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**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. *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). +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 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). **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. *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). +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). *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). **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). **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]. +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).