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

Stochastic Opinion Formation in Scale-Free Networks

The dynamics of opinion formation in large groups of people is a complex non-linear phenomenon whose investigation is just at the beginning. Both collective behaviour and personal view play an important role in this mechanism. In the present work we mimic the dynamics of opinion formation of a group of agents, represented by two state $\pm 1$, as a stochastic response of each of them to the opinion of his/her neighbours in the social network and to feedback from the average opinion of the whole. In the light of recent studies, a scale-free Barab\'asi-Albert network has been selected to simulate the topology of the interactions. A turbulent-like dynamics, characterized by an intermittent behaviour, is observed for a certain range of the model parameters. The problem of uncertainty in decision taking is also addressed both from a topological point of view, using random and targeted removal of agents from the network, and by implementing a three state model, where the third state, zero, is related to the information available to each agent. Finally, the results of the model are tested against the best known network of social interactions: the stock market. A time series of daily closures of the Dow Jones index has been used as an indicator of the possible applicability of our model in the financial context. Good qualitative agreement is found.Comment: 24 pages and 13 figures, Physical Review E, in pres

Control and Data Analysis of Complex Networks

abstract: This dissertation treats a number of related problems in control and data analysis of complex networks. First, in existing linear controllability frameworks, the ability to steer a network from any initiate state toward any desired state is measured by the minimum number of driver nodes. However, the associated optimal control energy can become unbearably large, preventing actual control from being realized. Here I develop a physical controllability framework and propose strategies to turn physically uncontrollable networks into physically controllable ones. I also discover that although full control can be guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control energy to achieve actual control, and my work provides a framework to address this issue. Second, in spite of recent progresses in linear controllability, controlling nonlinear dynamical networks remains an outstanding problem. Here I develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another. I introduce the concept of attractor network and formulate a quantifiable framework: a network is more controllable if the attractor network is more strongly connected. I test the control framework using examples from various models and demonstrate the beneficial role of noise in facilitating control. Third, I analyze large data sets from a diverse online social networking (OSN) systems and find that the growth dynamics of meme popularity exhibit characteristically different behaviors: linear, “S”-shape and exponential growths. Inspired by cell population growth model in microbial ecology, I construct a base growth model for meme popularity in OSNs. Then I incorporate human interest dynamics into the base model and propose a hybrid model which contains a small number of free parameters. The model successfully predicts the various distinct meme growth dynamics. At last, I propose a nonlinear dynamics model to characterize the controlling of WNT signaling pathway in the differentiation of neural progenitor cells. The model is able to predict experiment results and shed light on the understanding of WNT regulation mechanisms.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

A dynamical model of the distributed interaction of intracellular signals

A major goal of modern cell biology is to understand the regulation of cell behavior in the reductive terms of all the molecular interactions. This aim is made explicit by the assertion that understanding a cell\u27s response to stimuli requires a full inventory of details. Currently, no satisfactory explanation exists to explain why cells exhibit only a relatively small number of different behavioral modes. In this thesis, a discrete dynamical model is developed to study interactions between certain types of signaling proteins. The model is generic and connectionist in nature and incorporates important concepts from the biology. The emphasis is on examining dynamic properties that occur on short-term time scales and are independent of gene expression. A number of modeling assumptions are made. However, the framework is flexible enough to be extended in future studies. The dynamical states of the system are explored both computationally and analytically. Monte Carlo methods are used to study the state space of simulated networks over selected parameter regimes. Networks show a tendency to settle into fixed points or oscillations over a wide range of initial conditions. A genetic algorithm (GA) is also designed to explore properties of networks. It evolves a population of modeled cells, selecting and ranking them according to a fitness function, which is designed to mimic features of real biological evolution. An analogue of protein domain shuffling is used as the crossover operator and cells are reproduced asexually. The effects of changing the parameters of the GA are explored. A clustering algorithm is developed to test the effectiveness of the GA search at generating cells, which display a limited number of different behavioral modes. Stability properties of equilibrium states in small networks are analyzed. The ability to generalize these techniques to larger networks is discussed. Topological properties of networks generated by the GA are examined. Structural properties of networks are used to provide insight into their dynamic properties. The dynamic attractors exhibited by such signaling networks may provide a framework for understanding why cells persist in only a small number of stable behavioral modes

Neuromorphic Few-Shot Learning: Generalization in Multilayer Physical Neural Networks

Neuromorphic computing leverages the complex dynamics of physical systems for computation. The field has recently undergone an explosion in the range and sophistication of implementations, with rapidly improving performance. Neuromorphic schemes typically employ a single physical system, limiting the dimensionality and range of available dynamics - restricting strong performance to a few specific tasks. This is a critical roadblock facing the field, inhibiting the power and versatility of neuromorphic schemes. Here, we present a solution. We engineer a diverse suite of nanomagnetic arrays and show how tuning microstate space and geometry enables a broad range of dynamics and computing performance. We interconnect arrays in parallel, series and multilayered neural network architectures, where each network node is a distinct physical system. This networked approach grants extremely high dimensionality and enriched dynamics enabling meta-learning to be implemented on small training sets and exhibiting strong performance across a broad taskset. We showcase network performance via few-shot learning, rapidly adapting on-the-fly to previously unseen tasks

Angular velocity integration in a fly heading circuit

Many animals maintain an internal representation of their heading as they move through their surroundings. Such a compass representation was recently discovered in a neural population in the Drosophila melanogaster central complex, a brain region implicated in spatial navigation. Here, we use two-photon calcium imaging and electrophysiology in head-fixed walking flies to identify a different neural population that conjunctively encodes heading and angular velocity, and is excited selectively by turns in either the clockwise or counterclockwise direction. We show how these mirror-symmetric turn responses combine with the neurons' connectivity to the compass neurons to create an elegant mechanism for updating the fly's heading representation when the animal turns in darkness. This mechanism, which employs recurrent loops with an angular shift, bears a resemblance to those proposed in theoretical models for rodent head direction cells. Our results provide a striking example of structure matching function for a broadly relevant computation