Matching Items (3)
Description
Complex dynamical systems consisting interacting dynamical units are ubiquitous in nature and society. Predicting and reconstructing nonlinear dynamics of units and the complex interacting networks among them serves the base for the understanding of a variety of collective dynamical phenomena. I present a general method to address the two outstanding problems as a whole based solely on time-series measurements. The method is implemented by incorporating compressive sensing approach that enables an accurate reconstruction of complex dynamical systems in terms of both nodal equations that determines the self-dynamics of units and detailed coupling patterns among units. The representative advantages of the approach are (i) the sparse data requirement which allows for a successful reconstruction from limited measurements, and (ii) general applicability to identical and nonidentical nodal dynamics, and to networks with arbitrary interacting structure, strength and sizes. Another two challenging problem of significant interest in nonlinear dynamics: (i) predicting catastrophes in nonlinear dynamical systems in advance of their occurrences and (ii) predicting the future state for time-varying nonlinear dynamical systems, can be formulated and solved in the framework of compressive sensing using only limited measurements. Once the network structure can be inferred, the dynamics behavior on them can be investigated, for example optimize information spreading dynamics, suppress cascading dynamics and traffic congestion, enhance synchronization, game dynamics, etc. The results can yield insights to control strategies design in the real-world social and natural systems. Since 2004, there has been a tremendous amount of interest in graphene. The most amazing feature of graphene is that there exists linear energy-momentum relationship when energy is low. The quasi-particles inside the system can be treated as chiral, massless Dirac fermions obeying relativistic quantum mechanics. Therefore, the graphene provides one perfect test bed to investigate relativistic quantum phenomena, such as relativistic quantum chaotic scattering and abnormal electron paths induced by klein tunneling. This phenomenon has profound implications to the development of graphene based devices that require stable electronic properties.
ContributorsYang, Rui (Author) / Lai, Ying-Cheng (Thesis advisor) / Duman, Tolga M. (Committee member) / Akis, Richard (Committee member) / Huang, Liang (Committee member) / Arizona State University (Publisher)
Created2012
Description
The research on the topology and dynamics of complex networks is one of the most focused area in complex system science. The goals are to structure our understanding of the real-world social, economical, technological, and biological systems in the aspect of networks consisting a large number of interacting units and to develop corresponding detection, prediction, and control strategies. In this highly interdisciplinary field, my research mainly concentrates on universal estimation schemes, physical controllability, as well as mechanisms behind extreme events and cascading failure for complex networked systems.
Revealing the underlying structure and dynamics of complex networked systems from observed data without of any specific prior information is of fundamental importance to science, engineering, and society. We articulate a Markov network based model, the sparse dynamical Boltzmann machine (SDBM), as a universal network structural estimator and dynamics approximator based on techniques including compressive sensing and K-means algorithm. It recovers the network structure of the original system and predicts its short-term or even long-term dynamical behavior for a large variety of representative dynamical processes on model and real-world complex networks.
One of the most challenging problems in complex dynamical systems is to control complex networks.
Upon finding that the energy required to approach a target state with reasonable precision
is often unbearably large, and the energy of controlling a set of networks with similar structural properties follows a fat-tail distribution, we identify fundamental structural ``short boards'' that play a dominant role in the enormous energy and offer a theoretical interpretation for the fat-tail distribution and simple strategies to significantly reduce the energy.
Extreme events and cascading failure, a type of collective behavior in complex networked systems, often have catastrophic consequences. Utilizing transportation and evolutionary game dynamics as prototypical
settings, we investigate the emergence of extreme events in simplex complex networks, mobile ad-hoc networks and multi-layer interdependent networks. A striking resonance-like phenomenon and the emergence of global-scale cascading breakdown are discovered. We derive analytic theories to understand the mechanism of
control at a quantitative level and articulate cost-effective control schemes to significantly suppress extreme events and the cascading process.
Revealing the underlying structure and dynamics of complex networked systems from observed data without of any specific prior information is of fundamental importance to science, engineering, and society. We articulate a Markov network based model, the sparse dynamical Boltzmann machine (SDBM), as a universal network structural estimator and dynamics approximator based on techniques including compressive sensing and K-means algorithm. It recovers the network structure of the original system and predicts its short-term or even long-term dynamical behavior for a large variety of representative dynamical processes on model and real-world complex networks.
One of the most challenging problems in complex dynamical systems is to control complex networks.
Upon finding that the energy required to approach a target state with reasonable precision
is often unbearably large, and the energy of controlling a set of networks with similar structural properties follows a fat-tail distribution, we identify fundamental structural ``short boards'' that play a dominant role in the enormous energy and offer a theoretical interpretation for the fat-tail distribution and simple strategies to significantly reduce the energy.
Extreme events and cascading failure, a type of collective behavior in complex networked systems, often have catastrophic consequences. Utilizing transportation and evolutionary game dynamics as prototypical
settings, we investigate the emergence of extreme events in simplex complex networks, mobile ad-hoc networks and multi-layer interdependent networks. A striking resonance-like phenomenon and the emergence of global-scale cascading breakdown are discovered. We derive analytic theories to understand the mechanism of
control at a quantitative level and articulate cost-effective control schemes to significantly suppress extreme events and the cascading process.
ContributorsChen, Yuzhong (Author) / Lai, Ying-Cheng (Thesis advisor) / Spanias, Andreas (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Ying, Lei (Committee member) / Arizona State University (Publisher)
Created2016
Description
Hyperbolic geometry, which is a geometry which concerns itself with hyperbolic space, has caught the eye of certain circles in the machine learning community as of late. Lauded for its ability to encapsulate strong clustering as well as latent hierarchies in complex and social networks, hyperbolic geometry has proven itself to be an enduring presence in the network science community throughout the 2010s, with no signs of fading into obscurity anytime soon. Hyperbolic embeddings, which map a given graph to hyperbolic space, have particularly proven to be a powerful and dynamic tool for studying complex networks. Hyperbolic embeddings are exploited in this thesis to illustrate centrality in a graph. In network science, centrality quantifies the influence of individual nodes in a graph. Eigenvector centrality is one type of such measure, and assigns an influence weight to each node in a graph by solving for an eigenvector equation. A procedure is defined to embed a given network in a model of hyperbolic space, known as the Poincare disk, according to the influence weights computed by three eigenvector centrality measures: the PageRank algorithm, the Hyperlink-Induced Topic Search (HITS) algorithm, and the Pinski-Narin algorithm. The resulting embeddings are shown to accurately and meaningfully reflect each node's influence and proximity to influential nodes.
ContributorsChang, Alena (Author) / Xue, Guoliang (Thesis advisor) / Yang, Dejun (Committee member) / Yang, Yezhou (Committee member) / Arizona State University (Publisher)
Created2020