Nonlinear Theory and Its Applications, IEICE 

About: Nonlinear Theory and Its Applications, IEICE is an academic journal published by Institute of Electronics, Information and Communications Engineers. The journal publishes majorly in the area(s): Computer science & Nonlinear system. It has an ISSN identifier of 2185-4106. It is also open access. Over the lifetime, 573 publications have been published receiving 2349 citations. The journal is also known as: NOLTA.

Tensor decompositions for feature extraction and classification of high dimensional datasets

Abstract: Feature extraction and selection are key factors in model reduction, classification and pattern recognition problems. This is especially important for input data with large dimensions such as brain recording or multiview images, where appropriate feature extraction is a prerequisite to classification. To ensure that the reduced dataset contains maximum information about input data we propose algorithms for feature extraction and classification. This is achieved based on orthogonal or nonnegative tensor (multi-array) decompositions, and higher order (multilinear) discriminant analysis (HODA), whereby input data are considered as tensors instead of more conventional vector or matrix representations. The developed algorithms are verified on benchmark datasets, using constraints imposed on tensors and/or factor matrices such as orthogonality and nonnegativity.

Applied Koopman operator theory for power systems technology

Abstract: Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman operator itself is linear but infinite-dimensional (evolves on a function space). This linear operator captures the full information of the dynamics described by the original nonlinear system. In particular, spectral properties of the Koopman operator play a crucial role in analyzing the original system. In the first part of this paper, we review the so-called Koopman operator theory for nonlinear dynamical systems, with emphasis on modal decomposition and computation that are direct to wide applications. Then, in the second part, we present a series of applications of the Koopman operator theory to power systems technology. The applications are established as data-centric methods, namely, how to use massive quantities of data obtained numerically and experimentally, through spectral analysis of the Koopman operator: coherency identification of swings in coupled synchronous generators, precursor diagnostic of instabilities in the coupled swing dynamics, and stability assessment of power systems without any use of mathematical models. Future problems of this research direction are identified in the last concluding part of this paper.

Fractional-step Tow-Thomas biquad filters

Abstract: In this paper we propose the use of fractional capacitors in the Tow-Thomas biquad to realize both fractional lowpass and asymmetric bandpass filters of order 0 <α 1 + α2 ≤ 2, where α1 and α2 are the orders of the fractional capacitors and 0 <α 1,2 ≤ 1. We show how these filters can be designed using an integer-order transfer function approximation of the fractional capacitors. MATLAB and PSPICE simulations of first order fractional-step low and bandpass filters of order 1.1, 1.5, and 1.9 are given as examples. Experimental results of fractional low pass filters of order 1.5 implemented with silicon-fabricated fractional capacitors verify the operation of the fractional Tow-Thomas biquad.

Numerical verification methods for solutions of semilinear elliptic boundary value problems

Abstract: This article describes a survey on numerical verification methods for second-order semilinear elliptic boundary value problems introduced by authors and their colleagues. Here “numerical verification” means a computer-assisted numerical method for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. Three kinds of methods based on the infinite dimensional fixed-point theorems using Newton-like operator will be presented. In each verification method, a projection into a finite dimensional subspace and constructive error estimates of the projection play an important and essential role. It is shown that these methods are really useful for actual problems by illustrating numerical examples.

Amoeba-inspired algorithm for cognitive medium access

Abstract: The "tug-of-war (TOW) model" is a unique parallel search algorithm for solving the multi-armed bandit problem (BP), which was inspired by the photoavoidance behavior of a single-celled amoeboid organism, the true slime mold Physarum polycephalum (1-4). "The cognitive medium access (CMA) problem," which refers to multiuser channel allocations of the cognitive radio, can be interpreted as a "competitive multi-armed bandit problem (CBP) (5, 6)." Unlike the normal BP, the CBP considers a competitive situation in which more than one user selects a channel whose reward probability (probability of which channel is free) varies depending on the number and combination of the selecting users as indicated in a payoff matrix. Depending on the payoff matrix, the CBP provides a hard problem instance in which the users should not be attracted to the Nash equilibrium to achieve the "social maximum," which is the most desirable state to obtain the maximum total score (throughput) for all the users. In this study, we propose two variants of the TOW model (solid type and liquid type) for the CBP toward developing a CMA protocol using a distributed control in uncertain environments. Using the minimum CBP cases where both the users choose a channel from the two considered channels, we show that the performance of our solid-type TOW model is better than that of the well-known upper confidence bound 1 (UCB1)-tuned algorithm, particularly for the hard problem instances. The aim of this study is to explore how the users can achieve the social maximum in a decentralized manner. We also show that our liquid-type TOW model, which introduces direct interactions among the users for avoiding mutual collisions, makes it possible to achieve the social maximum for general CBP instances.