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*Research topics [#c9151935] *Complex Systems Mathematical Modeling [#o5308a2b] **Neuroscience [#s949d336] Our research aims at understanding various behaviors of the brain, and applying them to engineering. Our methods include construcing models of a neuron and their networks in the brain and extracting a non-evident mathematical structure from them. So far we have got into the problem of the information processing [1], the modeling study of neurotransmitter [2], and the theoretical framework for the learning rule [3]. In addition, we are implementing the neuron models using analog circuits. 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. +N. Masuda and K. Aihara, "Bridging Rate Coding and Temporal Spike Coding by Effect of Noise," Physical Review Letters, 88(24), 248101 (2002). +Kenji Morita, Kunichika Tsumoto, and Kazuyuki Aihara, "Possible effects of depolarizing GABAA conductance on the neuronal input-output relationship: a modeling study," J. Neurophysiol. 93, 3504-3523 (2005). +T. Toyoizumi, J.-P. Pfister, K. Aihara, and W. Gerstner, "Generalized Bienenstock-Cooper-Munro Rule for Spiking Neurons that Maximizes Information Transmission," PNAS, 102, 5239-5244 (2005). +T. Kohno and K. Aihara, "A MOSFET-based model of a class 2 nerve membrane," IEEE Trans. Neural Networks, 16, 754-773, (2005). **Nonlinear Science [#w096e4d4] Our aim of studying nonlinear science is to undestand the essence of complex behaviors through analyses of various 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 [1,2]. Furhter, we carry out some application studies including information processing based on nonlinear dynamics [3], information extraction from biological data [4], and deterministic chaos in wind. *Dynamics of Neural Networks and Its Applications [#ya44fbb1] +H. Suzuki, S. Ito, and K. Aihara, "Double rotations," Disc. Cont. Dyn. Syst. 13, 515-532, (2005). +G. Tanaka, M. A. F. Sanjuan, and K. Aihara, "Crisis-induced Intermittency in Two Coupled Chaotic Maps: Towards Understanding Chaotic Itinerancy," PRE, 71(1), 016219, (2005). +G. Tanaka and K. Aihara, "Multistate Associative Memory with Parametrically Coupled Map Networks," Int. J. Bifurcation Chaos, 15(4), 1395-1410, (2005). +Y. Hirata, K. Judd, and K. Aihara, ``Characterizing chaotic response of a squid axon through generating partitions,'' Physics Letters A, 346, 141 (2005). 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. **Mathematical Biology and Sociology [#p81d9698] Our society is a complex adaptive system. We choose actions by estimating others internal state from their actions or other external factors. In our laboratory, we make and analyze mathematical models of these phenomena using nonlinear dynamics, game theory, and multi-agent-system [1]. +N. Masuda and K. Aihara, "Spatial Prisoner's Dilemma optimally played in small-world networks," Phys. Lett. A, 485-490, (2003). #ref(数理生命情報学研究室/ 研究紹介/chaos_neurocomputer.jpg,,50%); **Genome Science [#f824e0cc] We analyze the nonlinear dynamics and stochasticity in genetic regulatory networks [1,2]. The major contributions are the followings: (1) We have proposed a systematic method to design a synthetic genetic switch [3]. (2) We have analytically shown that nonspecific interactions between regulatory proteins and background molecules can attenuate stochastic fluctuations. Moreover, we have numerically revealed that a genetic switch model with this mechanism is more stable than the one without this mechanism [4]. (3) We have proposed a systematic method based on the stoichiometric matrices of genetic regulatory networks and analytically decomposed stochastic fluctuation into its components [5]. -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). +T. Zhou, L. Chen and K. Aihara, "Molecular Communication through Stochastic Synchronization Induced by Extracellular Fructuations," PRL, 95, 178103, (2005). +D. Battogtokh, K. Aihara and J.J. Tyson, "Synchronization of Eukaryotic Cells by Periodic Forcing," PRL, 96, 148102, (2006). +T. Kobayashi, L. Chen, and K. Aihara, "Modeling Genetic Switches with Positive Feedback Loops," J. Theor. Biol., 221(3), 379-399 (2003). +Y. Morishita and K. Aihara, "Noise-Reduction through Interaction in Gene Expression and Biochemical Reaction Processes," J. Theor. Biol., 228, 315-325 (2004). +R. Tomioka, H. Kimura, T.J. Kobayashi and K. Aihara, "Multivariate Analysis of Noise in Genetic Regulatory Networks," J. Theor. Biol., 229, 501-521 (2004). *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).