Analysis of various steady states and transient phenomena in digital maps : foundation for theory construction and engineering applications

研究成果の概要 (和文) : デジタルマップ(Dmap)の解析と実装に関して以下のような成果を得た。まず、周期軌道の豊富さと安定性に関する特徴量を用いた解析法を考案し、典型例を解析し、現象の基本的な分類を行った。次に、簡素な進化計算によって所望のDmapを合成するアルゴリズムを考案した。アルゴリズムの個体はDmapに対応し、個体数は柔軟に変化する。典型的な例題によってアルゴリズムの妥当性を確認した。さらに、Dmapをデジタルスパイキングニューロン(DSN)によって実現する方法を構築した。DSNは2つのシフトレジスタと配線回路で構成され、様々なスパイク列を生成する。FPGAによる簡素な試作回路を構成し、動作を確認した。研究成果の概要 (英文) : We have studied analysis and implementation of digital maps (Dmaps). The major results are as the following. First, we have developed an analysis method based on two feature quantities. The first quantity characterizes plentifulness of periodic orbits and the second quantity characterizes stability of the periodic orbits. Applying the method, typical Dmap examples are analyzed and basic phenomena are classified. Second, we have developed a simple evolutionary algorithm to realize a desired Dmap. The algorithm uses individuals each of which corresponds to one Dmap and the number of individuals can vary flexibly. Using typical example problems, the algorithm efficiency is confirmed. Third, we have developed a realization method of Dmaps by means of digital spiking neurons (DSNs). The DSN consists of two shift registers connected by a wiring circuit and can generate various periodic spike-trains. Presenting a FPGA based simple test circuit, the DSN dynamics is confirmed

Model-Based and Machine Learning-Based Control of Biological Oscillators

Nonlinear oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. This dissertation investigates the dynamics of such oscillators arising in biology, and develops several control algorithms to modify their collective behavior. We demonstrate that these control algorithms have potential in devising treatments for Parkinson's disease, cardiac alternans, and jet lag. Phase reduction, a classical reduction technique, has been instrumental in understanding such biological oscillators. In this dissertation, we investigate a new reduction technique called augmented phase reduction, and calculate its associated analytical expressions for six dynamically different planar systems: This helps us to understand the dynamical regimes for which the use of augmented phase reduction is advantageous over the standard phase reduction. We further this study by developing a novel optimal control algorithm based on the augmented phase reduction to change the phase of a single oscillator using a minimum energy input. We show that our control algorithm is effective even when a large phase change is required or when the nontrivial Floquet multiplier of the oscillator is close to unity; in such cases, the previously proposed control algorithm based on the standard phase reduction fails.We then devise a novel framework to control a population of biological oscillators as a whole, and change their collective behavior. Our first two control algorithms are Lyapunov-based, and our third is an optimal control algorithm which minimizes the control energy consumption while achieving the desired collective behavior of an oscillator population. We show that the developed control algorithms can synchronize, desynchronize, cluster, and phase shift the population.We continue this investigation by developing two novel machine learning control algorithms, which have a simple and intelligent structure that makes them effective even with a sparse data set. We show that these algorithms are powerful enough to control a wide variety of dynamical systems and not just biological oscillators. We conclude this study by understanding how the developed machine learning algorithms work in terms of phase reduction.In this dissertation, we have developed all these algorithms with the goal of ease of experimental implementation, for which the model parameters/training data can be measured experimentally. We close the loop on this dissertation by carrying out robustness analysis for the developed algorithms; demonstrating their resilience to noise, and thus their suitability for controlling living biological tissue. They truly hold great potential in devising treatments for Parkinson's disease, cardiac alternans, and jet lag

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

NASA Thesaurus. Volume 1: Hierarchical listing

There are 16,713 postable terms and 3,716 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

NASA thesaurus. Volume 1: Hierarchical Listing

There are over 17,000 postable terms and nearly 4,000 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary and Volume 3 - Definitions

NASA Thesaurus. Volume 2: Access vocabulary

The NASA Thesaurus -- Volume 2, Access Vocabulary -- contains an alphabetical listing of all Thesaurus terms (postable and nonpostable) and permutations of all multiword and pseudo-multiword terms. Also included are Other Words (non-Thesaurus terms) consisting of abbreviations, chemical symbols, etc. The permutations and Other Words provide 'access' to the appropriate postable entries in the Thesaurus

Data Driven Techniques for Modeling Coupled Dynamics in Transient Processes

We study the problem of modeling coupled dynamics in transient processes that happen in a network. The problem is considered at two levels. At the node level, the coupling between underlying sub-processes of a node in a network is considered. At the network level, the direct influence among the nodes is considered. After the model is constructed, we develop a network-based approach for change detection in high dimension transient processes. The overall contribution of our work is a more accurate model to describe the underlying transient dynamics either for each individual node or for the whole network and a new statistic for change detection in multi-dimensional time series. Specifically, at the node level, we developed a model to represent the coupled dynamics between the two processes. We provide closed form formulas on the conditions for the existence of periodic trajectory and the stability of solutions. Numerical studies suggest that our model can capture the nonlinear characteristics of empirical data while reducing computation time by about 25% on average, compared to a benchmark modeling approach. In the last two problems, we provide a closed form formula for the bound in the sparse regression formulation, which helps to reduce the effort of trial and error to find an appropriate bound. Compared to other benchmark methods in inferring network structure from time series, our method reduces inference error by up to 5 orders of magnitudes and maintain better sparsity. We also develop a new method to infer dynamic network structure from a single time series. This method is the basis for introducing a new spectral graph statistic for change detection. This statistic can detect changes in simulation scenario with modified area under curve (mAUC) of 0.96. When applying to the problem of detecting seizure from EEG signal, our statistic can capture the physiology of the process while maintaining a detection rate of 40% by itself. Therefore, it can serve as an effective feature to detect change and can be added to the current set of features for detecting seizures from EEG signal