著者

Ken Umeno

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.7, no.1, pp.14-20, 2016 (Released:2016-01-01)

参考文献数

11

被引用文献数

2 13

---

We consider a family of ergodic transformations on the real line R preserving Cauchy laws. A dualistic nature between the ergodic transformation and the associated transformation of the scale parameter of a Cauchy law is proven to be hold, which provides a systematic view of explicit mixing property with the ergodic transformation having the Cauchy law as the limiting distribution.

著者

Atsuo Maki Yuu Miino Naoya Umeda Masahiro Sakai Tetsushi Ueta Hiroshi Kawakami

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.13, no.1, pp.2-24, 2022 (Released:2022-01-01)

参考文献数

53

被引用文献数

2

---

Capsizing is one of the worst scenarios in oceangoing vessels. It could lead to a high number of fatalities. A considerable number of studies have been conducted until the 1980s, and one of the discoveries is the weather criterion established by the International Maritime Organization (IMO). In the past, one of the biggest difficulties in revealing the behavior of ship-roll motion was the nonlinearity of the governing equation. On the other hand, after the mid-1980s, the complexity of the capsizing problem was uncovered with the aid of computers. In this study, we present the theoretical backgrounds of the capsizing problem from the viewpoint of nonlinear dynamics. Then, we discuss the theoretical conditions and mechanisms of the bifurcations of periodic solutions and numerical attempts for the bifurcations and capsizing.

著者

Yusuke Imoto Yasuaki Hiraoka

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.14, no.2, pp.92-105, 2023 (Released:2023-04-01)

参考文献数

33

---

Mapper, a topological data analysis method for high-dimensional data, represents a topological structure as a simplicial complex or graph based on the nerve of clusters. We propose V-Mapper (velocity Mapper), an extension of Mapper, for high-dimensional data with velocity. V-Mapper simultaneously describes a topological structure and flow as a weighted directed graph (V-Mapper graph) by embedding velocity in the edges of the Mapper graph. We apply V-Mapper to single-cell gene expression data using a method for inferring the velocity of gene expression. Moreover, the application of the Hodge decomposition on graph enhances the interpretation of the flow within V-Mapper graph.

著者

Tomoyuki Sasaki Hidehiro Nakano

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.13, no.2, pp.170-195, 2022 (Released:2022-04-01)

参考文献数

37

---

Swarm intelligence (SI) algorithms have been studied in solving real-world optimization problems called black-box optimization problems. Typical features of SI algorithms are: (1) being a population-based metaheuristics; (2) using fitness values of a given objective function; and (3) having very simple search rules which search agents follow. As such, SI algorithms have been applied to various black-box optimization problems. Particle swarm optimization is one of powerful SI algorithms, in which a swarm consists of plural particles as solution candidates. Particles directly fly a search space and share their own information each other, and thus PSO can find good quality of solutions. However, a PSO swarm is easily stuck in solving optimization problems whose search space is high-dimensional and complicated. In order to solve such problems, large numbers of particles and reference frame invariance are needed for PSO algorithms. Herein, we suggest a piecewise-linear particle swarm optimizer (PPSO) which is a deterministic PSO. PPSO has two simple search modes switched to another mode dynamically, whose search dynamics are complex. As such, PPSO algorithm can be implemented on hardware with low hardware costs because PPSO algorithm must not require many random number generators. In addition, PPSO algorithm can find a good quality of solution in solving complex optimization problems. We studied search performances of PPSO compared to PSO algorithms and provide theoretical analysis of reference frame invariance for PPSO. In order to verify search performances and theoretical analysis, we performed numerical simulations.

著者

Yota Tsukamoto Honami Tsushima Tohru Ikeguchi

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.13, no.2, pp.367-372, 2022 (Released:2022-04-01)

参考文献数

9

被引用文献数

3

---

In the field of neuroscience, it is widely acknowledged that neurons exhibit periodic, quasi-periodic, and chaotic responses to periodic inputs. In this study, we evaluated the responses of the Izhikevich neuron model stimulated by sinusoidal inputs. First, we analyzed the dynamical behavior of the Izhikevich neuron model to the sinusoidal inputs in the state space and found two types of responses: periodic and non-periodic. Next, we obtained the domains of the periodic and non-periodic responses on the frequency-amplitude plane of the sinusoidal inputs by evaluating the diversity index of the inter-spike intervals. Finally, we analyzed the responses of the Izhikevich neuron model using the stroboscopic plot. Consequently, we clarified that a periodic response is a limit cycle and an irregular response is a torus, which implies that the irregular responses of the Izhikevich neuron model stimulated by sinusoidal inputs are quasi-periodic responses.

著者

Toshimichi Saito

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.11, no.4, pp.373-390, 2020 (Released:2020-10-01)

参考文献数

71

被引用文献数

2

---

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.

著者

Shun-ichi Amari Ryo Karakida Masafumi Oizumi

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.10, no.4, pp.322-336, 2019 (Released:2019-10-01)

参考文献数

9

---

Deep neural networks are highly nonlinear hierarchical systems. Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a higher dimensional manifold of the next layer as a curved submanifold, provided the number of neurons is larger than that of inputs. We show geometrical features of the embedded manifold, proving that the manifold enlarges or shrinks locally isotropically so that it is always embedded conformally. We study the curvature of the embedded manifold. The scalar curvature converges to a constant or diverges to infinity slowly. The distance between two signals also changes, converging eventually to a stable fixed value, provided both the number of neurons in a layer and the number of layers tend to infinity. This causes a problem: When we consider a curve in the input space, it is mapped as a continuous curve of fractal nature, but our theory contradictorily suggests that the curve eventually converges to a discrete set of equally spaced points. In reality, the numbers of neurons and layers are finite and thus, it is expected that the finite size effect causes the discrepancies between our theory and reality. Further studies are necessary to understand their implications on information processing.

著者

Makito Oku

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.14, no.2, pp.242-253, 2023 (Released:2023-04-01)

参考文献数

18

---

Critical transitions and early warning signals are gaining attention in various fields such as ecology, climatology, and economics. However, quantitative estimation of the critical transition probability remains difficult. In this study, I propose a method to estimate the critical transition probability. It is based on a previous method using quadratic polynomial approximation, and skewness filtering is added as a reject option. The proposed method is applied to May model, a mathematical model of an ecosystem, as an example case. The results of numerical simulations show that the proposed method has much better precision than the previous method without skewness filtering, achieving a relative error of approximately ±50% for the mean escape time.

著者

Kunihiko Fukushima

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.10, no.4, pp.304-321, 2019 (Released:2019-10-01)

参考文献数

14

被引用文献数

13

---

Deep convolutional neural networks (deep CNN) show a large power for robust recognition of visual patterns. The neocognitron, which was first proposed by Fukushima (1979), is a network classified to this category. Its architecture was suggested by neurophysiological findings on the visual systems of mammals. It acquires the ability to recognize visual patterns robustly through learning. Although the neocognitron has a long history, improvements of the network are still continuing. This paper discusses the recent neocognitron, focusing on differences from the conventional deep CNN. Some other functions of the visual system can also be realized by networks extended from the neocognitron, for example, recognition of partly occluded patterns, the mechanism of selective attention, and so on.

著者

Shahrzad Mahboubi Indrapriyadarsini S Hiroshi Ninomiya Hideki Asai

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.12, no.3, pp.554-574, 2021 (Released:2021-07-01)

参考文献数

33

被引用文献数

1 3

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This paper describes a momentum acceleration technique for quasi-Newton (QN) based neural network training and verifies its performance and computational complexity. Recently, Nesterov's accelerated quasi-Newton method (NAQ) has been introduced and shown that the momentum term is effective in reducing the number of iterations and the total training time by incorporating Nesterov's accelerated gradient into QN. However, the gradients had to be calculated two times in one iteration in the NAQ training. This increased the computation time of a training loop compared with the conventional QN. The proposed technique is an improvement to NAQ done by approximating the Nesterov's accelerated gradient as a linear combination of the current and previous gradients. As a result, the gradient is calculated only once per iteration similar to that of QN. The performance of the proposed algorithm is evaluated in comparison to conventional algorithms in neural networks training on two types of problems - function approximation problems with high nonlinearity and classification problems. The results show a significant acceleration in the computation time without losing the quality of the solution compared with conventional training algorithms.

著者

Eiji Okamoto

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.12, no.3, pp.257-274, 2021 (Released:2021-07-01)

参考文献数

35

被引用文献数

2

---

In recent years, there have been several advances in wireless communication systems, including the increase in transmission rate, and as a result, they are playing an increasingly significant role in our lives. To meet the widespread application scope, the commercialization of the fifth-generation mobile communications system (5G) has been initialized. This paper gives an overview of the 5G system and discusses the nonlinear signal processing technologies that support its performance improvement. Here, the term “nonlinear signal processing” is defined as an algorithm for transmitting and receiving data in communications that uses a nonlinear mechanism. Because there is a significant shortage of frequency bands in wireless communications, advanced technologies are being integrated to maximize frequency utilization. In addition, unlike in the 4G era, there are additional use cases that require performance guarantees for quality, delay, and the number of multiple connections in the 5G system, and the performance requirements for wireless systems are becoming more stringent. Nonlinear signal processing is key to improving the performance of these systems, and this paper outlines the nonlinear technology used in 5G wireless access. We will introduce multiple-input multiple-output transmission and non-orthogonal multiple access (NOMA), which will help improve the performance of wireless systems. In addition, we introduce a radio wave-encrypted NOMA with a physical layer security that is proposed by the authors. Furthermore, the technical trend of 6G is briefly introduced.

著者

Kazuya Sawada Yutaka Shimada Tohru Ikeguchi

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.13, no.2, pp.385-390, 2022 (Released:2022-04-01)

参考文献数

22

---

State space reconstruction using time-delay coordinate systems is the most effective and significant technique for analyzing complex time series generated by nonlinear dynamical systems. In this study, we investigated the relationships between reconstruction parameters and the similarity of the structural properties of original and reconstructed attractors. In particular, we investigated the similarities between inter-point distance distributions on original and reconstructed attractors, while varying the reconstruction parameters for reconstructing a dynamical system using a time-delay coordinate system. The results show that the product of the reconstruction dimension and the time-delay should be constant to obtain high similarity.

著者

Yoshiki Sugitani Keiji Konishi

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.12, no.4, pp.612-624, 2021 (Released:2021-10-01)

参考文献数

41

被引用文献数

5

---

Delays can have a negative impact on the stability of various systems. However, it was reported that the transmission delays of signals among oscillators can stabilize unstable equilibrium points in coupled oscillators, which is called amplitude death (AD). AD caused by delays has been extensively researched in the field of nonlinear science and has attracted attention for various engineering applications. In this article, we review the latest studies on AD caused by delays in oscillator networks, in particular those that considered heterogeneous delays and time-varying networks.

著者

Mitsuhiko Shimomura Nicolas Chauvet Mikio Hasegawa Makoto Naruse

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.13, no.1, pp.101-111, 2022 (Released:2022-01-01)

参考文献数

10

---

High-bandwidth irregular oscillations caused by optical time-delayed feedback subjected to the laser cavity, known as laser chaos, have been investigated for various engineering applications. Recently, a fast decision-making algorithm for a multi-arm bandit problem by utilizing laser chaos time series has been demonstrated. Furthermore, the arms order recognition of the reward expectation for each arm has been successfully developed by incorporating the notion of the confidence interval regarding the reward estimate. However, in previous studies, the verification was limited to numerical experiments; real-world demonstrations were not conducted. This study experimentally demonstrated that the arm-order recognition algorithm is successfully operated in channel order recognition in wireless communications while revising the original strategy to take into account the wireless application requirements. Such accurate arm rank recognition involving non-best arms would be useful for various real-world applications such as channel bonding, among others.

著者

Yusuke Ide

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.10, no.1, pp.16-27, 2019 (Released:2019-01-01)

参考文献数

24

---

In this paper, we show reduction methods for search algorithms on graphs using quantum walks. By using a graph partitioning method called equitable partition for the the given graph, we determine “effective subspace” for the search algorithm to reduce the size of the problem. We introduce the equitable partition for quantum walk based search algorithms and show how to determine “effective subspace” and reduced operator.

著者

Makito Oku Kazuyuki Aihara

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.9, no.2, pp.166-184, 2018 (Released:2018-04-01)

参考文献数

49

被引用文献数

18

---

In this paper, we analyze the relation between the stability of a noisy dynamical system based on linear approximation and the covariance matrix of its stationary distribution. We reformulate the theory of dynamical network biomarkers in terms of the covariance matrix and clarify the limiting behavior of the covariance matrix when a dynamical system approaches a bifurcation point. We also discuss the relation between the Jacobian matrix and principal component analysis. An application to a simple nonlinear network model is also demonstrated.

著者

Atsushi Iwasaki Ken Umeno

出版者

一般社団法人 電子情報通信学会

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.8, no.3, pp.215-223, 2017 (Released:2017-07-01)

参考文献数

13

---

Vector Stream Cipher (VSC) is a stream cipher which consists of permutation polynomial over a ring of modulo 2w. The algorithm for generating key stream is very simple and the encryption is very fast. Some theoretical attacks for VSC have been reported so far since the invention of VSC in 2004. Then, the authors proposed some improvements and developed “Vector Stream Cipher 2.0 (VSC 2.0)” to be immune against the theoretical attacks. In this paper, we propose further improvement of VSC 2.0 to publish as a new chaos cipher “Vector Stream Cipher 2.1 (VSC2.1)”. VSC 2.1 is faster and more secure than VSC 2.0. Our result suggests that permutation polynomials over a ring of modulo 2w are useful for cryptography.

著者

Takashi Kohno Jing Li Kazuyuki Aihara

出版者

一般社団法人 電子情報通信学会

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.5, no.3, pp.379-390, 2014 (Released:2014-07-01)

参考文献数

39

被引用文献数

2 8

---

Neuromorphic systems are designed by mimicking or being inspired by the nervous system, which realizes robust, autonomous, and power-efficient information processing by highly parallel architecture. It is a candidate of the next-generation computing system that is expected to have advanced information processing ability by power-efficient and parallel architecture. A silicon neuronal network is a neuromorphic system with a most detailed level of analogy to the nervous system. It is a network of silicon neurons connected via silicon synapses;they are electronic circuits to reproduce the electrophysiological activity of neuronal cells and synapses, respectively. There is a trade-off between the proximity to the neuronal and synaptic activities and simplicity and power-consumption of the circuit. Power-efficient and simple silicon neurons assume uniform spikes, but biophysical experimental data suggest the possibility that variety of spikes given to a synapse is playing a certain role in the information processing in the brain. In this article, we review our design approach of silicon neuronal networks where uniform spikes are not assumed. Simplicity of the circuits is brought by mathematical techniques of qualitative neuronal modeling. Though it is neither simpler nor low-power consuming than above silicon neurons, it is expected to be more appropriate for silicon neuronal networks applied to brain-morphic computing.

著者

Yuzuru Sato Daisuke Shimaoka Koichi Fujimoto Gentaro Taga

出版者

一般社団法人 電子情報通信学会

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.7, no.2, pp.226-233, 2016 (Released:2016-04-01)

参考文献数

27

被引用文献数

1

---

We propose an extended framework of two dimensional neural field with network between distant cortical areas as a model of global brain dynamics, and the models whose geometry of the neural field changes depending on the field dynamics as a model for growing brains. As a characteristic pattern with non-local and network interactions in neural field, pulser and memory are constructed. Possible applications to quantitative measurements of cortical activities of mouse and human brain development are briefly discussed.

著者

Atsushi Iwasaki Ken Umeno

出版者

一般社団法人 電子情報通信学会

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.7, no.1, pp.30-37, 2016 (Released:2016-01-01)

参考文献数

7

被引用文献数

6

---

Vector Stream Cipher (VSC) is a stream cipher based on the chaos theory. The algorithm for generating stream keys is very simple and the encryption speed is very fast. Some theoretical attacks for VSC have been reported so far since the invention of VSC in 2004. In this paper, we improve the security of VSC and design a new cipher system “Vector Stream Cipher 2.0” so that the theoretical attacks cannot work. We show that the encryption speed of VSC 2.0 keeps more than 85% of that of VSC, and key-stream of VSC 2.0 has good randomness. The main result of this paper is that our proposed VSC 2.0 is shown to have provable security for attacks with linear masking. Because there is few cryptography based on the chaos theory which has proven security, VSC 2.0 is a rare example.