iBMath
国立研究開発法人日本医療研究開発機構／文部科学省 研究開発施設共有等促進費用補助金
創薬等ライフサイエンス研究支援基盤事業：生命動態システム科学推進拠点事業
転写の機構解明のための動態システム生物医学数理解析拠点
Institute for Biology and Mathematics of Dynamic Cellular Processes The University of Tokyo
東京大学 生物医学と数学の融合拠点
教授
時弘 哲治
Professor Tetsuji Tokihiro
所属： 東京大学 大学院数理科学研究科 教授
大学院数理科学研究科附属数理科学連携基盤センター センター長
専門分野： 応用数学・数理物理学
略歴：1981年　東京大学工学系大学院物理工学科修士課程修了
1983年　東京大学工学部物理工学科助手
1990年　　　　　　同専任講師
1995年　東京大学大学院数理科学研究科助教授
1999年　　　　　　同教授
学位：工学博士

研究概要

主として超離散系と呼ばれる連続的な方程式より導かれるセルオートマトン(Cellular Automaton, CA)系の研究をしている．
CAは，有限通りの状態をとるセルの集合からなり，時間，空間，各点での状態がすべて離散的な力学系である．簡単な時間発展規則から複雑なパターンを生成できるため，多くの複雑な自然・社会現象のモデルとして研究されている．
CAは，その離散性により，数値的なシミュレーションに向いているが，逆に解析的な手法が使いにくいため，大域的な性質を厳密に論じることは一般的には困難である．
ところが，1996年に，連続的な方程式から超離散化と呼ばれる極限操作によってCAを構成すれば，多くの解析的な手法を適用でき，大域的な性質も論じることができることが明らかになった．こうして構成されたCAは超離散系と呼ばれ，特にソリトン方程式やパンルヴェ方程式など非線形可積分方程式と呼ばれる系から構成された超離散系は，非常に広い分野（整数論，組合せ論，離散幾何学，表現論，情報理論など）と深く関わっており，現在も活発に研究が行われている．

最近は，p進数体から有限体への還元（reduction）によって構成された有限体上のCAの数理構造に興味を持って研究を行っている．特に，AGR（almost good reduction）という性質に注目して，クラスター代数から導かれるLaurent性（解が初期値のLaurent多項式となること）との関係などを調べている．
応用面では，こうしたCA系を，渋滞現象や生物などの形態生成に応用することを試みている．本プロジェクトにおいては，DNAからRNAへの転写現象をCA系あるいは超離散系によって解析することを目指す．遺伝子生物学の分野には，まだまだ未解決の問題が多く，われわれの新しい数学手法が遺伝子現象や蛋白質合成の解析，ひいてはそれを応用した創薬へとつながることを期待している．

原著論文

雑誌論文

  1. T.Tokihiro and E.Hanamura, "Nonlinear optical response of three-level atomic system", Prog. Theor. Phys. Supplement 69, pp.451-464 (1980).
  2. T.Tokihiro and E.Hanamura, "Multi-polariton scattering via excitonic molecules", Solid State Commun. 52, pp.771-774 (1984).
  3. K.Ueda, T.Fujiwara, H.Tsunetsugu and T.Tokihiro, "Some remarks on anormalous distribution of internal fields in $Al_{4}Mn$ quasicrystals", J. Phys. Soc. Jpn. 55, pp.1418-1419 (1986).
  4. H.Tsunetsugu, T.Fujiwara, K.Ueda and T.Tokihiro, "Eigenstates in 2-dimensional Penrose tiling", J. Phys. Soc. Jpn. 55, pp.1420-1423 (1986).
  5. M.Arai, T.Tokihiro and T.Fujiwara, "Electronic structure of a 2-D Penrose lattice in a magnetic field", J. Phys. Soc. Jpn. 56, pp.1642-1644 (1987).
  6. T.Fujiwara, T.Tokihiro and M.Arai, "Anomalous electronic structure in 2-D Penrose lattice", Material Science Form Vol. 22, pp.459-470 (1987).
  7. T.Fujiwara, M.Arai, T.Tokihiro and M.Kohmoto, "Localized states and self-similar states of electrons on atwo-dimensional Penrose lattice", Phys. Rev. B37, pp.2797-2804 (1988).
  8. M.Arai, T.Tokihiro, T.Fujiwara and M.Kohmoto, "Strictly localized states on a two-dimensional Penrose lattice", Phys. Rev. B38, pp.1621-1626 (1988).
  9. Y.Ohta, J.Satsuma, D.Takahashi and T.Tokihiro, "An elementary introduction to Sato theory", Prog. Theor. Phys. Supplement 94, pp.210-241 (1988).
  10. T.Tokihiro, T.Fujiwara and M.Arai, "Exact eigenstates on a two-dimensional Penrose lattice and their fractal dimensions", Phys. Rev. B38, pp.5981-5987 (1988).
  11. T.Tokihiro, "Electronic states of a quasiperiodic lattice with long-range electron transfer", Phys. Rev. B40, pp.2889-2900 (1989).
  12. T.Fujiwara, M.Kohmoto and T.Tokihiro, "Multifractal wavefunctions on a Fibonacci lattice", Phys. Rev. B40, pp.7413-7416 (1989).
  13. T.Tokihiro, "Antiferromagnetic Heisenberg model on a quasiperiodic lattice with hierarchical interactions", Phys. Rev. B41, pp.7334-7337 (1990).
  14. T.Tokihiro, "Quasiperiodic system with long-range hierarchical interactions", in Quasicrystals, ed. by T.Fujiwara and T.Ogawa, pp.179-188, (Springer-Verlag Berlin, Heiderberg 1990).
  15. H.Tsunetsugu, T.Fujiwara, K.Ueda and T.Tokihiro, "Electronic properties of Penrose lattice. I. Energy spectrum and wave functions", Phys. Rev. B43, pp.8879-8891 (1991).
  16. T.C.Lubensky, T.Tokihiro and S.R.Renn, "Polimer dissolved in a chiral nematic: a model for twist-grain-boundary phases", Phys. Rev. A43, pp.5449-5460 (1991).
  17. T.C.Lubensky, T.Tokihiro and S.R.Renn, "Quasicristallinity in a model of stacked polymers", Phys. Rev. Lett. 67, pp.89-92 (1991).
  18. T.C.Lubensky, S.R.Renn and T.Tokihiro, "Chiral smectics as quasicrystals", in Quasicrystals: The State of the Arts ed. By D.DiVincenzo and P.J.Steinhardt, pp.275-312, (World Scientific Publishing Co. Inc., Teaneck USA, 1991).
  19. T.Tokihiro, "Liquid-quasi-crystal", in China-Japan Seminar on Quasicrystals ed. by K.H.Kuo and T.Ninomiya, pp.410-416, (World Scientific Publishing Co. 1991).
  20. E.Hanamura, T.Tokihiro and Y.Manabe, "Superradiance of Frenkel Excitons", in Science and Technology of Mesoscopic Structures, ed. By S.Namba, C.Hamaguchi and T.Ando, pp.343-442, (Springer-Verlag, 1992).
  21. T.Tokihiro, Y.Manabe and E.Hanamura, "Superradiance of Frenkel excitons in linear systems", Phys. Rev. B47, pp.2019-2030 (1993).
  22. M.Idzumi, T.Tokihiro, K.Iohara, M.Jimbo, T.Miwa and T.Nakashima, "Quantum affine symmetry in vertex operators", Int. J. Mod. Phys. A8, pp.1479-1511 (1993).
  23. Y.Manabe, T.Tokihiro and E.Hanamura, "Superradiance of interacting Frenkel excitons in linear systems", Phys. Rev. { B48}, pp.2773-2776 (1993).
  24. T.Tokihiro and E.Hanamura, "Geometrical effects on one-dimensional excitons", Phys. Rev. Lett.71, pp.1423-1426 (1993).
  25. T.Tokihiro, "Liquid crystals and their topological defects", FORMA Vol.8, pp.83-97 (1993).
  26. M.Idzumi, T.Tokihiro and M.Arai, "Solvable nineteen-vertex models and related spin chains of spin one", J. Physique I 4, pp.1151-1159 (1994).
  27. H.Ezaki, T.Tokihiro, M.Gonokami, R.Shimano, K.Ema, E.Hanamura, B.Flugel, K.Meissner and N.Peyghambarian, "Excitonic n-string in linear chains", Solid State Commun. 88, pp.211-216 (1993).
  28. T.Tokihiro and H.Suzuura, "Laser spectroscopy of highly excited 1-D Frenkel excitons", J. of Luminescence 60&61, pp.792-794 (1994).
  29. H.Ezaki, T.Tokihiro and E.Hanamura, "Excitonic n-string in one-dimensional Frenkel exciton systems", J. of Luminescence 60&61, pp.805-808 (1994).
  30. H.Suzuura, T.Tokihiro and Y.Ohta, "High excitation emission spectra of one-dimensional Frenkel excitons", Phys. Rev. B49, pp.4344-4347 (1994).
  31. M.Kuwata-Gonokami, N.Peyghambarian, K.Meissner, B.Flugel, Y.Sata, K.Ema, R.Shimano, S.Mazumdar, F.Guo, T.Tokihiro, H.Ezaki, and E.Hanamura, "Exciton strings in an organic charge-transfer crystal", Nature 367, pp.47-48 (1994).
  32. H.Ezaki, T.Tokihiro and E.Hanamura, "Excitonic n-string in linear chains: Electronic structure and optical properties", Phys. Rev. B50, pp.10506-10515 (1994).
  33. H.Ezaki and T.Tokihiro, "Correlation effects on optical absorption in molecular chains with conformational disorder", Solid State Commun. 93, pp. 769-774 (1995).
  34. T.Tokihiro, Y.Manabe and E.Hanamura, "Superradiance of Frenkel excitons with any degree of excitation prepared by a short-pulse laser", Phys. Rev. B51, pp.7655-7668 (1995).
  35. T.Tokihiro and H.Ezaki, "Effects of quasiperiodic grating on surface-plasmon polariton", Solid State Commun. 96, pp. 73-78 (1995).
  36. T.Tokihiro, H.Suzuura and T.Tsujikawa, "Time response of polariton in small system by ultra-short pulse excitation", Jpn. J. Appl. Phys. 34 Suppl. 34-1, pp.214-216 (1995).
  37. H.Ezaki, T.Tokihiro and E.Hanamura, "Optical absorption of molecular chains with conformational disorder", Jpn. J. Appl. Phys. { 343} Suppl. 34-1, pp. 95-97 (1995).
  38. H.Suzuura, T.Tsujikawa and T.Tokihiro, "Quantum theory for exciton-polariton in real-space representation", Phys. Rev. B53, pp. 1294-1300 (1996).
  39. T.Tokihiro, D.Takahashi, J.Matsukidaira and J.Satsuma, "From soliton equations to integrable cellular automata through a limiting procedure", Phys. Rev. Lett. { 76}, pp. 3247-3250 (1996).
  40. S.Mazumdar, F.Guo, K.Meissner, B.Fluegel, N.Peighambarian, M.Kuwata-Gonokami, Y.Sato, K.Ema, R.Shimano, T.Tokihiro, H.Ezaki, and E.Hanamura, "A new class of collective excitations: Exciton strings" J. Chem. Phys. 104, pp. 9283-9291 (1996).
  41. S.Mazumdar, F.Guo, K.Meissner, B.Fluegel, N.Peighambarian, M.Kuwata-Gonokami, Y.Sato, K.Ema, R.Shimano, T.Tokihiro, H.Ezaki, and E.Hanamura, "Exciton-to-biexciton transition in quasi-one-dimensional organics" J. Chem. Phys. 104, pp. 9292-9296 (1996).
  42. J.Matsukidaira, J.Satsuma, D.Takahaashi, T.Tokihiro and M.Torii, "Toda type cellular automaton and its N-soliton solution", Phys. Lett. A225, pp. 287-295 (1997).
  43. A.Nagai, T.Tokihiro and J.Satsuma, "The Toda molecule equations and epsilon-algorithm", Mathamatics of Computation 67, pp. 1565-1575 (1998).
  44. T.Honda and T.Tokihiro, "Spontaneous lattice deformation on the Hofstadter problem", Phys. Rev. B55, pp. 10261-10269 (1997).
  45. S.Moriwaki, A.Nagai, J.Satsuma, T.Tokihiro, M.Torii, D.Takahashi and J. Matsukidaira, "Two-dimensional Toda cellular automaton", in Symmetries and Integrability of Difference Equations ed. by P.A.Clarkson and F.W.Nijhoff, London Math. Soc. Lecture Notes Series, 255, Cambridge Univ. Press., pp. 334--342 (1998).
  46. A.Nagai, T.Tokihiro, J.Satsuma, R.Willox and K.Kajiwara, "Two-dimensional Soliton Cellular Automaton of Deautonomized Toda-type" Phys. Lett. A234, pp. 301-309 (1997).
  47. R.Willox, T.Tokihiro and J.Satsuma, "Darboux and binary Darboux transformations for the nonautonomous discrete KP equation" J. Math. Phys. 38, pp. 6455-6469 (1997).
  48. D.Takahashi, T.Tokihiro, B.Grammaticos, Y.Ohta and A. Ramani, "Constructing solutions to the ultra-discrete Painleve equations" J. Phys. A30, pp. 7953-7963 (1997).
  49. T. Tokihiro, J.Satsuma and R.Willox, "On special function solutions to nonlinear integrable equations" Phys. Lett. A236, pp. 23-29 (1997).
  50. R.Willox, T.Tokihiro, I.Loris and J.Satsuma, "The fermionic approach to Darboux transformations" Inverse Problems 14, pp.745-762 (1998).
  51. A.Nagai, T.Tokihiro and J.Satsuma, "Ultra-discrete Toda molecule equation" Phys. Lett. A244, pp.383-388 (1998).
  52. A.Nagai, D. Takahashi and T.Tokihiro , "Soliton cellular automaton, Toda molecule equation and sorting algorithm" Physics Letters A 255, pp. 265-271 (1999).
  53. J. Inoue and T.Tokihiro, "Analysis on optical properties of one-dimensional Frenkel excitons in terms of the Haldane-Shastry model" Phys. Rev. B58, pp. 1134-1137 (1998).
  54. R. Willox, Y. Ohta, C. Gilson, T. Tokihiro and J. Satsuma, "Quadrilateral lattices and eigenfunction potentials for $N$-component KP hierarchies", Physics Letters A 252, pp. 163-172 (1999).
  55. T.Watanabe, T.Tokihiro and K.Nishinari, "The static strength of a random chopped glass/polypropylene composite estimated by a percoration model", JSME International Journal, Series A, vol.{ 42}, pp. 135-140 (1999).
  56. M. Kitamura and T.Tokihiro, "Squeezed states of light in a cavity with a local two-photon absorber" J. Opt. B: Quantum Semiclass. Opt. 1, pp. 546-556 (1999) .
  57. T. Tokihiro, A. Nagai and J. Satsuma, "Proof of solitonical nature of box and ball system by Means of Inverse Ultra-discretization", Inverse Problems 15, pp. 1639--1662 (1999).
  58. T. Tokihiro, D. Takahashi and J. Matsukidaira, "Box and ball system as a realization of ultradiscrete nonautonomous KP equation", J. Phys. A：Math. Gen. { 33}, pp. 607--619 (2000).
  59. G. Hatayama, K. Hikami, R. Inoue, A. Kuniba, T. Takagi and T. Tokihiro, "The $A_M^(1)$ automata related to crystals of symmetric tensors", J. Math. Phys. 42, pp. 274--308 (2001).
  60. A. Nobe, J. Satsuma and T. Tokihiro, "Stable Difference Equations Associated with Elementary Cellular Automata" Japan J. Indust. Appl. Math. 18, pp. 293--305 (2001).
  61. A. Nobe, J. Satsuma and T. Tokihiro, "From cellular automaton to difference equation: a general transformation method which preserves time evolution patterns" J. Phys. A: Math. Gen. 34, pp. L371--L379 (2001).
  62. N. Arikawa and T. Tokihiro, "On local thermal equilibrium given by an energy eigenstate in isolated quantum mechanical system" Phisics Letters A 286, pp. 314--320 (2001).
  63. A. Nagai, T. Tokihiro and J. Satsuma, "Conserved quantities of box ball system" Glasgow Math. J. 43A, pp. 91--97 (2001).
  64. F. Yura and T. Tokihiro, "On a periodic soliton cellular automaton" J. Phys. A：Math. Gen. 35, 3787--3801 (2002).
  65. W. Kunishima, T. Tokihiro and H. Tanaka, "Error estimation of Recursive Orthogonal Polynomial Expansion method for large Hamiltonian system" Computor Physics Communication 148 171-181 (2002).
  66. J.Satsuma, T.Tokihiro and R.Willox, "Scattering in cellular automata" in Scattering: Scattering and Inverse Scattering in Pure and Applied Science ed. by R.Pike and P.Sabatier, Academic Press (2001).
  67. D. Yoshihara, F. Yura and T.Tokihiro, "Fundamental Cycle of a Periodic Box-Ball System'' J. Phys. A：Math. Gen. 36, pp.99--121 (2003).
  68. T. Kimijima and T. Tokihiro, “Initial value problem of discrete periodic Toda equation and its ultradiscretization'' Inverse Problems 18, pp.1705--1732 (2002).
  69. T. Tokihiro, B. Grammaticos and A. Ramani, “From the continuous $P_{V}$ to discrete Painlevé equations" J. Phys. A：Math. Gen. 35, pp.5943--5950 (2002).
  70. J. Mada and T. Tokihiro, “Asymptotic behavior of fundamental cycle of periodic box-ball systems", J. Phys. A：Math. Gen.36, pp.7251--7268 (2003).
  71. J. Mada, M. Idzumi and T. Tokihiro, “Conserved quantities of generalized periodic box-ball systems constructed from the ndKP equation", J. Phys. A：Math. Gen. 37, pp.6531-6556 (2004).
  72. T. Tokihiro, “Ultradiscrete Systems (Cellular Automaton)", in Discrete Integrable Systems eds. by Basil Grammaticos, Yvette Kosmann-Schwarzbach and Thamizuarasi Tamizhmani, Lect. Notes. Phys. 644, pp.383--424 (2004).
  73. T. Tokihiro and J. Mada, ”Asymptotic behavior of fundamental cycle of periodic box-ball systems: a number theoretical aspect", Glasgow Math. J. 47A, pp.199--204 (2005).
  74. W. Kunishima, A. Nishiyama, H. Tanaka and T. Tokihiro, “ Differential equations can create complex cellular automaton patterns", J. Phys. Soc. Jpn. 73, pp.2033--2036 (2004).
  75. J. Mada, M. Idzumi and T. Tokihiro, “Path description of conserved quantities of generalized periodic box-ball systems", J. Math. Phys. 46, 022701(19pages) (2005).
  76. M. Kanai, K. Nishinari, and T. Tokihiro,“Stochastic optimal velocity model and its long-lived metastability”, Phys. Rev. E 72 (2005) 035102-5(Rapid Comm.)
  77. J. Mada, M. Idzumi and T. Tokihiro, “Fundamental cycle of a periodic box-ball system and solvable lattice models", J. Phys. A: Math. Gen. 39, pp.4985-4997 (2006).
  78. Jun Mada, Makoto Idzumi and Tetsuji Tokihiro，“The exact correspondence between conserved quantities of a periodic box-ball system and string solutions of the Bethe ansatz equations,” J. Math. Phys. 47, 053507 (2006).
  79. Jun Mada, Makoto Idzumi and Tetsuji Tokihiro，“On the initial value problem of a periodic box-ball system,” J. Phys. A: Math. Gen. 39, pp.L617-L623 (2006).
  80. M. Kanai, K. Nishinari and T. Tokihiro,“Analytical study on the criticality of the Stochastic Optimal Velocity model”, J. Phys. A 39, pp2921-2933 (2006).
  81. M. Kanai, K. Nishinari and T. Tokihiro, “Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring”, J. Phys. A 39, pp.9071-9079 (2006).
  82. T. Tokihiro, "On Fundamental Cycle of Periodic Box-Ball Systems", L. Fadeev et al. (eds.) Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete, Springer, pp.325-334 (2006).
  83. S. Iwao and T. Tokihiro, "Ultradiscretization of the theta function solution of pd Toda", J. Phys. A 40, pp.12987-13021 (2007).
  84. Jun Mada, Makoto Idzumi and Tetsuji Tokihiro, "The box-ball system and the N-soliton solution of the ultradiscrete KdV equation ", J. Phys. A, {41} 175207 (23pp) (2008)
  85. A. Nishiyama, H. Tanaka and T. Tokihiro, "An isotropic cellular automaton for excitable media", Physica A: Statistical Mechanics and its Applications, 387, 3129-3136 (2008).
  86. Hiroshi Tanaka, Asumi Nakajima, Akinobu Nishiyama, Tetsuji Tokihiro, "Derivation of a differential equation exhibiting replicative time-evolution patterns by inverse ultra-discretization", J. Phys. Soc. Jpn. 78, 034002 (5 pages) (2009).
  87. Masahiro Kanai, Shin Isojima, Katsuhiro Nishinari, and Tetsuji Tokihiro, "Ultradiscrete optimal velocity model: A cellular-automaton model for traffic flow and linear instability of high-flux traffic", Phys. Rev. E 79, 056108 (8 pages) (2009).
  88. M. Idzumi, S. Iwao, J. Mada and T. Tokihiro, "Solution to the initial value problem of the ultradiscrete periodic Toda equation", J. Phys. A: Math. Theor. 42 315209 (14 pages) (2009).
  89. A. Nishiyama, T. Tokihiro, M. Badoual and B. Grammaticos, “Modelling the morphology of migrating bacterial colonies", Physica D: Nonlinear Phenomena 239, pp.1573--1580 (2010).
  90. J. Mada and T. Tokihiro, “Correlation functions for a periodic box-ball system", J. Phys. A: Math. Theor. 43 135205 (15 pages) (2010).
  91. Masataka Kanki, Jun Mada and Tetsuji Tokihiro, “Conserved quantities and generalized solutions of the ultradiscrete KdV equation", J. Phys. A: Math. Theor. 44, 145202 (15 pages) (2011).
  92. J. Mada and T. Tokihiro, “Two point correlation functions for a periodic box-ball system", SIGMA 7, 027 (16 pages ) (2011).
  93. K. Matsuya and T. Tokihiro, “Existence and non-existence of global solutions for a discrete semilinear heat equation", Discrete and Continuous Dynamical Systems 31, 209--220 (2011).
  94. A. Nishiyama and T. Tokihiro, “Construction of an Isotropic Cellular Automaton for a Reaction-Diffusion Equation by Means of a Random Walk", J. Phys. Soc. Jpn. 80, No.5, 054003 (6p) (2011). DOI: 10.1143/JPSJ.80.054003
  95. S. Isojima, J. Satsuma and T. Tokihiro, “Direct ultradiscretization of Ai and Bi functions and special solutions to Painelevé II equation", J. Phys. A: Math. Theor. 45 155203 (13 pages) (2012).
  96. Masataka Kanki, Jun Mada and Tetsuji Tokihiro, “Soliton Solutions of a Generalized Discrete KdV Equation", J. Phys. Soc. Jpn. 81, 084002 (5 pages) (2012).
  97. Yoshihiro Ohta, Akinobu Nishiyama, Yoichiro Wada, Yijun Ruan, Tatsuhiko Kodama, Takashi Tsuboi, Tetsuji Tokihiro and Sigeo Ihara, “ A path preference cellular-automaton model for traffic flow through transit points and its application to the transcription process in biology", Phys. Rev. E 86, 021918 (11pages) (2012).
  98. M. Kanki, J. Mada, K. M. Tamizhmani and T. Tokihiro, “Discrete Painleve II equation over finite fields", J. Phys. A: Math. Theor. 45, 342001 (8pages) (2012).
  99. Masataka Kanki, Jun Mada and Tetsuji Tokihiro, “Discrete Integrable Equations over Finite Fields", SIGMA 8, 054 (12pages) (2012).

著書

  1. 時弘哲治「工学における特殊関数」共立出版（2006）
  2. 時弘哲治「箱玉系の数理」朝倉書店（2010）
  3. 谷口健二・時弘哲治「複素解析」裳華房（2013）