My major research interest is mathematical modelling of neural system and its applications. I have several interest including mathematical theory for modeling of biophysical system like a neural network of the brain and its application for physiology, medical science, and engineering. Current objectives are 1) to establish mathematical frameworks for analyzing network dynamics, statistical analysis, and data-driven modelling, 2) to elcidate pricipal of information processing on the brain with the modelling of the neural newotk and collaboration with physiologists, and 3) to develop a new framework of information processing based on the neural dynamics.
Modeling and analyses of spiking neural network with dynamic synapses as a local circuit of the prefrontal cortex contributing to the planning and execution of sequential action generation and flexible information representation. Constructed the leaky integrate-and-fire based network model and derive the corresponding mean field model for bifurcation analysis of population neural dynamics. Successfully modeled and reproduced the electrophysiological data observed in primates during a related task.
Modeling and analyses of map-based stochastic neural network with dynamics synapses. Based on the statistical physics approach, derived the mean field model and performed bifurcation analysis on the uniformly connected network and on the associative memory network, which exhibits sequential memory retrieval.
Modeling and analyses of spiking neural network with electrical couplings as a local circuit of inferior olive nucleus, which contribute to the motor learning in cerebellum. Quantitatively modeled the conductance-based neural network with electrophysiological data. Analyzed its bifurcation structure and found that pharmacological treatments on the nucleus cause bifurcation of the neural dynamics. Further, estimated parameters with Bayesian approach. Analyzed information transfer efficacy on the bases of information theory.
Designed neuromorphic hardware with FPGA implementation of spiking neural network. Designed neural dynamics with minimal hardware resource consumption, preserving the phase-plane and bifurcation structure. Implemented this neuron to FPGAs as an associative memory network and evaluated its performance.
Major Books and Papers
- Yuichi Katori, “Mathematical models of neural network”, Handbook on applied mathematics, Asakura-Publishing, Tokyo, Japan, (in Japanese).
- Ikkyu Aihara, Shigeki Tsuji, Yuichi Katori, Kazuyuki Aihara, “Mathematical modeling of the brain”, Introduction to Phenomenological mathematics, University of Tokyo Press, Tokyo, Japan, (in Japanese).
- Yuichi Katori, Yosuke Otsubo, Masato Okada, Kazuyuki Aihara, “Associative Memory Network with Dynamic Synapses”, Advances in Cognitive Neurodynamics Vol.4, Springer, (2014).
- Yuichi Katori, Kazuhiro Sakamoto, Naohiro Saito, Jun Tanji, Hajime Mushiake, Kazuyuki Aihara, “Representational Switching by Dynamical Reorganization of Attractor Structure in a Network Model of the Prefrontal Cortex”, PLoS Computational Biology, 7 (11): e1002266, (2011).
- Yuichi Katori, Yosuke Otsubo, Masato Okada, Kazuyuki Aihara, “Stability analysis of associative memory network composed of stochastic neurons and dynamic synapses”, Frontiers in Neuroscience, Vol. 7, 6, pp.1-12,.
- Yuichi Katori, Eric J. Lang, Miho Onizuka, Mistuo Kawato, Kazuyuki Aihara, “Quantitative Modeling on Spatio-temporal Dynamics of Inferior Olive Neurons with Simple Conductance-based Model”, International Journal of Bifurcation and Chaos, Vol. 20 No. 3, 583-603, (2010).
- Yuichi Katori, Yasuhiko Igarashi, Masato Okada, Kazuyuki Aihara, “Stability Analysis of Stochastic Neural Network with Depression and Facilitation Synapses”, Journal of the Physical Society of Japan, 81, 114007, (2012).
- Jing Li, Yuichi Katori, Tahashi Kohno, “An FPGA-based silicon neuronal network with selectable excitability silicon neurons”, Frontiers in Neuroscience, Vol. 6, 183, (2012).
- Miho Onizuka, Huu Hoangm Mitsuo Kawato, Isao T. Tokuda, Nicolas Schweighofer, Yuichi Katori, Kazuyuki Aihara, Eric J Lang, Keisuke Toyama, “Solution to the Inverse Problem of estimating Gap-Junctional and Inhibitory Conductance in Inferior Olive Neurons from the Spike Trains by Network Model Simulation”, Neural Networks, Vol.47, pp.51-63, (2013).
- Yoshito Hirata, Yuichi Katori, Hidetoshi Shimokawa, Hideyuki Suzuki, Timothy A. Blenkinsop, Eric J. Lang, Kazuyuki Aihara, “Testing a neural coding hypothesis using surrogate data.”, Journal of Neuroscience Methods, Vol. 172 (2), pp. 312-322, (2008).
- Yuichi Katori, Naoki Masuda, Kazuyuki Aihara, “Dynamic switching of neural codes in networks with gap junctions”, Neural Networks, Vol. 19, Issue 10, 2006, 1463-1466, (2006).
- Yuichi Katori, “Simple algorithm for location estimation from Wi-Fi signal strength”, IEEE Intelligent Systems, Vol. 23, No. 1, p.10 (2008).