Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles

Realizing strongly-correlated topological phases of ultracold gases is a central goal for ongoing experiments. And while fractional quantum Hall states could soon be implemented in small atomic ensembles, detecting their signatures in few-particle settings remains a fundamental challenge. In this work, we numerically analyze the center-of-mass Hall drift of a small ensemble of hardcore bosons, initially prepared in the ground state of the Harper-Hofstadter-Hubbard model in a box potential. By monitoring the Hall drift upon release, for a wide range of magnetic flux values, we identify an emergent Hall plateau compatible with a fractional Chern insulator state: the extracted Hall conductivity approaches a fractional value determined by the many-body Chern number, while the width of the plateau agrees with the spectral and topological properties of the prepared ground state. Besides, a direct application of Streda's formula indicates that such Hall plateaus can also be directly obtained from static density-profile measurements. Our calculations suggest that fractional Chern insulators can be detected in cold-atom experiments, using available detection methods.Comment: 13 pages, 11 figures; extended version accepted for publicatio

Flow Motifs Reveal Limitations of the Static Framework to Represent Human interactions

Networks are commonly used to define underlying interaction structures where infections, information, or other quantities may spread. Although the standard approach has been to aggregate all links into a static structure, some studies suggest that the time order in which the links are established may alter the dynamics of spreading. In this paper, we study the impact of the time ordering in the limits of flow on various empirical temporal networks. By using a random walk dynamics, we estimate the flow on links and convert the original undirected network (temporal and static) into a directed flow network. We then introduce the concept of flow motifs and quantify the divergence in the representativity of motifs when using the temporal and static frameworks. We find that the regularity of contacts and persistence of vertices (common in email communication and face-to-face interactions) result on little differences in the limits of flow for both frameworks. On the other hand, in the case of communication within a dating site (and of a sexual network), the flow between vertices changes significantly in the temporal framework such that the static approximation poorly represents the structure of contacts. We have also observed that cliques with 3 and 4 vertices con- taining only low-flow links are more represented than the same cliques with all high-flow links. The representativity of these low-flow cliques is higher in the temporal framework. Our results suggest that the flow between vertices connected in cliques depend on the topological context in which they are placed and in the time sequence in which the links are established. The structure of the clique alone does not completely characterize the potential of flow between the vertices

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

Recurrence-based time series analysis by means of complex network methods

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos (2011

Community Detection in Quantum Complex Networks

Determining community structure is a central topic in the study of complex networks, be it technological, social, biological or chemical, in static or interacting systems. In this paper, we extend the concept of community detection from classical to quantum systems---a crucial missing component of a theory of complex networks based on quantum mechanics. We demonstrate that certain quantum mechanical effects cannot be captured using current classical complex network tools and provide new methods that overcome these problems. Our approaches are based on defining closeness measures between nodes, and then maximizing modularity with hierarchical clustering. Our closeness functions are based on quantum transport probability and state fidelity, two important quantities in quantum information theory. To illustrate the effectiveness of our approach in detecting community structure in quantum systems, we provide several examples, including a naturally occurring light-harvesting complex, LHCII. The prediction of our simplest algorithm, semiclassical in nature, mostly agrees with a proposed partitioning for the LHCII found in quantum chemistry literature, whereas our fully quantum treatment of the problem uncovers a new, consistent, and appropriately quantum community structure.Comment: 16 pages, 4 figures, 1 tabl

Book Review

A Scholarly Review of “Error Control for Network-On-Chip Links” (Authors: Bo Fu and Paul Ampadu, 2012)Fu, B.; and Ampadu, P. 2012. Error Control for Network-On-Chip Links.Springer Science+Business Media, LLC, New York, NY, USA.Available: <http://dx.doi.org/10.1007/978-1-4419-9313-7>

Modelling and detection of faults in axial-flux permanent magnet machines

The development of various topologies and configurations of axial-flux permanent magnet machine has spurred its use for electromechanical energy conversion in several applications. As it becomes increasingly deployed, effective condition monitoring built on reliable and accurate fault detection techniques is needed to ensure its engineering integrity. Unlike induction machine which has been rigorously investigated for faults, axial-flux permanent magnet machine has not. Thus in this thesis, axial-flux permanent magnet machine is investigated under faulty conditions. Common faults associated with it namely; static eccentricity and interturn short circuit are modelled, and detection techniques are established. The modelling forms a basis for; developing a platform for precise fault replication on a developed experimental test-rig, predicting and analysing fault signatures using both finite element analysis and experimental analysis. In the detection, the motor current signature analysis, vibration analysis and electrical impedance spectroscopy are applied. Attention is paid to fault-feature extraction and fault discrimination. Using both frequency and time-frequency techniques, features are tracked in the line current under steady-state and transient conditions respectively. Results obtained provide rich information on the pattern of fault harmonics. Parametric spectral estimation is also explored as an alternative to the Fourier transform in the steady-state analysis of faulty conditions. It is found to be as effective as the Fourier transform and more amenable to short signal-measurement duration. Vibration analysis is applied in the detection of eccentricities; its efficacy in fault detection is hinged on proper determination of vibratory frequencies and quantification of corresponding tones. This is achieved using analytical formulations and signal processing techniques. Furthermore, the developed fault model is used to assess the influence of cogging torque minimization techniques and rotor topologies in axial-flux permanent magnet machine on current signal in the presence of static eccentricity. The double-sided topology is found to be tolerant to the presence of static eccentricity unlike the single-sided topology due to the opposing effect of the resulting asymmetrical properties of the airgap. The cogging torque minimization techniques do not impair on the established fault detection technique in the single-sided topology. By applying electrical broadband impedance spectroscopy, interturn faults are diagnosed; a high frequency winding model is developed to analyse the impedance-frequency response obtained