Research Subjects of Takashi Kanamaru

In this page, I briefly summarize my recent researches.


Dynamical Behaviors of the Brain

Recently, in the physiological experiments of the brain, dynamical behaviors of neurons, such as "oscillation and synchronization", "correlation of pulses", and "chaos" are reported by many researchers. Such dynamics are typically observed in the visual cortex and the hippocampus, and they might be related to the bindings of the visual information and the control of the synaptic plasticity. These experimental observations suggest that the brain might have richer and more complex dynamics than the conventional artificial neural network. I try to understand these dynamical behaviors using the theories of "nonlinear dynamics" and "statistical physics".

Usually, "oscillation and synchronization", "correlation of pulses", and "chaos" are considered to be the different behaviors, and they are treated separately. However, I regard them as three sections of the same high-dimensional dynamics of the brain, and I think that they should be treated together.

Recently, I am studying pulse neural networks with excitatory and inhibitory connections, and they show the above three behaviors. Thus, they might be effective to analyze the behavior of the brain from the pulse level.

ft Moreover, properties of neurons consisting of the brain, and structures of networks are not uniform. To analyze such systems, the probabilistic representation is crucial to understand their dynamics.

JeJi For example, let us consider a system consisting of 200 neurons as shown in the right figure. Because noise is injected to the system, each neuron fires randomly (shown with red points). Although it is difficult to analyze such stochastic systems directly, we can obtain the Fokker-Planck equation that governs the time-development of the probability density of the system in the limit of large number of neurons.

By integrating the Fokker-Planck equation numerically, we can obtain a smooth trajectory of a solution as shown in the left figure. We can perform precise analyses because the Fokker-Planck equation is a deterministic (partial) differential equation.

I am concerned with understanding the brain using the probabilistic methods.

You can simulate the above model with simple simulators written in Java in the following URLs.


Brain Computer based on Digital Technology

hwmodule There are two approaches to understand the dynamics of the brain. One is the theoretical approach, and the other is the constructive one, and they have been progressing compensatively each other.

By combining the knowledge obtained from the theoretical analyses with the recent digital technology, I try to develop the brain computer based on the digital pulse neural circuits.


Detecting chaotic structures in time series

chaosts The chaotic time series of the above pulse neural networks are generated by chaotic synchronization that is caused by noise-induced bifurcations; therefore, these chaotic time-series are inevitably polluted by noise.
If we assume that such phenomena take place in the biological system, and that chaos carries important information in the information processing, detecting chaos in noisy time series shall be important.

Thus, I apply the embedding-based-reconstruction method to the chaotic time series, and try to detect the deterministic structure using the normalized prediction error (NPE) and the surrogate data. This method has been extensively examined by many researchers, e.g., by Prof. J. Theiler, Prof. T. Sauer, and Prof. K. Aihara, and I try to extend this method to obtain the optimal results for the time series of our pulse neural networks in the following paper.
  • Takashi Kanamaru and Masatoshi Sekine,
    "Detecting chaotic structures in noisy pulse trains based on interspike interval reconstruction,"
    Biological Cybernetics, vol.92, no.5 (2005) pp. 333-338. (preprint PDF)


Image Recognition based on Wavelet Transformation

wavelet Unlike the Fourier transformation, the wavelet transformation is suitable for spatially and temporally localized signals such as images.

You can apply the wavelet transform to some images using the following Java applets. After applying the wavelet transformation in the pre-processing, we can use several techniques for the image recognition such as machine learnings and neural networks.


Sound Processing based on Wavelet Transformation

The speech signal of human is an non-stationary signal where the frequency of the signal largely changes over time. In the conventional sound recognition, the speech signals are divided into short frames, and Fourier analyses are performed in these frames.

Although the usual discrete wavelet transformation can treat only frequencies of powers of two, the wavelet packet can treat more detailed frequencies; therefore, the wavelet-packet is thought to be suitable for sound processing.



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