the nodes. For most systems of interest, the links are directional in that one node affects the dynamics of the other but not vice versa. Moreover, the strength of interaction can vary for different links. Reconstructing directed and weighted networks from dynamics is one of the biggest challenges in network research. We have studied directed and weighted networks modelled by noisy dynamical systems with nonlinear dynamics and developed a method that reconstructs the links and their directions using only the dynamics of the nodes as input. Our method is motivated by a mathematical result derived for dynamical systems that approach a fixed point in the noise-free limit. We show that our method gives good reconstruction results for several directed and weighted networks with different nonlinear dynamics. [Preview Abstract] |
Thursday, March 17, 2016 12:51PM - 1:03PM |
S43.00007: Hamiltonian-Based Model to Describe the Nonlinear Physics of Cascading Failures in Power-Grid Networks Yang Yang, Adilson Motter A local disturbance to the state of a power-grid system can trigger a protective response that disables some grid components, which leads to further responses, and may finally result in large-scale failures. In this talk, I will introduce a Hamiltonian-like model of cascading failures in power grids. This model includes the state variables of generators, which are determined by the nonlinear swing equations and power-flow equations, as well as the on/off status of the network components. This framework allows us to view a cascading failure in the power grid as a phase-space transition from a fixed point with high energy to a fixed point with lower energy. Using real power-grid networks, I will demonstrate that possible cascade outcomes can be predicted by analyzing the stability of the system's equilibria. This work adds an important new dimension to the current understanding of cascading failures. [Preview Abstract] |
Thursday, March 17, 2016 1:03PM - 1:15PM |
S43.00008: Cascading Failures in Flow-Driven Networks Induced by Multiple Initiators Alaa Moussawi, Noemi Derzsy, Xin Lin, Boleslaw Szymanski, Gyorgy Korniss Flow-driven networks are particularly prone to cascading failures. These failures are non self-averaging and this makes them very difficult to predict or subdue [1, 2]. Previous work has suggested that uniformly increasing edge or node capacities may lead to larger failures [1]. This suggests that some nodes/edges may act as fuses and mitigate cascading failures. We investigate this idea, and analyze how properties of the initiators of the cascade influence its outcome. We also discuss how stochastic node capacity allocation can be utilized to mitigate cascades induced by multiple initiators. We demonstrate the efficacy of these strategies on random geometric graphs (RGG) and the UCTE European electrical power transmission network, with capacities allocated in~a fashion similar to the industry standard. [1] A. Asztalos, S. Sreenivasan, B.K. Szymanski, and G. Korniss, "Cascading Failures in Spatially\textunderscore Embedded Random Networks", PLOS ONE 9(1): e84563 (2014). [2] Bernstein et al., ACM SIGMETRICS Performance Eval. Rev. 40, 33-37 (2012). [Preview Abstract] |
Thursday, March 17, 2016 1:15PM - 1:27PM |
S43.00009: Cascading processes on multiplex networks: Impact of weak layers Kyu-Min Lee, Kwang-Il Goh Many real-world complex systems such as biological and socio-technological systems consist of manifold layers in multiplex networks. The multiple network layers give rise to the nonlinear effect for the emergent dynamics of systems. Especially, the weak layers plays the significant role in nonlinearity of multiplex networks, which can be neglected in single-layer network framework overlaying all layers. Here we present a simple model of cascades on multiplex networks of heterogeneous layers. The model is simulated on the multiplex network of international trades. We found that the multiplex model produces more catastrophic cascading failures which were the result of collective behaviors from coupling layers rather than the simple summation effect. Therefore risks can be systematically underestimated in simply overlaid network system because the impact of weak layers is overlooked. Our simple theoretical model would have some implications to investigate and design optimal real-world complex systems. [Preview Abstract] |
Thursday, March 17, 2016 1:27PM - 1:39PM |
S43.00010: Long-term Failure Prediction based on an ARP Model of Global Risk Network Xin Lin, Alaa Moussawi, Boleslaw Szymanski, Gyorgy Korniss Risks that threaten modern societies form an intricately interconnected network. Hence, it is important to understand how risk materializations in distinct domains influence each other. In the paper \footnote{Szymanski et al., Sci. Rep. 5:10998 (2015)}, we study the global risks network defined by World Economic Forum experts in the form of Stochastic Block Model. We model risks as Alternating Renewal Processes with variable intensities driven by hidden values of exogenous and endogenous failure probabilities. Based on the expert assessments and historical status of each risk, we use Maximum Likelihood Evaluation to find the optimal model parameters and demonstrate that the model considering network effects significantly outperforms the others. In the talk, we discuss how the model can be used to provide quantitative means for measuring interdependencies and materialization of risks in the network. We also present recent results of long-term predictions in the form of predicated distributions of materializations over various time periods. Finally we show how the simulation of ARP’s enables us to probe limits of the predictability of the system parameters from historical data and ability to recover hidden variable. [Preview Abstract] |
Thursday, March 17, 2016 1:39PM - 1:51PM |
S43.00011: Hybrid dynamics in delay-coupled swarms with ``mothership" networks Jason Hindes, Ira Schwartz Swarming behavior continues to be a subject of immense interest because of its centrality in many naturally occurring systems in biology and physics. Moreover, the development of autonomous mobile agents that can mimic the behavior of swarms and can be engineered to perform complex tasks without constant intervention is a very active field of practical research. Here we examine the effects on delay-coupled swarm pattern formation from the inclusion of a small fraction of highly connected nodes, ``motherships", in the swarm interaction network. We find a variety of new behaviors and bifurcations, including new hybrid motions of previously analyzed patterns. Both numerical and analytic techniques are used to classify the dynamics and construct the phase diagram. The implications for swarm control and robustness from topological heterogeneity are also discussed. [Preview Abstract] |
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