Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Volume 11 , Issue 4
Showing 1-21 articles out of 21 articles from the selected issue
Special Issue on Recent Progress in Nonlinear Theory and Its Applications
  • Nordin Ramli, Hiroyuki Torikai
    Type: FOREWORD
    2020 Volume 11 Issue 4 Pages 372
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS
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  • Toshimichi Saito
    Type: Invited Paper
    2020 Volume 11 Issue 4 Pages 373-390
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    This review paper introduces piecewise linear switched dynamical systems in three topics. In the first topic of autonomous chaotic circuits, we introduce the manifold piecewise linear system and chaotic spiking oscillator. Using piecewise exact solutions and mapping procedure, we obtain rigorous proof of chaos generation. In the second topic of recurrent neural networks, we introduce the hysteresis neural network and its application to associative memories. Performing theoretical analysis based on the piecewise exact solutions, we obtain parameter conditions for guaranteed storage of any desired memories. In the third topic of multiobjective optimization problems, we introduce a two-objective problem in a piecewise linear model of switching power converter with photovoltaic input. Applying a simple multiobjective evolutionary algorithm, we clarify existence of a trade-off between the maximum input power and circuit stability.

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  • Haruna Matsushita, Hiroaki Kurokawa, Takuji Kousaka
    Type: Invited Paper
    2020 Volume 11 Issue 4 Pages 391-408
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    This paper explains a bifurcation parameter detection strategy based on particle swarm optimization (PSO), and it shows application examples on detection of local bifurcation parameters appearing in discrete-time dynamical systems and non-autonomous continuous dynamical systems. The algorithm design and analysis part shows that the PSO-based algorithm is fairly simple, easily understandable, and easily implementable. The method requires no careful initialization, exact calculation, gradient information of the system, or Lyapunov exponents. However, the simulation results show that the method accurately detects the local bifurcation parameters regardless of the stability of the periodic point.

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  • Indrapriyadarsini Sendilkkumaar, Shahrzad Mahboubi, Hiroshi Ninomiya, ...
    Type: Invited Paper
    2020 Volume 11 Issue 4 Pages 409-421
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    Recurrent Neural Networks (RNNs) are powerful sequence models that are particularly difficult to train. This paper proposes an adaptive stochastic Nesterov's accelerated quasi-Newton (aSNAQ) method for training RNNs. Several algorithms have been proposed earlier for training RNNs. However, due to high computational complexity, very few methods use second-order curvature information despite its ability to improve convergence. The proposed method is an accelerated second-order method that attempts to incorporate curvature information while maintaining a low per iteration cost. Furthermore, direction normalization has been introduced to solve the vanishing and/or exploding gradient problem that is prominent in training RNNs. The performance of the proposed method is evaluated in Tensorflow on benchmark sequence modeling problems. The results show that the proposed aSNAQ method is effective in training RNNs with a low per-iteration cost and improved performance compared to the second-order adaQN and first-order Adagrad and Adam methods.

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  • Kazuya Sawada, Yutaka Shimada, Tohru Ikeguchi
    Type: Invited Paper
    2020 Volume 11 Issue 4 Pages 422-432
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    The recent developments in measurement techniques have allowed us to observe multidimensional time series data in various fields. Thus, detecting causal relations between elements from multidimensional time series data is useful for prediction, model generation, and system control. In addition, causal relations between elements can be detected to estimate network connections. In other words, the network structure can be estimated from multidimensional time series data by using causality detection methods. Among the several methods for detecting causality, Granger causality is a well-known method that is widely used for causal estimation between time series. On the other hand, a method called convergent cross mapping (CCM) has been proposed, which can distinguish causality from pseudo-correlation. It is important to investigate whether CCM will be effective with increased number of elements, even though the evaluation of its performance with a few elements has been reported in the literature. Moreover, it is important to evaluate the performance with changing dynamics of the elements. In this study, to estimate the connectivity between elements in complex networks, we apply CCM to mathematical models of complex networks, or the Watts-Strogatz model. In particular, we investigate how complex network structures affect causal estimation, by applying CCM to multidimensional time series data produced from complex networks. According to the results, we find the connectivity estimation accuracies in the regular ring-lattice network to be slightly higher than those in random networks. Furthermore, we reveal that it is easier to perform connectivity estimation for a network with a community structure than a random structure.

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  • Chiemi Tanaka, Ferdinand Peper, Mikio Hasegawa
    Type: Invited Paper
    2020 Volume 11 Issue 4 Pages 433-445
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    Asynchronous Pulse-Code Multiple Access (APCMA) has been proposed as a brain-inspired communication protocol based on pulse-like signals (Peper et al, The Brain & Networks, 2018). Encoding data as intervals between pulses, APCMA allows multiple transmitters to transmit pulse trains at arbitrary times. While this typically causes collisions in conventional multiple access protocols, it does not do so in APCMA. Even if pulse trains collide and a receiver receives a mixture of them, they are disentangled by a demodulation algorithm that is based on a spike automaton, which is a type of finite automaton that is designed to recognize specific sequences of pulses. This makes APCMA especially suitable for data multiplexing in a communication system that lacks carrier-sense functionality. In this paper, we apply the APCMA protocol to an electrical power packet routing system. The power packet router lacks carrier-sense functionality, which would be necessary for transmission from multiple sources in a conventional communication protocol. We design and implement the modulation and the demodulation protocols of APCMA on a FPGA in power packet router devices. Our experimental results show that the proposed APCMA-based power routing system can transmit multiple power packets simultaneously without collisions.

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  • Kohei Inoue, Kenji Hara
    Type: Paper
    2020 Volume 11 Issue 4 Pages 446-453
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    In this paper, we show an equivalence between log-sum-exp approximation and entropy regularization in K-means clustering, which is a well-known algorithm for partitional clustering. We derive an identical equation for updating centroids of clusters from the two formulations. Additionally, we derive an alternative equation suitable for another formulation of entropy regularization, maximum entropy method. We also show experimental results which support the theoretical results.

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  • Muneki Yasuda, Yeo Xian En, Seishirou Ueno
    Type: Paper
    2020 Volume 11 Issue 4 Pages 454-465
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    In this study, classification problems based on feedforward neural networks in a data-imbalanced environment are considered. Learning from an imbalanced dataset is one of the most important practical problems in the field of machine learning. A weighted loss function (WLF) based on a cost-sensitive approach is a well-known and effective method for imbalanced datasets. A combination of WLF and batch normalization (BN) is considered in this study. BN is considered as a powerful standard technique in the recent developments in deep learning. A simple combination of both methods leads to a size-inconsistency problem due to a mismatch between the interpretations of the effective size of the dataset in both methods. A simple modification to BN, called weighted BN (WBN), is proposed to correct the size mismatch. The idea of WBN is simple and natural. The proposed method in a data-imbalanced environment is validated using numerical experiments.

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  • Aren Shinozaki, Takaya Miyano, Yoshihiko Horio
    Type: Paper
    2020 Volume 11 Issue 4 Pages 466-479
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    We have applied noisy echo state networks to the short-term forecasting of hyperchaotic and chaotic time series. The hyperchaotic time series were generated using the augmented Lorenz equations as a star network of Q nonidentical Lorenz systems and a four-dimensional Lorenz system. The echo state networks were used mainly in the recursive forecasting mode, wherein the output value of the network, i.e., the predicted value, at the current time step was recursively fed back to the input node at the next time step of prediction. The addition of external noise to the reservoir network has been found to considerably improve the fidelity of the geometrical structures of the chaotic attractors reconstructed from the predicted time series. We discuss these observations on the basis of Ueda's theory of chaos.

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  • Junya Ikemoto, Toshimitsu Ushio
    Type: Paper
    2020 Volume 11 Issue 4 Pages 480-500
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    Networked control systems (NCSs) have been attracted much attention thanks to the development of network technology. There are network delays caused by data transmissions in NCSs. These network delays may degrade control performances. In general, the network delays may fluctuate randomly and it is difficult to identify their probability distributions. Moreover, it is difficult to precisely identify models of plants. Thus, we propose a design method of networked controllers using deep reinforcement learning (DRL) taking network delays into consideration. Additionally, we consider the case where sensors cannot observe all state variables of plants. We introduce an extended state and propose a DRL-based controller design method.

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  • Nobuyuki Hirami, Ibuki Nakamura, Hisato Fujisaka
    Type: Paper
    2020 Volume 11 Issue 4 Pages 501-516
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    This paper proposes a probabilistic particle model of single-electrons on graphene. The behavior of a single-electron on graphene is described approximately by the massless Dirac equation. The electron is non-relativistic and given pseudo-spin. The Dirac equation originally describes the motion of a relativistic quantum particle with actual spin. Then, it has seemed difficult that the Nelson's stochastic quantization theory could build a particle model of the electron on graphene since the theory can deal with only non-relativistic quantum particles with spin not being taken into account. In this paper, Nelson's theory is interpreted by using probability density function and probability density current so that it can build a particle model of a single-electron on graphene. Single-electrons on a graphene nano-ribbon and on a graphene sheet in constant magnetic field were modeled as probabilistic particles. The models were described by nonlinear stochastic ordinary differential equations. It has been numerically confirmed that probability distributions of the electron models coincide with distributions derived from the wave functions.

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  • Seung-Il Cho, Minami Tsuchiya, Atsushi Tanaka, Muneki Yasuda, Tomochik ...
    Type: Paper
    2020 Volume 11 Issue 4 Pages 517-526
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    In this paper, the relation between estimated instantaneous sleep satisfaction using nonlinear multiple regression analysis and activity of the autonomic nervous system (ANS) is visualized and evaluated using the proposed scatter plot chart. We made a hypothesis and tested it such that the parasympathetic nerve activity (PNA) index representing the relaxation component rises as enhancement of the estimated instantaneous satisfaction level, and the sympathetic nerve activity index representing the stress component rises as reduction of the estimated instantaneous satisfaction level, during sleep. In the results of these experiments, when the average value per night of estimated instantaneous sleep satisfaction during sleep was level 3 or more, the number of points which are estimated satisfaction of level 3 or more, in the PNA index above the average value, was greater than that of less than level 3. It was found that the proposed method is effective for evaluating states of the ANS in sleep.

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  • Yuichi Tanji, Haruna Matsushita, Hiroo Sekiya
    Type: Paper
    2020 Volume 11 Issue 4 Pages 527-545
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    Class-E amplifier is one of the switching amplifiers. It is difficult to determine the circuit parameters satisfying the switching conditions. Although the Newton method was proposed to determine the passive elements, it requires a good initial solution that is obtained by using an analytical expression of the class-E amplifier. Even if the circuit configuration is slightly changed, the analytical expression must be re-derived. In this paper, the passive element value determination of class-E amplifier is defined as an optimization problem. This problem is solved by some methods which do not rely on the initial solution obtained by using the analytical expression. Furthermore, the objective function value for the optimization is efficiently calculated via a behavioral model of the class-E amplifier, which eases the optimum circuit design computationally and economically. Thus, an automated design procedure for the class-E amplifier will be presented in this paper.

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  • Ryo Yamazaki, Yutaka Shimada, Tohru Ikeguchi
    Type: Paper
    2020 Volume 11 Issue 4 Pages 546-560
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    The multiple-input multiple-output (MIMO) system is one of the wireless communication methods that use multiple transmit and receive antennas. To ensure security on the physical layer and also to enhance channel coding efficiency, a chaos MIMO (C-MIMO) system was previously proposed. In this system, a chaotic dynamical system is used for modulation. In this paper, we revealed that the original C-MIMO system does not effectively use the information of bits that are used for modulation, which results in a difficulty in distinguishing encrypted symbols. To solve this issue, we propose a new modulation method for the C-MIMO system. We evaluated the performance of the proposed C-MIMO system and showed that the proposed C-MIMO system significantly improves block error rates.

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  • Seiichiro Moro, Kohei Takamatsu
    Type: Paper
    2020 Volume 11 Issue 4 Pages 561-570
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    Recently, much attention have been paid to the methods for circuit analysis using wavelet transform. In particular, we have proposed the method which can choose the resolution of the wavelet adaptively. This method can fully bring out the orthogonal and the multiresolution properties of the wavelet, and the efficiency of the calculation can be improved. In this paper, we propose the method to analyze the steady-state periodic solutions of the nonlinear circuits driven by the periodic external input using Haar wavelet transform by applying the appropriate boundary conditions, and prove the effectiveness of the proposed method.

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  • Kiyotaka Miyauchi, Yoshihiko Horio, Takaya Miyano, Kenichiro Cho
    Type: Paper
    2020 Volume 11 Issue 4 Pages 571-579
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    A chaos-based stream cipher using an augmented Lorenz map has been proposed. It was shown through numerical simulations that this chaotic map can generate statistically secure pseudorandom numbers, although high-speed hardware is necessary for practical use. One of the problems in digital hardware realization is implementation of the nonlinearities included in the map. In this paper, we propose a nonlinear look-up table (LUT) technique to implement the sine function considering the distribution of the argument variable. We experimentally demonstrate through field programmable gate array(FPGA) prototyping, high-speed and small-sized digital hardware implementation of the pseudorandom number generator based on the augmented Lorenz map using the proposed nonlinear LUT method.

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  • Seiya Amoh, Daisuke Ito, Tetsushi Ueta
    Type: Paper
    2020 Volume 11 Issue 4 Pages 580-589
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    Coherent Ising machine (CIM) implemented by degenerate optical parametric oscillator (DOPO) networks can solve some combinatorial optimization problems. However, when the network structure has a certain type of symmetry, optimal solutions are not always detected since the search process may be trapped by local minima. In addition, a uniform pump rate for DOPOs in the conventional operation cannot overcome this problem. In this paper proposes a method to avoid trapping of the local minima by applying a control input in a pump rate of an appropriate node. This controller breaks the symmetrical property and causes to change the bifurcation structure temporarily, then it guides transient responses into the global minima. We show several numerical simulation results.

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  • Satoshi Moriya, Hideaki Yamamoto, Ayumi Hirano-Iwata, Shigeru Kubota, ...
    Type: Paper
    2020 Volume 11 Issue 4 Pages 590-600
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    Spiking neural networks with complex spatiotemporal dynamics support efficient information processing of time-series signals. Here, we investigate the relationship between complexity of network dynamics and modular topology of networks using numerical simulations and discuss their effect on the classification performance of spoken-digit recognition tasks. The results show that modular networks generate spatially complex dynamics in which partially and globally synchronous bursts coexist. The classification rate of the modular reservoir network was approximately 75%, a value of which was comparable to that of a random network. This was caused by the randomly-connection structure between the input-reservoir and reservoir-readout layers, thus appropriate inference methods and asymmetry of connections should be introduced to take advantage of the complex dynamics in modular networks.

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  • Seido Nagano
    Type: Paper
    2020 Volume 11 Issue 4 Pages 601-609
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    The ligand-receptor interaction is critical for signal transduction in biological systems. The binding interaction between a receptor and its cognate ligand has been extensively investigated at the molecular level. However, there are often many non-ligand molecules surrounding receptors, and it is very likely that they function as extraneous noise that disrupts authentic signal transduction. Herein we demonstrated that excitable receptor synchronization during signal transduction is key for noise reduction and signal enhancement.

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  • Naoki Kawamoto, Yoshihiko Susuki, Atsushi Ishigame
    Type: Paper
    2020 Volume 11 Issue 4 Pages 610-623
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    This paper introduces a problem on large-signal stability of an interconnection of AC and MTDC (Multi-Terminal DC) grids. We formulate the problem as an estimation of stability region (or basin of attraction) of an asymptotically stable equilibrium point that is exhibited by coupled nonlinear differential-algebraic equations. A candidate of Lyapunov function is introduced for the interconnected AC/MTDC grid in terms of composite dynamical systems. We visualize several slices of the stability region of the interconnected grid under a practical setting of the grid's parameters. The preliminary visualization shows that the stability region can be estimated with the candidate of composite Lyapunov function.

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  • Takemori Orima, Yoshihiko Horio
    Type: Paper
    2020 Volume 11 Issue 4 Pages 624-635
    Published: 2020
    Released: October 01, 2020
    JOURNAL FREE ACCESS

    A passive reflectionless transmission-line model is able to reproduce the physiological characteristics of the cochlea via parameter tuning. In this paper, we propose a quantitative design method for the passive reflectionless transmission-line model using parameter optimization techniques. The proposed design can achieve the overall physiological characteristics of the cochlea.

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