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*Neuroscience and Biological Information Processing [#md796902] Our research on neuroscience aims at understanding information processing and various behaviors in the brain. For instance, we have considered a relationship between neurophysiologic properties and neuronal functions through mathematical modeling of a neuron and neural networks [1,2]. We have derived a theoretical framework for an optimal learning rule in neuronal systems from the viewpoint of information theory [3]. Mathematical analysis of neuron models is also included in our research interests [4]. Moreover, we have been analyzing real data of neuronal spikes [5] and implementing analog devices based on neuronal properties for realizing a novel computation scheme. +K. Morita, K. Tsumoto, and K. Aihara, Biophys. J., Vol.90, pp.1925-1938 (2006). +Y. Katori, N. Masuda, and K. Aihara, Neural Networks, Vol.19, pp.1463-1466 (2006). +T. Toyoizumi, K. Aihara, and S. Amari, Phys. Rev. Lett., Vol.97, 098102 (2006). +K. Tsumoto, H. Kitajima, T. Yoshinaga, K. Aihara, and H. Kawakami, Neurocomput., Vol.69, pp.293-316 (2006). +K. Fujiwara, H. Fujiwara, M. Tsukada, and K. Aihara, Biosystems, in press (2007). *Complex Systems Mathematical Modeling [#o5308a2b] *Nonlinear Dynamical Systems and its Applications [#c84d3134] The aim of our research on nonlinear science is to understand the essence of complex behaviors through analyses of various complex nonlinear phenomena in biological, physical, and engineering systems. Putting the focus on nonlinearity, we investigate how highly complex phenomena arise in a simple nonlinear system and how self-organization takes place in a chaotic system, by developing the methods for bifurcation analysis, time series analysis, and statistical analysis [1-5]. Application studies include information processing based on nonlinear dynamics, information extraction from biological data, and deterministic chaos in wind. +H. Suetani, Y. Iba, and K. Aihara, J. Phys. A, Vol.39, pp.10723―10742 (2006). +H. Ando and K. Aihara, Phys. Rev. E, Vol.74, 066205 (2006). +G. Tanaka, B. Ibarz, M.A.F. Sanjuan, and K. Aihara, Chaos, Vol.16, 013113 (2006). +Y. Hirata, H. Suzuki, and K. Aihara, Phys. Rev. E, Vol.74, 026202 (2006). +N. Masuda, G. Jakimoski, K. Aihara, and L. Kocarev, IEEE Trans. Circ. Syst. I, Vol.53, pp.1341-1352 (2006). We study a variety of complex systems and problems―biological systems, social systems, economic systems, diseases, energy problems, natural disasters, and so on―through mathematical modeling and data analyses. We also try to establish fundamental theories and methods for analyzing those specific systems. We aim at further development of researches based on the joint works with the Collaborative Research Center for Innovative Mathematical Modelling. *Mathematical Modeling of Biochemical Systems [#t4a56ead] We study nonlinear dynamics in biochemical reactions in the cell in order to understand collective activities in the ensembles of cells. We have been studied the mechanism of biological rhythms by constructing a mathematical model of genome-proteome networks and attempted to propose a method to design artificial gene networks [1-7]. +D. Battogtokh, K. Aihara, and J. J. Tyson, Phys. Rev. Lett., Vol.96, 148102 (2006). +Y. Morishita, T. J. Kobayashi, and K. Aihara, Biophys. J., Vol.91, pp.2072-2081 (2006). +G. Kurosawa, K. Aihara, and Y. Iwasa, Biophys. J., Vol.91, pp.2015-2023 (2006). +C. Li, L. Chen, and K. Aihara, Physical Biology, Vol.3, pp.37-44 (2006). +C. Li, L. Chen, and K. Aihara, IEEE Trans. CAS-I, Vol.53, pp.2451-2458 (2006). +C. Li, L. Chen, and K. Aihara, PLoS Comput. Biol., Vol.2, e103 (2006). +R. Wang, L. Chen, and K. Aihara, J. Theor. Biol., Vol.242, pp.454-463 (2006). *Mathematical Modeling of Diseases [#kb74e6ec] We have been studied mathematical modeling of modern diseases that should be addressed emergently. Especially, we aim at understanding the essential mechanism and the origin of a disease and proposing a possible effective approach to avoid or treat the disease. We have discussed the efficacy of intermittent hormone suppression therapy for prostate cancer [1]. We have also carried out modeling of infection disease [2,3] and proposed a simulation system for analysis of the infection spread in the society. +A. Miyamura, G. Tanaka, T. Takeuchi, and K. Aihara, METR, University of Tokyo, 2006-32 (2006). +K. Ohtsuka, N. Konno, N. Masuda, and K. Aihara, Int. J. Bifurcation and Chaos, Vol.16, pp.3687-3693 (2006). +N. Sugimine, N. Masuda, N. Konno, and K. Aihara, Mathematical Biosciences, in press (2007). *Dynamics of Neural Networks and Its Applications [#ya44fbb1] We are trying to clarify the mechanism of real neural networks and to reveal the high-order functions of the brain through developing mathematical models of neurons/neural networks and identifying underlying non-trivial mathematical structure. As an application, we are also developing analog silicon neural networks and AI. #ref(数理生命情報学研究室/ 研究紹介/chaos_neurocomputer.jpg,,50%); -Recent publications --T. Sase, Y. Katori, M. Komuro, and K. Aihara: Front. Comp. Neurosci., Vol. 11, Article 18 (2017). --Y. Li, M. Oku, G. He, and K. Aihara: Neural Netw., Vol. 88, pp. 9-21 (2017). --T. Nanami and T. Kohno: Front. Neurosci., Vol. 10, Article No. 181 (2016). --C. I. Tajima, S. Tajima, K. Koida, H. Komatsu, K. Aihara, and H. Suzuki: Sci. Rep., Vol. 6, Article No. 22536 (2016). --T. Kiwaki and K. Aihara: Artif. Intell. Res., Vol. 4, No. 1, 53 (2015). --T. Leleu, K. Aihara: Phys. Rev. E, Vol. 91, 022804 (2015). *Nonlinear Systems Analysis and Its Applications to the Real World Systems [#i4e9d478] We are studying chaos and many other complex phenomena in the world that have some regularity behind the complexity, by using nonlinear dynamical systems theory. We focus on the "nonlinearity" of the target systems, develop mathematical models that can reproduce the complex phenomena, and analyze the models to reveal the essential factors. Topics include: synchronization of coupled oscillators, forecast of renewable energy generation, analysis of economic and seismic data, etc. #ref(数理生命情報学研究室/ 研究紹介/chaosNN_simulation.jpg,,100%) -Recent publications --T. Omi, Y. Hirata, and K. Aihara: Phys. Rev. E, Vol. 96, 012303 (2017). --K. Kamiyama, M. Komuro, and K. Aihara: IJBC, Vol. 27, No. 3, 1730012 (2017). --T. Yuan, K. Aihara, and G. Tanaka: Phys. Rev. E, Vol. 95, No. 1, 012315 (2017). --M. Chayama, and Y. Hirata: Phys. Lett. A, Vol. 380, pp. 2359-2365 (2016). --M. Fukino, Y. Hirata, and K. Aihara: Chaos, Vol. 26, No. 2, 023116 (2016). --T. Sase, J. Peña Ramírez, K. Kitajo, K. Aihara, and Y. Hirata: Phys. Lett. A, Vol. 380, pp. 1151-1163 (2016). --L. Speidel, R. Lambiotte, K. Aihara, N. Masuda: Phys. Rev. E, Vol. 91, 012806 (2015). *Quantum Artificial Brain and Combinatorial Optimization [#xc3f1488] We are mathematically studying a new paradigm of computation—quantum artificial brain—based on neural information processing and optical quantum computing. It aims for solving problems that are difficult for conventional computers such as combinatorial optimization problems in a rapid and accurate manner, which may contribute to resolve many social issues. -Recent publications --T. Inagaki, Y. Haribara, K. Igarashi, T. Sonobe, S. Tamate, T. Honjo, A. Marandi, P.L. McMahon, T. Umeki, K. Enbutsu, O. Tadanaga, H. Takenouchi, K. Aihara, K. Kawarabayashi, K. Inoue, S. Utsunomiya, and H. Takesue, Science, Vol. 354, No. 6312, pp. 603-606 (2016). --P.L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, R.L. Byer, M.M. Fejer, H. Mabuchi, and Y. Yamamoto, Science, Vol. 354, No.6312, pp.614-617 (2016). --H. Sakaguchi, K. Ogata, T. Isomura, S. Utsunomiya, Y. Yamamoto, and K. Aihara, Entropy, Vol. 18, No. 10, 365 (2016). --Y. Haribara, S. Utsunomiya, and Y. Yamamoto: Entropy, Vol. 18, No. 4, 151 (2016).