- 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
- 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
- Timothée Leleu Timothée Levi Takashi Kohno 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.281-294, 2018 (Released:2018-04-01)
- 参考文献数
- 26
Reconstructing accurately the structure of neural networks from biological data is essential for the analysis of simultaneous recordings from many neurons, and, in turn, for the understanding of neural codes and the design of neural prostheses. Classical techniques are generally based on cross-correlations and cannot reconstruct unambiguously the network structure. Recently, we have proposed a method for which there is one-to-one correspondence between statistical properties of packets of spikes (or avalanches) and the network structure, but this mapping was only proven for simpler neuronal model. In the following, we show using numerical simulation of the Izhikevich model that the proposed method is general, and is particularly well-fitted for the analysis of neural activity recorded from cultured neuronal networks coupled to microelectrode arrays.
- 著者
- Koji Iwayama Yoshito Hirata Hideyuki Suzuki 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.4, no.2, pp.160-171, 2013 (Released:2013-04-01)
- 参考文献数
- 40
- 被引用文献数
- 2 6
Change-point detection based on an observed time series has emerged as an important method for detecting changes in dynamics of real-world systems. Recently, recurrence networks have been shown to be useful, which are network representations of recurrences, to analyze underlying dynamics. In this paper, we propose a new method for detecting dynamical changes using recurrence networks. The proposed method extracts a group of time indices that share the same dynamics as a community of the recurrence network. In addition, some numerical simulations are presented to verify the validity of this method.