Researchers Database


FacultyFaculty Division of Natural Sciences Research Group of Environmental Sciences
Last Updated :2024/02/22


Profile and Settings

  • Name (Japanese)

  • Name (Kana)



  • Ph. D, Kyoto University

Research Areas

  • Life sciences, Ecology and environmental science

Research Experience

  • 2007, -:奈良女子大学大学院人間文化研究科准教授
  • 2000, -:奈良女子大学大学院人間文化研究科助教授
  • 1997, -:大阪大学大学院理学研究科講師
  • 1994, -:大阪大学理学部講師
  • 1994, -:大阪大学教養部講師
  • 1990, -:大阪市立大学理学部助手


  • 1990, Kyoto University, 理学研究科, 生物物理学専攻, Japan
  • 1990, Kyoto University, Graduate School, Division of Natural Science

Association Memberships

  • 日本数理生物学会
  • 日本数学会
  • 日本応用数理学会
  • 日本生態学会
  • 日本動物行動学会
  • 個体群生態学会


Published Papers

  • Refereed, Zoological Science, Zoological Society of Japan, Dynamics of Laterality in Relation to the Predator–Prey Interaction between the Piscivorous Chub “Hasu” and Its Prey “Ayu” in Lake Biwa, Michio Hori; Jyun-ichi Kitamura; Masayoshi Maehata; Satoshi Takahashi; Masaki Yasugi, A Japanese piscivorous chub, "hasu" (Opsariichthys uncirostris), and its main prey, "ayu" (Plecoglossus altivelis), both have laterally asymmetric bodies, similar to other fishes; each population consists of righty morphs and lefty morphs. This antisymmetric dimorphism has a genetic basis. Temporal changes in the ratios of laterality (i.e., frequency of righty morphs in a population) of these predator and prey fish species were investigated for a 20-year period at a pelagic site in the southwestern area of Lake Biwa, Japan. The dimorphism of each species was maintained dynamically throughout the period, and the ratio of laterality was found to change periodically in a semi-synchronized manner. Direct inspection of the relationship between the ratios of laterality of the two species indicated that the ratio of ayu followed that of hasu, suggesting that the predator-prey interaction was responsible for the semi-synchronized change. Stomach contents analysis of each hasu revealed that cross-predation, in which righty predators catch lefty prey and lefty predators catch righty prey, occurred more frequently than the reverse combination (parallel-predation). This differential predation is presumed to cause frequency-dependent selection on the two morphs of the predator and prey, and to drive semi-synchronized changes in the laterality of the two species. Some discussion pertaining to the atypical form of the semi-synchronized change in laterality found in this study is presented from the viewpoint of predator-prey interaction in fishes., 23 Mar. 2021, 38, 3, 231, 237, Scientific journal, False, 10.2108/zs200155
  • Refereed, Ecology and Evolution, Measuring and evaluating morphological asymmetry in fish: Distinct lateral dimorphism in the jaws of scale-eating cichlids, Hiroki Hata; Masaki Yasugi; Yuichi Takeuchi; Satoshi Takahashi; Michio Hori, The left-right asymmetry of scale-eating Tanganyikan cichlids is described as a unilateral topographical shift of the quadratomandibular joints. This morphological laterality has a genetic basis and has therefore been used as a model for studying negative frequency-dependent selection and the resulting oscillation in frequencies of two genotypes, lefty and righty, in a population. This study aims were to confirm this laterality in Perissodus microlepis Boulenger and P. straeleni (Poll) and evaluate an appropriate method for measuring and testing the asymmetry. Left-right differences in the height of the mandible posterior ends (HMPE) and the angle between the neurocranium and vertebrae of P. microlepis and P. straeleni were measured on skeletal specimens. Snout-bending angle was also measured using a dorsal image of the same individuals following a previous method. To define which distribution model, fluctuating asymmetry (FA), directional asymmetry (DA), or antisymmetry (AS), best fit to the lateral asymmetry of the traits, we provided an R package, IASD. As a result, HMPE and neurocranium-vertebrae angle of both species were best fitted to AS, suggesting that P. microlepis and P. straeleni showed a distinct dimorphism in these traits, although snout-bending angle of P. microlepis was best fitted to FA. Measurement error was low for HMPE comparing the snout-bending angle in P. microlepis, indicating that measuring HMPE is a more accurate method. The scale-eating tribe Perissodini showed distinct antisymmetry in the jaw skeleton and neurocranium-vertebrae angle, and this laterality remains a valid marker for further evolutionary studies. © 2013 The Authors., Nov. 2013, 3, 14, 4641, 4647, Scientific journal, 10.1002/ece3.849
  • Not Refereed, J. Theor. Biol., Sexual systems and dwarf males in barnacles: Integrating life history and sex allocation theories, TAKAHASHI Satoshi; S. Yamaguchi; Y. Yusa; K. Sawada, 2013, 320, 1, 9, 10.1016/j.jtbi.2012.12.001
  • Refereed, Theoretical Ecology, Springer Science and Business Media LLC, Sperm as a paternal investment: a model of sex allocation in sperm-digesting hermaphrodites, Sachi Yamaguchi; Kota Sawada; Yasuhiro Nakashima; Satoshi Takahashi, Feb. 2012, 5, 1, 99, 103, Scientific journal, 10.1007/s12080-010-0101-1
  • Refereed, Evolutionary Ecology Research, EVOLUTIONARY ECOLOGY LTD, Evolution of dwarf males and a variety of sexual modes in barnacles: an ESS approach, Satoru Urano; Sachi Yamaguchi; Shigeyuki Yamato; Satoshi Takahashi; Yoichi Yusa, Questions: Why do barnacles have many modes of sexuality, including hermaphroditism, androdioecy (large hermaphrodites with dwarf males), and dioecy (large females with dwarf males)? Can mating group size, relative body size, competitive advantage or survival rate of dwarf male individuals explain which type of sexuality is favoured by natural selection? Mathematical methods: We developed an ESS model to investigate factors affecting the optimal proportion of larvae that become dwarf males (q*). Allocation to male function of large hermaphrodites is calculated according to Charnov's sex allocation theory, although sperm competition with dwarf males is taken into account. Our model is based on a life history of androdioecious barnacles, which includes hermaphroditism (q* = 0) and dioecy (q* > 0 and the male allocation of large hermaphrodites = 0) as special cases. We incorporate average mating group size (m) into the model, together with body size, competitive advantage, and survival rate of dwarf males relative to large hermaphrodites. Results: The proportion of dwarf males, q*, increases from 0 (hermaphroditism) as mating group size decreases, and approaches 0.5 when group size, m, nears 0. At the latter extreme, large individuals should become females instead of hermaphrodites. Thus mating group size can explain the major trend of sexuality in barnacles: hermaphroditism in relatively large mating groups, androdioecy in smaller groups, and dioecy in even smaller groups. Relative body size, competitive advantage, and survival rate of dwarf males all have positive effects on the evolutionarily stable proportion of males. If there is a simple trade-off between body size and survival rate, survival rate will have the greater influence on sexuality., Jul. 2009, 11, 5, 713, 729, Scientific journal
  • Refereed, Journal of Theoretical Biology, ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, Mating group size and evolutionarily stable pattern of sexuality in barnacles, Sachi Yamaguchi; Yoichi Yusa; Shigeyuki Yamato; Satoru Urano; Satoshi Takahashi, Barnacles, marine crustaceans, have various patterns of sexuality depending on species including simultaneous hermaphroditism, androdioecy (hermaphrodites and dwarf males), and dioecy (females and dwarf males). We develop a model that predicts the pattern of sexuality in barnacles by two key environmental factors: (i) food availability and (ii) the fraction of larvae that settle on the sea floor. Populations in the model consist of small individuals and large ones. We calculate the optimal resource allocation toward male function, female function and growth for small and large barnacles that maximizes each barnacle's lifetime reproductive success using dynamic programming. The pattern of sexuality is defined by the combination of the optimal resource allocations. In our model, the mating group size is a dependent variable and we found that sexuality pattern changes with the food availability through the mating group size: simultaneous hermaphroditism appears in food-rich environments, where the mating group size is large, protandric simultaneous hermaphroditism appears in intermediate food environments, where the mating group size also takes intermediate value, the other sexuality patterns, androdioecy, dioecy, and sex change are observed in food-poor environments, where the mating group size is small. Our model is the first one where small males can control their growth to large individuals, and hence has ability to explain a rich spectrum of sexual patterns found in barnacles. © 2008 Elsevier Ltd. All rights reserved., 07 Jul. 2008, 253, 1, 61, 73, Scientific journal, 10.1016/j.jtbi.2008.01.025
  • Refereed, Journal of Theoretical Biology, ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, Do tiny males grow up? Sperm competition and optimal resource allocation schedule of dwarf males of barnacles, Sachi Yamaguchi; Yuki Ozaki; Yoichi Yusa; Satoshi Takahashi, Barnacles, marine crustaceans, have three sexual patterns: simultaneous hermaphroditism, dioecy and androdioecy. In dioecy and androdioecy, large individuals (females and hermaphrodites, respectively) are attached by dwarf males. Depending on species, some dwarf males grow up, others do not in their life time. To investigate which environmental conditions affect growth patterns of dwarf males of barnacles, we investigate the evolutionarily stable life history strategy of dwarf males using Pontryagin's maximum principle. Sperm competition among dwarf males and that among dwarf males and large hermaphrodites is taken into account. Dwarf males grow up in food-rich environments, while they do not grow at all in food-poor environments. ESS of the resource allocation schedule between reproduction and growth follows an "intermediate growth strategy" (simultaneous growth and reproduction) for dioecious species, in which sperm competition is not severe. On the other hand, it approaches "bang-bang control" (switching from allocating all resources toward growth then to reproduction), as sperm competition against surrounding large hermaphrodites becomes severe in androdioecious species. © 2006 Elsevier Ltd. All rights reserved., 21 Mar. 2007, 245, 2, 319, 328, Scientific journal, 10.1016/j.jtbi.2006.10.009
  • Refereed, Tropics, 日本熱帯生態学会, Spatial pattern of landslides due to heavy rains in a Mixed Dipterocarp Forest, north-western Borneo, TAKAHASHI Satoshi; Tatsuhiro OHKUBO; Masato TANI; Isao AKOJIMA; Satoshi TAKAHASHI; Takuo YAMAKURA; Akira ITOH; Mamoru KANZAKI; Hua Seng LEE; Peter S. ASHTON; Kazuhiko OGINO, 2007, 16, 1, 47, 57, 10.3759/tropics.16.59
  • Refereed, APPLIED ENTOMOLOGY AND ZOOLOGY, JAPAN SOC APPL ENTOMOL ZOOL, Effects of dormant duration, body size, self-burial and water condition on the long-term survival of the apple snail, Pomacea canaliculata (Gastropoda : Ampullariidae), Yoichi Yusa; Takashi Wada; Satoshi Takahashi, We investigated factors influencing the survival of the apple snail, Poinacea canalicidata during dormancy in the laboratory at 20-26 degrees C. We placed snails of three size classes in small pots with soil and water, drained the water to induce self-burial, and subsequently checked the snails' survival at intervals. The duration of the dormant period, body size and the success of self-burial all affected the survival of the snails. The effects of water conditions (dry or moist) affected the survival of the snails through interactions with body size and duration. The longest duration of survival under dry conditions was 11 months, and a small proportion of medium-sized and large snails survived the entire experimental period of 29 months under moist conditions., Nov. 2006, 41, 4, 627, 632, Scientific journal, 10.1303/aez.2006.627
  • Refereed, JOURNAL OF THEORETICAL BIOLOGY, ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD, Coexistence of competing species by the oscillation of polymorphisms, S Takahashi; M Hori, Scale-eating cichlids in Lake Tanganyika exhibit genetically determined lateral asymmetry, especially in their mouth-opening. Frequencies of the morphs oscillate due to strong frequency-dependent selection caused by the switching of prey's attention, and its delayed effect by their growth period. Two scale-eaters coexist in similar densities at south shore of the lake, with their morph frequencies oscillating in phase. We investigated the effect of the oscillation in morph frequencies to the coexistence of competing species. If the difference of two species' growth period is large, the oscillation facilitates the coexistence of the two species, while small difference of growth periods hinders their coexistence. In the latter case, the species with shorter growth period drives the other species to the extinction. (c) 2005 Elsevier Ltd. All rights reserved., Aug. 2005, 235, 4, 591, 596, Scientific journal, 10.1016/j.jtbi.2005.02.014
  • Refereed, Israel Journal of Mathematics, MAGNES PRESS, Dimension spectra of self-affine sets, TAKAHASHI Satoshi, The dimension spectrum H(delta) is a function characterizing the distribution of dimension of sections. Using the multifractal formula for sofic measures, we show that the dimension spectra of irreducible self-affine sets (McMullen's Carpet) coincide with the modified Legendre transform of the free energy Psi(d)(beta). This variational relation leads to the formula of Hausdorff dimension of self-affine sets, max(delta+H(delta)) = Psi(d) (eta), where 71 is the logarithmic ratio of the contraction rates of the affine maps., 2002, 127, 1, 18, Scientific journal
  • Refereed, JOURNAL OF THEORETICAL BIOLOGY, ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, Oscillation maintains polymorphisms - a model of lateral asymmetry in two competing scale-eating cichlids, S Takahashi; M Hori, Scale-eating cichlids in Lake Tanganyika exhibit lateral asymmetry polymorphism in their mouth-opening. Frequency of left- and right-handed phenotypes oscillates around unity. In the southern shore of the lake, two scale-eaters coexist in similar densities, where their oscillations synchronize. This phenomena is analysed by a time-delay differential equation model, and a new mechanism which maintains polymorphism is discovered. In a wide range of parameters, the oscillation keeps the frequencies of the same phenotype in the two species at a similar level, and prevents the fixation of one phenotype in either species. (C) 1998 Academic Press., Nov. 1998, 195, 1, 1, 12, Scientific journal, 10.1006/jtbi.1998.0744
  • Refereed, Tropics, JAPAN SOCIETY OF TROPICAL ECOLOGY, Fractal dimension of the spatial distribution of Dryobalanops lanceolata in a tropical rain forest, at Lambir, Sarawak, TAKAHASHI Satoshi; A. Iwasaki; S. Takahashi; T. Yamakura; M. Kanzaki; A. Itoh; T. Ohkubo; K. Ogino; E. O. K. Chai; H. S. Lee; P. S. Ashton, We analized the character of distributional pattern of Dryobalanops lanceolata by calculating the correlation dimension. We counted points reflected at the boundary as well as at the corner to correct the lack of points near the boundary. Its cerrelation dimension is about 1,33 with small scale and it has some remarkable decreases and increases in dimension, suggesting the change of the character of the distribution, Comparing the correlation dimension with the box dimension and I-delta index, correlation dimension is sensitive to the scale where the distributional character changes, Therefore the correlation dimension can be a new index that shows the change of the characters of distribution in scale., 1997, 7, 1, 1, 8, 10.3759/tropics.7.1
  • Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, A shape theorem for the spread of epidemics and forest fires in two-dimensional Euclidean space, M Kamae; S Takahashi, Dec. 1996, 33, 4, 915, 925, Scientific journal
  • Refereed, ISRAEL JOURNAL OF MATHEMATICS, MAGNES PRESS, Minimal cocycles with the scaling property and substitutions, JM Dumont; T Kamae; S Takahashi, 'Fractal' functions are formulated as a minimal cocycle on a topological dynamics which admits nontrivial scaling transformations. In this paper, it is proved that if in addition it admits a continuous family of scaling transformations, then its capacity is not in o(N-2). We define minimal cocycles with nontrivial scaling transformations coming from substitutions on a finite alphabet which are proved to have capacity O(N), so that they admit only a discrete family of scaling transformations. We also construct one which has capacity O(N-2) and admit a continuous family of scaling transformations., 1996, 95, 393, 410, Scientific journal
  • Refereed, The American Naturalist, University of Chicago Press, Unstable Evolutionarily Stable Strategy and Oscillation: A Model of Lateral Asymmetry in Scale-Eating Cichlids, Satoshi Takahashi; Michio Hori, Dec. 1994, 144, 6, 1001, 1020, Scientific journal, 10.1086/285722
  • Refereed, Journal of Mathematical Physics, AMER INST PHYSICS, Unstable geodesics and topological field theory, Yukinori Yasui; Satoshi Takahashi, A topological field theory is used to study the cohomology of mapping space. The cohomology is identified with the Becchi-Rouet-Stora-Tyutin cohomology realizing the physical Hilbert space and the coboundary operator given by the calculations of tunneling between the perturbative vacua. The method is illustrated by a simple example. © 1994 American Institute of Physics., 1994, 35, 9, 4547, 4567, Scientific journal, 10.1063/1.530803
  • Refereed, J. Analyse Math, A variational formula for dimension spectra of linear cellular automata, TAKAHASHI Satoshi, Space-time patterns of the evolution of linear cellular automata exhibit self-similar patterns. The distribution of fractal dimensions of space patterns is characterized by dimension spectra. Using multifractal formalism, the dimension spectrum is shown to be equal to the Legendre transformation of the free energy. © 1994 Hebrew University of Jerusalem., 1994, 64, 1, 1, 51, Scientific journal, 10.1007/BF03008404
  • Refereed, Theor. Popl. Biol., ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, Competitive coexistence in a seasonally fluctuating environment II. Multiple stable states and invasion success, TAKAHASHI Satoshi; T. Namba; S. Takahashi, 1993, 44, 3, 374, 402, Scientific journal
  • Refereed, J. Comput. Sytem Sci., ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, Self-similarity of linear cellular automata, TAKAHASHI Satoshi, 1992, 44, 1, 114, 140, Scientific journal, 10.1016/0022-0000(92)90007-6
  • Refereed, Physica D, ELSEVIER SCIENCE BV, Cellular automata and multifractals: dimension spectra of linear cellular automata, TAKAHASHI Satoshi, 1990, 45, 1-3, 36, 48, Scientific journal
  • Not Refereed, Proc. Japan Acad., Limiting behaviour of linear cellular automata, TAKAHASHI Satoshi, 1987, 63A, 182, 185
  • Refereed, Symmetry, MDPI AG, Dynamics of Laterality in Lake Tanganyika Scale-Eaters Driven by Cross-Predation, Michio Hori; Masanori Kohda; Satoshi Awata; Satoshi Takahashi, Scale-eating cichlid fishes, Perissodus spp., in Lake Tanganyika have laterally asymmetrical bodies, and each population is composed of righty and lefty morphs. Righty morphs attack the right side of prey and lefty morphs do the opposite. This anti-symmetric dimorphism has a genetic basis. Temporal changes in the frequencies of morphs in two cohabiting scale-eating species (Perissodus microlepis and P. straeleni) were investigated over a 31-year period on a rocky shore at the southern end of the lake. Dimorphism was maintained dynamically during the period in both species, and the frequencies oscillated with a period of about four years in a semi-synchronized manner. Recent studies have indicated that this type of anti-symmetric dimorphism is shared widely among fishes, and is maintained by frequency-dependent selection between predator and prey species. The combinations of laterality in each scale-eater and its victim were surveyed. The results showed that “cross-predation”, in which righty predators catch lefty prey and lefty predators catch righty prey, occurred more frequently than the reverse combination (“parallel-predation”). The cause of the predominance of cross-predation is discussed from the viewpoint of the physical and sensory abilities of fishes., 20 Jan. 2019, 11, 1, 119, 119, Scientific journal, 10.3390/sym11010119
  • Refereed, Zoological Science, Zoological Society of Japan, Laterality is Universal Among Fishes but Increasingly Cryptic Among Derived Groups, Michio Hori; Mifuyu Nakajima; Hiroki Hata; Masaki Yasugi; Satoshi Takahashi; Masanori Nakae; Kosaku Yamaoka; Masanori Kohda; Jyun-ichi Kitamura; Masayoshi Maehata; Hirokazu Tanaka; Norihiro Okada; Yuichi Takeuchi, 01 Aug. 2017, 34, 4, 267, 267, Scientific journal, 10.2108/zs160196
  • Refereed, Journal of Theoretical Biology, Elsevier BV, Small and poor females change sex: A theoretical and empirical study on protogynous sex change in a triggerfish under varying resource abundance, Sachi Yamaguchi; Satoko Seki; Kota Sawada; Satoshi Takahashi, Jan. 2013, 317, 186, 191, Scientific journal, 10.1016/j.jtbi.2012.10.020

Books etc

  • 生物の形の多様性と進化, 裳華房, 2003, Not Refereed
  • Macintosh ではじめる C, 牧野書店, 1996, Not Refereed
  • エルゴード理論とフラクタル, シュプリンガー・フェアラーク東京, 1993, Not Refereed
  • Chaos in Australia, World Scientific Publishing, 1993, Not Refereed
  • Chaos in Australia, World Scientific Publishing, 1993, Not Refereed
  • カオス, サイエンス社, 1990, Not Refereed
  • Lateral asymmetry in animals : predator-prey interactions, dynamics, and evolution, Springer, Hori, Michio; Takahashi, Satoshi, 2022, xii, 295 p., 9789811913402


  • 日本応用動物昆虫学会, ニクバエの蛹休眠を誘導する臨界日長の性比の進化, 2016
  • 日本応用動物昆虫学会, 半倍数性害虫における殺虫剤抵抗性発達, 2015
  • 日本生態学会, 繁殖干渉を伴う島の生物地理モデル, 2014
  • 浅見崇比呂; 八杉正樹; 堀道雄; 高橋智; Chirasak Sucharit; Somsak Panha, 日本進化学会, 樹上性カタツムリの左右二型にみる進化的安定性, 2013
  • 日本生態学会, 左利きホモはどのように消えていくか ― 魚類左右性多型の不和合性の進化, 2009
  • 日本生態学会, リッチなメスは性転換しない?ーツマジロモンガラの性転換の数理モデルー, 2009
  • 日本生態学会, ハクセンシオマネキの左右性の遺伝システムのモデル, 2009
  • 日本数理生物学会, Size dependent resource allocation and patterns of sexuality in sedentary marine animals, 2008
  • 日本動物行動学会, リッチなメスは性転換しない?, 2008
  • 個体群生態学会, 小さい雄は成長するか?-フジツボ類の矮雄の成長パターンと生活史戦略-, 2008
  • Japanese Society of Mathmatical Biology, A model on the evolution of cooperation in an asymmetric prisoner’s dilemma in an intertidal crab, 2008
  • 数理生物学会, 同性間伝播と異性間伝播の両方を考えた HIV のモデル, 2008
  • 日本数理生物学会, ハクセンシオマネキの左右性の遺伝システムのモデル, 2008
  • 行動学会, 左利きホモはなぜ存在しない?魚類左右性の遺伝システムの進化, 2008
  • 行動学会, ハクセンシオマネキの左右性の遺伝システムのモデル, 2008
  • The Society of Population Ecology, Oscillation induces the evolution of homozygote incompatibilities in the lateral asymmetry genetics of fish, 2008
  • 個体群生態学会, 干潟の蟹における非対称な囚人のジレンマの協力の進化, 2008
  • 個体群生態学会, ハクセンシオマネキの左右性の遺伝システムのモデル, 2008
  • Japanese Society of Mathematical Biology, Size dependent resource allocation and patterns of sexuality in sedentary marine animals, 2008
  • Japanese Society of Mathmatical Biology, A model on the evolution of cooperation in an asymmetric prisoner’s dilemma in an intertidal crab, 2008
  • The Society of Population Ecology, Oscillation induces the evolution of homozygote incompatibilities in the lateral asymmetry genetics of fish, 2008
  • S. Takahashi; M. Hori, CIJK-MB-2019, Oscillation of laterality in prey-predator system with time delay, due to predation or frequency dependence?, 2019
  • 高橋智; 小蕎圭太; 中嶋康裕, 日本動物行動学会, 非効率な軍備は維持されるか? — キヌハダモドキの性的共食いのモデル, 2018
  • S. Takahashi; M. Hori, Society of Mathematical Biology, Predation or frequency dependence, which of them controls dimorphism oscillations in prey predator system?, 2018


  • Zoological Science Award, 日本動物学会, Michio Hori;Mifuyu Nakajima;Hiroki Hata;Masaki Yasugi;Satoshi Takahashi;Masanori Nakae;Kosaku Yamaoka;Masanori Kohda;Jyun-ichi Kitamura;Masayoshi Maehata;Hirokazu Tanaka;Norihiro Okada;Yuichi Takeuchi, Jun. 2018, Laterality is Universal Among Fishes but Increasingly Cryptic Among Derived Groups

Research Projects

  • フラクタル図形の次元スペクトル, 0, 0, 0, Competitive research funding
  • 魚類の左右性多型の数理モデル, 0, 0, 0, Competitive research funding
  • Dimension spectra of fractals, 0, 0, 0, Competitive research funding
  • Mathematical model of lateral asymmetry plymorphisms in fish, 0, 0, 0, Competitive research funding
  • Grant-in-Aid for Scientific Research (B), 2008, 2010, 20340017, Aspects of Mathematics on Fractals, KIGAMI Jun; SHISHIKURA Mitsuhiro; KUMAGAI Takashi; AIKAWA Hiroaki; KAMEYAMA Atsushi; HINO Masanori; ITO Syunji; OSADA Hirofumi; KOTANI Motoko; HATTORI Tetsuya; TAKAHASHI Satoshi; KUWADA Kazumasa; WAKANO Isao; KUBO Masayoshi, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kyoto University, 18850000, 14500000, 4350000, We have studied various aspects of mathematical foundation of fractals. In particular, we have constructed intrinsic geometrical structure associated with analytical objects like stochastic processes on fractals. Furthermore, based on these geometric structure, we have investigated the asymptotic properties of stochastic processes on fractals and/or boundary behaviors of functions on domains with fractal boundary., kaken
  • Grant-in-Aid for Scientific Research (C), 2007, 2009, 19570020, The dynamics of laterality in aquatic animals and the evolution of its genetic system, TAKAHASHI Satoshi; WADA Keiji; HORI Michio; KOUDA Masanori, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Nara Women's University, 4420000, 3400000, 1020000, Oscillation of laterality frequency by the cross predation favors incompatibility genes against fertilization of lefty gene gemetes, which explains the lack of lefty homozygotes in fish., kaken
  • Grant-in-Aid for Scientific Research (C), 2002, 2004, 14540578, What factors govern the occurrence of highly developed territorial behavior termed barricade building in Ilyoplax pusilla (Crustacea ; Brachyura)?, WADA Keiji; TAKAHASHI Satoshi, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Nara Women's University, 3500000, 3500000, Factors governing the occurrence of unique territorial behavior termed barricade building by the brachyuran crab Ilyoplax pusilla (family Dotilllidae) living on tidal flat, have been explored for the following aspects. 1.Influence of external factors on frequency of barricade building The frequency of barricade building increased in the breeding season, but was not correlated with the tidal regime. The frequency was also not related with the population density or with difference of the substratum condition. 2.Relationship of barricade building with mating success Comparison of occurrence of barricade building between pairing males and non-pairing males revealed that the former made barricade building more frequently than the latter. This finding suggests that barricade functions advantageously for pair formation. 3.Interspecific comparison of earthen-structure avoiding tendency Comparison of response to artificial earthen structure between Ilyoplax pusilla and other two dotillid species without barricade building behavior, revealed that I.pusilla less frequently broke the structure or avoided it more frequently than the other two species. 4.Model construction In one model, three strategies each for barricader (build, do not build, build to smaller) and barricadee (destroy, do not destroy, destroy to smaller) are assigned, and the evolutionary dynamics of their frequency has been investigated. The model shows that cost by barricade should be frequency dependent to explain why only part of population members build barricades. However, the equilibrium is only neutrally stable and random genetic drift should turn the system with no barricade. Introduction of frequency depended strategy, destroy barricade depending on their frequency, made the equilibrium with intermediate barricade frequency stable. In the other model, life history strategies have been investigated by dynamic programming method. In ESS, barricade is built only in the breeding season, which coincides with field data, kaken
  • Grant-in-Aid for Scientific Research (C), 2000, 2003, 12640120, Multivariable multifractal analysis, TAKAHASHI Satoshi; FUJIWARA Akio; SUZUKI Joe; KAMO Hiroyasu, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Nara Women's University, 3600000, 3600000, Studies of multfractals so far have dealt with functions of single variables, singularity spectrum of single singularity, or free energy of single inverse tempreture parameter. However invariant sets of dynamical systems in higher dimensions have different expansion or contraction rate depending on the direction. We considered invariant measures on self-affine sets which have different contraction rates depending on the direction, and define the singularity spectrum with two different singularities, as well as free energy with two different inverse temperatures. Under certain asumptions on the measure, the singularity spectrum with two singularities coincides with the Legendre transform of the free energy with two inverse temperatures. We also defined dimension spectrum with two dimensions as parameter, and the corresponding free energy, for 3-dimensional self-affine sets. Applying multivariable multifractal formula for the projection of the natural measure on the self-affine sets, we have shown that the dimension spectrum with two dimension parameters coincides with the modified Legendre transform of the corresponding free energy. This result also impies that the Hausdorff dimension of 3-dimensional self-affine sets is represented by the free energy with its inverse temperatures being the ratios of the logarithmic contraction rates., kaken
  • Grant-in-Aid for Scientific Research (C), 1999, 2000, 11640115, Operational methods in quantum information theory, FUJIWARA Akio; MANABE Shojiro; SUGIMOTO Mitsuru; ENOKI Ichiro; TAKAGOSHI Kensho; YAMAMOTO Yoshikiko, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Osaka University, 3600000, 3600000, The purpose of this project is to investigate operational methods in quantum information theory. In particular, we have studied (a) novel operational characterizations of quantum entropies, and (b) quantum channel identification problem. The results of these studies are summarized as follows. (a) Let p be a probability measure on a Hilbert space H the support of which being a countable set of mutually nonparallel unit vectors. Let p^<(n)> be the probability measure on H^<【cross product】n> defined by the nth i.i.d. extension of p, and consider L^<(n)> random vectors X (1) , ..., X (L^<(n)>) on H^<【cross product】n> which are subjected to p^<(n)>. We have introduced several definitions of "asymptotic orthogonality" for the random vectors and have studied the corresponding orthogonality capacity, i.e., the supremum of lim sup_n log L_n/n over all sequences {L_n}_n that satisfy each orthogonality criterion. Under the weak orthogonality condition that represents the situation in which the vector X (1) is almost orthogonal to the other vectors, the orthogonality capacity has turned out to be identical to the von Neumann entropy for the density operator ρ that corresponds to the measure p. Moreover we have clarified that the noiseless quantum channel coding theorem by Hausladen et al. is a direct consequence of this characterization. Under the strong orthogonality condition that represents the situation in which the vectors X (1), ..., X (L^<(n)>) are mutually almost orthogonal, on the other hand, the orthogonality capacity has turned out to be identical to half the quantum Renyi entropy of degree 2. (b) A quantum channel identification problem is this : given a parametric family {Γ_θ}_θ of quantum channels, find the best strategy of estimating the true value of the parameter θ. We have studied this problem from a noncommutative statistical point of view. In particular, we have demonstrated a nontrivial aspect of this problem as follows. Let Γ_θ be the isotropic depolarization channel acting on the two-level quantum system, in which the parameter θ represents the magnitude of depolarization. By using the Stokes' parametrization, it is represented as (x, y, z) → (θx, θy, θz). Due to the requirement of complete positivity of the map Γ_θ, the parameter θ must lie in the closed interval [-1/3, 1]. Up to the second extension H 【cross product】 H of the quantum system, the best strategy of estimating the isotropic depolarization parameter θ is the following. For 1/(√<3>)【less than or equal】θ【less than or equal】1, use Γ_θ 【cross product】 Γ_θ and input a maximally entangled state ; For 1/3【less than or equal】θ【less than or equal】1/(√<3>) use Γ_θ 【cross product】 Γ_θ and input a disentangled state ; For-1/3【less than or equal】θ【less than or equal】1/3, use Γ_θ 【cross product】 Id and input a maximally entangled state. It is surprising that the seemingly homogeneous family {Γ_θ}_θ of depolarization channels involves a transitionlike behavior., kaken
  • 萌芽的研究, 1998, 1999, 10874023, ノンランダム確率過程の応用, 釜江 哲朗; 高橋 智; 伊達山 正人, 日本学術振興会, 科学研究費助成事業, 大阪市立大学, 1700000, 1700000, ブラウン運動は、その法則が1/2次の自己相似性をもった加法過程として特徴付けられる.ブラウン運動B_tを用いた確率過程X_t=H(B_t,t)でH(x,t)がxに関して2回連続微分可能でtに関して1回連続微分可能なものは伊藤過程と呼ばれ,.よく研究されており,また,株価変動のモデル等として広く用いられている.この確率過程の増分は無限大のエントロピーをもっており,現実のモデルとしては,実際以上にランダムネスを含み不適切との指摘もされている.自己相似性をもつ確率過程の定常増分のエントロピーは0か無限大であることが知られている. 本研究では,0エントロピーの定常増分と1/2次の自己相似性をもつ唯一エルゴード的な確率過程の一つであるN-processN_tを考察した.これは,従来知られていなかった決定論的な(deterministic)自己相似確率過程であり,無相関な増分をもち,ブラウン運動との類似性もある.これをブラウン運動の代わりに用いた確率過程X_t=H(N_t,t)に関して,過去のデータから如何にして未来を予測するかという問題を考察し,ブラウン運動の場合と異なり非常によい予測が成立することを示した.これは例えば、位相が不明の異なる周期の様々な周期関数の和の時間的累積として表現されるような現象で、自己相似性をあわせもつものに対する確率過程としての定式化でもある., kaken
  • Grant-in-Aid for Scientific Research (B), 1997, 1999, 09440032, Deformation of kahler manifolds via higher dimensiond guasi-conformd mapping, ENOKI Ichiro; MABUCHI Toshiki; NAGASE Michihiro; USUI Sanpei; TAKAHASHI Satoru; SAKUMA Makoto, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Osaka University, 12500000, 12500000, Since the advent of the Kodaira Embedding Theorem and the theory on deformations of complex structures, in particular, the stability theorem of Kahler structure, that is, since 1960's it has been a major question that very compact Kahler manifold can be deformed to a projective algebraic manifold. By the Kodaira Embedding Theorem, if a compact Kahler manifold has a Kahler class whose periods are all rational, it is a projective algebraic manifold. By the stability theorem of Kahler structure, any small deformation of a compact Kahler manifold is again Kahler. Moreover, Kahler classes can be chosen to deform continuously, and hence their periods vary also continuously. Therefore, many people conjectured that, one can deform nicely so that a Kahler class on the deformed manifold has rational periods, i.e., every compact Kahler manifold can be deformed to an algebraic manifold. This approach, examining variations of periods of Kahler classes under deformations of complex structures, however, has not yielded particular resuls on this question yet. Taking a more direct approach, we succeeded to answer this question affirmatively. First, we construct a C∞embedding, which is sufficiently near to be holomorphic, of a compact Kahler manifold to a complex projective space, by making use of the kernel of C∞ line bundle coefficient Dirac-type operator. Next, we show that the image of this embedding is a complex submanifold of the complex projective space. This emebedding mapping is the higher dimensional quasi-conformal mapping in the title of our research project. Finally, we show that the image of this embedding is a small deformation of the original Kahler manifold. Moreover, our proof give a sufficient condition for a sequence of rational cohomology classes which converges to a Kahler class can be obtained as a sequence of pull-back via diffeomorphisms of rational polarizations on a sequence of projective algebraic manifolds. In particular, rigid compact Kahler manifolds are projective algebraic manifolds whose Picard numbers are maximal., kaken
  • Grant-in-Aid for Scientific Research (A), 1997, 1999, 09304009, Global analysis of curves and surfaces, KOISO Norihito; SAKANE Yusuke; NAMBA Makoto; USAI Sampei; YAMASAKI Yohei; NISHITANI Tatsuo, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Osaka University, 27400000, 27400000, We studied types of Jacobi fields of constant mean curvature surfaces. If the rotational surface is critical in the sense of stability, the Jacobi fields are usually rotationally symmetric. However, we found also rotationally non-symmetric one. The existence of non-symmetric Jacobi fields is not surprising, but the existence on the critical surface means that even symmetric stable solution of a variational problem may splits into non-symmetric solutions. We proved that the hemi-sphere is the unique stable solutions of the free boundary problem of constant mean curvature surfaces with boundary in a plain. And, got a sufficient condition on the size of boundary and surface to be unique in the class of same boundary. We classified homogeneous Einstein metrics on certain homogeneous spaces. In the classification, simplification of the algebraic equation and the efficiency of the algorism of solving algebraic equations are essential. We prived that compact k-symmetric twister bundles over compact symmetric spaces are projected to compact symmetric spaces by primitive maps of finite type. We got new estimates from below of the spectrum of general infinite graphs. The estimate is sharp on many cases. We proved that global Sobolev-Bergman kernel can be analytically continued with respect to its Sobolev degree. We generalized the theorem of Omori-Yau concerning the growth of the volume on complete riemannian manifold and the maximum principle. We gave a sufficient condition to be strong solution of the weak solution of a boundary value problem with non constant rank of boundary matrix., kaken
  • 奨励研究(A), 1997, 1998, 09740144, 力学系の不変集合のマルチフラクタル解析, 高橋 智, 日本学術振興会, 科学研究費助成事業, 大阪大学, 2300000, 2300000, これまでマルチフラクタルとしての性質が厳密に調べられてきた測度は,多くの場合,準乗法的性質を持ち,その特異性スペクトルは全ての領域で自由エネルギーのルジャンドル変換と一致する(マルチフラクタル公式が成立する).準乗法的性質を持たない既約なソフィック測度に対して,特異性スペクトルの最大値を与える特異性の値よりも小さい領域で,マルチフラクタル公式が成立することを示し,また他の領域でマルチフラクタル公式が成立しない例を構成した. ソフィック測度のマルチフラクタル公式を使って,高次元の部分自己相似集合および2次元の部分自己アファイン集合の次元スペクトルの性質を調べ,次元スペクトルの最大値を与える次元よりも大きい次元の領域で,その自由エネルギーのルジャンドル変換と一致することを示し,また,部分自己アファイン集合のハウスドルフ次元と次元スペクトルとの関係を明らかにした. また,自己アファインコサイクルに対して,Mandelbrot-van Ness変換によりその性質を連続的に変化させることが出来ることを示した.自己アファインコサイクルのこれまでの構成法では,可算個の次数のスケーリングしかとりえず,その結果ヘルダー指数,ボックス次元なども可算個に限られる.MandelbrotとVan Ncssは時間的な相関のないブラウン運動に対して時間的な相関を積分で与える変換を考え,非整数ブラウン運動を構成した.Mandelbrotとvan Nessの変換を自己アファインコサイクルに適用し,その結果がまた自己アファインコサイクルとなることを示した.これにより,0と1との間の任意の次数のスケーリングをもつ自己アファインコサイクルを構成することができる.また,このようにして構成した自己アファインコサイクルのヘルダー指数,ボックス次元,パワースペクトルなどを調べた., kaken
  • Grant-in-Aid for Scientific Research (C), 1997, 1998, 09680367, Learning Baysian Networks based on the MDL principle, SUZUKI Joe; SATAKE Ikuo; KIKUCHI Kazunori; TAKAHASHI Satoshi; NAGATOMO Kiyokazu; MURAKAMI Jun, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Osaka University, 3300000, 3300000, In this study, the computational issue in the problem of learning Bayesian belief networks (BBNs) based on the minimum description length (MDL) principle is addressed.Based on an asymptotic formula of description length, we apply the branch and bound technique to finding true network structures.The resulting algorithm searches considerably saves the computation yet successfully searches the network structure with the minimum value of the formula.Thus far, there has been no search algorithm that finds the optimal solution for examples of practical size and a set of network structures in the sense of the maximum posterior probability, and heuristic searches such as K2 and K3 trap in local optima due to the greedy nature even when the sample size is large.The proposed algorithm, since it minimizes the description length, eventually selects the true network structure as the sample size goes to infinity., kaken
  • Grant-in-Aid for Scientific Research (A), 1996, 1998, 08304041, Dynamics of laterality in fish communities in Lake Biwa and the River Yodo water sytem, HORI Michio; TAKAHASHI Satoshi; MATSUDA Hiroyuki; KOHDA Masanori; YUMA Masahide; YAMAOKA Kosaku, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, KYOTO UNIVERSITY, 3200000, 3200000, 1. The examination on samples from Lake Biwa has turned out as follows. In most species the ratio of laterality (the ratio of sinistral individuals in population) changed yearly suggesting a oscillation with an amplitude 0.3 to 0.7 and a period of about 5 years. The oscillation seemingly synchronizes among species of same or similar feeding habit. These results coincide with that from Lake Tanganyika, In the native predator, the piscivorous chub, and its main prey, Ayu fish, the ratio of laterality oscillate in a characteristic way for 4-year survey period, suggesting that the dynamics of laterality were driven by prey-predator interaction in the community. These results suggest that the oscillations are also caused through the interspecific relationship among fish species in a community. Especially, prey predator relationship may be the most responsible to the incidence of the oscillation, because frequency dependent vigilance of prey fish against predators and the resultant minority advantage among predators are one of the most reliable and probable mechanisms to maintaining the polymorphism in animal populations. 2. The genetic system of the laterality was examined in laboratory rearing using a lizard goby. The result strongly suggests that the laterality in determined by a Mendelian one locus - two alleles system, in which dextrality is dominant over sinistrality, but the homozygote of dextrality seems to be lethal. 3. The results from the investigation using mathematical models are as follows. If two competing species have the lateral asymmetry polymorphisms, with their frequencies not oscillating, the polymorphisms will be lost as a consequence of random genetic drift. If the frequencies of lateral asymmetry polymorphisms are oscillating, it diminishes the difference of the sinistral frequencies of both of species, and maintains the lateral asymmetry polymorphisms in species. The oscillation of the lateral asymmetry polymorphisms contributes to the coexistence or the exclusion of competing species, if their growth periods are different. When the difference is small, the species with longer growth period will extinct. When the difference is large, the oscillation makes both species coexist., kaken
  • Grant-in-Aid for international Scientific Research, 1996, 1997, 08041155, Niche differentiation of Dipterocarpaceae and Fagaceae-a study in Asian rain forest-, YAMAKURA Takuo; WATANABE Mikio; TAMURA Minoru; OHKUBO Tatsuhiro; HARA Masatoshi; KANZAKI Mamoru, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Osaka City University, 10900000, 10900000, 1. Research on Dipterocarpaceae at a tropical lowland rainforest of Sarawak Distribution of 73 species and 9 subspecies of dipterocarps were analyzed in a 52 ha plot, and 73% of the examined species had distribution pattern depending on the topography. The fact suggest tht the topographical niche differentiation might contribute to enable the coexistence of dipterocarps in the plot. This analysis was also made for non-dipterocarp taxon, and same results were achieved. Canopy gap formation rate and recovery rate were estimated by using aerial photographs and by the land survey. There werer two types of gaps : one type was formed by the land slide associated with heavy rain and the other was formed by the tree falls. Two types of gap formation differed the frequency and recovery process and the various regeneration niches for the tree species were provided through two gap formation process. The contribution of the diversity of regeneration niche to the coexistence of tree species will be analyzed near future. Genetic analyzes were made for two species of genus Dryobalanops. Both of the species showed high genetic differentiation among the local populations located in 52 ha, indicating the high genetic diversity of the species. On the contrary, genetic distance between two sympatric species was quite small indicating niche differentiation and speciation of the two species had occurred recently. 2. Research on Fagaceae at a montane rainforest of Thailand A research plot of 15 hapiot was established and the tree census in 7.5 ha area and identification in 3.0 ha area were completed. Gaps in 3.0 ha area was also mapped. Preliminary data analysis clarified that many Fagaceae species showed the distribution pattern associated with special topography or gaps. The niche differentiation among Fagaceae species will be analyzed qualitatively near future., kaken
  • 奨励研究(A), 1996, 1996, 08740142, 次元スペクトルを用いたフラクタル集合の解析, 高橋 智, 日本学術振興会, 科学研究費助成事業, 大阪大学, 1100000, 1100000, フラクタル集合の断面の次元は,これまで測度1の集合で計算されてきた.断面の次元の分布のより詳しい指標として,次元スペクトル(それぞれの次元の値をとる断面の集合のハウスドルフ次元)がセルオートマトンの極限集合および部分自己アファイン集合に対して計算された.断面の次元は,フラクタル集合上の自然な測度を断面に垂直な軸へ射影して得られる測度の特異性と対応し,次元スペクトルは特異性スペクトル(それぞれの特異性の値をとる点の集合のハウスドルフ次元)と対応している.これらの集合では,射影した測度はソフィック測度(有限個の非負行列から構成される測度)となっている.ソフィック測度の特異性スペクトルが特異性の小さい側で自由エネルギーのルジャンドル変換として表されることから,次元スペクトルもまた,断面の次元の大きい側で,自由エネルギーをルジャンドル変換に類似した変換で表されることがわかる. ソフィック測度から,それぞれの特異性を持つ集合の測度が1となるギブス測度の族が構成できるが,そのフラクタル集合上への引き戻しを考えることにより,部分自己アファイン集合のハウスドルフ次元が断面の次元と次元スペクトルの和の最大値で下から評価できる.また,次元スペクトルが自由エネルギーの疑似ルジャンドル変換として表されることから,逆温度を部分自己アファイン集合の次数(縦方向の縮小率の対数と横方向の縮小率の対数との比)とした自由エネルギーが断面の次元と次元スペクトルの和の最大値と一致し,また,逆温度が次数のギブス測度の引き戻しの特異性を考えることにより,この自由エネルギーの値で部分自己アファイン集合のハウスドルフ次元が上から評価できる.したがって,部分自己アファィン集合のハウスドルフ次元が断面の次元と次元スペクトルの和の最大値と一致することがわかった., kaken
  • 基盤研究(C), 1996, 1996, 08640114, 階数2の不連続群と3次元多様体, 作間 誠; 高橋 智; 渡部 隆夫; 小磯 憲史; 臼井 三平; 伊吹山 知義, 日本学術振興会, 科学研究費助成事業, 大阪大学, 2100000, 2100000, 1。カスプ付双曲多様体内の最短垂直測地線の研究。 秋吉宏尚、中川義行との共同研究により、ホワイトヘッド絡み目補空間の(一方のエンドに関する)双曲的デーン手術で得られるカスプ付双曲多様体内の最短垂直測地線を決定し、それが、解消トンネルになっていることを確認した。これは、「カスプ付双曲多様体内の解消トンネルはその標準的分解の辺と同位であろう」という予想を支持し、円周上の穴開きトーラス束に関してはその予想が肯定的でありことを導く。また、この結果は、穴開きトーラス束、及び2橋結び目補空間の標準的分解、ひいては基本群が2元生成である双曲多様体を理解するための最初の一歩に相当する。 2。絡み目のザイフェルト曲面の研究。 平澤美可三との共同研究により、特殊交代絡み目の最小種数ザイフェルト曲面を分類し、それらから構成される垣水複体の構造を完全に決定した。特に、その垣水複体は球体に同相であることが示せたので、「垣水複体は可縮であろう」という垣水の予想を特殊交代絡み目に対して証明したことになる。バークレーで開催された国際研究集会で共同研究者の平澤美可三がこの結果を発表したところ、垣水複体複体の概念を一般の3次元多様体の2次元ホモロジー類に対するものに一般化して考察してはどうかという示唆をGabai氏より受けた。この問題は今後の重要な研究課題である。 3。絡み目の村杉分解の研究 特殊樹状絡み目のザイフェルト曲面からホップバンドを村杉分解で取り出す方法を研究し、特別なクラスに対しては、それを完全に解明した。これを用いるとそのクラス内の結び目の結び目解消操作が分類できる。この研究を一般の樹状絡み目、ひいては一般の結び目、特にファイバー結び目に関して行うことは、結び目解消操作の研究、及びファイバー結び目に関するGabaiの予想との関連で非常に重要である。, kaken
  • Grant-in-Aid for Scientific Research (B), 1995, 1996, 07454027, Symmetric systems and strongly hyperbolic systems, NISHITANI Tatsuo; TAKAHASHI Satoshi; TAKEGOSHI Kensho; SAKUMA Makoto; NAMBA Makoto; USUI Sampei, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Osaka University, 3100000, 3100000, Our research project has been organized as follows : (i) Clarify the structure of strongly hyperbolic systems which can not be symmetrizable. (ii) Study the stability of symmetrizable systems under hyperbolic perturbations. As for (i) we got the following results. Let L be a m*m system of patial differential operators of first order. Denoting by h the determinant of the principal symbol of L the general picture of our necessary condition for strong hyperbolicity of L could be stated as : if L is strongly hyperbolic then the Cauchy problem for h+k is correctly posed for every m-1-th minor k of L.Moreover if the reference characteristic z is involutive and the system is strongly hyperbolic then KerL (z) * ImL (z) = {0}. Thus the Taylor expansion of L along KerL starts with a linear term L_Z called the localization of L.Let z, w be characteristics of the original system and of the localization respectively. If (z, w) is involutive then KerL_z (w) * ImL_z (w) = {0}. As for (ii) we formulated non degenerate characteristic for first order system. We say that z is non degenerate if KerL (z) * ImL (z) = {0}, the dimension of L_Z is maximal and L_Z (w) is diagonalizable for every w. Then the main result is that every hyperbolic system is symmetrizable near non degenerate characteristic. From this we can derive stability of non degenerate characteristics. Namely we can not remove non degenerate characteristics by hyperbolic perturbations. We proceed this study and got the following result. Let L be a m*m sysmmetric first order hyperbolic system. Then if the dimension of L is greater than m (m+1) /2-m+2 then genericaly, every hyperbolic perturbation is trivial that is every hyperbolic system near L can be symmetrized., kaken
  • 奨励研究(A), 1995, 1995, 07740152, ソフィック測度上のマルチフラクタル解析とその応用, 高橋 智, 日本学術振興会, 科学研究費助成事業, 大阪大学, 1000000, 1000000, 測度に対する数学的に厳密なマルチフラクタル解析は,これまで主にヘルダー連続なポテンシャル関数に対するギブス測度について行われてきた.ヘルダー連続なギブス測度を含む最も広いクラスとして,準乗法的測度に対してマルチフラクタル解析が行われている.本研究ではヘルダー連続性や準乗法的性質を持たないソフィック測度に対して,マルチフラクタル解析を行った.ソフィック測度が既約のとき,ソフィック測度を構成する部分遷移行列の積から性質のよいものを探すことにより,ソフィック測度に対応する非負の逆温度を持つギブス測度の族が構成されることと,それらが混合性を持つことが示された.また,同様にしてソフィック測度の自由エネルギーが存在することが示された.ソフィック測度で特定の特異性を持つ集合上でのギブス測度の特異性を考察し,ビリングスレイの定理を適用することにより,ソフィック測度の特異性スペクトルが評価できる.ソフィック測度の特異性スペクトルは,特異性スペクトルが最大値をとる特異性以下で自由エネルギーのルジャンドル変換で与えられることが示された.また,特異性スペクトルの最大値を与える特異性よりも大きな特異性では,一般に自由エネルギーよりも特異性スペクトルが小さくなる.このことは,これまで数学的に研究されてきた準乗法的な測度では生じない現象である. フラクタル集合の断面の次元の分布を特徴づけるものとして,次元スペクトルがある.フラクタル集合の次元スペクトルは,フラクタル集合上の一様な測度を射影して得られる測度の特異性スペクトルと関連づけられる.自己アファイン集合上の一様な測度の射影はソフィック測度となるので,ソフィック測度の特異性スペクトルについて得られた結果を用いて,既約な自己アファイン集合の次元スペクトルとハウスドルフ次元の性質が調べられた., kaken
  • 一般研究(C), 1995, 1995, 07640112, 3次元多様体のへガード分解と群の階数, 作間 誠; 高橋 智; 梅原 雅顕; 竹腰 見昭; 榎 一郎; 伊吹山 知義, 日本学術振興会, 科学研究費助成事業, 大阪大学, 2400000, 2400000, 1.円周上の穴開きトーラス束の解消トンネルを完全に分類し、それが、Jprgensen,Floyd-Hatcherにより与えられたイデアル分解の“特別な"辺にアイソトピックであることを観察した。これは「解消トンネルはcanonical deccmpositionの辺にアイソトピックであろう」という予想を支持することになる。又、Jprgensenの未完成論文「On pairs of punctured tori」の結果を仮定すれば上記の結果はこの予想がトーラス束については正しいということを導びくため、Jprgensenの未完成論文を理解し証明を完成する努力をした。残念ながら証明を完成させることができなかったが、Jprgensenの基本的アイデアは理解できた様に思える。 2.特別交代絡み目の最小種数がイフェルト曲面を完全に分類し、それから構成される垣水複体MS(L)の構造を決定した。特にその実現|MS(L)|はn次元球体に同相であることを示したので、これは垣水予想「|MS(L)|は可縮である」の部分的解決を導びく。 絡み目のアーベル被服に関して以前得ていた結果、方法を複素曲面のアーベル分岐扱嚢の不正則類の研究に応用することにより、その不変量が“特別な"polynonial perrodiatyを持つことを証明した。, kaken
  • Grant-in-Aid for international Scientific Research, 1994, 1995, 06041094, Tropical Rain Forest Biodiversity Analyzed by a Large Research Plot, YAMAKURA Takuo; SHIBATA Kozo; ERNEST Chai; LEE Hua seng; OHKUBO Tatsuhiro; TAKAHASHI Satoshi; KANZAKI Mamoru, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Osaka City University, 14400000, 14400000, The species richness of a tropical rain forest was analyzed by using a large-scale research plot, which has a size of 52 ha and was established at the Lambir National Park, Sarawak, Malaysia in 1993. Questionnaires of the present study are mainly concerned with the tests of availability of two contrasting hypotheses, equilibrium hyporthesis (niche theory) and non-equilibrium hypothesis, for the explanations of working mechanisms of the biodiversity of tropical rain forest. By dividing the whole plot area into 1300,20mx20m stands, four topographic and five forest-structural variables were calculated for each of 1300 stands. The topographic variables suggested the steeply sloped, sharply undulating, and complexly bisected topography of the plot. The forest structural variables also suggested a huge and complex structure with superimposed forest layrs. Both topographic and structural variables were highly correlative, suggesting a predictability of forest structure with respect to topography. Out of the five forest structural variables, mean dbh per forest layr in a 20mx20m stand decreased with and increase of tree density per forest layr, showing a density dependency of individual tree growth. The total number of species in the plot was 1175, which was far greater than those at Pasoh (820 spp/50ha) in west Malaysia and BCI (306) spp/50ha) in Panama. The spatial patterns of some dominant species were also highly correlative with topographic variables. All these results suggested the predictable change of the huge and complex architecture of the rain forest at Lambir and seemed to be favored by the equilibrium hypothesis as a working mechanism of tropical biodiversity. The genetic diversity was studied by analyzing isozyme patterns in leaves and implied the importance of gene drifts for producing the rich tropical biodiversity., kaken
  • 一般研究(C), 1994, 1994, 06804005, 双曲的結び目のcanonical decomposition, 作間 誠; 高橋 智; 宇野 勝博; 臼井 三平; 伊吹山 知義; 真鍋 昭治郎, 日本学術振興会, 科学研究費助成事業, 大阪大学, 1900000, 1900000, 1. 森元勘治(拓殖大)、横田佳正(九大)との共同研究で、次の二つの研究成果を得た. (イ) トンネル数が1の結び目K_1、K_2で、その和K_1♯K_2のトンネル数が3となるものを具体的に構成した。 (ロ) 与えられた結び目がトンネル数1を持つための条件を与え、それを用いることにより、10交点以下の結び目のトンネル数を完全に決定し、又Monfesinos結び目がトンネル数1を持つための条件を求めた。 2. Elena Klimeuko(Novosibirsk)との共同研究により、Isom 1H^2の二つの元により生成される群が離散的となるための必要十分条件を求めた。応用として三角鏡映群の階数を決定し、これと上の1-ロの結果を合わせることにより、トンネル数1のMontesinos結び目を完全に決定した。, kaken
  • 一般研究(C), 1994, 1994, 06640042, 保型形式の次元公式, 伊吹山 知義; 高橋 智; 真鍋 昭治郎; 臼井 三平; 長瀬 道弘; 小磯 憲史, 日本学術振興会, 科学研究費助成事業, 大阪大学, 2100000, 2100000, 有界対称領域の保型の次元について、その跡公式による公式について、次のような研究を行った。離散群の中心的巾単元の次元公式への寄与を、概均質ベクトル空間のゼータ関数の特殊値で記述すること、およびその特殊値自身の研究。ここでいう概均質ベクトル空間は有界対称領域の正則自己同型群を与える代数群の極大放物型部分群の巾零根基の中心のなす、形式的実ジョルダン代数から得られる物であり、ゼータ関数は、これに付随する凸体のゼータ関数である。跡公式自身のゼータ関数の特殊値による表示は、III型の領域の一部に付いては新谷よる結果が20年近く前に知られていたが、それ以外に付いてはほとんどなにも知られていなかった。今回、ポアソン公式等を収束を込めてくわしく見ることで、概均質ベクトル空間の一般論には含まれず、また記述もできないデータ積分の間の新しい関数等式を得、これによって古典対称領域についての中心的巾単元の寄与に付いては、かなり一般的な定理を得た。ある程度まともな離散群について、寄与はみなゼータ関数の0または負での値で書ける。これらの定理は、みな具体的に記述でき、実際に次元を求めるのに役立つ。また、特殊値については、研究としてはかなり別のカテゴリーにはなるが、いずれも実際に値が記述できる(というよりむしろゼータ関数自身が分かりやすい関数でかける)という数年来筆者が行っている研究によれば具体的な次元公式にかなり近づいたといえる。以上に付いて、IV型に力点をおいて、代数学シンポジウムで報告(7月愛媛大)、概均質の一般的枠内での理論の集大成に付いて研究集会で報告(10月京大)、また古典有界対称領域の次元公式について研究集会で報告(1月京大)をおこなった。, kaken
  • 一般研究(C), 1993, 1993, 05640278, 飛躍型確率過程の極限定理, 小松 孝; 津島 行男; 原田 学; 高橋 智; 西尾 昌治; 藤井 準二, 日本学術振興会, 科学研究費助成事業, 大阪市立大学, 2100000, 2100000, 飛躍型の対称マルコフ過程には非局所ディリクレ形式が対応するが,その形式が,対称安定過程のディリクレ形式にある意味で類似であるとき,そのマルコフ過程を安定型過程と呼ぶことにする。この研究によって,かなり一般化した設定のもとで,安定型過程の推移確率の一様評価(すなわち,係数の正則性によらない,ヘルダー連続性の評価及び減少度合の評価)が得られた。これを周期的係数のディリクレ形式に対応する安定型過程の一様化問題に適用し,係数の連続性の仮定なしにその極限定理が成り立つことを示した。一様化問題はスモールパラメターを含むドライビング・ドリブン過程の極限定理の一種と考えることが出来る。その際,エルゴード的ドライビング過程の半群に対する解析的条件と共に,その確率過程の不変測度のある種の正則性が問題になる。このことを考察するには上記の推移確率の一様評価は有効ではなく,マルコフ過程の到達時間に関する評価が必要であり,レゾルベントの積分評価も必要である。これについて研究を行った結果,若干の成果を得たものの,当初の目標にはまだ到達していない。一方,研究分担者達によって,上記の内容に間接的に関係する形で,いくつかの成果が得られた。これらの成果は発表予定になっているものが多い。, kaken
  • 一般研究(C), 1993, 1993, 05640213, エルゴード理論の解析学の様々の分野への応用, 釜江 哲郎; 高橋 智; 伊達山 正人; 藤井 準二; 小松 孝, 日本学術振興会, 科学研究費助成事業, 大阪市立大学, 2000000, 2000000, エルゴード理論のフラクタル図形への応用に関して特に成果があったのでこれを中心に報告する。Peano関数のように到る所微分不可能な連続関数のあるクラスは自己線形性をもっている。このような関数のクラスを拡張し、『フラクタル』関数と呼ばれるに値する可能な限り広いクラスを設定した。同時に、各々の関数はその定義域を實軸からそれを含む自然な領域(ある種のコンパクト化)へと拡張し、その上の移動力学系に関するコサイクルとして定式化した。このようにして得られるコサイクルのクラスは、scaling propertyをもつ最小コサイクルと呼ばれる。本研究では、このコサイクルのクラスについての研究をおこなった。その結果、(1)このようなコサイクルを保存するscaling全体が正数の全体であるか、または、ある正数の整数冪の全体かのいずれかである。(2)これが正数全体となる例が存在する。(3)コサイクルの容量がある大きさ以下の場合は、(1)における後者の場合となる。(4)コサイクルによって生成される力学上には移動に関して不変な確率測度が唯一定まる。この確率測度は自己相似性をもっている。 以上の諸点が明らかとなった。, kaken
  • 重点領域研究, 1993, 1993, 05257209, スケールイーターの種内多型と多種共存の機構の理論的研究, 高橋 智, 日本学術振興会, 科学研究費助成事業, 大阪市立大学, 1100000, 1100000, スケールイーターについては,同一種内での左右比の変動の研究を踏まえ、複数種のなかにそれぞれ左右非対称性の多型がある場合にどうなるかがモデルによって調べられた.その結果,一般に,それぞれの種での左右比の振動が種間で同調することが明らかとなった.計画班の堀氏らによって,この結果がフィールドのデータで確かめられることが,今後期待される. 捕食被食関係による多型の維持と多種共存は,重点研究「地球共生系」のコアプロジェクトの,堀,松田,幸田氏らとの共同研究により,捕食共生という概念にまとめられた.これは,競争関係にある,捕食者どうし,あるいは,被食者どうしのあいだに,餌の警戒を分散させるなどの要因のため相利的な相互作用が働くことを指摘したものである.生物の多様性には,捕食共生が大きな要因として,働いていることが示唆された.捕食共生の特徴,タイプの分類などの研究が,現在続けられている. 周期的変動が生態系に与える影響については,競争系での難波氏との共同研究の結果を発展させ,捕食被食関係を通じた間接効果により,2種の捕食者や餌が共存する条件が調べられた.捕食者餌系では,系の変化の速さを表わす特性振動数が定義され,それが周期的変動の振動数よりも大きい時(系の変化が速いとき)には,捕食者の共存がみられ,小さいとき(系の変化が遅いとき)は,餌種の共存がみられることが明らかとなった. また,計画班の山村氏の血縁者間のコンフリクト解消のモデルに対し,コンフリクトが解消された状態が不安定で,コンフリクトの勝者と敗者が一定の時間間隔で逆転する可能性のあることが,理論とシミュレーションにより明らかとなった., kaken
  • 一般研究(C), 1992, 1992, 04640244, 非局所的放物型方程式に対応する確率過程の漸近理論, 小松 孝; 西尾 昌治; 高橋 智; 藤井 準二; 釜江 哲朗; 森本 治樹, 日本学術振興会, 科学研究費助成事業, 大阪市立大学, 1900000, 1900000, ユークリッド空間X及びYを考え、x〓Xをパラメターに持つレビィ型の生成作用素L^x_2を与える。その作用素はY上の連続関数に作用するフェラー半群を生成し、その半群T^x_tは不変測度をρ^xとするエルゴード性をみたしているとする。一方L^y_0はy〓Yをパラメターに持ちX上の関数に作用するレビィ型の作用素であるとする。作用素【numerical formula】が定めるX×Y上のマルコフ過程{(x_t,y_t),P^ε_}をドリブン・ドライブ過程という。ドリブン過程{x_t,P^ε_}のε↓0のときの様子を調べるというのが本研究の中心課題である。ニュートラル条件ρ^xa_1(x,・)=0を仮定したとき、もし作用素【numerical formula】が正当に定義出来て、〓に対するマルチンゲール問題の解の一意性が成り立てば、{x_t,P^ε_}はε↓0のとき〓定めるマルコフ過程に分布収束するというのが、この漸近理論の大筋である。 一般のレビィ型作用素L^y_0,L^x_2の場合にこの漸近定理を証明したのは本研究が最初であり、定理が成り立つための条件も本研究の中では弱められ具体的になっている。この成果は研究代表者によって学会発表されているが、この研究は一様化問題との関連も含めて今後更に続けられる予定である。また研究分担者達によって、上記の内容に直接的あるいは間接的に関係する形で、多くの成果が得られた。これらの成果は既発表のものもあるが、多くは発表予定になっている。, kaken
  • Grant-in-Aid for Scientific Research (B), 01 Apr. 2014, 31 Mar. 2017, 26287017, Relation between algebra, geometry and analysis on fractals, Kigami Jun; KOTANI Motoko; KAMEYAMA Atsushi; OHTA Shin-ichi; ITO Shunji; TAKAHASHI Satoshi, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kyoto University, 16380000, 12600000, 3780000, We have studied the relation between geometric and algebraic structures and analysis on fractals such as self-similar sets and invariant sets of various dynamical systems. For example, we have considered time changes of the Brownian motions on generalized Sierpinski carpets with respect to singular measures. We have established the notion of weakly exponential weakly exponential measures. If a measure is weakly exponential, then we have shown tcertain type of Poincare inequality, the existence of jointly continuous heat kernel and an asymptotic heat kernel estimate using the protodistance associated with the weakly exponential measure., kaken
  • Grant-in-Aid for Scientific Research (B), 01 Apr. 2011, 31 Mar. 2014, 23340025, Interaction between areas of Mathematics related to internal structures of fractals, KIGAMI Jun; KAMEYAMA Atsushi; AIKAWA Hiroaki; ITO Syunji; HINO Masanori; SHISHIKURA Mitsuhiro; KUMAGAI Takashi; OSADA Hirofumi; KOTANI Motoko; HATTORI Tetsuya; TAKAHASHI Satoshi; KUWADA Kazumasa; WAKANO Isao; KUBO Masayoshi, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kyoto University, 18590000, 14300000, 4290000, In this project, we have studied internal structure of fractal sets from the broad viewpoint of analysis, geometry and algebra. In particular, we have considered stochastic processes and potential theory on fractals, which are thought of as models of objects in the nature. For instance, we have obtained conditions to ensure the existence of scaling relation of space-time on the heat conductance on fractals. Moreover, we have studied equilibrium state of heat on spaces with infinitely many holes and obtained a condition for the equilibrium state to be smooth., kaken



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