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We study nervous systems from mathematical viewpoint and analyze experimental data to understand the information processing in the brain. The topics include nonlinear dynamics of neural network models, mathematical modeling of cognitive processes, and optimal synaptic learning rules. We have also proposed new methods for analyzing experimental data and developed analog computation devices based on mathematical neuronal models.
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We study a variety of complex dynamical phenomena in the real world through mathematical modeling and analyses based on nonlinear dynamical systems theory and time series analysis methods. The topics include hybrid dynamical systems, coupled oscillators, game theory, complex networks, recurrence plots, and associative memories. We have also analyzed real data related to weathers, biological systems, economical systems, social systems, earthquakes, and electrical grids.
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To understand diseases such as cancers and infectious diseases for which effective therapies and preventions have not yet been established, we are trying to make mathematical models and propose effective countermeasures for the diseases. We have investigated the efficacy of intermittent hormone therapy for prostate cancer using time series analysis and bifurcation analysis. We have also developed a system for a large-scale simulation of spread of pandemic flu by using person trip data.
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